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Personal Politics or Dialogue About Community Issues? Which Is More Important to You?
In the comments in Thursday’s article, “The Unanticipated Power of the Mayor in a Weak Mayoral System,” a dialogue took place about the 2011 council vacancy appointment process, with at least a partial focus on the personal politics and/or political calculations that may have gone into the decisions that night.
In answering the question of “who voted for whom?” I brought forward City Clerk Zoe Mirabile’s minutes of the process (see the Unanticipated Power of the Mayor in a Weak Mayoral System or Minutes of Special Joint Meeting City Council and Public Facilities Financing Authority), which showed clearly what each councilmember’s vote was in each of the five rounds of the process, with the final vote being Sue Greenwald, Joe Krovoza and Rochelle Swanson for the appointment of Dan Wolk, and Steve Souza for the appointment of attorney Paul Boylan.
What would be your options be for addressing the long-term implications of unfunded pension liabilities?
Taking into consideration upcoming items on the Long Range Calendar, including but not limited to the budget, please explain how you will prepare referencing at least 3 specific upcoming items. As appropriate, give specific examples of knowledge and qualifications you currently possess and what you would need to learn to prepare.
What is your position on additional big box retail and/or large malls within Davis or its planning area?
Please share with us your ideas for building stronger connections between our city government and neighborhoods. What would be your main objectives in this area?
Setting aside unfunded liabilities and unmet needs for a moment, what two things would you enjoy working on as a member of the Davis City Council?
The City Council has endorsed the “Road Diet” concept for the Fifth Street Corridor from A to L Streets. Do you support this concept or do you have another plan to address the safety concerns of this section of Davis’ roadway?
Please discuss issues, limitations and ideas for improvement to Olive Drive and the Richards Boulevard undercrossing (also known as Gateway), including impacts on residents and traffic.
The City currently has a 1% growth guideline, which equates to 325 houses per year. Would you consider growing at less than 325 units per year?
Many of these questions resonate just as strongly today as they did four years ago. Addressing the long-term implications of unfunded pension (and OPEB) liabilities was one of the questions raised by the Finance and Budget Commission on Monday night when they reviewed the proposed Budget and formulated advice for the Council’s Budget Adoption deliberations scheduled for Tuesday, June 30.
The Fifth Street Road Diet referenced in the sixth question has moved from “concept” to “reality” and in the process the amount of community dialogue (and angst) has been reduced to barely a whisper.
Conspicuous in its absence is any question about The Cannery, although the question about the 1 percent Growth Cap will have interesting traction in the next 36 to 48 months as The Cannery, Grande, Chiles Ranch, Trackside Center, and the 270 unit apartment proposal for the Families First site all vie for their share of the 325 houses per year. Community Development staff and the council will need to monitor each year’s issued building permits in order to be sure the 325 threshold is not exceeded.
Also conspicuously absent is any question regarding the Deferred Maintenance Backlog for Roads, Buildings & Facilities, Parks, etc.
Noting those differences, it is also interesting to see how the 2011 list of council-posed questions compares to the list of questions posed by Vanguard readers earlier this year.
What is the procedure for enrolling children in the summer Parks and Rec programs? Do City of Davis employees, and their friends and family members, still get first choice?
When do you anticipate addressing the issue of roads and infrastructure?
Do you think the city is economically viable without adding innovation parks, the hotel conference center, and/or Nishi?
Since you are concerned with pricing families out of Davis, do you anticipate adding either housing, workforce housing, or affordable housing in the near future?
Would you support mixed use at the innovation parks?
Do you anticipate raising salaries for employees between now and the end of your term as Mayor?
Will you actively support extending the joint management of the Davis and UCD fire departments?
Are you concerned about the 0.3 percent apartment vacancy rate, and, if so, what the current council might be doing to address that? Have you and the Chancellor ever talked about this issue during your weekly meetings?
I would like our City Council members to take the time to explain their thoughts on the CFD. Especially how providing $12 million to the developer is in the best interest of the city. Looking at our roads I wonder how $12 million might address the condition of our roads?
Do our City Council members think that the CFD will impact the new residents of the Cannery project when voting on parcel taxes? Much of what Davis provides to its citizens is included in the parcel taxes.
When I combine the nine questions from the council list with the eleven questions from Vanguard readers, I find thinking about and discussing those substantive community issues much more interesting than talking about personal politics and/or political calculations. | https://www.davisvanguard.org/2015/06/51042/ |
Mixtures of aggregate, sand and other binder materials used to create asphalt concrete samples in bins, Modified Asphalt Research Center. Research in the center focuses on ways to make asphalt more environmentally sustainable. Photo: Jeff Miller.
The MFCF group works on defining, addressing and advancing all aspects and challenges of utilizing engineering materials in the built structures and infrastructures. The group operates a few laboratories that include a wide range of tools and equipment for advanced characterization of materials including soils, aggregates, asphalts, cement, and polymer composites. The group aspires to connect science and engineering principles to improve construction materials, enhance their service life, render them more friendly to the environment, and better explain their physical and chemical behavior.
Professor Bu Wang’s research centers on the development and utilization of sustainable materials for civil engineering. Current focuses include waste material recycling and CO2 utilization in concrete production. His research interests also include understanding the composition-structure-property relationship of cementitious materials, as well as their mechanical and physical-chemical behaviors at different scales.
Professor Hussain Bahia’s research covers the highway construction materials and pavement design. His team works in cooperation scientists and engineers of bitumen producers, asphalt construction contractors, specialty additives’ manufacturers and other highway industry stakeholders. He currently leads the Modified Asphalt Research Center (MARC.wisc.edu) which focuses on research and education on specialty asphalts. Current research and education activities include advanced characterization of rheology and damage tolerance of modified asphalts and mixtures as well as environmentally sensitive “green” pavement technologies. His team utilizes imaging and micromechanics to understand how green paving mixes (high recycled content and reduced construction temperature) and specialty chemicals can be combined to deliver durable and high-performance (safe, quiet, and traffic resistant) mixes. The team contributes significantly to advancing modeling, implementation, and standards development.
Professor Greeshma Gadikota’s research focuses on integrating in-operando and in-silico characterization of complex hierarchical and heterogeneous materials with multi-scale reaction kinetics by connecting nano- and meso-scale measurements with process-scale developments and field-scale observations. Gadikota’s group is currently working on integrating carbon capture, utilization and storage with construction materials, chemical and morphological tuning of low carbon construction materials for enhanced durability and mechanical strength, and utilization of low value additives in construction materials.
Professor Andrea Hicks’s research focuses on the environmental impacts of new and novel products and often materials, using methods such as life cycle assessment. Hicks’s group conducts work on the environmental and economic impacts of materials such as nano-scale silver, waste to new materials, and transportation infrastructure materials. | https://www.engr.wisc.edu/department/civil-environmental-engineering/research-in-cee/materials-for-constructed-facilities/ |
Monday, March 29, 2021
Note: This blog was written by Brenna Foley, a research analyst at Anova, about her experience using benchmarking data to help her clients become more competitive.
Think about a sports team preparing for their season. The team spends all off-season practicing and preparing for action, but they never know how good they really are until they go up against their competition. The team needs a benchmark.
Benchmarking is also critical in the business world because it allows a company to better understand how their business compares to other providers in the market. By using industry benchmarks to see how their company ranks compared to competitors, business leaders can identify competitive advantages as well as areas for improvement and growth.
Now think about how benchmarking can impact a traditional win / loss program. In win / loss, interviews are conducted with a company’s prospects. The decision makers from the prospect give feedback and detail about what a company did right in the sales process and how that company can improve. Once multiple interviews are conducted and the results are aggregated, trends start to come out.
When doing win / loss, it is important for a company to evaluate its performance with broad context. While the data collected about the company allows the organization to understand its strengths and weaknesses within its own sphere, when industry-level data is added on top of this that sphere expands and the company can put its results into the context of the industry as a whole.
For instance, once the analysis is compared to a benchmark, the interpretation of the results begins to change. Now conclusions about what a company is doing well or not well can be verified by comparing results to how other competitors performed.
Let’s look at an example of this happening with an Anova client: a retirement services client completed a program and received relatively positive feedback on their participant website. Although some prospects considered the participant website a weakness, many more spoke positively about the ease of use and modern interface of the platform. Within the context of the program alone, it did not seem like the client needed to prioritize enhancing its participant portal.
However, when Anova’s industry benchmark was added to the analysis, the story changed. The Anova benchmark showed that mentions of the client’s participant website as a strength were 26% less than what Anova typically sees for similar clients. Although prospects noted the client’s participant website as being easy to use, there were very few mentions of the tools and functionality as a strength, especially compared to industry norms. Introducing Anova’s benchmark to the client’s findings allowed the client to understand their participant website was visually appealing, but the breadth of tools lagged compared to the competition.
This is one example of the importance of putting results into context. At Anova, our benchmarking data consists of feedback from over tens of thousands of interviews and 20 years of research with companies in financial services, technology, healthcare, and various other industries. Utilizing our benchmarking data allows us to provide our clients with a big picture view of their performance by comparing their results to what we have seen in other studies and provides a more comprehensive analysis than solely using program data.
Whether you conduct win / loss internally or partner with a third party, make sure you remember to not only look at your results in a vacuum, but also with as much context as you can. | https://theanovagroup.com/2021/03/benchmarkingblog/ |
Though a test based on the highly respected Programme for International Student Assessment is now available for schools in the U.S. to administer to their own students, two assessment researchers at the Indiana University School of Education advise school administrators to weigh the merits and disadvantages before deciding whether to participate.
David Rutkowski, assistant professor of educational leadership and policy studies, and Leslie Rutkowski, assistant professor of inquiry methodology, along with Jonathan Plucker, professor at the Neag School of Education at the University of Connecticut, outline concerns in the December 2014/January 2015 issue of the Phi Delta Kappan.
The article "Should individual U.S. schools participate in PISA?" highlights several areas of concern. PISA is an international test developed by the Paris-based Organisation for Economic Cooperation and Development to compare the proficiency of 15-year-olds in math, science and reading in 60-plus countries. The test, administered every three years, emphasizes one of these subject areas in each cycle.
Policymakers, education advocates and journalists frequently cite the performance of particular countries on the PISA exam compared to that of U.S. students collectively. Starting last year, the Organisation for Economic Cooperation and Development developed the OECD Test for Schools, a version of the PISA test that can be administered by U.S. schools. In the last school year, 285 U.S. schools participated.
"PISA is a high-quality, well-developed instrument whose design and administration make it a good assessment for lots of different settings,” Leslie Rutkowski said. ”But it’s probably not great for any particular country.”
The design of PISA presents a problem, the researchers say. PISA isn’t focused on measuring mastery of a particular curriculum, but rather what a 15-year-old knows and how the student can use that knowledge. Since the testing is linked to age, not grade, the U.S. participants often range from Grade 9 to 11. Nor are the tests linked to Common Core or similar state standards, such as those in Indiana.
"Given this aspect of the PISA design, there is no linkage between participating students and their teachers,” David Rutkowski said. “Such a disconnect likely limits the usefulness of PISA results for understanding the relationship between teaching and learning.”
The researchers also caution that PISA measures what the organization considers important for students of the 34 member countries to know to operate in a global economy and society. And although those sorts of skills are, of course, necessary, the test may not adequately capture important learning outcomes for U.S. students. They question whether the OECD Test for Schools would be relevant for the points of emphasis within U.S. schools.
"Given that the creation of large-scale assessments for the Common Core would charitably be described as complex and difficult, how effective with the OECD [Test for Schools] be in providing information about student progress relative to the Common Core?” David Rutkowski said.
There are better alternatives, they conclude. The National Assessment of Educational Progress is already administered across all states and focuses on specific grades and common curriculum across an array of subjects. It would allow comparisons of schools to similar students in other states, avoiding other pitfalls of adapting PISA.
The Trends in International Mathematics and Science Study is administered to measure fourth- and eighth-grade math and science achievement every four years and has a test for 12th-graders. It is also grade-based and measures based on an internationally accepted curriculum. The authors say it does lack an explicit link to workforce knowledge.
With shrinking state budgets and approximate costs of $8,000 to $11,500 per U.S. school paid to McGraw Hill for the 2013-14 school year PISA test, according to the education advocacy group American Achieves, educators might consider some lower-cost alternatives. For example, the researchers offer an alternative using existing resources. They suggest that U.S. educators develop an assessment using items taken from the National Assessment of Educational Progress to compare at the national level and the Trends in International Mathematics and Science Study to compare at the international level. Past questions are available from the National Center for Education Statistics. These free alternatives have some drawbacks but do allow schools to shape tests to better measure subject areas they are most interested in examining. | http://education.indiana.edu/news/2014-12-8-01.html |
When the student’s IEP (Individualized Education Plan) team convenes to add a Behavioral Intervention Plan as an addendum to the IEP, it is due to diagnostic data that has been provided and recorded by teachers, instructional assistants and other staff members that the student is in contact with on a daily basis. The plan will include student verification information that includes name, academic courses and teachers, grade level, date and the listing of IEP members who are part of the meeting. For students with ADHD (Attention Deficit Hyperactivity Disorder), ADD (Attention Deficit Disorder) and Hyperactivity, intervention plans can be more the norm of IEP addendums and not the exceptions in student files.
The case manager of the student’s IEP team will facilitate the meeting and present a compilation of information solicited and unsolicited from the student’s teachers on observed behavioral issues and concerns in the classroom. When a student’s behavior impacts their learning along with the learning environment of other classmates and effective teacher instruction, the red flag is raised and the student is referred to their case manager and IEP team for behavioral intervention and an intervention plan.
Components of the Intervention Plan
The “Behavioral Modification Plan” is composed of identified behaviors and corrected interventions individualized for each student. The components of the plan will contain specific behaviors that have been identified as interfering with a student’s ability to perform academically and behaviorally in the classroom along with specific interventions that will be used to address the behaviors. The plan contains the following components of behaviors and interventions.
Specific Behaviors and Interventions
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Classroom disruptions -Teachers and Instructional Assistants will monitor and chart each time a student disrupts the classroom and misbehaves. The teacher or instructional assistant will provide a defined signal to cue the student on the behavior and on the desired redirection of the disrupted behavior. The teacher can use visual tallies, points, or stars to provide the student with a visual when they have successfully redirected their behavior. If the student fails to redirect the behavior, the chart will reflect the loss of visual reinforcers and a possible consequence of spending extra time with the teacher or loss of a desired activity (i.e. recess, gym or a club activity).
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Rewards and Privileges - When a student sees their daily progress on a chart attached to rewards and privileges for good behavior and completion of assignments each week, the student may work harder to accomplish the expected behavioral goals.
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Structure of Independent Work - Students will be given an academic toolkit that contains a weekly calendar, packet of homework assignments for the class or classes in which they are having the most academic difficulty in completing work and additional instructional assistance to organize and meet work completion goals each week. Teachers will work with parents to add additional academic assignments for the student to complete at home.
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Classroom Arrangement - Students can be given a designed working area that may be a study cubicle to help them focus and avoid classroom disruptions. A student can be paired with a buddy for a pair share experience where a high performing student can provide peer assistance on work completion and learning focus in the classroom.
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Evaluation - Teachers and Instructional Assistants will keep a detailed log of completed academic work and student behavior in class to ascertain whether the interventions have been effective or need to be readjusted to provide additional structure and support.
Further Input
The various components of the student’s “Behavioral Intervention Plan” may include additional resource staff observations (i.e. nurse, psychologists, counselor, case manager) to assure that the student is benefiting from the plan and increasing learning outcomes and behavioral expectations in the classroom. If medication is being used to help the student behave effectively, the nurse’s evaluation is important in working with the student’s physician on medication effects that may provide additional data impacting a student’s classroom performance.
For students with “Behavioral Plans,” the IEP team collaboration and communication with parents provides an effective safety net of intervention and prevention if the monitoring and data collection are consistent and evaluated on a weekly basis and adjusted accordingly to maximize student behavioral and academic success. | https://www.brighthubeducation.com/special-ed-behavioral-disorders/23462-creating-a-behavioral-intervention-plan-for-students-with-adhd/ |
Summary:
The Quality Management Associate is responsible for ensuring services provided meet the established standards of quality in the domains of CCO/HH Care Coordination, customer satisfaction, and policy and procedure development. This role supports the operationalization and success of Prime Care Coordination's wholistic Quality Management Program.
Essential Job Functions
- Assist with drafting and maintaining policies, procedures, and standard operating procedures related to quality and compliance.
- Conduct and document internal audits and other quality improvement activities.
- Evaluate audit findings and implement appropriate corrective actions.
- Assist with monitoring risk management activities.
- Assist with developing, maintaining, and distributing reports on quality to include audit findings and analysis of trends, patterns, and potential quality improvement opportunities.
- Assist with devising sampling procedures and directions for recording and reporting quality data.
- Assist with the development, audit, and reporting of the Quality Management Program and all of its components.
- Assist with investigating customer complaints and non-conformance issues.
- Assist with supporting on-site audits conducted by external providers.
- Assist with collecting, compiling, and analyzing statistical quality data to identify areas for improvement in the quality system.
- Support in developing, recommending and monitoring corrective and preventive actions.
- Identify training needs and organize training interventions to meet quality standards.
- Interpret and implement quality improvement standards and procedures.
- Assist with evaluating adequacy of quality improvement standards.
- Assist with maintaining record management system and quality department tracking of HIPAA Violations, customer complaints,
- Ensure compliance with all federal/state laws and regulations, including affirmative action plan compliance.
- Perform any other related duties as required by supervisor.
Knowledge, Skills, and Abilities
- Knowledge of OPWDD and/or DOH regulations, programs, and service delivery systems including Medicaid Service Coordination, Care Coordination, Managed Care, Health Home Care Management and/or services for people with intellectual and developmental disabilities
- Knowledge of audit, policy / procedures, quality assurance regulations.
- Must be able to multi-task, establish priorities, and meet deadlines.
- Must demonstrate attention to detail, planning and organizational skills.
- Ability to work in a collaborative environment, work independently, and motivate others.
- Ability to communicate effectively, both orally and in writing.
- Ability to act quickly, assess, and act appropriately in crisis situations
- Proficient with technology and understanding of health records
- Data collection, management and analysis skills required
- Maintain appropriate confidentiality and discretion at all times.
Education and Experience:
- Bachelor's Degree in Healthcare, Business, Human Services Administration, or related field.
- Minimum 2 years of experience within a health care or human services setting.
- Possession of valid, unrestricted NYS driver's license required
All experience and education requirements, except when required by federal, state, or local laws or requirements, may be waived at the discretion of management with the approval of the Executive Director, in collaboration with Human Resources.
Physical Requirements/Working Conditions:
- Ability to sit continuously.
- Ability to reach above shoulder level.
- Ability to turn/twist upper body.
- Ability to use hand for repetitive action and fine manipulating for the purpose of keyboarding.
- Must be able to travel throughout covered territories in Upstate NY as needed.
* Reasonable accommodations may be made to the extent required under applicable law to enable individuals with disabilities to perform the essential functions of this position.
Corporate Qualifications/Expectations:
- Adhere to all Prime Care Coordination policies and procedures.
- Adhere to the Agency Mission, Vision, Shared Values, and Customer Service Standards.
- Attend mandatory education and training modules as scheduled; obtain and maintain required certifications/training by State regulations and PCC policy.
- Act as a professional representative of PCC in regard to appearance, behavior, temperament, communication, language, and dress. | https://primecareny.applicantpro.com/jobs/1251628.html |
A new reality is taking shape in cities, in Europe and globally. Cities have been the hardest hit by the pandemic and are facing serious social and economic consequences as well as other urgent challenges such as climate change.
Cities can and are working together in new and innovative ways to move beyond the crisis and emerge stronger. Eurocities 2020 will explore the pathways for recovery and resilience, and learn about what cities are doing to face the challenges that lie ahead.
The programme is:
4 November 2020
- 10:00 -11:30 CET: Future cities - do cities have a future?
- 15:00 - 16:30 CET: A stronger future: resilient cities
5 November 2020
- 10:00 - 11:30 CET: Green and just recovery in cities
The conference will take place online.
For more information on the conference sessions and the speakers, please visit the event website.
To register for the event, please visit the event registration page. | https://www.eltis.org/participate/events/eurocities-annual-conference-2020-reinventing-cities-beyond-urban-crises |
Book DescriptionThis is an account, from the original sources, of the early history of Quakerism, founded in England at the time of the Puritan revolution and the struggle for religious liberty. It is in part an account of its founder, George Fox, son of a weaver and apprentice to a shoemaker, whose learning extended little further than the pages of the Bible, but whose complete possession by this fresh truth transcended limitations of birth, health, education or occupation. It is also the account of Fox's disciples: James Naylor, William Dewsbury, Richard Farnsworth, Margaret Fell, and others who carried the word on as the movement gained force - of their conversion, their strength of conviction, and the punishments they were frequently forced to endure by those whom their faith outraged.
Buy Beginnings of Quakerism book by William C. Braithwaite from Australia's Online Bookstore, Boomerang Books.
Book DetailsISBN: 9780521082266
ISBN-10: 0521082269
(216mm x 140mm x 36mm)
Pages: 640
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 14-Oct-2008
Country of Publication: United Kingdom
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Other Editions...
Books By Author William C. Braithwaite
Second Period of Quakerism, Paperback (October 2008)» View all books by William C. Braithwaite
A reissue of the late William C. Braithwaite's Second Period of Quakerism.
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For every $20 you spend on books, you will receive $1 in Boomerang Bucks loyalty dollars. You can use your Boomerang Bucks as a credit towards a future purchase from Boomerang Books. Note that you must be a Member (free to sign up) and that conditions do apply. | http://www.boomerangbooks.com.au/Beginnings-of-Quakerism/William-C-Braithwaite/book_9780521082266.htm |
Licensing for systems within CONS3RT falls into one of the 4 categories listed below:
1. Operating Systems
– Covered by the cloud provider
2. DoD Wide Licenses
– If there is an available DoD wide license (e.g. Tenable Nessus, Java) CONS3RT will take care of the paperwork and request to make it available to the user community
3. Other DoD Licenses
– CONS3RT will coordinate user requirements with resources like the Mythics program office so the Government does not pay for licenses it already has
4. BYOL (Bring Your Own License)
– The balance of licenses are the responsibility of the customer to “bring your own”
More Help
Review this topic with our video tutorials: | https://cons3rt.com/kb/software-licenses/ |
We had a few days away in the campervan up North.
Saw a Minke whale at Stoer Head on the first night less than a mile off shore!
We then headed for Durness and took the opportunity to drop in and say, “Hello” to Julian and the team at Plasticatbay and chat about what they have been getting up to trying to tackle the plastic pollution on their bit of coast and the ways they are trying to successfully re-cycle it.
Julian kindly gave us the location of a secret beach which we visited and enjoyed the stunning scenery and thankfully very little plastic (4.1kg) due to the hard work of Connor the Plasticatbay Coastal Ranger. We did find a plastic bottle covered in goose barnacles which helps to show just how long this stuff hangs around in the marine environment and at Sango Sands we came across a huge fish bin lid (26kg) which had been manufactured in India. Mum and Dad really enjoyed lifting that off the beach !
Over the next couple of days we joined Plasticatbay on a coastal walk past the golf course and then on a longer 6km trip out to Old Grudie at the bottom of the Kyle of Durness. An amazing location for a house ! Much of the beach litter here is dominated by MOD webbing resulting from the parachute flares used during live firing at Cape Wrath. We collected approximately 100kg (our contribution was 61.3kg) which thankfully is a lot less than some of the hauls Julian has removed from there in the past. Read about their trip out to Old Grudie in May giving a lot more information on the MOD material that is found on this part of the coast.
We stopped at the motorhome facility at the Old Pier in Kinlochbervie on the way home. A great place which has room for 15 vehicles. An overnight stop including electric, water and chemical disposal is only £15 with all monies going into the community fund for future projects.
Sadly in the morning we could see that across the water Loch Clash beach was looking pretty bad for plastic pollution so we decided to delay going home and walk in to do a beach clean. 5 hours of hard work later, with a stop for a bit of swimming, we had dragged another 133kg of plastic rope, twine and other fishing equipment off the beach.
Including a few litter picks at our stop off points and overnight stays our total amount of rubbish removed and added to Ella’s Beach Clean Challenge for the week was 268.3kg.
This brings the running total up to 595.2kg, over a third of the way towards her 1500kg target. | https://ullapoolsharkambassador.com/campervan-travels-minke-whale-and-plasticatbay/ |
Weather Alert
Weather Alert
...WINTER WEATHER ADVISORY LATE THURSDAY NIGHT THROUGH EARLY
FRIDAY NIGHT...
.A WINTRY MIX, INCLUDING FREEZING DRIZZLE OR FREEZING RAIN, IS
ANTICIPATED TO AFFECT THE AREA LATE THURSDAY NIGHT THROUGH EARLY
FRIDAY. FREEZING DRIZZLE OR RAIN IS ANTICIPATED TO PROMOTE
HAZARDOUS CONDITIONS STEMMING FROM A LIGHT GLAZE OF ICE.
CHANGEOVER TO PREDOMINANTLY RAIN OR DRIZZLE, AND/OR SNOW IS
EXPECTED THEN IN THE AFTERNOON WITH ALL SNOW EXPECTED BY LATE
AFTERNOON. MEANWHILE, MODERATE SOUTHERLY WINDS WILL SWITCH TO THE
NORTHWEST FRIDAY EVENING DUE TO A STRONG COLD FRONT PASSING
THROUGH. STRONG WINDS ARE EXPECTED TO DEVELOP FRIDAY NIGHT WITH
PEAK GUSTS FORECAST AS HIGH AS 50 MPH, HIGHEST ACROSS NORTHERN
NEBRASKA.
...WINTER WEATHER ADVISORY IN EFFECT FROM MIDNIGHT TONIGHT TO
MIDNIGHT CST FRIDAY NIGHT...
* WHAT...MIXED PRECIPITATION EXPECTED. TOTAL SNOW ACCUMULATIONS OF
UP TO ONE INCH AND ICE ACCUMULATIONS OF A LIGHT GLAZE. WINDS
GUSTING AS HIGH AS 45 MPH FRIDAY NIGHT.
* WHERE...LINCOLN AND FRONTIER COUNTIES.
* WHEN...FROM MIDNIGHT TONIGHT TO MIDNIGHT CST FRIDAY NIGHT.
* IMPACTS...PLAN ON SLIPPERY ROAD CONDITIONS. THE HAZARDOUS
CONDITIONS COULD IMPACT THE FRIDAY MORNING AND EVENING COMMUTE.
* ADDITIONAL DETAILS...ROADS AND SIDEWALKS COULD BECOME ICE
COVERED AND HAZARDOUS.
PRECAUTIONARY/PREPAREDNESS ACTIONS...
SLOW DOWN AND USE CAUTION WHILE TRAVELING.
CALL NEBRASKA 511 FOR THE LATEST ROAD INFORMATION.
&&
Scammers use new meter installations as a chance to target customers
COLUMBUS — As Nebraska Public Power District installs new, upgraded digital meters around the state, scammers are trying to take advantage of customers by threatening them with shutting off their power.
NPPD received several reports Wednesday of scammers calling both NPPD customers and customers of other public power districts across the state. The scammers pose as NPPD representatives and tell the customers they will shut off their power if they do not pay hundreds of dollars for their “new” meter.
“NPPD is currently in the process of installing digital meters in several communities across the state, and there is no charge to the customer when this work is done,” said Tim Arlt, NPPD vice president and general manager of retail. “Anyone who receives such a call should not let their guard down and should contact our team and law enforcement immediately. Protecting our customers is a top priority.”Sometimes the scammer’s caller identification is falsified so it appears to originate from the utility company, a practice known as spoofing.
To help customers be wary of such scams, NPPD offers the following tips:
» NPPD, as a business practice, does not call to ask customers for a credit card number.
» NPPD does not demand payment with a prepaid card.
» Any customer receiving such a call should not attempt to make payment over the phone using a credit or debit card.
» Write down the call-back number or consider asking where the caller is located.
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Located in Rochester, Comfort Suites is close to Crossroads College and Olmsted County Fairgrounds. This hotel is within the vicinity of Apache Mall and Plummer House.
Rooms
Make yourself at home in one of the 84 air-conditioned rooms featuring refrigerators and flat-screen televisions. Complimentary wired and wireless Internet access keeps you connected, and cable programming provides entertainment. Conveniences include safes and desks, as well as phones with free local calls.
Amenities
Take advantage of recreational opportunities offered, including an indoor pool, a spa tub, and a fitness center. This hotel also features complimentary wireless Internet access, gift shops/newsstands, and a picnic area. Guests can get around on the complimentary shuttle, which operates within 10 mi.
Dining
Satisfy your appetite at a coffee shop/café serving guests of Comfort Suites. Mingle with other guests at a complimentary reception, held on select days.
Business, Other Amenities
Featured amenities include complimentary high-speed (wired) Internet access, a 24-hour business center, and complimentary newspapers in the lobby. Planning an event in Rochester? This hotel has facilities measuring 288 square feet (26 square meters), including meeting rooms. Free self parking is available onsite.
Hotel Facilities
- Number of floors - 3
- Free newspapers in lobby
- Smoke-free property
- Free RV, bus, truck parking
- Picnic area
- Coffee shop or café
- 24-hour business center
- 24-hour front desk
- Number of buildings/towers - 1
- Computer station
- Total number of rooms - 84
- Indoor pool
- Dry cleaning/laundry service
- Fitness facilities
- Free breakfast
- Conference space size (meters) - 26
- Free area shuttle
- Number of meeting rooms - 2
- Free WiFi
- Conference space size (feet) - 288
- Meeting rooms
- Free reception
- Gift shops or newsstand
- Laundry facilities
- Free wired high-speed Internet
- Elevator/lift
- Free self parking
- Spa tub
Room Facilities
- Iron/ironing board
- Free WiFi
- Minibar
- In-room climate control (air conditioning)
- Daily housekeeping
- Free wired high-speed Internet
- Cable TV service
- Coffee/tea maker
- Pay movies
- Microwave
- Hair dryer
- Connecting/adjoining rooms available
- Refrigerator
- In-room safe
- Free local calls
- Desk
- Flat-panel TV
- Sofa bed
- Air conditioning
- Free cribs/infant beds
- Phone
Hotel Policy
Know Before You Go
- Children 18 years old and younger stay free when occupying the parent or guardian's room, using existing bedding. Children may not be eligible for complimentary breakfast.
- The property has connecting/adjoining rooms, which are subject to availability and can be requested by contacting the property using the number on the booking confirmation. | https://www.zuji.com.sg/accommodation/comfort-suites-minnesotta-united-states-of-america/ |
Meditation is becoming increasingly popular. It’s no longer restricted to spiritual practitioners, but instead is used by everyone from athletes to artists to prisoners. As meditation grows in popularity, it can become harder and harder to understand what exactly it entails: there are so many traditions, variations and techniques that it’s hard to generalize it all with just one word. Meditation has a rich and storied history, and it is now practiced in many different forms.
In the Western society, many popular forms of meditation are based on Eastern forms of spirituality, including Buddhism, yoga and Hinduism. However, meditation has never been restricted to the East. Meditation is also an important part of other religions, including Christianity, Kabbalah and Islam. Different religions employ many different types of meditation with different goals and techniques.
What do all meditation practices have in common? They all exercise the mind. They train the mind to become focused, clear, calm and patient. They discourage attachment to negative or unnecessary thoughts and distractions. Likewise, they develop a connection to what is considered essential, whether that be a spiritual figure or a sense of grounding in the present moment.
Meditation has been practiced continuously for thousands of years, and meditators have even assumed the same posture for much of that time: legs crossed on the floor, with palms resting upright.
Indian religions and spiritual practices are among the most ancient — they have been practiced since long before the Common Era. Buddhism originally began as a branch of ancient Indian religion, and it prioritizes meditation as one of the central practices of spiritual life.
Practices such as prayer and counting rosary beads can also be a form of meditation: they are a chance for people to focus their attention and quiet the mind. Repetitive prayers, or mantras, are also used in religious traditions both Eastern and Western.
Scientific research is only just beginning to scratch the surface of understanding this ancient practice, and in fact, it’s not the type of thing that easily lends itself to scientific understanding. The mental, physical and spiritual effects of meditation are designed to be directly experienced by each person rather than intellectually described. However, there’s no doubt that meditation benefits the mind and body.
Meditation has always been in practice worldwide, but in the past century Eastern forms of meditation have experienced a great boost in popularity in the West.
Eastern spirituality first became popular in the West during the era of transcendentalism in the 19th century. There was another surge in popularity during the 1950s and 1960s, an era of visionary ideas. Popular poets such as Allen Ginsberg, Gary Snyder and Jack Kerouac incorporated Eastern religions such as Zen Buddhism into their literature, and this further popularized meditation for a wider audience. The boom in meditation that we see today can be traced back to this time.
New techniques of meditation have evolved from this cross-cultural exchange, and there are a few modern forms of meditation popular today.
In the West, meditation is often divided into two main types: focused meditation and mindfulness meditation. Each of the many meditation techniques can be divided into these two basic types, depending on whether they require focused attention on one specific object (such as the breath, an image, or a sound), or simply require an open awareness and observation of whatever passes through the mind.
Some of the most common forms of meditation currently practiced in the West include mindfulness, transcendental meditation, breath awareness, Yoga (including Kundalini), Zen, focused meditation, and insight (Vipassana) meditation. Some of these are rooted in spiritual tradition while others are secular, but most are practiced by a variety of people of differing religious inclinations.
Mindfulness meditation, breath awareness meditation and focused meditation are all secular methods: they do not involve any mention of spiritual figures, deities, or religious texts.
Mindfulness meditation is simple. It increases non-judgmental awareness of your thoughts, feelings and senses in order to reduce anxiety and improve mood. Mindfulness meditation is used in a therapeutic technique called Mindfulness-Based Stress Reduction (MSBR), which is designed to alleviate stress. This technique can even help chronic pain and illness. Mindfulness and MSBR are both derived from a combination of Eastern spiritual traditions as well as modern scientific and psychological research.
Focused meditation, too, can be traced back to spiritual forms of meditation that involve focusing your attention on one object. This object can be anything, which is why this practice easily lends itself to secularity. In religious meditation it might be a set of prayer beads, a chant, a certain deity or a religious principle. Others choose to focus on a candle, music, or an object in nature.
Breath awareness meditation is, in a sense, a type of focused meditation: it involves returning your attention to the breath over and over. This is a foundational technique used by many meditation traditions, but it’s also quite powerful when used on its own.
Zen meditation and Vipassana meditation are two popular examples of Buddhist meditation techniques.
Zen meditation comes from Zen Buddhism, a tradition common in Japan and China. It is perhaps the most popular form of Buddhist meditation practiced in the West, but it is just one of many. Zen meditation emphasizes an open-ended awareness of whatever passes through the mind, often using the breath as an anchor. Zen Buddhists believe that calm meditation is the main path to enlightenment.
Vipassana meditation is an integral part of Theravada Buddhism, which is common in Southeast Asia. Like Zen meditation, it uses awareness of the breath as a foundational technique. However, it has a different goal. Zen meditation aims to eventually achieve “no-mind,” a state of total non-attachment and equanimity. Vipassana meditation aims to achieve insight into the true nature of reality.
Yoga and Hinduism are both Indian spiritual traditions, and they are closely connected to one another. Some of the most popular Western meditation methods based on these traditions are actually quite modern, but they are all rooted in millennia-old practices.
Yoga meditation can take many different forms, and these meditations are often used to prepare the mind to do physical yoga sequences. Both physical yoga and yoga meditation are part of a set of practices designed to allow the soul to realize its true pure and infinite nature.
Kundalini and transcendental meditation are two modern types of meditation derived from yoga. Both involve focusing your attention on specific mantras or chants. Kundalini meditation also involves concentrating on certain parts of the body. This technique is purported to awaken vital energy in the body, leading to a variety of physical benefits in addition to mental clarity.
Other common forms of meditation are derived from specific Hindu traditions such as Vedanta. Deepak Chopra is one well-known practitioner of Vedanta, which uses a type of yoga meditation called “raja yoga” to train the mind. | https://www.meditation-music.com/about-meditation/types-and-traditions-of-meditation.html |
Technical Field
Background Art
Citation List
Patent Literature
Summary of Invention
Technical Problem
Solution to Problem
Brief Description of Drawings
Description of Embodiments
EXAMPLES
[Example 1]
[Output of Tabulation Results of Pore Diameter]
[Evaluation by Equivalent Diameter d]
[Evaluation of Collection Performance by Spatial Uniformity Index γ]
[Evaluation by Pressure Drop P]
x
[Evaluation of Pressure Drop by In-Plane Uniformity Index γ]
[Evaluation by Flow-Through Velocity T]
[Results of Classification by Equivalent Diameter d]
[Example 2]
e
[Evaluation by Pressure Drop Index P]
Industrial Applicability
Reference Signs List
The present invention relates to a microstructure analysis method, a program thereof, and a microstructure analysis device.
As one method to analyze microstructures such as pores in porous bodies, there has been proposed a method where 3 dimensional pixel data of a porous body is obtained by performing a CT scan, and analysis is performed based on this pixel data. For example, PTL 1 describes a pore continuity analysis method in which virtual spheres of various diameters are situated so as to fill in pixels of the pixel data representing space, so as to find continuity of pores from one exposed face of a porous body to another exposed face thereof, based on information relating to the situated virtual spheres.
JP 2011079732 A
Patent Literature 1: Japanese Patent Application Publication No.
HU DONG ET AL: "Pore-network extraction from micro-computerized-tomography images, PHYSICAL REVIEW E, vol. 80, no. 3, September 2009 (2009-09
) describes a modified maximal ball algorithm, to extract simplified networks of pores and throats with parametrized geometry and interconnectivity from images of the pore space. Starting with three dimensional scan data of a sample of material, the approach of this paper is first to build "maximal balls". Spheres are built at every void voxel in the three dimensional image. These are then all inflated until a solid or boundary voxel is reached along a limited set of direction lines, and then all deflated to ensure that the sphere does not include a solid voxel. The result is a collection of spheres, corresponding to each void voxel, and so the number of spheres is the same as the number of void voxels. Any sphere which is wholly included in another sphere is then removed. Thus, the approach is to generate a set of spheres (maximal balls) which together fill the space voxels.
Only after the generation of the entire set of maximal balls, the maximal balls are then sorted and categorised. The effect of this process is to identify the overlapping balls as a continuum. Based on the diameter of the balls identified as overlapping in sequence, the spaces are determined to be "pores" or "throats".
However, the method described in PTL 1 only uses virtual spheres to simulate the complicatedly-shaped pores of a porous body. Accordingly, there have been cases where microstructure analysis using virtual spheres situated according to the method in PTL 1 has been found to be insufficient in precision, with regard to performing evaluation of pressure drop and collection performance in a case of use of a porous member as a filter, for example. Accordingly, a microstructure analysis method with higher precision has been desired.
The present invention has been made to solve such problems, and it is a primary object thereof to analyze microstructures of porous bodies more precisely.
To achieve the above-described objects, the microstructure analysis method, the program thereof, and the microstructure analysis device, according to the present invention, employ the following means.
(a) a step to take a curved surface solid formed by combining a parent virtual sphere and one or more child virtual spheres with which a portion of pixels occupied by the parent virtual sphere overlap as a virtual curved surface solid, and place a group of said virtual curved surface solids in mutually different positions so as to fill in the space pixels with curved surface solid pixels which are pixels occupied by the virtual curved surface solid, referencing the porous body data, each virtual curved surface solid including only one parent virtual sphere; and
(b) a step to analyze microstructure of the porous body based on information relating to the group of virtual curved surface solids placed in the step (a); wherein in step (a), in each virtual curved surface solid, all child virtual curved spheres partially overlap pixels occupied by the parent virtual sphere.
The microstructure analysis method according to the present invention is a microstructure analysis method of a porous body, using porous body data in which correlated position information representing position of a pixel obtained by a 3 dimensional scan of the porous body, and pixel type information representing whether a space pixel representing that the pixel is space or a matter pixel representing that the pixel is matter, comprising;
With this microstructure analysis method, multiple virtual curved surface solids made up of a parent virtual sphere and child virtual spheres are placed so as to fill in space pixels with curved surface solid pixels occupied by the virtual curved surface solids, referencing porous body data in which position information and pixel type information are correlated. Thus, complicated shape space (pores) within the porous body are replaced with virtual curved surface solids of shapes where multiple spheres are combined, so space within the porous body can be better simulated as a group of multiple virtual curved surface solids. The microstructure of the porous body can then be analyzed more precisely by being based on information relating to these virtual curved surface solids. Now, "information relating to virtual curved surface solids" may be information such as center coordinates and diameter and so forth of the parent virtual sphere and child virtual spheres for each virtual curved surface solid, or may be position information of curved surface solid pixels which the virtual curved surface solid occupies. To "analyze a microstructure" may be, for example, to derive a numerical value representing a microstructure of a porous body such as porosity, average pore diameter, and so forth, or may be to derive a value relating to pressure drop property, collection performance, and so forth, of the porous body, or may be to perform evaluation of acceptability for such as pressure drop property, collection performance, and so forth. Also, the number of parent virtual spheres in one virtual curved surface solid is one.
With the microstructure analysis method according to the present invention, in the step (a), the virtual curved surface solid may be placed such that the center of a child virtual sphere configuring the virtual curved surface solid overlaps with the parent virtual sphere configuring the virtual curved surface solid. Also, in the step (a), the multiple virtual curved surface solids may be placed, permitting the virtual curved surface solids to overlap with each other. Thus, virtual curved surface solids with as great a volume as possible can be placed as compared with a case where virtual curved surface solids are placed so as to not overlap with other virtual spheres. Also, in the step (a), the multiple virtual curved surface solids may be placed so that the virtual curved surface solids do not overlap with each other. Further, in the step (a), the virtual curved surface solids may be placed so that the curved surface solid pixels do not overlap with the matter pixels. Placing the virtual curved surface solids so that the virtual curved surface solids do not overlap with each other or so that the curved surface solid pixels do not overlap with the matter pixels restricts the positions where the virtual curved surface solids can be placed, so processing time required to place the virtual curved surface solids can be reduced as compared with a case where overlapping is permitted.
With the microstructure analysis method according to the present invention, in the step (a), processing to place one virtual curved surface solid may be performed by placing the parent virtual sphere having the greatest spherical diameter that can be placed so as to fill in the space pixels, and placing one or more of the child virtual spheres such that pixels occupied by the child virtual spheres partially overlap with pixels occupied by the placed parent virtual sphere and fill in the space pixels, and the multiple virtual curved surface solids are placed by repeating this processing so that virtual curved surface solids are placed in mutually different positions. Thus, space pixels can be filled in with virtual curved surface solids as large as possible.
With the microstructure analysis method according to the present invention, in the step (a), processing to place one virtual curved surface solid may be performed by placing the parent virtual sphere having the greatest spherical diameter that can be placed so as to fill in the space pixels without overlapping with the matter pixels, and placing one or more of the child virtual spheres such that the center of the child virtual spheres overlaps with the placed parent virtual sphere, and such that pixels occupied by the child virtual spheres do not overlap with the matter pixels and fill in the space pixels, and the multiple virtual curved surface solids are placed by repeating this processing so that virtual curved surface solids are placed in mutually different positions, permitting pixels occupied by different virtual curved surface solids to mutually overlap. Thus, virtual curved surface solids as large a volume as possible can be placed, as compared with a case where virtual curved surface solids are placed so as to not overlap with other virtual curved surface solids. Also, the virtual curved surface solids are placed so that the curved surface solid pixels do not overlap with the matter pixels, so processing time required to place the virtual curved surface solids can be reduced as compared with a case where overlapping is permitted. Also, a parent virtual sphere having as large a sphere diameter as possible to be placed can be placed when placing virtual curved surface solids, so the space pixels can be filled in with virtual curved surface solids that have as large a volume as possible.
With the microstructure analysis method according to the present invention, in the step (a), processing to place one virtual curved surface solid may be performed by placing the parent virtual sphere having the greatest spherical diameter that can be placed so as to fill in the space pixels without overlapping with the matter pixels, and placing one or more of the child virtual spheres such that the center of the child virtual spheres overlaps with the placed parent virtual sphere, and such that pixels occupied by the child virtual spheres do not overlap with the matter pixels and fill in the space pixels, and the multiple virtual curved surface solids are placed by repeating this processing so that pixels occupied by different virtual curved surface solids do not mutually overlap. Thus, the virtual curved surface solids are placed so that the virtual curved surface solids themselves or the curved surface solid pixels and the matter pixels do not overlap, so processing time required to place the virtual curved surface solids can be reduced as compared with a case where overlapping is permitted. Also, the space pixels can be filled in with virtual curved surface solids that have as large a volume as possible.
f
fmean
f
e
e
W
p
fmean
e
e
W
p
With the microstructure analysis method according to the present invention, in the step (b), based on information relating to the virtual curved surface solids placed in the step (a) the microstructure of the porous body may be analyzed by deriving multiple path lengths L from one of a predetermined inflow face and a predetermined outflow face of the porous body to the other face following adjacent or overlapping virtual curved surface solids, deriving an average value L of the multiple path lengths L, and deriving a pressure drop index P by P = (wetted area A of space within porous body / pore volume V of space within porous body) × (1 / porosity ε of porous body) × (average value L / distance L between inflow face and outflow face). The present inventors have found that a pressure drop index P derived in this way as a high correlation with the actual pressure drop of the porous body. Accordingly, the pressure drop property of the porous body, for example, can be predicted or evaluated more precisely, by deriving this pressure drop index P as microstructure analysis. Now, the wetted area A, pore volume V, and porosity ε may be derived based on information relating to the space pixels and matter pixels, or may be calculated based on information relating to the virtual curved surface solids.
s
s
e
e
s
e
s
s
e
2
In this case, in the step (b), the microstructure of the porous body may be analyzed by deriving pressure drop P per unit thickness of the porous body by P = constant α × P + constant β × P. The present inventors have found that the pressure drop P per unit thickness of the porous body derived from the pressure drop index P in this way approximately matches the actual pressure drop of the porous body. Accordingly, the pressure drop property of the porous body can be predicted or evaluated more precisely, by deriving this pressure drop P as microstructure analysis. Note that the constant α is an integer and the constant β is a real number. Also, pressure drop P > 0 holds within the range of pressure drop index P > 0.
With the microstructure analysis method according the present invention, in the step (a), processing of placing the multiple virtual curved surface solids, and processing of deriving information relating to flow of a fluid for each space pixel at the time of the fluid passing through the interior of the porous body by performing fluid analysis based on the porous body data, may be performed; and in the step (b), the microstructure of the porous body may be analyzed based on information relating to the placed virtual curved surface solids and the derived information relating to flow. Here, "information relating to flow ... for each space pixel" may include at least flow velocity (vector or scalar) for each space pixel, or may include at least through-flow volume for each space pixel. "Fluid analysis" may be analysis by the lattice Boltzmann method. Also, for fluid analysis, fluid analysis may be performed regarding a case where there is inflow of fluid from a predetermined inflow face of the porous body, or fluid analysis may be performed regarding a case where there is inflow of fluid from a predetermined inflow face of the porous body to a predetermined outflow face.
x
x
x
x
x
<mrow><msub><mi mathvariant="italic">γ</mi><mi mathvariant="normal">x</mi></msub><mo>=</mo><mn mathvariant="normal">1</mn><mo>−</mo><mfrac><mn mathvariant="normal">1</mn><mn mathvariant="normal">2</mn></mfrac><mstyle displaystyle="true"><mrow><munderover><mrow><mo>∑</mo></mrow><mrow><mi mathvariant="normal">i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mi mathvariant="normal">n</mi></munderover></mrow></mstyle><mfrac><mrow><mfenced open="|" close="|" separators=""><msub><mi mathvariant="normal">u</mi><mi mathvariant="normal">i</mi></msub><mo>−</mo><msub><mi mathvariant="normal">u</mi><mi mathvariant="normal">mean</mi></msub></mfenced><mo>⋅</mo><msub><mi mathvariant="normal">A</mi><mi mathvariant="normal">i</mi></msub></mrow><mrow><msub><mi mathvariant="normal">u</mi><mi mathvariant="normal">mean</mi></msub><mo>⋅</mo><mi mathvariant="normal">A</mi></mrow></mfrac></mrow>
n: number [count] of virtual curved surface solids within cross-section
x: distance [m] between cross-section and inflow face
i
u: average flow velocity (i = 1, 2, ..., n) [m/s] for each of the n virtual curved surface solids at cross-section
mean
1
2
n
i
u: average value (= (u + u + ... + u)/n) [m/s] of average flow velocity u at cross-section
i
2
A : cross-sectional area (i = 1, 2, ..., n) [m] for each virtual curved surface solid within cross-section
1
2
n
2
A: total cross-sectional area (= A + A + ... + A) [m] of virtual curved surface solids at cross-section
With the microstructure analysis method according to an embodiment of the present invention performing the above-described fluid analysis, in the step (a), fluid analysis may be performed regarding a case of inflow of a fluid from a predetermined inflow face of the porous body, and deriving at least flow velocity for each space pixel as the information relating to flow; and in the step (b), the microstructure of the porous body may be analyzed by deriving one or more in-plane uniformity index γ of flow velocity at a cross-section on the porous body parallel to the inflow face, by the following Expression (1). Now, the more uniform the flow velocity of a fluid at a cross-section is, the greater (closer to value 1) the value of the in-plane uniformity index γ is, and the greater the irregularity in the flow velocity of a fluid at a cross-section is, the smaller the value is. Also, the present inventors have found that, in a case of using the porous body for a filter, the greater the value of the in-plane uniformity index γ is, the better the pressure drop property tends to be. Accordingly, deriving this in-plane uniformity index γ as analysis of a microstructure enables the pressure drop property of the porous body to be predicted and evaluated more precisely. Note that with the step (b), when the derived in-plane uniformity index γ is at or greater than a predetermined threshold, the pressure drop property of the porous body may be determined to be acceptable. The predetermined threshold may be the value 0.6, for example. Now, the flow velocity at each space pixel may be directly derived by fluid analysis for example, or may be derived by deriving the through-flow volume per unit time at each space pixel by fluid analysis, and the flow velocity being derived from the through-flow volume per unit time that has been derived and the area (cross-sectional area) of the portion of space pixels where the fluid passes through, or the like. Also, with fluid analysis, the flow velocity vector may be derived for each space pixel, with components of the flow velocity vectors which are in a direction perpendicular to the cross-section being taken as the flow velocity for each space pixel.
[Math. 1] where
x
x
x
<mrow><mi>γ</mi><mo>=</mo><mover><mrow><msub><mi>γ</mi><mi mathvariant="normal">x</mi></msub></mrow><mrow><mo>‾</mo></mrow></mover><mo>⋅</mo><mfenced separators=""><mn>1</mn><mo>−</mo><msub><mi>δ</mi><mi>γ</mi></msub></mfenced></mrow>
γ
x
x
: average value of γ
γ
x
δ: standard deviation of γ
In this case, in the step (b), the microstructure of the porous body may be analyzed by deriving the in-plane uniformity index γ regarding the multiple cross-sections of the porous body, and deriving a spatial uniformity index γ of flow velocity at the porous body by the following Expression (2) using the derived in-plane uniformity index γ. The spatial uniformity index γ thus derived is such that the smaller the irregularity in the in-plane uniformity index γ derived regarding multiple cross-sections is, the greater the value is, and the greater the irregularities, the smaller the value is. The present inventors have also found that collecting performance in the case of using the porous body for a filter tends to be better the greater the value of this spatial uniformity index γ is. Accordingly, by deriving this spatial uniformity index γ as analysis of a microstructure enables the collecting performance of the porous body to be predicted and evaluated more precisely, for example. Note that with the step (b), in the event that the derived spatial uniformity index γ is at or greater than a predetermined threshold, the collecting performance of the porous body may be determined to be acceptable. The predetermined threshold may be the value 0.5 for example, or may be the value 0.6.
[Math. 2] where
x
x
x
x
<mrow><mi mathvariant="normal">P</mi><mo>=</mo><mfrac><mrow><msub><mi mathvariant="normal">ΔP</mi><mi mathvariant="normal">x</mi></msub></mrow><mi mathvariant="normal">Δx</mi></mfrac><mo>=</mo><mfenced separators=""><mfrac><mn mathvariant="normal">200</mn><mn mathvariant="normal">3</mn></mfrac><mfrac><mn mathvariant="normal">1</mn><mrow><msup><mrow><msub><mi mathvariant="normal">D</mi><mi mathvariant="normal">hx</mi></msub></mrow><mn mathvariant="normal">2</mn></msup><mo>⋅</mo><msub><mi mathvariant="normal">ε</mi><mi mathvariant="normal">x</mi></msub></mrow></mfrac><mi mathvariant="italic">μ</mi><msub><mi mathvariant="normal">U</mi><mi mathvariant="normal">x</mi></msub><mo>+</mo><mfrac><mn mathvariant="normal">7</mn><mn mathvariant="normal">6</mn></mfrac><mfrac><mn mathvariant="normal">1</mn><mrow><msub><mi mathvariant="normal">D</mi><mi mathvariant="normal">hx</mi></msub><mo>⋅</mo><msup><mrow><msub><mi mathvariant="normal">ε</mi><mi mathvariant="normal">x</mi></msub></mrow><mn mathvariant="normal">2</mn></msup></mrow></mfrac><mi mathvariant="italic">ρ</mi><msup><mrow><msub><mi mathvariant="normal">U</mi><mi mathvariant="normal">x</mi></msub></mrow><mn mathvariant="normal">2</mn></msup></mfenced><mo>⋅</mo><msup><mrow><msub><mi mathvariant="italic">γ</mi><mi mathvariant="normal">x</mi></msub></mrow><mi mathvariant="normal">k</mi></msup></mrow>
Δx: cross-sectional thickness [m] at cross-section at distance x
x
ΔP: pressure drop [Pa] at cross-section at distance x
x
Dh: representative hydraulic diameter [m] of space (pores) at cross-section at distance x
x
ε: voidage (= number of space pixels / (number of space pixels + number of matter pixels)) at cross-section at distance x
µ: viscosity [Pa·s] of fluid
x
U: flow velocity average value [m/s] at each space pixel at cross-section at distance x
3
ρ: density of fluid [kg/m]
k: constant
With the microstructure analysis method according to an embodiment of the present invention deriving the in-plane uniformity index γ described above, in the step (b), the microstructure of the porous body may be analyzed by deriving pressure drop P per unit thickness of the porous body by the following Expression (3) using the derived in-plane uniformity index γ. This Expression (3) is one where a known Ergun's Equation representing pressure drop properties at the time of a fluid passing through a porous body, has been revised using the in-plane uniformity index γ. The present inventors have found that the pressure drop P per unit thickness derived in this way has higher correlation with the actual pressure drop of the porous body as compared to pressure drop derived by Ergun's Equation. Accordingly, the pressure drop property of the porous body, for example, can be predicted or evaluated more precisely, by deriving this pressure drop P per unit volume as microstructure analysis. Note that in the event that pressure drop P has been derived corresponding to each of in-plane uniformity indices γ, an average value of multiple pressure drops P may be derived. Also, the pressure drop property of the porous body may be predicted or evaluated from this average value of pressure drops P.
[Math. 3] where
2
f
in
in
f
f
f
f
With the microstructure analysis method according to an embodiment of the present invention performing the above-described fluid analysis, in the step (a), fluid analysis may be performed regarding a case of inflow of a fluid from a predetermined inflow face of the porous body, and deriving at least flow velocity for each space pixel as the information relating to flow; and in the step (b), the microstructure of the porous body may be analyzed by deriving through-flow volume Q of the fluid per unit time at the each placed virtual curved surface solid, based on the information relating to the placed virtual curved surface solids and the flow velocity for each space pixel, and deriving flow-through velocity T of each virtual curved surface solid by T = Q/(πd/4) based on the derived through-flow volume Q and an equivalent diameter d of the virtual curved surface solid (= 6 × volume V of virtual curved surface solid / surface area S of virtual curved surface solid). In this case, in the step (b), the microstructure of the porous body may be analyzed by classifying the virtual curved surface solids of which the derived flow-through velocity T is included in a low-flow-velocity as low-flow-velocity curved surface solids, or the microstructure of the porous body may be analyzed by classifying the virtual curved surface solids of which the derived flow-through velocity T is included in a high-flow-velocity as high-flow-velocity curved surface solids. Also, in the step (b), the microstructure of the porous body may be analyzed by classifying the virtual curved surface solids into low-flow-velocity curved surface solids, mid-flow-velocity curved surface solids, and high-flow-velocity curved surface solids, based on the magnitude of the value of the derived flow-through velocity T. Now, there are cases where pores of a porous body simulated with virtual curved surface solids of which the flow-through velocity T is small may not contribute much to transmittance of the fluid, leading increased pressure drop, and deterioration in thermal conductivity and thermal capacity of the material. Also, there are cases where pores of a porous body simulated with virtual curved surface solids of which the flow-through velocity T is great, exhibit great flow resistance when the fluid passes through, or the fluid may pass through in a short time and the pores do not contribute much to collecting performance. Accordingly, classifying a part of the virtual curved surface solids as low-flow-velocity curved surface solids with small flow-through velocity T and high-flow-velocity curved surface solids with great flow-through velocity T in this way enables the microstructure of the porous body to be analyzed with good precision. In this case, in the step (b), a flow velocity ratio T (=T/T) of the derived flow-through velocity T and an average flow velocity T of the fluid at the inflow face in the fluid analysis may be derived, the classification is performed such that, of the placed virtual curved surface solids, virtual curved surface solids where T < 2 are classified as the low-flow-velocity curved surface solids, virtual curved surface solids where 2 ≤ T < 8 as the mid-flow-velocity curved surface solids, and virtual curved surface solids where 8 ≤ T as the high-flow-velocity curved surface solids. Performing classification using the flow velocity ratio T in this way enables the microstructure of the porous body to be analyzed more precisely. Also, in the step (b), the performance of the porous body may be determined to be acceptable when the volume ratio of the low-flow-velocity curved surface solids in the multiple virtual curved surface solids is at or below a predetermined threshold. The predetermined threshold may be 20%, for example. Also, in the step (b), the performance of the porous body may be determined to be acceptable when the volume ratio of the high-flow-velocity curved surface solids in the multiple virtual curved surface solids is at or below a predetermined threshold. The predetermined threshold may be 10%, for example.
With the microstructure analysis method according to the present invention, in the step (b), the microstructure of the porous body may be analyzed by an equivalent diameter d of the placed virtual curved surface solids being derived by d = 6 × (volume V of virtual curved surface solid) / (surface area S of virtual curved surface solid). Thus, by deriving the equivalent diameter d of virtual curved surface solids as microstructure analysis enables the property of the pores of the porous body to be analyzed based on this equivalent diameter d, for example. In this case, with the step (b), the average value of the derived equivalent diameters d may be derived as the average pore diameter of the porous body. Also, in the step (b), the microstructure of the porous body may be analyzed by the virtual curved surface solids of which the derived equivalent diameter d is included in a predetermined shall-diameter region being classified into small-diameter curved surface solids, or the microstructure of the porous body may be analyzed by the virtual curved surface solids of which the derived equivalent diameter d is included in a predetermined large-diameter region being classified into large-diameter curved surface solids. Further, in the step (b), the microstructure of the porous body may be analyzed by classifying the virtual curved surface solids into small-diameter curved surface solids, mid-diameter curved surface solids, and large-diameter curved surface solid, based on the magnitude of the value of the derived equivalent diameter d. Now, with pores of the porous body simulated with virtual curved surface solids of which the equivalent diameter d is small, there are cases where the flow velocity of the fluid passing through is small, leading to increased pressure drop, or cases where the catalyst applied to the walls of the pores to use the porous body as a filter may not be appropriately applied, or the like. Also, with pores of the porous body simulated with virtual curved surface solids of which the equivalent diameter d is great, there are cases where the flow velocity of the fluid passing through is great to the point of not contributing to collecting performance very much when using the porous body as a filter. Accordingly, classifying a part of the virtual curved surface solids as virtual curved surface solids with small equivalent diameter d and virtual curved surface solids with great equivalent diameter d in this way enables the microstructure of the porous body to be analyzed with good precision. In this case, in the step (b), the classification may be performed such that, of the placed virtual curved surface solids, virtual curved surface solids where d < 10 µm are classified as the small-diameter curved surface solids, virtual curved surface solids where 10 µm ≤ d ≤ 25 µm are classified as the mid-diameter curved surface solids, and virtual curved surface solids where 25 µm < d are classified as the large-diameter curved surface solids. Also, in the step (b) the performance of the porous body may be determined to be acceptable when the volume ratio of the mid-diameter curved surface solid in the multiple virtual curved surface solids is at or above a predetermined threshold. The predetermined threshold may be 60%, for example, or may be 70%.
A program according to the present invention is to cause one or multiple computers to realize the steps of the microstructure analysis method of the present invention according to any one of the above-described embodiments. The program may be recorded in a computer-readable recording medium (e.g., hard disk, ROM, FD, DC, DVD, etc.), or may be transmitted from a certain computer to another computer via a transmission medium (communication network such as the Internet or a LAN), or may be exchanged by any other form. Executing this program by one computer or sharing the steps among multiple computers to be executed executes the steps of the above-described microstructure analysis method, whereby advantages the same as with the microstructure analysis method can be obtained.
storage unit configured to store porous body data in which is correlated position information representing position of a pixel obtained by a 3 dimensional scan of a porous body, and pixel type information representing whether a space pixel representing that the pixel is space or a matter pixel representing that the pixel is matter;
virtual curved surface solid placing unit configured to take a curved surface solid formed by combining a parent virtual sphere and one or more child virtual spheres with which a portion of pixels occupied by the parent virtual sphere overlap as a virtual curved surface solid, wherein, in each virtual curved surface solid, all child virtual curved spheres partially overlap pixels occupied by the parent virtual sphere, and place a group of said virtual curved surface solids in mutually different positions so as to fill in the space pixels with curved surface solid pixels which are pixels occupied by the virtual curved surface solids, referencing the porous body data, each virtual curved surface solid including only one parent virtual sphere; and
microstructure analyzing unit configured to analyze the microstructure of the porous body based on information relating to the placed group of virtual curved surface solids.
A microstructure analysis device according to the present invention includes:
This microstructure analysis device places multiple curved surface solids including a parent virtual sphere and one or more child virtual spheres partially overlapping pixels occupied by the parent virtual sphere to fill in space pixels with curved surface solid pixels which are pixels occupied by the virtual curved surface solids, referencing the porous body data, and analyzes the microstructure of the porous body based on information relating to the placed virtual curved surface solids. Thus, space (pores) having complicated shapes within the porous body are replaced with virtual curved surface solids of shapes having multiple spheres combined, so space within a porous body can be better simulated as a group of multiple virtual curved surface solids. Being based on information relating to the virtual curved surface solids enables the microstructure of the porous body to be analyzed more precisely. Note that the microstructure analysis device according to the present invention may have operations of the means added or other means added, so as to realize the steps of any of the microstructure analysis methods described above.
Fig. 1
is a configuration diagram of a user personal computer 20 according to the present embodiment.
Fig. 2
is a frontal diagram of the honeycomb filter 30 including the porous body partition 44.
Fig. 3
Fig. 2
is a cross-sectional view taken along A-A in .
Fig. 4
is a conceptual diagram of porous body data 60.
Fig. 5
is an explanatory diagram of porous body data 60.
Fig. 6
is a flowchart illustrating an example of an analysis processing routine.
Fig. 7
is a flowchart illustrating an example of virtual curved surface solid placement processing.
Fig. 8
is an explanatory diagram illustrating an example of a curved surface solid table 83.
Fig. 9
is an explanatory diagram of placement of a parent virtual sphere.
Fig. 10
is an explanatory diagram of placement of child virtual spheres and a virtual curved surface solid.
Fig. 11
is a flowchart illustrating an example of path length deriving processing.
Fig. 12
f
is an explanatory diagram illustrating the way in which a path length L is derived.
Fig. 13
f
is an explanatory diagram of deriving the path length L in a case where a branch exists in the path from the inflow face 61 to the outflow face 62.
Fig. 14
is a graph illustrating tabulation results of pore diameter (equivalent diameter d) of a porous body 1.
Fig. 15
is a graph illustrating tabulation results of pore diameter (equivalent diameter d) of a porous body 2 after application of a catalyst.
Fig. 16
is a graph illustrating the relation between spatial uniformity index γ and the number of leaked particles with porous bodies 3 through 8.
Fig. 17
is a graph illustrating the relation between the average value of pressure drop P derived with Expression (3) and pressure drop by the lattice Boltzmann method.
Fig. 18
is a graph illustrating the relation between the average value of pressure drop P derived by Ergun's Equation and pressure drop by the lattice Boltzmann method.
Fig. 19
x
is a graph illustrating the average value of in-plane uniformity index γ and actual pressure drop with porous bodies 13 and 14.
Fig. 20
f
in
is a graph illustrating virtual curved surface solids in porous bodies 15 and 16 being classified by flow velocity ratio T (= T/T).
Fig. 21
is a graph illustrating actual pressure drop with porous bodies 15 and 16.
Fig. 22
is a graph illustrating virtual curved surface solids in porous bodies 15 and 16 being classified by equivalent diameter d.
Fig. 23
e
is a graph illustrating the relation between pressure drop index P and actual pressure drop with porous bodies 17 through 21.
Next, an embodiment of the present invention will be described with reference to the drawings.
Fig. 1
is a configuration diagram schematically illustrating the configuration of a user personal computer (PC) 20 which is an embodiment of the microstructure analysis device according to the present invention. This user PC 20 has a controller 21 including a CPU 22 which executes various types of processing, ROM 23 which stores various types of processing programs and so forth, RAM 24 which temporarily stores data, and so forth, and a HDD 25 which is large-capacity memory to store various types of data such as various types of processing programs such as an analysis processing program 25a and porous body data 60 which is 3 dimensional pixel data of porous body and so forth. Note that the PC 20 has a display 26 for displaying various types of information on a screen, and an input device 27 such as a keyboard for a user to input various types of commands. The porous body data 60 stored in the HDD 25 includes a porous body table 71 and an inflow/outflow table 72, whereby the user PC 20 can analyze microstructures of porous body based on the porous body data 60 stored in the HDD 25, which will be described later. Also, in the process of analyzing microstructures, the RAM 24 stores porous body data 80. The porous body data 80 includes a porous body table 81, an inflow/outflow table 82, and a curved surface solid table 83, which will be described in detail later.
Fig. 2
Fig. 3
Fig. 2
Now, the porous body which the user PC 20 analyzes will be described. is a frontal view of a honeycomb filter 30 including a porous body partition 44 which is a porous body, and is a cross-sectional diagram taken along line A-A in .
Fig. 3
Fig. 3
2
2
the honeycomb filter 30 is a diesel particulate filter (DPF) having a function of filtering particulate matter (PM) in exhaust fumes from a diesel engine. This honeycomb filter 30 has multiple cells 34 (see ) sectioned by porous partitions 44, with an external protective portion 32 formed on the perimeter thereof. A ceramic material such as Si-bonded SiC, Cordierite, or the like is preferably used for the porous partition 44, from the perspective of strength and heat resistance. The thickness of the porous partition 44 is preferably 200 µm to less than 600 µm, and is 300 µm with the present embodiment. The porous partition 44 has an average pore diameter (by mercury intrusion technique) of 10 µm to less than 60 µm, and porosity (voidage) of 40% to less than 65%. The great number of cells 34 formed in the honeycomb filter 30 include inlet-opened cells 36 of which the inlet 36a is open and the outlet 36b has been sealed by an outlet sealant 38, and outlet-opened cells 40 of which an inlet 40a is sealed by an inlet sealant 42 and an outlet 40b is open, as illustrated in . These inlet-opened cells 36 and outlet-opened cells 40 are arrayed so as to be alternatingly adjacent. Cell density is, for example, 15 cells/cm to less than 65 cells/cm. The external protective portion 32 is a layer for protecting the outer periphery of the honeycomb filter 30, and may include the above-described inorganic particles, aluminosilicate, alumina, silica, zirconia, ceria, mullite, and like inorganic fibers, and colloidal silica, clay, and like bonding materials.
Fig. 3
This honeycomb filter 30 is installed downstream of a diesel engine not illustrated in the drawings, for example, and is used to purge exhaust gas including PM so as to be discharged into the atmosphere. Note that the arrow in illustrates the flow of exhaust gas at this time. The exhaust gas including PM from the diesel engine flows into inlet-opened cells 36 from the inlets 36a of the honeycomb filter 30, and then flows into adjacent outlet-opened cells 40 through the porous partitions 44, so as to be discharged from the outlets 40b of the outlet-opened cells 40 into the atmosphere. The PM is collected as the exhaust gas including PM flows through the porous partitions 44 from the inlet-opened cells 36 to the outlet-opened cells 40, the exhaust gas which flowing into the outlet-opened cells 40 is thus clean exhaust gas not including PM. The insides of the pores in the porous partition 44 are coated with an oxidation catalyst such as platinum or the like, which is not illustrated in the drawings, which oxidizes the collected PM so as to prevent deterioration in porosity of the porous body partition 44 and sudden increase in pressure drop.
Figs. 2 and 3
A green body or slurry prepared by mixing a substrate with a pore-forming agent and dispersant can be used as a material to fabricate the honeycomb filter 30. The ceramic material described above can be used for the substrate. For example, a mixture of 80:20 by mass of Sic powder and metal Si powder can be used for a substrate of SiC. The pore-forming agent preferably burns away in the later firing, examples thereof including starch, coke, foamed resin, or the like. A surfactant such as ethylene glycol or the like can be used for the dispersant. The means for preparing the green body are not restricted in particular, examples thereof including methods using a kneader, a vacuum kneading machine, and so forth. This green body is formed by extrusion into the shaft illustrated in using a mold with cells 34 arrayed, and the cells 34 sealed off by the outlet sealant 38 and inlet sealant 42, for example, and then dried, pre-fired, and fired, whereby the honeycomb filter 30 including the porous partitions 44 can be fabricated. The outlet sealant 38 and inlet sealant 42 may be formed of the material used to form the porous partitions 44. The pre-firing process is to burn away organic components included in the honeycomb filter 30, at a temperature lower than the firing temperature. The firing temperature can be 1400°C to 1450°C with cordierite material, and 1450°C with Si-bonded SiC. The honeycomb filter 30 including the porous partitions 44 is obtained through such processes.
Fig. 3
Fig. 2
The HDD 25 of the user PC 20 stores 3 dimensional pixel data of the porous partitions 44 obtained by performing a CT scan on this honeycomb filter 30, as porous body data 60. With the present embodiment, an X-Y plane indicated by the X direction and Y direction in is the cross-sectional plane of photography, along which a CT scan is taken by multiple images being shot in the Z direction in , thereby obtaining pixel data. With the present embodiment, the resolution in each of the X, Y, and Z directions is 1.2 µm, so a cube 1.2 µm in all dimensions is the smallest unit of the 3 dimensional pixel data, i.e., a pixel. The resolution in each of the X, Y, and Z directions may be set as appropriate, depending on the performance of the CT imaging device, the size of the particles to be analyzed, and so forth. Also, the resolution may be of different values in each direction. While not restrictive in particular, the resolution in each of the X, Y, and Z directions may be set to any value within a range of, for example, 0.5 µm to 3.0 µm. Note that the higher the resolution is (the smaller the length of the pixels in each of the X, Y, and Z directions is), the higher the precision of analysis is. From the perspective of precision of the analysis, the resolution in each of the X, Y, and Z directions is preferably 3.0 µm or smaller. Also, the higher the resolution is, the longer the analysis time (calculation time) becomes, but the resolution in each of the X, Y, and Z directions may be set to be smaller than 0.5 µm. For example, this may be 0.2 µm to 0.3 µm, or even smaller than 0.2 µm. The position of each pixel is expressed by XYZ coordinates (the coordinate value 1 corresponds to 1.2 µm, which is the length of each side of a pixel), and type information determining whether or not that pixel is space (pore) or object (constituent material of porous partition 44) is added thereto, and stored in the HDD 25. With the present embodiment, a value 0 is added as type information for pixels representing space (space pixels), and a value 9 is added as type information for pixels representing matter (matter pixels). Note that in reality, the data obtained by the CT scan is luminance data for each XYZ coordinate, for example. The porous body data 60 used with the present embodiment can be obtained by binarizing this luminance data at a predetermined threshold to determine whether a space pixel or matter pixel, for each coordinate. The predetermined threshold is a value set as a value capable of suitably distinguishing between space pixels and matter pixels. This threshold may be determined by experiment beforehand, so that the porosity of the porous partition 44 obtained by measurement, and the porosity in the pixel data after binarization, are approximately equal. This CT scan can be performed using an SMX-160CT-SV3, manufactured by Shimadzu Corporation, for example.
