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Unmanned Aerial Vehicles (UAVs) have become increasingly prominence in recent
years, finding applications in surveillance, package delivery, among many
others. Despite considerable efforts in developing algorithms that enable UAVs
to navigate through complex unknown environments autonomously, they often
require expensive hardware and sensors, such as RGB-D cameras and 3D-LiDAR,
leading to a persistent trade-off between performance and cost. To this end, we
propose RELAX, a novel end-to-end autonomous framework that is exceptionally
cost-efficient, requiring only a single 2D-LiDAR to enable UAVs operating in
unknown environments. Specifically, RELAX comprises three components: a
pre-processing map constructor; an offline mission planner; and a reinforcement
learning (RL)-based online re-planner. Experiments demonstrate that RELAX
offers more robust dynamic navigation compared to existing algorithms, while
only costing a fraction of the others. The code will be made public upon
acceptance.
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The purity of a reduced state for spins that is pure in the rest frame will
most likely appear to degrade because spin and momentum become mixed when
viewed by a moving observer. We show that such a boost-induced decrease in spin
purity observed in a moving reference frame is intrinsically related to the
spatial localization properties of the wave package observed in the rest frame.
Furthermore, we prove that, for any localized pure state with separable spin
and momentum in the rest frame, its reduced density matrix for spins inevitably
appears to be mixed whenever viewed from a moving reference frame.
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We derive a new Banks-Casher-type relation which relates the density of
complex Dirac eigenvalues at the origin to the BCS gap of quarks at high
density. Our relation is applicable to QCD and QCD-like theories without a sign
problem, such as two-color QCD and adjoint QCD with baryon chemical potential,
and QCD with isospin chemical potential. It provides us with a method to
measure the BCS gap through the Dirac spectrum on the lattice.
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The special relativity laws emerge as one-parameter (light speed)
generalizations of the corresponding laws of classical physics. These
generalizations, imposed by the Lorentz transformations, affect both the
definition of the various physical observables (e.g. momentum, energy, etc), as
well as the mathematical apparatus of the theory. Here, following the general
lines of [Phys. Rev. E {\bf 66}, 056125 (2002)], we show that the Lorentz
transformations impose also a proper one-parameter generalization of the
classical Boltzmann-Gibbs-Shannon entropy. The obtained relativistic entropy
permits to construct a coherent and selfconsistent relativistic statistical
theory, preserving the main features of the ordinary statistical theory, which
recovers in the classical limit. The predicted distribution function is a
one-parameter continuous deformation of the classical Maxwell-Boltzmann
distribution and has a simple analytic form, showing power law tails in
accordance with the experimental evidence. Furthermore the new statistical
mechanics can be obtained as stationary case of a generalized kinetic theory
governed by an evolution equation obeying the H-theorem and reproducing the
Boltzmann equation of the ordinary kinetics in the classical limit.
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We present energy spread and bunch length measurements at the Accelerator
Test Facility (ATF) at KEK, as functions of current, for different ring rf
voltages, and with the beam both on and off the coupling resonance. We fit the
on-coupling bunch shapes to those of an impedance model consisting of a
resistor and an inductor connected in series. We find that the fits are
reasonably good, but that the resulting impedance is unexpectedly large.
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With the construction of the Witten-Sakai-Sugimoto model in the D0-D4
background, we systematically investigate the holographic baryon spectrum in
the case of three flavors. The background geometry in this model is
holographically dual to $U\left(N_{c}\right)$ Yang-Mills theory in large
$N_{c}$ limit involving an excited state with a nonzero $\theta$ angle or glue
condensate $\left\langle \mathrm{Tr}\mathcal{F}\wedge\mathcal{F}\right\rangle
=8\pi^{2}N_{c}\tilde{\kappa}$, which is proportional to the charge density of
the smeared D0-branes through a parameter $b$ or $\tilde{\kappa}$. The
classical solution of baryon in this model can be modified by embedding the
Belavin-Polyakov-Schwarz-Tyupkin (BPST) instanton and we carry out the
quantization of the collective modes with this solution. Then we extend the
analysis to include the heavy flavor and find that the heavy meson is always
bound in the form of the zero mode of the flavor instanton in strong coupling
limit. The mass spectrum of heavy-light baryons in the situation with single-
and double-heavy baryon is derived by solving the eigen equation of the
quantized collective Hamiltonian. Afterwards we obtain that the constraint of
stable baryon states has to be $1<b<3$ and the difference in the baryon
spectrum becomes smaller as the D0 charge increases. It indicates that quarks
or mesons can not form stable baryons if the $\theta$ angle or glue condensate
is sufficiently large. Our work is an extension of the previous study of this
model and also agrees with those conclusions.
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Quantum phase transitions have captured the interest of a large community in
condensed-matter and atom physics research. The common feature of these very
different material classes lies in the fact that the competition between
low-energy scales can be tuned by a nonthermal parameter, such as pressure,
magnetic or electric field, and chemical composition for the condensed-matter
systems. In heavy-fermion materials, the strong exchange J between f-electrons
and conduction electrons can lead to quenching of the f-electron-derived
(nearly) localized magnetic moments via the Kondo effect or, if J becomes
weaker, to long-range magnetic order via the Ruderman-Kittel-Kasuya-Yosida
interaction mediated by the conduction electrons. In addition it has been
suggested that magnetic order can be suppressed by quantum fluctuations which
may be enhanced by geometric frustration. Here we report on the observation of
a quantum phase transition in a partially frustrated antiferromagnetic metallic
system. In antiferromagnetic CePdAl the magnetic Ce ions form a network of
equilateral triangles in the (001) plane, similar to the kagom\'e lattice, with
one third of the Ce moments not participating in long-range order. The N\'eel
temperature T_N = 2.7 K can be driven to zero upon replacing 14.4% of Pd by Ni.
Here the specific heat C exhibits a C/T ~ - log T dependence. Within the
Hertz-Millis-Moriya model of quantum criticality, this behavior can be
attributed to two-dimensional critical antiferromagnetic fluctuations arising
from the decoupling of three-dimensional magnetic order by frustration. The
intermediate planes of frustrated moments are a possible candidate for a
two-dimensional spin-liquid. The simultaneous presence of magnetic order,
geometric frustration, and Kondo effect in this system might thus entail a new
route to quantum criticality.
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We demonstrate effective equilibration for unitary quantum dynamics under
conditions of classical chaos. Focusing on the paradigmatic example of the
Dicke model, we show how a constructive description of the thermalization
process is facilitated by the Glauber $Q$ or Husimi function, for which the
evolution equation turns out to be of Fokker-Planck type. The equation
describes a competition of classical drift and quantum diffusion in contractive
and expansive directions. By this mechanism the system follows a 'quantum
smoothened' approach to equilibrium, which avoids the notorious singularities
inherent to classical chaotic flows.
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In this paper, the results of part I regarding a special case of Feynman
identity are extended. The sign rule for a path in terms of data encoded by its
word and formulas for the numbers of distinct equivalence classes of
nonperiodic paths of given length with positive or negative sign are obtained
for this case. Also, a connection is found between these numbers and the
generalized Witt formula for the dimension of certain graded Lie algebras.
Convergence of the infinite product in the identity is proved.
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X-ray characterisation methods have undoubtedly enabled cutting-edge advances
in all aspects of materials research. Despite the enormous breadth of
information that can be extracted from these techniques, the challenge of
radiation-induced sample change and damage remains prevalent. This is largely
due to the emergence of modern, high-intensity X-ray source technologies and
growing potential to carry out more complex, longer duration in-situ or
in-operando studies. The tunability of synchrotron beamlines enables the
routine application of photon energy-dependent experiments. This work explores
the structural stability of [Rh(COD)Cl]2, a widely used catalyst and precursor
in the chemical industry, across a range of beamline parameters that target
X-ray energies of 8 keV, 15 keV, 18 keV and 25 keV, on a powder X-ray
diffraction synchrotron beamline at room temperature. Structural changes are
discussed with respect to absorbed X-ray dose at each experimental setting
associated with the respective photon energy. In addition, the X-ray radiation
hardness of the catalyst is discussed, by utilising the diffraction data at the
different energies to determine a dose limit, which is often considered in
protein crystallography and typically overlooked in small molecule
crystallography. This work not only gives fundamental insight into how damage
manifests in this organometallic catalyst, but will encourage careful
consideration of experimental X-ray parameters before conducting diffraction on
similar radiation-sensitive organometallic materials.