Fig. 4
Fig. 4(a)
Fig. 3
Fig. 3
Fig. 3
Fig. 4(b)
Fig. 4(b)
Fig. 5
Fig. 5
Fig. 4(a)
is a conceptual diagram of the porous body data 60. is a conceptual diagram of the porous body data 60 obtained as pixel data by performing a CT scan of the porous partition 44 in region 50 in . With the present embodiment, this porous body data 60 is extraction of pixel data of a cuboid portion from the pixel data of the porous partition 44, of a cuboid 300 µm (= 1.2 µm × 250 pixels) which is the same value as the thickness of the porous partition 44 in the direction of exhaust gas passing through, in the X direction, 480 µm (= 1.2 µm × 400 pixels) in the Y direction, and 480 µm (= 1.2 µm × 400 pixels) in the Z direction. The later-described analysis processing is performed on this porous body data 60. The size of the porous body data 60 can be set as appropriate depending on the thickness and size of the porous partition 44, allowable calculation load, and so forth. For example, the length in the X direction is not restricted to 300 µm and may be any value, as long as the same value as the thickness of the porous partition 44 in the direction of exhaust gas passing through. Also, while this is preferably the same value as the thickness of the porous partition 44 in the direction of exhaust gas passing through, it does not have to be the same value. The lengths in the Y direction and Z direction also are not restricted to 480 µm and may be other values, and the length in the Y direction and the Z direction may be different. Two faces of the six faces of the cuboid porous body data 60 (faces parallel to the Y-Z plane) are an inflow face 61 (see ) which is the boundary face between the porous partition 44 and inlet-opened cell 36, and an outflow face 62 (see ) which is the boundary face between the porous partition 44 and outlet-opened cell 40 in the region 50, and the remaining four faces are cross-sections of the porous partition 44. is the X-Y plane (photography cross-section) 63 at the position in the porous body data 60 where the Z coordinate is value 3, and an enlarged diagram 64 of a part thereof. As illustrated in the enlarged diagram 64, the X-Y plane 63 is configured of an array of pixels of which each side is 1.2 µm, with each pixel being represented as being either a space pixel or a matter pixel. Note that while the photographed cross-section obtained by the CT scan is planar data with no thickness in the Z direction as illustrated in , each photographed cross-section is handled as having the thickness of the intervals between photographed cross-sections in the Z direction (1.2 µm), i.e., as each pixel being a cube of which each side is 1.2 µm, as described above. Note that the porous body data 60 is stored in the HDD 25 as data including a porous body table 71 correlating the XYZ coordinates serving as position information for each pixel with the type information, and an inflow/outflow table 72 representing the inflow face 61 and outflow face 62, as illustrated in . In , the "X=1" in the inflow/outflow table 72 means the plane X=1 on the XYZ coordinate system, and represents the inflow face 61 illustrated in . "X=251" represents the outflow face 62 in the same way. The HDD 25 also stores, besides this porous body data 60, many other porous body data 60 representing pixel data of the porous partition 44 other than the region 50 described above.
x
x
x
x
x
f
f
The analysis processing program 25a includes a virtual curved surface solid placement module 25b, a fluid analyzing module 25c, an in-plane uniformity evaluation module 25d, a spatial uniformity index evaluation module 25e, a pressure drop evaluation module 25f, a flow-through velocity evaluation module 25g, an equivalent diameter evaluation module 25h, and an analysis result output module 25i. The virtual curved surface solid placement module 25b has a function of referencing the porous body data 80, taking a curved surface solid including a parent virtual sphere and one or more child virtual spheres partially overlapping the parent virtual sphere with regard to occupied pixels, as a virtual curved surface solid, and placing multiple virtual curved surface solids so as to fill in space pixels with curved surface solid pixels which are pixels occupied by virtual curved surface solids. The fluid analyzing module 25c has a function of deriving information relating to the flow of fluid for each space pixel at the time of the fluid passing through the interior of the porous body, by performing fluid analysis based on the porous body data 80. The in-plane uniformity index evaluation module 25d has a function of deriving one or more in-plane uniformity index γ of flow velocity at a cross-section parallel to the inflow face 61 of the porous body data 80, based on information relating to the virtual curved surface solid placed by the virtual curved surface solid placement module 25b and information relating to flow that has been derived by the fluid analyzing module 25c, and evaluating the porous body based on the in-plane uniformity index γ. The spatial uniformity index evaluation module 25e has a function of deriving a spatial uniformity index γ of the flow velocity at the porous body using the in-plane uniformity index γ derived by the in-plane uniformity index evaluation module 25d, and evaluating the porous body based on the in-plane uniformity index γ. The pressure drop evaluation module 25f has functions of deriving pressure drop P per unit thickness of the porous body using the in-plane uniformity index γ derived by the in-plane uniformity index evaluation module 25d, and evaluating the porous body based on the pressure drop P. The flow-through velocity evaluation module 25g has functions of deriving flow-through velocity T and flow velocity ratio T for each virtual curved surface solid, based on information relating to position of virtual curved surface solids placed by the virtual curved surface solid placement module 25b and information relating to the flow derived by the fluid analyzing module 25c, classifying the virtual curved surface solids based on the flow-through velocity T and flow velocity ratio T, and evaluating the porous body based on the classification results. The equivalent diameter evaluation module 25h has functions of deriving equivalent diameter d for the virtual curved surface solids placed by the virtual curved surface solid placement module 25b, classifying the virtual curved surface solids based on the equivalent diameter d, and evaluating the porous body based on the classification results. The analysis result output module 25i has a function of compiling the various types of values and evaluation results and so forth that have been derived, and outputting to be stored in the HDD 25 as analysis result data. The controller 21 executing the analysis processing program 25a realizes the above-described functions of the virtual curved surface solid placement module 25b, fluid analyzing module 25c, in-plane uniformity evaluation module 25d, spatial uniformity index evaluation module 25e, pressure drop evaluation module 25f, flow-through velocity evaluation module 25g, equivalent diameter evaluation module 25h, and analysis result output module 25i.
Fig. 6
Next, the analysis processing which the user PC 20 performs with regard to the porous body data 60 will be described. is a flowchart of an analysis processing routine. This analysis processing routine is carried out by the CPU 22 executing the analysis processing program 25a stored in the ROM 23 upon the user giving an instruction via the input device 27 to perform analysis processing. Note that while a case of performing analysis processing on the porous body data 60 will be described hereinafter, analysis processing can be performed on other porous body data in the same way. Which porous body data is to be analyzed may be determined beforehand, or may be specified by the user.
Upon the analysis processing routine being executed, the CPU 22 first executes curved surface solid placement processing, which is processing to place virtual curved surface solids so as to fill in space pixels in the porous body data 60 (step S100).
Fig. 7
Now, we will depart from description of the analysis processing routine to describe the virtual curved surface solid placement processing. is a flowchart of the virtual curved surface solid placement processing. This virtual curved surface solid placement processing is performed by the virtual curved surface solid placement module 25b. Upon the virtual curved surface solid placement processing being executed, the virtual curved surface solid placement module 25b first reads out the porous body data 60 stored in the HDD 25 and stores this in the RAM 24 (step S200). Thus, the same data as the porous body data 60 including the porous body table 71 and inflow/outflow table 72 stored in the HDD 25 is stored in the RAM 24 as the porous body data 80 including the porous body table 81 and inflow/outflow table 82. Setting of virtual wall faces is performed regarding the porous body data 80 that has been read out (step S210). Specifically, based on the porous body data 80 which is a cuboid 300 µm × 480 µm × 480 µm, the user specifies the distance therefrom to a virtual wall face covering the periphery thereof by way of the input device 27, which the virtual curved surface solid placement module 25b accepts and stores in the RAM 24. For example, if the distance to the virtual wall face is specified as being 1 µm, the virtual curved surface solid placement module 25b presumes that there is a virtual wall face 1 µm on the outer side of each face of the porous body data 80 in the X, Y, and Z directions, and that the outer side thereof has all matter pixels placed thereat. That is to say, the porous body data 80 is a 300 µm × 480 µm × 480 µm cuboid, so this is presumed to be covered with a cuboid virtual wall face that is 302 µm × 482 µm × 482 µm. This virtual wall is set to restrict regions where virtual curved surface solids (parent virtual spheres and child virtual spheres) described later can be placed.
Next, the virtual curved surface solid placement module 25b sets a maximum value Ramax for the diameter Ra of the parent virtual sphere (step S220), and determines whether or not a parent virtual sphere of diameter Ra can be placed in the space pixels on the inner side of the virtual wall face set in step S210 (step S230). A parent virtual sphere with a diameter Ra is a virtual sphere having a size of a diameter of Ra (µm), with the center thereof at the center of one of the pixels. Whether or not this parent virtual sphere of diameter Ra can be placed is determined as follows, for example. First, any one pixel of space pixels (pixels of which the type information is value 0) at that point-in-time is selected. In the event that placing the parent virtual sphere of diameter Ra centered on the selected pixel causes the parent virtual sphere to overlap with a matter pixel or a virtual curved surface solid already placed, another space pixel is selected again as the center. One space pixel after another is selected, and in the event that the parent virtual sphere does not overlap a matter pixel or a virtual curved surface solid already placed, determination is made that the parent virtual sphere of diameter Ra can be placed at that position. Also, in the event that the parent virtual sphere overlaps a matter pixel or a virtual curved surface solid already placed regardless of every space pixel being selected as the center at that point-in-time, determination is made that the parent virtual sphere of diameter Ra cannot be placed. Note that the order of selecting pixels to serve as a center may be random, or may be performed in order from pixels on the inflow face 61 toward pixels on the outflow face 62. Also, the value of the maximum value Ramax may be any value as long as a value equal to or greater than the maximum value of the diameter of pores normally present in the porous partition 44, and for example, the value can be set by reference to a value obtained beforehand by experiment. Upon determining in step S230 that the parent virtual sphere cannot be placed, the diameter R is decremented by 1 (step S240), and the processing of step S230 and thereafter is performed. Note that while the decremented value is 1 with the present embodiment, this may be set as appropriate according to the allowable calculation load and so forth.
In the event that determination is made in step S230 that the parent virtual sphere can be placed, one parent virtual sphere of diameter Ra is placed at that position (step S250). Specifically, the type information corresponding to the pixel occupied by the parent virtual sphere when the parent virtual sphere of diameter Ra is placed, in the porous body table 71 of the porous body data 80 stored in the RAM 24 in step S200, is updated to a value 3, representing the pixel occupied by a parent virtual sphere. Note that while the type information of a pixel of which the center is included in the parent virtual sphere is updated to the value 3 with the present embodiment, the type information of the pixel may be updated to a value 3 when a predetermined percentage of the volume of the pixel (e.g., 50%) or more is occupied by the parent virtual sphere, just type information of pixels completely included in the parent virtual sphere may be updated to a value 3, or the type information of the pixel may be updated to a value 3 when even a part of the pixel is occupied by the parent virtual sphere. This holds true for pixels occupied by later-described child virtual spheres as well.
Next, the virtual curved surface solid placement module 25b sets a diameter Rb of a child virtual sphere to the same value as the diameter Ra (step S260), and determines whether or not a child virtual sphere of a diameter Rb can be placed in the space pixels on the inner side of the virtual wall face set in step S210 (step S270). A child virtual sphere with a diameter Rb is a virtual sphere having a size of a diameter of Rb (µm), with the center thereof at the center of one of the pixels, and with a part of the occupied pixels overlapping those of the parent virtual sphere. Also, the placement of the child virtual spheres is performed such that the center of the child virtual sphere overlaps the parent virtual sphere placed in step S250. Determination of whether or not this child virtual sphere of a diameter Rb can be placed is performed as follows, for example. First, any one pixel of pixels which the parent virtual sphere occupies at that point-in-time (a pixel with a type information value is 3) is selected. In the event that placing the child virtual sphere of diameter Rb centered on the selected pixel causes the child virtual sphere to overlap with a matter pixel or a virtual curved surface solid already placed, another pixel occupied by the parent virtual sphere is selected again as the center. One pixel after another is selected, and in the event that the child virtual sphere does not overlap a matter pixel or a virtual curved surface solid already placed, determination is made that the child virtual sphere of diameter Rb can be placed at that position. Also, in the event that the child virtual sphere overlaps a matter pixel or a virtual curved surface solid already placed regardless of every pixel occupied by the parent virtual sphere being selected as the center at that point-in-time, determination is made that the child virtual sphere of diameter Rb cannot be placed.
In the event that determination is made in step S270 that the child virtual sphere can be placed, one child virtual sphere of diameter Rb is placed at that position (step S280). Specifically, of the porous body table 81 of the porous body data 80 stored in the RAM 24 in step S200, the type information corresponding to the pixel occupied by the child virtual sphere when the child virtual sphere of diameter Rb is placed is updated to a value 4, representing being occupied by a child virtual sphere. Note that no updating of type information is performed for pixels with type information of value 3, which are pixels occupied by the parent virtual sphere. That is to say, pixels where the parent virtual sphere and child virtual sphere overlap are correlated with the type information of the parent virtual sphere. Upon having placed one child virtual sphere, the processing of step S270 and thereafter is performed, step S280 is repeated and child virtual spheres of diameter Rb are placed, until determination is made that no child virtual sphere of diameter Rb can be placed. Note that mutual overlapping of child virtual spheres is permitted. That is to say, overlapping of pixels which one child virtual sphere occupies and pixels which another child virtual sphere occupies is permitted.
Upon determination being made in step S270 that no child virtual sphere can be placed, the diameter Rb is decremented by a value 1 (step S290), determination is made regarding whether or not the diameter Rb is smaller than the minimum value Rbmin (step S300), and if equal to or greater than the minimum value Rbmin, the processing of step S270 and thereafter is performed. The minimum value Rbmin is the lower limit value of the diameter Rb of the child virtual sphere, and is a threshold determined to prevent placement of child virtual spheres with relatively small diameters that would not affect the analysis results very much, for example. With the present embodiment, Rbmin is 2 µm.
In the event that the diameter Rb is smaller than the minimum value Rbmin in step S300, a virtual curved surface solid formed of the parent virtual sphere placed in step S250 and child virtual spheres placed in step S280 (step S310). Specifically, of the porous body table 81 of the porous body data 80 stored in the RAM 24 in step S200, the type information corresponding to the pixels occupied by the parent virtual sphere (pixels of type information is value 3) and the pixels occupied by the child virtual sphere (pixels of type information is value 4) are updated to a value 5, representing being curved surface solid pixels occupied by the virtual curved surface solid. Also, an identification symbol of the virtual curved surface solid is correlated with the position information of the curved surface solid pixels updated to the value 5 this time. The identification symbol of the virtual curved surface solid is a value given to each virtual curved surface solid in accordance with the order of being placed, for example, and curved surface solid pixels configuring one virtual curved surface solid have the same identification symbol correlated therewith. Information relating to this virtual curved surface solid is stored in the RAM 24 (step S320), and determination is made regarding whether or not 99% or more of space pixels have been replaced with the curved surface solid (step S330). This determination is made specifically by referencing the type information of each pixel included in the porous body table 71 stored in the RAM 24, and determining whether or not the number of pixels of which the type information of value 5 is 99% or more of the total number of pixels, of the number of pixels of which the type information is of value 0 and the number of pixels of which the type information is of value 5. Note that the determination threshold is not restricted to 99%, and that other values may be used. In the event that determination is made in step S330 that less than 99% of space pixels have been replaced with the curved surface solid, processing of step SS230 and thereafter is performed, so as to situate the next virtual curved surface solid. On the other hand, in the event that determination is made in step S330 that 99% or more of space pixels have been replaced with the curved surface solid, the virtual curved surface solid placement processing ends.
Fig. 8
Note that in step S320, a virtual curved surface solid table 83 in which are correlated an identification symbol identifying the virtual curved surface solid, the center coordinates (X, Y, Z) and diameter of the parent virtual sphere configuring the virtual curved surface solid, and the center coordinates and diameter of the one or more child virtual spheres configuring the virtual curved surface solid, is stored as information relating to the virtual curved surface solid in the RAM 24, as part of the porous body data 80. illustrates an example of the virtual curved surface solid table 83. As illustrated in the drawing, the virtual curved surface solid table 83 has correlated therein for each of the multiple virtual curved surface solids placed by repeating steps S230 through S320, an identification symbol, the center coordinates and diameter of the parent virtual sphere, and the center coordinates and diameter of the one or more child virtual spheres configuring the virtual curved surface solid. Also, since there are cases where multiple child virtual spheres exist for a single virtual curved surface solid, information of multiple child virtual spheres is correlated in an identifiable manner, such as first child virtual sphere, second child virtual sphere ..., in accordance with the order of placement, for example. Note that a virtual curved surface solid in which not a single child virtual sphere exists, i.e., a virtual curved surface solid configured of a parent virtual sphere alone, is allowable.
Fig. 9
Fig. 10
Figs. 9
10
Fig. 9(a)
Fig. 9(b)
Fig. 10(a)
Fig. 9(b)
Fig. 10(b)
Fig. 9(a)
Fig. 9(b)
Fig. 10(a)
Fig. 10(b)
Due to this virtual curved surface solid placement processing, the virtual curved surface solid table 83 is stored in the RAM 24, and also the space pixels are replaced with curved surface solid pixels by the virtual curved surface solid that has been placed. Now, the way in which one virtual curved surface solid made up of a parent virtual sphere and child virtual spheres is placed by the virtual curved surface solid placing processing will be described. is an explanatory diagram of placement of a parent virtual sphere, and is an explanatory diagram of placement of child virtual spheres and a virtual curved surface solid. Note that and illustrate, of the porous body data 80, the appearance of a cross-section parallel to the X direction, with placement of the virtual curved surface solid being illustrated two-dimensionally, to facilitate description. is an explanatory diagram illustrating an example of the porous body data 80 immediately after having performed step S210, and before placing the virtual curved surface solid, and is an explanatory diagram illustrating a state in which one parent virtual sphere has been placed. is an explanatory diagram of a state where multiple child virtual spheres have been placed as to the parent virtual sphere that has been placed in . is an explanatory diagram of a state where a virtual curved surface solid made up of the parent virtual sphere and child virtual spheres has been placed. As illustrated in , the porous body data 80 is made up of matter pixels and space pixels, with the inflow face 61, outflow face 62, and a virtual wall face 85 having been set. The virtual curved surface solid (parent virtual sphere, child virtual sphere) is placed so as to not extend outside from the virtual wall face 85. If the diameter Ramax is set to a sufficiently great value, performing the processing of steps S220 through S250 decrements the value of the diameter Ra 1 at a time, and when the greatest diameter which can be placed in the porous body data 80 in a range of not overlapping a matter pixel and not protruding outside from the virtual wall face 85, and the diameter Ra, are equal, one parent virtual sphere is placed (). Next, steps S270 through S300 are repeated until the diameter Rb is determined in step S300 to be smaller than the minimum value Rbmin, whereby multiple child virtual spheres of various sizes of the diameter are placed so as to fill in the space pixels with the centers of the child virtual spheres overlapping the parent virtual sphere and also pixels which the child virtual spheres occupy not overlapping with matter pixels (). Upon the diameter Rb being determined in step S300 to be smaller than the minimum value Rbmin, one virtual curved surface solid made up of the parent virtual sphere and the child virtual spheres placed so far is placed (). The processing of steps S230 through S320 to place one virtual curved surface solid in this way is repeated until determination is made in step S330 that of the space pixels, the pixels replaced by curved surface solid pixels is 99% or more, whereby virtual curved surface solids are sequentially placed in other space pixels where a virtual curved surface solid is not yet placed, thereby filling up the space pixels with curved surface solid pixels. Thus, space (pores) having complicated shapes within the porous body are replaced with virtual curved surface solids of shapes having multiple spheres combined, so space within a porous body can be better simulated as a group of multiple virtual curved surface solids.
Fig. 6
in
in
in
-5
3
Let us return to the description of the analysis processing routine in . Upon the virtual curved surface solid placement processing of step S100 ending, the fluid analyzing module 25c performs fluid analysis processing to derive information relating to the flow of a fluid per space pixel at the time of a fluid passing through the interior of the porous body, by performing fluid analysis based on the porous body data 80 stored in the RAM 24 (step S110). This fluid analysis processing is performed by the lattice Boltzmann method. Specifically, fluid analysis is performed regarding a case of a fluid flowing in from the inflow face 61, where the centers of the pixels of the porous body data 80 are taken as the lattice points by the lattice Boltzmann method using a predetermined relational expression relating to the flow of fluid between each lattice point and adjacent lattice points. The a flow vector made up of flow velocity and flow direction for each space pixel in the porous body data 80 is derived as information relating to the flow of the fluid at each space pixel, and the flow velocity vectors of each space pixel are stored in the porous body table 81 of the porous body data 80 in the RAM 24 in a correlated manner. Note that numerical values necessary of this fluid analysis, such as the average flow velocity T of the fluid at the inflow face 61, viscosity µ of the fluid, density ρ of the fluid, and so forth, are set in the analysis processing program 25a beforehand for example, and these numerical values are used to perform the analysis. These numerical values may be set by the user by way of the input device 27. Note that the average flow velocity T is the average value of the flow velocity immediately prior to the fluid entering the porous body, and corresponds to the initial value of the flow velocity in fluid analysis. With the present embodiment, the average flow velocity T is set to 0.01 m/s. Also, air of 0°C and 1 atm is assumed for the fluid, with a viscosity µ of 1.73 × 10 [Pa·s], and density ρ of 1.25 [kg/m]. Note that the fluid analysis processing in step S110 does not take into consideration the virtual curved surface solid placed in step S100, and is performed as if curved surface solid pixels are also space pixels. While description has been made with the present embodiment that the fluid analysis processing in step S110 is performed based on the porous body data 80 stored in the RAM 24, this may be performed based on the porous body data 60 stored in the HDD 25.
x
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<mrow><msub><mi mathvariant="italic">γ</mi><mi mathvariant="normal">x</mi></msub><mo>=</mo><mn mathvariant="normal">1</mn><mo>−</mo><mfrac><mn mathvariant="normal">1</mn><mn mathvariant="normal">2</mn></mfrac><mstyle displaystyle="true"><mrow><munderover><mrow><mo>∑</mo></mrow><mrow><mi mathvariant="normal">i</mi><mo>=</mo><mn mathvariant="normal">1</mn></mrow><mi mathvariant="normal">n</mi></munderover></mrow></mstyle><mfrac><mrow><mfenced open="|" close="|" separators=""><msub><mi mathvariant="normal">u</mi><mi mathvariant="normal">i</mi></msub><mo>−</mo><msub><mi mathvariant="normal">u</mi><mi mathvariant="normal">mean</mi></msub></mfenced><mo>⋅</mo><msub><mi mathvariant="normal">A</mi><mi mathvariant="normal">i</mi></msub></mrow><mrow><msub><mi mathvariant="normal">u</mi><mi mathvariant="normal">mean</mi></msub><mo>⋅</mo><mi mathvariant="normal">A</mi></mrow></mfrac></mrow>
n: number [count] of virtual curved surface solids within cross-section
x: distance [m] between cross-section and inflow face
i
u: average flow velocity (i = 1, 2, ..., n) [m/s] for each of the n virtual curved surface solids at cross-section
mean
i
2
n
i
u: average value (=(u + u + ... + u)/n) [m/s] of average flow velocity u at cross-section
i
2
A: cross-sectional area (i = 1, 2, ..., n) [m] for each virtual curved surface solid within cross-section
1
2
2
A: total cross-sectional area (= A + A + ... + An) [m] of virtual curved surface solids at cross-section
Next, the in-plane uniformity index evaluation module 25d performs in-plane uniformity index evaluation where an in-plane uniformity index γ is derived, and evaluates the porous body by performing acceptability evaluation based on the derived value (step S120). The in-plane uniformity index γ is derived by deciding one cross-section parallel to the inflow face 61, and deriving from the following Expression (1) as a value at that cross-section. Note that an n number of average flow velocities u at the cross-section described below, and cross-sectional area A of each virtual curved surface solid within the cross-section, are derived as follows, for example. First, curved surface solid pixels included in a cross-section from which the in-plane uniformity index γ is to be derived are identified based on a distance x between cross-section and the inflow face 61, and the position information and type information in the porous body table 81 stored in the RAM 24. Next how many types of identification symbols there are in virtual curved surface solids correlated with the identified curved surface solid pixels is counted, and this number is taken as the number n of virtual curved surface solids within the cross-section. Next, one of the identification symbols of the virtual curved surface solids within the cross-section is selected. Next, with regard to the curved surface solid pixel correlated with the selected identification symbol, i.e., the curved surface solid pixels configuring one virtual curved surface solid, the flow velocity vector correlated with each curved surface solid pixel in the fluid analysis processing is found, the average value of the flow velocity components in a direction perpendicular to the cross-section for each curved surface solid pixel is derived, and this is taken as average flow velocity u. Also, the number of pixels is counted for the curved surface solid pixels correlated with the selected identification symbol, and the product of the number of pixels and the area of the curved surface solid pixels following the cross-section (1.44 µm in the case of the present embodiment) is taken as cross-section area A. In the same way, the selected identification symbol is sequentially changed, whereby the average flow velocity u, u, ..., u, and cross-section area A, A, ..., A can be derived for the n virtual curved surface solids within the cross-section. The in-plane uniformity index evaluation module 25d then derives the in-plane uniformity index γ for multiple cross-sections, e.g., 250 (= 300 µm / 1.2 µm) cross-sections with the distance x changed 1.2 µm at a time for example. Determination is made that the pressure drop property of the porous body is acceptable when the average value of the in-plane uniformity index γ is 0.6 or greater, and unacceptable when smaller than 0.6. Note that at the time of deriving the in-plane uniformity index γ, multiple in-plane uniformity indices γ are preferably derived by changing the distance x by a value the same as the X direction length of the pixels (1.2 µm with the present embodiment), i.e., shifting the cross-section which is the object of derivation one pixel at a time. However, an arrangement may be made not restricted to this, where the distance x is changed and multiple in-plane uniformity indices γ are derived. Also, an arrangement may be made where just one in-plane uniformity index γ is derived and acceptability determination is made by whether or not that value is 0.6 or greater.
[Math. 1] where
x
<mrow><mi>γ</mi><mo>=</mo><mover><mrow><msub><mi>γ</mi><mi mathvariant="normal">x</mi></msub></mrow><mrow><mo>‾</mo></mrow></mover><mo>⋅</mo><mfenced separators=""><mn>1</mn><mo>−</mo><msub><mi>δ</mi><mi>γ</mi></msub></mfenced></mrow>
γ
x
x
: average value of γ
γ
x
δ: standard deviation of γ
Next, the spatial uniformity index evaluation module 25e performs spatial uniformity index evaluation processing where a spatial uniformity index γ is derived, and acceptability determination is made on the derived value to evaluate the porous body (step S130). The spatial uniformity index γ is derived by the following Expression (2) using multiple in-plane uniformity indices γ derived in the in-plane uniformity index evaluation processing. Determination is made that the collection performance of the porous body is acceptable when the derived spatial uniformity index γ is 0.6 or greater, and unacceptable when smaller than 0.6. Also note that acceptability may be determined based on whether or not 0.5 or greater.
[Math. 2] where
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2
<mrow><mi mathvariant="normal">P</mi><mo>=</mo><mfrac><mrow><msub><mi mathvariant="normal">ΔP</mi><mi mathvariant="normal">x</mi></msub></mrow><mi mathvariant="normal">Δx</mi></mfrac><mo>=</mo><mfenced separators=""><mfrac><mn mathvariant="normal">200</mn><mn mathvariant="normal">3</mn></mfrac><mfrac><mn mathvariant="normal">1</mn><mrow><msup><mrow><msub><mi mathvariant="normal">D</mi><mi mathvariant="normal">hx</mi></msub></mrow><mn mathvariant="normal">2</mn></msup><mo>⋅</mo><msub><mi mathvariant="normal">ε</mi><mi mathvariant="normal">x</mi></msub></mrow></mfrac><mi mathvariant="italic">μ</mi><msub><mi mathvariant="normal">U</mi><mi mathvariant="normal">x</mi></msub><mo>+</mo><mfrac><mn mathvariant="normal">7</mn><mn mathvariant="normal">6</mn></mfrac><mfrac><mn mathvariant="normal">1</mn><mrow><msub><mi mathvariant="normal">D</mi><mi mathvariant="normal">hx</mi></msub><mo>⋅</mo><msup><mrow><msub><mi mathvariant="normal">ε</mi><mi mathvariant="normal">x</mi></msub></mrow><mn mathvariant="normal">2</mn></msup></mrow></mfrac><mi mathvariant="italic">ρ</mi><msup><mrow><msub><mi mathvariant="normal">U</mi><mi mathvariant="normal">x</mi></msub></mrow><mn mathvariant="normal">2</mn></msup></mfenced><mo>⋅</mo><msup><mrow><msub><mi mathvariant="italic">γ</mi><mi mathvariant="normal">x</mi></msub></mrow><mi mathvariant="normal">k</mi></msup></mrow>
Δx: cross-sectional thickness [m] at cross-section at distance x
x
ΔP: pressure drop [Pa] at cross-section at distance x
x
Dh: representative hydraulic diameter [m] of space (pores) at cross-section at distance x
x
ε: voidage (= number of space pixels / (number of space pixels + number of matter pixels)) at cross-section at distance x
µ: viscosity [Pa·s] of fluid
x
U: flow velocity average value [m/s] at each space pixel at cross-section at distance x
3
ρ: density of fluid [kg/m]
k: constant
Next, the pressure drop evaluation module 25f performs pressure drop evaluation processing where the pressure drop P per unit thickness is derived, and acceptability determination is made on the derived value to evaluate the porous body (step S140). The pressure drop P is derived by the following Expression (3) using multiple in-plane uniformity indices γ derived in the in-plane uniformity index evaluation processing. This Expression (3) is one where a known Ergun's Equation representing pressure drop properties at the time of a fluid passing through a porous body, has been revised using the in-plane uniformity index γ. Note that the representative hydraulic diameter Dh of the space (pores) at the cross-section at distance x is obtained as follows with the present embodiment. First, a total area A is derived, with the total area of space portions at the cross-section at distance x as A. This is derived as the product of the number of pixels of the space pixels at the cross-section at distance x (including curved surface solid pixels), and the cross-sectional area of each pixel (1.44 µm with the present embodiment). Next, the total wetted perimeter L is derived with the total of wetted perimeters at the cross-section at distance x as L. This is derived as the total of the length of boundary lines between space pixels (including curved surface solid pixels) and matter pixels. The representative hydraulic diameter Dh is then derived from representative hydraulic diameter Dh = 4 x total area A / total wetted perimeter L. Note that it is sufficient for the representative hydraulic diameter Dh to be a value representing the diameter of the space (pores) at the cross-section at distance x, and may be derived by another method. For example, a cross-sectional equivalent diameter Re of a virtual curved surface solid at the cross-section at the distance x may be obtained for each virtual curved surface solid within the cross-section, and the average value of this cross-sectional equivalent diameter Re may be derived as the representative hydraulic diameter Dh. The cross-sectional equivalent diameter Re of a virtual curved surface solid may be obtained by Re = 4 × cross-sectional area A / perimeter L, for example. In this Expression, the cross-sectional area Ai may be obtained by the method described above. The perimeter L may be obtained as the length of the cross-sectional outline of the virtual curved surface solid projected on the cross-section at the distance x, based on information included in the virtual curved surface solid table 73, for example. Also, a flow velocity average value U for every space pixel at the cross-section at the distance x described below may be derived by, for example, finding the flow velocity vectors correlated with each space pixel in the fluid analysis processing for the space pixels (including curved surface solid pixels) at the cross-section at the distance x, deriving the flow velocity component in a direction perpendicular to the cross-section of each space pixel, and deriving as the average value thereof. Note that a constant k can be obtained beforehand by experiment, for example, so that the correlation between the pressure drop P and the actual pressure drop of the porous body is higher. With the present embodiment, the constant k is set to the value "-2". Also, the acceptability determination based on pressure drop P is performed as follows, for example. First, the pressure drop P is derived for each of the multiple in-plane uniformity indices γ, and the average value of the multiple pressure drops P is derived. In the event that the average value of the pressure drops P is at or below a predetermined threshold (e.g., allowable upper limit value of pressure drop), determination is made that the pressure drop of the porous body is acceptable, and determined to be unacceptable if the predetermined threshold is exceeded. At the time of deriving the multiple pressure drops P with the present embodiment, the distance x is changed by a value the same as the X direction length of the pixels (1.2 µm with the present embodiment), i.e., shifting the cross-section which is the object of derivation one pixel at a time, and pressure drops P of a number corresponding to as many in-plane uniformity indices γ as there are pixels in the X direction are derived. However, the method for deriving the average value of pressure drops P is not restricted to this, and any method will suffice as long as pressure drops P corresponding to multiple in-plane uniformity indices γ are derived while changing the distance x, and the average thereof is derived.
[Math. 3] where
2
3
2
Next, the flow-through velocity evaluation module 25g performs flow-through velocity evaluation processing where the flow-through velocity T at each virtual curved surface solid is derived, the virtual curved surface solids are classified based on the derived values, and the porous body is evaluated based on the classification results (step S150). The flow-through velocity T at each virtual curved surface solid is derived as follows, for example. First, a through-flow volume Q per unit time of the fluid is derived for each virtual curved surface solid. The flow-through velocity T of each virtual curved surface solid is then derived by T = Q/(πd/4), based on the derived through-flow volume Q and an equivalent diameter d of the virtual curved surface solid (= 6 × volume V of virtual curved surface solid / surface area S of virtual curved surface solid). The through-flow volume Q, volume V, and surface area S of each virtual sphere is derived as follows, for example. First, one virtual curved surface solid is selected, and the curved surface solid pixels corresponding to the identification symbols of the selected virtual curved surface solid are found from the porous body table 81 in the RAM 24. The number of pixels of the curved surface solid pixels configuring the selected virtual curved surface solid is derived, and the product of the number of pixels and the volume of one curved surface solid pixel (1.728 µm with the present embodiment) is taken as the volume V. Also, the surface area S of the selected virtual curved surface solid is derived based on information (center coordinate and diameter of parent virtual sphere and child virtual spheres) included in the virtual curved surface solid table 83. Next, of the curved surface solid pixels configuring the selected virtual curved surface solid, the curved surface solid pixel configuring the surface of the virtual curved surface solid are identified based on the information included in the virtual curved surface solid table 83. The flow vectors correlated with the curved surface solid pixels configuring the surface are found using the porous body table 81 in the RAM 24, the curved surface solid pixels of which the flow velocity vector heads toward the inside of the virtual curved surface solid are identified, the magnitude of the flow velocity vectors of the identified curved surface solid pixels is obtained for each curved surface solid pixel, and derived as through-flow volume Q per unit time = (sum of magnitude of flow velocity vectors) × (number of identified curved surface solid pixels) × (area of one face of a curved surface solid pixel (= 1.44 µm)). Thus, the flow-through velocity T of the selected curved surface solid pixel can be derived. In the same way, the flow-through velocity T is derived for each of the multiple virtual curved surface solids.
f
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Classification of each of virtual curved surface solids in the flow-through velocity evaluation processing is performed as follows. First, one virtual curved surface solid is selected, and a flow velocity ratio T (= T/T) is derived from the flow-through velocity T of the selected virtual curved surface solid and the average flow velocity T in fluid analysis. In the event that T < 2, that virtual curved surface solid is classified as being a low-flow-velocity curved surface solid, in the event that 2 ≤ T < 8, as being a mid-flow-velocity curved surface solid, and in the event that 8 ≤ T, as being a high-flow-velocity curved surface solid. Each of the virtual curved surface solids are classified in the same way. In the event that the percentage of the total value of volume V of the low-flow-velocity curved surface solid is 20% or less as to the total value of volume V of the multiple virtual curved surface solids, and also the percentage of the total value of volume V of the high-flow-velocity curved surface solid is 10% or less, determination is made that the performance of the porous body is acceptable. On the other hand, in the event that the percentage of the total value of volume V of the low-flow-velocity curved surface solid is greater than 20%, or that the percentage of the total value of volume V of the high-flow-velocity curved surface solid is greater than 10%, determination is made that this is unacceptable.
Next, the equivalent diameter evaluation module 25h performs equivalent diameter evaluation processing in which the equivalent diameter d of each virtual sphere is derived, the virtual curved surface solids are classified based on the equivalent diameter d, and the porous body is evaluated based on the classification results (step S160). Classification of the virtual curved surface solids based on the equivalent diameter d is performed by taking a virtual curved surface solid where d < 10 µm as being a small-diameter curved surface solid, a virtual curved surface solid where 10 µm ≤ d ≤ 25 µm as being a mid-diameter curved surface solid, and a virtual curved surface solid where 25 µm < d as being a large-diameter curved surface solid. In the event that the percentage of the total value of volume V of mid-diameter curved surface solids as to the total value of volume V of the multiple virtual curved surface solids is 70% or more, determination is made that the performance of the porous body is acceptable, and in the case of less than 70%, determination is made that the performance of the porous body is unacceptable. Note that the equivalent diameter d and the volume V may be derived in the same way as with the flow-through velocity evaluation processing described above, or values derived in the flow-through velocity evaluation processing may be used without change.
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Upon performing each evaluation processing of steps S120 through S160, the analysis result output module 25i performs analysis result output processing in which the information and the like stored in the RAM 24 in the above processing is output as analysis result data and stored in the HDD 25 (step S170), and the present routine ends. The analysis result data includes, for example, the porous body data 80 including the porous body table 81, inflow/outflow table 82, and virtual curved surface solid table 83, stored in the RAM 24, the values and the result of acceptability determination of the in-plane uniformity index γ in the in-plane uniformity index evaluation processing, the values and the result of acceptability determination of the spatial uniformity index γ in the spatial uniformity index evaluation processing, the values and the result of acceptability determination of the pressure drop P in the pressure drop evaluation processing, the flow-through velocity T in the flow-through velocity evaluation processing, flow velocity ratio T value, percentage of the total value of volume V of low-flow-velocity curved surface solids, and percentage of the total value of volume V of high-flow-velocity curved surface solids and the result of acceptability determination, the values of equivalent diameter d in the equivalent diameter evaluation processing, and percentage of the total value of volume V of mid-diameter curved surface solids and the result of acceptability determination, and so forth. Values used for the fluid analysis processing, such as average flow velocity T, fluid viscosity µ, fluid density ρ, and so forth may also be included.
Note the correlation between the components of the present embodiment and the microstructure analysis device according to the present invention will be disclosed. The RAM 24 and HDD 25 according to the present embodiment correspond to storage unit of the present invention, the virtual curved surface solid placement module 25b corresponds to virtual curved surface solid placement unit, and the in-plane uniformity index evaluation module 25d, spatial uniformity index evaluation module 25e, pressure drop evaluation module 25f, flow-through velocity evaluation module 25g, and equivalent diameter evaluation module 25h correspond to microstructure analysis unit. Note that with the present embodiment, an example of the microstructure analysis method according to the present invention is also disclosed by describing the operations of the user PC 20.
According to the present embodiment described in detail above, porous body data 80 in which position information and type information is correlated is referenced to take a curved surface solid made up of a parent virtual sphere and child virtual spheres as a virtual curved surface solid, and multiple virtual curved surface solids are placed so as to fill in space pixels with curved surface solid pixels occupied by virtual curved surface solids, whereby the space inside a porous body can be simulated more precisely as a group of multiple virtual curved surface solids. The microstructures of porous bodies can then be analyzed more precisely, by being based on information relating to these virtual curved surface solids. Also, the virtual curved surface solids are placed so that the virtual curved surface solids do not overlap each other or curved surface solid pixels and matter pixels overlap each other, so the processing time necessary to place the virtual curved surface solids can be reduced as compared to a case where overlapping is permitted. Further, the diameter Ra is first set to the maximum value Rmax and whether or not a parent virtual sphere can be placed is determined while sequentially decrementing Ra, so the space pixels can be filled with as large a virtual curved surface solid as possible.
x
x
x
x
Also, the in-plane uniformity index γ is derived, and acceptability determination is performed based thereupon. Now, the more uniform the flow velocity of a fluid at a cross-section is, the greater (closer to value 1) the in-plane uniformity index γ is, and the greater the irregularity in the flow velocity of a fluid at a cross-section is, the smaller the value is. In a case of using the porous body for a filter, the greater the value of the in-plane uniformity index γ is, the better the pressure drop property tends to be. Accordingly, deriving this in-plane uniformity index γ and performing evaluation based thereupon enables the pressure drop property of the porous body to be evaluated more precisely, as microstructure analysis.
x
Further, the spatial uniformity index γ is derived and acceptability determination is performed based thereupon. Now, the smaller the irregularity in the in-plane uniformity index γ derived regarding multiple cross-sections is, the greater the spatial uniformity index γ is, and the greater the irregularities, the smaller the value is. The collecting performance in the case of using the porous body for a filter tends to be better the greater this spatial uniformity index γ is. Accordingly, by deriving this spatial uniformity index γ and performing evaluation based thereupon enables the collecting performance of the porous body to be evaluated more precisely, as microstructure analysis.
Moreover, the pressure drop P per unit thickness is derived, and acceptability determination is performed based thereupon. Now, the pressure drop P has greater correlation with the pressure drop of an actual porous body as compared with the pressure drop derived by Ergun's Equation. Accordingly, pressure drop property of a porous body, for example, can be evaluated more precisely by deriving this pressure drop P per unit volume and performing evaluation based thereupon, as microstructure analysis.
Also, the flow-through velocity T is derived, the virtual curved surface solids are classified based thereupon, and acceptability determination is performed based on the classification results. Now, there are cases where pores of a porous body simulated with virtual curved surface solids of which the flow-through velocity T is small may not contribute much to transmittance of the fluid, leading increased pressure drop, and deterioration in thermal conductivity and thermal capacity of the material. Also, there are cases where pores of a porous body simulated with virtual curved surface solids of which the flow-through velocity T is great exhibit great flow resistance when the fluid passes through, or the fluid may pass through in a short time and the pores do not contribute much to collecting performance. Accordingly, classifying a part of the virtual curved surface solids as low-flow-velocity curved surface solids with small flow-through velocity T and high-flow-velocity curved surface solid with great flow-through velocity T in this way, and performing evaluation based thereupon, enables the microstructure of the porous body to be analyzed precisely.
Also, the equivalent diameter d is derived, the virtual curved surface solids are classified based thereupon, and acceptability determination is performed based on the classification results. Now, there are cases where pores of the porous body simulated with virtual curved surface solids of which the equivalent diameter d is small, the flow velocity of the fluid passing through become small and leading to increased pressure drop, or the catalyst applied to the walls of the pores to use the porous body as a filter may not be appropriately applied, or the like. Also, there are cases where pores of the porous body simulated with virtual curved surface solids of which the equivalent diameter d is great, the flow velocity of the fluid passing through become great, and not contributing to collecting performance very much when using the porous body as a filter. Accordingly, classifying a part of the virtual curved surface solids as virtual curved surface solids with small equivalent diameter d and virtual curved surface solids with great equivalent diameter d in this way, and performing evaluation based thereupon, enables the microstructure of the porous body to be analyzed precisely.
Note that the present invention is not restricted to the above-described embodiment.
For example, with the above-described embodiment, the virtual curved surface solids have been placed in the virtual curved surface solid placement processing such that the center of child virtual spheres overlap the parent virtual sphere, but unrestricted to this, pixels occupied by a child virtual sphere and pixels occupied by a parent virtual sphere partially overlap.
With the above-described embodiment, the virtual curved surface solids have been placed in the virtual curved surface solid placement processing such that a virtual curved surface solid does not overlap pixels occupied by another virtual curved surface solid, but partial overlapping may be permitted. Also, the virtual curved surface solids have been placed such that curved surface solid pixels and matter pixels do not overlap, but partial overlapping may be permitted.
With the above-described embodiment, fluid analysis has been performed by the lattice Boltzmann method, but another fluid analysis method may be used.
With the above-described embodiment, determination has been made in the flow-through velocity evaluation processing that the performance of the porous body is acceptable in the event that the percentage of the total value of volume V of the low-flow-velocity curved surface solids is 20% or less as to the total value of volume V of the virtual curved surface solids, and also the percentage of the total value of volume V of the high-flow-velocity curved surface solid is 10% or less, however, the performance of the porous body may be determined to be acceptable when the volume ratio of the low-flow-velocity curved surface solids in the virtual curved surface solids is at or below a predetermined threshold, and the volume ratio of the high-flow-velocity curved surface solids in the virtual curved surface solids is at or below a predetermined threshold. The threshold for the low-flow-velocity curved surface solids and the threshold for the high-flow-velocity curved surface solids are not restricted to the above-described 20% and 10%, and may be values obtained by experiments, for example. Also, the performance of the porous body may be determined to be acceptable when the volume ratio of the low-flow-velocity curved surface solids in the virtual curved surface solids is at or below a predetermined threshold, or the performance of the porous body may be determined to be acceptable when the volume ratio of the high-flow-velocity curved surface solids in the virtual curved surface solids is at or below a predetermined threshold.
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Also, with the above-described embodiment, classification has been performed such that virtual curved surface solids where T < 2 are classified as the low-flow-velocity curved surface solids, virtual curved surface solids where 2 ≤ T < 8 as the mid-flow-velocity curved surface solids, and virtual curved surface solids where 8 ≤ T as the high-flow-velocity curved surface solids, but classification may be performed with other thresholds. And moreover classification of virtual curved surface solids is not restricted to that performed by the flow velocity ratio T, and classification may be performed by comparing the flow-through velocity T and threshold values.
With the above-described embodiment, in the equivalent diameter evaluation processing, a virtual curved surface solid where 10 µm ≤ d ≤ 25 µm has been taken as a mid-diameter curved surface solid, and in the event that the percentage of the total value of volume V of mid-diameter curved surface solids as to the total value of volume V of the virtual curved surface solids is 70% or more, determination has been made that the performance of the porous body is acceptable, but this is not restricted to 70%, and another threshold obtained by experiment may be used to determine acceptability. For example, determination may be made to be acceptable in the case of 60% or more. Also, classification and evaluation of curved surface solids may be made by another method. For example, virtual curved surface solids where d < 10 µm are taken as being small-diameter curved surface solids, and in the event that the percentage of the total value of volume V of the small-diameter curved surface solids as to the total value of volume V of the virtual curved surface solids is 25% or less, determination may be made that the porous body is acceptable. Also, virtual curved surface solids where 30 µm ≤ d may be taken as large-diameter curved surface solids, and in the event that the percentage of the total value of volume V of the large-diameter curved surface solids as to the total value of volume V of the virtual curved surface solids is 10% or less, determination may be made that the porous body is acceptable, or determination of being acceptable may be made with 5% or less. Further, virtual curved surface solids where 40 µm ≤ d may be taken as large-diameter curved surface solids, and determination may be made that the porous body is acceptable when no large-diameter curved surface solids exist.
x
With the above-described embodiment, the in-plane uniformity index γ, spatial uniformity index γ, and pressure drop P are derived and determination of acceptability has been performed in the analysis processing routine, but an arrangement may be made where the values are derived but determination of acceptability is not performed. Also, while deriving of the flow-through velocity T and equivalent diameter d, classification, and determination of acceptability have been performed in the analysis processing routine, but an arrangement may be made where determination of acceptability is not performed, or an arrangement may be made where classification and determination of acceptability are not performed.
With the above-described embodiment, each process of steps S120 through S140 have been performed, but one or both of steps S130 and S140 may be omitted, or all of steps S120 through S140 may be omitted. In the same way, one or more of each process of steps S150 through S170 may be omitted. Also, in the case of omitting all processes of steps SS120 through S160, the process of step S110 may be omitted.
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With the above-described embodiment, virtual curved surface solids where, of an n number of average flow velocities u, the average flow velocity u is of a value 0, may be excluded from the n virtual curved surface solids, deeming that this is a space enclosed by the component material of the porous partition 44 and does not affect flow of the fluid. For example, if there are five virtual curved surface solids within a cross-section, and the average flow velocity u of one virtual curved surface solid is of the value 0, this virtual curved surface solid may be ignored (deemed to be matter pixels), and the subsequent processing continued deeming that there are four virtual curved surface solids in the cross-section and the at the number n = 4. Other processing using the results of this fluid analysis may be the same.
3
With the above-described embodiment, in deriving the equivalent diameter d (= 6 × volume V of virtual curved surface solid / surface area S of virtual curved surface solid), the product of the number of pixels of the curved surface solid pixels configuring the virtual curved surface solid and the volume of one curved surface solid pixel (1.728 µm with the present embodiment) is taken as the volume V, but is not restricted to this. For example, the volume V of the virtual curved surface solid may be derived based on information (center coordinate and diameter of parent virtual sphere and child virtual spheres) included in the virtual curved surface solid table 83. That is to say, instead of volume in a case of considering the virtual curved surface solid to be a group of space pixels (the edge portion of the virtual curved surface solid is represented as the edge portion of space pixels, i.e., by straight lines and planes), the volume V may be taken as the volume in a case of considering the virtual curved surface solid to be a group of a parent virtual sphere and child virtual spheres represented by center coordinates and diameter (the edge portion of the virtual curved surface solid is represented by curves and curved surfaces).
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With the above-described embodiment, the cross-sectional area A (A, A, A, ..., A) has been derived from the product of the number of pixels and the area of the curved surface solid pixels following the cross-section (1.44 µm in the case of the present embodiment), but is not restricted to this. For example, the cross-sectional area A of a virtual curved surface solid may be derived based on the center coordinates and diameter of the parent virtual sphere and child virtual sphere included in the virtual curved surface solid table 83, and the position of the cross-section (distance x between cross-section and inflow face 61). That is to say, instead of area in a case of considering the virtual curved surface solid to be a group of space pixels (the edge portion of the cross-section is represented as the edge portion of space pixels, i.e., by straight lines), the cross-sectional area A may be taken as the area in a case of considering the virtual curved surface solid to be a group of a parent virtual sphere and child virtual spheres represented by center coordinates and diameter (the edge portion of the cross-section is represented by curves).
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With the above-described embodiment, the flow-through velocity T has ben derived by T = Q/(πd/4), but is not restricted to this. For example, flow-through velocity components Tx, Ty, and Tz may be derived for the X, Y, and Z directions of the virtual curved surface solid, with the flow-through velocity T being derived as flow-through velocity T = √(Tx + Ty + Tz). The flow-through velocity component Tx in this case is derived as follows. First, regarding the virtual curved surface solid which the flow-through velocity T is to be derived, a cross-section which passes through the center of the parent virtual sphere of a virtual curved surface solid, and also is perpendicular to the X direction, is identified, and curved surface solid pixels configuring that cross-section are identified. Next, the X direction components of the flow velocity vectors correlated with each of the identified curved surface solid pixels (magnitude of flow velocity vectors in the X direction) are found using the porous body table 81, and the average value thereof is taken as the flow-through velocity component Tx. In the same way, curved surface solid pixels configuring a cross-section which passes through the center of the parent virtual sphere of the virtual curved surface solid, and also is perpendicular to the Y direction, are identified. The average value of the Y direction components of the flow velocity vectors of the curved surface solid pixels is taken as the flow-through velocity component Ty. Also, curved surface solid pixels configuring a cross-section which passes through the center of the parent virtual sphere of the virtual curved surface solid, and also is perpendicular to the Z direction, are identified. The average value of the Z direction components of the flow velocity vectors of the curved surface solid pixels is taken as the flow-through velocity component Tz.
Fig. 7
With the above-described embodiment, in the virtual curved surface solid placement processing, the virtual curved surface solids have been placed such that a virtual curved surface solid does not overlap pixels occupied by another virtual curved surface solid, but overlapping of occupied pixels (the virtual curved surface solids overlapping each other) may be permitted. Thus, virtual curved surface solids with as large a volume as possible can be placed as compared with a case where virtual curved surface solids are placed so as to not overlap. Also, the space within the porous body can be simulated more precisely with virtual curved surface solids by placing virtual curved surface solid having as large a volume as possible. Also, avoiding placing virtual curved surface solids with small volume in a case of placing the virtual curved surface solids such that the virtual curved surface solids do not overlap with occupied pixels of another virtual curved surface solid, there are cases where space pixels where no virtual curved surface solid is placed increases. That is to say, there are cases where, of the space within the porous body, space which cannot be simulated with virtual curved surface solids increases. However, permitting the virtual curved surface solids to overlap each other enables reduction in such space which cannot be simulated with virtual curved surface solids. Permitting overlapping of virtual curved surface solids can be realized by permitting placement of a parent virtual sphere in step S230 in the virtual curved surface solid placement processing in described above, even in cases where placing a parent virtual sphere having a diameter Ra overlaps with an already-placed virtual curved surface solid. For example, determination may be made in step S230 that the parent virtual sphere of the diameter Ra can be placed at that position regardless of whether the parent virtual sphere overlaps an already-placed virtual curved surface solid, as long as the parent virtual sphere of the diameter Ra does not overlap matter pixels. In the same way, this can be realized by permitting placement of a child virtual sphere in step S270 even in cases where placing a child virtual sphere having a diameter Rb overlaps with an already-placed virtual curved surface solid. For example, determination may be made in step S270 that the child virtual sphere of the diameter Rb can be placed at that position regardless of whether the child virtual sphere overlaps an already-placed virtual curved surface solid, as long as the child virtual sphere of the diameter Rb does not overlap matter pixels. Note that in the case of permitting overlapping of virtual curved surface solids, the center of a parent virtual sphere or child virtual sphere may overlap a virtual curved surface solid already placed. Also, in the case of permitting overlapping of virtual curved surface solids, when deriving numerical values combining information relating to the multiple virtual curved surface solids such as the sum of volume or sum of cross-sectional area of the multiple virtual curved surface solids, calculation is preferably performed assuming that the portions where multiple virtual curved surface solids overlap belong to only one of the virtual curved surface solids. On the other hand, when calculating values regarding each of the individual virtual curved surface solids, such as when deriving the cross-sectional area or surface area of a virtual curved surface solid, or deriving the equivalent diameter d, or the like, calculation is preferably performed assuming that the portions where the multiple virtual curved surface solids overlap belong to each virtual curved surface solid. Note that in the event of making a portion where multiple virtual curved surface solids overlap to belong to one virtual curved surface solid, this may be made to belong to the virtual curved surface solid of which the diameter of he parent virtual sphere is the greatest, for example, or to belong to the virtual curved surface solid of which the equivalent diameter d is the greatest.
With the above-described embodiment, the center of the parent virtual sphere or child virtual sphere has been the center of a pixel, but is not restricted to this. It is sufficient for the center of the parent virtual sphere or child virtual sphere to be within a pixel. For example, the center of the parent virtual sphere or child virtual sphere may be at the edge of the pixel closest to the origin of the XYZ coordinates.
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With the above-described embodiment, the pressure drop evaluation module 25f has derived the pressure drop P per unit thickness, but in addition to or instead of this, may derive the pressure drop index P of the porous body. Hereinafter, the pressure drop index P will be described. The pressure drop index P is obtained by P = (wetted area A of space within porous body / pore volume V of space within porous body) × (1 / porosity ε of porous body) × (average value L / distance L between inflow face and outflow face). The wetted area A [µm] of space within the porous body is derived as the product of the number of boundaries between space pixels (including curved surface solid pixels) and matter pixels in the porous body data 80, and the area at one boundary face (1.44 µm in the embodiment described above). The pore volume V [µm] of space within the porous body is derived as the product of the number of space pixels (including curved surface solid pixels) in the porous body data 80, and the volume of one pixel (1.728 µm in the embodiment described above). The porosity ε is derived by deriving the number of space pixels (including curved surface solid pixels) and matter pixels in the porous body data 80, and derived by porosity ε = number of space pixels / (number of space pixels + number of matter pixels). The distance L [µm] between inflow face and outflow face is derived based on the inflow/outflow table 82. For example, with the above-described embodiment, the inflow face 61 is a plane where X = 1, and the outflow face 62 is a plane where X = 251, so the distance L = (251 - 1) × 1.2 µm = 300 µm. The average value L is obtained as follows. Multiple path lengths L are derived from one of a predetermined inflow face and a predetermined outflow face of the porous body to the other face, following adjacent or overlapping virtual curved surface solids. The average the microstructure of the porous body may be analyzed by deriving multiple path lengths L from one of a predetermined inflow face and a predetermined outflow face of the porous body to the other face following adjacent or overlapping virtual curved surface solids, deriving an average value of the multiple path lengths L is derived as the average value L.
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Fig. 11
Fig. 11
Fig. 11
Now, a method for deriving the path length L and average value L. is a flowchart illustrating an example of path length deriving processing. As illustrated in , with the path length deriving processing, first, one virtual curved surface solid including an inflow face 61 is selected (step S600). Whether or not a virtual curved surface solid includes an inflow face 61 can be determined from the center coordinates and diameter of the parent virtual sphere and the center coordinates and diameter of the child virtual spheres of each virtual curved surface solid stored in the virtual curved surface solid table 83 created in the virtual curved surface solid placement processing, and the mathematical expression (X = 1) expressing the inflow face 61 stored as the inflow/outflow table 82. Also, in step S600, virtual curved surface solids which are not selectable in the later-described step S630 or S655 is not selected. Next, virtual curved surface solids adjacent or overlapping the selected virtual curved surface solid are followed, and all are selected (step S610). Deriving of the virtual curved surface solids adjacent or overlapping the selected virtual curved surface solid is performed as follows, for example. First, of the curved surface solid pixels occupied by the selected virtual curved surface solid, one curved surface solid pixel situated on the surface of the virtual curved surface solid is selected. Whether or not there is another virtual curved surface solid occupying a curved surface solid pixel adjacent to that curved surface solid pixel is found, and in the event that there is, that virtual curved surface solid is derived as an adjacent virtual curved surface solid. In the same way, in the event that there are other virtual curved surface solids occupying curved surface solid pixels situated on the surface of the selected virtual curved surface solid, these virtual curved surface solids are derived as being overlapping virtual curved surface solids. Note that this is not restricted to the method using curved surface solid pixels in this way, and that virtual curved surface solids adjacent to or overlapping the selected virtual curved surface solid may be derived based on the center coordinates and diameter of the parent virtual sphere and the center coordinates and diameter of the child virtual spheres of each virtual curved surface solid stored in the virtual curved surface solid table 83, for example. Also, in the event of not permitting overlapping virtual curved surface solids in the virtual curved surface solid placement processing, it is sufficient to sequentially follow virtual curved surface solids adjacent to the selected virtual curved surface solid. Upon having performed the processing of step S610, determination is made regarding whether or not a virtual curved surface solid including the outflow face 62 has been reached (step S620). This processing is performed by determining whether or not there is a virtual curved surface solid including the outflow face 62 in the selected virtual curved surface solids. Note that the determination method of whether or not a virtual curved surface solid includes the outflow face 62 is the same as with the above determination of whether or not the inflow face 61 is included. In the event that a virtual curved surface solid including the outflow face 62 is not reached, all selected virtual curved surface solids are invalidated for selection (step S630), and processing of step S600 and thereafter is performed. On the other hand, in the event that a virtual curved surface solid including the outflow face 62 is reached in step S620, the path length L is derived based on the length of a line connecting the center points of the virtual curved surface solids on the path from the inflow face 61 to the outflow face 62 (S650). Note that the center point of a virtual curved surface solid means the center of the parent virtual sphere. Also, the path length L includes the distance from the inflow face 61 to the center of the virtual curved surface solid including the inflow face 61, and the distance from the outflow face 62 to the center of the virtual curved surface solid including the outflow face 62. Upon having derived the path length L in step S650, all virtual curved surface solids being selected are invalidated for selection (step S655). Determination is made regarding whether or not a predetermined number of path lengths L have been derived (step S660), and in the event that the number of derived path lengths L is less than a predetermined number, the processing of step S600 and thereafter is performed. Also, in the event that the number of path lengths L derived in step S660 has reached the predetermined number, the average value of the multiple derived path lengths L is derived as the average value L (step S670), and the path length deriving processing ends. Note that the predetermined number (number of path lengths L to be derived) in step S660 is preferably 600 or more. However, the number of path lengths L to be derived is not restricted to this, and may be set as appropriate in accordance with calculation load and precision. Also, while the path length deriving processing in has been described as processing where virtual curved surface solids adjacent or overlapping each other are followed from the inflow face of the porous body toward the outflow face to derive the path length L, but virtual curved surface solids may be followed from the outflow face of the porous body toward the inflow face to derive the path length L.
Fig. 12
Fig. 12
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is an explanatory diagram illustrating the way in which a path length L is derived. In the event that virtual curved surface solids a through f have been placed as in , the virtual curved surface solid a including the inflow face 61 is first selected in step S600 of the path length deriving processing. Then, in step S610, virtual curved surface solids adjacent to or overlapping this virtual curved surface solid a are sequentially followed, with virtual curved surface solids b through f being selected. Of the selected virtual curved surface solids a through f, the virtual curved surface solid c includes the outflow face 62, so in step S620 determination is made that a virtual curved surface solid including the outflow face 62 has been reached. In step S650, the path length L is derived based on the length of the line connecting the center points of the virtual curved surface solids on the path from the inflow face 61 to the outflow face 62. Specifically, this is derived as follows. First, the virtual curved surface solids a through c are on the path from the inflow face 61 to the outflow face 62, so the distance L1 between the center points of the virtual curved surface solids a and b, and the distance L2 between the center points of the virtual curved surface solids b and c, are derived. Next, the distance L0 from the inflow face 61 to the center of the virtual curved surface solid a, and the distance L3 from the outflow face 62 to the center of the virtual curved surface solid c, are derived. The total value of distance L0 through distance L3 is derived as the path length L. Note that the virtual curved surface solids d through f do not exist on the path from the inflow face 61 to the outflow face 62, and accordingly are unrelated to deriving of the path length L.
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Fig. 13
Fig. 13(a)
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Fig. 12
Fig. 13(b)
Note that when deriving the path length L, in the event that there are branches on the path from the inflow face 61 to the outflow face 62 made up of multiple virtual curved surface solids selected in steps S600 and S610, the average value of the multiple paths from the start of the branch to the end (merging point) is taken as the path length of the branching portion. A case where there are branches on the path include a case where there exists a path which branches off partway and merges again, a case where there exists a path which multiple virtual curved surface solids including the inflow face 61 merge, a case where there exists a path which branches off partway and multiple branches reach the outflow face 62 (there are multiple virtual curved surface solids reaching the outflow face 62), and so forth. is an explanatory diagram of deriving a path length L in the event that branches exist on the path from the inflow face 61 to the outflow face 62. is an example of placement of a virtual curved surface solid in a case where branches exist on the path from the inflow face 61 to the outflow face 62. is a schematic diagram of the path illustrated in and is an explanatory diagram of driving the path length L. Note that in , the virtual curved surface solids are represented by circles, for the sake of description. Let us say that there are virtual curved surface solids A1 through A2, B1 through B4, C1 through C7, D1 through D7, and E1 through E4, placed as illustrated in and that the virtual curved surface solid A1 including the inflow face 61 is selected in step S600 of the path length deriving processing. In this case, in the subsequent step S610, virtual curved surface solids adjacent to or overlapping the virtual curved surface solid A1 are followed sequentially, with the virtual curved surface solids A2, B1 through B4, C1 through C7, D1 through D7, and E1 through E4 being selected. Of the selected virtual curved surface solids, the virtual curved surface solids C7 and D7 include the outflow face 62, so in step S620 determination is made that a virtual curved surface solid including the outflow face 62 has been reached. Now, branches exist on the path from the inflow face 61 to the outflow face 62 made up of the selected virtual curved surface solids. Specifically, there are a path following the virtual curved surface solids A1 and A2 in that order from the inflow face 61 and a path following the virtual curved surface solids B1 through B4 and A2 in that order from the inflow face 61, and these paths merge at the virtual curved surface solid A2. Also, after having following the virtual curved surface solids A2 and C1 in this order, the paths branch from the virtual curved surface solid C1 to the virtual curved surface solids C2 and D1. The path branching from virtual curved surface solid C1 to virtual curved surface solid C2 follows the virtual curved surface solids C2 through C7 in that order, and reaches the outflow face 62 at the virtual curved surface solid C7. The path branching from the virtual curved surface solid C1 to the virtual curved surface solid D1 further branches at the virtual curved surface solid D1 to the virtual curved surface solids D2 and E1. The path branching from the virtual curved surface solid D1 to the virtual curved surface solid D2 follows the virtual curved surface solids D2 through D6 in that order, the path branching from the virtual curved surface solid D1 to the virtual curved surface solid E1 follows the virtual curved surface solids E1 through E4 and D6 in that order, and merge at the virtual curved surface solid D6. The path then follows from the virtual curved surface solid D6 to the virtual curved surface solid D7 and reaches the outflow face 62. Deriving the path length L in step S650 in the event that branches exist on the path from the inflow face 61 to the outflow face 62 will be described with reference to . In step S650, first, the path is sectioned into multiple sections at branching points and merging points, and the path length of each section is derived. Here, in the paths in are illustrated in a simplified manner, with the lengths a through h illustrated in representing the path length of each section. The length a is the path length of the section from the inflow face 61 through the virtual curved surface solid A1 to the virtual curved surface solid A2 which is the merging point. The length b is the path length of the section from the inflow face 61 through the virtual curved surface solids B1 through B4 to the virtual curved surface solid A2 which is the merging point. The length c is the path length of the section from the virtual curved surface solid A2 which is the merging point to the virtual curved surface solid C1 which is the branching point. The length d is the path length of the section from the virtual curved surface solid C1 which is the branching point through the virtual curved surface solids C2 through C7 and reaching to the outflow face 62. The length e is the path length of the section from the virtual curved surface solid C1 which is the branching point to the virtual curved surface solid D1 which is the next branching point. The length f is the path length of the section from the virtual curved surface solid D1 which is the branching point through the virtual curved surface solids D2 through D5 to the virtual curved surface solid D6 which is the merging point. The length g is the path length of the section from the virtual curved surface solid D1 which is the branching point through the virtual curved surface solids E1 through E4 to the virtual curved surface solid D6 which is the merging point. The length h is the path length of the section from the virtual curved surface solid D6 which is the merging point through the virtual curved surface solid D7 and reaching to the outflow face 62. Note that the path lengths of each of the sections (lengths a through h) are derived based on the length of lines connecting the center points of the virtual curved surface solids, the length from the inflow face 61 to the center point of a virtual curved surface solid including the inflow face 61, and the length from the outflow face 62 to the center point of a virtual curved surface solid including the outflow face 62, as described with . Deriving the path lengths of each section in this way the path length L is derived based on the path length of each section. Specifically, the path length of portions where multiple sections exist in parallel are taken as the average value of the path lengths of each section existing in parallel. Also, the path length of portions where multiple sections exist serially is the sum of the path length of each section existing serially. Thus, the path lengths of sections existing in parallel and the path length of sections existing serially are combined, and finally the path length L from the inflow face 61 to the outflow face 62 is derived. For example, in , there are two sections existing in parallel from the inflow face 61 to the virtual curved surface solid A2 which is the merging point, and the lengths of these sections are length a and length b, so the average length thereof (a + b)/2 is taken as the path length from the inflow face 61 to the virtual curved surface solid A2. There are two sections existing in parallel from the virtual curved surface solid D1 which is the branching point to the virtual curved surface solid D6 which is the merging point, and the lengths of these sections are length f and length g, so the average length thereof (f + g)/2 is taken as the path length from the virtual curved surface solid D1 to the virtual curved surface solid D6. The section from the virtual curved surface solid C1 which is the branching point to the virtual curved surface solid D1 which is the next branching point, the section from the virtual curved surface solid D1 to the virtual curved surface solid D6 which is the merging point, and the section from the virtual curved surface solid D6 to the outflow face 62, exist serially, and the lengths of the sections are length e, length (f + g)/2, length h, so the sum of length thereof e + (f + g)/2 + h is taken as the length of the section from the virtual curved surface solid C1 through the virtual curved surface solid D7 reaching the outflow face 62. There are two sections existing in parallel from the virtual curved surface solid C1 reaching to the outflow face 62, with the lengths of each section being length d and length e + (f + g)/2 + h, so the average length thereof [d + {e + (f + g)/2 + h}]/2 is taken as the path length of the section from the virtual curved surface solid C1 to the outflow face 62. The section from the inflow face 61 to the virtual curved surface solid A2, the section from the virtual curved surface solid A2 to the virtual curved surface solid C1, and the section from the virtual curved surface solid C1 to the outflow face 62, exist serially, and the lengths of each of the sections are length (a + b)/2, length c, and length [d + {e + (f + g)/2 + h}]/2, so the sum of length thereof (a + b)/2 + c + [d + {e + (f + g)/2 + h}]/2 is taken as the path length from the inflow face 61 to the outflow face 62, i.e., the path length L. By deriving the path length L in this way, even in cases where there are braches on the path from the inflow face 61 to the outflow face 62, the path length L taking into consideration the branches can be derived. Note that the path length L may be derived by other techniques, unrestricted to this.
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With the path length L derived in this way, the simpler the fluid path from the inflow face 61 to the outflow face 62 is (the closer to a straight line), the closer the value is to the distance L between the inflow face 61 and the outflow face 62. Also, the more complicated the fluid path from the inflow face 61 to the outflow face 62 is, the greater the value is as compared to the distance L between the inflow face 61 and the outflow face 62. Accordingly, the average value L of multiple path lengths L is a numerical value relating to the complexity of fluid paths (difficulty of fluid to flow) for the overall porous body, when a fluid flows through the space inside the porous body.
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By deriving the pressure drop index P in this way, the pressure drop index P is a value having a high correlation of the actual pressure drop of the porous body. Accordingly, by deriving this pressure drop index P, the pressure drop property of the porous body can be predicted and evaluated more precisely, for example. Also, the pressure drop evaluation module 25f may perform evaluation of the pressure drop property of the porous body by determining whether the value of the pressure drop index P is at or below a predetermined threshold, or the like, to derive evaluation results as well. Further, the pressure drop evaluation module 25f may analyze the microstructure of the porous body by deriving the pressure drop P per unit thickness of the porous body by P = constant α × P + constant β × P. The pressure drop P per unit thickness of the porous body derived from the pressure drop index P in this way approximately matches the actual pressure drop of the porous body. Accordingly, the pressure drop property of the porous body can be predicted or evaluated more precisely, by deriving this pressure drop P as microstructure analysis. Also, the pressure drop evaluation module 25f may evaluate the pressure drop property of the porous body by determining whether or not the pressure drop P is at or below a predetermined threshold, or the like. Note that the constant α is a positive number and the constant β is a real number. Also, pressure drop P > 0 holds within the range of pressure drop index P > 0. Also, constant α and constant β may be obtained by experiment for example, so that the pressure drop P and the actual pressure drop of the porous body match more precisely.
Hereinafter, examples of actually creating the analysis processing program and microstructure analysis device will be described as Examples.
As Example 1, an analysis processing program having the functions of the above-described embodiment was created. This program was then stored in the HDD of a computer having a controller including a CPU, ROM, and RAM, and a HDD, thereby yielding a microstructure analysis device according to Example 1.
Figs. 2 and 3
Fig. 14
Fig. 14
A plastic green body was fabricated by mixing SiC powder and metal Si powder at a ratio of 80:20 by mass, adding starch and foamed plastic as pre-forming agents, and further adding methylcellulose, hydroxypropoxyl methylcellulose, a surfactant, and water. This green body was formed by extrusion to the form illustrated in , and dried by microwave and heated air to yield a compact body. This compact body was degreased at approximately 400°C in atmosphere, and thereafter fired at approximately 1450°C in an Ar inactive atmosphere, thereby yielding a porous body 1 serving as the porous partition 44. Also, of pixel data obtained by performing a CT scan of the porous body 1, one data was extracted where the X direction is 300 µm (= 1.2 µm × 250 pixels) which is the same value as the thickness in the direction of exhaust gas passing direction, the Y direction is 480 µm (= 1.2 µm × 400 pixels), and the Z direction is 480 µm (= 1.2 µm × 400 pixels), which was stored in the HDD as the above-described porous body data 60, and the above-described analysis processing routine was executed regarding this porous body data 60. Analysis result data including the above-described porous body table, virtual curved surface solid table, and the values of equivalent diameter d and volume V of each virtual curved surface solid, was then obtained. is a graph illustrating tabulation results of the pore diameter (equivalent diameter d) of the porous body 1 based on this analysis result data. is a log differential pore volume distribution graph with the horizontal axis as the equivalent diameter d, and the vertical axis as the volume ratio [cc/cc] as to the volume of space pixels (= (the sum of volumes V of virtual curved surface solids corresponding to the equivalent diameters d) / (sum of volume of all space pixels)). It can be seen that with the microstructure analysis device, the equivalent diameters d of the placed virtual curved surface solids are derived, and the distribution of pore diameters within the porous body can be analyzed as a distribution of equivalent diameters d in the porous body by using this value, as illustrated in the drawings.
Fig. 15
Fig. 15
Fig. 14
Fig. 15
A porous body 2 tending to have greater pore diameter as compared to the porous body 1 was created using the same material and manufacturing process as with the porous body 1 described above. Of pixel data obtained by performing a CT scan of the porous body 2, one data was extracted where the X direction is 300 µm, the Y direction is 480 µm, and the Z direction is 480 µm, which was stored in the HDD as the above-described porous body data 60, in the same way as with the porous body 1, and the above-described analysis processing routine was executed regarding the porous body data 60 of this porous body 2. Analysis result data including the above-described porous body table, virtual curved surface solid table, and the values of equivalent diameter d and volume V of each virtual curved surface solid, was then obtained. Also, a catalyst was applied to the porous body 2, and porous body data 60 was created regarding the porous body 2 after application and the above-described analysis processing routine was performed. is a graph illustrating tabulation results of the pore diameter (equivalent diameter d of the virtual curved surface solid) of the porous body 2 based on the analysis result data before and after application of the catalyst. The vertical axis and horizontal axis in are the same as with . In , the volume ratio of virtual curved surface solids of which the equivalent diameter d exceeds 10 µm occupying as to the volume of space pixels has decreased after application of the catalyst as compared to before. On the other hand, the volume ratio of virtual curved surface solids of which the equivalent diameter d is 10 µm or smaller occupying as to the volume of space pixels exhibits little change before and after application. The cause of this can be thought to be that the catalyst was not applied to portions where virtual curved surface solids with equivalent diameter d of 10 µm or smaller were placed, and there was little change in volume before and after application of the catalyst. Accordingly, it can be conceived that the volume ratio of virtual curved surface solids with equivalent diameter d of 10 µm or smaller is preferably small. For example, the volume ratio of virtual curved surface solids with equivalent diameter of 10 µm or smaller is preferably 25% or less.
Note that application of the catalyst was performed as follows. First, alumina : platinum : ceria material were mixed at a predetermined mass ratio, and a catalyst slurry with water as a solvent was prepared. Next, the outlet edge face of the honeycomb filter (side where exhaust gas flows out) was dipped to a predetermined height, and suctioning was performed from the inlet edge face (side where exhaust gas flows in) for a predetermined time while adjusting to a predetermined suction pressure and suction flow, so that the catalyst was carried on the partitions, dried at 120°C for two hours, and baked at 550°C for one hour. The amount of catalyst per unit volume of the honeycomb filter was set to 30 g / L.
Fig. 16
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Porous bodies 3 through 8 were created using the same material and manufacturing process as with the porous body 1 described above. Of pixel data obtained by performing a CT scan of each of the porous bodies 3 through 8, one data was extracted where the X direction is 300 µm, the Y direction is 480 µm, and the Z direction is 480 µm, which was stored in the HDD as the above-described porous body data 60, in the same way as with the porous body 1, and the above-described analysis processing routine was executed regarding this porous body data 60 of the porous bodies 3 through 8. Analysis result data including the spatial uniformity index γ was obtained as analysis result data. A fluid including particulate material was passed through the porous bodies 3 through 8, the remainder of particulate material in the fluid following passage was measured as the number of leaked particles, and the number of leaked particles converted into the number of particles leaked per 1 km of passage distance [number/km] as obtained as a value indicating collecting performance. is a graph illustrating the relation between the spatial uniformity index γ obtained by the microstructure analysis device and the number of leaked particles actually measured for the porous bodies 3 through 8. As illustrated in the diagram, it can be seen that the greater the spatial uniformity index γ is, the smaller the number of leaked particles tends to be (the collecting performance is high). Also, it is conceivable to predict the number of leaked particles from the spatial uniformity index γ by using an approximation curve based on points plotted in the diagram. For example, if the spatial uniformity index γ is 0.6 or greater from the approximation curve, it can be understood that conditions of leaked particles of 6.0 × 10 or less which is an exhaust gas restriction value for automobiles (Euro 6) are satisfied, so it can be thought to be possible to determine acceptability of collecting performance based on whether or not the spatial uniformity index γ is 0.6 or greater. Note that while there are cases where the spatial uniformity index γ changes due to application of the catalyst, the spatial uniformity index γ after application of the catalyst is preferably 0.5 or higher.
Fig. 17
Fig. 18
Fig. 17 and Fig. 18
Porous bodies 9 through 12 were created using the same material and manufacturing process as with the porous body 1 described above. Of pixel data obtained by performing a CT scan of the porous body 9 through 12, one data was extracted where the X direction is 300 µm, the Y direction is 480 µm, and the Z direction is 480 µm, which was stored in the HDD as the above-described porous body data 60, in the same way as with the porous body 1, and the above-described analysis processing routine was executed regarding this porous body data 60 of porous bodies 9 through 12. Data including the average value of pressure drop P was obtained. Also, for comparison, the average value of the pressure drop P was derived with a method the same as with the microstructure analysis device according to Example 1 except for using Ergun's Equation instead of the above-described Expression (3), for each of the porous bodies 9 through 12. Also, pressure drop of the porous body 9 through 12 was derived following a known method based on fluid analysis results by the lattice Boltzmann method (this pressure drop will be written as "pressure drop according to the lattice Boltzmann method" hereinafter). is a graph illustrating the relation between the average value of pressure drop P derived from Expression (3) and pressure drop according to the lattice Boltzmann method, and is a graph illustrating the relation between the average value of pressure drop P derived by Ergun's Equation and pressure drop according to the lattice Boltzmann method. From , it can be seen that the correlation with pressure drop according to the lattice Boltzmann method is greater with the average value of pressure drop P derived with Expression (3) as compared to the average value of pressure drop P derived by Ergun's Equation. Also, the higher the average value of the pressure drop P is, the greater the deviation between the average value of pressure drop P derived by Ergun's Equation and the pressure drop according to the lattice Boltzmann method is, but this tendency is not observed regarding the average value of pressure drop P derived by Expression (3), and a value close to the pressure drop according to the lattice Boltzmann method is indicated regardless of the magnitude of the average value of the pressure drop P. From this, it can be seen that the actual pressure drop can be predicted with good precision and pressure drop can be evaluated with good prediction based on the average value of pressure drop P derived by Expression (3). Also, with the pressure drop according to the lattice Boltzmann method obtained with the known method, while pressure drop can be derived, which microstructure features of the porous body were affecting increase or decrease in pressure drop could not be analyzed. On the other hand, with the results this time, the correlation between the pressure drop according to Expression (3) and pressure drop according to the lattice Boltzmann method was high, so it can be seen that increase or decrease in pressure drop according to the lattice Boltzmann method is affected by the parameters in Expression (3), and accordingly it can be understood from Expression (3) how which parameters should be adjusted to reduce the pressure drop. Accordingly, it has been found that the parameters of Expression (3) can be used as an index to manufacture a porous body with the desired pressure drop.
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JP 2005114612 A
Fig. 19
Porous bodies 13 and 14 were created using the same material and manufacturing process as with the porous body 1 described above. Of pixel data obtained by performing a CT scan of the porous body 13 and 14, one data was extracted where the X direction is 300 µm, the Y direction is 480 µm, and the Z direction is 480 µm, which was stored in the HDD as the above-described porous body data 60, in the same way as with the porous body 1, and the above-described analysis processing routine was executed regarding this porous body data 60 of porous body 13 and 14. Data including the average value of in-plane uniformity index γ was obtained as analysis result data. Also, for comparison, the average value of pressure drop P was derived by the same method as with the microstructure analysis device according to Example 1 except for the point of using Ergun's Equation instead of the above-described Expression (3), using the same porous body data as above, for each of the porous bodies 13 and 14. As a result, the average value of pressure drop P in the case of using Ergun's Equation was approximately the same value in the porous bodies 13 and 14. Also, the actual pressure drop of the porous bodies 13 and 14 was measured according to a method described in the embodiments in Japanese Patent Application Publication No. . is a graph illustrating the average value of in-plane uniformity index γ and actual pressure drop for the porous bodies 13 and 14. As can be seen from the diagram, there is difference between the porous bodies 13 and 14 regarding actual pressure drop, regardless of the average value of pressure drop P having been the same using Ergun's Equation. Also, the porous body 14 with the greater in-plane uniformity index γ has a smaller value for actual pressure drop, so it can be seen that the greater the value of in-plane uniformity index γ is, the better the pressure drop property tends to be. Also, from the actual values of pressure drop for the porous bodies 13 and 14, it can be conceived that the pressure drop property of the porous body is acceptable when the in-plane uniformity index γ is 0.6 or greater.
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Fig. 20
Fig. 20 and Fig. 21
Porous bodies 15 and 16 were created using the same material and manufacturing process as with the porous body 1 described above. Of pixel data obtained by performing a CT scan of the porous body 15 and 16, one data was extracted where the X direction is 300 µm, the Y direction is 480 µm, and the Z direction is 480 µm, which was stored in the HDD as the above-described porous body data 60, in the same way as with the porous body 1, and the above-described analysis processing routine was executed regarding this porous body data 60 of porous body 15 and 16. Data including the volume V and flow velocity ratio T (= T/T) of each virtual curved surface solid was obtained as analysis result data. Also, the actual pressure drop of the porous bodies 15 and 16 was measured according to the method described in the embodiments in Japanese Patent Application Publication No. . is a graph illustrating the virtual curved surface solids in the porous bodies 15 and 16 having been classified by flow velocity ratio T (= T/T). is a graph illustrating actual pressure drop of the porous bodies 15 and 16. Note that in , the virtual curved surface solids are classified by flow velocity ratio T, the total value of volume V is derived for virtual curved surface solids of the same classification, the percentage of the total value of volume V for the virtual curved surface solids of each classification as to the total value of volume V of all virtual curved surface solids is obtained, and this percentage is the vertical axis. From , it can be seen that the porous body 16 of which the volume ratio of high-flow-velocity curved surface solids is small has smaller actual pressure drop, and accordingly the pressure drop property tends to be acceptable. Also, while the volume ratio of low-flow-velocity curved surface solids is 20% or less and the volume ratio of high-flow-velocity curved surface solids is 10% or less with the porous body 16, the volume ratio of low-flow-velocity curved surface solids is 20% or less but the volume ratio of high-flow-velocity curved surface solids exceeds 10% with the porous body 15. Accordingly, it can be conceived that performance of the porous body is acceptable with a volume ratio of high-flow-velocity curved surface solids of 10% or less. Also, it can be conceived that the volume ratio of low-flow-velocity curved surface solids of 20% or less and the volume ratio of high-flow-velocity curved surface solids of 10% or less is even more preferable.
Fig. 22
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Fig. 21
Fig. 22
Fig. 21
Equivalent diameter d and volume V values for the virtual curved surface solids of the porous bodies 15 and 16, and classification result data of the virtual curved surface solids thereby, were obtained from analysis result data obtained by executing the analysis processing routine on the porous bodies 15 and 16 described above. is a graph illustrating the way in which the virtual curved surface solids of analysis date with the porous bodies 15 and 16 were classified by the equivalent diameter d of the virtual curved surface solids. Note that in , the virtual curved surface solids are classified by equivalent diameter d, the total value of volume V is derived for virtual curved surface solids of the same classification, the percentage of the total value of volume V for the virtual curved surface solids of each classification as to the total value of volume V of all virtual curved surface solids is obtained, and this percentage is the vertical axis. As illustrated in the diagram, with the porous bodies 15 and 16, the volume ratio of mid-diameter curved surface solids (virtual curved surface solids of 10 µm ≤ equivalent diameter d ≤ 25 µm) was 60% or greater in either case. Also, the porous body 16 of which the volume ratio of mid-diameter curved surface solids was greater had smaller pressure drop (see ), and the performance of the porous body tended to be better. The volume ratio of small-diameter curved surface solids (virtual curved surface solids with equivalent diameter d < 10 µm) was 25% or less in either case of porous bodies 15 and 16. Note that as another classification method, when virtual curved surface solids of 30 µm ≤ equivalent diameter d were classified as large-diameter curved surface solids, the volume ratio of large-diameter curved surface solids exceeded 10% for the porous body 15, but was less than 10% for the porous body 16, as can be seen from . From this, and the values of actual pressure drop in , it can also be conceived that the performance of porous bodies is more acceptable with a volume ratio of 10% or less for virtual curved surface solids of 30 µm ≤ equivalent diameter d.
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An analysis processing program having the same functions as with Example 1, except for the point of mutual overlapping of virtual curved surface solids being permitted, and pressure drop index P being derived instead of pressure drop P, was created. This program was then stored in the HDD of a computer having a controller including a CPU, ROM, and RAM, and a HDD, thereby yielding a microstructure analysis device according to Example 2.
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2005-114612
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Porous bodies 17 through 21 were created using the same manufacturing process as with the porous body 1 described above, with material changed as appropriate from those of the porous body 1. Of pixel data obtained by performing a CT scan of the porous bodies 17 through 21, one data was extracted where the X direction is 300 µm, the Y direction is 480 µm, and the Z direction is 480 µm, which was stored in the HDD as the above-described porous body data 60, in the same way as with the porous body 1, and the above-described analysis processing routine was executed regarding this porous body data 60 of porous bodies 17 through 21. Analysis result data including pressure drop index P was obtained as analysis result data. Note that regarding deriving of the pressure drop index P, the predetermined number of step S660 of the path length deriving processing in (the number of path lengths L to be derived) was set to the value 1000. Also, the actual pressure drop of the porous bodies 17 through 21 (pressure drop per unit thickness [Pa/mm]) was measured according to the method described in the embodiments in Japanese Unexamined Patent Application Publication No. . is a graph illustrating the relation between the pressure drop index P and actual pressure drop of the porous bodies 17 through 21. Note that the curve in the drawing is an approximation curve where points illustrating the relation of pressure drop index P and actual pressure drop of the porous bodies 17 through 21 have been plotted, and the approximation curve is derived from these five points. From the plotted points and the approximation curve, it can be found that the actual pressure drop of the porous bodies can be expressed as a quadratic function of pressure drop index P passing through the origin. That is to say, it has been found that with pressure drop P = constant α × P + constant β × P using the pressure drop index P of the porous bodies 17 through 21, the pressure drop P and actual pressure drop approximately match. Note that the determination coefficient R obtained from the approximation curve in (actual pressure drop = constant α × P + constant β × P) and the five plotted points was the value 0.999. From the above, it has been found that the actual pressure drop of the porous body can be precisely predicted and evaluated by deriving pressure drop index P. Also, it has been round that by deriving the pressure drop P by P = constant α × P + constant β × P, a value approximately the same as the actual pressure drop can be derived as the pressure drop P. Further, since the materials of the porous bodies 17 through 21 differ from each other, it has been found that prediction and evaluation of pressure drop using pressure drop index P can be performed regardless of the material of the porous body.
The present invention is applicable to the manufacturing industry of porous bodies used as filters for purging exhaust gas emitted from stationary engines and burning appliances and the like for automobiles, construction equipment, and industrial use.
20 user personal computer (PC), 21 controller, 22 CPU, 23 ROM, 24 RAM, 25 HDD, 25a analysis processing program, 25b virtual curved surface solid placement module, 25c fluid analyzing module, 25d in-plane uniformity index evaluation module, 25e spatial uniformity index evaluation module, 25f pressure drop evaluation module, 25g flow-through velocity evaluation module, 25h equivalent diameter evaluation module, 25i analysis result output module, 26 display, 27 input device, 30 honeycomb filter, 32 external protective portion, 34 cell, 36 inlet-opened cell, 36a inlet, 36b outlet, 38 outlet sealant, 40 outlet-opened cell, 40a inlet, 40b outlet, 42 inlet sealant, 44 porous partition, 50 region, 60 porous body data, 61 inflow face, 62 outflow face, 63 X-Y plane, 64 enlarged drawing, 71 porous body table, 72 inflow/outflow table, 80 porous body data, 81 porous body table, 82 inflow/outflow table, 83 curved surface solid table, 85 virtual wall face | |
Where variables, such as stock size, can be observed directly, the concept of link models is largely redundant. However they are useful where only indirect observations can be made on these variables, and the relationships are complex, as is almost always the case. Separating link models from the population model is useful in several respects. It allows a number of indices to be incorporated into the fitting process, each with their own separate model describing how they are related to variables in the population model. Ideally link models avoid any time series effects, as unlike population models they should not represent a process. This means the link models are subject only to direct measurement or observation errors. Finally, link models are often linear in form. This has a distinct advantage in that linear parameters, which can be estimated directly, are separated from non-linear parameters, associated with the population model, which need to be estimated iteratively. This can significantly decrease the time needed to fit the model.
Link models will always add information to the population models if the number of parameters is less than the number of data points. However, clearly the fewer the parameters in the link model, the more information there will be for fitting the population model. So a biomass survey, which requires no parameters, is preferable to a biomass index which requires at least one parameter. In some cases a large number of parameters are required to account for changes having nothing to do with the stock. This will undermine the value of the data series.
5.1.1 Index Standardisation
5.1.2 Dis-aggregated Abundance Indices
5.1.3 Biomass Indices
For many indices there are a number of potential influences besides the variable we are interested in. For example, CPUE may be affected by the fishing area, season, gear, size of vessel, and number of crew as well as the stock size. Standardisation aims to separate these effects, in particular removing those that may bias the population size index, and to generate indices, which may be some of the fitted parameters. In order to be able to evaluate the quality of the index that is derived, a key statistic is the proportion of the variability that can be explained by the explanatory variables. This proportion is often quite low in these types of analysis, in the region of 50-60 %.
The analysis most often used is a special case of the generalized linear model approach (McCullagh and Nelder 1983). In the version applied in many fish stock assessments, the task is to find the variation in the data that can be allocated to vessel, time and area. This is done by applying a model of the form:
ln(CPUE) = Constant + Vessel + Area + Year +Season +Area.Season (35)
where the . operator refers to the interaction terms between factors (see McCullagh and Nelder 1983). In specific analyses, there may be fewer terms involved (e.g. if only one vessel is used in the survey and if the survey is confined to a particular season throughout the time series the vessel and season terms do not appear).
The analysis provides an estimate of the value of the explanatory parameters. These parameter values are often used as input for the subsequent stock assessment. For example, the year effect in an analysis of CPUE data from an abundance survey could be used as an estimate of relative annual abundance and the vessel effect is the relative fishing power.
The season effect is often interpreted as either difference in availability - fish concentration varies with the season - or as seasonal migrations. The migrations should make the interaction term (area.season) significant (i.e. the geographical distribution of fish varies through the year).
In many fish stock assessments, it is preferable to isolate individual analyses and investigate the data in subsets. For example, studies of the structure of the catch data, the abundance CPUE data from surveys and CPUE data from logbooks can be undertaken separately. Only when one is satisfied with the consistency of the data does it make sense to include the data in an integrated model. For this purpose, linear models are often used (Gavaris 1988, Kimura 1981, Large 1992).
This is the class of indices most often used in fish stock assessment based on the VPA analytical model. These indices are typical CPUE estimates from either well-defined commercial fleets or from abundance surveys using research vessels. The CPUE values are expressed in numbers-by-age per effort unit. The effort unit can be days-at-sea, trawl hours, search time, etc. Commercial CPUE data are obtained through sampling the commercial fisheries for biological information and linking this information with catch and effort statistics. Abundance surveys using research vessels provide these data directly, often from bottom trawl surveys expressed as numbers caught per hour trawling.
Survey data differ from commercial CPUE data in two respects:
· Survey data are obtained through a designed sampling programme and the data often represent the stock over a short time period.Whether the CPUE data are linearly (or otherwise) related to abundance is discussed separately for the two data sources as the problems are distinct. For commercial fishing, the sampling is probably not random relative to the population and there are a variety of fishing vessels with different fishing strategies and different fishing power involved in construction of the mean CPUE value. Surveys represent few samples, the largest surveys include 500-600 trawl stations per year, but the coverage, effort allocation and standardisation of gear and fishing strategy are under the control of the researcher. In the models to be studied below we assume a linear relation between CPUE and stock abundance. Experience with non-linear models has shown marked problems with over-estimation of stock size (and corresponding under-estimation of the fishing mortality), because of the random noise in the data.
· Commercial CPUE data represent the geographical distribution of fishing activities as well as fish abundance, but the data often represent the stock over a longer time period.
5.1.2.1 Commercial CPUE data
Even when it is possible to dis-aggregate commercial CPUE data, they are often only representative for a time period, e.g. a quarter or a year. The link model becomes:
(36)
The population model might need to be corrected to match the population relevant for the CPUE index. The model must not only account for any mortality occurring in the population before the index is measured, but also for any mortality occurring in the stock over the time period for which the index measurements are taken:
(37)
The constant a is the fraction of the total mortality that occurs before the index is relevant and b-a is the fraction of the mortality occurring while the index is relevant. In practice, these fractions are not known precisely and are approximated by the fraction of the year that has past prior to the measurement starting, while b-a refers to the period the observed CPUE applies.
The random noise is usually assumed to be log-normally distributed, but following Methot (1990) this may not be appropriate as the age composition is a mixture of a contribution of total catch - possibly log-normal - and the breakdown of this catch into age groups - possibly multinomial. The estimation is very similar to estimating the total catch in numbers. There is, however, an additional problem as the effort data available are usually the nominal effort. The efficiency of a nominal effort unit may well increase with time and the fishing strategy of a fleet may change with time (e.g. as a result of changes in the geographical distribution or abundance of the stock). These problems suggest that CPUE indices from commercial fisheries may only be applicable for shorter time periods.
Another approach could be to estimate the catch based on effort data and a linear link between effort and fishing mortality. For a set of terminal Fs, the cohort sizes are calculated back using the observed catches and the standard VPA methodology. Catches can then be estimated based on the cohort sizes at the beginning of each year and the effort. Hence, the expected catch becomes:
(38)
This method has the distinct disadvantage that the link model is non-linear, but the errors may be better behaved than using a CPUE index, particularly if F fluctuates widely during the time series to values greater than 1.0 year-1. Alternatively, the Fs calculated from the VPA may be fitted to the effort directly, which should be easier (see Section 5.2).
5.1.2.2 Survey data
These data are often the best stock size indicators available since such data should include sampling design to control and measure errors resulting from the stock distribution, gear design etc. The survey will not necessary take place at the start of the year and the CPUE therefore should be corrected for the mortality that takes place between the start of the year and the start of the survey. The survey often lasts a short period (e.g. a month). Even so it may be relevant to correct the survey CPUE for the mortality that takes place during the time of the survey and the model is therefore the same as that presented for the commercial CPUE data (Equation 37). Note, for surveys of short duration, where effectively b-a = 0, the last term in the model becomes zero.
Biomass indices are usually provided from two different sources: from commercial fishing where CPUE data (catch weight per trip, or per day-at-sea, or per trawl hour, etc.) may be available from logbook or landing reports. Such data may or may not be accompanied by biological sampling. It is therefore not possible in all cases to break these data down by number and by age group. Another data source that provides biomass indices are egg- and larvae surveys that provide estimates of the spawning stock biomass.
The model linking the CPUE biomass index to the stock is:
(39)
where the population,, is the appropriate adjusted population corresponding to the CPUE (Equation 37). As, in this case, the age dependency is not estimable, the model is formulated with a single (average) catchability parameter.
Spawning stock biomass estimates from egg- and larvae surveys can be obtained either in absolute terms or as indices. For establishing the link between these observations and the spawning stock biomass calculated from the analytical age dis-aggregated model, it is necessary to include a new data item, the maturity ogive (matay). This is an array of proportions, which gives the fraction of each age group in numbers that is mature at spawning time. This ogive probably varies between years and maturity data should therefore ideally be available by year. However, such data are often not collected routinely and then an average maturity ogive is used for a series of years. The expected spawning stock size index is calculated as:
(40)
where a is the proportion of the fishing mortality and b the proportion of the natural mortality that is exerted on the stock before spawning (i.e. proportion of the year between 1st January and spawning time). In this case the mean weights-at-age, Wa, should be those of the spawning stock, not of the total stock nor of the catch.
These indices are often assumed to be log-normally or normally distributed. The indices may not be estimated directly from the surveys, but result from separate analysis of the survey data (Pennington 1983, 1986).
Effort data are often provided through fisheries statistics. These data can be collected from logbooks, from landing reports or as interview surveys of skippers. The model most often included in assessments is the assumption of a linear relation between fishing mortality and nominal effort:
(41)
where the´Fy is the average fishing mortality of the fully recruited age groups. There may well be data from several fleets each representing a different segment of the age composition of the stock. These fleet data may all be valid stock indicators that preferably should be included in the assessment.
Nominal effort may not be linearly related to the fishing mortality. This is because fishing is not a random sampling of the stock, but all possible skills are used to find those grounds where the catch rates are highest. Another problem with the use of such data is the increase in efficiency that takes place over the years. (Squires 1994, Pascoe and Robinson 1996). Such efficiency increase would be reflected by a time dependence in the catchability q.
In Section 4.4, a separable VPA model was introduced as part of the population model. However, it can also be developed as a link model. In this case, Equation 41 is expanded to allow for different catchabilities for each age group:
(42)
We can then fit these estimated Fay to those in the VPA population model (Equation 7) given the terminal Fs (perhaps also derived from Equation 42). This approach assumes an error between the expected and observed fishing mortalities rather than catches, which may be considered more appropriate if catches are considered more accurate than nominal effort. Because both Equations 41 and 42 are linear, they usually add only a small cost to the fitting procedure (see Section 6.3 Finding the Least-squares Solution).
It should be noted that the effort data may already have been used to construct CPUE stock indices and in this case the effort data should not be used again as part of the estimation procedure.
5.3.1 Factors Affecting Length Frequencies
5.3.2 Length to Age Conversion
Although VPA methods use age, catch data is at best divided into size classes. The link between numbers-at-size and numbers-at-age is potentially a complex one. Therefore, this link is usually dealt with separately as a conversion from size to age frequency using a variety of different methods. Once the conversion is complete, the VPA proceeds as though all fish were aged.
There are several groups of species where it is not possible to age individuals, such as shrimps, nephrops, lobsters, crabs and many tropical fish species. Crustaceans do not possess bone structures that they keep throughout their life span and therefore their shells or exoskeletons cannot be used for ageing. The environment of tropical fish may not have sufficient seasonal differences to establish well-defined structures in otoliths and bones.1
1 This observation may very much depend on the species and local conditions. It may always be worthwhile exploring whether direct ageing techniques can be used for tropical fish for each fishery, as their use greatly enhances the scientific advice that can be given to help manage the fishery.In these cases, the approach is to use solely the length compositions in the population as the basis for establishing cohorts. Reproduction, even in tropical areas usually shows some seasonal pattern (e.g. based on the local rainy season) and this is reflected in the length compositions where a peak in the length composition will identify a cohort.
In length-based assessment we define a method that converts length composition into age composition without age data. This procedure is often called cohort slicing (the generic term). The basis of the procedure is to allocate an age to a proportion of the fish found in a length range. This is precisely what the ALK does with available size-age sample. The difference is that whereas ALK can identify different age groups among similarly sized fish, cohort slicing cannot, which may lead to inaccurate allocation of catches to cohorts.
Although we only use length in this discussion, other additional biological information might be used. In all cases, a good knowledge of the biology of the species being analysed can greatly assist in developing models. For example, it is possible to use the sex or location of capture of some species to assist in establishing the age structure.
The present discussion is an expansion of Lassen (1988). Several methods are implemented in the FAO/ICLARM software (Gayanilo Jr. et al. 1996). Common length based approaches are explained in Sparre and Venema (1998).
Observed length frequencies depend on relative year class strength, total mortality, average growth and variation in growth. This is illustrated in the following examples where individual parameters are varied to produce simulated length frequencies. In each case, the effect of the parameter is illustrated with respect to interpreting length frequency distribution, and in particular identifying modes in these distributions representing individual cohorts.
Figure 5.1 Theoretical length distributions for two sets of growth parameters, with the same mortality (1.0 year-1), for the Eastern Baltic cod fishery year classes 1966-1994. Modes representing cohorts can only be detected in the length frequencies for slow-growing fish.
Figure 5.2 Theoretical length distributions for slow-growing fish, with different mortalities. Lower mortality gives a greater chance of detecting modes for older cohorts if significant differences remain between sizes at these ages.
Figure 5.3 Theoretical length distributions for the same set of growth parameters and mortality, but with two levels of variation in growth. As variation in growth increases it becomes more difficult to detect modes as cohorts merge in size frequency.
Figure 5.4 Theoretical length distributions for the same set of growth parameters, mortality and growth variation, but with and without variable recruitment. Recruitment variability tends to mask modes of cohorts from weak recruitments. However tracing strong year classes through time may give indications of growth rates.
The conclusion from the examples is that simple identification of peaks in the length frequencies can be impossible. It will work when there is low growth and recruitment variability, but otherwise no modes would be apparent. Analysis of a set of length frequencies under the assumption of common growth can help, as this will guide where the peaks are considered to be on the length axis. Such analysis, in many cases, is critically dependent on the growth assumption being correct.
There are three approaches to decomposing size groups into ages. Each method links observations such as age and size samples to catches in numbers per age class, which are the variables used in the population models. Notice that it is hardly ever the case that catch-at-age is observed directly. The preferred method is to use age data through age-length keys (ALKs). In tropical fisheries, there is often a heavy reliance on size frequency data only, which will incur a significant penalty in accuracy. Wherever possible, ageing should be considered as part of the data collection programme.
5.3.2.1 Methods Using age-Age-Length keys (ALK)
Use of size frequencies can greatly enhance the use of ageing data, as ageing is generally expensive. Using size frequencies allows improved sampling techniques reducing the amount of ageing that needs to be done by making use of the information contained in fish size to help generate the age distribution. Unlike other methods it does not depend on size however, so even larger size groups can be broken down into age categories. All the usual sampling techniques apply. So, age samples should be stratified by size, but be random within each size group.
A link model can be used to define catches in each age group as a sum of catches from the size groups:
. (43)
where pla = the proportion (i.e. a probability) of fish in length group l of being age
a. The pla parameters can be estimated, for example, from age-at-length data using a multinomial model (McCullagh and Nelder 1983).
5.3.2.2 Methods Not Requiring a Growth Model
These methods rely on identifying modes in length frequency samples representing cohorts. For example, the Bhattacharya method uses the first mode in a sample to fit a normal curve representing the youngest cohort. This curve is then used to remove all fish belonging to this cohort from the sample. A similar procedure is then applied to the next mode, and so on. Methods include Bhattacharya (1967), Tanaka (1956), MIX: MacDonald and Pitcher (1979) and NormSep: Hasselblad and Tomlinson (1971).
5.3.2.3 Methods Requiring a Growth Model
The simplest case is Jones length-based cohort analysis (Jones and Van Zalinge 1981). In this growth is assumed deterministic and the sample is sliced up according to back-transformation of the von Bertalanffy growth equation.
The method is based on re-writing the survival equation into length differences:
for each size class (44)
(45)
where l1 and l2 are respectively the lower and upper bounds of the size class. Note that size classes should be chosen such that MDt should be less than 0.3.
Given the change in age over each size class (Dt), the population sizes within each class can be constructed in much the same way as a VPA. The method requires that the growth parameters are known. Methods such as ELEFAN may be used to estimate these. Provided appropriate averaging of the length compositions has been done so that the observed length compositions can be assumed to present the equilibrium length compositions, then a simple VPA back-calculation over length rather than age groups is possible.
The method has been investigated (Addison 1989, ICES 1995a,b) with the following conclusions:
· Cohort analysis works on a single length frequency sample assuming the population has been in a steady state. A number of length frequency samples from different times may be required to verify this.More realistically, other methods use the growth model (usually the von Bertalanffy model) to relate the age of a fish to a parameter of a probability distribution of its size. The parameter is usually taken to be a mean, and the probability distribution is the Normal. So given growth parameters, and some parameter summarising the variation in growth-at-age, we can define the probability (j) a fish of length l is age a as:
· The model is insensitive to errors in the terminal exploitation rate, if F >> M.
· The model is extremely sensitive to M.
· The narrowest length interval that makes data reasonably smooth should be used.
Considerable care should be taken with the method when only poor growth data are available or when individual variation in growth is high. Ensure the terminal length interval (plus group) has an initial length (lower bound) of less than 70 % of L¥. This will minimise errors in the models output due to errors in estimates and variances of L¥ and k. Any estimate of overall F should therefore cover only the smaller size interval representing the majority of the catch.
· Estimates of abundance should not be taken as absolute values. Use them only as indices to reflect relative changes.
(46)
The cumulative normal distribution can then be used to calculate the proportions of each length group, which should be allocated to each age group (pla in Equation 43). Other distributions, such as the log-normal may be used and in many cases may be more appropriate (see Beyer and Lassen 1994).
There are many methods to fit this and other similar functions to modes through one or more length frequency samples. They ignore modes if they do not conform to the growth models. These methods are complicated, but software is widely available, such as ELEFAN (Pauly 1987), SCLR (Shepherd 1987), MULTIFAN (Fournier et al. 1990).
The conversion from length to age based only on length frequency is usually subject to a variance much higher than that obtained in age readings. Most worryingly, this uncertainty is not quantified allowing a researcher to overestimate the accuracy of their assessment. Decomposition of the length distribution into age groups is less precise than ageing directly, and therefore should be used only when no ageing methods are available. | https://www.fao.org/3/x9026e/x9026e07.htm |
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1909 - 1962 World Events
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In 1909, in the year that Kevin Wilhelm Cloonan was born, Polish physician and medical researcher Paul Ehrlich found a cure for syphilis, which was a prevalent (but undiscussed) disease. He found that an arsenic compound completely cured syphilis within 3 weeks.
In 1924, when he was only 15 years old, in May, wealthy college students Nathan Leopold and Richard Loeb kidnapped and killed 14 year old Robert Franks "in the interest of science". Leopold and Loeb thought that they were intellectually superior and that they could commit the perfect crime and not be caught. They were brought in for questioning within 8 days and quickly confessed. Clarence Darrow was hired as their defense lawyer, getting them life imprisonment instead of a death sentence. Loeb was eventually killed in prison - Leopold was released after 33 years, dying of a heart attack at age 66.
In 1938, when he was 29 years old, on October 30th, a Sunday, The Mercury Theatre on the Air broadcast Orson Welles' special Halloween show The War of the World's. A clever take on H.G. Wells' novel, the show began with simulated "breaking news" of an invasion by Martians. Because of the realistic nature of the "news," there was a public outcry the next day, calling for regulation by the FCC. Although the current story is that many were fooled and panicked, in reality very few people were fooled. But the show made Orson Welles' career.
In 1946, he was 37 years old when pediatrician Dr. Benjamin Spock's book "The Common Sense Book of Baby and Child Care" was published. It sold half a million copies in the first six months. Aside from the Bible, it became the best selling book of the 20th century. A generation of Baby Boomers were raised by the advice of Dr. Spock.
In 1962, in the year of Kevin Wilhelm Cloonan's passing, on October 1st, African-American James H. Meredith, escorted by federal marshals, registered at the University of Mississippi - becoming the first African-American student admitted to the segregated college. He had been inspired by President Kennedy's inaugural address to apply for admission.
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These stories will warm your heart and inspire you to share photos and create biographies of the people from your past. | https://www.ancientfaces.com/person/kevin-wilhelm-cloonan-birth-1909-death-1962-austra/145052246 |
Introduction: Central Europe, February 25th 1931. Onboard the famous trans-European Budapest Express, you are with Karine Peaufiner, a famous French detective from Paris. You are traveling to Budapest to meet with other detectives showcasing the latest developments in crime scene forensics.
It is nighttime and you are passing slowly through the heart of Europe during a heavy snowstorm. You are reviewing case notes in your cabin with Karine and your colleagues. Suddenly there is a knock at the door, it is the train manager. He looks worried and asks you to come quickly to the First Class dining coach.
When you arrive, you see a man slumped over a restaurant table. He was Sir Clarence Hayden and he has been murdered!
The manager informs you that in one hour the train will stop at the next station, if the killer hasn’t been apprehended, they will be free to escape into the night and get away with this horrible crime!
Your reputation as brilliant detectives precedes you, he asks you to solve the crime so the murderer can be caught and brought to justice. You’re able to narrow down 5 suspects who were seen in the dining car around the time Sir Clarence was murdered.
Moving through the cabins and gathering evidence, the killer knows you are hot on their trail and has decided you are their next target. With you out of the picture they would be free to escape when the train stops.
Solve the riddles and puzzles, gather the evidence and solve the murder before it’s too late!
Do you have what it takes to find the killer before they find you? Time is of the essence!
Location: Escapology
Parking: Large parking infront
Date Completed: October 6, 2017
Number of Escape Artists: 6 (including 1 first timer)
Hint System: Penalties after 3rd hint Via TV Monitor.
Result: ESCAPED - 52 minutes 52 seconds
Creativity: 4
Difficulty: 4
Immersiveness: 4
Fun Factor: 5
OVERALL: 4
Note. For OVERALL means, 1 = WTF?; 2 = Take a gander; 3 = You can book it; 4 = You should book it now; 5 = OMG! You should've booked it yesterday!
Summary
- Recommend 3-5 escape artists
- Puzzles were on the difficult side
- After asking for 3 hints, time was deducted when a hint was requested
- Immersive AF
- Beautifully detailed escape room
- Good for seasoned escape artists, not for newbies
This was actually the first escape room that my girlfriend and I participated in together. The escape room lobby was beautifully designed and didn't feel like an office space.
This escape room was uniquely set up like a train and it felt like I was on a train. It was three rooms connected like a train. The puzzles were ranging in difficulty. I was lucky to be with experienced escape artists that knew what they were doing. This room was multi-linear and the biggest part was to remember certain clues since the starting the room as it would help with the final clue.
This escape room is not suggested for beginners and is a good challenge for escape artists that are looking to be challenged. | https://www.gtfo.blog/home/2018/1/1/budapest-express |
A couplet is a pair of lines that rhyme. Usually both lines have the same meter, or number of syllables. A couplet expresses a complete thought and can be funny or serious. Some poems are made from several couplets put together.15 mei 2019
What is a rhyming couplet for kids?
A Rhyming Couplet is two line of the same length that rhyme and complete one thought. There is no limit to the length of the lines. Rhyming words are words that sound the same when spoken, they don’t necessarily have to be spelt the same.
What is an example of a couplet poem?
Defining Rhyming Couplets
Double, double, toil and trouble; Fire burn and cauldron bubble. These famous lines are an epic example of a rhyming couplet. As you may have surmised from the name, rhyming couplets are two lines that rhyme, but they also often have the same meter, or rhythmic structure in a verse or line.
What is a couplet poetry?
A couplet is a pair of successive lines of metre in poetry. A couplet usually consists of two successive lines that rhyme and have the same metre. … In a formal (or closed) couplet, each of the two lines is end-stopped, implying that there is a grammatical pause at the end of a line of verse.
How do I write a couplet poem?
Write a Couplet
- First, choose a topic and come up with the first line of your poem.
- Next, list some words that rhyme with the last word.
- Then, write the second line of your couplet. …
- Finally, count the number of syllables (use your fingers or clap your hands) to make sure that it has the same meter as the first line.
15 мая 2019 г.
How do you identify a couplet?
Rhymed couplets are reasonably easy to identify because they are governed by clear rules. The most basic rule is that a rhymed couplet must be two lines in formal verse (poetry with meter and rhyme scheme) that share the same end-rhyme.
What is the difference between rhyme and rhythm?
Rhyme is a pattern of words that contain similar sounds. Rhythm: The dictionary tells us it is “a movement with uniform recurrence of a beat or accent.” In its crudest form rhythm has a beat with little or no meaning. … Rhyme is not only a recurrence but a matching of sounds.
What is an example of couplet?
Couplet refers to two lines of poetry that follow each other and rhyme. Couplets also sometimes have the same meter, meaning the same number of beats or the same rhythm. The sheep’s in the meadow, the cow in the corn.
What is the difference between a couplet and a heroic couplet?
What Is the Difference Between a Couplet and a Heroic Couplet? A heroic couplet is a specific type of couplet that discusses heroic themes and that usually uses iambic pentameter. An ordinary couplet, on the other hand, is simply two successive lines of poetry—often two lines that rhyme and that employ the same meter.
What is a Cinquain poem?
What is a Cinquain? A cinquain – which, by the way, is pronounced “sin-cane,” not “sin-kwane” – is a form of poetry that is very popular because of its simplicity. It was created by American poet Adelaide Crapsey about 100 years ago, and is similar to Japanese poetic forms, such as haiku and tanka. Cinquains…
Which is the best definition of a couplet?
A couplet is two lines of poetry that usually rhyme. Here’s a famous couplet: “Good night! Often whole poems are written in couplet form — two lines of rhyming poetry, followed by two more lines with a different rhyme, and so on. …
What is a meter in a poem?
In poetry, metre (British) or meter (American; see spelling differences) is the basic rhythmic structure of a verse or lines in verse.
What is meant by heroic couplet?
Heroic couplet, a couplet of rhyming iambic pentameters often forming a distinct rhetorical as well as metrical unit. The origin of the form in English poetry is unknown, but Geoffrey Chaucer in the 14th century was the first to make extensive use of it.
How many syllables are in a couplet? | https://www.inkbottlepress.com/poetry-tips/couplet-poetry-for-kids.html |
Swine flu: Real danger or media hype?
Just over two weeks after the outbreak of swine flu, sorry, H1N1, most of us have come round to the idea that a pandemic doesn't always necessitate panic. The infection is spreading steadily, but in most people it's relatively mild and only a very small number of people have died outside Mexico. In an editorial last week the medical journal The Lancet praised the British media, and the general public, for their "balanced and rational" reaction to the outbreak. Perhaps we're learning how to be on alert without losing our heads.
The Lancet was responding to a piece by the Guardian's Simon Jenkins (who has been previously noted on Plus) who dismissed initial coverage of the outbreak as exaggerated by media and scientists to sell papers and drugs. But according to The Lancet, Jenkins got hype confused with scientific uncertainty: in the face of the many unknowns that come with this new virus, scientists play out a range of different scenarios, including worst-case ones. If these don't happen, then this doesn't necessarily invalidate their methods — it might even mean that interventions made as a result of the predictions have worked.
But how do scientists make these predictions in the face of so many uncertainties? The biological side — understanding the virus and producing vaccines — is down to life scientists, but understanding how it will spread is a matter for mathematicians. They build mathematical models that mimic the progress of an infection. There is a range of tried-and-tested epidemiological models, but the devil is in the detail: the predictions of any one model depend crucially on the assumptions made about the nature of the virus. Hence the uncertainty.
Two times two times two...
As an example, imagine that a person infected with a new virus infects, on average, two other people a day. Starting with one sick person, we have two new sick people the next day, four new sick people the day after that, and so on. Assuming that people don't recover and become immune, it takes just over three weeks until the number of sick people is larger than the population of Britain. If a sick person infects three people a day on average, then the whole of Britain will be infected within just over two weeks. The exponential growth means that one extra infection a day per sick person makes the disease spread a lot faster.
One number does (almost) everything
The basic bit of information here — the average number of people a sick person will infect in a population that has no immunity against the virus — is the most important parameter in disease modelling. It's called the basic reproduction number of an infectious disease. It measures how fast the disease will spread, and, consequently, how hard it is to control, and it's therefore one of the first bits of information scientists will try and estimate when a new disease has broken out.
The reproductive number measures how fast a disease spreads.
Getting that estimate right is hugely important, but it's no easy feat, because data from the beginning of the outbreak isn't always readily available. The first analysis of H1N1 data from Mexico, published this week in Science, uses sophisticated mathematical machinery to make sense of incomplete information. The authors stress that "there are uncertainties about all aspects of this outbreak", and their estimate of the reproductive number for H1N1 is correspondingly vague, between 1.2 and 1.6. This compares to a value between 1.5 and 3 for normal seasonal influenza and between 12 and 18 for measles. The H1N1 number may seem low, but it's in the same range as reproduction numbers of previous flu pandemics. Assuming that the infection rate stays constant, only a reproduction number of less than 1 guarantees that the disease will die out of its own accord.
The reproduction number can also tell you quite a few things about possible interventions to control a disease. For example, it gives you a way of working out what proportion of the population should be vaccinated to prevent the infection from spiralling out of control. If an infected individual normally passes the disease to four others, then you should immunise just over 3/4 of the population: out of the four that would normally have been infected by one sick person, more than three would now be immune (on average), bringing the infection rate down to less than 1, and causing the disease to eventually die out. Similarly, for a general reproductive number R 0 , you can achieve so-called herd immunity by vaccinating a proportion of 1-1/R 0 of the population.
Challenging models
Taking aside the difficulty of getting good estimates of important numbers, there's the question of how to model the spread of a disease. The simple exponential model above is far too crude, as it ignores the fact that people can recover, become immune, or die. Accordingly, the model predicts that any disease with a reproduction number greater than 1 will continue to spread forever.
More sophisticated models divide the population into groups. In the SIR model, for example, people are either susceptible to the disease (S), infected and contagious (I), or have recovered and are immune (R). Every day (or whatever the unit of time you're using) a certain number of susceptible people become infected and a certain number of infected people recover. For example, if b is the average number of contacts a person has a day and S is the proportion of the population that is susceptible to the disease, then an infected person meets bS susceptible people a day on average. Assuming that the disease is passed on to all of them, bSI people pass from the susceptible to the infected class every day, where I is the current number of infected people.
The number of people who pass from the infected to the recovered class is worked out in terms of the average number of days a person is sick. If this is equal to d, then the chance of recovery on a given day is 1/d, so out of I infected people I/d pass over into the recovered class every day.
Mathematical models can be used to test interventions.
This simple model can be made more mathematical by rewriting it in terms of differential equations. Throwing in some general assumptions on the rate of births and deaths in the population, you can then run your model on a computer to simulate the long-term behaviour of the disease. All you need in this simple case are estimates of the average number of contacts a person has a day, b, and the average duration of the disease d. The reproductive number, according to this model, is bd/N, where N is the total size of the population. If this number is less than 1, then the disease will eventually die out. If it's greater than 1, then the model predicts that epidemics occur periodically for a while, until the proportion of infected people settles down to a constant value — the disease has become endemic.
The great thing about this type of compartmental model is that you can add extra compartments to make it more realistic. For example, you can add a group of people who are incubating the disease, but aren't yet contagious, or people who are contagious but don't yet show symptoms. You can also play around with the transition rates between compartments to predict the effect of interventions. For example, you can model the effect of antiviral drugs by reducing the average duration of the sickness, or you can predict the effect of quarantine by varying the contact rate.
Once you can mimic how a disease spreads between people who physically meet, you can combine this with models that describe people's travel behaviour to predict how and if a disease will spread around the globe. You can also use these more sophisticated models to find out what kind of interventions would be most effective. A study published last year, for example, used a compartmental model coupled with a travel model to show that traffic restrictions would have little effect on the evolution of a pandemic, a possible reason for the World Health Organisation's refusal to recommend a complete ban on travel in the face of H1N1. More encouragingly, the study found that treating 5% of the population with antiviral drugs would mitigate a pandemic for diseases with a reproductive number up to 1.9.
Effective as these epidemiological models may be, they are only ever as good as the underlying assumptions. If you're not sure about the basic characteristics of a virus, for example its reproductive number, then the predictions of any model will be necessarily vague. Even a relatively small change in one of the parameters can lead to significantly different predictions. Any good epidemiologist is explicit about the underlying assumptions of a model and the uncertainties concerning parameter estimates. But once the predictions hit the headlines, these caveats are often lost, leading casual readers to mistake uncertainty for falsity.
Further reading
You can find out more about the SIR model in the Plus article The mathematics of diseases;
article The mathematics of diseases; The Motivate video conferencing project has a write-up of a project involving disease modelling. It contains a spreadsheet which allows you to change disease parameters and see how the model's predictions change.
Back to the Mathematics of infectious disease package
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Ridgefield SAT scores exceed state average
Ridgefield High students scored significantly higher than the state average on both sections of the SAT. Ridgefield students averaged a collective Math score of 600 out of a possible 800 points, and a collective English Language Arts (ELA) score of 613 out of a possible 800 points. With those sections combined, Ridgefield students scored an average of 1213 out of 1600 points. The state average was 507 Math, and 524 ELA, or 1031 combined.
2017 Ridgefield High School SAT scores
College Board now scores the two sections of the SAT on a 400-1600 point-scale, opposed to the 2400 point-scale test administered prior to January of 2016. The essay section of the test is optional, and has three possible scores from 2 through 8. Essay score averages were not available at press time.
Ridgefield’s school district is part of District Reference Group (DRG) A, a state classification meant to evaluate districts based on their socioeconomic status. District A schools are rated as “very affluent, low-need suburban districts.”
While Ridgefield students’ combined average SAT scores were the second lowest among DRG-A school districts, Ridgefield also had the fourth-highest percentage of students who “met or exceeded” state benchmarks in both Math and ELA scores. 77.9% of students met or exceeded the state benchmark in Math, and 93% met or exceeded state benchmarks for ELA. Comparatively, of all Connecticut students only 41.3% met or exceeded benchmarks in Math; 65.4% met or exceeded benchmarks in ELA.
Ridgefield students’ math benchmarks are down from last year, while Language Arts have blipped upwards slightly.
Last year, 80.4% of Ridgefield students met or exceeded state benchmarks for Math, and 92.1% met or exceeded benchmarks for ELA.
To meet or exceed state benchmarks in Math, a student must score between 530 and 800 points on the Math section. For ELA, a student must score between 480 and 800 points.
Participation
Ridgefield averaged a slightly lower participation rate in the Connecticut School Day SAT. Out of 420 Ridgefield students, 400, or 95.2%, took the test at school. Overall 38,421 students— 96% of students required to take the test— took the SAT as part of a statewide assessment. This year marks the second year since CT has adopted the statewide SAT as its 11th grade assessment for college readiness.
The Standard Balanced Assessment Curriculum, or SBAC, was done away with beginning last year, in an effort to cut back on the number of standardized tests high schoolers are required to take. | |
BACKGROUND
Field
Description of the Related Art
SUMMARY
DETAILED DESCRIPTION
This disclosure relates to capacitive accelerometers and to acceleration sensors with movable rotors which may rotate out of a substrate plane when the accelerometer undergoes movement with an acceleration component perpendicular to the substrate plane. Such sensors may be combined with two other sensors which measure acceleration in the substrate plane to form a three-axis accelerometer. Such accelerometers may be used in automotive applications, such as Electronic Stability Control (ESP/ESC), Antilock Braking (ABS), Electric Parking Brake (EPB), Hill Start Assistance (HSA), Electronically Controlled Suspension (ECS), headlight levelling or airbag deployment.
Each capacitive sensor in a three-axis accelerometer may comprise a stator which is immobile in relation to the substrate and a rotor which is at least partly mobile in relation to the substrate. In this disclosure the terms “rotor” and “stator” both refer to interlinked micromechanical structures, such as bars or beams. The structures and their interconnections may be formed by etching a substrate, for example a silicon substrate.
In this disclosure, the terms “bar” and “beam” refer to elongated structures, for example made of silicon, which are rigid compared to more flexible structures which may be called “springs”. Rigidity and flexibility are relative terms. Although the bars and beams which constitute a rotor will have some flexibility, they will still to a good approximation retain their mutual positions in relation to each other when the rotor moves, and only the springs from which the rotor is suspended will undergo significant flexible deformation due to the movement.
Rotors and stators typically comprise electrically conducting electrode areas on at least some of their interlinked structures to facilitate electrical measurements between the rotor and the stator.
A three-axis accelerometer typically comprises a substrate plane, which may be labelled the xy-plane. Stators may be fixed structures in the substrate plane. Acceleration sensors may be implemented in the substrate plane with rotors which undergo linear motion along an axis in the plane in response to accelerating movement along that axis. This disclosure focuses primarily on acceleration sensors where the rotor is implemented as a seesaw, so that it is attached to one or more torsion springs and undergoes rotational motion about a rotational axis defined by the torsion springs in response to accelerating movement which is not parallel to that axis.
If the rotor is implemented as a seesaw, its center of mass should not coincide with the rotational axis, because that would make it unresponsive to linear acceleration. A seesaw rotor should therefore be an unbalanced seesaw, at least to some extent. A seesaw rotor may be implemented as a completely one-sided seesaw, so that all parts of the rotor lie on one side of the rotational axis. More precisely, a seesaw rotor is one-sided if it is possible to draw a plane which crosses its rotation axis so that the entire rotor lies on one side of the plane. A rotor implemented as a seesaw may also be two-sided, so that some parts of the rotor lie on one side of the axis and some parts on the opposite side of the axis. For a two-sided rotor, it is not possible to draw a plane which crosses its rotation axis so that the entire rotor lies on one side of the plane.
Document US2007119252 discloses a three-axis accelerometer comprising acceleration sensors for measuring acceleration in the substrate plane and for measuring out-of-plane acceleration, i.e. acceleration in the direction perpendicular to the substrate plane. A disadvantage with the rotors employed for out-of-plane measurement in this document is that they tend to be sensitive to vibration and mechanical shocks.
Document US20110023606 also discloses a three-axis accelerometer comprising acceleration sensors for measuring acceleration in the substrate plane and for measuring out-of-plane acceleration. A disadvantage with the rotors employed for out-of-plane measurement in this document is that they consume a lot of device area and are sensitive to external stresses.
An object of the present disclosure is to provide an apparatus for alleviating the above disadvantages.
The objects of the disclosure are achieved by an arrangement which is characterized by what is stated in the independent claims. The preferred embodiments of the disclosure are disclosed in the dependent claims.
The disclosure is based on the idea of implementing a z-axis acceleration sensor with a frame-shaped rotor which is a two-sided seesaw, and forming symmetrically placed damping areas on the seesaw on both sides of its axis of rotation.
An advantage of the arrangement of the disclosure is that the structure becomes robust against vibrations and produces efficient damping while consuming little device area.
The illustrations are schematic and have not been drawn to scale.
This disclosure describes a capacitive micromechanical accelerometer comprising a substrate which defines a substrate plane which extends in a transversal direction and a longitudinal direction, the transversal direction being perpendicular to the longitudinal direction, a first sensor for measuring acceleration along a vertical axis perpendicular to the substrate plane, and an accelerometer package with an inner package plane which is adjacent and parallel to the substrate plane above and/or below the substrate plane. The first sensor comprises a rotor which is mobile in relation to the substrate, a rotor suspender, and one or more stators which are immobile in relation to the substrate. The rotor comprises one or more rotor electrodes and the one or more stators comprises one or more stator electrodes, the electrodes being configured for differential capacitive measurements. The suspender comprises one or more anchored rotor suspender bars and first and second transversal torsion springs aligned on a transversal rotor rotation axis, wherein the first and second transversal torsion springs are attached to the rotor.
The rotor is a two-sided seesaw frame comprising at least a transversal rotor bar, a first longitudinal rotor bar attached to the transversal rotor bar and a second longitudinal rotor bar attached to the transversal rotor bar, wherein each longitudinal rotor bar extends from a first side of the transversal rotor rotation axis to a second side of the transversal rotor rotation axis. Each longitudinal rotor bar comprises one or more first damping plates on the first side of the transversal rotor rotation axis and one or more first damping plates on the second side of the transversal rotor rotation axis. One or more second damping plates are fixed to the inner package plane above and/or below at least some of the one or more first damping plates, so that at least one first damping plate overlaps with the projection of a second damping plate to the substrate plane in a first overlap area on the first side of the transversal rotor rotation axis, and at least one first damping plate overlaps with the projection of a second damping plate to the substrate plane in a second overlap area on the second side of the transversal rotor rotation axis.
When the transversal torsion springs are placed far away from each other, the sensor becomes robust against vibrations because the parasitic resonance modes can be raised to higher frequencies where their vibration amplitude is smaller. Furthermore, placing damping electrodes far from each other also increases robustness because it allows them to produce more damping in the lowest parasitic resonance mode, which makes the vibration amplitude smaller.
FIG. 1
illustrates schematically a first sensor in a capacitive accelerometer. The substrate plane corresponds in this disclosure to the xy-plane. In this disclosure the term “substrate” refers to the body from which the micromechanical structures which constitute the sensor have been prepared. When the structures are completed, the remaining parts of the substrate form a supporting body which surrounds the accelerometer. The substrate may, for example, be a silicon wafer. The micromechanical structures which constitute the sensor may be manufactured from the substrate by etching and coating methods. In other words, in this disclosure the term “substrate” refers to a thin substrate which forms the structure layer (or device layer) from which the microelectromechanical structures in the accelerometer are manufactured. This substrate typically requires structural support from a separate, much thicker handle wafer or support wafer.
FIG. 1
FIG. 1
FIG. 1
FIG. 1
FIG. 2
21
14
A vertical z-axis may be defined to be perpendicular to the xy-plane. Some of the micromechanical components depicted in may have the same thickness as the substrate, others may have a smaller thickness. In this disclosure, the substrate in its entire thickness constitutes the xy-plane, and the terms “above” and “below” refer to differences in z-coordinates from the surface of the substrate. In other words, an object “above” the substrate plane depicted in may be interpreted to lie closer to the viewer than the top surface of the components which is illustrated in , while an object “below” the substrate plane may be interpreted to lie further away from the viewer than the bottom surface of the components depicted in . illustrates an accelerometer package above the device component , which is in the substrate plane.
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13
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131
FIG. 1
The first sensor is configured for measuring acceleration in the direction of the z-axis, which will be referred to as the vertical axis in this disclosure, and which is perpendicular to the substrate plane. The first sensor comprises a rotor which comprises a transversal rotor bar and two longitudinal rotor bars and . Together, the transversal rotor bar and the two longitudinal rotor bars and form a frame which may partly surround other components on the substrate plane. The rotor also comprises a set of rotor electrode fingers , which function as rotor electrodes. The number of fingers may be much larger, and the separations between fingers much smaller, than what is schematically illustrated in .
FIG. 1
FIG. 1
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The sensor in also comprises two stators with transversal stator bars and and corresponding sets of stator electrode fingers and , which function as stator electrodes. The rotor and stator electrodes may be coated, and they may be vertically recessed from the top and/or bottom face of the substrate. As illustrated in , the frame-shaped rotor may partly surround the stators. The transversal stator bars and are fixed to the substrate at stator anchor points and . The term “anchor point” refers in this disclosure to a region where objects such as bars may be firmly attached to the substrate.
The location and number of rotor and stator electrodes, as well as their geometry and mutual positioning, may be optimized for capacitive measurements in many ways depending on the intended measurement application.
The rotor is suspended from a rotor suspender, which may be anchored to one or more rotor anchor points. In this disclosure, the term “suspender” refers to bars or beams which are connected in a sequence extending from the rotor anchor points to a pair of torsion springs. The rotor turns when the torsion springs, which are transversal, are twisted torsionally. In this disclosure, the bars or beams which constitute the suspenders do not themselves undergo a significant amount of bending or twisting. Their primary function is displacement. They allow the rotor anchor points to be located a certain distance from the torsion springs.
FIG. 1
In this disclosure, the term “torsion spring” refers to silicon structures with aspect ratios which make them susceptible to torsional twisting about their lengthwise dimension. In this case, a “transversal” torsion spring means a spring whose lengthwise dimension is parallel with the x-axis in . Transversal torsion springs may be narrow in the y-direction to allow torsional twisting, but thick in the vertical z-direction to prevent translational movement out of the xy-plane. Alternatively, the transversal torsion springs may have a meandering shape in the xy-plane and be thick in the z-direction. Meandering springs can allow torsional twisting about the x-axis, for example, without necessarily being narrow in the direction of the y-axis.
FIG. 1
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illustrates a sensor where the one or more anchored rotor suspender bars comprise a first transversal rotor suspender bar and a second transversal rotor suspender bar , and where the first transversal torsion spring is attached to the end of the first transversal rotor suspender bar , and the second transversal torsion spring is attached to the end of the second transversal rotor suspender bar . The transversal rotor suspender bars and are anchored to the rotor anchor point . In other embodiments described below, additional suspender bars may be added between the anchored suspender bars and the torsion springs. These additional suspender bars may extend either in the transversal or the longitudinal direction, as described below.
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FIG. 1
The rotor, which comprises the transversal rotor bar and the longitudinal rotor bars and , may be termed a “seesaw” because the transversal torsion springs and allow the rotor to pivot about the transversal rotor rotation axis (RRA) illustrated in . This axis is determined by the location of the torsion springs and . The two torsion springs must be aligned on the same axis to facilitate the rotation or pivoting of the rotor.
When the accelerometer undergoes accelerating motion in a vertical direction, the rotor can rotate about the transversal rotor rotation axis and this movement can be detected with a differential capacitive measurement conducted between the rotor and stator electrodes described above.
FIG. 1
14
15
The rotor illustrated in may also be characterized as a two sided-seesaw because it extends to both sides of the transversal rotor rotation axis (which may be hereafter referred to either as the RRA or as the transversal RRA). In other words, each longitudinal rotor bar and extends across the transversal rotor rotation axis, from a first side of the transversal rotor rotation axis to a second side.
FIG. 2
FIG. 1
FIG. 2
FIG. 2
14
21
211
14
14
191
193
This is illustrated from another angle in , which shows the cross-section A-A from . shows the first longitudinal rotor bar and the accelerometer package , with inner package plane adjacent to the substrate plane. The longitudinal rotor bar extends to both sides of the RRA. In other words, the rotor extends both in a first direction and in a second direction from the RRA. These two directions are diametrically opposed, because the rotor forms a planar structure which rotates about the RRA. In , first longitudinal rotor bar lies in the substrate plane. The first direction is the positive y-direction and the second direction is the negative y-direction. When the accelerometer experiences acceleration in the direction of the z-axis, the rotor rotates about the RRA, out of the xy-plane. The stiffness of the torsion springs and should be configured to reach suitable movement with desired accelerations that are application-specific.
21
FIG. 2
The package extends beyond the first sensor to the left and right. The package surrounds the accelerometer on all sides, but the parts of the package which lie distant from the sensor are not relevant to this disclosure and are not illustrated in . The space between the package and the sensors is a sealed space, typically filled with an inert gas.
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14
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101
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FIG. 1
The rotor comprises damping plates which, together with adjacent damping plates in the package , may be configured to damp vibrations in the movement of the rotor. The damping plates on the rotor may, for example, be symmetrical quadratic protrusions in the longitudinal rotor bars and , such as damping plates - in . However, the damping plates may also be protrusions in the longitudinal rotor bars with a rectangular form or any other form. Protrusions are required because the surface area of the narrow bar is by itself insufficient to generate a tangible damping effect.
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FIG. 2
In order to function as a damping plate, a first damping plate on the rotor (-) needs to be in close vertical proximity to a second damping plate on the accelerometer package. Second damping plates and may be manufactured on the inner package plane either above or below first damping plates and . An apparatus where the second damping plates have been manufactured above first damping plates and is illustrated in . Second damping plates and (not illustrated) may correspondingly be manufactured on the inner package plane either above or below first damping plates and , respectively, in close vertical proximity to first damping plates and . The vertical gap between the first and second damping plates may be between 0.5 μm and 5 μm. Separate stopping structures may be utilized to prevent the rotor from coming into contact with the package.
The first damping plates do not need to have exactly the same sizes, areas or xy-positions as the second damping plates. Damping takes place wherever a first damping plate overlaps with the projection of a second damping plate in the substrate plane. The projection of a second damping plate in the substrate plane is the area which lies in the xy-plane directly beneath the second damping plate in question. The area where the first damping plate overlaps with the projection may be called an overlap area. The first damping plates may be larger than the second damping plates, or vice versa.
FIG. 3
FIG. 4
101
102
201
202
31
32
201
101
102
41
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42
102
illustrates two first damping plates and projections of two second damping plates to the substrate plane. The overlap area is illustrated with stripes. In the illustrated configuration, the first damping plates and on the rotor are larger than the second damping plates and on the package, and they overlap partially. The first overlap area is and the second overlap area is . illustrates a configuration where there is only one second damping plate whose projection to the xy-plane covers both first damping plates and . In this case the first overlap area coincides with the damping plate , and the second overlap area coincides with the damping plate .
FIGS. 3 and 4
In one embodiment, the damping effect is achieved by configuring at least one overlap area on each side of the rotor rotation axis. In other embodiments, the damping effect is achieved by arranging the first and second overlap areas symmetrically in relation to the rotor rotation axis. One form of symmetry is when all pairs of first and second overlap areas share the same shape, area and distance from the rotor rotation axis, as they do case in both . The first and second overlap areas are in this case plane-symmetric in relation to the vertical plane where the transversal rotor rotation axis lies.
Symmetry in relation to the rotor rotation axis can also be understood in a less restricted way. The first and second overlap areas can be considered symmetric in relation to the transversal rotor rotation axis if the torsional damping coefficient in the first overlap area equals the torsional damping coefficient in the second overlap area. The torsional damping coefficient is present in the system's equation of motion for torsional movement
<math overflow="scroll"><mrow><mrow><mrow><mi>J</mi><mo>⁢</mo><mfrac><mrow><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mrow><msup><mi>d</mi><mn>2</mn></msup><mo>⁢</mo><mi>θ</mi></mrow></mrow><msup><mi>dt</mi><mn>2</mn></msup></mfrac></mrow><mo>+</mo><mrow><mi>c</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mfrac><mrow><mi>d</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>θ</mi></mrow><mi>dt</mi></mfrac></mrow><mo>+</mo><mrow><mi>κ</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>θ</mi></mrow></mrow><mo>=</mo><msub><mi>M</mi><mi>ext</mi></msub></mrow></math>
where c is the torsional damping coefficient, J is the moment of inertia, θ is the rotation angle, κ is the torsional spring constant, t is time,
<math overflow="scroll"><mfrac><mrow><msup><mi>d</mi><mn>2</mn></msup><mo>⁢</mo><mi>θ</mi></mrow><msup><mi>dt</mi><mn>2</mn></msup></mfrac></math>
is the second derivate of θ with respect to t,
<math overflow="scroll"><mfrac><mrow><mi>d</mi><mo>⁢</mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo>⁢</mo><mi>θ</mi></mrow><mi>dt</mi></mfrac></math>
ext
is the first derivate of θ with respect to t and Mis the external moment. The damping coefficient is a function of the damping area, the distance from the rotor rotation axis, the vertical gap between the first and the second damping plates and effective gas viscosity.
The accelerometer described above, with a first sensor configured to measure acceleration in a vertical direction perpendicular to the substrate plane, may be used in a three-axis accelerometer where two additional sensors are used for measuring accelerations in two orthogonal directions in the substrate plane. The three-axis accelerometer can be produced on a small area in the substrate plane if the frame-shaped first sensor partly surrounds these additional sensors. In the following description various alternative designs will be described for fitting several sensors on a small area.
A second sensor may be configured to measure acceleration in the direction of the x-axis, which may be referred to as the transversal axis in this disclosure. The second sensor may be a capacitive micromechanical acceleration sensor. A third sensor may be configured to measure acceleration in the direction of the y-axis, which may be referred to as the longitudinal axis in this disclosure. The transversal axis is orthogonal to the longitudinal axis. The third sensor may be a capacitive micromechanical acceleration sensor.
FIG. 1
131
13
In addition to consumed area, other design consideration pertaining to the first sensor include the distance from the transversal rotor rotation axis to the measurement electrodes on the rotor and stator electrodes. The longer the distance, the greater the displacement of the rotor electrodes in relation to the stator electrodes, and the stronger the capacitive signal, which may be a capacitance change. In , and in the embodiments described below, the rotor electrode fingers are attached only to the transversal rotor bar , so the distance between the electrodes and the rotor rotation axis can be represented by the distance L from the transversal rotor bar to the rotor rotation axis. The same distance optimization applies even if the rotor electrode fingers would be attached somewhere else on the rotor.
It is often beneficial to keep the rotor anchors and stator anchors fairly close to each other. Mechanical stresses will then move the rotor and stator approximately in the same way, and no error signal is produced in the differential capacitive measurement between the rotor and stator. The error signal is also smaller if the anchors are close to the transversal rotor bar where the finger electrodes are located. Furthermore, when the first and second torsion bars are far from each other on the rotor rotation axis, parasitic resonances move to higher frequencies. It is also beneficial to keep the damping plates far apart from each other in the transversal direction, because this allows the plates to effectively dampen vibrations mode where the rotor would rotate about its longitudinal axis of symmetry.
FIG. 5
FIG. 1
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In , reference numbers -, -, -, -, -, - and - indicate the same components as reference numbers -, -, -, -, -, - and -, respectively, in .
FIG. 1
FIG. 5
FIG. 1
FIG. 5
FIG. 5
182
51
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51
52
51
52
53
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581
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In the configuration illustrated in , the rotor anchor point lies on the rotor rotation axis. illustrates an embodiment where the accelerometer includes the same components as in , but in addition it also includes a second sensor for measuring acceleration along the transversal x-axis, and a third sensor for measuring acceleration along the longitudinal y-axis. The rotor (, , ) of the first sensor partly surrounds both the second sensor and the third sensor . In this disclosure, “the rotor partly surrounds the sensor” means that three sides of each rectangular sensor and face towards a part of the rotor. The upper sides of the sensors in face the transversal rotor bar , the left sides face the first longitudinal rotor bar , and the right sides face the second longitudinal rotor bar . In the lower side of the sensors face the transversal rotor suspenders and .
FIG. 5
581
583
591
581
593
583
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In the embodiment illustrated in , the one or more anchored rotor suspender bars comprise the first transversal rotor suspender bar and the second transversal rotor suspender bar . The first transversal torsion spring is attached to the end of the first transversal rotor suspender bar , and the second transversal torsion spring is attached to the end of the second transversal rotor suspender bar . A long distance L is achieved in this configuration, but the rotor anchor point lies quite far from the stator anchor points and .
One way to shift the rotor anchor point closer to the stator anchor points, while still retaining a long distance L between the rotor rotation axis and the transversal rotor bar, is to attach the transversal torsion bars to longitudinal displacement bars. The other end of the longitudinal displacement bars, the end which does not lie on the rotor rotation axis, may be attached directly to anchor points or transversal bars.
FIG. 6
FIG. 5
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In , reference numbers -, -, -, -, -, - and - indicate the same components as reference numbers -, -, -, -, -, - and -, respectively, in .
FIG. 6
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illustrates an embodiment where the first transversal torsion spring is attached to a first longitudinal displacement bar , and the first longitudinal displacement bar is attached to the first transversal rotor suspender bar . Similarly, the second transversal torsion spring is attached to a second longitudinal displacement bar , and the second longitudinal displacement bar is attached to the second transversal rotor suspender bar . The first longitudinal displacement bar extends from the first transversal rotor suspender bar in the negative y-direction. In other words, it extends in a direction which points away from the transversal rotor bar . The second longitudinal displacement bar similarly extends from the second transversal rotor suspender bar away from the transversal rotor bar . This allows the rotor anchor point to be located close to the stator anchor points and , but the distance L is still long. The distance D between the transversal line which crosses the rotor anchor point and the transversal rotor bar is shorter than the distance L, because the two longitudinal displacement bars and shift the rotor rotation axis further away from the transversal rotor bar . The rotor partly surrounds both the second sensor and the third sensor .
When suspender bars and displacement bars are connected in sequence between the anchor point and the torsion bars, it is not necessary to attach each bar precisely to the end of the preceding bar. The attachment could also be made somewhere closer to the midpoint of the preceding bar.
FIG. 7
FIG. 5
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In , reference numbers -, -, -, -, - and - indicate the same components as reference numbers -, -, -, -, - and -, respectively, in .
FIG. 7
FIG. 7
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illustrates an embodiment where the one or more anchored rotor suspender bars comprise a first longitudinal displacement bar and a second longitudinal displacement bar . In other words, first longitudinal displacement bar is attached from one end to first rotor anchor point and second longitudinal displacement bar is attached from one end to second rotor anchor point . The first transversal torsion spring is attached to the other end of the first longitudinal displacement bar , and the second transversal torsion spring is attached to the other end of the second longitudinal displacement bar . As seen in , both longitudinal displacement bars , extend from their respective anchor points , away from the transversal rotor bar . As before, the rotor partly surrounds both the second sensor and the third sensor .
FIG. 8
FIG. 5
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In , reference numbers -, -, -, -, - and - indicate the same components as reference numbers -, -, -, -, - and -, respectively, in .
FIG. 8
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illustrates an embodiment where there is only one anchored rotor suspender bar. This is the longitudinal rotor suspender bar which lies on the longitudinal symmetry axis of the rotor and is attached to the rotor anchor point . The first transversal torsion spring is attached to the end of a first transversal suspender bar , and the other end of the first transversal suspender bar is attached to the longitudinal rotor suspender bar . The second transversal torsion spring is attached to the end of a second transversal suspender bar , and the other end of the second transversal suspender bar is attached to the longitudinal rotor suspender bar . As before, the rotor partly surrounds both the second sensor and the third sensor .
FIG. 8
FIG. 8
884
891
893
It is also possible to alter the embodiment illustrated in by making the longitudinal rotor suspender bar longer. The first and second transversal suspender bars are thereby shifted downward in the figure. First and second longitudinal displacement bars may be attached from one end to the end of the first and second transversal suspension bars, respectively, and the other end of the first and second longitudinal displacement bars may be attached to the first and second transversal torsion springs and , respectively. This arrangement may, for example, be employed if the second and third sensor are too large to fit inside the suspender and the suspender frame as indicated in .
The damping plates described above may also be used for other purposes. For example, the accelerometer may be equipped with a self-test function. When a self-test is performed, an actuation force is applied to the rotor in the first sensor, so that the rotor rotates about its transversal rotation axis. If the actuation force is known, and the response to the self-test is measured with a capacitive measurement from the rotor and stator electrodes of the first sensor, the test can be used to check if the sensitivity or measurement range of the sensor has changed. The accelerometer can perform this self-test autonomously, with a range of different actuation forces.
If one or more first damping plates, and at least the second damping plate whose projection to the substrate plane overlaps with this first damping plate, are electrically conducting electrodes connected to a voltage source, the actuation force required for self-testing can be applied to the rotor by applying a voltage to these opposing electrodes. If the rotor and the suspender are sufficiently rigid to resist rotational movement about the longitudinal symmetry axis of the first sensor, the self-test electrodes may be placed on only one first damping plate-second damping plate pair. Self-tests may also be performed with symmetric actuation using one electrode pair on damping plates on the left side of the longitudinal symmetry axis (LSA), and one electrode on the right side of the longitudinal symmetry axis.
In other words, a method for performing a self-test in an accelerometer described in this disclosure may comprise applying an actuation force to the rotor in the first sensor by applying a test voltage to damping plates with electrically conducting electrodes, and reading a test response signal with a capacitive measurement from the rotor and stator electrodes.
BRIEF DESCRIPTION OF THE DRAWINGS
In the following the disclosure will be described in greater detail by means of preferred embodiments with reference to the accompanying drawings, in which
FIG. 1
illustrates a first sensor in a capacitive accelerometer.
FIG. 2
FIG. 1
illustrates a part of the first sensor and the accelerometer package in the cross-section A-A from .
FIG. 3
illustrates a first example of areal overlap between first and second damping plates.
FIG. 4
illustrates a second example of areal overlap between first and second damping plates.
FIGS. 5-8
illustrate embodiments where the accelerometer also includes second and third sensors.
FIG. 9
illustrates a method described in this disclosure. | |
The Sunyaev-Zeldovich (SZ) effect is a spectral distortion in the Cosmic Microwave Background (CMB), due to up-scattering of CMB photons by high energy electrons in clusters of galaxies or any cosmic structure. The Planck satellite mission has measured the spectral distortion with great sensitivity and has produced a full-sky SZ (y) map, which can be used to trace the large-scale structure of the Universe.In this dissertation, I construct the average SZ (y) profile of ∼ 65,000 Luminous Red Galaxies (LRGs) from the Sloan Digital Sky Survey Data Release 7 (SDSS/DR7) using the Planck y map and compare the measured profile with predictions from the cosmo-OWLS suite of cosmological hydrodynamical simulations. This comparison agrees well for models that include feedback from active galactic nuclei (AGN feedback).In addition, I search for the SZ signal due to gas filaments between ∼260,000 pairs of LRGs taken from the Sloan Digital Sky Survey Data Release 12 (SDSS/DR12), lying between 6-10 h −1 Mpc of each other in the tangential direction and within 6h −1 Mpc in the radial direction. I find a statistically significant SZ signal between the LRG pairs. This is the first detection of gas plausibly located in filaments, expected to exist in the large-scale structure of the universe. I compare this result with the BAHAMAS suite of cosmological hydrodynamical simulations and find that it predicts a slightly lower, but marginally consistent result.As an extension of my MSc. thesis work, I study CMB polarization. The B-mode component of CMB polarization is an important observable to test the theory of inflation in the early universe. However, foreground emissions in our own galaxy dominates the B-mode signal and therefore multi-frequency observations will be required to separate any CMB signal from the foreground emission. I assess the value of adding a new low-frequency channel at 10 GHz for the foreground removal problem by simulating realistic experimental data. I find that such a channel can greatly improve our determination of the synchrotron component which, in turn, significantly improves the reliability of the CMB separation.