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In this manuscript, we present a novel method for estimating the stochastic
stability characteristics of metastable legged systems using the unscented
transformation. Prior methods for stability analysis in such systems often
required high-dimensional state space discretization and a broad set of initial
conditions, resulting in significant computational complexity. Our approach
aims to alleviate this issue by reducing the dimensionality of the system and
utilizing the unscented transformation to estimate the output distribution.
This technique allows us to account for multiple sources of uncertainty and
high-dimensional system dynamics, while leveraging prior knowledge of noise
statistics to inform the selection of initial conditions for experiments. As a
result, our method enables the efficient assessment of controller performance
and analysis of parametric dependencies with fewer experiments. To demonstrate
the efficacy of our proposed method, we apply it to the analysis of a
one-dimensional hopper and an underactuated bipedal walking simulation with a
hybrid zero dynamics controller.
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We focus on the chiral and heavy quark mass expansion of mesons masses and
decay constants. We propose a light-front QCD formalism for the evaluation of
these quantities, consistent with chiral perturbation theory and heavy quark
effective theory.
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High-Performance Computing (HPC) in the public cloud democratizes the
supercomputing power that most users cannot afford to purchase and maintain.
Researchers have studied its viability, performance, and usability. However,
HPC in the cloud has a unique feature -- users have to export data and
computation to somewhat untrusted cloud platforms. Users will either fully
trust cloud providers to protect from all kinds of attacks or keep sensitive
assets in-house instead. With the recent deployment of the Trusted Execution
Environment (TEE) in the cloud, confidential computing for HPC in the cloud is
becoming practical for addressing users' privacy concerns. This paper discusses
the threat models, unique challenges, possible solutions, and significant gaps,
focusing on TEE-based confidential HPC computing. We hope this discussion will
improve the understanding of this new topic for HPC in the cloud and promote
new research directions.
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A submanifold in a real space form attaining equality in the DDVV inequality
at every point is called a Wintgen ideal submanifold. They are invariant
objects under the Moebius transformations. In this paper, we classify those
Wintgen ideal submanifolds of dimension m>3 which are Moebius homogeneous.
There are three classes of non-trivial examples, each related with a famous
class of homogeneous minimal surfaces in $S^n$ or $CP^n$: the cones over the
Veronese surfaces $S^2$ in $S^n$, the cones over homogeneous flat minimal
surfaces in $S^n$, and the Hopf bundle over the Veronese embeddings of $CP^1$
in $CP^n$.
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CEMP-s stars are long-lived low-mass stars with a very low iron content as
well as overabundances of carbon and s-elements. Their peculiar chemical
pattern is often explained by pollution from a AGB star companion. Recent
observations have shown that most of the CEMP-s stars are in a binary system,
providing support to the AGB companion scenario. A few CEMP-s stars, however,
appear to be single. We inspect four apparently single CEMP-s stars and discuss
the possibility that they formed from the ejecta of a previous-generation
massive star, referred to as the "source" star. In order to investigate this
scenario, we computed low-metallicity massive star models with and without
rotation and including complete s-process nucleosynthesis. We find that
non-rotating source stars cannot explain the observed abundance of any of the
four CEMP-s stars. Three out of the four CEMP-s stars can be explained by a
$25$ $M_{\odot}$ source star with $v_{\rm ini} \sim 500$ km s$^{-1}$
(spinstar). The fourth CEMP-s star has a high Pb abundance that cannot be
explained by any of the models we computed. Since spinstars and AGB predict
different ranges of [O/Fe] and [ls/hs], these ratios could be an interesting
way to further test these two scenarios.
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Recent developments in bremsstrahlung from electrons colliding with atoms and
nuclei at energies between 0.1 MeV and 500 MeV are reviewed. Considered are
cross sections differential in the photon degrees of freedom, including
coincidence geometries of photon and scattered electron. Also spin asymmetries
and polarization transfer for polarized electron beams are investigated. An
interpretation of the measurements in terms of the current bremsstrahlung
theories is furnished.
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We demonstrate coherent Doppler-free three-photon excitation of the
$^{1}S_{0}$$\leftrightarrow$$^{3}P_{0}$ optical clock transition and the
$^{1}S_{0}$$\leftrightarrow$$^{3}P_{1}$ intercombination transition in
free-space thermal clouds of $^{88}$Sr atoms. By appropriate orientation of the
wavevectors of three lasers incident on the atoms, the first-order Doppler
shift can be eliminated for all velocity classes. Three-photon excitation of
the $^{1}S_{0}$$\leftrightarrow$$^{3}P_{1}$ transition enables high-contrast
Ramsey spectroscopy with interrogation times comparable to the 21$\mu$s natural
lifetime using a single near-resonant laser source. Three-photon spectroscopy
on the $^{1}S_{0}$$\leftrightarrow$$^{3}P_{0}$ clock transition, using only
laser frequencies nearly resonant with the
$^{1}S_{0}$$\leftrightarrow$$^{3}P_{0}$ and
$^{1}S_{0}$$\leftrightarrow$$^{3}P_{1}$ transitions, enables a reduction in
Doppler broadening by two orders of magnitude and a corresponding $\sim470$Hz
linewidth without a confining potential.
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A simple model for the instanton ensemble at finite temperature T is
proposed, including ``random" and strongly correlated ``molecular" component.
T-dependence of fermionic zero modes naturally leads to chiral symmetry
restoration, without instanton suppression. Moreover, at $T=(1-2) T_c$ the
non-perturbative effects due to ``molecules" are so strong, that they even
dominate the global thermodynamics. % two figures are enclosed as .ps files
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In a previous paper, we defined a higher dimensional analog of Thompson's
group V, and proved that it is simple, infinite, finitely generated, and not
isomorphic to any of the known Thompson groups. There are other Thompson groups
that are infinite, simple and finitely presented. Here we show that the new
group is also finitely presented by calculating an explicit finite
presentation.
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In the derivation of low-energy effective models for solids targeting the
bands near the Fermi level, the constrained random phase approximation (cRPA)
has become an appreciated tool to compute the effective interactions. The
Wick-ordered constrained functional renormalization group (cfRG) generalizes
the cRPA approach by including all interaction channels in an unbiased way.
Here we present applications of the cfRG to two simple multi-band systems and
compare the resulting effective interactions to the cRPA. First we consider a
multiband model for monolayer graphene, where we integrate out the
$\sigma$-bands to get an effective theory for $\pi$-bands. It turns out that
terms beyond cRPA are strongly suppressed by the different $xy$-plane
reflection symmetry of the bands. In our model the cfRG-corrections to cRPA
become visible when one disturbs this symmetry difference slightly, however
without qualitative changes. This study shows that the embedding or layering of
two-dimensional electronic systems can alter the effective interaction
parameters beyond what is expected from screening considerations. The second
example is a one-dimensional model for a diatomic system reminiscent of a CuO
chain, where we consider an effective theory for Cu 3d-like orbitals. Here the
fRG data shows relevant and qualitative corrections compared to the cRPA
results. We argue that the new interaction terms affect the magnetic properties
of the low-energy model.
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In this article we present an intrinsec construction of foliated Brownian
motion via stochastic calculus adapted to foliation. The stochastic approach
together with a proposed foliated vector calculus provide a natural method to
work on harmonic measures. Other results include a decomposition of the
Laplacian in terms of the foliated and basic Laplacians, a characterization of
totally invariant measures and a differential equation for the density of
harmonic measures.