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Master's Student Supervision (2010 - 2020)
In this MS.c. thesis, we demonstrate a method for estimating the expansion history of the universe using the hydrogen intensity map from the Canadian Hydrogen Intensity Mapping Experiment (CHIME), which will be generated in the near future. This map will be in angular and redshift space, where redshift of the hydrogen due to the expansion serves as a time variable. The expansion history, dependent on cosmological parameters via the Einstein equations, determines the distance away from us in units of a grid comoving with the expansion at which light of each redshift was emitted. We use knowledge of the fixed comoving distance, approximately 150 megaparsecs, that baryon acoustic oscillations, or primordial sound waves, traveled away from the centers of matter perturbations, where there is a corresponding peak in the matter correlation function subject to uncertainty of the initial quantum mechanical fluctuations. We explain the method by which we fit the correlation function to a model for expansion determined by the equation of state of dark energy, to constrain this parameter. We test the method using a three-dimensional realization of the theoretical matter power spectrum calculated from CAMB (Code for Anisotropies in the Microwave Background), providing an estimate of constraints obtained from a small redshift region spanning one sound horizon diameter in redshift space assuming a constant equation of state of dark energy and fixed values of the other cosmological parameters. We explain how to generalize this method to a more complete analysis.
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The Canadian Hydrogen Intensity Mapping Experiment (CHIME) is a transit interferometer located at the Dominion Radio Astrophysical Observatory in Penticton, BC. It is designed to map large- scale structure in the universe by observing 21 cm emission from the hyperfine transition of neutral hydrogen between redshifts 0.8 and 2.5. CHIME will perform the largest volume survey of the universe yet attempted and will characterize the BAO scale and expansion history of the universe with unprecedented precision in this redshift range. CHIME achieved first light in the fall of 2017 and instrument commissioning is underway. In this work I present sensitivity forecasts and derive constraints on cosmological parameters given CHIME’s nominal survey. The broad redshift range of the observations will enable tight constraints to be placed on the Hubble constant H0 , independent of CMB or local recession velocity measurements. Precision measurements of this epoch will shed new light on the tension between direct measurements of the Hubble constant vs. those inferred from high-redshift observations, notably the CMB anisotropy. CHIME measurements together with a prior on the baryon density from measurements of deuterium abundance are enough to place constraints on H0 at the 0.5% level assuming a flat ΛCDM model, with uncertainty increasing to ∼ 1% if curvature is allowed to vary, or up to ∼ 3% for a dark energy equation of state with w/= −1. Including priors from CMB measurements, in the scenario where the datasets are consistent, narrows these uncertainties further, most significantly in the model where w is a free parameter.
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The polarization of Cosmic Microwave Background can help us probe theearly universe. The polarization pattern can be classified into E-mode and B-mode. The B-mode polarization is a smoking gun of cosmological inflation.PIXIE is an in-proposal space telescope observing CMB polarization. Itis extremely powerful to extract CMB polarization signal from foregroundcontamination. The second chapter of this thesis summarizes my work onoptimizing the optical system of PIXIE. I run a Monte-Carlo Markov Chainfor the instrument parameters to maximize the value ”Good” which judgesthe behavior of the instrument. For the optimized instrument, with all kindsof noises from inside instrument and wrong polarization taken into account,good rays from the sky make up of 15.27% of all the rays received by thedetector. The instrument has a 1.1° top-hat beam response.The third chapter summarizes my work on studying the potential con-tamination in the reconstructed y map by doing cross-correlation betweentSZ signal and weak lensing. The weak lensing data is the convergence mapfrom the Red Sequence Cluster Lensing Survey. I reconstruct the tSZ mapwith a Needlet Internal Linear Combination method with 6 HFI sky mapsmade by Planck satellite. The reconstructed cross correlation is consistentwith Planck NILC SZ map. I take Cosmic Infrared Background (CIB) andgalactic dust as two potential source of contamination in the reconstructedmap. I find that κ × CIB contributes (5.8 ± 4.6)% in my reconstructed NILCy map for 500
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The following document describes pursued studies to understand the properties of radio frequency interference (RFI) which affects the quality of the data of the Canadian Hydrogen Intensity Mapping Experiment Pathfinder at the Dominion Radio Astronomy Observatory in Penticton, British Columbia. The Canadian Hydrogen Intensity Mapping Experiment is a challenging project aimed to trace large scale structure by observing the 21cm emission line of neutral hydrogen in the frequency spectrum 400-800MHz to research the nature of Dark Energy.RFI is terrestrial signal caused by radio bands, TV stations, satellites etc. that produces unwanted disturbances in the frequency spectrum which adds power to the data. It represents a challenge to measure faint sources in the sky and we seek ways to identify it based on its statistical properties such as non-Gaussianity.We have designed algorithms that aim to identify and flag RFI in our data. Digital TV bands cause permanent corruption in the affected frequency bins and account for a 19% loss of bandwidth.The 5 sigma threshold cut searches for time-varying RFI in each frequency bin. Outliers above 5 standard deviations are iteratively flagged but not all of the occurring RFI were recognized due to non-Gaussianity.The median absolute deviation cut is a robust statistical method that uses sky data only. Identification of short-lived and long-lived RFI occurrences originating mainly from the sky has been successful.A correlation coefficient algorithm uses a combination of a reference RFI antenna sensitive to the horizon and a sky antenna to find correlated signals that are significantly above expected thermal noise of the radiometer while disregarding correlation due to sky signal. RFI at the horizon is well recognized by this method.
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The fluctuations in the cosmic microwave background(CMB) contain a lot of information on the history and composition of our universe. In particular, the rich detail about our early universe is included in the angular power spectra of the CMB fluctuations, which constrains the cosmological parameters in current models of the universe. The latest cosmological data strongly support an inflationary Lambda CDM cosmology with a minimal six parameters to describe our universe. The next challenge in cosmology is to probe the physics of the inflationary period by looking for the signature of primordial gravitational waves in the polarized CMB. CMB polarization was generated at last scattering by scalar and tensor perturbations in the primordial fluid. The tensor perturbations are produced by the stretching of space-time by gravitational wave fluctuations, while scalar perturbations are produced by density fluctuations in the primordial fluid. The ratio of the tensor to scalar perturbation amplitude, r, is a key tracer of the physics of the inflationary epoch, which is deeply connected to the energy scale of inflation in a standard inflationary model. A local quadrupole anisotropy in the radiation field at the time of decoupling causes the linear polarization in CMB through Thomson scattering by electrons. The CMB polarization can be decomposed into two rotationally invariant quantities, called E and B. The CMB B-mode is a direct tracer of the tensor perturbations caused by gravitational waves in the inflationary period of the universe. Thus, the detection of B-mode has currently been dubbed the ''smoking gun'' of inflation. However, the galactic foreground emissions also have much stronger E- and B-modes polarization. We intend to produce half-sky maps of total intensity and linear polarization at 10 GHz. This data would probe galactic synchrotron emission and also can help constrain the so-called anomalous emission. Therefore, the maps can be used with other surveys such as WMAP and Planck to subtract galactic foreground emissions and obtain more precise CMB data. In addition, the data will give us information about galactic emission components such as synchrotron, free-free, thermal dust and anomalous emission in the microwave range.
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Program Affiliations
Department(s)
If this is your researcher profile you can log in to the Faculty & Staff portal to update your details and provide recruitment preferences. | https://www.grad.ubc.ca/researcher/13452-hinshaw |
2020-5-18 · Nickel-mining companies in Indonesia have pitched the government to allow them to dump their waste, or tailings, into the sea. The country is the world''s biggest producer of nickel, one of the ...
2021-12-22 · The Kolosori Nickel Project is 80% owned by Pacific Nickel, with the balance 20% held by landowners. Based on independent scoping study for the development, the project will be shallow open pit mining operation and eliminates the need for processing or tailings dams.
2022-1-4 · Kambalda district explorer Lunnon Metals (ASX: LM8) reports hitting 3.54% nickel in the Warren shoot, part of the nickel mineralisation that supported the old Foster mine.. The intersection, over a length of 8.72m, is significant because Warren, along with the Baker target, have been identified by Lunnon as high priority targets.
2021-12-6 · Its nickel mining operation, Nickel West, is located in Western Australia, and BHP is continuing to expand the nickel business. The company produced 89,000 tons of nickel during its fiscal year ending in June 2021, selling over 85% of its nickel to the EV battery industry .
2020-9-11 · With demand expected to increase from 2.2 million metric tons to somewhere in the range of 3.5 million to 4.0 million metric tons by 2030, the nickel market could become constrained. As per recent media attention, when Tesla''s …
2021-12-25 · Nickel production in the Philippines is set to expand by 3% to 355kt in 2019 and then rise to 381.4kt by 2023. This will be supported by the commencement of the Acoje and Mindoro projects, which have a combined nickel production capacity of 38kt and are expected to start operations in 2021 and 2023, respectively.
2020-9-11 · With demand expected to increase from 2.2 million metric tons to somewhere in the range of 3.5 million to 4.0 million metric tons by 2030, the …
2021-12-31 · SHANGHAI, Dec 21 (SMM) – CATARC Co. recently released the "2021 Energy-saving and New Energy Vehicle Development Report." Bao Wenjun, head of market analysis for metals and mining at BHP Billiton, said at the press conference that "in the next ten years, the demand for primary nickel is expected to increase by 1.3 million mt.
2021-10-14 · emphasise, any mining companies out there, please mine more nickel. Okay. Wherever you are in the world, please mine more nickel and don''t wait for nickel to go back to some long —some high point that you experienced some five years ago, whatever. Go for efficiency, obviously environmentally friendly nickel mining at high volume.
2021-12-6 · The Pala''wan tribe and farmers in this southernmost tip of Palawan island have relied on the mountain for generations. It is also here, in the 1970s, when miners came and dug up the earth to help sustain the nickel needs of the world. Now ore reserves in Rio Tuba Nickel Mining Corp.''s 990-hectare site will soon be depleted.
2021-6-23 · Auroch Minerals (ASX: AOU) has confirmed that it will drill deep under a historically producing nickel mine in a few weeks'' time. AOU will be chasing extensions to the existing nickel mineralisation – 3,000m of drilling will take place – large, high grade nickel intercepts should be positively received by the market.
2021-7-15 · Nickel Mining includes flash and electric smelting methods for the production of nickel. ... Smelting a nickel sulfide flotation deliberate needs an MgO echelon of 6% otherwise the warmth at which the smelting will be scuttle at will be too towering and guide to superior operating prices. After producing the nickel matte, auxiliary processing ...
2021-12-8 · Subscribe. Nickel Mines (NIC) is proceeding with the 70 per cent acquisition of the Oracle Nickel Project in Indonesia. NIC has signed a definitive deal with Shanghai Decent to jointly develop the project, which comprises four rotary kiln electric furnace lines and associated facilities. The buy is said to cost a total of US$525 million (A$735 ...
2020-10-6 · clipboard. Electric vehicle trailblazer Tesla could need up to 1.15 million tonnes of nickel a year — almost 50 per cent of current global supply — by 2030 to meet ambitious production targets. Tesla is jumping into cathode and …
2021-12-6 · The International Energy Agency estimates surging demand for nickel (up 441 per cent), lithium (659 per cent) and cobalt (413 per cent) from 2020 to 2030, assuming governments make good on their ...
2020-7-24 · Nickel mining has been associated with environmental havoc across the globe. The high temperatures needed for melting, the amount of dirty liquid byproducts like slag, and carcinogens in the air ...
2021-8-4 · A $57 billion gap separates the top 3 from the rest of the group. In fourth place comes Glencore ($55B) with its mixed operations of trading and mining metals, agricultural products, and oil and gas.. The automotive industry is a big …
2021-7-5 · Stay Updated on Nickel Mining Stocks with WALLSTNOW. Nickel production is an important resource to maintain our lives today and prepare for the future. It has an impact on so many aspects of our lives. From the latest biotech development to battling aggressive cancers to even battery metals in our smartwatches, we need nickel.
The country needs Minnesota. Many of the metals the U.S. needs are found in Minnesota. In fact, the deposit contains 34% of U.S. copper reserves, 95% of U.S. nickel reserves, 88% of U.S. cobalt reserves and 75% of U.S. platinum-group resources. 4, 5. The Twin Metals project targets minerals in one area of the Duluth Complex called the Maturi ...
The limited availability of mining locations also creates a highly dependent market with the few mining countries. Substitutes can have a significant impact on the prices of nickel. During the 2007 crisis low grade nickel was used to produce so-called pig iron steel, which is of lower quality but much cheaper.
2021-6-2 · Poseidon Nickel stock opened the day at A$0.11 after a previous close of A$0.11. The latest price was A$0.11 (25 minute delay). Poseidon Nickel is listed on the Australian Securities Exchange (ASX) and has a trailing 12-month revenue of around AUD₽738,000. All prices are listed in Australian Dollars.
2021-12-21 · An alternative approach is to identify and buy nickel mining stocks, and other nickel stocks that give exposure to various parts of the sector. This means investors can still benefit from the booming nickel market but do so by holding a position in stocks that are an easier to manage and more cost-effective asset group.
2021-7-30 · If Tesla did partner with another nickel mining company, and that mining company happened to be one that Nova Royalty owns the royalties for, that could be a big deal for investors. On the flip side, the natural resources sector is known for being volatile, and there are always pros and cons with any type of investment.
2021-12-23 · From mining natural graphite to manufacturing battery anodes, China dominates every stage of the graphite supply chain. For example, in 2020, 59% of global natural graphite production came from China. Mozambique, the second-largest producer, churned out 120,000 tonnes —just one-fifth of Chinese production. Country.
2021-12-3 · EV Nickel, classified as a Tier 2 issuer, is a Canadian nickel exploration company, focused on the Shaw Dome area, south of Timmins, Ontario. The Shaw Dome area is home to its Langmuir project, which includes W4, the basis of a 2010 historical estimate of 677,000 tonnes at 1% nickel for approximately 15 million pounds of Class 1 nickel.
2021-12-6 · ESG in nickel mining: Producing sustainable nickel As the world moves toward green energy, the need for lithium-ion batteries for use in EVs and energy storage systems will only continue to increase.
Nickel element extraction, mining technique – flash ... | https://autobanden-bleiswijk.nl/2021-08-39875.html |
Q:
Select organizations that their income represent around 60% of the total income SQL Server2008
In this data warehouse, we have organization which composed of multiple Organizations,
I have [FactFinance] table which has information about the income of each organization.
I have the following query in data warehouse which select the (Organization Name) from the [organization dimension table] and its (Total Income Amount) from [FactFinance table] and what its (Total Income Amount) represent as a percentage from the total income amount of the whole organization
select [DimOrganization].[OrganizationName] , SUM([Amount])as TotalAmountIncome , SUM([FactFinance].[Amount])/(select sum([FactFinance].[Amount])
from [FactFinance] ) PercentageOfTotalSales
from [FactFinance] , [DimOrganization]
Where [FactFinance].[OrganizationKey]= [DimOrganization].[OrganizationKey]
group by ([DimOrganization].[OrganizationName])
order by SUM([Amount]) desc
The Result is the following table:
+--------------------+-------------------+------------------------+
| OrganizationName | TotalAmountIncome | PercentageOfTotalSales |
+--------------------+-------------------+------------------------+
| Canadian Division | 292174782.72 | 0.215049383184007 |
| Southeast Division | 279284663.6 | 0.205561869784944 |
| Southwest Division | 232365970.6 | 0.171028307731715 |
| Central Division | 149032081.6 | 0.109692071726198 |
| Northwest Division | 138922888.8 | 0.102251403315702 |
| Northeast Division | 134003346.4 | 0.0986304728958399 |
| France | 66963799.96 | 0.0492873606099529 |
| Australia | 35553074.99 | 0.0261681270906303 |
| Germany | 30339804.03 | 0.0223310036610101 |
+--------------------+-------------------+------------------------+
I want to modify this query in order to select only the organizations that have the maximum income and represent almost 60% of the total income of the whole organization.
if I calculate the percentage in the first three rows, which are the organizations that have the maximum income
+------------------------+
| PercentageOfTotalSales |
+------------------------+
| 0.215049383 |
| 0.20556187 |
| 0.171028308 |
+------------------------+
the result will be: 0.591639561
it is almost 60%
so the result must be the first three rows (which means almost 60% of the total income of the whole organization?)
I tried the following query, but it gives me error (Invalid column name 'PercentageOfTotalSales').
AND SUM(PercentageOfTotalSales) >= 0.60
group by ([DimOrganization].[OrganizationName])
order by SUM([Amount]) desc
I tried different ways, but it always gives me errors.
can I get any advice?
A:
you can use Running Total query and use your returned table as sub query as the following:
SELECT [DimOrganization].OrganizationName , Value from (
SELECT x, Value, (SELECT SUM(Value) FROM (select top 10 [FactFinance].[OrganizationKey] as x,SUM([Amount]) as [Amount] , SUM([Amount]) /
(select sum([Amount]) from [FactFinance])as Value
FROM [FactFinance] group by([FactFinance].[OrganizationKey]) order by SUM([Amount]) desc) T2
WHERE T1.value <= T2.value) AS RunningTotal
FROM (select top 10 [FactFinance].[OrganizationKey] as x,SUM([FactFinance].[Amount])as [Amount] , SUM([FactFinance].[Amount])/(select sum([FactFinance].[Amount])
from [FactFinance])as Value
from [FactFinance] group by([FactFinance].[OrganizationKey]) order by SUM([FactFinance].[Amount]) desc) T1 ) allTable , [DimOrganization] where allTable.x = [DimOrganization].OrganizationKey AND RunningTotal<0.6
| |
The pound abbreviated as "lb" is a unit of mass that is commonly used in the United States. But the International System of Units, or the metric system, defines the kilogram as a unit of mass. In addition, grams and tons often express weights in the metric system, as well. Use a calculator to convert the mass in pounds to the metric system units.
Things You'll Need
- Calculator
-
Multiply the weight in pounds by 0.4536 to convert it to kilograms. For example, 23 pounds will be converted to 23 x 0.4536 = 10.4328 kilograms.
-
Multiply the weight by 453.5924 to convert pounds to grams. For instance, the weight of 2.3 pounds corresponds to 2.3 x 453.5924 = 1,043.2625 grams.
-
Multiply the weight by 0.00045359 to convert pounds to tons. For instance, the weight of 5,675 pounds is converted as to 5,675 x 0.00045359 = 2.5741 tons.
References
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Your Results:
The answer for each question is indicated by a .
1
Resources are adequate, but demand varies widely over the life of the project. Delaying noncritical activities to lower peak demand on resources is known as resource
A)
Shifting
B)
Effectiveness
C)
Manipulating
D)
Smoothing
E)
Allocation
2
Which of the following is NOT a potential consequence of failing to identify limited resources before project implementation?
A)
Activity delays
B)
Project delays
C)
Difficulty in taking quick ive action
D)
Increase costs
E)
Scope creep
3
When developing a new software package, logically, the software must be designed before the code is written, and the code must be written before it is tested. These activities are dependent on each other by _________ constraints.
A)
Physical
B)
Technical
C)
Resource
D)
Schedule
E)
Time
4
Sam, the project engineer, has been scheduled to run the product system test at the same time he is to build a marketing prototype. This is an example of what type of resource constraint?
A)
Physical
B)
Technical
C)
People
D)
Equipment
E)
Time
5
Most of the scheduling methods available today require the project manager to classify the project as either _______ constrained or ______ constrained.
A)
Time, quality
B)
Quality, resource
C)
Cost, time
D)
Quality, cost
E)
Time, resource
6
In reviewing the status of her project with top management, Shirley was told that there are only two programmers that she can use for her project. Her project is classified as __________ constrained.
A)
Time
B)
Quality
C)
Cost
D)
Performance
E)
Resource
7
Technical constraints have been carefully considered when developing a project network. Which of the following is true at this point?
A)
Resources have been assigned to each activity so they are adequate to complete the project on time
B)
Activity 4 cannot be completed before activity 1
C)
The project completion date can be established
D)
The project is ready to be implemented
E)
All of these are true statements once technical constraints have been established
8
Resource leveling or smoothing can have all the following results on a project EXCEPT
A)
Lower peak resource demand
B)
Reduced resource need over the life of the project
C)
Reduced fluctuations in resource demand
D)
A longer project duration
E)
A more sensitive network
9
In a resource-constrained project, which of the following is most likely to be changed?
A)
The completion date
B)
The budget
C)
Project quality
D)
Resource levels
E)
Scope creep
10
In a resource-constrained project the second priority in assigning resources is usually given to activities with the
A)
Smallest duration
B)
Least slack
C)
Most slack
D)
Lowest identification number
E)
Highest cost
11
Tony has realized that two activities in his project cannot be done at the same time because not enough resources are available. Activity 3 is critical and has a duration of 5 days. Activity 4 has 2 days of slack and a duration of 2 days. How will he decide which activity should be scheduled first?
A)
The activity with the smallest duration
B)
The activity with the least slack
C)
The activity with the most slack
D)
The activity with the lowest identification number
E)
The activity with the highest cost
12
Splitting an activity can result in all of the following EXCEPT
A)
Less people needed to work on an activity
B)
Possible startup and shutdown costs
C)
A resource may being moved from one activity to another and then back again
D)
Activity work being placed on hold for a period of time until more resources are available
E)
A better project schedule
13
All of the following are benefits of scheduling resources before project implementation EXCEPT:
A)
It allows time for considering reasonable options if resource constraints do exist
B)
The project completion date can be established
C)
Work packages can be time-phased
D)
It allows managers to share resources with other project managers if it is requested without negatively impacting their project.
E)
It ensures low network sensitivity
14
These are all guidelines a project manager should consider when assigning project work EXCEPT
A)
Select people with compatible work habits and personalities
B)
Always assign the best people to the most difficult tasks
C)
When possible, team veterans up with new hires
D)
Select individuals with skillsets that complement each other
E)
Have people work together early so that they can become familiar with each other
15
Why is it necessary to have a time-phased budget baseline? | https://www.homeworksolving.com/scheduling-resources-and-costs-questions/ |
---
abstract: 'Bifurcation with symmetry is considered in the case of an isotropy subgroup with a two-dimensional fixed point subspace and non-zero quadratic terms. In general, there are one or three branches of solutions, and five qualitatively different phase portraits, provided that two non-degeneracy conditions are satisfied. Conditions are also derived to determine which of the five possible phase portraits occurs, given the coefficients of the quadratic terms. The results are applied to the problem of bifurcation with spherical symmetry, where there are six irreducible representations for which the subspace of solutions with cubic symmetry is two-dimensional. In each case, the number of solutions and their stability is found.'
author:
- |
P.C. Matthews,\
School of Mathematical Sciences,\
University of Nottingham, Nottingham NG7 2RD, UK\
[email protected]
title: 'Bifurcation in two-dimensional fixed point subspaces'
---
Introduction
============
The topic of bifurcation with symmetry has wide-ranging applications, including buckling of rods, convection patterns in fluids and the structure of tumours and embryos. In the physical context, a highly symmetric state becomes unstable as a control parameter is varied, leading to a state with reduced symmetry. If there is a high degree of symmetry, then the stability problem is degenerate, in the sense that several eigenvalues pass through zero simultaneously as the parameter is varied; the number of eigenvalues is equal to the dimension of one of the irreducible representations of the original symmetry group. This means that the dynamics in the neighbourhood of the bifurcation is governed by a number of coupled, nonlinear equations which in general cannot be solved.
This complicated multi-dimensional problem can be simplified by restricting attention to the flow-invariant fixed-point subspace of a subgroup of the original symmetry group. If this subspace is one-dimensional, then the problem reduces to a single differential equation, so that the usual methods of bifurcation theory can be applied, leading to a bifurcation of transcritical or pitchfork type. This is essentially the equivariant branching lemma (Vanderbauwhede 1980, Cicogna 1981, Golubitsky, Stewart and Schaeffer 1988): if the fixed-point subspace is one-dimensional, then a unique branch of solutions exists in the vicinity of the bifurcation. For example, in the problem of the buckling of a rod with square cross-section, solutions exist in which the rod buckles either parallel to two of the sides or diagonally. The equivariant branching lemma is known to generalize to the case where the dimension of the fixed-point subspace is odd, but it is in general untrue when the dimension is even.
In this paper, the case of a two-dimensional fixed-point subspace is considered, following on from earlier work. Mcleod and Sattinger (1973) studied this problem, and showed that there are one or three solution branches for generic values of the coefficients of the quadratic terms, corresponding to five different phase portraits; however they regarded the double zero eigenvalue as a degeneracy rather than a consequence of symmetry. Lauterbach (1992), Leblanc [*et al.*]{} (1994) and Lari-Lavassani [*et al.*]{} (1994) formulated the problem in the context of equivariant bifurcation theory and obtained specific bifurcation theorems. In section 2 below, the basic theory of the subject is recalled, together with a summary of some of the known bifurcation theorems. Section 3 gives specific conditions under which bifurcation can be guaranteed, in terms of the coefficients of the quadratic terms, and also gives the relationship between these coefficients and the five possible phase portraits. In section 4 these results are applied to the problem of bifurcation from spherical symmetry, $O(3)$, in the fixed point subspace of the symmetry group of the cube, which is two-dimensional for six of the irreducible representations of $O(3)$.
Branching in two dimensions {#sec:2}
===========================
There is no simple generalization of the equivariant branching lemma (EBL) to the case of a two-dimensional fixed point subspace. In this section, some of the key definitions of the subject of bifurcation with symmetry are recalled and some of the known results are summarised.
Near a multiple bifurcation point, the eigenfunctions form the basis of a vector space $V$. The symmetry group $G$ acts on $V$ by multiplying points in $V$ by matrices that form a representation of $G$. In most cases this representation is irreducible, meaning that there is no proper $G$-invariant subspace of $V$. The symmetry of a point $v$ in $V$ is described by its isotropy subgroup, defined by $\{g \in G: g v = v \}$.
For any subgroup $H \subset G$, the fixed-point subspace of $H$ is $$\mbox{Fix}(H) = \{ v \in V : h v = v \mbox{ for all } h \in H\}.$$ Fixed-point subspaces are important because they are invariant subspaces: if an initial condition lies in $\mbox{Fix}(H)$ then the system remains in $\mbox{Fix}(H)$ for all time.
The normalizer $N(H)$ is defined by $$N(H) = \{g \in G : g^{-1} H g = H\}.$$ This is the largest subgroup of $G$ in which $H$ is normal. Equivalently, this is the subgroup of $G$ which maps $\mbox{Fix}(H)$ to itself: $$N(H) = \{g\in G : g y \in \mbox{Fix}(H)
\mbox{ for all } y \in \mbox{Fix}(H)\}.\label{neq}$$ Clearly $H \subset N(H)$, and if $N(H)=H$ then there is no symmetry within $\mbox{Fix}(H)$, since all elements of $H$ act as the identity in $\mbox{Fix}(H)$. In general, the symmetry group acting on $\mbox{Fix}(H)$ is the quotient group $N(H)/H$.
Henceforth it will be assumed that the bifurcation problem with a symmetry group $G$ satisfies the following conditions.
1. $G$ is a compact Lie group acting absolutely irreducibly on a vector space $V$. This implies that $\mbox{Fix}(G) = 0$ or $\mbox{Fix}(G) = V$. The latter case only holds for the trivial one-dimensional representation of $G$, so we may assume that $\mbox{Fix}(G) = 0$.
2. The function $f: R \times V \rightarrow V$ is smooth and $G$-equivariant, i.e. $f(\lambda, g v) = g f(\lambda,v)$ for all $g
\in G$, $v\in V$. This implies that $f(\lambda, 0) = g f(\lambda,0)$, and hence $f(\lambda, 0) \in \mbox{Fix}(G)$, so $f(\lambda,0) = 0$. Since the action of $G$ is absolutely irreducible, the linearization of $f$ is a scalar multiple of the identity, $h(\lambda) I$.
3. $h(0)=0$, and $h'(0)\ne 0 $, i.e. there is a stationary bifurcation at $\lambda=0$ and the eigenvalue passes transversely through zero as $\lambda$ passes through zero.
4. $H$ is an isotropy subgroup of $G$ with $\mbox{Dim(Fix}(H)) = 2$.
5. The quadratic terms in the Taylor expansion of $f$ do not all vanish in $\mbox{Fix}(H)$.
Note that the first three conditions are the standard ones for the application of the EBL (Ihrig and Golubitsky 1984, Golubitsky, Stewart and Schaeffer 1988, Chossat and Lauterbach 2000).
The equations $f(\lambda, v) = 0$ within $\mbox{Fix}(H)$ can then be scaled, for small $\lambda$, by $\lambda = \epsilon \mu/h'(0)$, $v =
\epsilon x$, to give, as $\epsilon \rightarrow 0$, $$\begin{aligned}
0 & = & \mu x + a x^2 + b x y + c y^2, \label{e1}\\
0 & = & \mu y + p x^2 + q x y + r y^2, \label{e2}\end{aligned}$$ involving six constants $a$, $b$, $c$, $p$, $q$, $r$; from the last of the above conditions, not all of these are zero.
These two equations were discussed by Mcleod and Sattinger (1973), who showed that for generic values of the six constants there exist either one or three solutions. However, a general bifurcation theorem cannot be deduced from this, because in the context of equivariant bifurcation theory the six constants are not independent. There are two types of constraints on these coefficients (see, for example, Stewart and Dias 2000). The first type of constraint arises from normaliser symmetries which act on $\mbox{Fix}(H)$ as shown in (\[neq\]); for example, there may be a normaliser symmetry acting as a reflection $y\to -y$, in which case $p=b=r=0$. Secondly, there may be other constraints arising from equivariance with respect to the original symmetry group $G$; these are sometimes referred to as ‘hidden’ symmetries.
An example to illustrate this point is the symmetry group of the tetrahedron including reflections, which is isomorphic to the symmetric group $S_4$ and also the group $O$ of rotations of the cube. In the natural three-dimensional irreducible representation, the group is generated by permutations of the three Cartesian coordinate axes and a sign change of any two, and the bifurcation equations consistent with these symmetries to quadratic order are $$0 = \mu x + y z = \mu y + x z = \mu z + x y .$$ Note that there is only one equivariant quadratic term; this is a feature common to many bifurcation problems, including the cases of $S_N$ symmetry and $O(3)$ symmetry, although there are also examples where this is not the case, such as icosahedral symmetry (Hoyle 2003). The fixed point subspace of the symmetry group $Z_2$ generated by $y \leftrightarrow z$ is two-dimensional and the bifurcation equations reduce to $$0 = \mu x + y^2 = \mu y + x y. \label{tet2}$$ The normaliser is $Z_2 \times Z_2$, including the element $(y,z)\to
(-y,-z)$, and so the normaliser symmetries force $p=b=r=0$ in (\[tet2\]), but we also have $a=0$ and $c=q$, arising from the original symmetry group. Furthermore, there are only two non-zero solutions to (\[tet2\]), $x=-\mu$, $y=\pm \mu$, not one or three as expected from (\[e1\], \[e2\]). (In fact, in this example, a third solution in which $y=z=0$ does exist when cubic terms are included, as required by the EBL since this subspace is one-dimensional.)
Some rigorous results on bifurcation in two-dimensional subspaces are as follows. A result of Lauterbach (1992) (Theorem 1.2), obtained using degree theory, is that at least one non-zero solution exists if, in addition to the five conditions above, $$Q^{-1}(0) = 0, \quad \mbox{i.e.} \quad Q = 0 { \Rightarrow }x=y=0,
\label{laut}$$ where $Q$ represents the quadratic terms in (\[e1\], \[e2\]).
Lauterbach’s condition (\[laut\]) is sufficient but not necessary. Leblanc [*et al.*]{} (1994) showed (Theorem 2.1) that in the case of gradient dynamics, when $Q$ can be written as the gradient of a scalar quantity, a branch of solutions to the truncated problem (\[e1\], \[e2\]) always exists. Furthermore (Theorem 3.2), they showed that a smooth branch of solutions of the non-truncated problem exists if either $Q^{-1}(0) \ne 0$ or a fourth-order polynomial in the six coefficients $a\ldots r$ is non-zero.
Hence, by combining the results of Lauterbach (1992) and Leblanc [*et al.*]{} (1994), bifurcation to non-zero solutions always occurs occurs in the case of gradient dynamics, since both the cases $Q^{-1}(0) = 0$ and $Q^{-1}(0) \ne 0$ are covered.
Phase portraits
===============
In this section, solutions to the system (\[e1\], \[e2\]) are considered in more detail. First, the condition under which there are one or three roots is derived.
Multiplying (\[e1\]) by $y$, (\[e2\]) by $x$ and subtracting yields the cubic equation $$0 = c z^3 + (b-r)z^2 + (a-q) z - p \label{cubic}$$ for $z=y/x$, which generically has one or three solutions. The condition for the existence of three roots depends on the quantity $$P \equiv 27 c^2 p^2-18 c p (b-r)(q-a)-4 p (b-r)^3-4 c (q-a)^3-(q-a)^2
(b-r)^2 .
\label{3roots}$$ There are three roots if $P < 0$, one root if $P > 0$, and a double root if $P = 0$. An alternative derivation of the existence of one or three solutions, employing the implicit function theorem, is given by Mcleod and Sattinger (1973). Given a solution for $z = y/x$, substitution into (\[e1\]) gives either the trivial solution $x=0$ or $x = -\mu/(a+bz+cz^2)$. This fails to give a finite solution if the denominator is zero, and it is straightforward to show that this occurs if the quantity $$R \equiv (a r-p c)^2 + (c q-b r) (a q-b p) \label{res}$$ is zero. $R$ is the resultant of the two quadratic polynomials appearing in (\[e1\], \[e2\]). It is a well known result of algebraic geometry that these two homogeneous polynomials have a non-zero solution if and only if the resultant is zero (see, for example, Cox, Little and O’Shea, 1998). Thus the non-degeneracy condition $R\ne 0$ is exactly the condition (\[laut\]), $Q^{-1}(0) = 0$. The degenerate case $R = 0$ corresponds to a solution at infinity.
The non-degeneracy conditions giving one or three solutions are therefore $P\ne 0$ and $R\ne 0$. These conditions have not been given explicitly in earlier work, although Leblanc [*et al.*]{} (1994) give $P$ in the special case of gradient dynamics.
It is also of interest to consider the two-dimensional phase portraits within $\mbox{Fix}(H)$, by considering the time dependent form of (\[e1\], \[e2\]): $$\begin{aligned}
\dot x & = & \mu x + a x^2 + b x y + c y^2, \label{et1}\\
\dot y & = & \mu y + p x^2 + q x y + r y^2 \label{et2}. \end{aligned}$$ In this system, the straight line passing through the origin and any fixed point is an invariant line, since if $z=y/x$ satisfies (\[cubic\]) then $\dot z = (\dot y x - \dot x y)/x^2$ which is zero, since this is proportional to the same cubic appearing in (\[cubic\]). This observation forces all fixed points to be saddles or nodes, and prohibits the existence of any periodic orbits. The invariance of these lines is a consequence of the truncation, and is broken at higher order.
Stability of the fixed points is determined by the eigenvalues of the Jacobian $$J =\pmatrix{{\mu + 2 a x + b y} & b x + 2 c y \cr
2 p x + q y & \mu + 2 r y + q x} . \label{jac}$$ One eigenvalue is $-\mu$, corresponding to the eigenvector lying along the invariant line. In general, there are five possible different types of phase portrait (McLeod and Sattinger 1973). Which of these occurs is determined by the values of $P$ and $R$ and a third quantity, $$I = a q + b r - b p - c q .$$ The following result gives the conditions on $P$, $R$ and $I$ that determine the phase portrait.
[**Theorem**]{}\
In the system (\[et1\], \[et2\]),\
(a) If $P > 0$ and $R > 0$ there is one fixed point, which is a saddle point.\
(b) If $P > 0$ and $R < 0$ there is one fixed point, which is a node.\
(c) If $P < 0$ and $R > 0$ there are three fixed points, one node and two saddles.\
(d) If $P < 0$, $R < 0$ and $I > 0$ there are three fixed points, two nodes and one saddle.\
(e) If $P < 0$, $R < 0$ and $I < 0$ there are three fixed points, all of which are saddles.
[**Proof**]{}\
Note first that $P$, $R$ and $I$ are invariant under rotation of coordinate axes. This can be verified by determining that under an infinitesimal rotation through an angle $\theta$, $$\frac{d a}{d\theta} = b + p , \quad \frac{d b}{d\theta} = q+2c-2a, \quad
\frac{d c}{d\theta} = r - b ,$$ $$\frac{d p}{d\theta} = q - a , \quad \frac{d q}{d\theta} = 2r-2p-b , \quad
\frac{d r}{d\theta} = -c-q .$$ To check that $I$ is invariant, we expand $$\frac{d I}{d\theta} = q (b+p)+(r-p)(q+2c-2a)-q (r - b)-b(q - a)
+(a-c)(2r-2p-b ) - b(c+q)$$ and verify that this quantity is zero, and similarly for $P$ and $R$.
Exploiting the rotation invariance and the fact that there is always at least one non-zero fixed point for $P\ne 0$, $R\ne 0$, we can always rotate coordinates so that a fixed point lies on the $x$ axis with $x < 0$. After this rotation, it follows from (\[et2\]) that $p = 0$ and from (\[et1\]) that the fixed point is at $x=-\mu/a$. It can be assumed that $\mu > 0$, because the case $\mu < 0$ is equivalent under a sign change of $x$, $y$ and $t$, and so $a > 0$. The eigenvalues of the fixed point at $x=-\mu/a$, $y=0$ are, from (\[jac\]), $-\mu $ and $\mu (1-q/a)$, so the fixed point is a saddle point if $a>q$ and a node if $a<q$. Consider now the five cases above in turn.
\(a) If $P > 0$ and $R > 0$, then after rotating so that $p=0$ and $a>0$, $P>0$ gives $$4c (a-q ) > (b-r)^2 \label{p01}$$ so that either $c>0$ and $a>q$, or $c<0$ and $a<q$. The condition $R>0$ becomes $$a r^2 + c q^2 - brq >0,$$ which can be written as $$(a-q)r^2 + c q^2 - rq(b-r) > 0.$$ Now if $c<0$ and $a<q$, this quadratic function of $r$ must have real roots for the inequality to be satisfied, so $(b-r)^2 > 4 (a-q) c$, which contradicts (\[p01\]). Thus the only possibility is $c>0$ and $a>q$, so the fixed point is a saddle point. The phase portrait in this case is shown in figure 1(a).
\(b) If $P > 0$ and $R < 0$ then (\[p01\]) holds and $R<0$ can be written as $$(a-q)r^2 + c q^2 - rq(b-r) < 0.$$ Using the same argument as in the previous case, if $a>q$ and $c > 0$ the inequality can only be satisfied if $(b-r)^2 > 4 (a-q) c$, contradicting (\[p01\]). Therefore $c<0$ and $a<q$, and the fixed point is a node, as shown in figure 1(b).
\(c) If $P < 0$ and $R > 0$ there are three fixed points. Using the result of Mcleod and Sattinger (1973) that at least one of these is a saddle point, a rotation of coordinates can be carried out so that $p=0$ and a saddle point lies at $x=-\mu/a$, $y=0$; hence $a>q$. The quadratic equations for the coordinates $(x_1, y_1)$ and $(x_2, y_2)$ at the other fixed points, obtained from (\[e1\]) and (\[e2\]), are $$\begin{aligned}
(a r^2 + c q^2 - brq)x^2 + (r^2-br+2cq)\mu x + c\mu^2 & = & 0 \label{x2eq},\\
(a r^2 + c q^2 - brq)y^2 + (2ar-rq-bq)\mu y + (a-q)\mu^2 & = & 0 \label{y2eq}.\end{aligned}$$ Since $R>0$, the leading term in each quadratic is positive, and so from (\[y2eq\]), $y_1 y_2 > 0$. Thus all three fixed points lie in the same half plane, $y\geq 0$ or $y \leq 0$. In the case that all lie in the upper half plane, consider an anticlockwise rotation that brings the next fixed point onto the negative axis. After this rotation, the two points not on the $x$ axis have $y_1 y_2 < 0$, so $a<q$ and so the point on the axis must be a node. After a further rotation so that the third fixed point lies on the $x$ axis, both other fixed points have $y < 0$, so $a>q$ and the point on the axis is a saddle. Hence for $P < 0$ and $R > 0$, there are three fixed point in the same half plane, and the middle of the three is a node while the other two are saddle points (figure 1(c)).
\(d) If $P < 0$, $R < 0$ and $I > 0$, then $4c(a-q)<(b-r)^2$ and $a^2 r^2 + (cq - br) aq <0$, so $cq-br$ and $aq$ must have opposite signs. Since $I>0$, $aq + br -cq > 0$ and so both $aq$ and $br -cq$ must be positive. Since $P<0$, there are three fixed points. After a rotation of coordinates, one lies on the $x$ axis and the other two satisfy (\[x2eq\], \[y2eq\]). At the other two fixed points, one eigenvalue is $-\mu$ and the other, from (\[jac\]), is $3\mu + (2a+q)x + (2r+b)y$. The sum of the ‘non-radial’ eigenvalues at these fixed points can be found using the sums of the roots obtained from (\[x2eq\], \[y2eq\]). The result is $q a \mu ( r^2 + b^2 -2br + 4 c q - 4a c ) /R$, which is negative. Thus, at least one of these fixed points must be a stable node. Given that one fixed point is a node, this point can be rotated onto the $x$ axis and an argument exactly analogous to that of case 3 can be followed, leading to the conclusions that the three fixed points lie in the same half plane, the middle one is a saddle point and the other two are nodes (figure 1(d)).
\(e) If $P < 0$, $R < 0$ and $I < 0$ then, as in case (d), $cq-br$ and $aq$ must have opposite signs. In this case $aq + br -cq < 0$, so $aq< 0$ and $br - cq < 0$. Hence $a^2 - a q > 0$ and so the fixed point on the $x$ axis is a saddle point. Thus in this case all three fixed points are saddles, as shown in figure 1(e).
[**Remarks**]{}
1. The five possible phase portraits are illustrated in figure 1, for $\mu > 0$. The case $\mu < 0$ is obtained by reversing all the arrows and rotating through $\pi$.
2. Stable fixed points can only occur in cases (b), (c) and (d). Of course, these stability assignments only apply within Fix$(H)$, and there are directions transverse to Fix$(H)$ which may be stable or unstable. In fact, it is generally the case that all solution branches obtained are unstable in the full system, since it can be shown that one eigenvalue is $-\mu$ but the sum of the eigenvalues is $n\mu$, where $n$ is the dimension of the representation (see, for example, Chossat [*et al.*]{} 1990).
3. As $P$ passes through zero there is a saddle-node bifurcation, leading to a transition from case (a) to case (c) or from case (b) to case (d). As $R$ passes through zero, a fixed point passes through infinity, giving transitions between cases (a) and (b), (c) and (d) or (c) and (e). There can be no direct transition between cases (d) and (e) because $I=0$ is incompatible with $R<0$.
4. In the case of gradient-like dynamics, there are additional constraints $b = 2p$ and $q = 2c$. Under these conditions it can easily be shown that $P>0 { \Rightarrow }R>0$ and $R < 0 { \Rightarrow }I < 0$, so that there are only three possible phase portraits, (a), (c) and (e).
0.9
Application to bifurcation with spherical symmetry {#sec:app}
==================================================
An interesting example of bifurcation with symmetry is the problem of bifurcation from an initial state with spherical symmetry. This problem has many physical applications and has been studied at length by Sattinger (1978, 1979), Ihrig and Golubitsky (1984), Chossat [*et al.*]{} (1990), and Matthews (2003). The irreducible representations have dimension $2l + 1$ and the eigenfunctions are the spherical harmonics of degree $l$. Of particular interest are patterns with the symmetry groups of rotations of the Platonic solids: the tetrahedron, $T$, with 12 elements, the cube / octahedron, $O$, with 24 elements, containing $T$, and the icosahedron / dodecahedron, $I$, with 60 elements, also containing $T$. When $l$ is odd, the quotient group $N(H)/H$ always includes the group $Z_2^C$, generated by point inversion through the origin, corresponding to a rotation through $\pi$ if $\mbox{Dim(Fix}(H)) =2$, so the quadratic terms are all forced to be zero by the normaliser symmetry. For even $l$, the isotropy subgroups are all of the form $H \oplus Z_2^C$, where $H$ is a subgroup of SO(3) and $\oplus$ indicates a direct product. The groups $O\oplus Z_2^C$ and $I\oplus Z_2^C$ are maximal isotropy subgroups, and satisfy the condition $N(H)=H$. The dimensions of their fixed-point subspaces are $[l/4] + [l/3] - l/2 + 1$ for $O\oplus Z_2^C$ and $[l/5] + [l/3] - l/2 + 1$ for $I\oplus Z_2^C$, where $[x]$ is the largest integer less than or equal to $x$.
The dynamics is gradient-like, so the following two existence results follow directly from the observation at the end of section 2, by determining the values of $l$ for which $\mbox{Dim(Fix}(H)) = 2$.
1. There exists at least one, but not more than three branches of solutions with isotropy $O\oplus Z_2^C$ for $l=12$, 16, 18, 20, 22, 26.
2. There exists at least one, but not more than three branches of solutions with isotropy $I\oplus Z_2^C$ for $l=30$, 36, 40, 42, 46, 48, 50, 52, 54, 56, 58, 62, 64, 68, 74.
Since the dynamics is gradient-like, the phase portraits within the two-dimensional subspace $\mbox{Fix}(H)$ may have any of the three forms shown in figure 1(a), (c) or (e) provided that the non-degeneracy conditions $P\ne 0$, $R\ne 0$ are satisfied. For the case $l=12$, $H = O\oplus Z_2^C$, the computation of the coefficients was carried out by Leblanc [*et al.*]{} (1994); the result is, after removing some common factors, $$a = - \frac{9913 \sqrt{8398}} {390}, \quad
c = \frac{73501\sqrt{8398}} {4940}, \quad
p = \frac{104\sqrt{5313}} {3}, \quad
r = -\frac{339119\sqrt{5313}} {4370},$$ with $b=2p$ and $q=2c$. Calculating the values of $P$, $R$ and $I$ shows that all three are negative. Hence there are three distinct branches of solutions with isotropy $O\oplus Z_2^C$ for $l=12$, and within this subspace, all three are saddle points.
A similar calculation was carried out for the other values of $l$ for which $\mbox{Dim(Fix}(O\oplus Z_2^C)) = 2$, using the computer algebra package Maple to do the cumbersome manipulations. First, the $2l+1$ equations for the amplitudes of the spherical harmonics $Y_l^m(\theta,\phi)$, $m=-l\ldots l$ are constructed using the fact that the quadratic coefficients are the Clebsch–Gordan coefficients (Sattinger, 1978). The subspace $\mbox{Fix}(D_4\oplus Z_2^C)$ of dimension $1 + [l/4]$ is found simply by restricting to those modes in which $m$ is a multiple of four. The subspace $\mbox{Fix}(O\oplus
Z_2^C)$ is then obtained from this by imposing invariance under a rotation of $\pi/2$. The results of these calculations are as follows. For $l=12$, $16$, $22$ and $26$, $P$, $R$ and $I$ are all negative, so there are three stationary solutions and each solution is a saddle point in $\mbox{Fix}(O\oplus Z_2^C)$, as in figure 1(e). For $l=18$, $P<0$ and $R>0$, so there are three solutions, one of which is a node and the other two are saddles (figure 1(c)). For $l=20$, $P>0$ and $R>0$, so there is only one solution, which is a saddle point.
References {#references .unnumbered}
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Chossat, P. and Lauterbach, R., 2000, [*Methods in Equivariant Bifurcations and Dynamical Systems*]{} (World Scientific).
Chossat, P., Lauterbach, R. and Melbourne, I., 1990, Steady-state bifurcation with O(3) symmetry. [*Arch. Rat. Mech. Anal.*]{} [**113**]{}, 313–376.
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Cox, D., Little, J. and O’Shea, D., 1998, [*Using Algebraic Geometry*]{} (Springer).
Golubitsky, M., Stewart, I. and Schaeffer, D.G., 1988, [*Singularities and Groups in Bifurcation Theory*]{} (Springer).
Hoyle, R.B., 2003, Shapes and cycles arising at the steady bifurcation with icosahedral symmetry. [*Physica*]{} D, submitted.
Ihrig, E. and Golubitsky, M., 1984, Pattern selection with O(3) symmetry. [*Physica*]{} [**13D**]{}, 1–33.
Lari-Lavassani, A., Langford, W.F. and Huseyin, K., 1994, Symmetry-breaking bifurcations on multidimensional fixed point subspaces. [*Dynamics and Stability of Systems*]{} [**9**]{}, 345–373.
Lauterbach, L., 1992, Spontaneous symmetry breaking in higher dimensional fixed point spaces [*ZAMP*]{} [**43**]{}, 430–448.
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Matthews, P.C., 2003, Transcritical bifurcation with $O(3)$ symmetry. [*Nonlinearity*]{}, in press.
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Sattinger, D., 1979, [*Group Theoretic Methods in Bifurcation Theory*]{} (Springer).
Stewart, I. and Dias, A.P.S., 2000, Hilbert series for equivariant mappings restricted to invariant hyperplanes [*J. Pure and Applied Algebra*]{} [**151**]{}, 89–106.
Vanderbauwhede, A., 1980, Symmetry and bifurcation near families of solution. [*J. Differential Equations*]{} [**36**]{}, 173–178.
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Johnson, Thompson help WKU hold off Old Dominion 75-68
NORFOLK, Va. (AP) -- Justin Johnson and Darius Thompson combined for 49 points and 9 of Western Kentucky's 10 3-pointers as the Hilltoppers defeated Old Dominion 75-68 Thursday night in a clash of Conference USA unbeatens.
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Georgetown wasn’t the only local team to pull off a stunning comeback on Tuesday. Virginia overcame a 10-point deficit in the final 76 seconds to defeat Wake Forest, 72-71, on Darius Thompson’s buzzer-beating three-pointer off the glass. Thompson, who hadn’t attempted a shot before the one that snapped Virginia’s three-game road losing streak, didn’t call bank. […]
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The NHL Stats and Information team reminisces on memorable moments and achievements of the past decade. The nine-part series culminates with a look at “The Moments” – one from each calendar year of the 2010s.
Jan. 1, 2010
The decade begins with the third Winter Classic, now a staple on New Year’s Day and one of the most anticipated events on the NHL calendar. Patrice Bergeron and Zdeno Chara assist on the first game-winning goal of the 2010s, in overtime outdoors at Fenway Park in Boston.
Oct. 9, 2011
The city of Winnipeg hosts an NHL game for the first time since 1996 as 15,004 fans pack the arena, but the visiting Canadiens spoil the Jets’ party with a 5-1 victory. Nik Antropov scores the lone goal for Winnipeg with assists to Mark Stuart and Alexander Burmistrov.
Feb. 2, 2012
Edmonton’s Sam Gagner collects 4-4—8 against Chicago, the most points by one player in a game during the 2010s. Prior to Gagner, the last eight-point performance in the NHL was by Pittsburgh’s Mario Lemieux against New Jersey on New Year’s Eve in 1988 (5-3—8).
June 24, 2013
With the 2013 Stanley Cup Final seemingly bound for a Game 7, the Blackhawks score twice in a span of 17 seconds to erase a 2-1 deficit and earn a Cup-clinching win in Boston. It marks their second of three championships during the decade (also 2010 and 2015) – the most of any team.
Jan. 1, 2014
The NHL begins the year with a bang – and a pile of snow – as a record-breaking crowd of 105,491 fill “The Big House” in Ann Arbor, Mich., for the Winter Classic on New Year’s Day. Tyler Bozak nets the decisive tally in the shootout to lift Toronto to victory over Detroit.
Oct. 13, 2015
Connor McDavid scores his first NHL goal after making his highly-anticipated debut five days earlier. No. 97 has more than lived up to the hype as he concludes the decade with the highest points-per-game rate of any player (1.33) along with two scoring titles and three 100-point seasons.
Sept. 29, 2016
Brad Marchand scores a shorthanded goal with 43.1 seconds left in regulation to lift Team Canada to the World Cup of Hockey championship. Canada captain Sidney Crosby claims tournament MVP honors after leading all players with seven assists, 10 points and a +8 rating in six games.
Oct. 10, 2017
After a 2-0-0 start on the road, the Golden Knights contest their first game on home ice as James Neal scores his third straight game-winning goal in front of a sold-out crowd in Vegas. The club wins eight of its first nine games and embarks on an unprecedented run to the Stanley Cup Final.
Nov. 24, 2018
After scoring six times in a span of three games from Nov. 19-23, 20-year-old Patrik Laine scores five goals against the Blues – tied for the most in one game during the 2010s (also Johan Franzen in 2011). Laine also becomes the third player in NHL history to accomplish the feat before age 21, joining Wayne Gretzky (2x) and Don Murdoch (1x).
Oct. 29, 2019
Carolina’s Andrei Svechnikov pulls off the NHL’s first-ever lacrosse-style goal against Calgary. The 19-year-old scores on the move again less than two months later – this time against Winnipeg on Dec. 17 – for a pair of last-minute entries for the “Goal of the Decade” title. | http://megasportsnews.com/?m=201912 |
Q:
Plotting a curve in 3D
Say I have two polynomials in $\mathbb{R}[X,Y,Z]$, whose intersection of zero loci correspond to a curve in the 3D space.
What is the best way to plot the curve?
Example:
$$
f = X^2+Y^2-Z^2, \qquad g = 2X^3+Y^3-Z
$$
I want to plot the curve given by
$$
\begin{cases}
&X^2+Y^2=Z^2 \\\\
&2X^3+Y^3=Z
\end{cases}
$$
A:
Directly from Highlight the Intersection of Two Surfaces
Is this what you are looking for?
h = x^2 + y^2 - z^2;
g = 2 x^3 + y^3 - z;
ContourPlot3D[{h == 0, g == 0}, {x, -2, 2}, {y, -2, 2}, {z, -2, 2},
MeshFunctions -> {Function[{x, y, z, f}, h - g]},
MeshStyle -> {{Thick, Blue}}, Mesh -> {{0}}, ContourStyle -> Directive[Orange,
Opacity[0.5], Specularity[White, 30]]]
| |
Actress Kate Garven Height, Weight, Measurements, Bra Size, Wiki, Biography details. Kate Garven is an Australian Actress. She became popular through her role as Jade Sutherland in the TV series “Home and Away”. Also, she played her role in Jade in the Home and Away DVD Specials, Home and Away; Secrets and the City, and Home and Away: Hearts Divided. She played Barbarella in the 2000 film Angst.
Kate Garven was born on 18 February 1986 in Sydney, Australia. Her parent’s and siblings’ names are not known. Kate Garven got married to Ben Field in 2004. The couple has four children.
Kate Garven’s height is around 5 feet 3 inches tall and her body weight is 54 kilograms. Her body measurement is 34-24-35 inches. She wearing to be a dress size 4 (US) and her shoes size 5 (US). Kate Garven’s hair color is blonde and her eye color is blue.
Kate Garven Personal Details
- Date Of Birth: 18 February 1986
- Birth Place: Sydney, Australia
- Birth Name: Kathryn Garven
- Nickname: Kate
- Zodiac Sign: Aquarius
- Occupation: Actress
- Nationality: Australian
- Race/Ethnicity: White
- Religion: Christianity
- Hair Color: Blonde
- Eye Color: Blue
- Sexual Orientation: Straight
Kate Garven Body Statistics
- Weight in Pounds: 119 lbs
- Weight in Kilogram: 54 kg
- Height in Feet: 5′ 3″
- Height in Meters: 1.60 m
- Body Build/Type: Slim
- Body Measurements: 34-24-35 in (86-61-89 cm)
- Breast Size: 34 inches (86 cm)
- Waist Size: 24 inches (61 cm)
- Hips Size: 35 inches (89 cm)
- Bra Size/Cup Size: 32B
- Feet/Shoe Size: 5 (US)
- Dress Size: 4 (US)
Kate Garven Family Details
- Father: Unknown
- Mother: Unknown
- Spouse/Husband: Ben Field (m. 2004)
- Children: 4
- Siblings: Unknown
Kate Garven Education
- Not available
Kate Garven Facts
- She was born on February 18, 1986, in Sydney, Australia.
- Her full name is Kathryn Garven.
- She played Jade Sutherland in the Australian soap opera Home and Away from 2000 to 2004.
- She married Ben Field in May 2004, aged 18.
Also Read, Carla Jimenez and Damla Sönmez.
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Q:
Collatz conjecture pattern (3n + 1 problem).
I have a pattern I found in Collatz Conjecture I want to share. Afterwards, I would like to know, if I could try harder at this pattern (I am stuck), if it could lead to a proof. Or it would just be other thing to waste my time here.
I made this spreadsheet, which you can download and play and see it for yourself, how the pattern shows itself.
At "end of column" I calculate a number that, when plugged at the odd function $3n + 1$, will produce a number that is only divisible by 2. That formula is given by $S=\frac{4^k-1}{3}$. S would be the number I will choose to stop at each column. And K would be a natural number in sequence. If I start with k=0, then I have only 0 at the end of the column, which is good, zero has a column all by himself, as equal as 1. So, I could plug 2, and get 5. So, I have a column of just 0, one for 1, and column 2, would have 3 and 5. Then column 3 would have 7, 9, 11, 13, 15, 17, 19 and 21. As 21 is S, when k = 3.
The funny thing is that S is also a formula for partial sum of $4^k$. That also means that each column is 4 times greater than the one before.
I then, because I am only interested by what happens with odd natural numbers, start by putting all natural numbers ordered in sequence. Then, I stop when I find a number calculated by the previous formula ("End of column" sheet).
Then, I continue the sequence of odd natural numbers in the next column of the "collatz sheet".
I can make this sheet as big as I want (natural numbers are infinite). The only limits to that would be (as I used my own Excel sheet, running on my 2011 computer) hard disk space, memory and cpu power. If you make it big, it will run in these issues. Which you can make it less agravating, if you choose to transform the formulas in values, after you calculated the numbers you wanted. I don't know how this would turn out in google spread sheet I am sharing with you.
The pattern is: if you take these odd numbers, compute the next odd numbers, you will see that the numbers will repeat as a clockwork in the next columns (in position-wise).
Examples are colored in the spreadsheet I shared. Example: 21 and 85 are the last one of their colums, and they turn directly to 1, as the formula would give, of course. Then, 19, and 77 are the last part of a 7/8 position [explaining, there are numbers (7, 9, 11, 13, 15, 17, 19, 21 and 19 is the 7th); (23, 25, 27, ... , 75, 77, 79, 81, 83, 85 and 77 is at the end of 7/8 position block). So, this pattern shows that each 7/8 position will cook the number 19 after just the first iteration.
The numbers are coloured for you to see them, how they happen. First, I coloured the background colour, to show that the numbers follow their position. Then, I coloured the font, to show that new numbers of the next column fit in the next column afterwards and so on and so on. Explaining (look at 23, 25, 27, they produce 35, 19, 41, that are also produced by 93, 101, 109). That is, the same position percentile-wise one number occupies in the position of the natural numbers distributed as I created and showed in this spreadsheet, produces a pattern that not only repeats itself, as it grows, to fill the new spaces. I mean. The first pattern has 8 numbers, the next one has the same 8 numbers (each in their position) + 24 new ones (which will keep their positions on the next column.
Note, if you want to create a bigger sheet, just plug in whatever the size size you want. And then, just copy-paste the formula, it will just self-referentiate nicely from each one cell you choose.
Now, the question is: can I keek this work to develop a proof of the Collatz Conjecture, knowing this will have to have lots of work of arithimetic and geometric progression and mathematic induction, all mixed and much more that I don't know yet or is this already fruitless endeavour?
Edit:
@NickGuerrero
The numbers in this example sheet, from cell A1 to E128, are just the natural numbers, odd ones, which continue above when they encounter, 5, 21, 85, 341, 1365 and so on (given by $\frac{4^k-1}{3}$).
The next set of numbers are given by a spreadsheet formula, that uses "IF" functions inside other "IF" funcions (nested "IF"s). There is a limit about how much you do it. I just, in my example, custructed the "IF" condition, to ask if the result from $3n+1$ would be divided by $2^{24}$, then, divide it by $2^{24}$, if not, ask if it was divided by $2^{23}$, then divide it by it, if not... till I divide it and it rests a number that is not divided by 2, that is, it is next odd number from iteration from odd function and even function of Collatz conjecture algorithm.
A:
I will answer your question: I bet you won't like my answer but it is answer so I hope you keep that in mind.
Your question was: "I would like to know, if I could try harder at this pattern (I am stuck), if it could lead to a proof. Or it would just be other thing to waste my time here."
When I was a younger math nerd I attempted to take the P vs NP problem very seriously and after burning out a few times a mathematician and mentor of mine told me that "This is not to be done." He wanted me to focus on acquiring some mathematical tools and some experience that would help me become a more competent math nerd and wanted to give me a warning about diving into exceptionally difficult mysteries without sufficient experience.
Questions like the Collatz conjecture are good for getting mathematicians to wake up but not a good place to spend your time.
I mean that this is the type of thing that mathematicians as a culture should be on the same page about: when you see a young and-up-and-coming mathematician (Or really any non pro) making serious efforts towards a problem that has been open for a century we should dissuade them from getting bogged down in these mental traps.
This is a great puzzle. And it's very accessible which makes it a nice tool to get students excited about open mathematics. But also very very impressive mathematicians have said things along the lines of "we're not quite ready to solve such mathematical mysteries. We don't have all the tools yet."
The reasons you should not spend more time on this puzzle.
1) With probablity approaching 1, better mathematicians have already attempted a route similar to the one above. Which (and without any insult intended here) doesn't look particularly novel.
2) The problem isn't of particular interest. We have more important work to be doing: work that we can actually make real progress on.
3) It's probably a dead end. I mean... thus far all the numbers we have tested head to one... and all of the attempts we have made(for a century) have led to either undecidable generalizations or just a flat failure to say anything interesting.
You should enter the mathematical community with burning questions like this one... and then when you seen the human effort put toward this question and have read Conway's book on the 3x+1 problem and checked out Lagarias and whoever else you need to convince yourself that very impressive minds have spent considerable energy on this...
You should put down these puzzles and help make genuine mathematical progress. It will be better for you and the mathematical community at large.
| |
Coronavirus live updates: US reports over 100,000 new cases for sixth straight day
(NEW YORK) — A pandemic of the novel coronavirus has now killed more than 1.2 million people worldwide.
Over 50.4 million people across the globe have been diagnosed with COVID-19, the disease caused by the new respiratory virus, according to data compiled by the Center for Systems Science and Engineering at Johns Hopkins University. The actual numbers are believed to be much higher due to testing shortages, many unreported cases and suspicions that some national governments are hiding or downplaying the scope of their outbreaks. The criteria for diagnosis — through clinical means or a lab test — has also varied from country to country.
Since the first cases were detected in China in December, the virus has rapidly spread to every continent except Antarctica. The United States is the worst-affected nation, with more than 10 million diagnosed cases and at least 238,251 deaths.
Nearly 200 vaccine candidates for COVID-19 are being tracked by the World Health Organization, at least 10 of which are in crucial phase three studies. Of those 10 potential vaccines in late-stage trials, there are currently five that will be available in the United States if approved.
Authorities in China’s largest city have quarantined dozens of people after an airport employee tested positive for COVID-19.
A 51-year-old man who works as a freight handler at Shanghai Pudong International Airport, a major aviation hub of East Asia, was confirmed to be infected on Monday and has since been transferred to an area hospital for treatment, authorities said.
It’s the first domestic case of COVID-19 reported in Shanghai in months, and it remains unclear how the patient contracted the disease. He has not left Shanghai and reported no history of being in high-risk areas in the 14 days prior to the onset of illness. He also has no history of contact with anyone infected with COVID-19 and has not been to any other hospitals within the past three months, according to authorities.
Twenty-six close contacts, including the man’s family members and colleagues, have been quarantined and have all tested negative for COVID-19. More than 100 others were also placed in isolation for medical observation, authorities said.
So far, no additional cases have been found.
The local health authority has raised the COVID-19 risk area to medium in the village where the patient lives in Shanghai’s district of Pudong. The rest of Shanghai remains low-risk.
Nov 10, 4:38 am US sees highest number of COVID-19 hospitalizations since July
There were 59,275 people currently hospitalized with COVID-19 across the United States on Monday, according to data collected by The COVID Tracking Project.
That figure — up from 56,768 on Sunday — marks the largest single-day increase since July 10 and the highest total amount since July 25, The COVID Tracking Project said.
Nov 10, 4:24 am US reports over 100,000 new cases for sixth straight day
There were 119,944 new cases of COVID-19 identified in the United States on Monday, according to a real-time count kept by Johns Hopkins University.
It’s the sixth straight day that the country has reported over 100,000 new infections. The latest daily tally is slightly less than the nation’s all-time high of 128,412 new cases set on Saturday.
An additional 670 fatalities from COVID-19 were also registered nationwide Monday, down from a peak of 2,666 new deaths in mid-April.
A total of 10,110,552 people in the United States have been diagnosed with COVID-19 since the pandemic began, and at least 238,251 of them have died, according to Johns Hopkins. The cases include people from all 50 U.S. states, Washington, D.C. and other U.S. territories as well as repatriated citizens.
Much of the country was under lockdown by the end of March as the first wave of pandemic hit. By May 20, all U.S. states had begun lifting stay-at-home orders and other restrictions put in place to curb the spread of the novel coronavirus. The day-to-day increase in the country’s cases then hovered around 20,000 for a couple of weeks before shooting back up and crossing 100,000 for the first time on Nov. 4.
Coronavirus live updates: US reports over 100,000 new cases for sixth straight day
(NEW YORK) — A pandemic of the novel coronavirus has now killed more than 1.2 million people worldwide.
Over 50.4 million people across the globe have been diagnosed with COVID-19, the disease caused by the new respiratory virus, according to data compiled by the Center for Systems Science and Engineering at Johns Hopkins University. The actual numbers are believed to be much higher due to testing shortages, many unreported cases and suspicions that some national governments are hiding or downplaying the scope of their outbreaks. The criteria for diagnosis — through clinical means or a lab test — has also varied from country to country.
Since the first cases were detected in China in December, the virus has rapidly spread to every continent except Antarctica. The United States is the worst-affected nation, with more than 10 million diagnosed cases and at least 238,251 deaths.
Nearly 200 vaccine candidates for COVID-19 are being tracked by the World Health Organization, at least 10 of which are in crucial phase three studies. Of those 10 potential vaccines in late-stage trials, there are currently five that will be available in the United States if approved.
Authorities in China’s largest city have quarantined dozens of people after an airport employee tested positive for COVID-19.
A 51-year-old man who works as a freight handler at Shanghai Pudong International Airport, a major aviation hub of East Asia, was confirmed to be infected on Monday and has since been transferred to an area hospital for treatment, authorities said.
It’s the first domestic case of COVID-19 reported in Shanghai in months, and it remains unclear how the patient contracted the disease. He has not left Shanghai and reported no history of being in high-risk areas in the 14 days prior to the onset of illness. He also has no history of contact with anyone infected with COVID-19 and has not been to any other hospitals within the past three months, according to authorities.
Twenty-six close contacts, including the man’s family members and colleagues, have been quarantined and have all tested negative for COVID-19. More than 100 others were also placed in isolation for medical observation, authorities said.
So far, no additional cases have been found.
The local health authority has raised the COVID-19 risk area to medium in the village where the patient lives in Shanghai’s district of Pudong. The rest of Shanghai remains low-risk.
Nov 10, 4:38 am US sees highest number of COVID-19 hospitalizations since July
There were 59,275 people currently hospitalized with COVID-19 across the United States on Monday, according to data collected by The COVID Tracking Project.
That figure — up from 56,768 on Sunday — marks the largest single-day increase since July 10 and the highest total amount since July 25, The COVID Tracking Project said.
Nov 10, 4:24 am US reports over 100,000 new cases for sixth straight day
There were 119,944 new cases of COVID-19 identified in the United States on Monday, according to a real-time count kept by Johns Hopkins University.
It’s the sixth straight day that the country has reported over 100,000 new infections. The latest daily tally is slightly less than the nation’s all-time high of 128,412 new cases set on Saturday.
An additional 670 fatalities from COVID-19 were also registered nationwide Monday, down from a peak of 2,666 new deaths in mid-April.
A total of 10,110,552 people in the United States have been diagnosed with COVID-19 since the pandemic began, and at least 238,251 of them have died, according to Johns Hopkins. The cases include people from all 50 U.S. states, Washington, D.C. and other U.S. territories as well as repatriated citizens.
Much of the country was under lockdown by the end of March as the first wave of pandemic hit. By May 20, all U.S. states had begun lifting stay-at-home orders and other restrictions put in place to curb the spread of the novel coronavirus. The day-to-day increase in the country’s cases then hovered around 20,000 for a couple of weeks before shooting back up and crossing 100,000 for the first time on Nov. 4. | |
---
abstract: 'Near-infrared properties of 451 galaxies with distances $D \leq$ 10 Mpc are considered basing on the all-sky two micron survey (2MASS). A luminosity function of the galaxies in the K-band is derived within $[-25,-11]$ mag. The local ($D < 8$ Mpc) luminosity density is estimated to be $6.8\times 10^8 L_{\odot}$/Mpc$^3$ that exceeds (1.5$\pm$0.1) times the global cosmic density in the $K$-band. Virial mass-to-K-luminosity ratios are determined for nearby groups and clusters. In the luminosity range of ($5\times 10^{10} - 2\times 10^{13})L_{\odot}$, the groups and clusters follow the relation $\lg(M/L_K) \propto (0.27\pm0.03) \lg(L_K)$ with a scatter of $\sim$0.1 comparable to errors of the observables. The mean ratio $<M/L_K> \simeq (20-25) M_{\odot}/L_{\odot}$ for the galaxy systems turns out to be significantly lower than the global ratio, $(80-90)M_{\odot}/L_{\odot}$, expected in the standard cosmological model with the matter density of $\Omega_m =0.27$. This discrepancy can be resolved if most of dark matter in the universe is not associated with galaxies and their systems.'
---
[**Infrared luminosities of galaxies in the Local Volume**]{}
[I.D.Karachentsev$^1$ and A.M.Kut’kin$^2$]{}
$^1$ Special Astrophysical Observatory, Russian Academy of Sciences, Russia
$^2$ Moscow State University, Russia
Introduction
============
Recently published catalog of nearby galaxies (Karachentsev et al. 2004) contains basic observational data on 451 galaxies with distances within 10 Mpc. Along with distances and radial velocities it contains different optical characteristics of galaxies: apparent magnitude in B-band, angular size, morphological type, and also neutral hydrogen line flux and width of HI line. Data presented in the catalog allow one to determine such important properties of the Local Volume as luminosity function, local luminosity density, mass density of baryonic matter or of neutral hydrogen. Being marginally affected by selectional effects, distance (not flux) limited sample of galaxies is the proper standard for comparison with distant samples (like Deep Hubble Field) in analyzing effects of galaxies evolution.
However detailed research of evolutional effects needs in photometric data on the Local Volume not only in B-band, but also in other bands, especially in near Infrared. There are two main reasons for this: 1) variable luminosity of young stellar population of galaxies, that is increasing with star formation rate, introduce small contribution in integral infrared (IR) luminosity of galaxy; 2) decreasing of galaxy’s IR-luminosity due to light extinction in galaxy’s dusty clouds is far less than in B-band. That is why galaxy’s IR luminosity is more reliable indicator of baryonic mass than optical luminosity.
In recent years all-sky survey in IR-bands ( J(1.1 -1.36) microns, H(1.50-1.80) microns, and Ks(2.00-2.32) microns) called 2MASS survey was conducted. This survey became the base for extended objects survey, XSC, that contains near 1.65 millions galaxies with apparent magnitudes in Ks-band $<$ 14 mag and angular sizes $> 10$ arcsec (Cutri et al., 1998, Jarrett, 2000). Different photometric and morphological properties of that huge galaxies sample is described by Jarrett et al.(2000, 2003). We used the 2MASS survey data for determination J, H, K magnitudes of galaxies in the Local Volume.
Galaxies in the Local Volume, visible in the 2MASS survey.
===========================================================
Infrared J, H, K images of all galaxies with distance estimates within 10 Mpc were examined with NASA Extragalactic Database (NED). After excluding of some cases with questionable identifications of distant 2MASS sources with a nearby galaxy we obtained the sample of 122 galaxies for which the 2MASS XSC catalog contains J, H, K- “extended” magnitudes. Unlike measured (isophot) magnitudes, J ,H, K extended magnitudes take into account contribution of faint external parts of galaxy by extrapolation along it’s standard brightness profile. Thus, only 27% of the Local Volume galaxies are seen in the 2MASS survey.