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We prove ballistic transport of all orders, that is, $\lVert
x^m\mathrm{e}^{-\mathrm{i}tH}\psi\rVert\asymp t^m$, for the following models:
the adjacency matrix on $\mathbb{Z}^d$, the Laplace operator on $\mathbb{R}^d$,
periodic Schr\"odinger operators on $\mathbb{R}^d$, and discrete periodic
Schr\"odinger operators on periodic graphs. In all cases we give the exact
expression of the limit of $\lVert x^m\mathrm{e}^{-\mathrm{i}tH}\psi\rVert/t^m$
as $t\to+\infty$. We then move to universal covers of finite graphs (these are
infinite trees) and prove ballistic transport in mean when the potential is
lifted naturally, giving a periodic model, and when the tree is endowed with
random i.i.d.\ potential, giving an Anderson model. The limiting distributions
are then discussed, enriching the transport theory. Some general upper bounds
are detailed in the appendix.
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We study the spontaneous ''sliding'' of histone spools (nucleosomes) along
DNA as a result of thermally activated single base pair twist defects. To this
end we map the system onto a suitably extended Frenkel-Kontorova model.
Combining results from several recent experiments we are able to estimate the
nucleosome mobility without adjustable parameters. Our model shows also how the
local mobility is intimately linked to the underlying base pair sequence.
|
In this paper we present genetic algorithms based search technique for the
linear optics schemes, performing two-qubit quantum gates. We successfully
applied this technique for finding heralded two-qubit gates and obtained the
new schemes with performance parameters equal to the best currently known. The
new simple metrics is introduced which enables comparison of schemes with
different heralding mechanisms. The scheme performance degradation is discussed
for the cases when detectors in the heralding part of the scheme are not
photon-number-resolving. We propose a procedure for overcoming this drawback
which allows us to restore the reliable heralding signal even with
not-photon-number-resolving detectors.
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The capacity of the two-user Gaussian interference channel has been open for
thirty years. The understanding on this problem has been limited. The best
known achievable region is due to Han-Kobayashi but its characterization is
very complicated. It is also not known how tight the existing outer bounds are.
In this work, we show that the existing outer bounds can in fact be arbitrarily
loose in some parameter ranges, and by deriving new outer bounds, we show that
a simplified Han-Kobayashi type scheme can achieve to within a single bit the
capacity for all values of the channel parameters. We also show that the scheme
is asymptotically optimal at certain high SNR regimes. Using our results, we
provide a natural generalization of the point-to-point classical notion of
degrees of freedom to interference-limited scenarios.
|
We consider type inference in the Hindley/Milner system extended with type
annotations and constraints with a particular focus on Haskell-style type
classes. We observe that standard inference algorithms are incomplete in the
presence of nested type annotations. To improve the situation we introduce a
novel inference scheme for checking type annotations. Our inference scheme is
also incomplete in general but improves over existing implementations as found
e.g. in the Glasgow Haskell Compiler (GHC). For certain cases (e.g. Haskell 98)
our inference scheme is complete. Our approach has been fully implemented as
part of the Chameleon system (experimental version of Haskell).
|
Motivated by the analogous properties of the $Z_c(3900/3885)$ and
$Z_{cs}(3985/4000)$, we tentatively assign the $Z_c(4020/4025)$ as the
$A\bar{A}$-type hidden-charm tetraquark state with the $J^{PC}=1^{+-}$, where
the $A$ denotes the axialvector diquark states, and explore the $A\bar{A}$-type
tetraquark states without strange, with strange and with hidden-strange via the
QCD sum rules in a consistent way. Then we explore the hadronic coupling
constants in the two-body strong decays of the tetraquark states without
strange and with strange via the QCD sum rules based on rigorous quark-hadron
duality, and acquire the partial decay widths and total decay widths. The
present calculations support assigning the $Z_c(4020/4025)$ as the
$A\bar{A}$-type tetraquark state with the $J^{PC}=1^{+-}$, while the
predictions for its strange cousin $Z_{cs}$ state can be confronted to the
experimental data in the future.
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We re-examine the threshold bound state problem on the wrong sign Taub-Nut
space; the metric on which describes the relative moduli space of well
separated BPS monopoles. The quantum mechanics gives rise to a continuous
family of threshold bound states, in distinction to the unique one found on the
Atiyah-Hitchin metric.
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The magnetic field $B$ dependence of the critical current $I_c$ for the
vortex phase of a disordered superconductor is studied numerically at zero
temperature. The $I_{c}(B)$ increases rapidly near the upper critical field
$B_{c2}$ similar to the peak effect (PE) phenomenon observed in many
superconductors. The real space configuration across the PE changes
continuously from a partially ordered domain (polycrystalline) state into an
amorphous state. The topological defect density $n_{d}(B)\sim e^{\alpha B^{k}}$
with $k>1$ for $B\geq 0.4B_{c2}$. There is no evidence of a phase transition in
the vicinity of the PE suggesting that an order-disorder transition is not
essential for the occurrence of the PE phenomenon. An alternative view is
presented wherein the vortex system with high dislocation density undergoes
jamming at the onset of the PE.
|
AMANDA-II is the largest neutrino telescope collecting data at the moment,
and its main goal is to search for sources of high energy extra-terrestrial
neutrinos. The detection of such sources could give non-controversial evidence
for the acceleration of charged hadrons in cosmic objects like Supernova
Remnants, Micro-quasars, Active Galactic Nuclei or Gamma Ray Bursts. No
significant excess has been found in searching for neutrinos from both
point-like and non-localized sources. However AMANDA-II has significantly
improved analysis techniques for better signal-to-noise optimization. The
km$^3$-scale IceCube telescope will enlarge the observable energy range and
improve the sensitivities of high energy neutrino searches due to its 30 times
larger effective area.
|
Analog Compute-in-Memory (CiM) accelerators use analog-digital converters
(ADCs) to read the analog values that they compute. ADCs can consume
significant energy and area, so architecture-level ADC decisions such as ADC
resolution or number of ADCs can significantly impact overall CiM accelerator
energy and area. Therefore, modeling how architecture-level decisions affect
ADC energy and area is critical for performing architecture-level design space
exploration of CiM accelerators.
This work presents an open-source architecture-level model to estimate ADC
energy and area. To enable fast design space exploration, the model uses only
architecture-level attributes while abstracting circuit-level details. Our
model enables researchers to quickly and easily model key architecture-level
tradeoffs in accelerators that use ADCs.
|
Consider a complex symplectic manifold $X$ and the algebroid $W_X$ of
quantization-deformation. For two regular holonomic modules $L_i$ ($i=0,1$)
supported by smooth Lagrangian manifolds, we prove that the complex
$Rhom_{W_X}(L_1,L_0)$ is constructible and perverse and dual to the complex
$Rhom_{W_X}(L_0,L_1)$.
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We answer some questions from a paper of Krupi\'nski by giving suitable
examples of small Polish structures. First, we present a class of small Polish
group structures without generic elements. Next, we construct a first example
of a small non-zero-dimensional Polish $G$-group.
|
In this paper we prove that all irrational numbers from totally real cubic
number fields are well approximable by rationals (i.e. the partial quotients in
the continued fraction expansion of such a number are unbounded). This settles
the long standing open question of whether or not well approximable algebraic
numbers exist. Our proof uses a number theoretic classification of
approximations to algebraic numbers, together with a result of Lindenstrauss
and Weiss which is an application of Ratner's orbit closure theorem.
|
By using Malliavin calculus, Bismut derivative formulae are established for a
class of stochastic (functional) differential equations driven by fractional
Brownian motions. As applications, Harnack type inequalities and strong Feller
property are presented.
|
We discuss some features of the regular supergravity solution for fractional
branes on a deformed conifold, recently found by Klebanov-Strassler, mostly
adapting it to a type 0 non-sypersymmetric context. The non-supersymmetric
gauge theory is SU(M)*SU(M) with two bi-fundamental Weyl fermions. The tachyon
is now stabilized by the RR antisymmetric tensor flux. We briefly discuss the
most general non-supersymmetric theory on electric, magnetic and fractional
type 0 D3-branes on a conifold. This includes the pure SU(N) theory.