The reason for absence of many nearby galaxies is relatively short exposition time ($\sim$8 sec per frame). And, as a consequence, galaxies of low surface brightness fall below the survey sensitivity threshold, K = 20 mag/sq.arcsec. The low detection rate in the 2MASS survey is typical indeed for galaxy samples limited by distance. For instance, the spiral galaxies of RFGC catalog with angular diameters larger than 0.6 arcmin have a detection rate in the 2MASS about 71% (Karachentsev et al., 2002). Appearance of a galaxy in the 2MASS survey depends on it’s different characteristics: morphological type, absolute magnitude, mean surface brightness. To estimate the J, H, K magnitudes for galaxies of the Local Volume, that are not seen in the 2MASS, we built dependence of color indexes B-K, J-K, H-K for detected galaxies on their morphological types and other parameters. Distribution of 122 nearby galaxies on color index B-K and morphological type in de Vaucouleur’s classification scheme is resulted in upper side of plot 1. Each galaxy is shown as a cross and the median values of color index B-K are shown as diamonds. All apparent magnitudes were corrected for galaxy extinction: $A_J=0.209A_B , A_H=0.133A_B,$ and $ A_K=0.085A_B$, where $A_B$ is the magnitude of extinction in the B-band from Schlegel et al. (1998). These data show a systematic trend of the mean color index from $<B-K> \simeq 4.0$ for early types to $<B-K> \simeq
2.0-2.5$ for later classes. Similar tendency is also visible for color indexes J-K (lower side in plot 1). The obtained color index dependences on galaxies type satisfactorily match data presented in Jarrett et al. (2003) on plot 20 and 23 for more numerous sample of galaxies of different types. Following Jarrett et al. (2003) correlations “type - color index” were used for determination of J, H, K-magnitudes for nearby galaxies from their B-magnitudes contained in the catalog (Karachentsev et al. 2004). Results are presented in Appendix accessible as an electronic file. The most useable names of the nearby galaxies are given in the same sequence as in the parent catalog. The infrared magnitudes from 2MASS are shown with two signs after dot, and the calculated magnitudes J, H, K are presented with one sign after dot. Comparison of different methods in estimation of the J, H, K magnitudes showed that a typical error in IR-magnitudes determination is about 0.5 mag.
Luminosity function of galaxies in the K-band.
==============================================
We determined absolute magnitudes of all galaxies from the Local Volume (LV) basing on J, H, K values from Appendix, using galaxy distance estimates from the catalog (Karachentsev et al., 2004) and taking into account Galactic extinction from Schlegel et al. (1998). Plot 2 shows distribution of sample of the nearest galaxies along absolute magnitudes in J (crosses), H (diamands), and K (circles) bands. The most bright galaxy in the LV, NGC 4594 (“Sombrerro”) has absolute magnitude $M_K=-24.91$, and the most faint dwarf systems of the Ursa Minoris type have $M_K
\sim-11$. The maximum of the luminosity function in all J, H, K-bands falls on interval \[-15, -17\].
Recently Cole et al. (2001) made an attempt to determine galaxy’s luminosity functions in J and K band. They used the 2MASS photometry of 17173 galaxies with measured redshifts from 2dF survey. Accordingly Cole et al. (2001), luminosity function in the K-band is well represented by Shechter’s function with parameters: $M^* = -24.15 (H_0 = 72$ km/s Mpc) and $\alpha = -0.96$ on an interval from $-26^m$ to $-18^m$. Luminosity function comparison for the 2MASS/2dF sample (squares) and the LV (solid circles) sample is presented in upper side of Plot 3. Statistical errors, $(N)^{1/2}$ are shown as vertical bars. Mutual normalization of two the samples is done near $M_K = -20.5^m$, where statistical errors for these samples are comparable. The luminosity function for the LV galaxies expectedly reaches far away (on seven magnitudes) toward dwarf galaxies. In overlapping region, for $M_K = [-25^m, -18^m]$, consistency of luminosity functions can be treated as satisfactory, although differences run up to 2-3 standard deviations for some bins. There’s a remarkable flattering of the 2dF luminosity function in $M_K = [-19^m, -18^m]$ region. The obvious reason is because of systematic incompleteness in the 2MASS/2dF sample, so there are many low luminosity dwarf galaxies with low surface brightness that are not detected in the 2MASS survey. That is why there’s a much better consistency of luminosity function for the LV based on only 122 detected in the 2MASS objects (crosses) with Cole’s sample (Cole et al., 2001).
Another possibility for comparison is data on the Virgo cluster of galaxies that can be found in Internet on http://goldmine.mib.infn.it/. This sample contains K-magnitudes for bright members of the Virgo cluster. We estimated K-magnitudes of fainter members being based on their B-magnitudes and dependency of mean color index $< B - K >$ on morphological type that was found in Jarrett et al. (2003). As a result, the luminosity function for 680 members of the Virgo cluster was obtained (triangles in low side of Plot 3). Mutual normalization of distributions for the Virgo cluster, the LV sample (circles) and the 2MASS/2dF sample (squares) was made for $M_K = -20.5$. The distance to the Virgo cluster was taken equal to 17.0 Mpc (Tonry et al. 2000). As can be seen, the Virgo cluster luminosity function reveals some excess in supergiant galaxies that is expected in terms of formation scenario for the most massive galaxies as a merging result for normal and dwarf galaxies. On the faint end it extends up to $M_K = -13^m$, that is on 5 magnitudes further than for the 2MASS/2dF sample. Systematic differences between the Virgo cluster and the LV samples on the faintest absolute magnitudes are obviously due to underestimation in number of cluster’s dwarf members, for which estimations of radial velocities are still missing. The last fact doesn’t allow one to either rank them as members of the Virgo cluster or as just background galaxies.
Using distribution of the LV galaxies on absolute magnitudes and distances we calculated the mean luminosity density as a function of sphere radius centered in our Galaxy. Plot 4 shows a luminosity density (in sun luminosity per cubic Mpc units) dependence on distance separately for J, H and K-bands. The mean luminosity density falls down on two orders of magnitude on scales from 1 to 10 Mpc, reflecting fractal character of galaxies distribution. Completeness of the catalog was estimated as on 70% level within distance D=8 Mpc. Some dwarf galaxies in outlying regions of the LV $(D \simeq 5 - 10$ Mpc) and in regions of strong extinction on galactic latitudes I$b$I $\leq 10^{\circ}$ could be easly missed from the catalog. However lack of dwarf galaxies in practice doesn’t affect on estimation of luminosity density because more than 90% of the integrated luminosity accounts on bright galaxies constituting interval that is within 4 magnitudes from the level of the brightest galaxy.
Photometry of galaxies in the 2MASS survey was used by Kochanek et al. (2001) and Bell et al. (2003) for global mean luminosity density estimation in K-band, $j_K$. Using data on redshifts for galaxies from the Sloan sky survey and other sources, these authors obtained values $j_K = (5.1\pm0.5)10^8
L_{\odot}$/Mpc$^3$ and $(4.2\pm1.3)\times 10^8L_{\odot}$/ Mpc$^3$, correspondingly. These values are shown as two horizontal lines on Plot 4. Thus, our calculated K-band mean luminosity density within 8 Mpc, $6.8\times10^8L_{\odot}$/ Mpc$^3$, (1.4-1.6) times exceeds the global one. Note that a ratio of local to global mean luminosity density in the B - band, that is (1.4 - 2.0), contains more uncertainty because of different methods for accounting of internal absorption in galaxies.
Mass-to-K-luminosity ratio for nearby galaxies.
===============================================
Almost 2/3 of the LV galaxies were detected in the HI line. That allowed us to determine mass of hydrogen in these galaxies, M(HI), using observed flux in HI, as well as the total galaxy mass inside the standard radius, $M_{25}$, using a width of the HI line corrected for the galaxy inclination. The total mass-to-luminosity ratio and the HI mass-to-luminosity ratio are important global parameters of a galaxy that depend on the features of galaxy evolution: star formation rate, frequency of merges etc. Mass-to-blue luminosity ratio distribution for the LV galaxies was discussed by Karachentsev et al.(2004). Distribution of $M_{25}/L$ calculated for the B and the K-bands for the nearby galaxies is shown in the upper side of Plot 5. Similar ratio for hydrogen mass per unit luminosity in the B and the K-bands is shown in the lower side of Plot 5. Galaxies with directly determined K magnitudes from the 2MASS survey are shown as squares and galaxies with estimations of IR-luminosities through their color (B - K) and morphological type shown as crosses. As can be seen the transition from optical to infrared luminosities of galaxies doesn’t lead to expected decreasing in dispersions for $M_{25}/L$ and M(HI)/L values. This obviously results from a low accuracy in determination of IR-luminosity for nearby galaxies, which are mostly low surface brightness dwarf galaxies.
Distribution of integrated K-luminosity and $M_{25}/L_K$ ratio for the LV galaxies is shown in logarithmic scale in Plot 6. It is evident from these data that the mean mass-to-luminosity ratio remains nearly constant over the IR-luminosity range of 5 orders being equal to $(1.5\pm0.2) M_{\odot}/L_{\odot}$. Basing on Salpeter’s conception on initial stellar mass function, Persic& Salucci (1992), Fukugita et al. (1996), Kochanek et al. (2001), and Cole et al. (2001) estimated the mean stellar mass density in the Universe. Following them and Bell et al. (2003), the stellar component contains $\Omega_* = (2.8\pm0.8)\times10^{-3}$ from the critical density with H=72 km/s Mpc or $(M/{L_K})_* = 0.95\pm0.27$ in solar mass and luminosity units. Thus, the stellar mass component (+ mass of gas) consistent within error range with the mean galaxy mass inside it’s standard radius. Consequently, nonvisible forms of matter (dark halo) contribute secondary in the integrated mass of galaxy inside it’s standard radius. This is considered both to normal and dwarf galaxies within $10^{11}$ to $10^6 L_{\odot}$ luminosity range.
Mass-to-K-luminosity ratio in systems of galaxies
==================================================
As well known, mass-to-luminosity ratio in systems of galaxies increases with transition from double and triple systems to groups, clusters and superclusters. Character of this dependency in the B- band was discussed by Karachentsev (1966), Bahcall et al. (2000) and many others. There are reasons to believe that this dependence must be clearer in IR then in optical. Recently Lin et al. (2003) explored IR properties of 27 galaxy clusters and showed that mass dependence on K-luminosity of clusters expresses in relation $M/L_K\propto M^{0.31\pm0.09}$, where masses of clusters were obtained using their X-ray fluxes. Estimations of $M/L_K$ were made for some others systems of galaxies too. Summary of these data can be found in Table 1, where we also show masses and K-luminosities obtained for nearby groups of galaxies. First column indicates name of galaxy or system, in some cases we give the spatial scale using in the mass determination. Second column indicates integrated K-band luminosity of the object/system in units of solar luminosity. Third and fourth columns indicate total mass and mass-to-K-luminosity ratio, respectively. And the last one contains information about sources of the mass estimations.
---------------------- --------------- --------------- -------------- -------------------------------------
Object $L_K$ $M$ $M/L_K$ Notes
$(L_{\odot})$ $(M_{\odot})$ $(\odot)$
LV galaxies 1.0 E07 1.5 E07 1.5$\pm$0.2 $M_{25}/L$
LV galaxies 1.0 E09 1.3 E09 1.3$\pm$0.2 $M_{25}/L$
LV galaxies 1.0 E11 1.1 E11 1.1$\pm$0.2 $M_{25}/L$
NGC 5128 ($<$80kpc) 1.1 E11 5.0 E11 4.7 Peng et al.(2004)
NGC 4636 ($<$35kpc) 1.6 E11 1.5 E12 9.7 Loewenstein & Mushotsky (2002)
NGC 1399 ($<$106kpc) 2.8 E11 5.2 E12 18.7$\pm$5.7 Jones et al.(1997)
M31 group 6.3 E10 8.4 E11 13.4 Karachentsev (2005)
Local Group 1.1 E11 1.2 E12 11.2$\pm$3.5 Karachentsev (2005)
M81 group 1.5 E11 1.6 E12 10.6 Karachentsev (2005)
IC 342 group 5.6 E10 7.6 E11 13.5 Karachentsev (2005)
Maffei group 7.2 E10 1.0 E12 14.0 Karachentsev (2005)
M83 group 6.8 E10 1.0 E12 15.2 Karachentsev (2005)
CenA group 1.4 E11 3.0 E12 21.3 Karachentsev (2005)
Leo-I group 3.5 E11 7.2 E12 20.5 Karachentsev & Karachentseva (2004)
NGC 6946 group 6.8 E10 8.0 E11 11.7 Karachentsev et al.(2000)
Poor groups 7.6 E10 1.3 E12 17.0$\pm$2.9 Guzik & Seljak (2002)
Fornax 1.8 E12 5.9 E13 32 Desai et al.(2003)
Virgo ($<$1.6Mpc) 8.8 E12 4.2 E14 48$\pm$6 McLaughlin (1999)
0024+1654 1.5 E13 6.1 E14 40$\pm$7 Kneib et al.(2003)
MS0302+17 ($<$8Mpc) 8.9 E12 4.4 E14 50$\pm$5 Gavazzi et al.(2004)
Abell clusters 1.1 E13 5.2 E14 47$\pm$3 Lin et al.(2003)
Coma ($<$14Mpc) 2.7 E13 1.4 E15 54$\pm$17 Rines et al.(2001)
---------------------- --------------- --------------- -------------- -------------------------------------
: Mass-to-luminosity ratios for galaxies and systems of galaxies in the K-band.
All data in Table 1 correspond to the Hubble constant $H_0 = 72$ km/s Mpc and the solar absolute magnitude $M_{K,\odot}$ = 3.39 mag (Kochanek et al., 2001).
It is not out of place to make some comments on values given in Table 1. First three lines represent the mean values of masses inside the standard radius for the LV galaxies, divided in three luminosity intervals. The mean ratios $M_{25}/L_K$ and their standard deviations are derived from data in Plot 6. Next three lines contains estimations of total masses for individual galaxies on larger scales. They were made using dispersions of radial velocities of planetary nebulas in elliptical galaxy NGC 5128 (on scale of 80 Kpc) or using value of X-ray flux from ellipticals NGC 4636 (in the Virgo cluster) and NGC 1399 (in the Fornax cluster). The K-values for these galaxies were obtained in the 2MASS.
Next seven lines contain data on masses and luminosities for the nearest groups around the giant galaxies: M31, M81, IC 342, Maffei 1, M83 and Cen A = NGC 5128 as well as for the Local Group. Population and dynamics of these groups were discussed by Karachentsev (2005). Presented masses of these group correspond to the mean of two estimates: one made using Virial theorem and other one basing on orbital motions of companions around their principal galaxies. The value of total mass of the Local Group as a whole was obtained from relation $M_t=(\pi^2/8G)\times R^3_0/T^2_0$, where $R_0$ is the observed radius of “the zero velocity sphere”, $T_0$ is the age of the Universe, and G is the gravitational constant. Another two groups of the LV were added to those listed above: Leo-I and NGC 6946. Their virial masses were estimated by Karachentsev & Karachentseva (2004) and Karachentsev et al. (2000), respectively, with additional data on radial velocities from Makarov et al. (2003).
Guzik & Seljak (2002) and Hoekstra et al. (2004) explored effects of weak gravitational lensing that produced by single galaxies of high luminosities seen in SDSS and RCS surveys. Such galaxies are usually inhabit centers of pure populated (loose) groups. Accordingly authors, lensing galaxies with the mean optical luminosity $L_B=1.9\times10^{10}L_{\odot}$ have characteristic masses ($1.3\pm0.2)
\times10^{12} M_{\odot}$ on scales $R\leq 260$ Kpc. Supposing the mean color for these field galaxies to be $< B - K > = 3.5$, we obtain the estimation of mass-to-K-luminosity ratio ($17\pm3)M_{\odot}/L_{\odot}$ that is in good agreement with the data on nearby groups of galaxies mentioned above.
Last six lines in Table 1 refer to clusters and superclusters. According to Tonry et al. (2001) and Jerjen (2003) the distance to pure populated southern cluster in Fornax is $20\pm$2 Mpc. A catalog of 2678 galaxies from that cluster was published by Ferguson (1989). With a velocity dispersion of the Fornax members being $\sim$400 km/s, the virial mass of that cluster is $5.9\times 10^{13} M_{\odot}$ (Desai et al. 2004). The infrared luminosity of the Fornax cluster presented in Table 1 was obtained by us from the 2MASS survey data.
Analogous method was used to estimate the integrated K-luminosity for other nearest galaxy cluster in Virgo. With the Virgo cluster distance being equal D = 17 Mpc, we obtained $L_K$(Virgo)$=8.8\times10^{12}L_{\odot}$ for the virialised region of the cluster within 6 deg from the center. The virial mass of the cluster was obtained by McLanghlin (1999) from a velocity dispersion of galaxies and from an X-ray flux of virialized hot gas within cluster. The mass of the Vigro is $(4.2\pm0.5) 10^{14} M_{\odot}$ within 1.6 Mpc radius. That gives $M/L_K
=(48\pm6)M_{\odot}/L_{\odot}$. It is worth to say that according to a model of galaxy motions around the Virgo as an attractor, Tully & Shaya (1984) and Tonry et al. (2000) obtained mass of the cluster $7\times 10^{14}
M_{\odot}$. However this estimate concerns larger cluster radius up to $\sim$8 Mpc, and the integrated K-luminosity of the volume is not determined so far.
Recently Kneib et al. (2003) and Gavazzi et al. (2004) used effects of gravitational lensing for mass determination of two rich clusters: 0024+1654 and MS0302+17. Their results are presentin Table 1. The authors measured K-luminosity for first cluster. Estimation of K-luminosity for second one was made using known luminosity in B-band in suggestion that cluster is inhabited by galaxies of early types with the mean color index $< B - K >$ = 4.0.
Two the last lines in Table present the mean mass and K-luminosity for 27 clusters that were studied by Lin et al. (2003) and also for the Coma supercluster (Rines et al. 2001). In last case $M/L_K$ ratio was measured using redshift survey of 1779 galaxies and their 2MASS photometry. Authors point that obtained mass-to-luminosity ratio remains nearly constant while move out from central virialized region $\sim$3.5 Mpc in radius to a scale $\sim$14 Mpc, that characterizes a region of bulk motion for surrounding galaxies toward Coma as an attractor.
Data on masses and K-luminosities of galaxies and systems of galaxies summarized in Table 1 are presented in Figure 7. The estimates of M/L for individual galaxies, groups, and clusters/superclusters are shown as circles, triangles and squares, respectively. We can get the global value $(M/L_K)_{global}$ that characterizes fairish (on scales $>$ 100 Mpc) regions of the Universe calculating ratio of critical density $\rho_c = (3H_0^2/8\pi G$) (that equals $1.43\times 10^{11}M_{\odot}$ Mpc$^{-3}$ for $H_0 = 72$ km/s Mpc) to mean luminosity density in the K-band, $j_K$ .Using estimations of $j_K$ from Kochanek et al.(2001) and Bell et al. (2003) we obtain $(M/L_K)_{global} = 287$ and $345
M_{\odot}/L_{\odot}$, respectively. These values are shown as dashed lines in right upper corner of Figure 7. We accepted their mean $(316\pm29)M_{\odot}/L_{\odot}$ for calibration of density scale in units of the critical density. The last is shown on the right side.
The mean stellar mass density, $(0.95\pm0.27)M_{\odot}/L_{\odot}$ from Bell et al. (2003), is shown at the bottom of the Figure 7 as horizontal line. Other horizontal line corresponds to the mean baryonic mass density, $\Omega_b = 0.047\pm0.006$ or $<M/L_K>_b=
(14.8\pm1.9)M_{\odot}/L_{\odot}$ according to Spergel et al. (2003). Dashed line with a weak slope corresponds to a trend of the mean mass (inside standard radius) to luminosity ratio for the LV galaxies. Analysis of the data presented allows one to make some general conclusions:
1\) The value of stellar mass density and gas density per unit luminosity is quite enough to explain the mean mass-to-luminosity ratio inside the standard radius both for giant, normal and dwarf galaxies. With all this going on, contribution of gaseous component, that can be expressed through relation $M(HI)/M_{25}$, increases with decreasing galaxy’s luminosity, reaching values $\sim$(1-3) for the smallest dwarf systems (compare Fig. 10 in Karachentsev et al., 2004)
2\) Transition from visible regions of galaxies with sizes (1-30) Kpc to groups dominated by one galaxy (scales 50-300 Kpc) is accompanied by increasing of mass on near order of magnitude with almost constant luminosity. The mean ratio $M/L_K$ for groups of galaxies is actually coincide with the mean ratio for baryonic mass, $(14.8\pm1.9)M_{\odot}/L_{\odot}$.
3\) Galaxy groups, clusters and superclusters follow a relation $\lg(M/L_K)\propto
(0.27\pm0.03)\lg L_K$ within luminosities interval from $5\times10^{10}$ to $2\times10^{13}L_{\odot}$. This relation has a typical dispersion $\sim$0.1 that is comparable with uncertainties in measuring of integral luminosities and masses. At the same time mutual differences in mass estimations based on virial motions, X-ray flux or lensing turn out to be inessential.
4\) The largest and the most inhabited systems of galaxies — rich clusters/superclusters are characterized by values of mass-to-luminosity ratios being $M/L_K\simeq 50 M_{\odot}/L_{\odot}$, that constitutes only 16% from the global value $(M/L_K)_{global} = (316\pm29)M_{\odot}/L_{\odot}$. Since only small part of galaxies ($\sim$10-20% constitute to such supersystems, an ensemble averaged $<M/L_K>\simeq(20-25)M_{\odot}/L_{\odot}$ turns out to be certainly lower than that expected $<M/L_K>_m = (80-90)M_{\odot}/L_{\odot}$ in the standard cosmological model (Spergel et al. 2003) with $\Omega_m = 0.27$ and $\Omega_{\lambda} = 0.73$. To adjust together the ensemble averaged value $\Omega_{DM}\sim 0.07$ with the global value $\Omega_m = 0.27$ one needs to suppose that most part of dark matter in the Universe is not associated with galaxies or their systems (Karachentsev, 2005).
Concluding remark.
===================
As can be seen from the results above, IR-luminosities of nearby galaxies play important role in exploring dynamics and evolution of galaxy systems. Realization of the all-sky survey in J, H, K-bands and creation of the XSC 2MASS catalog allow one to investigate different properties for big samples of galaxies in unified photometric system. Determination of IR characteristics for a sample of nearby galaxies, which is distance, but not flux-limited, is an important task. Parameters of such sample must be marginally affected by different selectional effects, which complicate interpretation of initial data from observations. Unfortunately, among 450 galaxies of the Local volume within D = 10 Mpc only a small part (27%) is seen in the 2MASS because of low luminosity, low surface brightness or blue color. That is why measuring J, H, K-magnitudes for all galaxies inside the LV for the purpose of formation of reference sample seems to be a very promising aim. This sample could be an etalon while comparing it with deeper samples on different redshifts.
[**Acknowledgements.**]{} This work was partially supported by RFBR grant 04-02-16115 and DFG-RFBR grant 02-02-04012.
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My mind is amorphous,
refusing, like a cloud,
to retain its form.
My mind is a rabbit hopping
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stretching languidly until
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That is the winter mind,
informed by cold, crystal
pinpoints in the frigid air.
.
II. Spring
The spring mind, like
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Clusters of flowers
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My mind is amorphous,
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like a clump of fresh-
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.
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Heat radiates through
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for the time that “seasons
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fruitfulness” will be over. | https://gardenliteraryreview.com/2021/07/12/cartography-of-the-seasons/ |
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CONTINUING DATA
This application is a 371 of PCT/IBO2/03365, which was filed on Jul. 9, 2002. This application claims foreign priority to Italy M 101A001508, which was filed on Jul. 13, 2001.
The present invention relates to methods for finding optimal paths (routing) quickly and efficiently within telecommunications networks and in particular with SDH or WDM traffic.
The ever wider spreading of telecommunications services and the complexity of the apparatuses making up telecommunications networks bring considerable problems of design and implementation of routing algorithms which would be efficient and give satisfactory performance.
In the architecture of networks all the SDH or WDM apparatuses of the current generation do not play an active role in shortest path calculation and all the data concerning the network is memorized in a single database containing a complete view of the network.
In this centralized architecture the data describing the present status of the network must therefore be loaded from the database when the routing algorithm is to be applied for calculation of the shortest path and data routing. This generates not a few problems, especially if the present size of telecommunications networks is considered and especially their tendency to grow. Indeed, present-day networks are made up of several thousand apparatuses connected by a number of links proportionate to the number of apparatuses and the present rate of growth promises reaching tens of thousands in a short time to then proceed to hundreds of thousands in the not distant future.
It is clear that recovering such a large amount of data every time calculation of a shortest path is required involves a considerable effort and therefore too long response times. Accesses to the data base indeed constitute a set of very costly operations from the time viewpoint. The time employed in accesses proves to be much longer than the time actually spent on calculation. The large memory requirement for loading all the data contained in the database must also be remembered. In addition, restrictions on routing of the network members imply a posteriori verification of results with possible failures and the need to repeat the search algorithm. One proposed solution was to partition the network to secure the advantages of needing less memory (having a smaller graph) and securing a faster routing algorithm. But partitioning alone makes it possible to attack only part of the problems.
The general purpose of the present invention is to remedy the above mentioned shortcomings by making available a method enabling routing in telecommunications networks with greater efficiency, scalable so as not to be affected in an unacceptable manner by the increase in apparatuses and links in the network, and which would allow tracing the optimal path while respecting any connection restrictions of the apparatuses making up the network.
R
i
In view of this purpose it was sought to provide in accordance with the present invention a method for routing in telecommunications networks comprising the steps of partitioning the graph G of the network and creating a reduced graph Gon the partitions Pin a preprocessing step in which a dual graph of the network is constructed and the graph is reduced using connections restricted by the characteristics of the apparatuses and performing the routing on the graph thus converted.
FIG. 1
With reference to the figures, shows a generic example of a network. This network can be first of all partitioned so as to secure a certain number of partitions or subnetworks easier to manage. It is agreed that:
1. Each apparatus of the network belongs to a single partition. One partition contains multiple apparatuses. This implies that the intersection between the set of apparatuses belonging to one partition and the set of those belonging to another partition chosen at random is the empty set.
2. One partition does not contain other partitions. Partitioning of the network thus takes place at a single level of abstraction.
Interlink; these links connect two apparatuses belonging to two separate partitions. An interlink is characterized by the pair <source node, source partition> and <destination node, destination partition>.
Intralink; these links connect two apparatuses belonging to the same partition; an intralink is characterized by the triplet of values <source node, destination node, partition>.
3. The original links of the network are classified as:
4. No link can be classified at the same time interlink and intralink.
5. For both the partitions it connects, each interlink constitutes a port through which traffic can flow. The traffic actually flowing within the port will have a concordant direction with the <source partition, destination partition> arrangement. For this reason the same link fulfills the role of output port for the source partition and input port for the destination port.
i
i
i
i
k
To secure partitioning of a network represented by a graph with N nodes (apparatuses), M arches (links) and a cost function C(M), define a set of partitions P and assign to each partition P, nnodes and marches belonging to the original graph in such a manner that for each of these arches the tail and head nodes belong to P(intralinks). The remaining marches (i,j) with nodes i and j belonging to two different partitions are the interlinks.
k
The partitions P are connected through marches (interlinks) of the original graph.
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Application of rules (1) and (2) gives:
FIG. 1
FIG. 2
shows an example of a possible network which we shall call original network and shows a possible partitioning of this network in three subnetworks A, B and C. Of course with the increase in the size of the networks partitioning also generates subnetworks of excessive size as concerns database management. On the other hand partitioning of the network has a limit in the need to avoid excessive fragmentation of the network with resulting excessive number of partitions.
The purpose it is desired to pursue is to memorize an assemblage of basic data which summarize the present status of the network so as to avoid having to memorize a complete copy of the original graph, whether subnetwork or network, and thus avoid having to load all the data describing the network.
R
In accordance with the present invention, a reduced graph G is therefore extracted from the graph Gof the original network.
To construct this reduced graph the following steps are taken:
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1. Assign to each interlink of the original graph a node nin the reduced graph G.
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Divide the set of ports in the two input and output port sets.
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At partition level Passociate with each of the fictitious nodes ncreated under paragraph 1 representing a port (interlink) of partition Pa fictitious node which will be a fictitious input node nor output node ndepending on the direction of the associated port.
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Connect the fictitious node nor nwith the node which in the original graph is connected to the port in question. To avoid counting the same cost twice, assign cost to the arch which has the node nas its head. The cost of the arch having as its tail the node nremains unchanged at c.
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Calculate the shortest path from each fictitious input node nto each fictitious output node n; each path is characterized by a set of arches of the original graph which connect the <input port, output port> node pair.
2. For each partition P:
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3. Arch set calculated in paragraph 2 an arch in the reduced graph mconnecting the nodes nrepresenting the two ports. If the path between the two fictitious nodes does not exist and thus the set of arches associated with said path is the empty set, do not insert the arch in the reduced graph.
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the list L of arches of the original graph traversed by the path which in the original graph connects the ports for the fictitious nodes nand n,
the cost, which is the sum of the costs of the arches traversed by the path in the original graph, and
the name of the partition in which the path was calculated.
4. The following data are associated with each arch mof the reduced graph:
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(G(P)) is defined as the set of arches of Gwhose list of arches L was calculated within the partition P. In equivalent manner, (G(P)) represents the set of arches of Gwhose partition field is P.
FIG. 3
FIG. 1
FIG. 4
shows the addition of fictitious nodes for partition A of . shows the reduced graph representing the original partition A created by following the above mentioned steps.
To clarify understanding of the reduced graph construction, the costs of the arches were not inserted in the figures, so as to not complicate the illustration.
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1. List L: L={<,; >, <;>, <;>, <;>, <; ,>}.
2. Total cost of this path.
3. The partition name, A.
It is conjectured for example that the shortest path within partition A from port , to port , is {,; ; ; ; ; ,}. The data associated with the arch of reduced GR <,; ,> will thus be:
Again for the sake of clarity the path is designated as a succession of arches in which to each arch has been assigned as the identifier the pair of names of the associated tail and head nodes. Of course this wording does not apply if there is more than one arch connecting the same pair of nodes in the same direction.
Another simplification, again with the purpose of understanding this example, is to designate by different names the nodes belonging to different partitions; in reality an apparatus is distinguished by the ‘name, partition’ pair of values and it is therefore possible that two apparatuses belonging to two different partitions share the same name.
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When a connection request R arrives for a pair of nodes identified by the coordinates <source node n, source partition P>, <destination node n, destination partition P> it is necessary to complete the reduced graph by taking the following steps:
1. Add to the reduced graph the source and destination nodes of the original graph.
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Take from the database all and only the data for the source partition,
calculate the shortest paths from the source node to all the output ports of the source partition,
associate with each path calculated under the above paragraph an arch containing the same data contained by the other arches of the reduced graph (list of arches traversed on the source partition, total cost, name of the source partition).
2. For the pair <n, P>;
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take from the database all and only the data for the destination partition,
calculate the shortest paths from all the input ports of the destination partition to the destination node,
associate with each path calculated under the preceding paragraph an arch containing the same data contained by the other arches of the reduced graph (list of arches traversed in the destination partition, total cost, name of the destination partition).
3. For the pair <n, P>;
FIG. 5
FIG. 4
R
1
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shows an example of dynamic completion of the reduced graph applied to the Gof necessary for calculation of the path from node of partition A (<,A>) to node of partition C (<,C>).
When the reduced graph is complete it is possible to calculate the shortest required path by operating directly on the reduced graph.
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So an ordered list of arches <n,n> of the reduced graph Gis found. With each member of the list, that is with each arch mof the reduced graph, is associated the list of arches of the original graph which are traversed by the shortest path between the two ports associated with the fictitious nodes nand n.
The last step, necessary for supplying the required solution, consists of linearizing the list by following the order of the arches of the reduced graph making up the solution and of course avoiding repetition of the interlink arches.
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FIG. 5
FIG. 6
FIG. 6
Assume for example that the shortest path from node of partition A <,A> to node of partition C<,C> calculated on the reduced graph of is the one shown in . As may be seen in , this shortest path is made up of the sequence of three arches of the reduced graph, to wit the arch <,A; ,> and the arch <,; ,C> which were added during dynamic completion of the reduced graph and the arch <,; ,> which was introduced during construction of the reduced graph.
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L={<;>, <;>, <;,>}.
1
Cost c=12.
Partition name: A.
1. Arch <,A; ,>:
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L={<,;>, <;>, <;>, <;>, <;, >}
2
Cost c=5
Partition name: B.
2. Arch <,; ,>
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L={<,; >, <;>, <;>, <;>}
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Cost c=6
Partition name: C.
3. Arch <,; ,C>:
Assume that the following data are associated with the three arches:
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The shortest path from node to node in the original graph thus has a cost equal to the sum of the costs of these three arches, c=c+c+c=23, and is made up of the following sequence of arches: path ={<;>, <;>, <;>, <;>, <;>, <;>, <;>, <;>, <;>, <,>}.
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FIG. 7
The path found from node to node on the original graph is thus the one shown in .
FIG. 8
It should be noted that the routing method proposed ensures that the optimal path is calculated even in the special case where the optimal path passes through the same partition several times as shown by way of example in .
This is very important where the source and destination nodes belong to the same partition. In this case it may be advantageous to load all the data associated with the partition containing the two nodes and attempt first to calculate the shortest path between the two nodes inside the partition without using the reduced graph. The path thus calculated is not necessarily the optimal one which could pass through other partitions and then return within the partition containing the two nodes but it is a valid solution to the problem of creating a connection because in general the number of links making up the path can be limited. If this first attempt fails because the path within the partition does not exist, it does not mean that it does not exist in the original network; for this reason, if the path was not found, it suffices to extend the calculation to the entire reduced graph, proceeding by the method in accordance with the present invention as in the general case.
Again with reference to calculation of the shortest path on the reduced graph, cancellation on the reduced graph of the source and destination nodes and associated incident arches can be performed at any time before calculation of the following connection. On this point it may be advantageous to cancel this data only when a new connection request arrives. This way, if the new source or destination node coincides with the previous source or destination node the previous data can be reused.
It will of course be necessary to update the links which may have become inconsistent after calculation of the previous connection.
This is a general requirement; a solution being supplied, it is necessary to ensure consistency of the reduced graph with the original graph. The reduced graph must at all times summarize the present state of the network.
There are different situations which could generate consistency problems. The main ones can be summarized as the use of resources already allocated, release of a connection, insertion of a new node or link in a partition, cancellation of a node or link in a partition, insertion of an interlink, and cancellation of an interlink.
These main case are examined below.
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For example, to avoid a subsequent connection being able to use the resources of the one just calculated, the resources used by the solution found should be assigned; in this manner a subsequent connection request cannot use these resources until they are released. The problem of consistency, which in this case we can define as the ‘resource occupation problem’, occurs for all the mlinks of the reduced graph Gbelonging to the path found and for all the links of the reduced graph Gcontaining in their list L a link G belonging to the solution found. On the contrary, the consistency problem in this case does not occur for all the links of Gcalculated in G partitions not traversed by the connection set up and for all those links of Gnot containing in their lists one of the links belonging to the solution found; the shortest path remains unchanged as regards the case in which the resources had not yet been assigned.
An identical consistency problem with an identical solution is had when a node or link of a partition is cancelled. On the other hand, upon release of a connection there is the situation, dual of the preceding one, which can generate consistency problems because of the resources previously occupied by a connection become available for calculation of new connections. In the presence of such an event therefore it is necessary to update all the paths calculated in the partitions of G which are traversed by the released connection.
Identical consistency problems are had with the insertion of a new node or link in a partition and it is again necessary to update all the paths calculated in the partition where the new node or link is installed.
But when an interlink is inserted, a new node belonging to GR is associated with the new arch of G. Insertion of this new node involves calculation of the paths of all the input ports up to the interlink in question within the partition containing the tail node and calculation from the interlink to all the output ports within the partition containing the head node.
On the contrary, upon cancellation of an interlink the node of GR which represented this port must be cancelled together with all the input and output arches affecting it. As may be seen, some diligence is necessary to keep the reduced graph always consistent. The doubt may arise that the diligence expended to keep the reduced graph consistent annuls the advantage of using it and that better response times are not had than when all data are extracted from the database each time a new connection request arrives.
In reality it has been proven that the time necessary to update the reduced graph can be tranquilly spent after exposure of the path found and therefore in the dead time between two requests. On the client's part, if the routing algorithm uses the reduced graph there is thus the undoubted advantage of receiving an immediate response because the updating time of the reduced graph does not weigh on the client.
The only accesses to the database made in the lapse of time between arrival of the connection request and viewing of the response concern only the two source and destination partitions; it is recalled that these data are necessary for dynamic completion of the reduced graph. It is clear that in this manner the purpose of acceding as little as possible to the database is achieved.
In addition, it was observed experimentally that the number of links making up a connection is very small as compared to network size.
The small number of arches making up a connection allows it to be stated that the probability that the connection will traverse few partitions is very high and this means that having to load a considerable amount of date from the database is unlikely. Only in the reduced graph construction step is access had to the database to take all the data of the network and this preprocessing step once ended no longer affects response time.
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At the same time, given a partition Ptraversed by the connection just set up, it is unlikely that all the arches of (G(P)) will have to be calculated again because as the number of arches of the connection belonging to the partition Pis not high it is unlikely that an arch of G(P) will contain in its list L one of the arches of the connection. In reality, this last aspect depends strongly on the topology and distribution of costs of the various partitions and in the construction of the reduced graph it may happen that several arches of G(p) will contain the same link if there are obligatory paths or arches in the Pespecially advantageous in terms of cost.
The possibility of ‘paralellizing’ the algorithm should not be undervalued. Since the apparatuses managed do not fulfill an active role in calculation of the shortest path and hence it is impossible at the moment to realize a distributed algorithm, the only way to achieve this purpose is to make the best use of the calculators designed for network management. These calculators are multiprocessor machines with shared memory and very powerful.
Use of the reduced graph added to partitioning of the network allows distribution of the workload over various processors on the basis of a geographical distribution of resources and it may be sought to associate a thread with each partition so as to perform the operations of construction and updating of the reduced graph in parallel. In telecommunications networks some SDH or WDM apparatuses distributed in the network introduce connection restrictions which considerably complicate the routing algorithm. A connection restriction implies that it is not always possible, given an established input port, to connect it with just any output port.
ports without restrictions for which a signal reaching the input to the apparatus through one of the ports belonging to this set can leave the apparatus through any output port belonging to this set,
ports with total restriction or ‘fixed cross connection’ ports; a signal reaching the apparatus input through one of the ports belonging to this set is forced to leave the apparatus through a predetermined output port belonging to this set, and
ports with partial restriction or protection; these ports are used to protect the connections which were set up using the ports of other sets. The restrictions of this set of ports depend on which connections are to be protected. To these connection restrictions which limit switching operations are added for example those due to the impossibility of connecting an optical signal from a certain channel characterized by a certain wavelength to another channel also characterized by its own wavelength. This problem appears for example in the multiplexing of several signals from the SDH domain to the WDM domain which takes place through the use of appropriate cards and a multiplexer (MUX).
The ports of an apparatus can be arranged for example in three possible sets depending on the connection restrictions they have. The following can be distinguished:
Each of these cards must of course transmit its signal to the multiplexer using a wavelength different from all those with which the other signals input to the MUX coming from other cards are sent. The MUX has the function of multiplexing these different signals in a single WDM signal and transporting them with different wavelengths within the same fiber. The wavelength at which the signal is sent from the card to the MUX is set through hardware. In truth there are different studies aimed at allowing setting of the appropriate ë by software, which would introduce higher degrees of freedom in the routing process.
All these limitations entail solving the shortest path problem with penalties and prohibitions; with each pair of arches (i,j)(j,k) is associated a penalty indicating the cost of switching an input signal at node j from the arch (i,j) to the arch (j,k). If the switching is not allowed the penalty is infinite.
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With a dual network at each arch of the original graph is associated a node in a ‘converted graph’. An arch is associated with each penalty. A disallowed switching is simply shown as absence of the arch in the converted graph. It was surprisingly found that among the various possible conversions a dual graph conversion or dual graph appears to be the most satisfactory. Just for the dual conversion characteristic, in a telecommunications network where the nodes are much smaller in number than the connections, the conversion into a dual graph should generate an unacceptable increase in complexity. In the dual graph the number of nodes is equal to the number of arches in the original graph and the arches of the converted network represent the admissible cross connections in the network apparatuses. The most obvious problem of the dual graph applied to the world of SDH or WDM telecommunications is that to represent some restrictions introduced by some apparatuses the same conversion must be performed for all the apparatuses. This implies that the conversion must also be performed for all those apparatuses which do not introduce connection restrictions and for which the preparatory physical expansion work of the nodes is therefore too costly; an apparatus which has no connection restrictions is exploded through the dual graph into a number of nodes Ò=(Ò+Ò) where Òrepresents the number of input links to the apparatus in the original graph and Òrepresents the number of output links from the apparatus of the original graph and into a number of arches equal to M=(Ò×Ò).
It is seen below that the use of dual conversion and reduced graph and partitions of the present invention gives rise to what can be called ‘clever dual graph’ conversion which cancels the disadvantages of the dual graph and, on the contrary, allows achievement of high routing efficiency.
This method uses dual conversion to construct graphs associated with the various partitions; once the paths necessary for construction or updating the reduced graph are calculated, said graphs are cancelled.
It is thus achieved once again that the the only data structure kept permanently and updated regularly is the reduced graph. Calculation of the paths from the input ports to the output ports of each partition ensures that the connection restrictions of the apparatuses are respected. The connection established by operating directly on the reduced graph GR thus respects the restrictions because it is the linking together of various paths which are all admissible.
On the reduced graph therefore it is not necessary to perform any conversion but the above described is used directly for seeking the shortest path in the unrestricted case.
By using partitioning of the network, growth of the number of nodes and arches is limited to the partitions involved each time in updating of the network. To underscore this fact, suffice it to think what it means to load from the database all the data concerning the network and operate the conversion on such a large amount of data each time a connection request arrives.
Assume a network G(V,A) where |V|=N and |A|=M and designate by W the average number of input links to each apparatus. Since an input link to an apparatus is an output link from another apparatus, W also represents the average number of output links from each apparatus.
To avoid possible misunderstandings it is observed that W was defined herefrom as the average number of input or output links to or from each apparatus which are actually installed in the network. It is wrong to confuse this number with that of the links which the apparatus can manage at input or output; these two values coincide only in the worst case, from the viewpoint of size of the converted network, in which each apparatus has at input or output the maximum number of installable links.
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In the worst case, in which all possible cross-connections are admitted, the dual graph conversion generates a network consisting of M nodes and N×Warches since each arch becomes a node and for each apparatus there are Warches. Each input link can be connected to each output link and the average number of input and output links is W.
From the foregoing it is clear that to construct and update the reduced graph it is necessary to perform the shortest path search algorithm several times. The choice of which shortest path algorithm to use is therefore one of the critical points.
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A choice based on efficiency can advise the use of the Dijkstra algorithm implemented with the particular data structure of the Fibonacci Heap. In this implementation of the Dijkstra algorithm the computational complexity on a network with N nodes and M arches is equal to O(M+N×log(N)), substituting for M the value N×W and for N the value M it is found that the complexity of the converted network is:
O(N×W+M×log(M))
It is observed that the value W is limited above by the maximum number of links manageable by the apparatus and accordingly the previous complexity becomes:
O(N+M×log(M))
In practice however the value of W is important especially in networks made up of few nodes and arches.
R
At this point the following consideration becomes necessary. SDH traffic is structured traffic and consequently each connection request must specify the type of traffic desired in addition to the pair of source and destination nodes; this implies that a reduced Gfor each type of traffic is kept in the memory.
In theory, at the level of creation of the graph representing the network (regardless of the use of the reduced graph) this situation would involve an expansion of each link into a number of arches equal to the number of containers available on that link in relation to the type of traffic requested. The basic observation is that the connection restriction concerns the pair of input or output links and not a particular container chosen within the two links. In this manner, in the data taking step, it is possible to choose any one of the containers available for support of the type of traffic requested. To ensure correct traffic distribution the cost of the arches is established on the basis of a linear combination of the cost assigned by the client to that link and the availability of traffic on that link.
The same reasoning applied for SDH traffic is valid for WDM traffic where the optical apparatus is able to make a complete wavelength conversion. Even in this case, indeed, it is possible to choose any one of the channels available on the optical link instead of exploding the link into the number of channels available and assign a cost in accordance with the criterion proposed for SDH traffic. Besides, other wavelength assignment policies can be applied.
Clearly the apparatus input and output links to and from the apparatus can be exploded so as to assign costs which favor cross connections which do not make wavelength conversion if this operation takes place without conversion of the optical domain signal into the electronic one and vice versa (OEO conversion).
For WDM single-hop networks on the other hand it is necessary to explode each link into a number of links equal to the number of channels available.
Single-hop networks, indeed, introduce the ‘wavelength continuous restriction’ in which the connection which is to be established will use the same wavelength in each of its links. To obtain an admissible solution it is necessary to insert into the converted network only the arches representing a cross connection between two identical wavelengths. From the viewpoint of the restriction introduced we can compare the wavelength continuous restriction with the fixed cross-connections.
We wrote above about the apparent increase in complexity which the use of a dual graph should introduce. In reality, with partitioning in accordance with the present invention it is possible to divide the apparatus into sets which have as a characteristic the fact that they possess connection restrictions and sets which do not have connection restrictions. In this manner there are apparatuses without connection restrictions in the partitions and the dual graph is not used but the preferred ‘single shortest path algorithm’ is applied directly. If in the same partition there are both types of apparatus, with and without restrictions, the following procedure termed ‘clever dual network’ may be applied. In other words the dual network is not efficient for network members without restrictions. In this case a variation is possible on the method or algorithm (clever dual network) which uses the fact that these nodes are characterized by each input being able to reach an output without any penalty. Each arch is therefore with zero penalty. In this manner the arch from p^2 to 2p is possible.
It consists of the following steps.
FIG. 9
A apparatuses without connection restrictions; any input port can be connected to any output port,
B apparatuses with partial connection restrictions; there is at least one set made up of input and output ports within which it is possible to connect any input port with any output port, and
C apparatuses with total connection restrictions; each input port has restrictions to be respected.
1. Divide the apparatuses in the following three classes (an example of apparatuses in the three classes is given in ):
2. Associate with each type A and B apparatus a fictitious node Nf in the converted graph.
3. Associate with each link having as tail or head a port with connection restrictions a fictitious node Lf in the converted graph; this takes place if one of the two nodes of the original graph is type C or B and the port used has restrictions.
for each fictitious node Lf created under paragraph 3 and concerning it insert a link connecting Lf to Nf if the original arch for Lf was input to the original node for Nf; the cost of this arch must be that of the original arch represented by Lf;
for each fictitious Lf node created under paragraph 3 and concerning it insert a costless link connecting Nf to Lf if the original arch for Lf was output for the original node associated with Nf; and
consider the arches of the original graph not having undergone the conversion described in paragraph 3 and which have in the original graph the node for Nf as head or tail; for each arch connect Nf to the other fictitious node associated with the tail or head node of the original graph while keeping the same cost of the arch of the original graph.
4. For each fictitious node Nf of the converted graph associated with an original type A node;
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consider all the fictitious Lfor Lfnodes created under paragraph 3 for input or output arches of the original graph in a port with restrictions to or from the node for the fictitious node Nf and for each of these fictitious nodes Lfinsert a link connecting Lfto the other fictitious Lfnodes; this connection must be made only for the pairs of fictitious nodes Lf, Lfcorresponding to pairs of arches of the original graph which are connectable; the cost of the arch must be equal to the sum of the cost of the original arch represented by Lfand the cost of the penalty to be paid for connecting the two arches in the original graph;
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consider all the fictitious nodes Lf, Lfcreated under paragraph 3 for input or output arches of the original graph in a port without restrictions to or from the node for the fictitious node Nf and insert for each of these fictitious nodes Lfa link connecting the fictitious node Lfto the fictitious node Nf while keeping the cost of the original arch represented by Lf, and for each of these fictitious nodes Lfinsert a link connecting the fictitious node Nf to the fictitious node Lfat zero cost;
consider the arches of the original graph which have not undergone the conversion described under paragraph 3 and which in the original graph have the node represented by Nf as head or tail; for each arch connect Nf to the other fictitious node associated with the tail or head node of the original graph while keeping the same cost of the original graph arch.
5. For each fictitious node Nf of the converted graph associated with an original type B node;
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all the fictitious nodes Lfor Lfcreated under paragraph 3 are associated with input or output arches of the original graph in a port with restrictions to or from the node represented by Nf; insert an arch for all the Lfor Lfpairs which represent two arches connectable in the original graph.
6. For each fictitious node Nf of the converted graph associated with an original type C node;
FIG. 10
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shows by way of example an original network to which the steps of the above described method are applied. In particular the figures, from to show steps 2, 3, 4, 5 and 6 of the conversion respectively.
We described above how partitioning of the network in accordance with the present invention allows limiting the size of the dual graph; network conversion is applied individually to each partition to allow construction operations, dynamic completion and updating of the reduced graph.
By so doing, each partition has a smaller number of nodes and links than the whole network. After each of these operations the data structures representing the dual graph of the partitions involved are cancelled.
These remarks do not change if clever dual network is considered in place of the dual graph.
But the clever dual network of the source and destination partitions involved in dynamic completion of the reduced graph must also be constructed when a connection request arrives. In addition, it must be possible to identify the nodes of the request in the converted network.
Starting from the above observations the following further steps can be formulated for dynamic completion of the reduced graph.
1. During the construction operations of the clever dual network for the source or destination partition, if the source or destination node is type C a fictitious node is added; if the source node is type A or B the node of the converted network is created directly during the normal operations necessary for construction of the clever dual network.
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2. Consider the source node nand if nis type A no action is taken; if nis type B add for each output port with connection restrictions an arch between the fictitious node representing nin the converted graph and the fictitious node representing the link on that port; if nis type C add for each output port an arch between the fictitious node representing nin the converted graph and the fictitious node representing the link on that port.
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3. Consider the destination node nand if nis type A no action is taken; if nis type B add for each input port with connection restrictions an arch between the fictitious node representing the link on that port and the fictitious node representing the nin the converted graph; if nis type C add for each output port an arch between the fictitious node representing the link on that port and the fictitious node representing nin the converted graph.
preprocessing,
routing on the converted graph, and
updating the graph.
In other words, to sum up, the method proposed therefore consists of three steps, to wit:
construction of the dual network, and
reduction of the graph using the fixed connections;
realizing this operation may be an option.
The preprocessing consists of two steps, to wit:
Each time a routing for a type of traffic not yet considered is requested, a reduced graph for that traffic is constructed, canceling the arch of the original graph which does not support that traffic.
For each type of traffic the reduced graph developed by applying the partitioning of the graph described above is kept in memory.
Routing on the converted graph is done in such a way that for each request from node s in partition A to node d in partition B, type of traffic tr, the part of the graph associated with traffic tr and partitions A and B is relplaced by two subgraphs giving least cost from node s to the nodes on the edge of partition A and least cost from the nodes on the edge of partition B to node d.
To this final graph is applied a shortest path search algorithm and, the path being found, the associated resources are reserved.
Updating of the graph is necessary before the next routing but is applied only to the partitions used by the routing. In particular it is necessary to update only the paths of the converted graph which in the original graph share at least one arch with the calculated routing.
This updating is necessary even when a node is inserted, changed or canceled.
FIG. 12
FIG. 13
FIG. 12
FIG. 14
2
shows an example of a network. shows the dual network for subnetwork of . In this example all the penalties are equal to 1: òij,jk=1 for each ij,jk. The corresponding reduced graph is shown in . It is seen that if Min(p) and Mout(p) designate the number of I/O arches from and to a partition, in the converted graph there are no more that Min(p)×Mout(p) arches for each partition p.
FIG. 15
The members of networks A and D have complete connection restrictions,
the member of network B has partial restrictions on the connection, and
the member of network C has no connection restriction.
shows an example of some apparatuses making up the network and having connection limitations. For example, the limitations are as follows:
full restriction on connection; all I/O connections become nodes;
no restriction on connection; all connections connecting the network member with the network members with connection restriction become nodes; all connections connecting the network member with network members without connection restrictions become a single connection connecting the node without restrictions to a new fictitious node related to the network member without connection restrictions.
To convert the network, three different rules are applied depending on the characteristics of the network members. The first two rules are as follows:
FIG. 15
FIG. 16
Applying these first two rules to the original network of we obtain the graph of .
The third rule concerns the case of partial connection restrictions; a set of completely connectable ports are represented by a single node; ports with connection restrictions are treated in accordance with the rules of full connection restrictions.
FIG. 17
Applying this rule also, the final network is the one shown in outline in .
To summarize what is written above, a summarizing example setting forth the operations necessary for identification of a shortest path in a network with apparatuses which introduce connection restrictions is shown below.
FIG. 18
In accordance with the method of the present invention the first step consists of partitioning the original network at one level and classifying the various apparatuses inside the partitions according to the connection restrictions they display. This first step is shown in .
FIG. 19
Subsequently, for each partition, it is necessary to insert the fictitious nodes representing the interlinks of the original graph and perform the clever dual network conversion following the operations described above. This step is shown in .
FIG. 18
FIG. 20
For each partition the shortest paths connecting the <input port & output port> pairs are calculated. If for a pair of such ports there is no path, no arch is inserted in the reduced graph. Proceeding as explained above, the reduced graph GR is constructed. The reduced graph associated with the network of is shown in .
FIG. 21
FIG. 22
When a connection request (<S,Pa>, <D,Pc>) arrives it is necessary to complete dynamically the reduced graph as explained above while allowing for the clever dual network conversion. This step is shown in where the clever dual network of the partitions involved in the dynamic completion of the reduced graph is seen while the final result of the completed reduced graph for calculation of the (<S,Pa>, <D,Pc>) connection is shown in .
It is emphasized that as concerns node S belonging to the type A node category no node was added because the fictitious node Sf is created automatically during construction of the clever dual network of Pa. For node D belonging to the type C node category it is necessary to insert a fictitious node Df which, being a destination node, represents the head node of all the arches connecting it to the nodes representing the links appearing on the input ports of D.
FIG. 22
FIG. 23
FIG. 24
Lastly, the required path is calculated on the reduced graph of to find the result shown in to which corresponds the path represented in in the original graph.
It is now clear that the predetermined purposes have been achieved.
R
Among the various advantages of the method of the present invention the dual conversion allows subsequent and simpler development of the protection techniques of the network which are basic because of the enormous band supplied by optical fiber communications. On the converted network generated by the dual conversion, shortest path algorithms used in the normal circuit switching networks among which, for example is the algorithm of Dijkstra, can still be used. In addition, the size of the converted network decreases with the increase in the number of connection restrictions in the apparatuses. The fixed cross connection for example considerably reduces the number of arches in the dual network. Lastly, the work of conversion of the original network in the dual network is considerably limited due to the use of network partitioning. Once the reduced graph Gis constructed, indeed, this work is done only on the source and destination partitions to supply the response to the connection request and on the partitions traversed by the path in the subsequent updating phase which does not burden the client.
Naturally the above description of an embodiment applying the innovative principles of the present invention is given by way of non-limiting example of said principles within the scope of the exclusive right claimed here.
To clarify the explanation of the innovative principles of the present invention and its advantages compared with the prior art there is described below with the aid of the annexed drawings a possible embodiment thereof by way of non-limiting example applying said principles. In the drawings:
FIG. 1
shows a graph of an example of a network,
FIG. 2
FIG. 1
shows a possible partitioning of the network of in three subnetworks A, B and C,
FIG. 3
FIG. 1
shows the addition of fictitious nodes for partition A of ,
FIG. 4
shows the reduced graph of the original partition A and created by following the method of the present invention,
FIG. 5
shows an example of dynamic completion of the reduced graph,
FIG. 6
shows an example of the shortest path found on the reduced graph,
FIG. 7
FIG. 6
shows the shortest path of transferred onto the original graph,
FIG. 8
shows an example of a network graph with an optimal path passing through the same partition several times,
FIG. 9
shows a schematic subdivision of apparatuses on the basis of connection restrictions.
FIG. 10
shows an outline of an original network example to which is applied a ‘clever dual network’ method in accordance with the present invention,
FIGS. 11
FIG. 10
a
e
11
to show graphically successive steps of the method applied to the network of ,
FIGS. 12 to 14
show an example of an application of steps of the method in accordance with the present invention,
FIGS. 15 to 17
show another example of an extended application of steps of the method in accordance with the present invention, and
FIGS. 18 to 24
show an extended example of an application of the method in accordance with the present invention. | |
Q:
Do all integrable functions on $[0,1]$ form a vector space?
Does the set of all functions integrable over $[0,1]$ form a vector space?
(Here we are assuming "standard" definitions of addition and multiplication).
Here is what I have tried:
Define $\mathcal{F}=\lbrace f(x) | \int\limits_{0}^1f(x)dx\in\mathbb{R}\rbrace$.
For $f,g,h\in\mathcal{F}$ the following hold:
I proved several of the properties (commutativity of addition, associativity of addition, additive identity with $z(x)=0$). I am stuck as to how to prove that there is an additive inverse and multiplicative inverse for all $f\in\mathcal{F}$.
A:
First of all, multiplication is not needed for vector space. What is needed is multiplication by scalar.
So, the operations are
$$(f+g)(x) = f(x) + g(x),\ (\alpha f)(x) = \alpha f(x), \forall f,g\in\mathcal F, \alpha\in\mathbb R$$
and we need to show that they are well defined. This is a direct consequence of linearity of integral:
$$\int(\alpha f+\beta g)(x)\,dx = \alpha\int f(x)\,dx + \beta\int g(x)\,dx.$$
Additive inverse is $(-f)(x) = -f(x)$.
The rest of the vector space axioms can be checked easily - they are consequence of the same axioms holding in $\mathbb R$.
| |
Loto is a upland variety from the Emilia-Romagna region of Italy. It is classified as a “risotto type”.
Our initial seed some came from Sherck Seeds and has been successively direct seeded for 2 years.
Three packet options, minimum:
a) 50 choice hand selected seeds
b) 7 grams
c) 28 grams (1 ounce
Seeds weight 2.8 grams per 100 seeds. | https://greatlakesstapleseeds.com/products/loto-upland-rice |
Sitting with your back upright and in a comfortable position. Close your eyes. Take a few moments to feel the movement of the air around you. And breathe in and out in a relaxed, gentle rhythm.
Begin to notice how the air is moving into your nostrils as you breathe. Linger with your attention on this movement for ten more revolutions of breathing and as you do so, feel your body and mind relax. Becoming more and more relaxed with every breath that you take in.
Imagine now that in your mind’s eye that you find yourself in a place of deep comfort, a place where your mind can go to seek solace and relax. It may be a place you have been to physically before, or perhaps be somewhere from pure imagination; a waterfall, seashore, a cornfield or perhaps at the foot of your favourite tree. Make the image of your chosen place as vivid, as real in your mind’s eye as possible. Feel the touch of the air on your skin, breathe in the scents and listen to all the sounds that swirl around you. Now here in your place of comfort, imagine before you an ornate archway, a doorway if you will to another realm. Make this picture as clear as you can with your inner eye. If a clear picture evades you, simply see if you can sense or feel its presence.
And now taking a gentle breath inwards, step through the archway.
You find yourself at the top of a rocky cavern, which opens up to the earthly realms below. Ten stone steps lead downwards into the womb of the great mother. And the steps are lit on either side by flaming crystal torches that illuminate the steps and cavern walls.
Breathe deep and step down onto the tenth top step and as you do feel yourself let go of extraneous thoughts and relax. Now breathing gently and rhythmically step onto the ninth step and relax even more. Now continue to breathe and walk, down each step feeling more and more relaxed with every step that you take. Step eight, seven, six and step five, now rest on the fifth step for just a moment and notice your surroundings.
Continue with another breath inwards down onto step four, feeling even more relaxed. Step three, breathing gently, to step two and now feeling completely relaxed and at peace walk down onto the final step. Breathe deep once more and step down onto the soft belly of the earth.
You are in a glorious cavern, crystal rock formations sparkle all around you, shimmering with light.
Stalactites majestically rise up from the floor of the cavern to greet pure white stalagmites clinging to the cavern ceiling.
Take a few moments now to centre yourself in this place. How do you feel?
Listen carefully now, here in the mother’s inner temple. The sound of moving water is flowing in rhythm like music. Let the sound of trickling water guide you forward, step and breathe until you see before you three tranquil pools of water, clear and calm, nestled between every growing calcite rock formations. These are the waters of divine manifestation, the reflective mirrors of the God herself.
Approach the first pool and look into the water’s depths. This is the pool of your younger self. The instinctual self. The self that wishes to learn, explore, play and create. Your younger self-aware for the first time that it is conscious. Look deeply into these waters. What do you see, hear, taste and sense?
The time has come to move to the second pool of water that you see. Breath gently and approach.
This is the pool of your talking self. The self who has experienced itself manifest, as human, as a conscious expression of the great mother, the self that can communicate with the physical world and all other physical expressions of the divine. This is the self that learns from experience. The self that strives to express what it has found.
Look deeply into these waters. What do you see, hear, taste and sense?
Move now to the third and final pool, breath gently and approach.
This is the pool of your Godself. Of God herself. The self which is always in communion with the divine mother, that understands that it is a spark of divine ever evolving. This is the endlessly creative, compassionate, understanding and boundless self. The self which is connected and understands the true nature of love.
Look deeply into the waters. What do you see, hear, taste and sense?
The music of the waters drifts back into your ears, a call to depart this place and return to the earthly realm above. Take a moment longer, close your eyes and listen. Are there any words or images which the Goddess wishes to impart to you here in her wise womb before you leave?
With gratitude for all you have experienced here, move forward towards the stone steps that guided you into the mother’s cavern.
At the bottom of the staircase begin breathing gently and rhythmically. Now begin your ascent up the stairway.
As you climb feel yourself becoming more and more awake and more refreshed, step one, two, three and four. Now step onto the fifth step and notice just how energized you are feeling. You are bringing earth energy up within you.
Now place your feet onto step six, feeling more alert, seven, eight and nine. You are now about to step onto the final step, and as you do so, you are aware that when you walk onto the top step, you will be able to see the ornate archway which led you to the stone stairway. Step onto the final step and on seeing the archway walk through it once again.
Once more imagine your sanctuary place, your place of comfort. Breathe and allow the room in which you sit become clear in your vision. Breathe deep.
And on the count of three, you will open your eyes. Fully present in your body, refreshed and awake. One, two three.
Open your eyes.
Feel yourself fully present in your body and say your name out loud three times.
If you have your journal to hand, sit for a few minutes and write down as much detail of your journey as you can. | http://torstone.org/featured-articles/meditations/the-three-souls |
True fact…I was told by a reliable source ,that studies the alternative universe, years ago that I am in fact 90% fairy 10% human…totally agree but I prefer the term Pixie.
My Pixie really comes out whenever I have a run…as you can see I was full on 90% Pixie for the Georgia Half Marathon and it was exciting to see some fellow Pixies at the start line…
It’s not just about the attitude that makes one a Pixie but the ever important uniform…
Standard Pixie uniform:
- Wings (on back and shoes)
- Magic Wand or Scarf if you misplaced your Wand
- A Rainbow somewhere represented
- Sparkles…lot’s of Sparkles
Any other Fairy/ Pixies out there???
Power to the Pixies! | https://jsy-styleblog.com/2013/03/20/90-fairy-10-human/ |
writing a abstract is a skill. its a short scientific summary of your research work. to make it simple and clear you need indicate the objective, methodology and salient findings of your research ... PDF Developing Hypothesis and Research Questions RESEARCH QUESTIONS. Qualitative Approach. The use of Research Questions as opposed to objectives or hypothesis, is more frequent. Characteristics Use of words- what or how. Specify whether the study: discovers, seeks to understand, explores or describes the experiences. Use of non-directional wording in the question. Research Methods: Writing: Introduction In this section the researcher might discuss the nature of the research, the purpose of the research, the significance of the research problem, and the research question(s) to be addressed. Three essential parts of a good introduction are:
Top-100 Nursing Research Paper Topics
Got a great handout a while back that I stumbled over today, hopefully it's as helpful to you as it was to me. Here are the steps for writing good (mass communication of course) qualitative research questions: Specify the research problem: the practical issue that leads to a need for your study. How to Write a Science Research Question Humans are a very curious species. We are always asking questions. But the way we formulate a question is very important when we think about science and research. Here we'll lay out how to form a science research question and the concepts needed to formulate a good research question. Luckily, we've got some handy visuals to help you along. 100 Original Research Paper Topics For Students in 2019 ... Ideas for Research Paper Topics. Without a good topic, writing a research paper can be a student's worst nightmare. So, how do you come up with one? There are dozens of ways to brainstorm, such as discussing with classmates, reading topic prompts, sample papers, magazines, journals, blogs, or books. How to write Qualitative Research Questions and ... Learn how to create a qualitative research survey question to have a better understanding of a particular topic or to inspect a new subject to know the nerve of respondents in terms of their experiences. In this blog, we discuss points to keep in mind while designing qualitative survey research questions.
This Chapter outlines the logical steps to writing a good research paper. To achieve supreme excellence or perfection in anything you do, you need more than just the knowledge. Like the Olympic athlete aiming for the gold medal, you must have a positive attitude and the belief that you have the ability to achieve it.
A good research question is essential to guide your research paper, project or thesis. It pinpoints exactly what you want to find out and gives your work a clear 10 Research Question Examples to Guide your Research Project Learn how to turn a weak research question into a strong one with examples suitable for a research paper, thesis or dissertation. How to Write Good Survey Questions | Qualtrics UK Writing good market research survey questions is an art. Follow these simple tips to help you write questions that will deliver the best information (PDF) How to…write a good research question
bad research questions | patter - patthomson.net
Research Paper Question - The Purpose of the Paper Once you have a good research paper question, you can then begin to generate a testable hypothesis or research question, and construct your paper around this. At the end of the research, you will be able to refer your results and discussion back to the research paper question, adding a little more information to the store of human knowledge. Guidelines for Writing Good Questions A few focused questions are much more useful than a collection of general ones. Make sure that the student knows how you expect them to respond to a question e.g. do they have to tick/cross underline/write their own answer etc. Avoid double-barrelled questions, as students might want to respond differently to each part e.g. | https://myblog2021henal.netlify.app/annese20638cily/how-to-write-good-research-questions-ligy.html |
FIELD OF THE INVENTION
BACKGROUND OF THE INVENTION
SUMMARY OF THE INVENTION
DETAILED DESCRIPTION OF THE INVENTION
The invention relates in general to avoiding register errors in the process and control of a printing mechanism.
In the printing industry, various processes are used to avoid and correct compass and register errors. Compass or register errors occur when an image is imprinted at an incorrect location on a printing image carrying element or on a printing medium. The term “in compass” or “in register” identifies a condition in which the printed image is imprinted at the correct location on a printing medium, i.e., the image is imprinted at the proper level or in the proper position. In multi-color printing, the term “compass” is standardly used, while in mono-color printing, the term “register” is used. To avoid compass and/or register errors, register marks or marks that are imprinted on a carrying element of the printing machine or on the printing medium, are often used in order to check the printing medium's register or compass; i.e., whether the compass or register is free of error. In the foregoing, the term “mark” will be used exclusively to describe both terms (compass and register).
The carrying element is often the conveyor belt that carries the printing medium or, in the case of electrophotographic printing, the master cylinder that carries the printed image. Marks come in various shapes, sizes, and colors. Outside of the printing machine, marks are manually measured by an operator with the aid of a magnifying lens and measuring mechanisms. Inside the printing machine marks are automatically measured with the aid of sensors, whereby any shifting of the printed image will be identified. Identification of a compass and/or register error is accomplished either before imprintation, as a means of calibrating the printing machine, or during the imprintation, i.e., on the fly.
The quality of the correct positioning of the compass and/or register is a significant factor for the quality of the printing result. With increasingly higher demands for quality printing and for proper positioning of the imprinted image, attempts are made to adjust the register with even greater precision.
In view of the above, this invention is directed to ensuring proper compass and register positioning during printing. The invention avoids compass and register errors in a printing machine, whereby marks are imprinted on a carrying element and at least one sensor detects the marks on the carrying element and a second sensor detects a seam on the carrying element. Beneficially, the sensor values read by the first sensor in the area of the seam that is detected by the second sensor are discarded in a control mechanism. Sensor values that are influenced by the seam lead to false corrections and their use is avoided by discarding them.
In one embodiment of the invention, the area in which the sensor values of the first sensor are discarded is 18.5 mm long upstream of the seam and 18.5 mm long downstream of the seam in relation to the carrying element's direction of conveyance compass and register errors are specifically avoided when the area in which sensor values of the first sensor are discarded is 12.8 mm long upstream from the seam and 12.8 mm long downstream from the seam in relation to the carrying element's direction of conveyance. The listed areas are specified for the particular purpose of avoiding compass and register errors.
In an alternative embodiment of the invention, the sensor values read by the first sensor are examined in the control mechanism and as a result of this examination, those sensor values read by the first sensor, that come from detection of the seam by the first sensor are discarded. Therefore, the necessity for a second sensor for detecting the seam is removed.
The invention, and its objects and advantages, will become more apparent in the detailed description of the preferred embodiment presented below.
FIG. 1
30
1
1
2
1
1
Referring now to the accompanying drawings, shows an embodiment of the invention with a schematic side view of an imaging mechanism and a carrying element , which are secured in an electrophotographic printing machine. Shown is a carrying element , which in this embodiment is a conveyor belt that conveys printing media through a printing machine in the direction indicated by the arrow designated by the numeral . The carrying element can also be, for example, a cylinder in an electrophotographic printing machine that carries images on its outer surface, such as an imaging cylinder. The carrying element is stretched across several rollers and is of a closed loop configuration. In the course of manufacturing, various methods are used to join the ends of the carrying element , and in this example, the ends of the conveyer belt are welded together.
FIG. 5
11
1
1
30
3
4
5
5
3
3
6
As shown in , a seam forms along the welded ends of the carrying element . Above the carrying element , the imaging mechanism of the electrophotographic printing machine is depicted. Four printing modules or printing mechanisms are arranged in a series, each of which represents one print color, for example, cyan, magenta, yellow, and black. The print colors are impressed one over the other, after which they blend to produce a full color picture. In each printing module, electrostatically loaded images are transferred onto an imaging cylinder by a print mechanism , which is continually supplied with toner from toner stations . The toner from toner stations clings electrostatically to the outer surface of the imaging cylinder and a visible image is formed. In this embodiment, each of the individual color images of imaging cylinder is transferred to an intermediate cylinder which has a rubber coating and which transfers the individual color images onto a printing medium. On the printing medium, the partial pictures blend together into a complete multi-colored picture.
7
1
8
1
12
1
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1
FIG. 5
A second sensor is located upstream of the four print modules, above the carrying element , while a first sensor is located above the carrying element , downstream of the print modules. Provision can be made for additional sensors. For the present embodiment, a calibration run is run for an electrophotographic printing machine before printing orders or jobs are executed. During calibration, marks (see ) from the four print modules are imprinted on the printing medium, such as a sheet of paper, or onto the carrying element , which are then detected by the first sensor downstream from the print modules. Specifically, each print module imprints a colored mark onto the carrying element .
8
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15
5
The first sensor , downstream of the print modules, is activated by the second sensor , upstream of the print modules after a certain number of clock pulses from the angle of rotation of the sensor/transmitter . Using the marks , a determination is made concerning how close to compass and/or register the individual colors are being imprinted. Deviations from the desired compass and/or register (i.e., from the imprintation of the marks in the correct places) are measured, and subsequent corrections to the deviations are made in various ways. During the calibration run of the printing machine, the second sensor sends out a signal that simulates the leading edge of a sheet of paper to a control mechanism (see FIG. ).
12
12
7
In order to generate a signal to simulate the leading edge of a sheet of paper, provision can alternatively be made for an additional sensor (not shown). This simulated point serves as a reference point for the marks , and each mark is evaluated in reference to the signal from the second sensor . From this evaluation, corrective parameters are derived that are then used to set various parameters of the printing machine. Overall, it is desirable that the corrective parameters be identified as accurately as possible, that the compass and register be error free, and that measurement errors be avoided.
FIG. 2
FIG. 5
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shows a graph of the compass and/or register errors as a function of the patterns (see ) and marks that are imprinted on the carrying element . Each pattern incorporates a mark for each color, such as cyan, magenta, yellow, and black. Compass and register errors are defined as shiftings of the marks in the printing medium's direction of travel, the so-called “in-tracks” or “in-track errors”. The compass and register error units are measured, for example, in micrometers. The imprinted patterns of marks are identified by numbers, whereby, each pattern number in this embodiment incorporates four marks , of one color each. Therefore, there is one mark for each color. The four colored marks are also called “patterns ” or “patches”.
FIG. 2
13
12
11
In , the x-axis is identified by numbers that range approximately from zero up to one hundred and forty patterns of marks . Essentially, the register errors vary around zero in a range between −150 micrometers and +150 micrometers. These are the common compass and/or register errors that are not influenced by seam , that are detected and corrected.
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FIG. 5
At each eleventh pattern of mark , however, the compass and/or register errors spread out and assume substantially higher values, mainly between −700 micrometers and −1400 micrometers. This can be explained as follows: The first sensor detects eleven patterns of marks for each rotation of the carrying element ; after eleven measurements of patterns by the first sensor , the carrying element has made one rotation around the rollers and is back to its starting position. During the course of each rotation, however, the first sensor also detects the seam , at which the two ends of the carrying element are welded together. The measuring signal for the patterns of marks at this seam are obviously severely inaccurate such that the compass and/or register errors for this area at the seam are unusable. The seam is recognized by the first sensor either mistakenly as marks , or the measurement of marks are so inaccurate because of the seam , that the impression of a large compass and/or register error incorrectly arises, i.e., an error that does not actually exist, as shown in FIG. . When the measured and displayed compass and/or register errors are accepted without being examined, large measurement errors are obtained that lead to incorrect provisions during the calibration, and ultimately to compass and/or register errors during subsequent printing operations. The above-described inaccurate measurements cannot be completely removed with the use of software in a control mechanism (see ) belonging to the printing machine, because the order of magnitude of the apparent compass and/or register errors, i.e. the spread values, can be mistaken for ordinary compass and/or register errors.
FIG. 3
FIG. 2
FIG. 2
12
12
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shows a graph similar to that shown in , where on the y-axis, compass and/or register errors are shown, in relation to the black printing color. The mark of the black color is used here as the reference for the marks of the other colors. On the x-axis, the numbers of patterns are shown, from zero to approximately one hundred forty. Similar to , it can be seen that at every eleventh pattern of marks , an obvious spread in measurement values occurs. The compass and/or register errors at every eleventh measuring value of each color falls essentially in the range of 750 micrometers to 1200 micrometers, while the compass and/or register errors in the case of the remaining patterns of marks vary around the zero point and show spreads only in the range of about −100 micrometers to +100 micrometers.
FIG. 4
FIGS. 2 and 3
13
12
1
4
3
shows a graph of values for the corrected positions of the compasses and/or registers based on the graphs shown in , as a function of the patterns of marks that are imprinted in three colors onto the carrying element . The values for the fourth color are similar. The values of the corrected positions of the compasses and/or registers are obtained when the compass and/or register error is measured and evaluated on the basis of the measurements of the corresponding error in the direction of travel. From these the corrected values, correction parameters are derived and the printing machine is calibrated so that the number of compass and/or register errors is reduced during the subsequent printing process. The correction parameters are referenced, for example, by the moment of imaging at which the colored partial pictures are transferred from the print mechanisms to the imaging cylinder .
1
3
6
1
Provisions can also be made for the use of additional correction parameters for the correction of compass and/or register errors, such as a change in the speed of travel of the carrying element , or the imaging cylinder and the intermediate cylinder . Using the aforementioned measures, adjustments can be made to the points at which during calibration the image is imprinted onto the carrying element and during the printing process onto the printing medium. The individual colors are shown through various geometrical symbols, the color yellow by rhombuses, the color magenta by triangles, and the color cyan by squares.
13
12
The x-axis shows approximately one hundred-fifty patterns with marks . It is clear that the positions of the compasses and/or the registers for the color yellow, varies across a range of approximately 2000 μm. The positions for the color magenta vary across a range of approximately 2200 μm, and for the color cyan vary across a range of approximately 2300 μm.
13
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FIG. 5
FIGS. 2 and 3
FIG. 4
The fact that in the range of numbers from sixty to eighty-five the correction values of the patterns deviate significantly from the remaining correction values is noteworthy. These inaccurate values arise from the fact that a computing mechanism (see ) that is incorporated in the control mechanism gives spreads such as those shown in , the same ordinary values that identify routine compass and/or register errors and that vary only moderately in the graphs shown by all of the figures. However, the spreads consist of values that are detected in the area of the seam . Particularly notable are spreads of marks that are imprinted directly on the seam of the carrying element . They fall in the range of approximately 1100 μm to 1300 μm and differ from the remaining values by approximately 700 μm to 900 μm, as seen in , whereby after increments of eleven patterns , two downward spreads for each color occur. In this case the inaccurate measurements in the area of pattern numbers ranging from approximately sixty to approximately ninety result in inaccurate correction parameters during the printing machine's calibration run.
Inaccurate correction values during calibration should usually be viewed more critically than correction values of individual faulty measurements arising during a printing job, because the correction values arising during calibration are usually used over a longer period of time and thus cause more damage with respect to compass and/or register errors.
FIG. 5
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shows a basic model of an embodiment of the invention using a schematic overhead view of a section of a carrying element that is designed to be a continuous loop and has a seam where the carrying element is welded together. A calibration run to adjust and calibrate the printing machine prior to imprinting printing media is depicted. Above the carrying element and downstream of the printing modules, a first sensor is secured, which detects marks that are imprinted on the carrying element . The marks are shaped like dashes and are grouped into a pattern of marks . The figure shows four marks for four respective colors, each from one print module. The marks are each imprinted onto the carrying element by one print module.
8
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FIG. 1
The first sensor is connected to the computing mechanism . Mounted upstream of the print modules is a second sensor that detects the seam and that is connected to the computing mechanism . Provision is also made for an angle of rotation sensor/transmitter or web encoder, which is attached to a roller (see ) that has a drive shaft of the carrying element , and is connected to the computing mechanism .
1
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For each rotation of the carrying element , the angle of rotation sensor/transmitter emits 62500 pulses, which are counted. When the second sensor detects the seam, the continuously increasing count on the angle of rotation sensor/transmitter is read and stored. When at a certain point in time, the point at which the seam is located is reported, the actual count of the angle of rotation sensor/transmitter is read and from this, the count that was stored the last time the seam was detected is subtracted. The difference derived therefrom, a number of impulses, is simply converted into a unit of length whereby the distance between the seam and the second sensor is ascertained.
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The printing of each mark , onto the carrying element , is triggered by an electronically generated pulse from the second sensor . In the course of the calibration process, the pulse mimics the leading edge of a sheet of paper during a printing operation, i.e., the leading edge is simulated. During the printing process the marks are ideally imprinted onto the sheet of paper at a particular, known distance from the leading edge of the sheet of paper. When the pulse from the second sensor is transmitted to the computing mechanism , for each print mechanism that is used for imaging the imaging cylinder , clock pulses are counted off, in accordance with which the imaging cylinder receives information. Therefore, the marks are essentially imprinted at a known distance from the leading edge of the sheet of paper. In the course of the present calibration, the marks are imprinted at the desired places on the carrying element . The first sensor detects the marks downstream from the print modules and transmits a pulse for each mark to the computing mechanism , in which set values are stored that identify the points in time at which the marks are detected by sensor when no compass and/or register errors exist. The set values are compared with the actual values measured by the sensor , whereby a compass and/or register error is identified for each color corresponding to each mark . This is the deviation of the actual value from the set value in the form of a unit of time that characterizes the distance of a mark between an error-free position and an incorrect position of such a mark . In this case, it is a deviation in the direction of travel.
FIGS. 2 through 4
11
15
As described above and depicted in , the calculated compass and/or register error becomes skewed by the presence of the seam . The result is measurement errors amounting to several hundred micrometers. Consequently, the correction parameters assigned from the calculated compass and/or register errors are incorrectly identified by the control mechanism , i.e., the adjustment mechanism used for adjusting print parameters by correction parameters during the calibration of the printing machine is distorted.
11
7
10
1
11
1
8
8
12
8
16
12
By detecting the seam with the second sensor working together with the angle of rotation sensor/transmitter , which ascertains the position of the carrying element by counting off pulses, the position of the seam on the carrying element becomes known. If the seam is in a certain area around a detection point of the first sensor where the first sensor detects the marks , then the sensor values of the first sensor , transmitted to the computing mechanism upon detection of the marks , are not used for calculating a compass and/or register error. Rather, these sensor values are discarded.
8
11
11
7
8
7
11
8
FIG. 5
The area in which the sensor values of the first sensor are discarded is defined in by the length d. The length d may be freely selected, but is preferably 37 mm, in particular, 25.6 mm, i.e., 18.5 mm or 12.8 mm in front of and behind the point of detection. A faulty measurement based upon the seam is precluded when the distance between the seam and the second sensor is greater than the distance between the first sensor and the second sensor . In such a case the seam is not within the range of measurement of the first sensor .
11
7
16
7
11
10
10
11
11
7
8
7
11
7
The distance between the seam and the second sensor can be calculated in the computing mechanism from a sensor signal generated when the second sensor detects the seam and from the knowledge of the number of clock pulses per unit of length coming from the angle of rotation sensor/transmitters . This distance is calculated from the number of clock pulses counted by the angle of rotation sensor/transmitter since the last detection of the seam . When the distance between the seam and the second sensor is smaller than the distance between the first sensor and the second sensor , the seam is moving toward the first sensor . In such a case it is possible that an inaccurate measurement will result.
7
11
8
11
12
11
In an alternative to the above embodiment, only those sensor values coming from the second sensor are discarded, which come from the detection of the seam . In this case, not all of the sensor values that are located within the distance d, are discarded. This case assumes that the first sensor and the control mechanism downstream from the print modules are capable of distinguishing between the seam and the marks . In the prescribed manner, spread values based upon the seam are discarded, the correction parameters for adjusting the printing machine parameters during the calibration run are significantly improved, and ultimately, the compass and/or register errors during the printing process are more successfully avoided.
The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variation and modifications can be effected within the spirit and scope of the invention.
BRIEF DESCRIPTION OF THE DRAWINGS
In the detailed description of the preferred embodiment of the invention presented below, reference is made to the accompanying drawings, in which:
FIG. 1
shows a schematic side view of an imaging mechanism and a carrying element of an electrophotographic printing machine;
FIG. 2
shows a graph of register errors as a function of patterns of marks at four printing colors;
FIG. 3
shows a graph of register errors as function of patterns of mark at three printing colors, in relation to a black printing color;
FIG. 4
shows a graph of corrected positions of compasses and/or registers as a function of patterns of marks at three printing colors; and
FIG. 5
shows a schematic block diagram of an embodiment of the invention to illustrate its objective. | |
Restricted Functioning Of Delhi High Court To Continue Till Nov. 30
The Delhi High Court on Thursday decided to extend its restricted functioning till Nov. 30 in view of the persisting coronavirus pandemic in the national capital.
The Chief Justice of the Delhi High Court decided to extend the restricted functioning on the same terms as earlier orders, the office of Registrar General Manoj Jain said.
The office order also said that the cases instituted in the years 2018, 2019 and 2020 shall also be taken up, as per roster, from Nov. 17.
It further stated that the cases already listed before the high court from Oct. 9 to Oct. 20 shall be adjourned en bloc to corresponding dates between Dec.15 to Dec. 24.
"With effect from Oct.12, two courts of Joint Registrars (Judicial) shall take up the matters through physical mode while the others shall continue to hold court through videoconferencing as per roster to be notified on the website.
"All the courts of Joint Registrars (Judicial) shall also record evidence in cases involving urgency or where any direction for expeditious/time bound disposal has been received from this Court or the Supreme Court. The recording of evidence may be by physical mode or by video conferencing as the case may be," the office order said.
The high court had, on March 25, restricted its functioning as well as that of the district courts till April 14. It was subsequently extended to May 3, May 17, May 23, May 31, June 14, June 29, July 15, July 31, Aug. 14, Aug. 31 and Sept. 30.
On Aug. 27, the high court decided to partially resume physical hearing of matters from Sept. 1 by two division bench and three single judge benches on a rotation basis.
The number of benches was later scaled down to one division bench and two single judge benches in view of the rise in Covid-19 cases in Delhi and a majority of the lawyers indicating their preference for virtual hearing of cases. | https://www.bloombergquint.com/law-and-policy/restricted-functioning-of-delhi-hc-to-continue-till-november-30 |
You'll receive all travel documents about 14 days before departure. They contain the exact hotel address and further information. Please arrive by about 6:00 p.m. You'll meet your group and the guide. After discussing the tour, the group will go to dinner together.
Second – From Reutte to Warth – 65 km, 840 m elevation gain
We will slowly head uphill in the magnificent Lech valley. Suspension bridges and beautiful Tyrolean landscapes line our way. After lunch, we'll climb up to Warth. In the evening, we'll relax at a 4-star spa hotel.
Third day – From Warth to Schruns/Montafon – 60 km, 580 m elevation gain
On a small back road, we'll roll into glamorous Lech am Arlberg. On our climb up Flexen Pass, the mountains seem close enough to touch. Then we'll head down into Klostertal past rock formations and avalanche paths. Our trail takes us into the picturesque village of Schruns in the Montafon. A 4-star wellness hotel awaits us.
Fourth day – From Schruns to Ischgl – 53 km, 750 m elevation gain
Today the Silvretta Alps are on the schedule. After comfortably warming up, we'll ride uphill deep into Montafon. The cable car will rapidly bring us up to Trominieran mountain station at an altitude of 1700 meters. Riding through an underground tunnel, surrounded by spectacular rock scenery, we'll reach Lake Vermunt. Lunch break with a sensational view of the snow-covered Piz Buin peak. In a relaxed manner, we'll roll downhill into Paznaun, riding through Galtür on our way to Ischgl.
Fifth day – From Ischgl to Lafairs – 62 km, 830 m elevation gain
The path into the valley leads us down to the lake. We'll gain 400 meters elevation before we break for lunch with a view of the Tyrolean mountains. We'll follow the Inn up to the upper Inn valley and Lafairs. We'll spend the night in a 4-star spa hotel.
Sixth day – From Zernez to Maloja – 60 km, 850 m elevation gain
The bus takes us up to Zernez, Switzerland. That's where today's stage through the enchanting mountains of the Engadine starts. Lunch break at Lej da Staz, by St. Moritz. We'll pass by small mountain lakes and quaint houses on our way to Maloja.
Seventh day – From Maloja to Lake Como – 77 km, 480 m elevation gain
Bella Italia, we’re coming. From now on it’s downhill. Riding through Europe's largest chestnut forest, we reach the border. Italian lifestyle awaits us. In the evening light, we will reach the Mediterranean climate of Lake Como / Lake Mezzola.
Eighth day – Departure
After breakfast, the bikes are loaded onto the bus. Return trip by bus back to Reutte. Upon arrival, everyone travels home individually.
My tip for Trekking Engadine
„Everything's just right here. I wanted to put together an alpine crossing for trekking bikes through the great Engadine landscape. However, it was important that the route not be too difficult or have too much elevation gain. The guests have also been more than enthusiastic so far. Spectacular mountain scenery and great hotels – what more could you ask for?“
Travel information
Level 1-2: Physical fitness Riding technique
Arrival: Arrival by car or train to Reutte/Austria.
Type of route: Bike paths, asphalt secondary roads and easy gravel roads.
Daily distance: 480-850 m elevation gain, 53-77 kilometers
Total distance: 4300 m elevation gain, 370 kilometers
Included in the price: Guided tour with 7 overnight stays and half board (breakfast buffet, multi-course dinner menus) in mostly 4-star hotels in a double room, often with wellness areas. Luggage transport, shuttle bus transfer, return transfer in a comfortable bus.
Minimum number of participants: 8 people
Single Room Supplement: | https://www.go-alps.com/trekkingbike/trekking-engadine |
Change: The Carpenter, the Tools and the Wood
In some ways, the analogy of a carpenter using his tools to shape wood is a good analogy for the process of psychotherapy. It also brings out some of the important relationships between psychotherapist, client and the person the client wants to be, and perhaps shows them in an unexpected way.
The carpenter
To expand further, a carpenter sees the wood and sees the way that he or she would like to shape it. He imagines it different and he takes his time to imagine how he could transform it into something different; something functional, something purposeful, perhaps something beautiful. He hopes that he has the skill to do this, and he takes the time that the work needs, and resists the impulse to rush and do a poor job of it.
The tools
The tools that the carpenter will use for the job are prepared, oiled and sharpened. He wants to make sure he uses the right tool for the job, shifting tools as appropriate and in response to what needs to happen next. The carpenter trusts his tools, but he also knows that they're only as good as is his ability to make use of them. He respects them, but he knows that they have their limitations.
The wood
The piece of wood has been selected, from all the other possible pieces of wood. Like all pieces of wood, it has knots and the grain runs in distinctive ways. Even when the work is finished, it will still have knots and the grain will still run in distinctive ways. But the carpenter knows this before he starts and factors this into the final look of the piece; in the end the knots and the distinctive grain are part of it. Without them, it wouldn't really be wood.
The client is the carpenter, not the therapist
It's important to understand that the carpenter isn't the psychotherapist but the client. It isn't the psychotherapist’s vision being created, but the client’s. Instead, a psychotherapist is the tool that the client wields; the carpenter’s strength and the therapist’s edge work as one to shape the client as he takes himself closer towards the ultimately unreachable goal of perfection.
– Tim Hill
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. | http://timhillpsychotherapy.com/the-carpenter-the-tools-and-the-wood-1363/ |
I painted this fanciful and colorful rendition of summer flowers in a purple vase. I originally called it Rainbow Bouquet in a Purple Vase.
But when a family with a little girl, Hannah, visited my Riga apartment, she was drawn to this painting and told her mommy that she made it. Everyone smiled.
Hence, I now call it Hannah’s Flowers. | http://charlesdavidkelley.com/portfolio/hannahs_flowers/ |
Printed From:
http://www.dlnexus.com/lexicon/21273.aspx
|
|
Windriders
Article written by Ambro
Windriders are an ancient elven organization that exists among the Kagonesti Elves, Silvanesti Elves, and the Qualinesti Elves. Regardless of their national affiliation all Windriders are Warriors that fight on Griffons.
Kagonesti Windriders tend to care more about their mounts than other Elves. Silvanesti members tend to get lost in their own superiority, but will be pleasant to their allies. The Windriders of Qualinesti tend to be more down to earth compared with their Silvanesti cousins. They are trained with the Longsword, the Bow, and the lance to use in battle.
The only permanent settlement of Windriders is the village of Avalune in the Anviltop Mountains. Also, most Kagonesti Windriders are found on the island of Cristyne.
History of the Windriders
Age of Dreams
In 2190 PC, the Windriders were formed when Kith-Kanan and his brother Sithas traveled to the Khalkist Mountains. Vedvedsica provided the twins with a magical scroll. Sithas used the scroll and bonded the griffons with the elven people. Kith-Kanan later formed the Windriders. Kith-Kanan opened up the Windriders to anyone regardless of house.
Many elves left Silvanesti to form the new nation of Qualinesti in 2073 PC. This split the Windriders among the two nations. The Silvanesti eventually started to restrict membership to the Windriders to be of House Protector.
Third Dragon War
Centuries later during the Third Dragon War, the Windriders of both elven nations participated. The Silvanesit allowed Wizards of House Mystic to join the Windriders during the War. By the time the war ended the griffons of Ansalon were greatly diminished. The Windriders of both nations disbanded for a time to allow the griffons to repopulate.
War of the Lance
During the War of the Lance, the head of House Protector, Lord Garan, led the Windriders of Silvanesti. When Lorac's Nightmare occurred the Silvanesti Elves including the Windriders had to leave their homeland. Porthios Kanan led the Windrider of Qualinesti during the war. Both nations fought in the Whitestone Army and some Windriders even fought on Dragons.
Post War of the Lance
When the Silvanesti returned to their homeland the Windriders were diminished to seven under the poor military leadership of Reyl Konnal. Hundreds of Qualinesti Windriders came to their cousins' aid to reclaim their ancestral homeland.
Age of Mortals
During the Age of Mortals, the Silvanesti shut themselves behind the Silvanesti Shield and the Qualinesti were ruled by Dark Knights. The Silvanesti group were hindered and weakened by the shield and the Qualinesti where not allowed to form while they were under the marshal law of the Dark Knights.
War of Souls
During the Second Battle of Sanction some Windriders rode on dragon back.
Post War of Souls
After the War of Souls, both elven nations of Ansalon were shattered, but their people united in exile under one banner. The Speaker of the Sun and Stars Gilthas Kanan had two Wings of the united Windriders watch over their old homelands and scattered to rest across the continent to help the elven people make it to Inath-Wakenti.
Becoming a Windrider
Kith-Kanan formed the organization with the hope that any skilled elf could join. The Silvanesti eventually restricted its membership to House Protector (with some wizards from House Mystic). In Qualinesti, the Windriders were generally kept open as their nation's founder wanted. After the War of Souls, the combined Windriders are closer to Qualinesit view on membership.
In the post War of Souls years the way to become a Windrider is to petition for membership. The potential member is tested. Their fighting skills and ability to get along with griffons is checked. Those that fail are offered positions in the Wildrunners. While this is the usual method, the need for skilled members has caused the Windriders to sometimes recruit new elves. Once an initiate skills are tested and trained they are sent to Avalune to be bonded with a griffon.
Officer Ranks
Sky Warden
Note: Qualinesti and Silvanesti Windriders used the same rank structure.
Military Units
Note: Qualinesti and Silvanesti Windriders used the same unit structure.
References
Article Tools
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Subcategories
There are 2 subcategories in this category, shown below. More pages may available in each subcategory.
Pages in category "Windriders"
There are 10 pages in this section of this category.
This article has been viewed 3,074 times. It was added on November 13, 2008, and was last modified on November 14, 2008.
Information presented in the Dragonlance Lexicon has been independently researched by a team of volunteers, and original sources have been cited for each article. This and any other Lexicon articles are intended for personal use only and may NOT be posted on any other web site or otherwise distributed. | http://dlnexus.com/lexicon/21273.aspx |
The Litchfield High School wrestling team ended their run at the 58-team Abe’s Rumble dual team tournament in Springfield with a win on Thursday, Dec. 30, taking fifth place in the nine-team Copper Bracket.
Filling 10 of the 14 weight classes at most, the Panthers were giving up 18 to 24 points in most of the matches, making wins in the pool portion of the tournament on Dec. 29 hard to come by.
Litchfield opened up with West Frankfort and fell to the Redbirds 54-30. The difference in the 24-point decision was in part to 24 forfeit points the Redbirds received.
In contested matches, Litchfield fared well, winning five of the 10 matches, all by fall. Alex Powell (106), Ashtin Carver (145) and Hunter Hancock (182) all won in the first period, needing less than a minute to get the pin, while Seth Kenter (160) and Isaiah Johnson (113) got wins by fall in the second and third periods respectively.
In their next match, Litchfield would give up 24 points again as Reed-Custer defeated the Panthers 66-12. Litchfield’s wins came from Alex Powell, who picked up his second pin, and Isaiah Johnson, who won by forfeit.
The Panthers’ closest match in pool play was against Riverdale, who won 48-30 with 18 points coming from forfeits.
Alex Powell won again by fall, this time just before time ran out in the second period, while Hunter Hancock and Corbin Schneck (285) also picked up pins. Isaiah Johnson and Devin Hansel (195) had Litchfield’s other 12 points with forfeit victories.
In their final match in the pool, Litchfield fell to Beardstown 54-20, with the Tigers getting 30 free points from forfeits.
Alex Powell completed his sweep of Wednesday’s opponents with a 16-0 tech fall victory, while Ian Mitchell (126), Seth Kenter and Hunter Hancock all picked up wins as well. Mitchell’s win came in a 13-10 decision, while Kenter and Hancock won by fall.
On Thursday, Litchfield moved to the nine-team Copper Bracket, where they drew Olympia in their first match. The Spartans picked up a 46-24 win over the Panthers, getting 24 forfeit points, en route to an overall win in the Copper Bracket.
Alex Powell picked up where he left off with a 7-0 decision win against Dylan Eimer, while Seth Kenter also won by decision. Ian Mitchell and Kaleb Crabtree both won by fall, while Corbin Schneck got six points as well in a forfeit.
After the loss, Litchfield came back to win 24-18 over Walther Christian Academy. Seven classes went down as double forfeits, with Clayton Logsdon, Corbin Schneck and Seth Kenter winning forfeits for Litchfield and Walther Christian getting six free points at 138-pounds.
Litchfield’s lone contested victory came from Alex Powell, who improved to 6-0 at the tournament with his fourth pin.
Next up for the Panthers was Sparta, who won 36-29 with 12 forfeit points from Litchfield. The Spartans also gave up six forfeit points, with Alex Powell getting the free pass.
Isaiah Johnson, Seth Kenter and Hunter Hancock all won by fall, while Ian Mitchell picked up a tech fall victory, 22-6.
In their final dual of the tournament Litchfield picked up a 42-36 win over Wilmington. Thirty-six points in the match came from forfeits, with Wilmington getting 18 and Alex Powell, Isaiah Johnson, and Kaleb Crabtree getting six free points for Litchfield.
Seth Kenter would be one of the few to get a contested match and beat Dezirae Yankee by fall in 57 seconds to earn his sixth win and fourth pin of the tournament.
Of Litchfield’s 34 individual wins in eight duals, only 11 were by forfeit. Eighteen were won by fall, with three decisions and two tech fall victories.
Alex Powell led the team with eight wins, followed by Seth Kenter with six, Isaiah Johnson with five, Hunter Hancock with four, Corbin Schneck and Ian Mitchell with three, Kaleb Crabtree with two and Devin Hansel, Clayton Logsdon and Ashtin Carver with one each.
The Panthers will go from the frying pan to the fire as they travel to another elite tournament, the Princeton Invitational, on Jan. 7-8. | https://thejournal-news.net/stories/panthers-battle-back-at-springfield-tourney,75195? |
of 1293?
False
Is 1342 a multiple of 3?
False
Is 53331 a multiple of 140?
False
Is 607 a multiple of 10?
False
Is 20 a factor of 80?
True
Is 21476 a multiple of 17?
False
Does 86 divide 17114?
True
Is 501 a multiple of 33?
False
Is 49221 a multiple of 27?
True
Is 1749 a multiple of 11?
True
Does 41 divide 1346?
False
Is 14 a factor of 16632?
True
Does 11 divide 4625?
False
Does 92 divide 54730?
False
Is 43260 a multiple of 12?
True
Is 9 a factor of 4698?
True
Does 6 divide 35156?
False
Does 218 divide 10328?
False
Is 3 a factor of 45?
True
Is 2120 a multiple of 67?
False
Does 27 divide 124?
False
Is 36 a factor of 6399?
False
Is 21 a factor of 2772?
True
Is 19 a factor of 182?
False
Is 40 a factor of 592?
False
Does 2 divide 751?
False
Is 20724 a multiple of 66?
True
Is 19 a factor of 2303?
False
Is 15824 a multiple of 13?
False
Is 686 a multiple of 8?
False
Is 710 a multiple of 15?
False
Does 46 divide 19607?
False
Does 28 divide 2324?
True
Is 15 a factor of 181?
False
Does 25 divide 3200?
True
Does 65 divide 60258?
False
Is 5925 a multiple of 47?
False
Is 25 a factor of 1071?
False
Is 3 a factor of 469?
False
Does 28 divide 2617?
False
Is 5 a factor of 970?
True
Is 1911 a multiple of 21?
True
Is 945 a multiple of 15?
True
Is 6 a factor of 6282?
True
Is 44 a factor of 29964?
True
Does 2 divide 301?
False
Does 12 divide 8651?
False
Is 67 a factor of 13065?
True
Does 153 divide 16113?
False
Is 18 a factor of 2249?
False
Does 3 divide 72?
True
Does 19 divide 1425?
True
Is 6664 a multiple of 23?
False
Does 77 divide 1278?
False
Is 1920 a multiple of 24?
True
Is 5656 a multiple of 20?
False
Is 3548 a multiple of 2?
True
Does 9 divide 171?
True
Is 20049 a multiple of 49?
False
Is 76 a factor of 14822?
False
Is 8 a factor of 33?
False
Is 3 a factor of 1248?
True
Does 9 divide 324?
True
Is 6 a factor of 552?
True
Is 13 a factor of 4979?
True
Is 232 a multiple of 29?
True
Does 74 divide 2025?
False
Is 20 a factor of 2933?
False
Is 40 a factor of 5280?
True
Does 7 divide 16191?
True
Does 73 divide 730?
True
Is 18 a factor of 572?
False
Does 26 divide 988?
True
Does 26 divide 546?
True
Is 33 a factor of 899?
False
Is 13 a factor of 3316?
False
Is 9 a factor of 767?
False
Does 24 divide 12360?
True
Is 506 a multiple of 2?
True
Does 7 divide 3795?
False
Is 6 a factor of 1825?
False
Is 46 a factor of 322?
True
Is 21 a multiple of 6?
False
Is 740 a multiple of 37?
True
Does 58 divide 5974?
True
Does 17 divide 204?
True
Does 11 divide 4429?
False
Is 589 a multiple of 19?
True
Is 1484 a multiple of 28?
True
Does 14 divide 33215?
False
Is 7264 a multiple of 6?
False
Is 92 a multiple of 4?
True
Is 40 a factor of 4160?
True
Is 96 a factor of 2792?
False
Is 1390 a multiple of 127?
False
Does 13 divide 51359?
False
Is 10 a factor of 1526?
False
Is 43510 a multiple of 103?
False
Is 2214 a multiple of 18?
True
Is 4368 a multiple of 91?
True
Does 98 divide 1406?
False
Does 17 divide 527?
True
Is 40 a factor of 34712?
False
Is 3140 a multiple of 4?
True
Does 87 divide 36453?
True
Is 57 a factor of 228?
True
Does 16 divide 3743?
False
Is 720 a multiple of 80?
True
Is 6 a factor of 447?
False
Is 20196 a multiple of 11?
True
Is 32 a factor of 1248?
True
Does 15 divide 1545?
True
Does 61 divide 11651?
True
Is 21 a factor of 568?
False
Is 46803 a multiple of 20?
False
Does 134 divide 22746?
False
Does 10 divide 6320?
True
Is 7 a factor of 487?
False
Is 726 a multiple of 6?
True
Is 67 a factor of 1631?
False
Does 37 divide 17760?
True
Is 8 a factor of 28152?
True
Does 4 divide 2256?
True
Is 2239 a multiple of 2?
False
Is 6 a factor of 948?
True
Does 15 divide 2375?
False
Is 1096 a multiple of 8?
True
Is 420 a multiple of 42?
True
Is 256 a multiple of 8?
True
Is 2480 a multiple of 40?
True
Is 30 a multiple of 15?
True
Does 99 divide 3170?
False
Is 427 a multiple of 23?
False
Is 37 a factor of 14134?
True
Is 10692 a multiple of 110?
False
Does 29 divide 7830?
True
Is 27946 a multiple of 16?
False
Does 72 divide 105503?
False
Is 26244 a multiple of 36?
True
Is 22 a factor of 12534?
False
Is 3049 a multiple of 26?
False
Is 287 a multiple of 7?
True
Is 2 a factor of 1564?
True
Is 16834 a multiple of 27?
False
Is 4530 a multiple of 5?
True
Is 9 a factor of 3771?
True
Is 3 a factor of 284?
False
Is 25085 a multiple of 9?
False
Is 84 a factor of 2167?
False
Is 239 a factor of 84128?
True
Is 15588 a multiple of 9?
True
Does 30 divide 33425?
False
Does 36 divide 1035?
False
Does 5 divide 779?
False
Is 2992 a multiple of 8?
True
Is 63 a factor of 1236?
False
Does 5 divide 1165?
True
Is 4401 a multiple of 27?
True
Is 94 a factor of 1223?
False
Does 9 divide 85?
False
Is 4535 a multiple of 18?
False
Is 24026 a multiple of 57?
False
Does 6 divide 399?
False
Does 8 divide 9947?
False
Is 3 a factor of 548?
False
Does 39 divide 174?
False
Is 62 a factor of 3133?
False
Does 18 divide 58?
False
Does 7 divide 182?
True
Is 4388 a multiple of 79?
False
Is 20 a factor of 8207?
False
Is 1488 a multiple of 50?
False
Does 10 divide 360?
True
Is 18 a factor of 21765?
False
Does 157 divide 3223?
False
Is 50544 a multiple of 243?
True
Is 1334 a multiple of 29?
True
Is 113370 a multiple of 30?
True
Does 3 divide 1180?
False
Is 29 a factor of 767?
False
Is 889 a multiple of 5?
False
Is 5 a factor of 1730?
True
Is 155508 a multiple of 474?
False
Is 63 a factor of 2205?
True
Does 295 divide 1909?
False
Does 51 divide 306?
True
Is 3 a factor of 11?
False
Does 11 divide 308?
True
Does 82 divide 1722?
True
Is 50083 a multiple of 29?
True
Does 60 divide 960?
True
Is 4400 a multiple of 110?
True
Is 31 a factor of 31?
True
Is 1913 even?
False
Is 5 a factor of 1124?
False
Does 7 divide 1127?
True
Does 6 divide 175?
False
Does 18 divide 2758?
False
Is 12144 a multiple of 11?
True
Does 8 divide 2600?
True
Is 3 a factor of 988?
False
Is 5 a factor of 55?
True
Does 13 divide 1872?
True
Is 22 a factor of 32581?
False
Is 16 a factor of 913?
False
Is 94672 a multiple of 16?
True
Is 211 a factor of 31372?
False
Does 45 divide 1031?
False
Does 27 divide 7685?
False
Is 38 a factor of 2098?
False
Is 46 a factor of 361?
False
Is 38 a factor of 1900?
True
Does 27 divide 540?
True
Is 447 a multiple of 7?
False
Is 14 a factor of 30744?
True
Is 476 a multiple of 26?
False
Is 66 a factor of 1056?
True
Is 93 a factor of 33015?
True
Does 94 divide 39569?
False
Is 14 a factor of 1148?
True
Does 98 divide 2743?
False
Is 16 a factor of 8298?
False
Is 41 a factor of 64548?
False
Is 11 a factor of 1067?
True
Does 63 divide 1071?
True
Is 63 a factor of 3278?
False
Is 104 a factor of 73140?
False
Does 14 divide 1064?
True
Is 1720 a multiple of 20?
True
Is 21679 a multiple of 101?
False
Is 16 a factor of 96?
True
Is 43 a factor of 1041?
False
Does 18 divide 61992?
True
Is 192 a multiple of 16?
True
Is 4816 a multiple of 14?
True
Is 68 a factor of 7743?
False
Is 231 a multiple of 11?
True
Is 315 a multiple of 7?
True
Is 10318 a multiple of 11?
True
Is 80 a factor of 1120?
True
Does 21 divide 11277?
True
Is 632 a multiple of 8?
True
Does 89 divide 676?
False
Does 8 divide 8368?
True
Does 138 divide 5574?
False
Is 684 a multiple of 25?
False
Is 51 a factor of 13056?
True
Does 8 divide 264?
True
Does 14 divide 1008?
True
Is 20 a factor of 37200?
True
Is 11 a factor of 1551?
True
Is 299 a multiple of 11?
False
Is 27 a factor of 3804?
False
Does 26 divide 41768?
False
Is 47 a factor of 3552?
False
Is 37 a factor of 962?
True
Is 1583 a multiple of 72?
False
Is 5809 a multiple of 81?
False
Does 215 divide 10965?
True
Is 12 a factor of 6928?
False
Does 10 divide 6106?
False
Does 69 divide 116?
False
Is 4 a factor of 943?
False
Is 2726 a multiple of 29?
True
Is 532 even?
True
Does 6 divide 12063?
False
Does 15 divide 2790?
True
Is 1318 a multiple of 159?
False
Is 16506 a multiple of 131?
True
Does 14 divide 2776?
False
Does 15 divide 31170?
True
Is 22 a factor of 4872?
False
Does 13 divide 4199?
True
Is 28 a factor of 27664?
True
Is 1134 a multiple of 27?
True
Is 140 a multiple of 14?
True
Does 21 divide 567?
True
Is 17 a factor of 187?
True
Does 10 divide 24321?
False
Does 50 divide 80433?
False
Is 14 a factor of 168?
True
Is 4229 a multiple of 8?
False
Is 4252 a multiple of 4?
True
Is 110328 a multiple of 14?
False
Is 1380 a multiple of 21?
F
| |
Q:
Fourier coefficients assume a maximum and minimum?
Let $f:\mathbb R\to\mathbb R$ be continuously differentiable and periodic with period $2\pi$.
The Fourier coefficients are defined by $$\hat f_n=\int_{-\pi}^\pi f(x)\exp(-inx)dx$$
My questions: Is $\widehat {f}_n$ bounded? Does $\widehat {f}_n$ assume a maximum or minimum?
My attempt: Since $f'$ is continuous on the compact interval $[-\pi,\pi]$, $f'$ assumes a maximum and minimum, so we get $|f'(x)|\leq C$. So we get
$$\left|\widehat {f}_n\right|=\left|\frac{1}{2\pi in}\int_{-\pi}^\pi f'(x)\exp(-inx)\,dx\right|\leq\frac{1}{2\pi |n|}\int_{-\pi}^\pi C \, dx=\frac C{|n|}
$$
So $\widehat f_n$ is bounded.
But does the Fourier coefficient of a continuous function assume a maximum/minimum or do we get just a supremum/infimum? I couldn't have thought about a counterexample so I would say yes but I am really unsure about it.
Anybody has an idea how to show it or a counterexample?
A:
Observe that $\hat f_n$ may be a complex number, and that $\mathbb{C}$ is not an ordered field. In particular, the supremum and infimum of $\{\hat f_n\}$ are not defined in general.
You have shown that $\{\hat f_n\}$ is bounded and $\lim_{|n|\to\infty}\hat f_n=0$. Fron this you should be able to prove that $\{|\hat f_n|\}$ attains its maximum, but unless some coefficient equals cero, not its infimum.
| |
London Marathon 2013: An amazing day of human triumph
Today was my first London Marathon experience… and what an amazing day it was. One of my best and oldest friends was running her first marathon for Cancer Research UK in memory of her mother, who sadly lost her battle with cancer last year. As soon as she signed up to do the marathon, I knew I was going to be there cheering her on by hell or high water.
It is undeniably a long day covering a large space of London. But as a spectator, you’re willing to put in the time and footwork, which let’s face it, is nowhere near as exerting as what the runners have gone through. I had watched both the Olympic Men’s Marathon and Paralympic Marathon last summer and loved the atmosphere and camaraderie of it all. Of course, this year’s Marathon was more than an opportunity for runners to test their bodies to the limit and raise lots of money for charity, it was also a show of defiance. Six days earlier, three people had been killed near the finish line of the Boston Marathon so today was an opportunity to remember those who lost their lives and were injured and unify the international marathon community further.
Through a combination of phone apps, maps and calculations, a group of us managed to keep track of our friend and find her amidst the 36,000 runners at Mile 9, 11, and 23. Fortunately the sun came out and the rain stayed away, although the strong rays at lunchtime may have been hampering to some runners. At Mile 9 in Surrey Quays, there was a particularly good atmosphere. The crowds were deep, a sound system blasted out dance music creating a party atmosphere and the runners kept up their speeds and still had a smile on their faces. Spectators were shouting out names of runners who were strangers to them. I found myself shouting out people’s names to give them a boost, particularly when they looked like they were struggling or were wearing a hot or comfortable costume. It was lovely to see such a widespread mood of excitement and friendliness – something us Londoners have been accused of lacking by visitors. By 23 miles at Tower Hill, the runners had understandably slowed down and I can’t imagine the willpower you would need to get you through those final miles. It was emotional to see our friend at this stage – just three miles away from the finish, yet it must have still felt so far. Although I missed my friend cross the 26 mile finish line, I stopped for a period at the 600 metres from the finish mark and shouted some encouragement to runners who may have needed that final boost after an exhausting day.
I must confess watching the marathon made me feel a little inadequate about my own fitness, but I take my hat off to anyone who completes a marathon. It is an amazing feat and such a great way to raise money for charity. Of course, I am fiercely proud of my friend and was glad to see in her one piece – and still standing – when we had a celebratory drink at the pub. While at this point of my life, I doubt I will ever run a marathon, I will definitely watch it again. What a special thing to witness.
Posted on 21 Apr 2013, in Activities, London, Sport, Tourist Attractions. Bookmark the permalink. 5 Comments. | https://memoirsofametrogirl.com/2013/04/21/london-marathon-2013-review-photos-an-amazing-day-of-human-triumph/ |
Want to help stop the widespread decline of bees and other airborne insects? Here are some notes on the Garden’s plants most visited by bumble bees, hive bees, hoverflies and the occasional butterfly. Most of these plants are easy to grow.
One of the main aims of the Living Field garden is to allow native cropland plants some space away from weedkiller treatment and competition with crops. Recent scientific reports have drawn attention to the widespread loss of invertebrate life and insect life in particular. The declines are happening all over the world.
Everyone who owns or manages land can do their bit to support flying insects. Here we show some of the Garden’s plants and plant groups that have offered food and shelter to flower-visitors over the years.
The legumes
The legumes (family: Fabaceae), just ahead of the Composites, are the single most important group supporting wild flyers. The legumes as a whole offer probably the greatest variety and longest flowering season of all plant groups in the garden. They fix their own nitrogen from the air. All parts of the plant are high in protein.
Sainfoin, the melilots and lucerne were once grown or tried as forage crops in Scotland. The clovers, mainly white and red, are still sown, but the red is more commonly seen in the wild. The bumble bees’ favourite of them all is the blue-flowered, tufted vetch (lower images in the panel) – its strings of flowers produced for months on indeterminate sprawling and clinging stems.
The composites – thistles and knapweeds
Next are the composites (family : Asteraceae), each flowering head consisting of many individual florets. Not all species are equally visited, but the best here for pollinators are thistles and knapweeds. The great cotton thistle grows like a small tree, supporting large heads several centimetres across, bumble bees often bustling two or three to a head.
The greater and common knapweeds, hemp agrimony and tansy shown above are perennials, whereas the thistles in the garden tend to be biennial – germinating one year, overwintering as a rosette and flowering the next. The weedy perennial creeping thistle is too invasive in the garden’s small space and though it supports insects is discouraged in favour of other thistles.
Field scabious and teasel
Of all the species in the garden, field scabious (family: Dipsacaceae) is the one that offers sustenance to flyers for the longest period. A perennial, growing mainly in the meadow, plants put out flower after flower from early summer to late autumn (except in the very dry 2018). If there was one plant that we could grow for the bees, it would be this.
Teasel is a close relative that also grows well here. It self seeds and is mostly biennial. Plants are moved at the rosette stage in autumn or early spring to form clumps that flower in the medicinals bed.
Labiates – mints, sages, deadnettles and woundworts
The labiate family (Lamiaceae), including mints, sages, woundworts, deadnettles, hempnettles and basils – are well represented among the medicinals and herbs. They grow in sun, in shade and as occasionals anywhere. The large flowered types such as the herb sage are most frequently visited by the Bombus species, while betony tends to attract more of the smaller carder bees.
The smaller flowered species, such as meadow clary (a perennial n the meadow), fields mints, hempnettle and wild basil are less attractive to larger flying insects but have their own specialist range of inverts.
And many more when the weather’s right
These are not the only plants that offer food and shelter for flying insects. Among the first in the year are the flowers and leaves on the garden’s native trees and shrubs. Early summer in the hedges, flowers of wild roses offer a welcoming landing platform for grazing hoverflies.
One of the longest flowering species, not shown here in the photographs, is viper’s bugloss Echium vulgare, one of the borage family. (See it at the Bee plants links below.) Borage itself and the comfreys are also well visited.
Populations of bees and other flower-visitors were very badly affected here by the dry 2018. There was little left in flower by the end of August, while in most years the field scabious and viper’s bugloss are still visited in late October.
The coming year’s weather is uncertain as always, but we’ll try to manage the plants to give the longest possible season to the resident insects and spiders. First out will be the willow ….. .
But not the main crops
Nearly all the plants referred to here are native species or ones introduced long ago and now naturalised. Very few of the crops grown in the region (and the garden) – barley, wheat, oats, peas – support or need pollinating insects.
Oilseed rape fields provide a crop-based source of food for a few weeks early in the year and field beans also offer high-protein flowers much later. But the main sown crops and leys that could provide the right seasonal habitat – the legume forages and grass-clover mixtures – are rare and mostly long gone.
In the broader landscape therefore, the main source of food for flying insects lies in the broadleaf ‘weed’ species that live in crop fields and disturbed margins – in fact most of those shown in the panels above belong in this category. These arable plants, mostly not injurious to crops, have declined over the last century to the point where many of the plants themselves are now rare. It’s no wonder insects apart from pests are having a hard time in cropland.
Contacts
The Living Field’s page on Bee plants give further notes and images of the individual species most frequently visited in the garden.
As usual, the plants are grown and tended by Gladys Wright and Jackie Thompson with help from the farm.
The photographs of the insects on field scabious were taken by Linda Ford on an ideal summer day a few years ago, the others by Geoff Squire. Colleagues from the farm cut the Living Field meadow once a year and trim the hedges in sequence every few years to allow flowering and fruiting (e.g. for roses, willow, hazel). | http://www.livingfield.co.uk/food-web/pollinator-plants/ |
Peter Nobbs View Condolences - Whitby, Ontario | Barnes Memorial Funeral Home Ltd.
Condolence: I was one of the swimmers that Peter Nobbs coached at the Hudson Yacht Club. I wanted to send my sincere condolences to the family but I also wanted to add a story in tribute to Peter. In 2010 I had breakfast with my best friend Jack Layton who, like me, was one of Peter’s successful swimmers. That particular morning I brought with me the Centennial Book of the Hudson Yacht Club entitled “Our Spirit Lives On”. Among other things, that book talks about the many great swimmers Peter Nobbs helped produce. On reading about the pool, Jack and I reminisced about how Peter Nobbs really got us started in swimming and how much that swimming experience had helped us over the years. Peter made our swimming fun but he also expected a lot from us. Jack, being Jack, said let’s call him right now and thank him for the wonderful contribution he had made in our lives. So Jack did call him right then but, sadly, we were unable to reach Peter. Please know that Peter did make many wonderful contributions to the lives of many people. Truly his spirit lives on! | https://barnesmemorialfuneralhome.com/book-of-memories/3636511/Nobbs-Peter/view-condolences.php |
FIELD OF THE INVENTION
BACKGROUND OF THE INVENTION
SUMMARY OF THE INVENTION
DESCRIPTION OF THE PREFERRED EMBODIMENT
The present invention relates to the mechanisms for rotation transfer. More specifically, the invention set forth arrangement for rotation transfer using a chain of balls engaging periodic elements on surfaces of cooperating parts. Such devices are actively developed now as can be used in drives of all-purpose machines and mechanisms. Transmitting units with ball engagements bear marks of enhanced load-bearing ability and reliability. They are simpler and decreased in dimensions in comparison to tooth gearings for equivalent loadings and gear ratios.
Known ball gearings can be subdivided into gearings in which the ball cooperates with periodic elements provided in three and more parts (U.S. Pat. No. 5,016,487, U.S. Pat. No. 4,960,003, RU2179272); or with periodic elements of two parts (U.S. Pat. No. 4,829,851, U.S. Pat. No. 4,643,047, RU2179672). Ball engagement with two parts is used in transfers where one of parts makes planetary moving (U.S. Pat. No. 4,829,851, U.S. Pat. No. 4,643,047), or in transfers with parallel shafts (RU2179672). In transfers with ball engagements, the guide grooves on surfaces of cooperating parts represent periodic grooves of corresponding cross sections and the various forms. In these cases, the “guide groove” is a recession with its cross-section coinciding with the form of a ball, or through slot with the width equal to diameter of a ball, Le., in a general way, it is either extended equiangularly spaced flutes (RU2179272, SU 1260604), through slots (SU1399548, SU1569470, U.S. Pat. No. 5,312,306), hemispherical (RU2179672) or toroidal (U.S. Pat. No. 4,829,851) dimples, or closed periodically bent grooves with generating lines in the forms of trochoidal curve, cycloidal curve, sinusoids or a circle, etc. (M. F. Pashkevich Vestnik mashinostroyenija, No. 7, 1985). Said periodic guide grooves (periodic surface elements) may mate to each other in various combinations depending on purpose and features of a transfer design.
FIG. 1
3
4
1
2
3
4
1
2
1
2
1
1
2
2
As a prototype we choose a face-mounted ball engagement of “three-sinusoidal” ball gear (R. M. Ignatishchev, “Vestnik mashinostroyenija” No. 2, 1987 p). In this gear, closed periodically bent grooves are made in extreme disk parts; the intermediate part is made with equiangularly spaced slots. In such device, to keep contact of a ball with all grooves, the depth of the periodic grooves cannot exceed ⅓ of a ball diameter. At all advantages of ball transfers, above requirement essentially influences forces distribution when torque is transmitted, to worsen this distribution. shows force distribution in such gearing, where F is the force acting a ball from the drive part, N is reaction force of a driven part. Forces F and N are applied to walls edges of the grooves and , and each said forces have two components: F, Fand N, N, respectively. Forces Fand Nare useful forces, and force Noperates in an axial direction to push apart the driving parts and from each other, thereby causing a disengagement ball with grooves. And, certainly, this component Nincreases friction and reduces transfer efficiency. Further, a ball affects to edges of walls and , thereby increasing the probability of their destruction.
Accordingly, it is a principal object of the invention to provide a ball gearing with increasing both an efficiency and reliability, and especially, it is when high torque is transmitted. The technical result of the invention is improvement of forces distribution in interaction of a ball and grooves walls, and other result is displacement of a ball contact area from wall edge toward its bottom.
Ball engagement accordingly to the invention, as well as the prototype, comprises, a number of parts provided with periodic grooves in faced each other surfaces of said parts; and a chain of balls simultaneously engaging the grooves of all parts, wherein ball engagement the sum amplitude of the periodic interacting grooves is no more than the ball diameter. Unlike the prototype, faced each other surfaces of parts which surfaces having grooves actuating by their side walls to a ball are made mutually stepped meeting, and said grooves are cut in these stepped meeting surfaces, and said groves are so conjugate each other that the height of one sidewall of each groove is increased to exceed the ball radius by means of reducing of opposite thereto groove sidewalls of the other parts. Due to the increased height of the groove sidewalls the point of a ball contact with the sidewall is so shifted that forces acting ball from this sidewall lie along the same straight line thereby having only single component performing useful effect. The invention is applicable to any kind of ball gearing and to any known forms of the conjugated grooves. It can be gearing of a ball with two parts, or with three and more. Grooves can be executed either in flat surfaces of disks (flat ball gearing), or in cylindrical or spherical surfaces. Grooves can be bent either in axial or in radial directions and accordingly to cause periodic movement of a ball.
Further, the invention is explained in conjunction with the accompanying drawings wherein interaction of a ball with different types of periodic grooves in conjugated gearing parts is shown.
FIGS. 2
FIGS. 3 and 4
FIGS. 3 and 4
3
4
1
2
3
4
3
4
5
6
7
3
8
9
4
1
7
2
8
6
9
6
9
6
9
5
6
9
Referring now to the drawings wherein corresponding parts are identified by the same reference numeral. A flat ball gearing shown in , , composed of disk parts and in surfaces of which periodic grooves and are made in the form of closed periodically bent ball races with different number of the periods and identical amplitudes A. Basically, amplitudes of said grooves can be different, this condition does not limit a scope of the invention. At points of intersecting of grooves and there are placed balls contacting with walls of both said grooves. Each closed groove has two side walls. The edges of these grooves have the form of curves equidistantly shifted inside and outside from the central line L of a periodic path. These walls are and in groove , and walls and in the groove (). It should be noted that forms of these curves are different from each other, and also from the form of the central line L that is well shown in . The difference is most significant when balls are of large diameter, or when a number of the periods is big, or when there is low amplitude of oscillation (these are conditions of high load transfer). An undercutting of a groove also increases this difference. Thus, in ball gearing for high load transfers, the opposite walls of multi-periodical grooves have, as a rule, the different angles of rise. Loading is transferred basically by means of wall with a high angle of rise, and the opposite wall only fixes each ball in the certain position and returns ball in the necessary position during a nonworking part of a cycle. In the disk , this loaded (working) wall is a wall , and in the disk, this loaded wall is a wall . Opposite walls and are non-working; their height can be reduced, as because of effect of undercutting these walls contact to balls not by lines and , but by sites located more deeply. Non-working walls and only fix position of each ball in gearing. Such gearing is used mainly in high-speed transfers. At high speeds of rotation there are significant centrifugal forces acting to balls can disturb movement of a ball, if ball has not fixed position in space. Therefore, it is impossible to cut off the non-working walls and entirely in the gearing, as for them is very important the function of return balls during a non-working part of transfer cycle.
7
6
7
3
7
3
4
9
4
7
3
4
8
6
3
1
2
2
1
2
FIG. 3
FIG. 2
Disposing of a wall with higher rise angle depends on embodiment of the ball gearing. For cycloid grooves the following rule is fairly. If the number of periods in a groove is more than number of balls then rise angle of external wall is higher than rise angle of an internal wall , and wall is more loaded. illustrates this rule, where the number of balls is 28 a groove has 29 periods. For improvement of forces distribution in gearing, the external wall has its height exceeding radius of a ball by certain value h (see ). So that the ball has not left contact to walls of both grooves and , a wall in the groove , which wall is opposite to the increased wall in the groove , is made with the height reduced by value h. Accordingly, a groove with number of the periods 27 has internal wall as working wall which is made with increased height by reduction height of opposite to it wall of a groove . For realization of above in practice, the conjugating faced each other surfaces having said grooves are made mutually stepped meeting in the areas of grooves accommodation, and said grooves are cut in these stepped meeting surfaces. As parts and should have an opportunity to rotate relative to each other, such change of walls height is possible only for grooves of which total amplitude does not exceed a ball diameter. Only in this case during rotation of parts relative to each other there walls with the increased height are opposite to walls with reduced height, and are not hooked with each other. r shows the distribution of the forces acting to both walls of groove and to a ball. It is seen that these forces F and N have only radial components which are in value larger of corresponding force components in the prototype. Absence another components of these forces reduces friction in gearing and remotes the necessity in additional spring-loading of disks and to each other. Furthermore, the area of a ball contact with a groove's wall is displaced from its edge, thereby reducing probability of its destruction.
FIG. 5
FIGS. 6 and 7
3
10
10
1
2
3
11
12
11
5
10
13
2
10
14
13
5
3
4
12
3
1
15
16
3
2
17
18
1
1
2
2
19
20
1
20
2
1
1
2
1
In other embodiment shown in , the ball gearing is formed by the closed periodic groove conjugated with toroid dimples . Each of dimples is formed by rotating a circle having radius equal to a ball radius. Such gearing is intended for transmitting unit consisting of two disk parts and , periodic grooves of which are shown in . Side walls of the closed groove are designated by and . The height of side wall exceeds the radius of a ball by a value h; accordingly, the height of dimples walls is reduced by the same value h in opposite area of a disk . Walls height of dimples in the area laying opposite to the area is increased accuracy to the value h. For maintenance of contact of a ball with both grooves and the height of a wall is reduced in the groove . The surface of a disk is formed by steps and at the joint of which there is cut the groove . The surface of a disk also is formed by steps , but these steps in comparison with a disk have exchanged places, i.e. surfaces of disks and are in steps mated each other. All the above-stated explaining away force distribution, and away increasing of durability, is fair for this gearing also. In the gearing, said disk is mounted at the eccentric of an input shaft . Said disk is aligned with an axis of the input shaft by means of bearing. The disk makes parallel-plane orbital motion relative to the disk , and both the disk and the disk have an opportunity to rotate around of their own axes. If one of disks, for example a disk , is sopped from rotation, the other disk rotates around own movable axis with certain transfer ratio.
FIG. 8
FIGS. 9 and 10
3
22
3
22
1
2
1
2
11
3
23
22
3
22
12
3
24
22
1
2
15
16
17
18
1
19
19
20
shows example of the ball gearing wherein the closed periodic groove conjugates with hemispherical dimples . Said groove and hemispherical dimples are made in surfaces faced to each other of both disk parts and . show disks and with their periodical members. In this gearing, the wall of the periodic groove has the height exceeding a ball radius. The part of a wall of the hemispherical dimple has the height exceeding a ball radius. Accordingly, sites of groove and dimple , laying opposite of increased walls, have reduced by the same value walls height. They are a wall of the groove and a part wall of a dimple . Faced to each other surfaces of disks and are made stepped, and steps and of one disk are mated steps and of another disk. In the gearing said disk is rotatably mounted on an eccentric , the eccentric is carried by rotating input shaft for rotation therewith.
FIGS. 5 and 8
1
2
It should be noted that gearings represented on the above described Figures can be used in two designs of transfers. The first design is a planetary transfer, in which one of disks is mounted on an eccentric of an input shaft (as it is shown in ). In the second design, disks and are both rotatbly mounted in the casing and their axes are offset from each other. The last transfer is similar to a usual tooth gearing with parallel shafts, only gearing occurs by means of balls. The two designs have the different transfer ratio, but both have greater load range and higher efficiency.
FIGS. 11 and 12
FIG. 11
FIG. 12
FIG. 2
1
2
3
1
25
2
26
5
27
28
5
27
27
26
3
1
7
26
7
3
29
25
3
5
25
3
25
30
30
30
25
30
3
3
1
2
31
32
2
33
34
31
32
1
3
Now, pass to the description of units in which balls cooperate with periodic elements of three parts. In the three-part gearing, as a rule, a ball makes oscillatory moving relative to all three parts. It is essential that ball does not go beyond lands between slots during wave moving relative to a part having equiangularly spaced slots. The example of this gearing is shown in . Herein, two disk parts and are provided with periodic grooves cut in faced each other surfaces of said disk parts. Said grooves are: periodic bent continuous groove in the disk , and equiangularly spaced slots in the disk . The third part of the gearing is disk acting upon a ball by a groove in its side . The ball contacts to groove in the bottom region of the last. The groove may be either of single-periodic, multiperiodic, or annular. In the last occurrence, disk should make planetary movement. The periodic groove in the disk has only one sidewall ; opposite sidewall is cut off so that the disk being able installed. The sidewall of the groove is increased in height by h and so walls of slots are decreased in opposite area. Now, the contact area of a groove with ball (reference by A in ) lays along of straight line agreeing with direction of yield force F. Accordingly, the walls of equiangularly spaced slots which walls are opposite to cut off walls of the groove , are to be increased in height so that tangential force F() passing through a ball center did act to these walls normal to their surfaces. The increased walls of slots form projections . At that, projections are to have such axial thickness L in the area of ball moving that ball center did not go beyond limits of projections during ball moving along slots . Therefore, surfaces of projections faced to periodic groove are convex and inscribable into surface of groove . Practically, the surface of the disk faced to the disk is composed of two steps and (). Similarly, the surface of the disk is composed of two steps and mutually mating with steps and of the disk , accordingly.
FIGS. 13
14
15
35
36
37
38
39
40
41
42
43
44
35
45
42
44
35
46
35
Refer now to , , and wherein is shown other embodiment of ball gearing in which closed periodic grooves and are cut in cages and . Equiangularly spaced slots in the form of through slots are cut in a complex part composed of two cylinders , of different diameters, which cylinders are connected by component in which, properly speaking, said through slots with bridges are made. Height of a sidewall of a groove exceeds the ball radius, and height of sidewalls of slots is decreased in the area opposite to the sidewall . Another sidewall of the groove is cut off. A sidewall of a groove also has a height exceeding a ball radius.
46
36
47
42
36
42
48
49
35
36
42
5
FIG. 13
The sidewall of the groove also has the height exceeding the ball radius with the appropriate height decreasing of sidewalls of slots in opposite area. The second sidewall of the groove is cut off. Sidewalls of slots in the fields of the balls centers movement are made of the increased thickness and have the form of two opposite directed convexes and inscribable in surfaces of grooves and accordingly. As a result, the sidewalls thickness D of slots is increased in a plane of an arrangement of the balls centers, and the center of a ball (points A and B of ) does not go beyond the limits of slots sidewalls during wave radial movements of a ball. Meeting of this condition provides acting of tangential pressure forces balls upon walls of slots in a normal direction to surfaces of said walls.
FIGS. 16 and 17
50
51
52
53
54
55
56
57
51
50
55
58
59
56
57
53
58
59
60
52
54
50
51
52
5
61
53
62
61
52
54
Referring to , we consider one more embodiment of three-part ball engagement according to the invention. Here, one continuous groove is in the flat surface of a disk . Another continuous periodic groove and equiangularly spaced radial slots are disposed in the intersection of planes of cages and . Being made in appropriate steps and of surface disk the internal sidewall of a groove has increased height; the external side wall has decreased height, accordingly. Opposite thereto surface of cage also is made stepped composed of steps and mating to steps and accordingly. As a result, sidewalls of slots disposing in area of step are increased in height, and sidewalls of the same slots in area of step are decreased in height. To mate thereto, external sidewall of a groove in a cage , which sidewall is opposite to decreased sidewall of a groove in the disk , is increased in height, and internal side wall of a groove is cut off. To prevent the center of the ball from going beyond limits of bridges between radial slots , the external sides of bridges have convexes inscribable in the groove surface of the cage .
FIG. 18
63
64
65
63
66
64
65
67
64
68
65
69
66
70
68
71
68
67
72
73
66
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74
67
Above, we considered the invention in application to flat ball gearing. However, all reasoning and requirements also are correct for cylindrical or spherical gearing in which grooves act balls by edges of their sidewalls. By “cylindrical gearing” in this case is named the gearing in which grooves are cut in side cylindrical surface of the parts having the form of cages. We shall consider for an example the cylindrical ball gearing shown in . The gearing consists of an embraced cage and embracing cages and . In an external cylindrical surface of the cage a periodic groove is cut. In this case it is an inclined groove. Periodic elements are cut in cages and in a place of joint cages in their internal cylindrical surfaces. Periodically bent in axial direction grooves is cut in the cage , and axial equiangularly spaced slots are cut in the cage . A side wall of the groove is increased in height to exceed a ball radius, with appropriate height decreasing sidewalls of slots in opposite area. Accordingly in other area of said slots their sidewalls are increased in heights. The groove has a sidewall increased in height, with appropriate height decreasing of opposite sidewall of the inclined groove . To prevent ball from going beyond bridges between axial slots , their external surfaces are made convex and inscribable in the surface of the groove .
It is necessary to note, that the scope of declared ball gearing is not limited by designs shown in figures. It is applicable in any gearing wherein torque is transferred by means of interacting balls and grooves forcing balls by an edge of their sidewall.
2
3
4
1
2
3
5
4
3
7
7
5
8
4
5
7
8
1
3
4
1
2
7
8
5
1
2
Operating of the device we show on an example of the engagement a ball with two periodic elements in the form of the closed cycloid grooves shown on r , and . Assuming that a disk is driving member and it is brought in plane-parallel planetary movement having eccentricity relative to an immovable disk . A groove has a number of periods which is more then numbers of balls by 1, and a groove has a number of periods which is less than number of balls by 1. A working wall of the groove is the external wall having higher angles of rise. Pressure of a wall is transferred by ball to a wall of the groove . Interaction of a ball and walls and results in turning of the disk around of the immovable axis by angle depending on the numbers periods of both grooves and on disks and . The additional mechanism is provided to absorb the revolution component and to transmit only the rotational component. Such mechanisms well-known and bear no relation to a subject of the invention. As the heights of counteracting walls and is increased and exceeding radius of a ball by h, the force of a ball will be applied rather not to edges of these walls but to some area displaced from edges. And forces of pressure walls and balls to each other are directed along one straight line, and these forces have not an axial components pushing apart disks and from each other and increasing friction forces.
FIGS. 5-10
20
19
1
3
2
5
11
3
14
10
1
2
1
11
3
14
10
Operation of other embodiment ball gearing composed of the closed periodic groove and of dimples the various forms shown in differs from the above described gearing only in gear ratios. Rotation of an input shaft with the eccentric section causes plane-parallel planetary movement of a disk with the closed periodic groove . Disk is an immovable part. Ball interaction with walls of the groove and with walls of the dimples causes turning of the disk relative to the immovable disk . Since the disk makes rotation around of own axis together with orbiting then an additional mechanism is necessary to absorb the revolution component and to transmit only the rotational component. (It is not shown). Due to the wall of the groove exceeds a ball radius; and the area of the dimple exceeds a ball radius, the distribution of the forces is improved between walls of periodic elements and a ball. There is not a force pushing apart said disks from each other, and this fact increases an efficiency of the ball gearing. Displacement from wall edge the interaction area of groove walls with a ball reduces wall deterioration, and increases service life.
FIGS. 8
9
10
5
22
3
Operation of the devices shown in , , wherein a ball sits in hemispherical dimple and engages closed periodic groove , is similar to the operation of the above described gearing except that the ball only rotates in hemispherical dimples during operating. All other previous reasoning is fair for this device.
FIGS. 11 and 12
FIG. 3
FIG. 12
26
5
27
1
3
5
25
7
3
2
25
1
30
26
7
3
3
2
1
30
25
30
1
2
3
In operation of a ball gearing wherein periodic elements in the form of periodic closed grooves and radial equiangularly spaced slots are cut in three interacting parts which is shown in . Floating annulus forces balls by bottom of its groove . Disk is a reaction immovable part having a groove . Balls movement along of radial slots and orbital moving caused by their interaction with the sidewall of immovable periodic groove , both result in turning of the disk with radial slots , relative to disk . Herewith, any ball in radial slot runs in range marked by points A and B, and in that range height of walls exceeds a ball radius. Thus, a force F acting upon ball from floating annulus , and a force N acting upon a ball from a sidewall of a groove , both act not to the edge of the groove. Under the action of both these forces, the ball is displaced along the walls of the continuous groove in an azimuth direction while pressing walls of the radial slot by force F() thereby driving in movement the disk relative to the disk . It is seen from that the ball acts upon projection of bridge between slots , a height of which projection exceeds a ball radios. Thus, the interaction ball with all three grooves occurs at some depth from its edges rather then acting at its edges thereby reducing destruction probabilities of grooves due to wear. All forces of the interaction make useful work and they have no components for increasing friction force or components for pushing disks and apart each other.
FIGS. 13-17
The operation of others embodiments of the three-part units with ball engagement () is similar to above. In all these units the working area of grooves walls has the increased height with appropriate decreasing height of opposite inoperative wall areas of other driving parts.
FIG. 18
63
66
5
67
64
68
65
64
65
3
Operation of cylindrical three-parts gearing shown in is similar to above. Rotation of a cage with inclined groove causes ball to move in axial direction. In this moving the ball simultaneously interacts with continuous periodic groove of a cage and with axial slot of a cage . In one of said cages and is immovable, the other cage rotates by angle determined by number of periods the groove . The ball practically always is space confined by walls of increased height; and forces of interaction ball with walls of grooves have only axial and tangential components (for axial slots), which forces make useful work. Herein, efficiency of a ball gearing and its reliability are increased, as well as in embodiments above described.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1 and 2
are schematic, sectional views of a ball engagement with two disc parts;
FIGS. 3 and 4
FIG. 2
show schematic views of periodical grooves in all parts of gearing in ;
FIG. 5
shows a section through the two-part disc gear having toroid dimples in one of parts;
FIGS. 6 and 7
FIG. 5
show view of periodical grooves in parts of gearing in ;
FIG. 8
shows a section through the two-part disc gear having conjugated cycloid groove and semispherical dimples;
FIGS. 9 and 10
FIG. 8
show view of periodical grooves in parts of gearing in ;
FIG. 11
illustrates a variant of three-part ball gearing;
FIG. 12
FIG. 11
depicts the part with spaced radial slots of gearing in ;
FIG. 13
illustrates a second embodiment of three-part gearing;
FIG. 14
FIG. 13
is an exploded detail view of the ball gearing shown in ;
FIG. 15
FIG. 13
shows view of partially cut one part of the ball gearing in ;
FIGS. 16 and 17
illustrate a third embodiment of three-part ball gearing, sectional view and exploded detailed view, accordingly,
FIG. 18
shows a section one of embodiments of cylindrical gearing with axial movement of balls. | |
Guilty. That was the verdict six impartial jury members, which included County Supervisor Mark Stone and cycling activist Charlie Dixon, rendered Saturday against the automobile and its crimes against humanity and the Earth. As part of International Day of Climate Action on Saturday, SC 350 Coalition initiative put a 1980s Honda hatchback on the defensive during a mock trial against the automobile culture. This was one of more than 5,200 events hosted in 181 countries worldwide Saturday to address global warming. The event is a precursor to a larger rally planned in December, to coincide with a meeting of world leaders in Denmark to construct a global treaty on emissions. The number 350 represents the amount of carbon dioxide in parts per million the Earth can handle for humans to survive, scientists said. Currently, there’s 387 parts per million in the atmosphere. The people of the globe are encouraged to reduce their daily carbon emissions to help slow climate change and the impacts that come with it. Those impacts include the melting of the polar ice caps, longer periods of drought, intense storms, the death of the coral reefs, the collapse of the Amazon rain Forest and the flooding of low lying urban areas. On Saturday, the car faced charges of creating greenhouse gases, a public health nuisance, murder, disturbing the peace, causing congestion, racketeering, fraudulent advertising and parading around without a permit. During the trial, testimony against the automobile came from two teens and a redwood tree. All said they suffered badly from run-ins with the automobile. One teen, named Daisy Sunshine told the jury and the 100 people gathered at the Clock Tower Plaza Saturday that she had asthma from the automobile’s exhaust and many sleepless nights because of the noise the car creates. She also testified that her parents often spend more money than they have on medicine treating her medical condition. Another teen, Ellen Squashblossom sat bandaged up in her wheelchair after a car hit her as she rode the wrong way on the sidewalk down Mission Street. “You were riding illegally when you were hit by the car,” said Micah Posner, a cycling advocate who served as the automobile’s defense attorney during the trial. He cross-examined the witness. “The police found you at fault.” Meanwhile the redwood tree, which represented Mother Earth, cited that the United States is the largest producer of greenhouse gases, pumping out 19 tons of carbon dioxide each year, compared to China’s annual contribution of six tons. On the car’s defensive team were “Vicky Stationwagon” and “Joe the Plumber.” Both testified that the automobile plays an integral role in their daily lives. For the Stationwagon family, the car was a means to get everyone to their appointments, school, sporting events and other activities. For Plumber, he commuted up to five hours each day in his truck to get to jobs all over California. In issuing his sentence, Fred Keeley, the presiding judge and county treasurer-tax collector, ruled that the car must be made better, rather than cease to exist. He ordered that a tree be planted in the Honda. As for their day-to-day lives, Stationwagon and Plumber were encouraged to find ways to reduce their carbon footprint. For the Stationwagon family, that included, encouraging their children to ride their bikes or walk to school, arranging carpools and considering taking the bus. As for Plumber, he was encouraged to find work closer to home, to save on fuel consumption and costs, as well as reduce traffic congestion. The end result for both would mean a reduced impact on the environment, while adding more time to spend with family. For information on the things you can do to help reduce your carbon footprint, visit www.30x20.org, www.ecoact.org, www.sccrtc.org, www.scmtd.com or www.commutesolutions.org.
This entry was posted in alternative transportation, Bicycling, bus, consumer affairs, driver education, fuel conservation, Metro, Mission Street, pedestrians, Special events, traffic, Uncategorized and tagged alternative transportation, Bicycling, carpooling, fuel conservation, ride the bus, SC 350, walking. Bookmark the permalink.
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This invention relates to a method for providing the maximum film gloss of a dried waterborne coating composition.
Waterborne coating compositions such as paints containing emulsion- polymerized binders are frequently applied to substrates for decorative as well as protective reasons. A fundamental appearance parameter is the gloss of the dried coating. In many instances high gloss is required and this has been difficult to achieve with paints based on aqueous emulsion polymer binders.
U.S. Pat. No. 5,084,505 discloses a polymeric composition comprising a polymer and less than about 1 weight percent surfactant, the polymer having about 25 to about 60 weight percent of a soft monomer whose homopolymer has a Tg of less than about -20 C. and about 40 to about 75 weight percent of a hard monomer whose homopolymer has a Tg of greater than about 30 C. and has a calculated Tg of about 15 to about 35 C., an actual Tg of about 10 to about 60 C., and a particle size of less than about 250 nm. The polymeric composition is used in a high gloss latex paint.
The problem faced by the invention is the provision of a method for providing the maximum film gloss of dried waterborne coatings.
STATEMENT OF THE INVENTION
The invention provides a method for providing the maximum film gloss of a dried film of a waterborne coating composition by (a) forming a waterborne coating composition containing less than 30%, by volume based on the volume of the non-volatile components of the coating composition, of a predominant pigment; 30% to 80%, by volume based on the volume of the non-volatile components of the coating composition, of a first emulsion-polymerized addition polymer having a Tg from -30 C. to 50 C. and having an average particle diameter of 70% to 140% of the average particle size of the predominant pigment; 15% to 40%, by volume based on the volume of the non-volatile components of the coating composition, of a second emulsion-polymerized addition polymer having a Tg from -30 C. to 50 C. and having an average particle diameter of less than 35% of the average particle diameter of the predominant pigment; and pigment dispersant and surfactant in amounts effective to stabilize the coating composition; (b) applying the waterborne coating composition to a surface; and (c) drying the waterborne coating composition.
DETAILED DESCRIPTION
By "maximum film gloss" herein is meant that the specular gloss of a dried film of a waterborne coating composition measured at an incident angle of 20 degrees is equal to or greater than 90% of the maximum gloss calculated using the maximum achievable coating reflectance (R.sub.max) as defined hereinbelow.
A "waterborne polymeric composition" herein is defined as a composition containing pigment, and a first and a second emulsion- polymerized addition polymer dispersed in an evaporable medium which is predominantly composed of water. The evaporable medium may contain, in addition to water, at least one water-miscible solvent such as, for example, isopropanol, propylene glycol, ethylene glycol methyl ether, ethylene glycol butyl ether, and propylene glycol propyl ether.
The waterborne coating composition contains less than 30%, by volume based on the volume of the coating composition, of a predominant pigment. The predominant pigment is selected from inorganic and organic pigments such as, for example, titanium dioxide, calcium carbonate, carbon black, iron oxide, chromium oxide, and phthalocyanine blue on the basis of color and opacity. Preferred is less than 20%, by volume based on the volume of the coating composition, of a predominant pigment. Preferred is titanium dioxide as the predominant pigment; lesser amounts of other pigments may be employed for various reasons such as, for example, tinting and corrosion protection.
The first and second emulsion-polymerized addition polymers in the waterborne polymeric composition may be prepared by the polymerization of at least one ethylenically unsaturated monomer such as, for example, esters of (meth)acrylic acid, vinyl esters, styrene, and butadiene. Polar monomers such as (meth)acrylic acid, itaconic acid, acrylonitrile, dimethylaminoethyl (meth)acrylate, and hydroxyethyl (meth) acrylate may also be incorporated in the polymer. Chain transfer agents such as, for example, mercaptans may be used in order to moderate the molecular weight of the polymer. The first and second emulsion- polymerized addition polymers may be composed of the same monomers or of different monomers as is desired.
The emulsion-polymerized polymers used in this invention are substantially thermoplastic, or substantially uncrosslinked, polymer when it is applied to the substrate, although low levels of deliberate or adventitious crosslinking may be present. When low levels of precrosslinking or gel content are desired low levels of multi- ethylenically unsaturated monomers such as, for example, 0.1%-5%, by weight based on the weight of the emulsion-polymerized polymer, allyl methacrylate, diallyl phthalate, 1,3-butylene glycol dimethacrylate, 1,6- hexanedioldiacrylate, and divinyl benzene may be used. It is important, however, that the quality of the film formation is not materially impaired. Post-film formation crosslinking of the emulsion-polymerized polymers used in this invention may be effected such as, for example, via ionic, oxidative, covalent coreactant, and UV or visible light means.
The polymerization techniques used to prepare such emulsion- polymerized addition polymers are well known in the art. Conventional surfactants may be used such as, for example, anionic and/or nonionic emulsifiers such as alkali or ammonium alkyl sulfates, alkyl sulfonic acids, fatty acids, and oxyethylated alkyl phenols. The amount of surfactant used is usually 0.1% to 6% by weight, based on the weight of total monomer. Either thermal or redox initiation processes may be used. Conventional free radical initiators may be used such as, for example, hydrogen peroxide, t-butyl hydroperoxide, and ammonium and/or alkali persulfates, typically at a level of 0.05% to 3.0% by weight, based on the weight of total monomer. Redox systems using the same initiators coupled with a suitable reductant such as, for example, isoascorbic acid and sodium bisulfite may be used at similar levels.