|
A search for dark matter using an underground single-phase liquid xenon
detector was conducted at the Kamioka Observatory in Japan, particularly for
Weakly Interacting Massive Particles (WIMPs). We have used 705.9 live days of
data in a fiducial volume containing 97 kg of liquid xenon at the center of the
detector. The event rate in the fiducial volume after the data reduction was
${\rm (4.2 \pm 0.2) \times 10^{-3} \, day^{-1}kg^{-1} keV_{ee}^{-1}}$ at ${\rm
5 \, keV_{ee}}$, with a signal efficiency of ${\rm 20\%}$. All the remaining
events are consistent with our background evaluation, mostly of the
"mis-reconstructed events" originated from $^{210}$Pb in the copper plates
lining the detector's inner surface. The obtained upper limit on a
spin-independent WIMP-nucleon cross section was ${\rm 2.2 \times 10^{-44} \,
cm^{2}}$ for a WIMP mass of ${\rm 60 \, GeV/c^{2}}$ at the $90\%$ confidence
level, which was the most stringent limit among results from single-phase
liquid xenon detectors.
|
We study the enhancement of the magnetic dipole induced excitation
probability of the hyperfine ground state of Doppler-broadened muonic hydrogen
($p \mu^{-}$) by a nanosecond laser pulse in the mid-infrared range with
Gaussian temporal shape such that the pulse bandwidth is broader than the
Doppler width at 10~K. The enhancement is achieved by shrinking the
cross-section of the laser pulse and placing the muonic hydrogen medium in a
multipass cavity, while preserving the total irradiated target volume. We
numerically solve a set of Maxwell-Schr$\ddot{\rm o}$dinger equations to obtain
the excitation probability and the total efficiency for various densities of
the muonic hydrogen atomic medium and at various positions in the multipass
cavity. For the typical range of densities of muonic hydrogen atoms at major
proton accelerator facilities such as the J-PARC (density $\sim$
$10^5$cm$^{-3}$), the laser propagation effect is insignificant. For such
cases, the total efficiency increases by an order of two for 100 reflections
with a uniform polarization. If the density exceeds the value of
$10^{17}$cm$^{-3}$ as might be in the future advances, the laser propagation
effect has to be taken into account, and the total efficiency decreases with
the number of reflections giving rise to a pulsed polarization of the beam. Our
study can serve as a guideline for the development of a polarized muonic beam
for a precise measurement of the ground state hyperfine splitting of muonic
hydrogen, or for $\mu$SR experiments.
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An important challenge in the field of materials design and synthesis is to
deliberately design mesoscopic objects starting from well-defined precursors
and inducing directed movements in them to emulate biological processes.
Recently, mesoscopic metal-oxide based Soft Oxo Metalates (SOMs) have been
synthesized from well-defined molecular precursors transcending the regime of
translational periodicity. Here we show that it is actually possible to
controllably move such an asymmetric SOM-with the shape of a `pea-pod' along
complex paths using tailor-made sophisticated optical potentials created by
spin-orbit interaction due to a tightly focused linearly polarized Gaussian
beam propagating through stratified media in an optical trap. We demonstrate
motion of individual trapped SOMs along circular paths of more than 15 $\mu$m
in a perfectly controlled manner by simply varying the input polarization of
the trapping laser. Such controlled motion can have a wide range of application
starting from catalysis to the construction of dynamic mesoscopic
architectures.
|
We study the planar problem of two satellites attracted by a center of force.
Assuming that the center of mass of the two-satellite system is on a circular
orbit around the center of force and using Levi-Civita regularization we prove
the existence of an almost periodic orbit with an infinite number of collision
between the satellites.
|
We derive a set of spectral statistics whose power spectrum is characterized,
in the case of chaotic quantum systems, by colored noise $1/f^{\gamma}$, where
the integer parameter $\gamma$ critically depends on the specific energy-level
statistic considered. In the case of regular quantum systems these spectral
statistics show $1/f^{\gamma+1}$ noise.
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Transparent materials do not absorb light but have profound influence on the
phase evolution of transmitted radiation. One consequence is chromatic
dispersion, i.e., light of different frequencies travels at different
velocities, causing ultrashort laser pulses to elongate in time while
propagating. Here we experimentally demonstrate ultrathin nanostructured
coatings that resolve this challenge: we tailor the dispersion of silicon
nanopillar arrays such that they temporally reshape pulses upon transmission
using slow light effects and act as ultrashort laser pulse compressors. The
coatings induce anomalous group delay dispersion in the visible to
near-infrared spectral region around 800 nm wavelength over an 80 nm bandwidth.
We characterize the arrays' performance in the spectral domain via white light
interferometry and directly demonstrate the temporal compression of femtosecond
laser pulses. Applying these coatings to conventional optics renders them
ultrashort pulse compatible and suitable for a wide range of applications.
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Dengue control in India is a challenging task due to complex healthcare
settings. In yesteryears, an amplification of dengue infections in India posed
the need for introspection of existing dengue control policies. Prior
understanding of the impacts of control interventions is necessary for their
future implementation. In this paper, we propose and analyze a compartmental
model of dengue to assess the impact of active case finding (ACF) on dengue
disease transmission. Currently, primary prevention of dengue is possible only
with vector control and personal protection from the bites of infected
mosquitoes. Although a few experimental studies are performed to assess ACF in
dengue disease, but this is the first attempt to represent and study the
dynamics of disease using ACF as a control strategy. Local and global dynamics
of the system are studied. We use sensitivity analysis to see the effects of
controllable parameters of the model on the basic reproduction number and total
number of infective population. We find that decrease in the biting rate of
mosquitoes, and increase in the rate of hospitalization and/or notification,
death rate of mosquitoes and ACF for asymptomatic and symptomatic individuals
play crucial role for the reduction of disease prevalence. We calibrate our
model to the yearly dengue cases in eight dengue endemic states of India. The
results of our study show that ACF of symptomatic individuals will have
significant effect on dengue case reduction but ACF of asymptomatic individuals
cannot be ignored. Our findings indicate that the healthcare organizations must
focus on ACF of symptomatic as well as asymptomatic individuals along with
personal protection and mosquitoes control to achieve rapid reduction of dengue
cases in India.
|
Quantitative experiments are described on spatio-temporal patterns of
coherent chemical signaling activity in populations of {\it Dictyostelium
discoideum} amoebae. We observe competition between spontaneously firing
centers and rotating spiral waves that depends strongly on the overall cell
density. At low densities, no complete spirals appear and chemotactic
aggregation is driven by periodic concentric waves, whereas at high densities
the firing centers seen at early times nucleate and are apparently entrained by
spiral waves whose cores ultimately serve as aggregation centers. Possible
mechanisms for these observations are discussed.
|
A new scheme is proposed for rotations of a double-donor charge qubit whose
logical states are defined by the two lowest energy states of a single electron
localized around one or another donor. It is shown that making use of the
microwave pulses tuned to the resonance with an auxiliary excited molecular
level allows for implementation of various one-qubit operations in very short
times. Decoherence effects are analyzed by the example of the P$_2^+$:Si system
and shown to be weak enough for experimental realization of this scheme being
possible.
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In the setting of real vector spaces, we establish a general set-valued
Ekeland variational principle (briefly, denoted by EVP), where the objective
function is a set-valued map taking values in a real vector space quasi-ordered
by a convex cone $K$ and the perturbation consists of a $K$-convex subset $H$
of the ordering cone $K$ multiplied by the distance function. Here, the
assumption on lower boundedness of the objective function is taken to be the
weakest kind. From the general set-valued EVP, we deduce a number of particular
versions of set-valued EVP, which extend and improve the related results in the
literature. In particular, we give several EVPs for approximately efficient
solutions in set-valued optimization, where a usual assumption for
$K$-boundedness (by scalarization) of the objective function's range is
removed. Moreover, still under the weakest lower boundedness condition, we
present a set-valued EVP, where the objective function is a set-valued map
taking values in a quasi-ordered topological vector space and the perturbation
consists of a $\sigma$-convex subset of the ordering cone multiplied by the
distance function.
|
In robotic applications, a key requirement for safe and efficient motion
planning is the ability to map obstacle-free space in unknown, cluttered 3D
environments. However, commodity-grade RGB-D cameras commonly used for sensing
fail to register valid depth values on shiny, glossy, bright, or distant
surfaces, leading to missing data in the map. To address this issue, we propose
a framework leveraging probabilistic depth completion as an additional input
for spatial mapping. We introduce a deep learning architecture providing
uncertainty estimates for the depth completion of RGB-D images. Our pipeline
exploits the inferred missing depth values and depth uncertainty to complement
raw depth images and improve the speed and quality of free space mapping.
Evaluations on synthetic data show that our approach maps significantly more
correct free space with relatively low error when compared against using raw
data alone in different indoor environments; thereby producing more complete
maps that can be directly used for robotic navigation tasks. The performance of
our framework is validated using real-world data.
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For triangulated surfaces, we introduce the combinatorial Calabi flow which
is an analogue of smooth Calabi flow. We prove that the solution of
combinatorial Calabi flow exists for all time. Moreover, the solution converges
if and only if Thurston's circle packing exists. As a consequence,
combinatorial Calabi flow provides a new algorithm to find circle packings with
prescribed curvatures. The proofs rely on careful analysis of combinatorial
Calabi energy, combinatorial Ricci potential and discrete dual-Laplacians.
|
Rechargeable Zn batteries with aqueous electrolytes have been considered as
promising alternative energy storage technology, with various advantages such
as low cost, high volumetric capacity, environmentally friendly, and high
safety. However, a lack of reliable cathode materials has largely pledged their
applications. Herein, we developed a machine learning (ML) based approach to
predict cathodes with high capacity (>150 mAh/g) and high voltage (>0.5V). We
screened over ~130,000 inorganic materials from the Materials Project database
and applied the crystal graph convolutional neural network (CGCNN) based ML
approach with data from the AFLOW database. The combination of these two could
not only screen cathode materials that match well with the experimental data
but also predict new promising candidates for further experimental validations.
We hope this study could spur further interests in ML-based advanced
theoretical tools for battery materials discovery.
|
We study conductance spectroscopy of a two-dimensional junction between a
normal metal and a strongly-correlated superconductor in an applied magnetic
field in the Pauli limit. Depending on the field strength the superconductor is
either in the Bardeen-Cooper-Schrieffer (BCS), or in the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of the Fulde-Ferrell (FF) type.
The strong correlations are accounted for by means of the Gutzwiller method
what leads naturally to the emergence of the spin-dependent masses (SDM) of
quasiparticles when the system is spin-polarized. The case without strong
correlations (with the spin-independent masses, SIM) is analyzed for
comparison. We consider both the s-wave and the d-wave symmetries of the
superconducting gap and concentrate on the parallel orientation of the Cooper
pair momentum Q with respect to the junction interface. The junction
conductance is presented for selected barrier strengths (i.e., in the contact,
intermediate, and tunneling limits). The conductance spectra in the cases with
and without strong correlations differ essentially. Our analysis provides thus
an experimentally accessible test for the presence of strong-correlations in
the superconducting state. Namely, correlations alter the distance between the
conductance peaks (or related conductance features) for carriers with spin-up
and spin-down. In the uncorrelated case, this distance is twice the Zeeman
energy. In the correlated case, the corresponding distance is about 30-50%
smaller, but other models may provide even stronger difference, depending on
details of the system electronic structure. It turns out that the strong
correlations manifest themselves most clearly in the case of the junction with
the BCS, rather than the FFLO superconductor, what should make the experimental
verification of the present results simpler.
|
We present a macroscopic calculation of coherent electro-magnetic radiation
from air showers initiated by ultra-high energy cosmic rays, based on currents
obtained from three-dimensional Monte Carlo simulations of air showers in a
realistic geo-magnetic field. We discuss the importance of a correct treatment
of the index of refraction in air, given by the law of Gladstone and Dale,
which affects the pulses enormously for certain configurations, compared to a
simplified treatment using a constant index. We predict in particular a
geomagnetic Cherenkov radiation, which provides strong signals at high
frequencies (GHz), for certain geometries together with "normal radiation" from
the shower maximum, leading to a double peak structure in the frequency
spectrum. We also provide some information about the numerical procedures
referred to as EVA 1.0.
|
The modular $A_4$ symmetry with three moduli is investigated. We assign
different moduli to charged leptons, neutrinos, and quarks. We analyze these
moduli at their fixed points where a residual symmetry exists. We consider two
possibilities for right-handed neutrinos. First, they are assumed to be
singlets under modular symmetry. In this case, we show that the lepton masses
and mixing can be obtained consistently with experimental observations. Second,
they are assigned non-trivially under modular symmetry. We emphasize that a
small deviation from their fixed point is required in this case. Finally, the
quark masses and mixing are generated correctly around the fixed point of their
modulus. In our analysis, we only consider the simple case of weight 2.
|
Bipartite Riemann-Finsler geometries with complementary Finsler structures
are constructed. Calculable examples are presented based on a bilinear-form
coefficient for explicit Lorentz violation.
|
In this paper we look for solutions of a semilinear Maxwell type equation, in
even dimension, greater than four. These solutions are critical points of a
functional which is strongly degenerate because of the presence of the exterior
derivative. We prove that, assuming a suitable convexity condition on the
nonlinearity, the equation possesses infinitely many finite energy solutions.
|
Topic modeling is commonly used to analyze and understand large document
collections. However, in practice, users want to focus on specific aspects or
"targets" rather than the entire corpus. For example, given a large collection
of documents, users may want only a smaller subset which more closely aligns
with their interests, tasks, and domains. In particular, our paper focuses on
large-scale document retrieval with high recall where any missed relevant
documents can be critical. A simple keyword matching search is generally not
effective nor efficient as 1) it is difficult to find a list of keyword queries
that can cover the documents of interest before exploring the dataset, 2) some
documents may not contain the exact keywords of interest but may still be
highly relevant, and 3) some words have multiple meanings, which would result
in irrelevant documents included in the retrieved subset. In this paper, we
present TopicSifter, a visual analytics system for interactive search space
reduction. Our system utilizes targeted topic modeling based on nonnegative
matrix factorization and allows users to give relevance feedback in order to
refine their target and guide the topic modeling to the most relevant results.
|
In the domain of pattern recognition, using the CovDs (Covariance
Descriptors) to represent data and taking the metrics of the resulting
Riemannian manifold into account have been widely adopted for the task of image
set classification. Recently, it has been proven that infinite-dimensional
CovDs are more discriminative than their low-dimensional counterparts. However,
the form of infinite-dimensional CovDs is implicit and the computational load
is high. We propose a novel framework for representing image sets by
approximating infinite-dimensional CovDs in the paradigm of the Nystr\"om
method based on a Riemannian kernel. We start by modeling the images via CovDs,
which lie on the Riemannian manifold spanned by SPD (Symmetric Positive
Definite) matrices. We then extend the Nystr\"om method to the SPD manifold and
obtain the approximations of CovDs in RKHS (Reproducing Kernel Hilbert Space).
Finally, we approximate infinite-dimensional CovDs via these approximations.
Empirically, we apply our framework to the task of image set classification.
The experimental results obtained on three benchmark datasets show that our
proposed approximate infinite-dimensional CovDs outperform the original CovDs.
|
The Novikov equation is a Camassa-Holm type equation with cubic nonlinearity.
This paper aims to prove the asymptotic stability of peakons solutions under
$H^1(\mathbb{R})$-perturbations satisfying that their associated momentum
density defines a non-negative Radon measure. Motivated by Molinet's work, we
shall first prove a Liouville property for $H^1(\mathbb{R})$ global solutions
belonging to a certain class of almost localized functions. More precisely, we
show that such solutions have to be a peakon. The main difficulty in our
analysis in comparison to the Camassa-Holm case comes from the fact that the
momentum is not conserved and may be unbounded along the trajectory. Also, to
prove the Liouville property, we used a new Lyapunov functional not related to
the (not conserved) momentum of the equation.
|
Deep neural networks have achieved remarkable success in a wide range of
practical problems. However, due to the inherent large parameter space, deep
models are notoriously prone to overfitting and difficult to be deployed in
portable devices with limited memory. In this paper, we propose an iterative
hard thresholding (IHT) approach to train Skinny Deep Neural Networks (SDNNs).