In another aspect of the present invention the first or second emulsion-polymerized addition polymers may be prepared by a multistage emulsion addition polymerization process, in which at least two stages differing in composition are polymerized in sequential fashion. Such a process usually results in the formation of at least two mutually incompatible polymer compositions, thereby resulting in the formation of at least two phases within the polymer particles. Such particles are composed of two or more phases of various geometries such as, for example, core/shell or core/sheath particles, core/shell particles with shell phases incompletely encapsulating the core, core/shell particles with a multiplicity of cores, and interpenetrating network particles. In all of these cases the majority of the surface area of the particle will be occupied by at least one outer phase and the interior of the particle will be occupied by at least one inner phase. Each of the stages of the multi-staged emulsion-polymerized polymer may contain the same monomers, chain transfer agents, etc. as disclosed herein-above for the emulsion- polymerized addition polymer. The emulsion polymerization techniques used to prepare such dispersions are well known in the art such as, for example, U.S. Pat. Nos. 4,325,856; 4,654,397; and 4,814,373.
In another aspect of the present invention the first and second emulsion-polymerized addition polymers may be prepared in a single integrated process. Processes yielding polymodal particle size distributions such as those disclosed in U.S. Pat. Nos. 4,384,056 and 4, 539,361, for example, may be employed.
The first emulsion-polymerized addition polymer has a calculated glass transition temperature, Tg, from -30 C. to 50 C. and an average particle diameter of 70% to 140% of the average particle diameter of the predominant pigment.
The second emulsion-polymerized addition polymer has a calculated glass transition temperature, Tg, from -30 C. to 50 C.; and an average particle diameter of less than 35% of the average particle diameter of the predominant pigment.
Glass transition temperatures (Tgs) herein are those calculated as a weight fraction-weighted average of the homopolymer Tg values, that is, for example, calculating the Tg of a copolymer of monomers M1 and M2,
Tg(calc.)=w(M1)×Tg(M1)+w(M2)×Tg(M2)
,wherein
Tg(calc.) is the glass transition temperature calculated for the copolymer
w(M1) is the weight fraction of monomer M1 in the copolymer
w(M2) is the weight fraction of monomer M2 in the copolymer
Tg(M1) is the glass transition temperature of the homopolymer of M1 Tg(M2) is the glass transition temperature of the homopolymer of M2
The glass transition temperature of homopolymers may be found, for example, in "Polymer Handbook", edited by J. Brandrup and E. H. Immergut, Interscience Publishers.
The waterborne coating composition is prepared by paint making techniques which are well known in the coatings art. First, the pigment(s) is well-dispersed in a waterborne medium under high shear such as is afforded by a COWLES (R) mixer. Then the first and second emulsion- polymerized addition polymers are added under low shear stirring along with other coatings adjuvants as desired. The waterborne coating composition may contain, in addition to the pigment(s) and the polymers, conventional coatings adjuvants such as, for example, emulsifiers, coalescing agents, curing agents, thickeners, humectants, wetting agents, biocides, plasticizers, antifoaming agents, colorants, waxes, and anti- oxidants.
For the purposes of this invention it is necessary to achieve a stable pigment dispersion, stable not only on formation and in storage, but also preferably stable during the drying of the coating composition. Preferred as dispersant is a copolymer of methacrylic acid with a methacrylate ester at a level in the grind of greater than 3% by weight based on pigment weight. Preferred as surfactant is an anionic surfactant at a level of 2% to 5% by weight, including the weight of the surfactant used in the preparation of the emulsion polymer, based on the total weight of the polymeric components of the coating composition.
The solids content of the waterborne coating composition may be from about 20% to about 50% by volume. The viscosity of the waterborne polymeric composition may be from about 50 centipoise to about 10,000 centipoise, as measured using a Brookfield viscometer (Model LVT using spindle #3 at 12 rpm); the viscosities appropriate for different application methods vary considerably.
The waterborne coating composition may be applied to a surface such as, for example, metal, wood, and plastic, using conventional coatings application methods such as, for example, brush, roller, drawdown, dipping, curtain coater, and spraying methods such as, for example, air- assisted spray, airless spray, high volume low pressure spray, and air- assisted electrostatic spray.
The waterborne coating composition which has been applied to a surface is then dried under ambient conditions or at elevated temperatures, as may be desired. The use of polymeric components with a Tg sufficiently below the drying temperature or, in the alternative, the use of levels of volatile coalescents or plasticizers effective to provide a film formation temperature sufficiently below the drying temperature, thereby effecting the formation of a continuous film, is well-known in the art. Preferred is drying under ambient conditions.
The gloss of a dried film of a coating composition is determined by measuring the specular gloss, as described in the Experimental Methods section herein-below. The measured gloss is a relative specular reflectance of the coating surface compared to that of a standard (as per ASTM D 523, an optically smooth black glass tile with a refractive index n=1.567 was used) with reflectances measured at incident angles of 20 degrees, 60 degrees, or 85 degrees, using the equation:
Gloss=Reflectance of Coating/Reflectance of Standard× 100
The maximum achievable coating reflectance (R.sub.max) herein is taken as related to the refractive index of the polymeric component(s), as calculated by the modified Fresnel equation:
R.sub.max =1/2[{[cos i-(n.sup.2 -sin.sup.2 i ).sup.1/2 ]/[cos i+ (n. sup.2 -sin.sup.2 i).sup.1/2 ]}.sup.2 +{[n.sup.2 cos i-(n.sup.2 -sin. sup. 2 i).sup.1/2 ]/[n.sup.2 cos i+(n.sup.2 -sin.sup.2 i).sup.1/2 ]}.sup. 2 ]
The maximum gloss (G.sub.max) is calculated from R.sub.max using the following equation:
G.sub.max =R.sub.max /Reflectance of Standard×100
Experimental Methods
Measurement of Gloss
A drawdown of the test sample on glass was made with a 10 mil gap blade and dried at 25 C./50% Relative Humidity for 7 days. The specular gloss was measured using a GLOSSGARD II Glossmeter (Hunter Associates Laboratory, Inc.) as per ASTM D 523-89 at one of three angles of reflection, i.e., 20, 60, or 85 degrees.
Measurement of Refractive Index
The refractive index of polymer films at 25° C. and 589 nm wavelength (Na D-line) was measured with an Abbe refractometer, (Bausch & Lomb Model 3L or AO Scientific Instruments Mark II models), according to the instructions provided by the manufacturer for the measurement of solid samples. The use of the Abbe refractometer for determinations on polymer films is further described in Encyclopedia of Polymer Science and Engineering, Volume 14, p. 269, Wiley-Interscience, 1988. ASTM D 542-90 also provides procedures for preparation of test specimens and measurement technique with the Abbe refractometer, especially for harder organic polymer compositions. For soft, flexible polymer films, sufficient optical contact with the refracting prism was achieved by simply pressing a rectangular piece of the film, somewhat smaller than the prism, directly against it. For harder films, optical contact with the prism was achieved by first placing a small drop of an optical contact liquid on the prism, or, if the film was thin enough, by placing contact liquid on both sides of the film and closing the hinged prism assembly on the film. A non-solvent optical contact fluid, as described in Chamot and Mason, Handbook of Chemical Microscopy, 3rd edition, p. 327, John Wiley & Sons, 1958 was used in this work, a glycerol solution of potassium mercuric iodide, which had a refractive index, n.sub.D.sup.25 =1.65.
Measurement of Particle Size
Particle sizes of the latex and the predominant pigment were measured using either the BI-90 or CHDF instruments. Particle sizes may be determined using a Brookhaven BI-90 Particle Sizer which employs a light scattering technique. CHDF measurements of particle diameter were performed using a Matec Applied Sciences CHDF 1100 instrument using samples at 0.5 to 5.0% solids content. Both the emulsion polymers and the predominant pigment are measured using the same instrument.
EXAMPLE 1.
Preparation and gloss evaluation of waterborne coating composition.
Preparation of first emulsion-polymerized addition polymer (Sample 1-1)
In a first stage, the kettle water/soap were heated to 85° C. with stirring under N.sub.2. The Monomer Emulsion ("M.E.") preform and rinse were added. After two minutes the kettle ammonium persulfate (APS) was added. Eighteen minutes later the M.E. addition was begun at a rate to feed over 160 min, and Initiator solution ("Init.") to feed over 180 min. When M.E. was in, the feed line was rinsed. When Init. addition was completed, the reaction mixture was held at 85° C. for 30 min. The reaction mixture was cooled and filtered through a 100 mesh screen.
TABLE 1-1
______________________________________
Ingredients for first stage polymerization
Kettle charge (g)
Monomer Emulsion Initiator
______________________________________
H.sub.2 O 530
H.sub.2 O 165 APS/water
CO-436 (61.5%) 6.9
CO-436 2.1 1.4/70
EHA 252
M.E. preform 44
STY 420
(rinse) 10 MAA 28
APS/water 0.7/14
rinse 30 T.S.: 45.5%
Na.sub.2 CO.sub.3 /water 2.8/28
______________________________________
In a second stage, the kettle water was heated to 85° C. with stirring under Nitrogen. The First Stage polymer and rinse were added. After 2 minutes the M.E. was begun at a rate to feed over 160 min, and theInit. to feed over 180 min. When M.E. addition was complete, the feed line was rinsed. When the Init. feed was complete, the reaction mixture was held at 85° C. for 30 min. The reaction mixture was cooled, pH adjusted to 8.5 with NH.sub.3 ; and filtered through a 100 mesh screen. Particle diameter was 298 nanometers.
TABLE 1-2
______________________________________
Ingredients for second stage polymerization
Kettle (g) Monomer Emulsion Initiator
______________________________________
H.sub.2 O 510 H.sub.2 O 165 APS/water
CO-436 2.1 1.4/70
First stage (20 g solid) (˜45)
EHA 252
(rinse) 10 STY 420
MAA 28
rinse 30
______________________________________
Preparation of second emulsion-polymerized addition polymer (Sample 1- 2)
The kettle water/soap were heated to 85° C. with stirring under N.sub.2. The kettle ammonium persulfate (APS) was added. Two minutes later the M.E. addition was begun at a rate to feed over 120 min, and Init. to feed over 140 min. When M.E. addition was completed, the feed line was rinsed. When Init. addition was completed, the reaction mixture was held at 85° C. for 30 min. The reaction mixture was cooled, the pH adjusted to 8.5 with ammonia, and then filtered through a 100 mesh screen. Particle diameter was 54 nanometers.
TABLE 1-3
______________________________________
Ingredients for polymerization of sample 1-2.
Kettle (g) Monomer Emulsion Initiator
______________________________________
H.sub.2 O 1000
H.sub.2 O 165 APS/water
CO-436 (61.5%) 20.9
CO-436 2.3 1.4/70
EHA 252
APS/water 0.7/15
STY 420
MAA 28
rinse 30
______________________________________
A series of styrene/acrylic emulsion polymer binder paints were prepared at 18 PVC using Titanium Dioxide (TI-PURE R-700 from DuPont) of 285 nanometer particle diameter as the predominant pigment, according to the formulation given in Table 1-4. Additional soap was added slowly to the latex with stirring. Sample 1-1 was used at a level of 70% based on the volume of the dry addition polymers. Sample 1-2 was used at a level of 30% based on the volume of the dry addition polymers. The results are presented in Table 1-5.
TABLE 1-4
______________________________________
Preparation of coating compositions
The following materials were combined and ground in a
Cowles mill at high speed for 15 minutes. (All quantities are in
grams)
Propylene Glycol 1.8
Anionic Dispersant (35% solids)
2.14
(TAMOL QR-681M)
Aqueous Ammonia (28%) 0.05
Diethyleneglycol methyl ether
1.0
Defoamer 0.25
(BYK 022)
Urethane rheology modifier (20% sollids)
1.76
(ACRYSOL RM-1020)
Titanium dioxide 15.26
(TI-PURE R-700)
To the grind were added the following, in order,
with slow stirring:
Polymeric binder (blend) 44.37
TEXANOL 3.77
Defoamer 0.15
(BYK 022)
Urethane rheology modifier (20% solids)
2.08
(ACRYSOL RM-1020)
Water 1.66
______________________________________
The aqueous coating composition was allowed to equilibrate overnight.
TABLE 1-5
______________________________________
Effect of soap level on dried film gloss
Anionic Soap Level
Composition
(wt. based on polymer wt.)
Gloss (20/60)
______________________________________
1-1 0.7% 65/94
1-2 3.0% 86/98
1-3 5.0% 89/99
G.sub.max = 94/97
______________________________________
Dried films of the waterborne compositions 1-2 and 1-3 of this invention exhibit maximum film gloss.
EXAMPLE 2
Effect of particle diameter of first emulsion polymer and particle diameter of second emulsion polymer on dried film gloss
A series of styrene/acrylic emulsion polymer binder paints were prepared at 18 PVC using Titanium Dioxide (TI-PURE R-700) of 285 nanometer particle diameter as the predominant pigment. The second emulsion-polymerized addition polymer had a particle diameter of 55 nanometers and was used at 25% based on the volume of the coating composition. The anionic surfactant level was used at 5% (by weight bsed on the weight of polymer solids). Various first emulsion-polymerized addition polymer diameters used at 57% based on the volume of the coating composition were evaluated as shown in Table 2-1.
TABLE 2.1
______________________________________
Effect of first emulsion polymer particle diameter
Composition
Particle diameter (nanometers)
20 degree Gloss
______________________________________
2-1 250 76
2-2 260 76
2-3 290 76
2-4 310 78
2-5 320 80
2-6 360 81
2-7 405 73
2-8 445 73
G max 85
______________________________________
A series of styrene/acrylic emulsion polymer binder paints were prepared at 18 PVC using Titanium Dioxide (TI-PURE R-700) of 285 nanometer particle diameter as the predominant pigment. The first emulsion-polymerized addition polymer had a particle diameter of 356 nanometers and was used at 57% based on the volume of the coating composition. The anionic surfactant level was used at 5% (by weight bsed on the weight of polymer solids). Various second emulsion-polymerized addition polymer diameters (the volume % of this polymer was used at 25% based on the volume of the coating composition) were evaluated as shown in Table 2-2.
TABLE 2.2
______________________________________
Effect of second emulsion polymer particle diameter
Composition
Particle diameter (nanometers)
20 degree Gloss
______________________________________
2-9 43 81
2-10 55 81
2-11 70 82
2-12 100 74
G.sub.max 85
______________________________________
Dried films of the waterborne compositions of this invention 2- 1 to 2- 6 and 2-9 to 2-11 of this invention exhibit maximum film gloss.
EXAMPLE 3
Effect of anionic surfactant level on dried film gloss
A series of styrene/acrylic emulsion polymer binder paints were prepared at 18 PVC using Titanium Dioxide (TI-PURE R-700) of 285 nanometer particle diameter as the predominant pigment. The first emulsion-polymerized addition polymer had a particle diameter of 356 nanometers and the volume % was 57% based on the volume of the coating composition. The second emulsion-polymerized addition polymer had a particle diameter of 55 nanometers and the volume % was 25% based on the volume of the coating composition. The anionic surfactant (ALIPAL CO- 436) levels are given as weight % based on polymer weight. Results of evaluation are presented in Table 3-1.
TABLE 3-1
______________________________________
Effect of anionic surfactant level on dried film gloss
Composition Soap Level
20 degree Gloss
______________________________________
3-1 0.7 56
3-2 1.7 64
3-3 2.7 71
3-4 3.7 77
3-5 4.7 83
G.sub.max 85
______________________________________
Dried films of the waterborne compositions of this invention 3- 4 and 3- 5 of this invention exhibit maximum film gloss.
EXAMPLE 4
Effect of dispersant level on dried film gloss
A series of styrene/acrylic emulsion polymer binder paints were prepared at 18 PVC using Titanium Dioxide (TI-PURE R-700) of 285 nanometer particle diameter as the predominant pigment. The first emulsion-polymerized addition polymer had a particle diameter of 276 nanometers and its volume % was 66% based on the volume of the coating composition. The second emulsion-polymerized addition polymer had a particle diameter of 53 nanometers and its volume % was 16% based on the volume of the coating composition. The copolymer of methacrylic acid with a methacrylate ester dispersant (TAMOL 681) levels, all used in the pigment grind, are given as weight % based on pigment weight. Results of evaluation are presented in Table 4-1.
TABLE 4-1
______________________________________
Effect of dispersant level on dried film gloss
Composition Dispersant Level
20 degree Gloss
______________________________________
4-1 0.7 58
4-2 3.0 70
4-3 5.0 83
G.sub.max 85
______________________________________
Dried film of the waterborne composition of this invention 4-3 exhibits maximum film gloss.
EXAMPLE 5
Effect of second emulsion polymer level on dried film gloss
A series of styrene/acrylic emulsion polymer binder paints were prepared at 18 PVC using Titanium Dioxide (TI-PURE R-700) of 285 nanometer particle diameter as the predominant pigment. The first emulsion-polymerized addition polymer had a particle diameter of 322 nanometers and its volume % was (82-x) % based on the volume of the coating composition. The second emulsion-polymerized addition polymer had a particle diameter of 55 nanometers and its volume % was x % based on the volume of the coating composition. Results of evaluation are presented in Table 5-1.
TABLE 5-1
______________________________________
Effect of second emulsion polymer level on dried film gloss
Composition x % 20 degree Gloss
______________________________________
5-1 0 63
5-2 8 66
5-3 16 75
5-4 25 77
5-5 41 76
5-6 82 70
G.sub.max 85
______________________________________
Dried film of the waterborne composition of this invention 5-4 exhibits maximum film gloss.
EXAMPLE 6
Effect of high Tg second emulsion polymer level on dried film gloss
A series of styrene/acrylic emulsion polymer binder paints were prepared at 18 PVC using Titanium Dioxide (TI-PURE R-700) of 285 nanometer particle diameter as the predominant pigment. The first emulsion-polymerized addition polymer had a particle diameter of 356 nanometers and its volume % was 57% based on the volume of the coating composition. The second emulsion-polymerized addition polymer was a blend of second emulsion polymer 1, which had a particle diameter of 40 nanometers, a Tg of 10 C., and its volume % was (25-x) % based on the volume of the coating composition, and second emulsion polymer 2, which had a particle diameter of 65 nanometers, a Tg of 84 C., and its volume % was x % based on the volume of the coating composition. Results of evaluation are presented in Table 6-1.
TABLE 6-1
______________________________________
Effect of second emulsion polymer 2 level on dried film gloss
Composition x % 20 degree Gloss
______________________________________
6-1 0 76
6-2 6.2 75
6-3 12.3 59
6-4 24.6 41
G.sub.max 83
______________________________________
Dried films of the waterborne compositions of this invention 6- 1 and 6- 2 exhibit maximum film gloss. Compositions 6-3 and 6-4 contain higher levels of second emulsion polymer 2 which reduce the level of second emulsion-polymerized addition polymer 1 having a Tg from -30 C. to 50 C. and having an average particle diameter of less than 35% of the average particle diameter of the predominant pigment to less than 15% to 40%, by volume based on the volume of the non-volatile components of said coating composition do not exhibit maximum film gloss.
EXAMPLE 7
Effect of PVC level on dried film gloss
A series of styrene/acrylic emulsion polymer binder paints were prepared at various PVCs using Titanium Dioxide (TI-PURE R-700) of 285 nanometer particle diameter as the predominant pigment. The first emulsion-polymerized addition polymer had a particle diameter of 356 nanometers and its volume % was (75-x) % based on the volume of the coating composition. The second emulsion-polymerized addition polymer had a particle diameter of 55 nanometers and its volume % was 25% based on the volume of the coating composition. Anionic soap level was 5 weight % based on polymer weight. Results of evaluation are presented in Table 7-1.
TABLE 7
______________________________________
Effect of PVC level on dried film gloss measured at 20 degrees
PVC % of Gmax
______________________________________
0 100
10 100
20 99
30 65
40 20
______________________________________
Dried films of a waterborne composition of this invention at 0, 10, and 20 PVC exhibit maximum film gloss. | |
Many questions have surrounded this subject over the last years. One of my friends asked me some time ago about my thoughts on this subject so I decided to do a little research about teleportation. Would teleportation work?
Is it possible? Is it just a ‘spooky action at a distance’ as Einstein claimed or is it a real phenomenon as the scientists claim?
Professor Hanson, His Theories and Experiments
Scientists and researchers claim that the laws of physics don’t make the teleportation of humans impossible at all. So did Star Trek know something way ahead of its time? Would teleportation work? Or are we hoping for a little too much?
Dr Hanson has said that ‘If you believe we are nothing more than a collection of atoms strung together in a particular way, then in principle it should be possible to teleport ourselves from one place to another.’
To prove this, Professor Hanson and his team made one unique experiment.
This great team of scientists teleported information, encoded into subatomic particles at a distance of three meters with complete success.
In other words, they demonstrated and proved that it is possible.
This was the first step in building an internet network – the future quantum internet. It is said to be a way of securing a one hundred percent secure communication platform because nobody can intercept this information.
Einstein had previously disagreed with this theory many years before, saying that is impossible for a signal to pass between particles at the speed of light, but our great minds don’t give up.
What next?
In the near future (actually in July 2016) a new planned experiment will take place which will attempt to prove that Einstein was in fact, wrong.
An attempt will be made to try to teleport a signal at a larger distance between two buildings. This experiment will be carried out at a university where Professor Hanson teaches.
This time, the distance will be extended from 3 meters to 1300 meters. So this experiment is a lot more ambitious.
Once the results of this experiment are released I will be reporting on them, so I will let you know my thoughts as soon as I can.
For now, we just sit in hope that they will succeed with this experiment.
Other Opinions
Last year, another great physicist by the name of Alex Kuzmich shows a form of information teleportation by entangling a computer’s atoms and photons on demand.
If you can build a quantum computer, the physicists are aiming to build ‘quantum networks’ that will link many computers together. One of the main benefits of this discovery is the security.
Another professor, Michio Kaku, claims that the teleportation of a living person from one place to another will be possible in the next decades. He also claims that time travel and invisibility will be soon possible too.
In fact, he goes on to mention about a potential experiment where an atom can be teleported. He says that as we have been able to teleport light, it would be also possible to teleport atoms and molecules.
A new record in quantum teleportation was made by researchers in US and information encoded in particles of light has been teleported over 100 km of optical fiber.
News 2017
Whats scientists achieved new in teleportation? You would not believe:) They have teleported a photon to a distance of 1400 km(870 miles), to a satellite named Micius, in space. In fact, what is teleportation? Is just sending not really the thing its self somewhere but just the state of a thing. Can this happen and with the human body? Teleportation relies on a phenomenon named quantum entanglement.What means this?When two particles are created at the same place, at the same time and have the same existence it occurs a quantum entanglement.
A Romanian scientist at the University of Bristol, Professor Popescu Sandu is working at this phenomenon since 1990.So how he explained this works? If are two entangled particles and a third one is interacting with the first one so we can see the change from the first particle, also in second identical particle while they have the same existence and are twins.
So in their experiment, Chinese scientists created many pairs of entangled photos, thousands and then beamed one photon of each pair to the Earth satellite Micius and the conclusion was that those photons are identical twins and maybe more than this.But photons are very fragile and if they interact with the matter on Earth’s atmosphere they lose their entanglement. The good news is that in space they can extend indefinitely.
Some updates
So ,to be possible human teleportation are only two ways but both of them are difficult to be done, almost impossible;
- we can transmit one person like using a fax:) . the human body should be translated into data to be possible to be transmitted and than,in the destination place to be changed into matter. Possible?
- another way is to deconstruct human body in atoms and reconstruct it at the destination point.
There is a ‘ small ‘ problem here. Even if it was possible, to break the human body into data it will require as much as the UK energy supplies for a million years and more and will need about five millions years to transfer the data, according to the University of Leicester studies.But Kaku has a different opinion. he claims that all this problems will be resolved in the next decades and he propose a teleporter that will work as a Ultra MRI scanner.
So he think that is a better idea to use x rays to transmit a human body date, to beam it into space into a satellite and than send to the destination point.
Still everything is in theory. Scientists are working to teleport photons and soon will be possible to teleport atoms. Kaku thinks that in the next decade will be possible the transport of a molecule and the next step is the whole DNA.
If in 2010 physicists ( Jian -Wei Pan and his team)at the University of Shanghai ( Chine) teleported photons without fiber optics more than 16 km now they repeated this experiment and achieved the distance of 97 km. Big difference I think.
So..we will see soon 🙂
These are a few updated in 2019 but if i find something new i will let you know.
Conclusion
So as you can see there are conflicts of opinions. Some say teleportation can be possible (just like the example in Star Trek) in the future, and others not. What do you think?
Is it just a fantasy or is it something that can be achieved?
Now listen, I know that this subject is very involved and to be honest, we can talk about different areas that can leave you with a headache.
As I said before, I want this website to offer certain information without getting too technical and confusing.
Do you have an opinion on teleportation? Maybe you have read some information before that can be shared here?
If so I would love to hear from you, just leave a comment below. | https://yourtimetravelexperience.com/would-teleportation-work-opinions |
Number puzzles 1 – 10 clearly introduces one to one number correspondence to children. Count the dots and match with a number symbol. Check answers by fitting the puzzle pieces together – control of error.
Contents:
20 wooden puzzle pieces
manual
wooden box (16 x 9 x 5 cm)
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Apart from ship structural failure or poor machinery conditions, inadequate sailing preparation may also lead to a fatality at sea. To improve deck safety, crew, therefore, need to be well prepared before proceeding to sea. Sailing preparations may include many complexities, and this is the reason why a bunch of things should be considered and prepared carefully, to ensure a smooth voyage passage and safe navigation. Any prudent master will arrange and guide his crew to prepare the vessel for a sail out in safety from one port. Summarized below are some essential check items. These procedures are only indicative, not exhaustive, and must always be guided by practices of good seamanship.
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Securing for Sea
Closure of Openings
Cargo Operation Safety
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Prior departure make sure all crew present on board : Deck dept., Engine dept. & Catering dept.
Replenishment of bunkers, lubes, stores and spares
Replenishment of provisions and freshwater.
Confirmation of draft , stability and hull strength as per
"Procedures for Confirming draft , stability and hull strength
Confirmation of water tightness of openings as per
"Procedures for Confirming Closure of Openings
Confirmation of necessary legal documents, trading certificates and port clearance
Completion of cargo and related work including lashings
Disembarkation of labors/ stevedores/ terminal personnel / agent etc
Confirmation of securing or lashing of movable objects
Completion of repairs and disembarkation of workers/ contractors/ technicians etc
Disembarkation of all visitors & collection of passes issued to visitors, any missing passes reported to SSO
Stowaway search carried out (as per SSP search cards)
Engine Room given adequate (at least 1 hour) notice for preparing M/E / Bow Thruster
Confirmation of readiness for main engine trial (condition of gangway, bow and stem, manifolds, and others)
Stations for departure planned & crew advised of Stand-By time
Confirmation of power supply & operation of winches and windlass
Passage Plan for intended voyage prepared and signed
All charts and publications for voyage up to date and courses laid
Latest weather forecast and navigational warnings for area at hand
Tidal calculations for departure ready
Main Engine tried out ahead and astern, correct print-out on telegraph logger (where fitted)
Fig :Container ship loaded condition
Confirmation of binoculars and daylight signal lights
Preparation of Pilot card and information exchange and bell book
Ships clocks checked and synchronized, including with E/R
Steering gear tested individually and as per SOLAS V/26
AIS correctly set to sea mode (transmission power, etc) & ship data updated. SVDR status checked - NO ALARMS
Bow Thruster tried out (where fitted)
Compass repeaters aligned (incl. in strg flat where fitted)
Gyro error checked and magnetic compass illuminated
Whistle tried out (unless prohibited)
Radars on standby (operational only when permitted by port), speed input set for ARPA through water
Echo sounder switched on / Zero alignment done / annotated
Confirmation of VHF channel in use
Navtex receiver set to correct station & information checked
"Course Recorder checked for paper and time/course synchronization, and annotated"
GMDSS equipment switched on and functional
Navigation lights switched ON and tested
Other equipment checked
Confirmation of meeting with the Pilot about passage plan
Sailing report required by Port Regulations including notification to VTS if applicable
Confirmation for watch schedule
Fire detection system operational
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Notes: Stanley hasn't played since Game Four (Michigan). Head coach Brian Kelly recently explained redshirt rules in a unique manner, suggesting any Irish player that doesn't appear from Game Six forward, and who hasn't played in more than three of his team's games previously, could be eligible for a redshirt designation from the NCAA. Stanley would fall under that category.
Redshirt-freshman Nick Martin appears to be set as the team's No. 2 left tackle at present.
LEFT GUARDSenior Chris Watt 6'3" 310 pounds (2)
Sophomore Conor Hanratty 6'5" 305 pounds (4)
Notes: Hanratty saw extended action in the blowout of Miami and would likely be the first guard off the bench should either Watt or Mike Golic (below) go down.
CENTER- 5th-year senior Braxston Cave 6'3" 304 pounds (1)
- 5th-year senior Mike Golic, Jr. 6'3" 295 pounds (1)
- Sophomore Matt Hegarty 6'5" 296 pounds (4)
Notes: Hegarty is the only varsity center returning for 2013. Golic would replace Cave in an emergent, competitive game situation but Hegarty will likely receive second team work should the Irish pull away in a game as they did vs. Miami in Game Five.
RIGHT GUARD5th-year senior Mike Golic, Jr. 6'3" 295 pounds (1)
Sophomore Conor Hanratty 6'5" 305 pounds (4)
Sophomore Nick Martin 6'4" 290 (4)
Notes: Martin is technically listed as the team's backup right guard, but his work as the No. 2 left tackle in Soldier Field vs. Miami suggests otherwise. Junior Bruce Heggie filled in at RG with Hanratty on the left side as the Irish went to their second unit in the fourth quarter of that contest. Hanratty, as noted previously, would likely be the first guard off the bench on either the left or right side.
RIGHT TACKLEJunior Christian Lombard, 6'5" 309 pounds (3)
- Junior Tate Nichols, 6'8" 325 pounds (3)
Notes: Nichols made his college debut in the Game Five win over Miami. After redshirting in 2010 as a true freshman, Nichols redshirted last fall due to knee and shoulder injuries. He missed the first four games of 2012 with a patella tendon injury as well. Lombard has started all six games this season, the first of his career in the opener vs. Navy.
TIGHT ENDSenior Tyler Eifert, 6'6" 251 pounds (2)
Sophomore Troy Niklas, 6'7" 260 pounds (3)
Sophomore Ben Koyack, 6'5" 253 pounds (3)
Notes: Niklas is a de facto 12th offensive starter, earning as many snaps as any receiver this season with the exception of T.J. Jones and, of course, Eifert. Koyack played his best quarter of football since the season opener as a run-blocking tight end vs. Miami but played sparingly last week vs. Stanford. During limited action, Koyack executed a first-drive seal block that afforded quarterback Everett Golson room over the left side for first down yardage on a designed run to his side.
(Z) SLOT RECEIVERSenior Robby Toma, 5'9" 185 pounds (1)
Freshman Davonte' Neal, 5'9" 171 pounds (4/5)
Notes: Toma receives the lion's share of snaps with Neal playing an occasional snap or two in the first half of recent contests. Toma ranks fifth on the squad with 18 pass targets through six games, securing 12 passes to date. The greatest road block to playing time for Neal is likely his perimeter blocking technique as a true freshman, as Toma has improved greatly in that regard as a senior contributor. Neal has not been targeted for a pass since Game Three at Michigan State; he's served as the team's punt returner each week, though with just 10 return opportunities -- precious few offering room to maneuver post-catch.
(X) WIDE RECEIVERJunior T.J. Jones, 5'11" 190 pounds (2)
Sophomore DaVaris Daniels, 6'2" 190 pounds (4)
Notes: True freshman Justin Ferguson has settled into a special teams role (kick return as a first-line blocker) after catching a pass late in the season opener vs. Navy. Jones ranks third on the team with 31 pass targets, corralling 19 catches including 17 for first down yardage. Daniels is fourth on the team with 14 receptions while leading the regular rotation players at 16.5 yards per catch. He played extensively alongside Jones last week with John Goodman out due to a back injury.
(W) WIDE RECEIVER5th-year senior John Goodman, 6'3" 215 pounds (1)
Junior Daniel Smith, 6'4" 215 pounds (2)
Freshman Chris Brown, 6'2" 172 pounds (4/5)
Notes: Brown started vs. both Michigan and Miami and was targeted downfield on the first drive of both. He's yet to secure (or touch) his first collegiate pass despite three targets. Smith played more snaps than his usual last week with Goodman out. He's shown quality blocking on the perimeter each week and Saturday vs. Stanford saved the Irish (Golson) from a sure grounding penalty by coming back toward a ball thrown intentionally out of bounds. The grounding call would have resulted in a safety as Golson threw the ball away from his own end zone.
RUNNING BACKSenior Theo Riddick, 5'11" 200 pounds (1) OR
Senior Cierre Wood, 6'0" 215 pounds (2) OR
Sophomore George Atkinson, 6'1" 210 pounds (3)
Notes: Riddick leads the team in rushing yards, attempts, touchdowns (tied with Atkinson), pass receptions, and pass targets. Atkinson leads the team in yards per carry while Wood is the leading rusher since his return in Week Three from a two-game suspension, amassing 279 yards and two scores on 47 carries (5.9 per rush).
QUARTERBACKJunior Tommy Rees was announced Saturday morning as the game's starter.
Sophomore Everett Golson, 6'0" 185 pounds (4) OR
Junior Andrew Hendrix, 6'2" 225 pounds (3)
Notes: Kelly noted at his Thursday evening press conference that Golson would be a game-time decision due to his recovery from a concussion suffered last week vs. Stanford.
Rees has appeared in each of the team's six games this season, starting once (due to a violation of team rules by Golson) and finishing all three homes games for Golson due to a trio of disparate reasons. Rees threw his first touchdown pass of the season last week, the 7-yard slant to T.J. Jones provided the winning score in overtime. He and Golson have combined to complete eight straight passes for the position heading into Saturday's contest. Saturday's win vs. Stanford included Golson's fourth, fifth, and sixth turnover in three home starts to date.
Golson's crucial game-tying touchdown pass to Eifert in the fourth quarter Saturday was his first TD toss since Week Three in East Lansing and, occurring on 3rd and 18, one of the best passes of his early Irish career. He's accounted for six scores: four passing and two rushing. | http://www.scout.com/college/notre-dame/story/1231344-depth-chart-irish-offense |
From the war in Ukraine, inflation, supply chain issues and the recovery from the Covid-19 pandemic, market turbulence has been at the forefront of investor’s minds. It is impossible to know how the market will react to global or economic events on any given day. It is also difficult to manage emotions in situations like these.
Market turbulence is an unavoidable occurrence in investing. However, with the proper understanding of historic market performance, and a well-documented and proactively managed plan, investors should stay the course; and if they don’t already have expert advice, seek an experienced financial planner.
What is Market Turbulence?
Market turbulence is defined as the unexpected rising and falling of the stock market and the value of stocks and bonds associated with it. Since its inception, the stock market has experienced waves of highs and lows. The volatility of the stock market is affected by a variety of factors including government policy, major global events, or economic hardship at the consumer level.
Market turbulence is usually accompanied by an influx of investment and financial statistics and analysis of government actions. Experts and investors present analysis in order to predict how the market will react in the future. Many investors question their current strategy when market turbulence is underway. Attempting to forecast market trends by economic analysis leads investors to make drastic, and often times detrimental, decisions regarding their portfolios in an attempt to make up for losses due to market turbulence. Regardless of the market’s performance or turbulence, it is impossible to predict future trends with complete certainty. It is important for investors to reflect upon their investment goals, and if their portfolio still supports those long-term goals, they shouldn’t abandon their positions even in times of extreme or even moderate market turbulence.
Since the beginning of 2022, market turbulence has been in full swing at the hands of rising volatility and geopolitical uncertainty. One thing investors should always understand in times of high market volatility and turbulence is that is normal. Market responses to major global events or government action is considered healthy for the market and as shown by past market pull-backs, the market will bounce back. Investors can make logical decisions about their portfolio rather than making rash decisions in an effort to minimize losses.
For many, years of their hard-earned money and retirement funds are contingent on the performance of the stock market. Market turbulence is a threat to millions of people’s livelihood, so it is important to have a clear understanding of factors that may lead to market turbulence as well as how to prepare yourself for any major economic shifts in the market.
Factors Leading to Market Turbulence
Market turbulence can occur for a wide array of reasons. Even minuscule changes in policy or global events can lead to market turbulence. The market as a whole is less volatile than individual investments, but when the entire market experiences turbulence it can mean major losses for investors.
The war in Ukraine has had economic impacts across the entire globe. The United Nations has issued a variety of sanctions on Russia leading to heightened prices in the food and energy industries. Russia produces a large percentage of the world’s wheat and is a major distributor of oil and other refined fossil fuels. Furthermore, many companies have refused to operate within or trade with Russia as a result of the sanctions in place. All these factors, and more, have led to the war in Ukraine having a negative impact on the stock market and increased market turbulence.
The Federal Reserve is the central banking system of the United States and one of the main dictators of market performance. The Federal Reserve, also referred to as the Fed, has adopted an aggressive approach to interest rates as a result of major economic growth following the Covid-19 pandemic. As a result, inflation continues to rise and reach highs that the United States have not experienced in some time. The Fed was designed to centralize the banking system in the United States in order to prevent or control major economic crisis and their actions to raise interest rates are a result of this notion.
The culmination of inflation and an energy crisis due to the war in Ukraine have also led to higher prices on commodities such as food and gas. When consumers have less money to spend investing because of higher prices on necessities, the market traditionally will respond with initial pull-back and market turbulence. However, savings for many Americans is very strong, as is the U.S. economy.
How to be Prepared for Market Turbulence
Facing a volatile and turbulent market can be a complex task to handle. You may have a grasp on the market and understand your goals for investing, but do not know where to start. Finding the right financial advisor can put your investments at an advantage and provide peace of mind knowing that your goals are shared with someone who focuses in this area.
Regardless of the state of the market, having an expert financial advisor, a teammate, in your corner while you make decisions for your money can lead to a path of success.
Financial advisors can help you plan for the future by providing insights, strategies and proactive management that you may not have considered on your own. Advisors have access to forecasting trends, the market’s response to various global events, market declines, or even healthcare so your investment portfolio can stay on track.
Fragasso Financial Advisors, wealth management Pittsburgh, PA recently published an article titled, Understanding Marketing Turbulence, which can provide you more information on this topic. They understand the complexity behind turbulent markets as they have been in the industry for fifty years. Just think of all the events that have negatively and positively impacted the market in the past five decades! Their in-house team of portfolio management professionals provide insightful blog posts on relevant topics such as inflation, energy costs, and the market response to the war in Ukraine.
Investment advice offered by investment advisor representatives through Fragasso Financial Advisors, a registered investment advisor. | https://www.businessmagazine.org/understanding-the-current-market-turbulence-23639/ |
We serve breakfast buffet every morning in the dining room which has a stunning view of the famous volcano Hekla and the great surrounding countryside around þjórsá .
Here we also serve lunch and dinner upon request. We use a lot of local produce, the trout is for example from our own lake, such as the rhubarbs is from our garden and a lot of the herbs and berries we are using when we create the food is hand picked by us.
Normally we have two main courses and a dessert menu to choose from every night, you can pre-book your dinner by contacting us before arrival.
Kitchen closes 20:00 every night if nothing else is agreed. Please contact us if you expect to eat later.
Please contact us for order and menu before arrival or if you want a offer on group menus and special arrangements!
And let us know about any food allergies and food preferences before arrival so we can arrange the best for you. | http://www.denami.is/our-services/dining/ |
Irish Wolfhound Gives Birth to Identical Twin Puppies
August 24, 2017
|
6,864
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Story at-a-glance
During a cesarean section delivery, an Irish wolfhound gave birth to two puppies attached to the same placenta; typically, each puppy in a litter has its own placenta
Genetic testing revealed the puppies to be identical twins
The pups had similar, but not identical, markings; the slight differences are the result of differing genetic expression
By Dr. Becker
The average number of puppies in a litter depends on the mother’s breed, size and other factors, but typically includes two to six pups. Those puppies are technically fraternal twins, meaning they each developed from different eggs and have unique DNA. They may look similar and have similar behaviors, which is to be expected, since they’re siblings from the same litter.
In some cases, an egg may split and form two embryos, which leads to identical twins. Identical twins are known to occur, albeit rarely, in a number of species, including dogs, pigs, cattle, horses and armadillos,1 but it wasn’t until 2016 that a case was scientifically identified in dogs.
Irish Wolfhound Gives Birth to Identical Twin Puppies
A 4-year-old Irish wolfhound in South Africa was taken to a veterinarian after being in labor for two hours with no progress. The veterinarian, Kurt de Cramer, performed a caesarean section and soon noticed an “unusual bulging by her uterus.”2 It turned out there were two puppies attached to the same placenta, a very unusual finding that tipped de Cramer off that the puppies might be identical twins. Typically, each puppy in a litter has its own placenta.
"When I realized that the puppies were of the same gender and that they had very similar markings, I also immediately suspected that they might be identical twins having originated from the splitting of an embryo," he told BBC News.3
When the pups were 2 weeks old, they underwent genetic testing that revealed they are, in fact, identical twins, the first case that’s been genetically confirmed in a dog.4 Although the twins had slight differences in markings on their paws, chests and tips of their tails, this is likely the result of differing genetic expression.
"Human identical twins also have the same genes, but because those genes are expressed differently in each person, they have different freckle and fingerprint patterns," de Cramer explained.5 This is the first case of identical twins formally identified in a dog, but that doesn’t mean it’s the first time it’s ever happened.
Under ordinary circumstances, most dogs give birth naturally, and determining whether each puppy had its own placenta could be difficult, especially since dogs tend to eat the placentas soon after birth. Many dogs also have similar markings, which means the only way to determine if they were identical or fraternal twins would be via genetic testing. As Dr. Jerry Klein, chief veterinary officer of the American Kennel Club wrote:6
“It will be interesting to see how these brothers grow and how similarly their appearance, behavior, and health develop. If they do go to different homes, it would also be interesting to see what part genetics and environment may play in the expression of their genetic make-up.”
Thinking About Adopting Two Pups From the Same Litter?
If a litter of pups is brought into your local shelter, you may be tempted to take home a pair of littermates instead of just one. While this can work out fine, it’s important to be aware of the potential for littermate syndrome, which can lead to some undesirable behaviors.
For instance, two siblings adopted together may bond intensely with each other, such that one becomes the leader and the other the follower. The second-in-command dog may then look to its sibling as its leader rather than looking to you for social cues and commands.
In some cases, littermates may also develop separation anxiety when they’re separated for even short time periods or may become aggressive toward one another. Again, this doesn’t happen with every pair of littermates raised in the same home, but it happens often enough that some animal behaviorists, dog trainers and rescue professionals discourage dog guardians from acquiring puppy littermates.
If you already have a pair of littermates, take steps to treat them as individual dogs to help discourage an unhealthy emotional dependence from developing. You should, for example, enroll each in separate training sessions and give them separate spaces (i.e., crates) at home. At least some of the time, take each dog for walks independent of the other, and even engage them in play sessions at different times so they can each come into their own.
Are You Interested in Your Dog’s Genetic Background?
Whether you have a pair of littermates you suspect may be identical twins or a rescue dog that you’re intrigued to know the breed of, genetic testing for dogs is now available. DNA tests are available for varying costs that can tell you your dog’s breed, ancestry and risk of certain genetic diseases.
No matter what such tests reveal, keep in mind that your dog’s personality, health and behavior are the result of both nature (i.e., genetics) and nurture (i.e., environment), which means you can influence your dog’s genetic destiny for the better by providing appropriate nutrition, exercise and mental stimulation.
On a larger scale, a citizen science research project currently underway to understand how specific genes control the behavior and health of our canine companions is Darwin's Dogs, led by Elinor K. Karlsson, Ph.D., a canine geneticist and assistant professor at the University of Massachusetts Medical School.
Karlsson and her team are asking dog guardians to record their own observations of their pet's behavior and personality, and collect doggy DNA at home using mouth swabs provided by Darwin's Dogs.
There's no cost to the dog owner, and the researchers share any information they find, including how genetics may relate to certain behaviors and personality traits in dogs. As in humans, it’s likely that the now-confirmed existence of identical twins in dogs will reveal that, despite their identical appearance and DNA, each dog is an individual, a product of both her genes and her environment.
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we bought a cotinus [Grace] a couple of months ago from a very good nursery [Waterperry]and it's still a collection of 'small sticks' only a few tiny leaves on two of the stems and nothing on the other. Should we dig it up and take it back?It's planted in a south facing sandy soil to which we added nutrients as instructed when planting.it has now had plenty of rain and plenty of sun, what do you think?
- 30 May, 2012
Answers
This shrub can be slow to start with, seem to take forever, but if you can, I'd return it and get one that's in full leaf now instead...
30 May, 2012
thank you for answering Bamboo. Yes, I agree, think we will take it back and try to buy another one.
30 May, 2012
Horrible lanky shrubs unless you pinch them.
30 May, 2012
Pay for postage or collect, You can have my Cotinus Royal purple. Prune it back the more agressive it gets!
Been in the ground 2 years, Its coming out. Let me Know you are welcome to it.
30 May, 2012
Oh, no, Japon - Cotinus Royal Purple is probably my favourite plant. It does need a lot of room, which is why I don't have one now, but a 10 foot high one is a thing of beauty, specially when it develops the red 'blanket stitch' effect as the leaves turn in autumn. A beautiful shrub.
31 May, 2012
Horrible plant...............Im suprissed at you Bamboo!!
31 May, 2012
Yes, mine has only just come into leaf. Ditto, Bamboo, one of the best shrubs I have bought.
1 Jun, 2012
I just wish they'd produce a smaller version...
1 Jun, 2012
thanks for answers everyone. Thank you Japon for offering your plant to us, but it is the Cotinus Grace I have been wanting[and found hard to track down.]All the Cotinus family look lovely I must say.
2 Jun, 2012
Previous question
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Q:
Localization at a prime ideal and quotient module
Problem.
Let $A$ be a commutative ring with 1, and let $M$ be a finitely generated $A$-module. If $p$ is a prime ideal of $A$, prove that $M/pM$ is non zero if and only if the localization $M_p$is non zero.
I think it's true..
Let $S$ be a $A-p$ , then if $M_p$ is zero, there exist some $s$ in $A-p$
such that given $x$ in M, $sx$=$0$. so the left looks trivial
but if we can find a module s.t $M_0$=$0$ (localization at zero ideal)
then we can talk $M$ is nonzero
Help me
A:
The statement that they are equivalent is false, but one direction is true. I provide a proof of this direction and a counterexample to the other direction below. Fix a commutative ring $A$ with unit, a finitely generated $A$-module $M$ and a prime ideal $\mathfrak{p}$ of $A$.
Claim. $M/\mathfrak{p}M=0 \implies M_\mathfrak{p}=0.$
Proof. If $M/\mathfrak{p}M=0$ then $M=\mathfrak{p}M.$ Localising this expression at $\mathfrak{p}$ we get $M_\mathfrak{p}=(\mathfrak{p}M)_\mathfrak{p}=\mathfrak{p}_\mathfrak{p}M_\mathfrak{p}.$ But now this is all happening as $A_\mathfrak{p}$-modules, which is a local ring with unique maximal ideal, and hence Jacobson radical, $\mathfrak{p}_\mathfrak{p}$. Thus, by Nakayama's Lemma, we have that $M_\mathfrak{p}=0$ as $M_\mathfrak{p}=\mathfrak{p}_\mathfrak{p}M$ and this finishes the proof. $\square$
Now for the counterexample to the converse, which states that if $M/\mathfrak{p}M\neq0$ then $M_\mathfrak{p}\neq 0$ (equivalently, $M_\mathfrak{p}=0 \implies M/\mathfrak{p}M=0$). Let $A := \mathbb{Z}, M := \mathbb{Z}/2\mathbb{Z}$ and $\mathfrak{p}=(0).$ Thus, we have $\mathfrak{p}M=(0)\cdot \mathbb{Z}/2\mathbb{Z}=0,$ so $M/\mathfrak{p}M=M/0=M\neq 0.$
Now we will show that $M_\mathfrak{p}=0$. We have a short exact sequence $$ 0\to 2\mathbb{Z}\to \mathbb{Z}\to M\to 0$$ of $\mathbb{Z}$-modules. Localisation is exact so, in particular, localising at $\mathfrak{p}=(0)$ is exact. Therefore, we get the following exact sequence: $$ 0\to (2\mathbb{Z})_{(0)}\to\mathbb{Z}_{(0)}\to M_\mathfrak{p}\to 0.$$
But localising at $\mathfrak{p}=0$ is the same as inverting all non-zero elements of $\mathbb{Z}$, so $\mathbb{Z}_{(0)}=\mathbb{Q}$ and $(2\mathbb{Z})_{(0)}=\mathbb{Q}$, where the localisation of the inclusion $2\mathbb{Z}\hookrightarrow \mathbb{Z}$ becomes an isomorphism. (Since $\mathbb{Z}_{(0)}=\mathbb{Q}$, it has just two submodules -- $0$ and itself -- so the image of this inclusion must be the whole of $\mathbb{Q}$ since $(2\mathbb{Z})_{(0)}\neq0$ and the localisation of the inclusion is still an inclusion.)
Hence, the short exact sequence obtained after the localisation tells us that $M_\mathfrak{p}=0$. (The idea is that localising at $(0)$ inverts $2$ in $M=\mathbb{Z}/2\mathbb{Z}$ which is very bad as 2 is a zero-divisor!)
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A prefix is a syllable or two that has a specific meaning and can be attached to the beginning of many root words, such as re- (review, revise, redo) or un- (unnecessary, unbelievable, undone).
Do you specifically teach prefixes to your English students? When I first started teaching, I would only share a prefix’s meaning if it came up in class. Then one day I decided to share a list of common prefixes with my intermediate‑level students, and I noticed it helped them pick up new vocabulary more easily. It gave my students confidence to see a new word and realize they already knew half the meaning.
The key is moderation. We don’t want to give our students a list of 100 prefixes—that’s overwhelming and frustrating. Instead, try presenting the condensed list of 23 common prefixes below, or try teaching only one a day. And practice makes perfect! The review activities suggested below will help the new meanings stick.
Prefix Chart
Check out our Grammar & Usage resource on Prefixes for a list of common prefixes and a practice activity.
Prefix Activities
Here are some other activities you can do with your students! Some of these activities use flashcards. You’ll find Prefix Flashcards in our Grammar & Usage Resources section, but most activities can be adapted by writing the prefix on the board instead of holding up a flashcard.
What Does It Mean?
Divide the class into two teams. Hold up a flashcard in front of the class. Whoever calls out the meaning first gets a point for their team.
How Many Words?
Divide the class into two teams. Hold up one prefix and have students shout out as many words beginning with that prefix as they can. Alternatively, challenge pairs to write lists of words that match the prefixes you hold up. The team or pair with the most words for a given prefix is the winner of that round.
Rooting Around
As a review of common prefixes + root words, have students sit in a circle, and place the prefix flashcards face up in the center. Call out a root word, and any student can jump up and grab a matching prefix (or have them take turns to avoid collisions). Some roots may have more than one answer (e.g., review, preview) for bonus points.
Quiz Time
Put students into small groups or pairs and give them a set of flashcards. Have them take turns quizzing each other. If a student says the correct meaning, he or she can keep the card. The student with the most cards at the end is the winner.
Mix & Match
Give pairs 20 slips of paper each and have them create a list of 10 words that use a prefix. They must write the prefix on one slip and the corresponding root word on the other. Then each pair can mix up their cards and pass them to another group. Challenge students to reassemble their classmates’ words by matching the prefixes and root words.
Board Race
On the board, write the meanings of the prefixes in two columns (use the same words in both columns but mix up the order so that it’s harder to cheat off the other team). Then divide students into two teams and have them line up at the back of the class. Team members (one at a time per team) must run up to the board and fill in one of the prefixes. The next person in the team can only go when the first person has run back and tagged them. The first team to complete their list correctly is the winner! | https://esllibrary.com/blog/prefixes |
At the head of the Baltoro Glacier, at the end of one of the world’s most famed mountain walks, lies the heaviest and most remote concentration of high peaks on the planet.
Gasherbrum II is part of the greater Gasherbrum group of 5 peaks, 2 of which soar over 8000m, and is the world’s 13th highest mountain. She is roundly held as one of the most straight-forward and accessible of the fourteen, and climbers on her normal route, if sufficiently resourced and prepared, enjoy reasonable summit rates inclement weather.
It was first climbed on July 8, 1956, by Fritz Moravec, Josef Larch and Hans Willen part of an Austrian expedition. Its total estimated height is 8035 meters.
Day 01 : Arrival Islamabad. overnight hotel. | https://hal.com.pk/index.php/gashabrum-ii/ |
Children ages 2 through 4 love to climb on the castle or ride on the horse available here. These active youngsters enjoy a fun playtime, a simple Bible story, activity and snack. This room is usually staffed by one paid employee who is there each week to provide the security and continuity this age group needs.
To have a safe, secure and loving place that demonstrates to toddlers and their families that God made them, God loves them, and God has a good plan for their life.
To make the Toddler room a wonderful place to teach and grow. | https://shccweb.org/ministries/toddlers |
Guns, Anarchy, and Leviathan
The University of Wisconsin political scientist Andrew Kydd offers an interesting critique of the spread of concealed carry and stand your ground statutes. Departing from a Weberian definition of the state as a monopoly on the legitimate use of force, Kydd suggests that “[t]he United States is now embarked on an unprecedented experiment, in that it is a strong state, fully capable of suppressing private violence, but it is increasingly choosing not to.” Kydd attributes loosening restrictions on the possession and use of guns to a libertarian fantasy that “the absence of the state will lead to a paradise for individuals.” But he follows Hobbes in predicting grimmer consequences: the replacement of violence under law by anarchic clashes between mercenaries, clans, and vigilantes.
I share Kydd’s concern about the decriminalization of gun violence, which looks to me like a risky solution to an exaggerated problem (violent crime has been falling for years). But his thinking about the relation between violence and the state is too Hobbesian to be convincing. For Hobbes, the “state of war” and the juridical state were mutually exclusive; violence was subject either to monopoly control or anarchic diffusion. For Kydd, similarly, the choice is between, say, the modern UK, in which firearms are very tightly regulated, and Afghanistan, where the strong do what they can, and the weak do what they must.
In the history of political thought, however, this is a false alternative. Following Hobbes, Kydd ignores the (small “r”) republican model of organized violence, in which the law is executed by an armed citizen body. The classical republic is not a state in the Weberian sense because it lacks a standing army or regular police force. On the other hand, it is not simply anarchic: citizens who possess the means of coercion cooperate on a relatively informal basis to enforce laws whose authority they all recognize.
The republic, in this sense, has always been more ideal than reality. But it is an ideal that has played an important role in the development of American political culture, particularly in connection with guns. For the republican tradition, particularly as transmitted by the Country party in British politics, a well-armed, self-organized citizenry poses less of a threat to safety and liberty than a strong state. That is the reasoning behind the 2nd Amendment.
There are serious and perhaps insurmountable obstacles to the revival of this tradition today. Apart from technological changes since the 18th century, the republican theory of violence presumes a relatively small, mostly agrarian society with a strong conception of public virtue. The contemporary United States, by contrast, is more like a multinational empire: a political form that has historically required much more coercive practices of government. Even so, the republican tradition reminds us that Leviathan is not the only possible source of order. We can acknowledge its necessity without regretting its evil. | https://www.theamericanconservative.com/guns-anarchy-and-leviathan/ |
I’ve been asked many times to write an article on posing and instead of trying to cram everything into one article, I thought I’d cover small chunks at a time. This article covers the importance of communication in posing before and during the shoot as well as some tips on how to effectively communicate about posing for models and photographers.
Let’s start by talking briefly about some of the things that might affect posing in a shoot. This isn’t an exhaustive list, but it does include some of the most common factors:
- Shoot process – certain styles of photography require the model to hold a pose for several seconds or more, others will need the model to move more quickly.
- Model’s posing style – each model tends to develop a posing style that we default to in terms of how we physically change poses (ex: gradually shifting or completely switching up poses), how often we move (ex: every shutter click or until the photographer prompts us to move), etc.
- Pose difficulty/physical challenges – there are some poses that are very difficult to hold either in general or for some models based on their body.
- Limits – a model’s limits (or a photographer’s limits) often come into play for nude or more erotic concepts.
- Understanding the concept/goal – everyone should be on the same page as far as what the goal/concept/mood for the image is.
If you are the photographer and you are hiring the model and/or if it is your concept, you’ll want to address these factors to make sure you get a model who is comfortable and able to pose in the way you need. This doesn’t mean you have to actually go through that list and address every single one individually, but perhaps the few that affect your shoot the most. For example:
- If your shoot process requires slower posing or for the model to hold poses, make sure you express that before you start shooting.
- If your concept involves nudity or erotic themes, I strongly suggest finding a model who is very comfortable posing in that style (versus one who seems borderline).
Don’t hesitate to ask the model if you have any concerns. They may be able to come up with a solution to a problem you see or be able to offer a possible compromise, particularly if they are somewhat experienced.
As a model it is always a good idea to find out what the concept is and what sort of posing you’ll be doing. If you’re being hired, the photographer should let you know, but if they don’t, make sure to ask. I find it’s usually easiest to ask what the concept or theme is for the shoot and go from there.
If you’re collaborating it is often part of the model’s contribution to bring the concept to life in which case you’ll often be providing the base poses (or possibly the poses entirely). In this case, you may want to practice or study a few poses beforehand.
Models, if you have any restrictions in posing physically within the concept be sure to mention those. You will also want to be mindful of your limits and how the concept might fall inside or outside of those. Don’t be afraid to speak up if you’re concerned.
Both models and photographers may find it helpful to keep things on track by keeping notes on what you discuss on your phone or in a notebook and bringing them with you to the shoot. You might also want to save any inspiration images to refer to while you are shooting as well.
Communication on posing during the shoot is definitely extremely important to creating the best images possible. Here are a few tips:
- Photographers, remember that the model cannot see the photo the way you do and your angle to the model can strongly affect how the pose looks. If you like what the model is doing, be sure to let them know.
- Photographers, if you don’t mind sharing a peek at the back of the camera, that can often be very helpful for models in visualizing changing they need to make or how the light is falling.
- Models, it’s okay to occasionally ask for feedback while you’re shooting. Sometimes the photographer is so focused on getting the shot that they may not realize you’re not sure if you’re doing okay or not.
- Try keeping a dialogue going next time you shoot. It doesn’t have to be constant chatter, but the occasional check-in can be quite helpful.
I firmly believe that maintaining open communication is a very important key to creating the best images possible and that is especially apparent in posing.
I hope you’ve found this article helpful and if you did, please share it and consider leaving a tip in my tip jar so I can keep this resource up and running. | http://advice.dekilah.com/communication-in-posing/ |
The release of the Australian Digital Inclusion Index in 2016 provides a clear insight into the the demographics of those most in need of digital inclusion interventions, and will enable the development of collaborative and targeted approaches to digital empowerment in regional, rural and remote areas. This stream will look specifically at the challenges and barriers to creating a fully digitally enabled Australia, and explore the best practice models that are proving successful.
Theme Chair: Apolline Kohen – Chair Broadband for the Bush Committee
Mini Menu: Featured Speaker, Keynotes and main speakers, Program, Delegates – accommodation info, Registration
Community Liaison Librarian, State Library of Western Australia.
[email protected]
John has worked for the State Library of WA for almost 10 years in a variety of roles with his most recent roles including Community Liaison Librarian: Better Beginnings, and eLearning Librarian. For the last few years, John has been involved in the State Library’s Storylines project, as well as the Ideas Box project, among others. In his spare time, John is an avid LEGO collector and blogger, as well as a husband and first time father to be.
John’s contribution: Launching Western Australia’s first Ideas Box
The State Library of Western Australia took the Ideas Box, a portable ultra-modern compact library on wheels, to a community in the West Kimberley. What happens when the kids in the community are let loose on iPads, android tablets, games and books? The short answer, the Principal could not get them to go to lunch. Join me as I give a brief overview of Libraries without Borders, the Ideas Box and the State Library of WA launch of the Ideas Box in Yungngora Community.
The Ideas Box is a portable, ultra-modern compact library on wheels conceived by Libraries Without Borders (Bibliotheques Sans Frontieres) from France to provide vulnerable and isolated populations access to books, technology, and information. The Ideas Box fits on two pallets, and the contents are customisable for each community. The State Library installed the Ideas Box in Yungngora Aboriginal Community near Fitzroy Crossing.
Discussion questions:
- What happens when packages like the Ideas Box are taken into communities?
- What kind of community engagement would you expect from a socially or culturally isolated community?
- What is the first step in trying to engage a remote community in WA?
- What are other options for reaching communities with limited or no internet connection?
- How do you increase Digital Literacy without the internet?
Hitnet – robust, co-designed technology in remote Australia.
Julie Gibson, Director & Co-founder
Nickeema Williams, Community Connector
Hitnet
Julie is a ‘technologist at heart’ having spent many years working in corporate IT before joining Hitnet in 2005. She now manages the evolution of Hitnet’s technology platform while ensuring Hitnet remains a thriving social business. She’s passionate about creatively using technology to scale and further Hitnet’s social impact.
Nickeema joined Hitnet in 2015 to take on the vital role of liaising with communities to bring the My Place modules to life.
As an artist, designer and photographer living and working in Woorabinda, her creative talents are being well used to address the issues facing Indigenous people. She’s been heavily involved in exhibiting at the Cairns Indigenous Art Fair for the past few years.
Hitnet co-designs and innovates with remote Indigenous communities to develop technology that is robust, useful and simple to use. The Hitnet WiFi hotspot, turning a touchscreen kiosk into a digital hub, is a recent example. Hitnet codesigned with young people in Cape York, a mobile landing page with easy links to useful everyday online activities. This has provided a safe, curated, free online experience for remote Indigenous people, using locally stored content wherever possible.
Digital readiness of remote Indigenous researchers, are we there yet?
Aurelie Girard and Valda Shannon
Whole of Community Engagement initiative, Charles Darwin University
Aurelie Girard has been working in the digital world for over 10 years and was exposed to the rapid-changing technology her entire life (GenY). Aurelie is the project coordinator of the Whole of Community Engagement initiative since 2015. She is currently undertaking a Master of Education international with CDU and her areas of research are language, literacy and Indigenous researchers and digital technology.
Valda Napurrula Shannon Wandaparri is a Walpiri/Warumungu woman who has been living and working in Jurnkurakurr since 1992. Valda’s most recent work has included writing culturally relevant programs for the Mental Health Association of Central Australian Suicide Prevention initiative which led her to draw on culture to connect with communities. Valda presented her work on the importance of addressing suicide through cultural practices at the United Nations Indigenous Forum in 2014. Her focus is ‘Walking in confidence in two worlds’ and embedding Indigenous culture within education, employment and processes to strengthen community cohesion through improved communication and information sharing.
In recent decades Indigenous research, has shifted from research ‘on’ to research ‘with’, and shifted from ‘research ‘for’ to ‘by’. It makes sense that active participation of Indigenous peoples and researchers creates clarity and understanding of the research and findings. A 2014 study (AITSIS and AIGI) said use of digital technologies in Indigenous research is an enabler and a barrier, particularly within action research projects, which is the common way that research is conducted. What are the consequences of this?
We will share some stories about what it is like being an Indigenous researcher. We will focus on the experiences of the Indigenous researchers in collecting, recording, analysing and sharing data, communicating and working within and across research teams to meet research output and project requirements. We will highlight digital literacy barriers and enablers faced by remote Indigenous researchers. We will share what software, hardware and techniques we use and see if the audience uses alternatives. We will focus on the impact of poor broadband and connectivity as one of the factors impacting on people’s participation. Can Indigenous people develop digital literacy when their online experiences are limited?
We will use a roundtable technique to ask our audience what they have experienced and what barriers they have found. We will use a collection activity to gather ideas about potential solutions. These will be fed into the key ideas of the forum. | http://broadbandforthebush.com.au/speakers-digital-inclusion-strand/ |
Researchers investigate how a stressed brain can make asthma worse
Researchers at the University of Wisconsin–Madison are investigating cross-talk between the brain and lungs of people with asthma in a four-year, $2.5 million study to understand how psychological stress can make asthma symptoms worse.
Through a clinical study called AsthMatic Inflammation and Neurocircuitry Activation, or MINA, the team hopes to decipher exactly how mind and body connect when people with asthma experience stress and find ways to alter brain-lung communication to help them manage their disease.
The effort is led by two groups with international reputations in the two areas united by the study: a team led by William Busse, a professor of asthma, pulmonary and critical care medicine at the UW–Madison School of Medicine and Public Health and a team headed by Richard Davidson, William James and Vilas Professor of Psychology and Psychiatry at the UW-Madison Center for Healthy Minds.
A project 20 years in the making
The new study represents a partnership between Busse and Davidson that extends back to 1995, when the pair participated in a scientific meeting focused on how stress may alter a person’s susceptibility to worsening asthma.
Combining their expertise, the researchers conducted work that hinted at connections between the nervous system, the immune system and asthma, a chronic lung disease that causes wheezing, shortness of breath, and acute attacks called exacerbations that can be deadly if not managed properly.
“Our efforts brought together two areas of research not commonly linked,” Busse says. So far, their collaboration has led to a series of studies joining these once disparate fields.
“The fact that psychosocial stress can provoke an exacerbation of asthma symptoms clearly indicates that the brain must be involved since it is the brain that transduces stressful events into biological signals that ultimately influence lung function,” Davidson says.
Their endeavors open entirely new ways of looking at asthma that could have profound affects for patients living with the disease.
“My greatest hope for this study is that our knowledge about the way that the brain and immune system interact in asthma is refined so that we can start tweaking how we treat the disease, and offer different and better treatment modalities,” says Melissa Rosenkranz, an associate scientist in Davidson’s laboratory who leads the brain scan experiments for the study.
Poking the brain and probing the lung
The MINA study, funded by the National Institutes of Health, is considerably larger and more comprehensive than prior investigations.
In the first part of the study, the research team will investigate lung-to-brain communication in research subjects with mild to moderate asthma.
Asthma and pulmonary clinicians will characterize the subjects’ disease by measuring their lung function and analyzing features of airway inflammation. They accomplish this by placing a small amount of a substance each subject is allergic to, such as ragweed or cat dander, into an isolated part of their airway to trigger allergic inflammation without activating an asthma attack, Rosenkranz explains.
The subjects will then undergo functional MRI scans to assess activity in areas of their brains, particularly those which might be responsive to stress.
About 48 hours later – while the inflammatory response is at its peak – each study participant will undergo another functional MRI during which they will be asked to perform tasks, like naming the color of asthma-related words presented on a screen, in order to activate specific brain pathways.
“You can think of it as a way to probe the reactivity of these brain regions, says Rosenkranz, who studies links between the nervous and immune system, as well as the biochemical mechanisms underlying resilience or vulnerability to disease.
These regions of the brain, or neurocircuits, can then be evaluated in relation to the development of allergic inflammation.
“What is signaling the brain when you have inflammation in the lungs,” Rosenkranz asks. “How does the brain respond, and what are the consequences?”
Scientists will also use standard psychological questionnaires to determine subjects’ chronic life stress levels and evaluate them for depression or anxiety, producing what Rosenkranz says is “a rich set of psychological information on these subjects.”
Researchers will also collect a treasure trove of cellular and molecular data on each study participant. Subjects will provide lung fluid and cell and blood samples to pulmonary scientists like Stephane Esnault, a senior scientist in the Busse laboratory, who will use them to conduct a battery of tests to quantify how much inflammation is occurring in lung cells and tissue.
The project will also involve a molecular analysis technique called RNA-seq, which will help researchers identify which genes are activated in each study subject. “RNA-seq will help us find new molecular pathways involved in this process that we don’t know about yet,” Esnault says.
Putting the pressure on
The second part of the MINA study will examine the process in reverse: Rather than study communication from lung-to-brain, researchers will explore communication from brain-to-lung.
To do this, study volunteers with mild-to-moderate asthma will undergo a socially stressful laboratory experiment, akin to making a public speech in front of an unfriendly crowd, Rosenkranz explains.
Using a technique already described in a 2016 study conducted by the team, researchers will then identify regions of the brain that activate metabolically during the experiment.
Next, research subjects will return to the clinic, where a pulmonology team will administer a whole-lung challenge, inducing inflammation. They will track lung function and gather samples over the following 24 hours, following up on research findings from 2016 to determine whether priming the lung with inflammation leads to a more severe response to allergens, says Rosenkranz.
She is confident the effort will yield valuable data and yield new and meaningful insight into the mind-lung connection in asthma.
Toward new therapies
For Busse, the results could help him and others improve treatments for asthma patients, he says. With better information about immune responses in the lung and how they affect the brain, “I might treat an asthma patient differently,” perhaps looking to the brain to manage their lung responses, Busse says. This could include mindfulness training.
“Certain forms of meditation can alter brain circuits that include those we have found to be associated with inflammation in the lung,” says Davidson. “We reasoned that meditation might be helpful in reducing symptoms of asthma through its impact on these neural circuits.”
For Busse, the MINA study represents the culmination of decades of work, and a new frontier. | https://news.wisc.edu/researchers-investigate-how-a-stressed-brain-can-make-asthma-worse/ |
Using natural resources to shape our environment requires the use of energy—invisibly inherent in materials as so-called grey energy. This includes the energy used for raw material extraction, production, transport and installation of elements. In the sense of resource-saving construction, this must be made visible – new ways of conservation and utilisation are necessary. Understanding how to deal with grey energy forms the basis of a holistic approach towards material, aesthetic and inclusive sustainability for the development of cities and regions.
Recognising, conserving and using this energy is the goal of the Institute for Grey Energy.
The institute is made up of three sections. In the Atelier, a collective of young planners develops strategies for radical conservation of the object. The Archive will be a place of knowledge generation: here we will explore the emergence of grey energy since the beginning of modernity and its transformation as a current challenge of the 21st century. The Living Lab, a former granary in Oßmannstedt (Thuringia), is a pivotal point, home and first project for the institute at the same time. A public centre for collaborative spatial development is being created here, where inclusive planning approaches for spaces beyond the metropolises are being devised.
Generate knowledge
We consider the in-depth exploration of further dimensions of grey energy beyond its energetic significance as an important basis for our actions. The bound energy as a resource is inevitably to be understood as part of our environment, so that numerous interactions arise between the built and the grown. Are cyclical regeneration and processes of appropriation only seeming contradictions in this context?
We understand grey energy as a culturally conditioned resource. Its use requires a critical examination of the conditions of origin and historical contexts. It is not only in this context that we question outdated images and ideas of urban and rural space.
Important findings are brought together with existing knowledge in the Institute’s archive, discussed with interested stakeholders and made available in the long term. Other topics such as repair culture, sustainable building, urban mining or existing concepts of stock transformation flow into the institute in this way and provide new impulses. The mostly urban strategies are not copied, however, but radically rethought for the regional embedding of the institute.
Adapt practices
The spatial focus of our work is the landscapes of deindustrialisation and economic transformation. In these landscapes of industrial culture, there are countless areas and buildings of remarkable size, most of which were previously used for industrial purposes, which often lie fallow and whose spaciousness we see as a special potential and starting point. Especially buildings that were used for industrial production have a particularly high level of unused grey energy due to their complex construction process and difficult transformability. We see this energy as a crucial resource in the challenge to reduce greenhouse gases and want to initiate a radical change in the way it has been used so far.
The focus is on strategies for the preservationeseconversion and re-use of this building stock. Up to now, the preservation and transformation of these structures has usually been associated with considerable interventions and high energy costs, so that a renewed conversion in the future seems impossible—or again swallows up huge amounts of energy and resources. Low-threshold appropriation concepts are intended to create an alternative to energy-intensive total conversion or demolition.
Grey energy—a common good?
Grey energy is considered non-renewable in most cases, which is why we at the Institute for Grey Energy are developing new resource-saving approaches for the circular reuse and saving of this energy. Adaptive use concepts can achieve a certain degree of renewability of this resource. This energy is considered a public good. Reuse and upgrading must not reproduce economic inequalities of land use, but can contribute to a distributive justice of public goods.
To this end, we leave the urban centres, test the approaches in the Living Lab and carry the findings through the Atelier to other places in Central Germany and, at best, to other European regions. The site of a granary in Oßmannstedt (Thuringia) serves as the pivotal point, home and first project of the institute. Due to the history of its construction and use, we consider it a challenging cultural and ecological heritage and thus a crystallisation point for our topics.
Persons involved
The institute is an association of various people from the disciplines of design, architecture, urbanism and related fields such as monument conservation, art or the crafts. | https://www.institut-graue-energie.de/en/what-is-grey-energy/ |
September 15, 2021: The African Airlines Association (AFRAA), Lufthansa Consulting and Kenya Airways staged a high level workshop on September 14, 2021 on African airlines consolidation to discuss the reasons for few partnerships and limited airline consolidation, the challenges and benefits of consolidation and measures for action by industry stakeholders to address the situation.
Abderahmane Berthe, AFRAA secretary general, in his remarks stated, “The aviation sector is reeling from the impacts of Covid-19 pandemic. We need to devise new approaches of doing business in the face of increasing concerns on the sustainability of African Airlines. A crucial element in the success of the African airlines is consolidation and collaboration. The engagement of States, airlines and all the relevant stakeholders is necessary to effectively achieve the required outcomes on airline consolidation in Africa.”
Speaking during the workshop, Kenya Airways CEO Allan Kilavuka, said, ”It is crucial to retrace and learn from the footprints of consolidation from different parts of the world as we reset Africa’s aviation towards our collective dream for flying to a better future. Consolidation and collaboration are essential ingredients for resilience and sustainable business operations of airlines. The ripple effect of strengthened collaboration amongst airlines will be an increase in the industry’s contribution to the sustainable development of Africa and therefore we must elevate the tenor of discourse and make the airline industry matter in and for Africa.”