An SDNN has much fewer parameters yet can achieve competitive or even better
performance than its full CNN counterpart. More concretely, the IHT approach
trains an SDNN through following two alternative phases: (I) perform hard
thresholding to drop connections with small activations and fine-tune the other
significant filters; (II)~re-activate the frozen connections and train the
entire network to improve its overall discriminative capability. We verify the
superiority of SDNNs in terms of efficiency and classification performance on
four benchmark object recognition datasets, including CIFAR-10, CIFAR-100,
MNIST and ImageNet. Experimental results clearly demonstrate that IHT can be
applied for training SDNN based on various CNN architectures such as NIN and
AlexNet.
|
We generalise the finite range momentum and density dependent
Seyler-Blanchard nucleon-nucleon effective interaction to the case of
interaction between two baryons. This effective interaction is then used to
describe dense hadronic matter relevant to neutron stars in the nonrelativistic
Thomas-Fermi approach. We investigate the behaviour of nuclear symmetry energy
in dense nuclear and hyperon matter relevant to neutron stars. It is found that
the nuclear symmetry energy always increases with density in hyperon matter
unlike the situation in nuclear matter. This rising characteristic of the
symmetry energy in presence of hyperons may have significant implications on
the mass-radius relationship and the cooling properties of neutron stars. We
have also noted that with the appearance of hyperons, the equation of state
calculated in this model remains causal at high density.
|
In this paper we study a new conjecture concerning Kato's Euler system of
zeta elements for elliptic curves $E$ over $\mathbb{Q}$. This conjecture, which
we refer to as the `Generalized Perrin-Riou Conjecture', predicts a precise
congruence relation between a `Darmon-type derivative' of the zeta element of
$E$ over an arbitrary real abelian field and the critical value of an
appropriate higher derivative of the $L$-function of $E$ over $\mathbb{Q}$. We
prove that the conjecture specializes in the relevant case of analytic rank one
to recover Perrin-Riou's conjecture on the logarithm of Kato's zeta element.
Under mild hypotheses we also prove that the `order of vanishing' part of the
conjecture is valid in arbitrary rank. An Iwasawa-theoretic analysis of our
approach leads to the formulation and proof of a natural higher rank
generalization of Rubin's formula concerning derivatives of $p$-adic
$L$-functions. In addition, we establish a concrete and apparently new
connection between the $p$-part of the classical Birch and Swinnerton-Dyer
Formula and the Iwasawa Main Conjecture in arbitrary rank and for arbitrary
reduction at $p$. In a forthcoming paper we will show that the Generalized
Perrin-Riou Conjecture implies (in arbitrary rank) the conjecture of Mazur and
Tate concerning congruences for modular elements and, by using this approach,
we are able to give a proof, under certain mild and natural hypotheses, that
the Mazur-Tate Conjecture is valid in analytic rank one.
|
We develop the formalism required to study the nonlinear interaction of modes
in rotating Newtonian stars in the weakly nonlinear regime. The formalism
simplifies and extends previous treatments. At linear order, we elucidate and
extend slightly a formalism due to Schutz, show how to decompose a general
motion of a rotating star into a sum over modes, and obtain uncoupled equations
of motion for the mode amplitudes under the influence of an external force.
Nonlinear effects are added perturbatively via three-mode couplings. We
describe a new, efficient way to compute the coupling coefficients, to zeroth
order in the stellar rotation rate, using spin-weighted spherical harmonics.
We apply this formalism to derive some properties of the coupling
coefficients relevant to the nonlinear interactions of unstable r-modes in
neutron stars, postponing numerical integrations of the coupled equations of
motion to a later paper. From an astrophysical viewpoint, the most interesting
result of this paper is that many couplings of r-modes to other rotational
modes (modes with zero frequencies in the non-rotating limit) are small: either
they vanish altogether because of various selection rules, or they vanish to
lowest order in the angular velocity. In zero-buoyancy stars, the coupling of
three r-modes is forbidden entirely and the coupling of two r-modes to one
hybrid rotational mode vanishes to zeroth order in rotation frequency. In
incompressible stars, the coupling of any three rotational modes vanishes to
zeroth order in rotation frequency.
|
The set-colouring Ramsey number $R_{r,s}(k)$ is defined to be the minimum $n$
such that if each edge of the complete graph $K_n$ is assigned a set of $s$
colours from $\{1,\ldots,r\}$, then one of the colours contains a monochromatic
clique of size $k$. The case $s = 1$ is the usual $r$-colour Ramsey number, and
the case $s = r - 1$ was studied by Erd\H{o}s, Hajnal and Rado in 1965, and by
Erd\H{o}s and Szemer\'edi in 1972.
The first significant results for general $s$ were obtained only recently, by
Conlon, Fox, He, Mubayi, Suk and Verstra\"ete, who showed that $R_{r,s}(k) =
2^{\Theta(kr)}$ if $s/r$ is bounded away from $0$ and $1$. In the range $s = r
- o(r)$, however, their upper and lower bounds diverge significantly. In this
note we introduce a new (random) colouring, and use it to determine
$R_{r,s}(k)$ up to polylogarithmic factors in the exponent for essentially all
$r$, $s$ and $k$.
|
This paper studies the q-learning, recently coined as the continuous time
counterpart of Q-learning by Jia and Zhou (2023), for continuous time
Mckean-Vlasov control problems in the setting of entropy-regularized
reinforcement learning. In contrast to the single agent's control problem in
Jia and Zhou (2023), the mean-field interaction of agents renders the
definition of the q-function more subtle, for which we reveal that two distinct
q-functions naturally arise: (i) the integrated q-function (denoted by $q$) as
the first-order approximation of the integrated Q-function introduced in Gu,
Guo, Wei and Xu (2023), which can be learnt by a weak martingale condition
involving test policies; and (ii) the essential q-function (denoted by $q_e$)
that is employed in the policy improvement iterations. We show that two
q-functions are related via an integral representation under all test policies.
Based on the weak martingale condition and our proposed searching method of
test policies, some model-free learning algorithms are devised. In two
examples, one in LQ control framework and one beyond LQ control framework, we
can obtain the exact parameterization of the optimal value function and
q-functions and illustrate our algorithms with simulation experiments.
|
Building up on our previous works regarding $q$-deformed $P$-partitions, we
introduce a new family of subalgebras for the ring of quasisymmetric functions.
Each of these subalgebras admits as a basis a $q$-analogue to Gessel's
fundamental quasisymmetric functions where $q$ is equal to a complex root of
unity. Interestingly, the basis elements are indexed by sets corresponding to
an intermediary statistic between peak and descent sets of permutations that we
call extended peak.
|
The thermodynamic and kinetic properties of mono and di-vacancy defects in
cubic (para-electric) barium titanate are studied by means of
density-functional theory calculations. It is determined which vacancy types
prevail for given thermodynamic boundary conditions. The calculations confirm
the established picture that vacancies occur in their nominal charge states
almost over the entire band gap. For the dominating range of the band gap the
di-vacancy binding energies are constant and negative. The system, therefore,
strives to achieve a state in which under metal-rich (oxygen-rich) conditions
all metal (oxygen) vacancies are bound in di-vacancy clusters. The migration
barriers are calculated for mono-vacancies in different charge states. Since
oxygen vacancies are found to readily migrate at typical growth temperatures,
di-vacancies can be formed at ease. The key results of the present study with
respect to the thermodynamic behavior of mono and di-vacancies influence the
initial defect distribution in the ferroelectric phases and therefore the
conditions for aging.
|
An experimental group at Beijing[Yueyang Zhai, ${\it et. al.}$, Phys. Rev. A
${\bf 87}$, 063638 (2013)] introduced the method of standing-wave pulse
sequence for efficiently preparing ultracold bosonic atoms into a specific
excited band in a 1-dimensional optical lattice. Here, we report a theoretical
extension of their work to the problem of 1-dimensional bichromatic
superlattice. We find that varying the lattice parameters leads to the
so-called Dirac point where a pair of excited bands crosses. This paper thus
discusses ${\it simultaneously}$ the efficient excitation of the wave packet to
the proximity of the Dirac point and its subsequent dynamics in the force field
of a parabolic trap. With the aid of a toy model, we theoretically unravel the
mechanism of the efficient preparation, and then numerically explore optimal
pulse-sequence parameters for a realistic situation. We find an optimized
sequence of a bichromatic optical lattice that excites more than 99% of the
atoms to the 1st and 2nd excited bands within 100 $\mu$s without the harmonic
trap. Our main finding is that the system permitting the Dirac point possesses
a region of parameters where the excited energy bands become nearly parabolic,
conducive to robust coherence and isochronicity. We also provide an appropriate
data set for future experimentation, including effects of the atom-atom
interaction by way of the mean-field nonlinear term.
|
We consider a free liquid sheet, taking into account the dependence of
surface tension on temperature, or concentration of some pollutant. The sheet
dynamics are described within a long-wavelength description. In the presence of
viscosity, local thinning of the sheet is driven by a strong temperature
gradient across the pinch region, resembling a shock. As a result, for long
times the sheet thins exponentially, leading to breakup. We describe the quasi
one-dimensional thickness, velocity, and temperature profiles in the pinch
region in terms of similarity solutions, which posses a universal structure.
Our analytical description agrees quantitatively with numerical simulations.
|
Paircorrelations and the magnetic susceptibility of electrons in a spherical
cavity are studied both for grand canonical and the canonical ensemble. The
coupling constant of the $BCS$ Hamiltonian is adjusted to experimental values
of the gap parameter. The gap parameter is found to increase for small grains
as a consequence of the pronounced shell structure in the spectrum of the
spherical cavity. The sharp phase transition at $T_c$ is smeared out for the
canonical ensemble. The strong paramagnetic susceptibility of the normal
electrons in the cavity is reduced by the superconductivity, but it remains
positive.
|
A new type of stepsize, which was recently introduced by Liu and Liu
(Optimization, 67(3), 427-440, 2018), is called approximately optimal stepsize
and is quit efficient for gradient method. Interestingly, all gradient methods
can be regarded as gradient methods with approximately optimal stepsizes. In
this paper, based on the work (Numer. Algorithms 78(1), 21-39, 2018), we
present an improved gradient method with approximately optimal stepsize based
on conic model for unconstrained optimization. If the objective function $ f $
is not close to a quadratic on the line segment between the current and latest
iterates, we construct a conic model to generate approximately optimal stepsize
for gradient method if the conic model can be used; otherwise, we construct
some quadratic models to generate approximately optimal stepsizes for gradient
method. The convergence of the proposed method is analyzed under suitable
conditions. Numerical comparisons with some well-known conjugate gradient
software packages such as CG$ \_ $DESCENT (SIAM J. Optim. 16(1), 170-192, 2005)
and CGOPT (SIAM J. Optim. 23(1), 296-320, 2013) indicate the proposed method is
very promising.
|
Offloading compute-intensive kernels to hardware accelerators relies on the
large degree of parallelism offered by these platforms. However, the effective
bandwidth of the memory interface often causes a bottleneck, hindering the
accelerator's effective performance. Techniques enabling data reuse, such as
tiling, lower the pressure on memory traffic but still often leave the
accelerators I/O-bound. A further increase in effective bandwidth is possible
by using burst rather than element-wise accesses, provided the data is
contiguous in memory.
In this paper, we propose a memory allocation technique, and provide a
proof-of-concept source-to-source compiler pass, that enables such burst
transfers by modifying the data layout in external memory. We assess how this
technique pushes up the memory throughput, leaving room for exploiting
additional parallelism, for a minimal logic overhead.
|
A family $\mathscr{I} \subseteq [\omega]^\omega$ such that for all finite
$\{X_i\}_{i\in n}\subseteq \mathcal I$ and $A \in \mathscr{I} \setminus
\{X_i\}_{i\in n}$, the set $A \setminus \bigcup_{i < n} X_i$ is infinite, is
said to be ideal independent. An ideal independent family which is maximal
under inclusion is said to be a maximal ideal independent family and the least
cardinality of such family is denoted $\mathfrak{s}_{mm}$.
We show that $\mathfrak{u}\leq\mathfrak{s}_{mm}$, which in particular
establishes the independence of $\mathfrak{s}_{mm}$ and $\mathfrak{i}$. Given
an arbitrary set $C$ of uncountable cardinals, we show how to simultaneously
adjoin via forcing maximal ideal independent families of cardinality $\lambda$
for each $\lambda\in C$, thus establishing the consistency of $C\subseteq
\hbox{spec}(\mathfrak{s}_{mm})$. Assuming $\mathsf{CH}$, we construct a maximal
ideal independent family, which remains maximal after forcing with any proper,
$^\omega\omega$-bounding, $p$-point preserving forcing notion and evaluate
$\mathfrak{s}_{mm}$ in several well studied forcing extensions.
|
We prove the commutativity of the first two nontrivial integrals of motion
for quantum spin chains with elliptic form of the exchange interaction. We also
show thair linear independence for the numbers of spins larger than 4. As a
byproduct, we obtained several identities between elliptic Weierstrass
functions of three and four arguments.
|
Employing a microscopic transport model we investigate the evolution of high
energetic jets moving through a viscous medium. For the scenario of an
unstoppable jet we observe a clearly strong collective behavior for a low
dissipative system $\eta/s \approx 0.005$, leading to the observation of
cone-like structures. Increasing the dissipation of the system to $\eta/s
\approx 0.32$ the Mach Cone structure vanishes. Furthermore, we investigate
jet-associated particle correlations. A double-peak structure, as observed in
experimental data, is even for low-dissipative systems not supported, because
of the large influence of the head shock.
|
The hadronic properties of the $\rho$ meson produced in the inclusive
photonuclear reaction have been investigated. The elementary reaction occurring
in the nucleus is assumed as $\gamma N \to \rho^0 N$. The $\rho$ meson, while
propagating through the nucleus, interacts with the nuclear particles, and
therefore, the properties of the $\rho$ meson can be modified because of this
interaction. Being a short-lived particle, the $\rho$ meson decays to various
elementary particles, such as, $e^+e^-$, $\pi^+\pi^-$, .... etc. The $e^+e^-$
invariant mass, i.e., the $\rho$ meson mass, distribution spectra have been
calculated to extract the information about the parameters, viz., mass and
width, of the $\rho$ meson in the nucleus. The calculated results have been
compared with the data reported from Jefferson Laboratory.
|
Li et al. (Science Advances, 29 January, p. eabe3068) claim the discovery of
two improper ferroelectrics, dabcoHClO4 and dabcoHBF4 (dabco =
1,4-diazabicyclo[2.2.2]octane), and that these materials exhibit superior
pyroelectric figures of merit. This information is misleading due to the
fundamental methodological errors and false conclusions, not to mention that
these ferroelectrics were reported over 20 years ago. They are proper
ferroelectrics, for which the spontaneous polarization is the macroscopic order
parameter. We show that the useful pyroelectric coefficients of these materials
are about 103 times lower than these reported by Li et al.
|
The motivations for the magnetic moment solution to the solar neutrino
problem are briefly reviewed and the expected values for a number of
observables to be measured by the SNO experiment are calculated assuming three
different solar magnetic field profiles. The observables examined are the
charged current event rate, the ratio of the neutral current to the charged
current event rates and the charged current electron spectrum as well as their
first and second moments. The dependence of results on the hep neutrino flux is
also analysed and a comparison is made with the corresponding oscillation
results.