Catrin Drawer, head of market Africa, Lufthansa Consulting stated, “We require to meet the challenges of the “New Normal”, a reset in our thinking and approach. We require new business models, meaningful innovations in operations, adaptive management open to change, a growing true synergistic relationship between airlines and other relevant stakeholders. New challenges need new solutions now and in future to bring both resilience, and sustained success. Thus, synergy and meaningful partnering, whether through existing contracts and alliances or new agreements, will be essential. We cannot bring back yesterday but we may together shape the future.”
Lufthansa consulting experts provided an in-depth analysis and background of consolidation of airlines from a global to an African perspective. The impacts of consolidation for African airlines, passengers, cargo, air transport growth and connectivity were discussed. Case studies were presented at C-level by Kenya Airways, Air Afrique and Ethiopian Airlines to enrich the discussions with first-hand experiences on the challenges, benefits of consolidation as well as the lessons learnt.
Industry recommendations
- Consideration of various models of consolidation including equity partnerships between two airlines or across a group of investments, cooperation between two or more well-matched airlines, or the formation of a new common airline. The concept of “Air Afrique” remains a valid consideration for Africa.
- Implementation of appropriate corporate governance structure is necessary for consolidation. Political interference in the airline management is to be avoided.
- Call to Development Finance Institutions (DFIs) to finance the feasibility study of consolidation models.
- Call for uniform implementation of harmonized regulations and the establishment of an enabling working relationship between regulators, airlines and Regional Economic Communities (RECs).
- Enhancement of cooperation among African airlines (alliance of airlines, pooling resources, code sharing and interlining).
- Call for support and commitment from Governments for airline consolidation in Africa.
- Urge airlines to carry out careful evaluation of potential consolidation/partnerships based on factual data.
- Exploration of cargo opportunities for air cargo consolidation.
- Call for government and private sector collaboration to achieve concrete steps in airline consolidation.
- “Walk the Talk” - translate ongoing discussions into action in the interest of delivering accelerated benefits to the aviation ecosystem
The important workshop brought together over 200 participants comprising airline CEOs, C-level representatives from airports, CAAs and other African air transport decision makers as well as the media. | https://www.logupdateafrica.com/afraa-lufthansa-consulting-kenya-airways-workshop-discuss-partnerships-airline-consolidation-aviation |
Wachs, Amy-JD, specializes in Jewish and Eastern European genealogy. She taught law in Latvia and Moldova, and visited state archives in Lithuania, Poland, Ukraine, and Moldova.
10:15 AM - 11:15 AM
T03-Guidelines for Finding Polish Records
This presentation will provide information about resources available in state archives in Poland and neighboring countries and provide tips for effective research there.
2:45 PM - 3:45 PM
T18-History and Geography: Tools for Eastern European Research
This presentation will offer guidance for using a region’s historical events and geography to help fill in the gaps and move past brick walls. | https://www.ogsconference.org/speaker/amy-wachs/ |
Loss of the RNA-binding protein fragile X mental retardation protein (FMRP) represents the most common form of inherited intellectual disability. Studies with heterologous expression systems indicate that FMRP interacts directly with Slack Na(+)-activated K(+) channels (K(Na)), producing an enhancement of channel activity. We have now used Aplysia bag cell (BC) neurons, which regulate reproductive behaviors, to examine the effects of Slack and FMRP on excitability. FMRP and Slack immunoreactivity were colocalized at the periphery of isolated BC neurons, and the two proteins could be reciprocally coimmunoprecipitated. Intracellular injection of FMRP lacking its mRNA binding domain rapidly induced a biphasic outward current, with an early transient tetrodotoxin-sensitive component followed by a slowly activating sustained component. The properties of this current matched that of the native Slack potassium current, which was identified using an siRNA approach. Addition of FMRP to inside-out patches containing native Aplysia Slack channels increased channel opening and, in current-clamp recordings, produced narrowing of action potentials. Suppression of Slack expression did not alter the ability of BC neurons to undergo a characteristic prolonged discharge in response to synaptic stimulation, but prevented recovery from a prolonged inhibitory period that normally follows the discharge. Recovery from the inhibited period was also inhibited by the protein synthesis inhibitor anisomycin. Our studies indicate that, in BC neurons, Slack channels are required for prolonged changes in neuronal excitability that require new protein synthesis, and raise the possibility that channel-FMRP interactions may link changes in neuronal firing to changes in protein translation.
Pubmed ID: 23115170 RIS Download
Mesh terms: Animals | Anisomycin | Aplysia | CHO Cells | Cloning, Molecular | Cricetinae | Cricetulus | Electrophysiological Phenomena | Fragile X Mental Retardation Protein | Immunohistochemistry | Immunoprecipitation | Neurons | Patch-Clamp Techniques | Potassium Channels | Protein Synthesis Inhibitors | RNA Interference | RNA, Small Interfering | Sodium | Synapses
Publication data is provided by the National Library of Medicine ® and PubMed ®. Data is retrieved from PubMed ® on a weekly schedule. For terms and conditions see the National Library of Medicine Terms and Conditions. | https://scicrunch.org/23115170/resource/nif-0000-07730 |
The Academy of Nutrition and Dietetics, together with the Department of Agriculture, have declared March “National Nutrition March. Throughout the month, physicians are encouraged to highlight the importance of making healthy food decisions and promote development of sound eating and exercise behaviors as nutritional awareness is paramount to improving health and wellness among pediatric patients.
Developing stories highlight the effectiveness of worldwide efforts to improve children’s access to water and nationally rich foods, decrease student access to sugary drinks and evaluate the eating habits of children, in order to better apply effective policies in schools. Infectious Diseases in Children highlights five informative and noteworthy recent stories in child nutrition news.
“Throughout the month, USDA is highlighting the results of our efforts to improve access to safe, healthy food for all Americans and supporting the health of our next generation,” USDA officials wrote in a press release. “For example, since the updated school nutrition standards were implemented in school year 2013-14, school breakfasts are healthier than ever before, including a serving of fruit, whole-grain-rich grains, and low fat or fat free milk.”
Policies effectively curb availability of sugary drinks in Boston schools
Recent research in Preventing Chronic Disease reported that districtwide mandatory policies instituted in Boston to regulate the availability of sugar-sweetened beverages effectively reduced student exposure to these beverages.
“Our study is a unique evaluation of a district-level competitive beverage policy 9 years after implementation. We provided evidence for sustainability and effectiveness in ensuring access to healthy competitive beverages,” Rebecca S. Mozaffarian, MS, MPH, of the department of social and behavioral sciences at the Harvard T.H. Chan School of Public Health, and colleagues wrote. Read more.
School water coolers associated with reduced BMI among students
The installation of water coolers was linked to reduced weight and BMI of elementary and middle school students, according to recent research in JAMA Pediatrics.
“The goal of this study was to estimate the impact of a relatively low-cost, school-based water availability intervention, water jets, on standardized BMI, overweight, and obesity in elementary school and middle school students,” Amy Ellen Schwartz, PhD, of the Maxwell School of Citizenship and Public Affairs at Syracuse University, and colleagues wrote. Read more.
WHO: Sugar tax, reduced exposure to unhealthy foods may cut childhood obesity
The Commission on Ending Childhood Obesity recently recommended numerous global policy changes, such as sugar taxes and limits on marketing unhealthy food to children, in response to the increasing levels of worldwide childhood obesity, according to a report presented at the WHO Executive Board Meeting.
“The obesity epidemic has the potential to negate many of the health benefits that have contributed to the increased longevity observed in the world,” Sir Peter David Gluckman, MBChB, MMedSc, DSc, the commission’s co-chairman, and colleagues wrote. Read more.
Children who choose healthy foods equally likely to eat junk food
The healthy eating habits of preschool-aged children living in a low-income area were independent of unhealthy food habits, according to recent research in the Maternal and Child Health Journal.
“The inverse relationship we hypothesized between children’s frequency of intake of healthy foods and unhealthy foods was not supported by the data from our study,” Sarah E. Anderson, PhD, of the division of epidemiology at The Ohio State University College of Public Health, and colleagues wrote. Read more.
Legislation successfully improves nutritional value of school meals
The nutritional value of student meal choices was improved after the implementation of the 2010 Healthy Hunger-Free Kids Act, according to recent research in JAMA Pediatrics.
“We found that the implementation of the new meal standards was associated with the improved nutritional quality of meals selected by students,” Donna B. Johnson, PhD, professor of health services at the center for public health nutrition at the University of Washington, and colleagues wrote. Read more. | https://www.healio.com/news/pediatrics/20160318/top-5-pediatric-nutrition-stories-for-national-nutrition-month |
The burnout of motherhood certainly is real. If You didn't see that twist ending, stop reading. Otherwise, Victoria Pedretti answers all our burning questions about saying farewell to Love.
Warning: Do not read further if you haven't finished season three. Buuuuut, as Joe Goldberg-minus-Quinn (Penn Badgley) stalks his soulmate in Paris, we're left to wonder what could have been if Love (Victoria Pedretti) conquered all. The grieving bakery owner and new mom just wanted a Fresh Tart in Madre Linda, but her impulse control issues—plus, you know, those handful of attempted murders—made it inevitable that Joe would continue on without the Love of his life.
You's Victoria Pedrettiexclusively bid farewell to Love in an emotional interview with E! News on Oct. 22. "I've been talking about obsession, about how she kind of obsesses over other people and desires being obsessed over, and [she] kind of deals in other people and doesn't really deal with herself," Pedretti shared of her character. "She engulfs herself in others and engulfs others, like her child."
To Pedretti, Love's fiery passion embodies how often we fail to notice, or deal with, burn-out. Of course, it took watching Love literally burn alive in her own kitchen to get the message across.
"I really hope that that can help us reflect on the importance of taking care of ourselves and confronting ourselves, and dealing with ourselves," Pedretti continued. "[We need to be] knowing ourselves and loving ourselves and exploring what it might mean to be authentic to yourself in order to contribute more to the world and have better relationships."
Netflix
She added, "And not date a serial killer! Because how do you date a serial killer and not expect to get murdered?"
Ultimately, Love's denial turned out to be her downfall, with Pedretti joking, "And marry him and have a child and you think, 'It won't be me.' You're kidding yourself!"
Showrunner Sera Gamblerevealed that Love and Joe's relationship was an exaggerated reflection of what many couples experience.
Netflix
"The formula that we talk about in the writers room with the directors is that the plot, the story, can be completely bats––t crazy," Gamble explained. "Joe's life is not progressing along a normal avenue and his behavior is not always normal. But we keep the emotion and the relationships as grounded as we can."
The couples counseling scenes were particularly poignant. "We want you to really feel the feelings, so when we're writing a scene where two characters are talking about how they feel, the job of whichever writer is writing that scene is being as honest as they can," Gamble admitted.
"I always know I've hit a vein when I'm almost a little embarrassed because I feel like maybe people will read it and feel like I've revealed something about myself. That's the standard that we're holding the emotional character life of the show to."
With Love officially dead and presumably buried (hey, we can still hope for a ghost appearance in season four, à la her brother Forty), Joe will start anew, abroad. It's not just Fresh Tarts, but rather a fresh French pastry to look forward to.
"I would love to do a season where Joe stepped outside the United States and was an American fish out of water," Gamble hinted. | |
Steven Ortiz (associate professor of archaeology and biblical backgrounds and director of the Tandy Institute for Archaeology at Southwestern Baptist Theological Seminary) has an excellent chapter in the book, Buried Hope or Risen Savior? The Search for the Jesus Tomb, ed. Charles L. Quarles (B&H Academic, 2008), entitled, “The Use and Abuse of Archaeological Interpretation.” It’s worth keeping on hand for the next time you hear of some blockbuster archaeological discovery being touted in the media that overturns biblical truth or the majority opinion.
“The scripts for all of these amateur portrayals,” he writes, “are similar and follow the same basic 10 points”:
- The prevailing hypothesis affirmed by the consensus of the scholarly community is wrong.
- The “discoverer” is not a trained archaeologist but is self-taught, and he knows the “true story” that all others have overlooked.
- An expedition is planned for one season, and (lo and behold) at the first attempt they find exactly what they are looking for.
- This is all documented while a camera crew happens to be filming the discovery.
- The process is “detective work” that has been missed by the academic community, and they (amateur archaeologists) are the ones who are able to unravel the mystery or solve the problem that has perplexed the experts.
- No new date is presented, only a reworking of previously published data. A corollary is that not all the data is consulted.
- Upon the presentation of the discovery, the scholarly community scoffs at the find, and it is claimed that there is a secret monopoly by those in power to suppress the information.
- The amateurs sensationalize the “discovery” by claiming that it is so revolutionary that it will change our way or thinking and our lifestyle.
- The old “discovery” is presented to the media as a “brand-new” discovery.
- Usually a book or movie comes out within a week of the “new” discovery. (pp. 29-30)
Professor Ortiz was writing several years ago when James Tabor and Simcha Jacobovici were making the rounds with their discovery of The Jesus Family Tomb. Fast-forward to 2012, and they’re back with a new discovery and a new book: The Jesus Discovery: The New Archaeological Find that Reveals the Birth of Christianity.
James Hoffmeier, a noted Egyptologist and archaeologist (and the co-editor of Do Historical Matters Matter to Faith?), recently explained how serious (as opposed to sensationalist) archaeologists do their work:
As a field archaeologist I spent the past decade surveying and excavating in north Sinai (Egypt). I made some pretty significant discoveries, but never did I speak to a western reporter, nor did any attention-grabbing headline appear like “Egyptian Fort from Exodus Period Discovered!” It is normal practice for archaeologists who make significant discoveries to first present their finds at professional conferences where other experts can evaluate their discovery and their interpretation of it. Then a preliminary report is written which is submitted to a peer review journal in the relevant field where it is fully vetted by two or three authorities (I have been a referee for several academic journals).
At this stage, provisional interpretations are cautiously offered. Finally, after more time is given to complete the excavations, study and evaluate the finds by specialists, the final scientific report is published with all the data reproduced for all to see. This careful and deliberative process is how serious archaeological discoveries are handled before going public and popularizing the results. This time-honored process is even more critical when matters related to the Bible are involved because much is at stake.
When an archaeologist makes an end run around their professional colleagues and goes directly to the press, we naturally have to ask “why”? Tabor and Jacobovici evidently do not want to be scrutinized and their views challenged before publishing their popular book. By going to the press and the public with a splashy news conference, sales of their book will skyrocket. Academic books don’t sell; popular ones that are slickly promoted with sensational titles do. This approach is not the one taken, however, by serious, objective scholars. | https://www.thegospelcoalition.org/blogs/justin-taylor/the-jesus-discovery-and-sensational-archaeology/ |
Bachelor of Business Administration (BBA)
Our Westcliff Business Degree, Bachelor of Business Administration (BBA) program, whether taught via the online or hybrid platform, leads undergraduate students onto the next step in their business careers. At Westcliff University, BBA students become knowledgeable about a wide variety of disciplines, including finance, accounting, marketing, operations, sales, and information technology.
Our professors, all of whom are senior managers in their respective fields, partner with BBA students to develop their verbal and written communication skills. Students lead group discussions and make presentations in class, and are encouraged to share their distinct perspectives.
Students also learn how to present their ideas professionally so that hiring managers really see what they have to offer. Learning how to think critically, analyze data, and problem solve are integral components to an Westcliff Business Degree (Bachelor of Business BBA) degree.
BBA Program Description
The Bachelor of Business Administration (BBA) degree prepares graduates to seek employment in entry-level positions in various industries of budgeting, accounting, payroll, personnel, computer systems, risk management, facilities planning and management.
The performance outcomes which are required for the completion of the program include: class participation, response to discussion questions, writing research papers, presentations, case study analyses, quizzes, mid-term and final examinations (Comprehensive Learning Assessments). | https://www.westcliff.edu/academics/college-of-business/bachelor-of-business-administration-bba/ |
The Obama administration is signaling support to innovate the venerable Endangered Species Act (ESA) that would, among other things, more engage the states -- a move that comes as Congress considers overhauling the 40-year-old law to take some authority away from federal agencies.
Late Monday the Department of Interior's U.S. Fish and Wildlife Service (FWS) and National Marine Fisheries Service (NMFS) announced a suite of actions to improve the "effectiveness" of the ESA and demonstrate its flexibility. The actions include collaborating more with the states, as well as promoting the use of best available science and transparency. The proposal also would encourage more voluntary conservation efforts.
"The proposed policies would result in a more nimble, transparent and ultimately more effective Endangered Species Act," said FWS Director Dan Ashe. "By improving and streamlining our processes, we are ensuring the limited resources of state and federal agencies are best spent actually protecting and restoring imperiled species."
The effort would focus on recovering species and strive to make administrative and regulatory improvements. No legislative changes to the ESA are sought because the agencies "believe that implementation can be significantly improved through rulemaking and policy formulation."
Interior Secretary Sally Jewell said the policies "will make an effective and robust law even more successful, and will also reinforce the importance of states, landowners and sound science in that effort."
The announcement to innovate the ESA preceded an oversight hearing Tuesday by the House Committee on Natural Resources regarding whether states are doing an adequate job of managing the dwindling greater sage grouse population (see related story). A Senate committee earlier this month heard testimony regarding several bills to amend the ESA, including one that would require federal regulators to recognize for at least six years state conservation plans for sage grouse (see Daily GPI, May 6).
The greater sage grouse, whose habitat is spread across 11 western states, became a candidate for protection under the ESA in 2010, but following a court settlement in 2011, Interior agreed to delay a decision on listing until the end of September (see Daily GPI, Dec. 30, 2011).
Last Friday, Colorado Gov. John Hickenlooper issued an executive order for state agencies to step up their efforts to protect the greater sage grouse in hopes of preventing an ESA listing.
Many of the regulations implementing ESA, which was signed into law by President Nixon in 1973, were promulgated in the 1980s and "do not reflect advances in conservation biology and genetics, as well as recent court decisions interpreting the act's provisions," Interior said. The Obama administration first recommended updates in 2011, and the latest steps would, among other things, ensure states are "partners in the process by which imperiled species are considered for listing under the act."
The proposed changes would require petitioners for listings to solicit information from relevant state wildlife agencies before submitting petitions. Any information provided by the states would have to be included in the petitions.
"State fish and wildlife agencies, by virtue of their responsibilities and expertise, are essential partners in efforts to conserve threatened and endangered species," Interior said.
The FWS and NMFS would implement the revised petition regulations to update policy regarding the role of state agencies to reflect advancements in collaborating with the federal agencies.
"For decades, the Endangered Species Act has helped protect threatened species and their habitats," said Secretary of Commerce Penny Pritzker. "The changes announced...amount to an improved way of doing business, one that advances the likelihood of conservation gains across the nation while reducing burdens and promoting certainty."
According to Interior, the changes would provide more clarity to the public and to the states "on what information would best inform the evaluation of a species' status and result in better coordination with state wildlife agencies, which often have unique information and insights on imperiled species."
Additional proposals to be unveiled over the coming year also are designed to improve science and increase transparency by strengthening procedures to ensure that all information is publicly disclosed. The proposals also are to lead to more rigorous procedures to ensure "consistent, transparent, and objective peer-review of proposed decisions.
Voluntary conservation programs, such as safe harbor agreements and candidate conservation agreements also are planned. The FWS and NMFS plan to update guidance on the use of these tools to establish consistent standards and adopt a policy to promote "expanded use of conservation banking and other advanced mitigation tools."
In addition, the agencies plan to focus some resources to dovetail with other work ongoing regarding threatened species. This would include the National Oceanic and Atmospheric Administration's initiative to reduce, stabilize and reverse by 2020 the rate of decline of vulnerable marine species. The agencies also plan to update the Habitat Conservation Planning Handbook to make permitting plans more efficient.
"Consistent with the intent of the ESA that listing decisions be based on the best available science, we appreciate...due recognition of, and requirement to, incorporate the data and information of state fish and wildlife agencies for the formulation of listing petitions," said Association of Fish and Wildlife Agencies President Larry Voyles.
Public comments are to be accepted for 60 days once the proposed rule is published in the Federal Register, expected this week. | https://www.naturalgasintel.com/articles/102376-interior-proposing-flexible-endangered-species-act-more-state-input |
Stanislaus 2030 is committed to creating in-person and virtual opportunities for authentic community discussion and feedback to shape a locally-owned and truly collaborative vision for our future economy.
Through our words and actions, we seek to build an equitable public process that brings a diversity of viewpoints and participation across all of Stanislaus County. We seek engagement from individuals of all ages, in-language and in a culturally appropriate manner to the maximum extent possible.
Opportunities for public engagement include a combination of focus groups, online polls or surveys, community events and forums. Follow our Facebook and Instagram accounts for community conversation opportunities.
To do all this, we are working with local community engagement firm Debrief. For the latest on our community engagement efforts, click the link below.
Focus Groups
Focus Groups allow for facilitated in-depth discussion amongst a small group of people.
Online Polls or Surveys
Polls or Surveys allow us to ask many Stanislaus County Residents a small number of questions either in-person or online.
Community Forums and Meetings
Community Forums and meetings will take place in cities throughout the County. | https://www.stanislaus2030.com/engage |
A pianist ( US: /piːˈænɪst/ pee-AN-ist, also /ˈpiːənɪst/ PEE-ə-nist) is an individual musician who plays the piano. Since most forms of Western music can make use of the piano, pianists have a wide repertoire and a wide variety of styles to choose from, among them traditional classical music, jazz, blues, and all sorts of popular music, including rock and roll. Most pianists can, to an extent, easily play other keyboard-related instruments such as the synthesizer, harpsichord, celesta, and the organ.
Modern classical pianists dedicate their careers to performing, recording, teaching, researching, and learning new works to expand their repertoire. They generally do not write or transcribe music as pianists did in the 19th century. Some classical pianists might specialize in accompaniment and chamber music, while others (though comparatively few) will perform as full-time soloists.
Mozart could be considered the first "concert pianist" as he performed widely on the piano. Composers Beethoven and Clementi from the classical era were also famed for their playing, as were, from the romantic era, Liszt, Brahms, Chopin, Mendelssohn, Rachmaninoff, and Schumann. It was during the Classical period that the piano begins to establish its place in the hearts and homes of everyday people. From that era, leading performers less known as composers were Clara Schumann and Hans von Bülow. However, as we do not have modern audio recordings of most of these pianists, we rely mainly on written commentary to give us an account of their technique and style.
Jazz pianists almost always perform with other musicians. Their playing is more free than that of classical pianists and they create an air of spontaneity in their performances. They generally do not write down their compositions; improvisation is a significant part of their work. Well known jazz pianists include Art Tatum, Duke Ellington, Thelonious Monk, Oscar Peterson and Bud Powell.
Popular pianists might work as live performers (concert, theatre, etc.), session musicians, arrangers most likely feel at home with synthesizers and other electronic keyboard instruments. Notable popular pianists include Victor Borge who performed as a comedian; Richard Clayderman, who is known for his covers of popular tunes; and singer and entertainer Liberace, who at the height of his fame, was one of the highest-paid entertainers in the world.
A single listing of pianists in all genres would be impractical, given the multitude of musicians noted for their performances on the instrument. Below are links to lists of well-known or influential pianists divided by genres:
Many important composers were also virtuoso pianists. The following is an incomplete list of such musicians.
Some people, having received a solid piano training in their youth, decide not to continue their musical careers but choose nonmusical ones. As a result, there are prominent communities of amateur pianists all over the world that play at quite a high level and give concerts not to earn money but just for the love of music. The International Piano Competition for Outstanding Amateurs, held annually in Paris, attracts about one thousand listeners each year and is broadcast on French radio.
It is notable that Jon Nakamatsu, the Gold Medal winner of the Van Cliburn International Piano Competition for professional pianists in Fort Worth, Texas (1997) was at the moment of his victory technically an amateur: he never attended a music conservatory or majored in music, and worked as a high school German teacher at the time; it was only after the competition that he started pursuing a career as a classical pianist.
The German pianist Davide Martello is known for traveling around conflict zones to play his moving piano. Martello has previously been recognised by the European parliament for his “outstanding contribution to European cooperation and the promotion of common values”.
Carl Czerny was an Austrian composer, teacher, and pianist of Czech origin whose music spanned the late Classical and early Romantic eras. His vast musical production amounted to over a thousand works and his books of studies for the piano are still widely used in piano teaching. He was one of Ludwig van Beethoven's best-known pupils.
Claudio Arrau León was a Chilean pianist known for his interpretations of a vast repertoire spanning the baroque to 20th-century composers, especially Bach, Beethoven, Schubert, Chopin, Schumann, Liszt and Brahms. He is widely considered one of the greatest pianists of the twentieth century.
A piano trio is a group of piano and two other instruments, usually a violin and a cello, or a piece of music written for such a group. It is one of the most common forms found in classical chamber music. The term can also refer to a group of musicians who regularly play this repertoire together; for a number of well-known piano trios, see below.
John Field, was an Irish pianist, composer, and teacher. Field is best known as the inventor of the nocturne, but there is evidence to suggest that this is a posthumous accolade. He is mentioned in passing in War and Peace when Countess Rostova calls on the Rostov household musician to play her favourite nocturne.
Johann Nepomuk Hummel was an Austrian composer and virtuoso pianist. His music reflects the transition from the Classical to the Romantic musical era.
A piano concerto is a type of concerto, a solo composition in the classical music genre which is composed for a piano player, which is typically accompanied by an orchestra or other large ensemble. Piano concertos are typically virtuoso showpieces which require an advanced level of technique on the instrument, including melodic lines interspersed with rapid scales, arpeggios, chords, complex contrapuntal parts and other challenging material. When piano concertos are performed by a professional concert pianist, a large grand piano is almost always used, as the grand piano has a fuller tone and more projection than an upright piano. Piano concertos are typically written out in music notation, including sheet music for the pianist, orchestra parts for the orchestra members, and a full score for the conductor, who leads the orchestra in the accompaniment of the soloist.
Benno Moiseiwitsch CBE was a Russian-born British pianist.
Shura Cherkassky was a Ukrainian-American concert pianist known for his performances of the romantic repertoire. His playing was characterized by a virtuoso technique and singing piano tone. For much of his later life, Cherkassky resided in London.
Ruth Laredo was an American classical pianist.
Sergio Fiorentino was a 20th-century Italian classical pianist whose sporadic performing career spanned five decades. There is quite a bit of footage his playing that survives, in addition to audio recordings. Recently, a complete concert recorded on video in 1994 has surfaced.
Viktoria Valentinovna Postnikova is a Russian pianist.
Peter Roy Katin was a British classical pianist and teacher.
Albert Ferber was a Swiss pianist who had an international performing career that spanned four decades and took him across the world.
Carol Rosenberger is a classical pianist. In 1976, Rosenberger was chosen to represent America's women concert artists by the President's National Commission on the Observance of International Women's Year. She has given performance workshops for young musicians on campuses nationwide. Rosenberger recorded over 30 albums on the Delos Productions, Inc. recording label. Rosenberger's memoir, To Play Again: A Memoir of Musical Survival was published in 2018 by She Writes Press.
Valentin Gheorghiu is a Romanian classical pianist and composer.
Marina Goglidze-Mdivani is a Soviet and Canadian virtuoso pianist of Georgian descent.
Barbara Nissman is an American pianist. She is especially known for her interpretations and performances of the works of Alberto Ginastera and Sergei Prokofiev which feature prominently in her repertoire. She is also a writer and a producer of a new DVD series, and a guest clinician presenting concerts, master classes and lectures world-wide.
Claude Kahn is a French classical pianist. Internationally renowned concert performer, known for his interpretations of Romantic music and more precisely the music of Chopin, but also of French music as soloist or accompanied by great orchestras in the world.
The Abegg Trio was a German piano trio. Since its foundation in 1976, it played in the original line-up. | https://wikimili.com/en/Pianist |
CDA shares information through material presented to participants which is basic, useful, and measurable. Material contained in each course manual is used to facilitate the learning of information presented. CDA materials are copyrighted and unique to this organization. They are clearly written and provide ballet vocabulary used, when and in what form steps are taught including music. Later, manuals become a reference to help plan daily lessons and know what to work on next.
The following is a brief incomplete overview of the Six Class Program to give a general idea of the progression of work from Elementary to Advanced. It is not meant to be comprehensive or inclusive. Courses must be taken in sequence.
The First Year of the Six Year Program for the Study of Classical Ballet
including the "First Three Days" of the Elementary Work
In 1969, Vera Kostrovitskaya was personally asked to work out a syllabus for a six-year course of study (so-called “experimental class”) starting at twelve, rather than at ten years of age. This syllabus is worked out so that the entire eight-year course is accelerated and passed in six years (Kostrovitskaya, 1995. p.17). In the First Year, the first three days differ from the end of September’s work. Basic principles are first introduced followed by the first exercises for a person to adapt to classical dance training at the Barre and in the Center Exercise. The basic stance, positions of the feet, arms and head are taught. Gradually and methodically the elementary habits of movement coordination are introduced and begin to be established in October, November, and December’s work (including Allegro and Pointe Work). By the second half of the year, the exercises already established in the program increase in quantity and are taught at a faster tempo. By the end of the year, to develop strong feet and legs, movements alternate first on the whole foot then on demi-pointe and elementary combinations of movements are taught.
The Second Year of the Six Year Program for the Study of Classical Ballet
Completion of the Elementary Work
In the Second Year, tempos are somewhat faster. The length of the Barre Exercise should now take approximately 35 minutes. The exercises on demi-pointe (begun in the Barre Exercise in the First Class) continue with more repetition. Battement tendus jeté, ronds de jambe par terre, battements frappés and petits battements are practiced in both 1/4 and in 1/8 (alternating 1/4 and 1/8 notes) in the second half of the year. The exercises on demi- pointe (begun in the First Class at the Barre) begin to be studied in the Center Exercise, until they are practiced entirely on demi-pointe, by the end of the first part of the year. The easiest movements, en tournant, begin to be taught in the Center Exercise. Adagios are constructed using the poses that have already been covered. New Allegro and Pointe vocabulary is introduced. Tours and batterie begin to be studied. Tour en l’air, for the boy’s class, is studied in the second half of the year.
The Third Year of the Six Year Program for the Study of Classical Ballet
First Half of the Intermediate Working
In the Third Year emphasis is placed on stability (aplomb) through control of the weight of the body in coordination with the head, arms and legs in various turns and in exercises on demi-pointe and on pointe. “The basis of stability lies in the preservation of the vertical axis, which passes through the middle of the head and body to the ball of the supporting foot when one is standing on demi-pointe and in front of the heels when one is standing on the whole foot” (Kostrovitskaya, 1995, p.62). Plasticity is developed in the arms and in the torso and when moving from one pose to another pose. (For example, slow turns from one big pose to another involving movements of the torso.) Turns in the big poses are introduced. From different preparations, the technique of beats and turns begins to be mastered. Elevation begins to be developed in big jumps.
The Fourth Year of the Six Year Program for the Study of Classical Ballet
Completion of the Intermediate Work
In the Fourth Year exercises of the preceding year are combined with two tours from V and II positions followed by a degagé and then, for example, 7 ronds de jambe en l'air in 1/8. Fic-flac takes place from one big pose to another big pose. Combinations at the Barre become more difficult and complex. Center Exercises are executed en tournant. Different kinds of fouetté movements are introduced such as Grand fouetté effacé forward and backward (en dehors and en dedans). Emphasis is placed on all kinds of preparatory movements such as coupé, step-coupé, glissade, sissonne tombée which are practiced before big jumps such as Grande Jeté, Grande Assemblé en tournant and Saut de Basque etc. Pointe work includes beats, various pas de bourrée on pointe are placed into more complicated combinations. Included in Pointe Work are Grand Jeté and Grande Sissonne Ouverte with plié relevé en pointe. Grand Cabriole is taught in the Men's Class at the end of the year.
The Fifth Year of the Six Year Program for the Study of Classical Ballet
First Part of Advanced Level
Working to continue improving all basic movements already learned and to finish learning all classical dance movements that were studied in the previous classes. Rond de jambe en l'air can now be practiced at 90⁰ in the Barre Exercise. The Big Adagio in the Center Exercise can be concluded in a number of interesting ways including an uncomplicated jump. Fouetté at 45⁰ and for the men's class, Grand pirouette with relevé, eight tours. Renversé from a pose croisée, en dehors and en dedans. Beats include Entrechat-Six are now practiced. Big jumps including Grande cabriole in all of the poses and other big jumps are practiced such as Grand Assemblé Entrechat-Six de Volé. Pointe exercises include Tours Chaîné and Tours from V position en dehors, traveling forward en diagonale etc.
The Sixth Year of the Six Year Program for Classical Ballet
Last Year - Advanced Level
There is further perfection of classical dance movements and emphasis is placed on finishing the dancer for the stage. More dancy combinations of adagio, allegro and pointe are created. Teachers are trying to develop the virtuoso execution and artistry of each dancer. Different movements are taught according to the different abilities of each student. A movement such as Grande Sissonne en tournant with two tours, finishing in a Big Pose might be taught to a talented student.
Reference
Kostrovitskaya, V., & Pisarev, A. & Barker, J (Trans.). (1979). School of classical dance. Moscow: Progress Publishers. | https://www.classicaldancealliance.org/curriculum-and-course-manuals |
In the course of this seminar, relevant methods of predicitive analysis in the context of the relevant business application are studied. Use cases will be utilized to practice data preprocessing techniques as well as model tuning and sampling / resampling. Well-known regression models are studied in the context of concrete business cases. Classification Models (Decision Trees, Rule Induction, K-Nearest Neigbours, Naive Bayesian, Neural Networks, Support Vector Machines, Ensemble Learners, Classification Trees, Rule Based Models) and Methods of Machine Learning (Information Based Learning, Similarity Based Learning, Probability Based Learning , Error Based Learning) are presented in an application-oriented way. Finally, the topics Model Evaluation and Time Series Forecasting are studied.
Learning outcomes
The graduate is able to put predictive analytics into practice for a variety of business applications. They master the practical use of all necessary tools and can weigh the advantages and weaknesses of the individual tools.
Recommended or required reading and other learning resources / tools
Books: Vijay Kotu: Predictive Analytics and Data Mining, Max Kuhn: Applied Predictive Modeling, Daniel Covington: Analytics: Data Sicence, Data Analysis and Predictive Analytics for Business, John D. Kelleher: Fundamentals of Machine Learning for Predicitive Data Analyitcs: Algorithms, Worked Examples and Case Studies, Steven Finlay: Predictive Analytics, Data mining and Big Data
Journals: | https://www.fh-joanneum.at/data-science-and-artificial-intelligence/master/en/course/business-and-law-1/180807304-predictive-analytics-for-business-applications-2018/ws/2020/ |
Related Web site:
About the Project:
Project size: 117,000 square feet of renovation
Construction began: May 2007
Construction ended: August 2008
Architect: Gould Evans
Construction Manager: Hensel Phelps
Mechanical, Plumbing and Electrical:
Structural: Paragon Structural Design
Landscape Architecture: Wheat Scharf Associates
Civil Engineering: GLHN
Technology Consulting: The Sextant Group
The James E. Rogers College of Law has been scattered across multiple areas on and around campus since May of 2007.
But today, gutted and reborn, the new University of Arizona building is open to its students, faculty and staff. At the start of the new academic year, it's perfect timing. The building is fully complete and was constructed within its budget.
“That’s incredible given the time and the moving parts,” said Toni Massaro, dean of the college.
Also amazing is the look and feel of the Rogers College of Law building, which is a striking contrast to its former self.
As students return to class, the impression among many at the college is that the fresh space is a fusion of history, heritage and modern conveniences and will provide a greater sense of professionalism, interaction and community engagement.
Rigel Massaro, a UA law student in the third year of her juris doctorate program, was among those to take more than 150 new students on a tour around the new building.
“Everyone is really excited,” said Massaro, who is also president of the Student Bar Association and is not related to the dean. “It’s very clear that the dean and the associate deans have spent a long time planning this and listening to what the students needed.”
The building is a union of tradition and modernity, of space and accessibility. Nearly 100-year-old chairs and benches that have been mainstay features decade after decade remain in the new building, which has larger and more versatile classroom and meeting spaces, among other additions.
“Students today, in terms of what we’re seeing in trends in education, want to be in open areas, they want more interaction and they want access to natural light,” said Tamara Shroll, vice president for Gould Evans, the project's architect.
“In the past, some of the most vibrant programs were in some of the most desolate areas in the building,” said Shroll, who is also a project manager. “One project goal was to get those spaces out and visible where the students could interact with each other and to also have the teaching spaces in open areas.”
A major feature in the building, a concrete stairwell dips into the ground just below walls covered by an engineered walnut wood plank flooring system. Below ground, accents of bright green mingle with UA red with an acoustical wood ceiling and a compact shelving system is not only high-tech, but also frees up even more space in the building.
“Our architecture team at Gould Evans helped us overcome some of our more traditional ideas about what a law library looked like,” said Michael Chiorazzi, the college’s associate dean for information services. “That's important because libraries are used differently these days, and that should be reflected aesthetically.”
Natural light filters though environmentally conscious windows and ceiling, transforming what was once a closed and often dark building.
“There's a growing body of thought and research on what we intuitively know – that good lighting has a real impact on learning. So I think the biggest change is making natural light a prominent feature of the Law Commons on all three floors,” Chiorazzi said.
He also added that having appropriately sized classrooms with built-in technology is not only critical, “but it also builds a sense of community and enhances interaction in ways that a small class – lost in a large lecture hall – cannot.”
The $21 million project renovated nearly 117,000 square feet of space, resulting in more space for common areas, the library, lounge areas, classroom space, faculty offices and new space for student organizations, the Arizona Law Review and the Arizona Journal of International and Comparative Law.
Shroll said completing the building has been “one of the best experience we’ve ever had in that the University has continued to challenge us to create something incredible and unique.”
The “heartbeat” of the renovation project is the library, which is located downstairs, said Massaro, the college dean.
Also downstairs are study rooms and niche spaces for students to work in smaller groups or alone.
Rigel Massaro said the highlights of the new building include the amount of space available – including a conference room exclusively for student use.
“There is a variety of space to be social, to study, for classes. And we’ve transformed the basement into a beautifully, naturally lit floor that can’t really be called a basement anymore,” the law student said.
Chiorazzi, who is also the editor of the college’s Legal Reference Services Quarterly journal and who teaches information resources and library science for the college, said the space will benefit “a very active College of Law community” whether they are UA students, faculty and staff or community members.
Such changes and additions will allow the college to “facilitate learning in new ways," Toni Massaro said. | https://uanews.arizona.edu/story/new-law-commons-opens |
Context: Mass gatherings like the 1996 Olympic Games require medical services for large populations assembled under unusual circumstances.
Objective: To examine delivery of medical services and to provide data for planning future events.
Design: Observational cohort study, with review of medical records at Olympics medical facilities.
Setting: One large multipurpose clinic and 128 medical aid stations operating at Olympics-sponsored sites in the vicinity of Atlanta, Ga.
Participants: A total of 10715 patients, including 1804 athletes, 890 officials, 480 Olympic dignitaries, 3280 volunteers, 3482 spectators, and 779 others who received medical care from a physician at an Olympic medical station.
Main outcome measures: Number of injuries and cases of heat-related illness among participant categories, medical use rates among participants with official Games credentials, and use rates per 10000 persons attending athletic competitions.
Results: Injuries, accounting for 35% of all medical visits, were more common among athletes (51.9% of their visits, P < .001) than among other groups. Injuries accounted for 31.4% of all other groups combined. Spectators and volunteers accounted for most (88.9%, P < .001) of the 1059 visits for heat-related illness. The rates for number of medical encounters treated by a physician were highest for athletes (16.2 per 100 persons, P < .001) and lowest for volunteers (2.0 per 100). Overall physician treatment rate was 4.2 per 10000 in attendance (range, 1.6-30.1 per 10000). A total of 432 patients were transferred to hospitals.
Conclusions: Organizers used these data during the Games to monitor the health of participants and to redirect medical and other resources to areas of increased need. These data should be useful for planning medical services for future mass gatherings. | https://pubmed.ncbi.nlm.nih.gov/9600481/?dopt=Abstract |
What is Hacking?
Contents
Hacking is the activity of identifying weaknesses in a computer system or a network to exploit the security to gain access to personal data or business data. An example of computer hacking can be: using a password cracking algorithm to gain access to a computer system.
Computers have become mandatory to run a successful businesses. It is not enough to have isolated computers systems; they need to be networked to facilitate communication with external businesses. This exposes them to the outside world and hacking. System hacking means using computers to commit fraudulent acts such as fraud, privacy invasion, stealing corporate/personal data, etc. Cyber crimes cost many organizations millions of dollars every year. Businesses need to protect themselves against such attacks.
In this hacking tutorial, we will learn-
Time needed: 4 minutes.
- Common Hacking Terminologies
- What is Cyber Crime?
- Types of Cyber Crime
- What is Ethical Hacking?
- Why Ethical Hacking?
- Legality of Ethical Hacking
- Summary
Before we learn hacking, let’s look at the introduction of hacking and some of the most commonly used terminologies in the world of hacking.
Who is a Hacker?
A Hacker is a person who finds and exploits the weakness in computer systems and/or networks to gain access. Hackers are usually skilled computer programmers with knowledge of computer security.
Types of Hackers
Hackers are classified according to the intent of their actions. The following list classifies types of hackers according to their intent:
Introduction of Cybercrime
Cybercrime is the activity of using computers and networks to perform illegal activities like spreading computer viruses, online bullying, performing unauthorized electronic fund transfers, etc. Most cybercrime hacks are committed through the internet, and some cybercrimes are performed using Mobile phones via SMS and online chatting applications.
Type of Cybercrime
- The following list presents the common types of cybercrimes:
- Computer Fraud: Intentional deception for personal gain via the use of computer systems.
- Privacy violation: Exposing personal information such as email addresses, phone number, account details, etc. on social media, hacking a websites, etc.
- Identity Theft: Stealing personal information from somebody and impersonating that person.
- Sharing copyrighted files/information: This involves distributing copyright protected files such as eBooks and computer programs etc.
- Electronic funds transfer: This involves gaining an un-authorized access to bank computer networks and making illegal fund transfers.
- Electronic money laundering: This involves the use of the computer to launder money.
- ATM Fraud: This involves intercepting ATM card details such as account number and PIN numbers. These details are then used to withdraw funds from the intercepted accounts.
- Denial of Service Attacks: This involves the use of computers in multiple locations to attack servers with a view of shutting them down.
- Spam: Sending unauthorized emails. These emails usually contain advertisements.
What is Ethical Hacking?
Ethical Hacking is identifying weakness in computer systems and/or computer networks and coming with countermeasures that protect the weaknesses. Ethical hackers must abide by the following rules.
- Get written permission from the owner of the computer system and/or computer network before hacking.
- Protect the privacy of the organization been hacked.
- Transparently report all the identified weaknesses in the computer system to the organization.
- Inform hardware and software vendors of the identified weaknesses.
Why Ethical Hacking?
- Information is one of the most valuable assets of an organization. Keeping information secure can protect an organization’s image and save an organization a lot of money.
- Fake hacking can lead to loss of business for organizations that deal in finance such as PayPal. Ethical hacking puts them a step ahead of the cyber criminals who would otherwise lead to loss of business.
Legality of Ethical Hacking
Ethical Hacking is legal if the hacker abides by the rules stipulated in the above section on the definition of ethical hacking. The International Council of E-Commerce Consultants (EC-Council) provides a certification program that tests individual’s skills. Those who pass the examination are awarded with certificates. The certificates are supposed to be renewed after some time.
Summary
- Hacking is identifying and exploiting weaknesses in computer systems and/or computer networks.
- Cybercrime is committing a crime with the aid of computers and information technology infrastructure.
- Ethical Hacking is about improving the security of computer systems and/or computer networks.
- Ethical Hacking is legal. | https://www.technocp.com/what-is-hacking-types-of-hackers-introduction-to-cybercrime/ |
With this series of photos, I have explored abstraction and the concept of ‘Flat Life’, focusing on the homogeneity of social housing and tower-blocks.
Arguably, design for modern life has the aim reducing our thinking time: we live in an image saturated, overstimulated world which demands our concentration at every juncture. Architecturally, we have adapted to living in spaces that are easily understood: tall rows and columns of uniform apartments, designed to look, feel and be experienced in the same way.
Artists like Andreas Gursky capture this sensation with photographs of flattened apartment buildings that fill the frame, giving the audience a heightened, surreal version of their every day environments. I approached this concept by using my own photographs of ‘Flat Life’, and visually translating into collages to become more like abstract pattern than the original buildings that they represent.
For each of the photographs I have selected, there is a corresponding collage. These collages are representative of my personal visual translation of what was a 3D space into an abstracted, flattened image. | https://cicelypilkington.com/society |
Alphabetical list:
A B C D E F G H I J K L M N O P R S T U V W X Y Q Z 1 2 3 4 5 6 7 8 9
News: December 4, 2009
Antidepressants May Change Your PersonalityDecember 4, 2009
Taking antidepressants may not only help alleviate depression, but could make you more extraverted and less neurotic, new research suggests.
Extraversion, which is associated with positive emotions, is believed to help protect from depression, while neuroticism, the tendency to experience negative emotions and emotional instability, is thought to contribute to depression.
Becoming more extraverted and less neurotic may help prevent a relapse of depression, said lead study author Tony Tang, an adjunct professor of psychology at Northwestern University in Evanston, Ill.
"People's personalities actually do change and quite substantially when they go through these antidepressant treatments," Tang said. "In the past, we tended to dismiss the personality changes as a side effect or something not very important. But our study suggests it's actually very important to treatment outcomes."
Extraversion and neuroticism are associated with the serotonin system, the brain's reward center that helps regulate mood, sleep and appetite. In this study, participants took paroxetine, which is sold under the brand name Paxil, a selective serotonin reuptake inhibitor. Other SSRIs include Prozac, Zoloft and Celexa. Though those drugs were not tested, Tang said the impact on the personality would likely be similar.
The study findings are published in the December issue of Archives of General Psychiatry.
The researchers divided 240 adults with a major depressive disorder into three groups: 120 received paroxetine, 60 underwent cognitive therapy and 60 took a placebo. Personalities and depressive symptoms were assessed before, during and after treatment.
All groups experienced some improvement in their depression. But participants taking paroxetine became less neurotic and more extraverted than those receiving cognitive therapy or placebo.
It wasn't that the depressed patients suddenly became happy-go-lucky, carefree social butterflies, Tang said. On scales of extraversion and neuroticism, their levels were still barely in the normal range - but they were better than they were before.
Relapsing after stopping treatment, or even while still receiving treatment, is a problem for people with depression. About two-thirds of patients relapse within a year of halting medications, while about 45 percent to 50 percent relapse even if they're still on medication, Tang said.
"Our findings seem to suggest one of the very good predictors for how well you'll do over the long term is how much your personality changes in response to the medication," he said. "For example, how much your neuroticism improved predicted how likely you were to relapse in a year after the treatment."
Bernard Carroll, scientific director of the Pacific Behavioral Research Foundation in Carmel, Calif., said any excitement over the results should be tempered by the fact that the improvements in depression from taking paroxetine weren't much better than from a placebo or cognitive therapy.
"The study confirms that paroxetine is not an especially effective antidepressant drug," said Carroll, past chairman of the U.S. Food and Drug Administration's (FDA) advisory committee for psychiatric drugs. "In this sample, it barely beat the placebo."
Instead, paroxetine is more commonly prescribed for anxiety disorders, which is why researchers may have noted the personality changes. "Paroxetine wouldn't be anybody's number one choice for depression," Carroll said. "But it just might make sense that improving certain personality dimensions helps the patient's resilience against future relapse."
Deciding whether to take an SSRI or not has to be weighed against possible side effects, Carroll said, citing a recent study in the British Journal of Psychiatry that found that many people taking SSRIs reported feeling that the medications had blunted their emotions, both negative and positive ones. Other side effects may include headache, changes in sleep patterns, gastrointestinal upset and changes in sexual functioning, according to background information in that study.
"This business about the drugs affecting personality is not all necessarily good," Carroll said.
In another study from the December issue of Archives of General Psychiatry, patients with bipolar disorder who were taking antiepileptic drugs did not have an increased risk of suicide.
Anti-seizure drugs - including gabapentin, pregabalin, topiramate and carbamazepine - are not only used to treat epilepsy, but nerve disorder and bipolar disorder, according to background information in study.
Last year, the FDA warned of increased risk of suicidal thoughts and behavior related to the use of anti-seizure drugs but voted not to require a black box warning label about suicide risk.
Researchers from the University of Illinois at Chicago analyzed data on 47,918 patients with bipolar disorder, of which 13,385 patients received one of 11 anti-seizure drugs, while others received lithium or no treatment.
The rates of suicide among those taking anti-seizure drugs were no higher than for those taking lithium or those who received no treatment. And for patients taking anti-seizure drugs, suicide rates were five times higher before starting treatment than afterward.
The researchers said those with more severe illness may be more likely to be prescribed anti-seizure drugs or lithium.
Archive issues: (50)
Archive list: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 May 19, 2012 | Senate Passes FDA Safety And Innovation Act
Bill Makes Some Improvements to Medical Device Oversight But Important Patient Safety Protections Still Missing WASHINGTON, May 24, 2012 /PRNewswire-USNewswire/ -- The Senate approved the Food and Drug Administration Safety and Innovation Act today. While the legislation includes some improvements over current law, it leaves significant flaws with ...March 10, 2012 | Calcium Supplements May Be Bad for Your Heart
Many older Americans take calcium supplements to prevent bone loss, but they may be significantly increasing their risk for a heart attack, a new study suggests. These supplements do not help prevent heart ...
Related articles:
Treatment - medicationAs recently as a decade ago, treatments available were limited to the use of astringent instillations, such as chlorpactin (oxychlorosene) or silver nitrate, designed to kill "infection" and/or strip off the bladder lining. In 2005, our understanding of IC/PBS has improved dramatically and these therapies are now no longer done. Rather, IC/PBS therapy is typically multi-modal, including the use of a bladder coating, an antihistamine to help control mast cell activity and a low dose ...
Section: Interstitial cystitis
Treatment - pain controlPain control is usually necessary in the IC/PBS treatment plan. The pain of IC/PBS has been rated equivalent to cancer pain and may lead to central sensitization if untreated. Medication. The use of a variety of traditional pain medications, including opiates and synthetic opioids like tramadol, is often necessary to treat the varying degrees of pain. Even children with IC/PBS should be appropriately addressed regarding pelvic pain, and receive necessary ...
Section: Interstitial cystitis
Chronic prostatitis/chronic pelvic pain syndrome - treatmentNo treatment required. It is standard practice for men with infertility and category IV prostatitis to be given a trial of antibiotics and/or anti-inflammatories however evidence for efficacy are weak. Since signs of asymptomatic prostatic inflammation may sometimes be associated with prostate cancer, this can be addressed by tests that assess the ratio of free-to-total PSA. The results of these tests were significantly different in prostate cancer and category IV prostatitis in one study. | http://www.arcfabinc.com/news/12-04-09/page/17.htm |
From artistry to politics, ancient Greece left a considerable impression on world history. Learn why Greek and Roman gods share so many similarities, how the alphabet got its name, and how the legacy of ancient Greece has evolved over thousands of years.
Transcript
Art. Philosophy. Democracy. And heroes. These are just a few achievements of the legendary civilization known… as ancient Greece.
Ancient Greece was born on the shores of the Aegean Sea about four thousand years ago. In over a millennium, it expanded to lands as far west as Spain and as far east as India.
Throughout this age of empire, the ancient Greeks made political, militaristic, and cultural achievements that resonated long after their empire fell.
Part of the ancient Greeks’ legacy involved politics. One of which was the political system of Greece itself.
Unlike many nations that were under unified rule, Greece was a collection of over 1,500 territories that acted as sovereign nations. Called city-states, these territories had their own rulers and sometimes fought each other.
Another political development was the institution of the first large-scale democracy.
Developed in the city-state of Athens, democratic rule was a way to give the Greek people representation and political power.
The Greeks also earned a strong reputation for their military.
The military helped expand the Greek empire by establishing colonies overseas, and it protected Greece itself from foreign invaders, like the Persian Empire. When such a threat occurred, city-states united to defend their homeland.
Many Greeks, particularly in Sparta, took immense pride in their military, and regarded their soldiers as heroes.
Their heroism was often turned into legend, thanks to literary works like the
Iliad.
War heroes also inspired the creation of the Olympics, which celebrated physical competition.
Of all aspects of ancient Greek civilization, their cultural contributions left a considerable mark on the Western world.
Particularly noteworthy were the ancient Greeks’ art and architecture.
They created incredible sculptural works, such as standing figures and reliefs;
plus, they developed three types of columns and incorporated them into structures like the Parthenon.
This artistry was imitated by other civilizations and spread throughout the globe for thousands of years.
How the Greeks interpreted their world was also reflected in other cultures.
Greek religion, which was comprised of many anthropomorphic deities, helped shape the spiritual beliefs of the Etruscans and, later, the ancient Romans.
Greek philosophy, which explored matters of reason, ethics, and natural law, influenced later civilizations’ achievements in politics and science.
Greek language made quite an impact, as well. Ancient Greek, at about 3400 years old, provided the basis of many modern languages.
The English language alone has thousands of words with Greek roots.
Ancient Greece’s artistry, regard for heroes, and democratic rule left a considerable impression on world history.
With contributions that lasted for millennia, the civilization of ancient Greece is nothing short of legendary.
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Ancient Greece 101
From artistry to politics, ancient Greece left a considerable impression on world history. Learn why Greek and Roman gods share so many similarities, how the alphabet got its name, and how the legacy of ancient Greece has evolved over thousands of years.
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© 1996-2015 National Geographic Society.
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All rights reserved. | https://video.nationalgeographic.com/video/101-videos/00000162-b662-d72d-a9fa-b7f367360000?gc=%2Fvideo%2Fpeople-culture&gs=recent |
The Bachelor of Engineering Psychology programme on the Tuttlingen Campus combines psychology and engineering. In 7 semesters you will learn how humans perceive, process and act upon information. The Engineering Psychology programme focuses on man, product development and the most important methodology. It takes into account psychological, cognitive, social and ergonomic aspects of the technical creation process.
You will be examining human behaviour in dealing with machines: user-friendliness, functionality, enjoyment and safety in use. You will also be taught research and evaluation methods to be able to analyse this behaviour when using technical systems. Engineering principles and development know-how are also covered on the course, so that you have the theoretical knowledge to support the technical product creation.
An internship semester is carried out in the 4th semester.
Engineering Psychology – a study programme run in cooperation with industry
On the Tuttlingen Campus you will be studying in cooperation with over 100 companies. The Engineering Psychology programme is therefore workplace-oriented and offers excellent perspectives.
- Introduction to the specialist area of Engineering Psychology through visits to companies
- Practicals in the Internal link opens in the same window:labs of the Faculty of Industrial Technologies
- Practicals in the labs of cooperating companies
- Project work in cooperation with companies
- Lecture series with experts from business
- Mentoring by specialists and management from industry
Degree awarded
After completion of the bachelor's thesis in the 7th semester, the Bachelor of Science (BSc) degree is awarded.
Semester
Learning outcomes - Engineering Psychology (IP), Bachelor of Science (BSc)
Subject knowledge and skills
Our graduates:
- have a fundamental knowledge of engineering and psychology
- have a good understanding of the theory and practice of design and monitoring of man-machine
- interactions from a psychological and engineering point of view
- can plan, execute, evaluate and interpret empirical investigations
- are familiar with the product design process
- have an understanding of management methods and can apply these
Transferable skills
Our graduates...
- have developed design and analytical skills for the solution of man-machine interaction problems
- have key and soft skills
- can work in interdisciplinary teams to solve problems
- have subject-specific proficiency in spoken and written English
Employability Skills
Our graduates... | https://www.hs-furtwangen.de/en/programmes/engineering-psychology-bachelor/details-of-engineering-psychology-programme/ |
when reason is granted sovereignty and practical reason is given primacy. Kant therefore rejects the rationalist view that sensibility is only a confused species of intellectual cognition, and he replaces this with his own view that sensibility is distinct from understanding and brings to perception its own subjective forms of space and time a view that. In a footnote to this passage, Kant explains that we know freedom a priori because were there no freedom, the moral law would not be encountered at all in ourselves, and on Kants view everyone does encounter the moral law a priori (5:4). But although Kant holds that the morality of an action depends on the form of its maxim rather than its end or goal, he nevertheless claims both that every human action has an end and that we are unavoidably concerned with the consequences of our. On the compatibilist view, as Kant understands it, I am free whenever the cause of my action is within. The project of the Critique is to examine whether, how, and to what extent human reason is capable of a priori knowledge. Feder (17401821) 9 and it was the dominant way of interpreting Kants transcendental idealism during his own lifetime. Furthermore, we can believe that the highest good is possible only if we also believe in the immortality of the soul and the existence of God, according to Kant. If we distinguish between involuntary convulsions and voluntary bodily movements, then on this view free actions are just voluntary bodily movements.
Communication in workplace essay
British essayist midnight oil
Perhaps the central and most controversial thesis of patriotism of india essay the Critique of Pure Reason is that human beings experience only appearances, not things in themselves; and that space and time are only subjective forms of human intuition that would not subsist in themselves if one were. But the Critique claims that pure understanding too, rather than giving us insight into an intelligible world, is limited to providing forms which he calls pure or a priori concepts that structure our cognition of the sensible world. Rather, experience of an objective world must be constructed by exercising an a priori capacity to judge, which Kant calls the faculty of understanding (A8081/B106). The New Elucidation in particular shows the influence of Christian August Crusius (17151775 a German critic of Wolff. So, on his view, the fact of reason is the practical basis for our belief or practical knowledge that we are free. 18 The most important implication of Kants claim that the understanding constructs a single whole of experience to which all of our representations can be related is that, since he defines nature regarded materially as the sum total of all appearances and he has argued. One problem with this view, Kant believes, is that there is no such representational content that is invariably present in experience, so the sense of an ongoing self cannot possibly arise from that non-existent content (what Locke calls consciousness) being present in each of ones. Religion through its holiness and legislation through its majesty commonly seek to exempt themselves from. For as we saw in the previous section, Kant holds that every human action has an end and that the sum of all moral duties is to promote the highest good. If only my noumenal self is free, and freedom is required for moral responsibility, then my phenomenal self is not morally responsible. | http://northcarolinaemeralds.info/27271-buy-john-locke-essay-nidditch/ |
The invention relates to a tread pattern for a tread of a tire, and more particularly to a tread pattern which evolves as the tread becomes worn; the invention also relates to a mold for molding such an evolving tread pattern.
A tread of a tire is generally formed by at least one elastomer and is provided with a tread pattern formed of elements in relief (such as ribs or blocks) separated from each other in the circumferential direction and/or in the transverse direction by grooves having cross-sections which have widths typically greater than 2 mm and depths at most equal to the thickness of the tread.
A tire traveling over long distances results in gradual wear of the tread of said tire up to a maximum level of wear which determines what is called the wear life of the tire, which requires either the replacement of the tire or the renovation of the tread thereof by recapping and putting on a new tread.
The elements in relief of a tread play a fundamental role as far as the adhesion of the tire is concerned, both in the transverse direction and in the circumferential direction, and very particularly when traveling on wet and/or snowy ground. In fact, the ridges of the elements in relief, by cutting the film of water present on the surface of the road, make it possible to keep the tread in contact with the road; secondly, the grooves act as preferred passages for evacuating the water in this case.
Obtaining a good level of performance of a tread pattern of a tire also lies in the conformity between said tread pattern of the new tire and the rigidity of the tread. xe2x80x9cRigidityxe2x80x9d is understood, among other things, to mean the rigidity of said tread when it is subjected both to loading forces (compressive forces) in the region affected by the contact with the road, for example, and to forces tangential to said region (these latter forces are comparable with shearing forces).
For a given nature of the rubber mix forming the tread, this loading resistance under compressive and shearing stresses depends on the dimensions of the contact surfaces of the elements in relief in contact with the ground and on the height of said elements, that is to say the depth of the grooves defining said elements. The different performances in terms of wear, behavior on dry or wet ground, or of adhesion of a tread of a tire are highly dependent on the rigidity of this tread in the zone affected by the loading.
Furthermore, and in order to increase the number of rubber ridges in contact with the road, a greater or lesser number of incisions or slits is frequently produced in the elements in relief, the width of which incisions or slits is very much less than the width of the grooves defining the elements in relief. The width of an incision, which is variable according to the dimension of the tire in question, is generally less than 2 mm. As a general rule, the incisions have the same depth as the grooves, but they may also affect only the surface part of the tread so as not to reduce too far the initial rigidity of said tread and thus to achieve an acceptable compromise.
The presence of a greater or lesser number of incisions modifies in proportion the rigidity of the elements in relief provided with such incisions, and consequently the rigidity of the tread is affected to a greater or lesser extent thereby.
The assembly formed by these circumferential and/or transverse grooves associated with the incisions produced in the elements in relief of the pattern of a tread imparts to the new tire provided with said tread a level of performance which is entirely satisfactory to the user, whatever the type of roads and/or the climatic conditions encountered.
Nevertheless, the reduction in the thickness of the tread resulting from the progressive wear of the tire results in a reduction in the depth of the grooves and hence in a reduction in the height of the elements in relief. Furthermore, this reduction in the height of the elements in relief results in an increase in the rigidity of each element, and consequently of said tread. Associated with this wear, there is generally noted a loss of effectiveness of the tread pattern after a greater or lesser fraction of the life of the tire. To take account of this, provision may be made to achieve a compromise on the tire when new by providing it with a tread pattern, the optimum point of operation of which is only achieved after a level of wear of its tread.
Another means making it possible to achieve satisfactory operation on the new tire and after a given amount of wear of the tread consists, as described in European Patent 0,378,090, in providing the tread of a new tire with a plurality of incisions having in cross-section a trace, formed of a first rectilinear part extending radially to the inside of the tire over a depth of between 35% and 55% of the total depth of the trace, this first part being divided into at least two branches extending radially to the inside of the tire over the remaining depth such that the number of incisions is multiplied by a coefficient of at least 1,5 starting from the inner end of the first rectilinear part of the trace.
Although this solution achieves good results, it is however not totally satisfactory, because, since the wear of the tread involves a reduction in the volume determined by the grooves and possibly the incisions if present, there results a reduction in the ability of the grooves to evacuate the water present on the road in the case of traveling on a wet road. To overcome this disadvantage, it is known, for example in the field of heavy-vehicle tires, to regenerate the tread pattern after partial wear of the tread by removing material to form new grooves according to a pre-established trace.
The problem on which the invention is based is to produce a tread of a tire which is optimized from the point of view of the adhesion and behavior performance (that is to say, ensuring perfect control of the road-holding of a vehicle equipped with tires provided with said tread pattern), whether in the initial state or during the life of the tire without this adversely affecting the performance of said tire in terms of its wear life.
Another object of the invention is to provide a tread pattern imparting to a tread a rigidity in the region affected by the contact which is adapted according to the successive states of wear of said tread.
According to the invention, there is proposed a tread of thickness E for a tire, said tread having a running surface, limited transversely by lateral edges, said tread being provided when new with a tread pattern comprising at least a plurality of rubber blocks arranged circumferentially on at least one of its lateral edges, said rubber blocks being separated from each other by grooves oriented virtually transversely and separated from the tread pattern motifs located axially to the inside by grooves oriented mainly circumferentially, the tread being characterized in that it comprises on at least one of its edges comprising a plurality of rubber blocks when new and radially to the inside of each of said blocks:
at least one channel of average width at least equal to the width of the transverse grooves, each channel having an average trace identical to the average trace of said transverse grooves and being intended to form a groove opening radially towards the outside of the tread after wear of the tread of between 15% and 45% of the thickness E of said tread, each channel extending within the remaining thickness of the tread, and
at least one incision, of low width compared with the average width of each channel, having, in a radial projection on the running surface of the tread when new, an average transverse orientation identical or virtually identical to that of the channel(s) projected on the same surface, each incision opening radially to the running surface at the latest at the time of the appearance of a channel on said running surface and extending, in the thickness of the tread, over the entire depth of the adjacent channel(s) on the same level in the thickness of the tread.
It is judicious for the channels intended to form new grooves to extend in depth at least as far as the maximum level of wear of the tread, so as to maintain good drainage during the entire time of use of the tire provided with a tread according to the invention.
Another object of the invention is to propose a mold for manufacturing a tire for molding such a tread, said mold firstly permitting the molding of a plurality of motifs located radially beneath the running surface of said tread and extending in a substantially transverse direction, and secondly the demolding of the tire using the forces exerted by the material constituting the tread on said mold, so as to reduce the overall molding force and to facilitate the latter.
Usually, a tire mold comprises several parts which, once assembled, define a molding surface corresponding to the outer surface of the tire to be molded. One type of known mold comprises a part forming a ring, intended to mold the tread of a tire, and two parts forming shells intended to mold the sidewalls of said tire. The ring molding the tread is composed of a plurality of sectors, each sector, being able to be displaced in a substantially radial direction of molding/demolding, is provided with a mold fitting composed of a plurality of elements in relief for molding motifs in said tread. Using this known technique, the elements in relief have to have geometries which permit demolding after vulcanization of the tire, that is to say the extraction of said elements from the tread. Consequently, elements in relief having undercut parts are difficult to demold using this technique. Likewise, this technique does not make it possible to mold elements which do not open on to the surface of the tread when new.
For molding channels beneath the running surface of the tread of a new tire, it is known, in particular in U.S. Pat. No. 1,733,064, to produce a plurality of holes in a shell of a tire mold so as to permit the introduction of needles into the rubber forming the tread of a tire once the latter has been molded. Furthermore, means external to said mold are provided for forcing said needles to penetrate the rubber, these same means then serving to cause the needles to emerge again before proceeding to demould the tire by opening the different parts constituting the mold. This mold is particularly complex to produce, and requires at least one shell to be pierced; in the case of a modification, for example of the number of needles, it is necessary to renovate another shell, which is expensive. Furthermore, the presence of holes on the shell involves greater or lesser penetration of the rubber thereinto, which results, after molding, in the presence of molding defects on the sidewalls of the tire.
To solve the problems mentioned above, there is proposed a mold for molding a tire provided with a tread extending axially via the sidewalls as far as the bead zones, said mold comprising two shells provided with molding surfaces each for molding a tire sidewall and a structure forming a ring concentric to the two shells for molding the tread of the tire. The ring and the shells forming the mold according to the invention, in the closed position of the mold, are in contact via their lateral ends so as to define the total molding surface of a tire.
The mold according to the invention is characterized in that:
at least one shell is formed of at least two annular shell parts concentric to each other, such that the molding surfaces of said parts, in the molding configuration, are in the extension one of the other for molding an entire sidewall,
at least one of the shell parts is provided with at least a plurality of elements in relief projecting onto the molding surface of said shell part, said elements in relief of the same shell part having virtually the same geometry and the same orientation defined as being the direction between the point of anchoring of an element on the shell part and the end of said axially outermost element of said shell part,
each of the shell parts bearing elements in relief is mounted to be mobile in the circumferential direction relative to the other parts of the same shell, so as to permit the rotation of each of said parts relative to the other parts of the same shell at least under the action of the forces exerted by the rubber mixes on the elements in relief during demoulding, with the aim of facilitating the demoulding of the tire.
In this manner, it is possible to reduce the forces necessary for demolding the elements in relief borne by each shell part, since under the action of the reaction forces produced by the vulcanized rubber mixes during the demolding on said elements, each part will rotate relative to the other parts of the same shell.
A mold according to the invention makes it possible, in simple manner, to effect molding and demolding of tires comprising tread pattern motifs opening on to at least one edge of the tread, said motifs having an orientation which is overall different from the transverse direction of the tire. The mold according to the invention also makes it possible to mold tread pattern motifs with elements in relief having highly non-demoldable geometries (that is to say, geometries such that the molding in a non-elastically deformable material cannot be followed by demolding without degrading either the elements in relief or the molded material).
A mold according to the invention may comprise at least one shell formed by the assembly of several annular parts concentric to one another, of which at least two of said parts are circumferentially mobile relative to a fixed part of said shell to permit, for example, the production of several levels of tread pattern in a tread (an arrangement which is particularly advantageous in the case of tires for heavy vehicles having treads of a thickness which is relatively greater than that of passenger car tires). Advantageously, the shell parts bearing elements in relief are mobile independently of each other.
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Future of Work: Productivity Trends 2022
The future of work is all about change, and it’s time to recognize that “normal” is no longer a thing. While new companies and startup organizations usually embrace the notion of constant change, major enterprises around the world are discovering that they must do the same. For instance, companies like Shopify, Twitter and Facebook confirmed that they are establishing permanent policies that let people work from home, which is a big shift from how they used to operate. Here are four workplace trends for 2022.
1. Hybrid Workplace Opportunities
In 2022, it’s going to be more common to see hybrid work opportunities that allow employees to choose from three main work environment models. These will be traditional workplaces, remote options and a combination of both. The big thing that will change for employees is that they’ll be able to choose whether they work from home, at the office or go hybrid and do both.
Companies are starting to shift away from a traditional office setting that involves a centralized workplace. When the pandemic was at its most extreme in 2020, an estimated 69% of large companies predicted that they would be decreasing how much office space they needed.
Hybrid models will vary from companies keeping some permanent central offices that feature hot-desking to allow for employees who will be working remotely more often to eliminating office space completely and using co-working offices and rentable meeting rooms that they can use to support their remote staff members.
According to a report published by PWC, technology developments will change the way that people work during the next five to 10 years. Demographic shifts will also transform how people work as will climate change.
In 2022, companies will start to reveal their stances on political and societal issues. They’ll be doing this because workers are starting to want to work for companies that share their values. This sentiment has been growing for a while, but during 2020, it grew even more. According to an article published by the Harvard Business Review, around 74% of workers believe that their employers will involve themselves in current cultural debates.
2. AI Assistance
The World Economic Forum issued a report stating that by 2025, AI and automation will bring about the development of 97 million new jobs. Along with this, many people will see change in their current roles. AI and automation will enhance the abilities of workers.
At first, companies will use AI to automate a job’s repetitive elements. This will let your staff focus on tasks that require human thinking such as creativity, high-level strategies and emotional intelligence. For instance, a lawyer may use advanced technology to review case histories and search precedents. A doctor will use it in a similar way to review medical records while in the retail industry, managers may use technology for inventory planning. Technology will increase productivity and improve worker experience.
People will begin moving away from the idea that a person learns one profession and works at one company where he or she remains until retirement. Workplace trends for 2022 include trying several different occupations throughout one’s life. In fact, there are even scholarships available for adults who are returning to college.
3. A Bigger Focus on Skills
Instead of focusing on people’s roles, company’s will look to increase productivity by focusing on the skills of their workers. You’ll want to hire people who have the skills that you need to manage core business challenges as well as the competencies that you need to conquer them.
Many businesses have already started this trend by shifting away from hierarchical teams to organizational structures that are basically flat. They are implementing a direct reporting approach to solving problems and communicating. When you focus on skills instead of roles, you’ll be supporting innovation and driving your company toward success.
On the employee side, working toward skill development instead of a company’s role puts them in a better place to take advantage of new career opportunities. The switchover from prioritizing skills over roles is looking to be a trend for both companies and employees in 2022.
4. Additional Monitoring and Assessing
While it may be controversial, work trends show that companies are starting to use technology that will help them monitor and assess the effectiveness of their employees. They’re using this information to increase efficiency. Aware is a program that lets companies monitor employee behavior over email while Slack allows them to track productivity. These types of platforms make it easier for managers to oversee remote workers.
Some programs let companies track how often people are going to the bathroom and who spends the most time chatting with their coworkers instead of being at their workstation. If used to intrude on worker behavior, this type of platform could be harmful, but if you use it just to get a broad view of how people are spending their time, then it could be helpful.
A workplace trend in 2022 will be to offer mental health support. The pandemic has revealed that people need mental health assistance, which is encouraging companies to provide it since they are now seeing that good mental health is good for the workplace.
The Future of Work
The way that people work is everchanging. With new developments, people can do their jobs more efficiently and effectively. If you need help guiding your staff through changes like a hybrid workplace or advanced technology, contact me at the Productivity Intelligence Institute. | https://productivityintelligenceinstitute.com/increase-productivity/future-of-work-productivity-trends-2022/ |
We, the Franklin Regional School community, strive for excellence, learning, achievement, and citizenship in all we do.
Excellence: We are committed to excellence. Students, families, staff, administrators, and community partners work every day to make our school more vibrant, rigorous, creative, adaptable, and fun.
Learning: We are committed to learning as a multi-faceted, life-long process and the focus of everything we do. We expect everyone to develop knowledge, skills, and self-awareness.
Achievement: We are committed to growth in academics. We promote, recognize, and value our accomplishments.
Citizenship: We act with integrity and in an ethical and responsible manner. In this way, we promote each person's ability to be a productive, contributing, thoughtful, respectful, and socially responsible citizen.
Everyone is expected to act with honesty and integrity.
Everyone deserves the opportunity to be valued and respected.
Everyone is a contributing partner in the educational process.
Everyone is entitled to an environment that promotes high expectations and accountability through challenging and meaningful work.
Everyone is encouraged to embrace a lifelong quest for learning.
Everyone is responsible for the effective utilization of resources.
Everyone is expected to appreciate the importance, contribution, and impact of diversity in our global society.
Everyone is entitled to and shares responsibility for maintaining a safe, supportive environment.
Everyone is expected to learn to engage in dialogue and discuss differences with civility.
A safe and healthy educational environment by serving as effective stewards of all District resources and capital assets.
A world-class educational system that develops college and career-ready students.
Improved performance and growth levels in all areas -- academic, artistic, and athletic.
Outstanding customer service, family partnerships, stakeholder relationships, and community engagement through communication that is professional, responsive, clear, and timely.
Fiscal integrity, efficiency, and governance effectiveness in all operational areas. | https://franklinregional.k12.pa.us/cms/One.aspx?portalId=76350&pageId=154806 |
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