|
We consider the design and analysis of numerical methods for approximating
positive solutions to nonlinear geometric elliptic partial differential
equations containing critical exponents. This class of problems includes the
Yamabe problem and the Einstein constraint equations, which simultaneously
contain several challenging features: high spatial dimension n >= 3, varying
(potentially non-smooth) coefficients, critical (even super-critical)
nonlinearity, non-monotone nonlinearity (arising from a non-convex energy), and
spatial domains that are typically Riemannian manifolds rather than simply open
sets in Rn. These problems may exhibit multiple solutions, although only
positive solutions typically have meaning. This creates additional complexities
in both the theory and numerical treatment of such problems, as this feature
introduces both non-uniqueness as well as the need to incorporate an inequality
constraint into the formulation. In this work, we consider numerical methods
based on Galerkin-type discretization, covering any standard bases construction
(finite element, spectral, or wavelet), and the combination of a barrier method
for nonconvex optimization and global inexact Newton-type methods for dealing
with nonconvexity and the presence of inequality constraints. We first give an
overview of barrier methods in non-convex optimization, and then develop and
analyze both a primal barrier energy method for this class of problems. We then
consider a sequence of numerical experiments using this type of barrier method,
based on a particular Galerkin method, namely the piecewise linear finite
element method, leverage the FETK modeling package. We illustrate the behavior
of the primal barrier energy method for several examples, including the Yamabe
problem and the Hamiltonian constraint.
|
The cosmology of a brane-universe embedded in a higher dimensional bulk
spacetime presents some peculiarities not seen in ordinary (3+1) dimensional
gravity. I summarize the current understanding, with emphasis on the suggestion
by Randall and Sundrum that the bulk is 5-D anti-deSitter space, leading to a
solution of the weak scale hierarchy problem.
|
We study the regularity of weak solutions to the 3D valued stationary Hall
magnetohydrodynamic equations on $ \Bbb R^2$. We prove that every weak solution
is smooth. Furthermore, we prove a Liouville type theorem for the Hall
equations.
|
The structure of magnetic flux ropes injected into the solar wind during
reconnection in the coronal atmosphere is explored with particle-in-cell
simulations and compared with in situ measurements of magnetic "switchbacks"
from the Parker Solar Probe. We suggest that multi-x-line reconnection between
open and closed flux in the corona injects flux ropes into the solar wind and
that these flux ropes convect outward over long distances before eroding due to
reconnection. Simulations that explore the magnetic structure of flux ropes in
the solar wind reproduce the following key features of the switchback
observations: a rapid rotation of the radial magnetic field into the transverse
direction, which is a consequence of reconnection with a strong guide field;
and the potential to reverse the radial field component. The potential
implication of the injection of large numbers of flux ropes in the coronal
atmosphere for understanding the generation of the solar wind is discussed.
|
The quantum transport properties of a graphene kirigami similar to those
studied in recent experiments are calculated in the regime of elastic,
reversible deformations. Our results show that, at low electronic densities,
the conductance profile of such structures replicates that of a system of
coupled quantum dots, characterized by a sequence of minibands and stop-gaps.
The conductance and I-V curves have different characteristics in the distinct
stages of elastic deformation that characterize the elongation of these
structures. Notably, the effective coupling between localized states is
strongly reduced in the small elongation stage, whereas in the large elongation
regime the development of strong, localized pseudomagnetic field barriers can
reinforce the coupling and reestablish resonant tunneling across the kirigami.
This provides an interesting example of interplay between geometry and
pseudomagnetic field-induced confinement. The alternating miniband and
stop-gaps in the transmission lead to I-V characteristics with negative
differential conductance in well defined energy/doping ranges. These effects
should be stable in a realistic scenario that includes edge roughness and
Coulomb interactions, as these are expected to further promote localization of
states at low energies in narrow segments of graphene nanostructures.
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In this paper we find monomial bases for the integer cohomology rings of
compact wonderful models of toric arrangements. In the description of the
monomials various combinatorial objects come into play: building sets, nested
sets, and the fan of a suitable toric variety. We provide some examples
computed via a SageMath program and then we focus on the case of the toric
arrangements associated with root systems of type A. Here the combinatorial
description of our basis offers a geometrical point of view on the relation
between some Eulerian statistics on the symmetric group.
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In this paper we investigate the stochastic 3D Navier-Stokes equations
perturbed by linear multiplicative Gaussian noise of convolution type by
transformation to random PDEs. We are not interested in the regularity of the
initial data. We focus on obtaining bounds from below for the life span
associated with regular initial data. The key point of the proof is the fixed
point argument.
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Here, we provide revised gene models for D. ananassae, D. yakuba, and D.
simulans, which include UTRs and empirically verified intron-exon boundaries,
as well as ortholog groups identified using a fuzzy reciprocal-best-hit blast
comparison. Using these revised annotations, we perform differential expression
testing using the cufflinks suite to provide a broad overview of differential
expression between reproductive tissues and the carcass. We identify thousands
of genes that are differentially expressed across tissues in D. yakuba and D.
simulans, with roughly 60% agreement in expression patterns of orthologs in D.
yakuba and D. simulans. We identify several cases of putative polycistronic
transcripts, pointing to a combination of transcriptional read-through in the
genome as well as putative gene fusion and fission events across taxa. We
furthermore identify hundreds of lineage specific genes in each species with no
blast hits among transcripts of any other Drosophila species, which are
candidates for neofunctionalized proteins and a potential source of genetic
novelty.
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The interatomic exchange interactions and Curie temperatures in Ni-based full
Heusler alloys Ni2MnX with X=Ga, In, Sn and Sb are studied within the framework
of the density-functional theory. The calculation of the exchange parameters is
based on the frozen-magnon approach. Despite closeness of the experimental
Curie temperatures for all four systems their magnetism appeared to differ
strongly. This difference involves both the Mn-Mn and Mn-Ni exchange
interactions. The Curie temperatures, Tc, are calculated within the mean-field
approximation by solving a matrix equation for a multi-sublattice system. Good
agreement with experiment for all four systems is obtained. The role of
different exchange interactions in the formation of Tc of the systems is
discussed.
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In this paper, memories built from components subject to transient faults are
considered. A fault-tolerant memory architecture based on low-density
parity-check codes is proposed and the existence of reliable memories for the
adversarial failure model is proved. The proof relies on the expansion property
of the underlying Tanner graph of the code. An equivalence between the
Taylor-Kuznetsov (TK) scheme and Gallager B algorithm is established and the
results are extended to the independent failure model. It is also shown that
the proposed memory architecture has lower redundancy compared to the TK
scheme. The results are illustrated with specific numerical examples.
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Weak-scale supersymmetry remains to be one of the best-motivated theories of
physics beyond the Standard Model. We evaluate the sensitivities of the High
Luminosity (HL) and High Energy (HE) upgrades of the LHC to gluinos and stops,
decaying through the simplified topologies $\tilde{g} \to q \bar{q} \chi^0$,
$\tilde{g} \to t \bar{t} \chi^0$ and $\tilde{t} \to t \tilde{\chi}^0$. Our
HL-LHC analyses improve on existing experimental projections by optimizing the
acceptance of kinematic variables. The HE-LHC studies represent the first 27
TeV analyses. We find that the HL-(HE-)LHC with 3 ab$^{-1}$ (15 ab$^{-1}$) of
integrated luminosity will be sensitive to the masses of gluinos and stops at
3.2 (5.7) TeV and 1.5 (2.7) TeV, respectively, decaying to massless
neutralinos.
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We study initial-boundary value problems for the Lagrangian averaged alpha
models for the equations of motion for the corotational Maxwell and inviscid
fluids in 2D and 3D. We show existence of (global in time) dissipative
solutions to these problems. We also discuss the idea of dissipative solution
in an abstract Hilbert space framework.
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We study the complexity of computing the commuting-operator value $\omega^*$
of entangled XOR games with any number of players. We introduce necessary and
sufficient criteria for an XOR game to have $\omega^* = 1$, and use these
criteria to derive the following results:
1. An algorithm for symmetric games that decides in polynomial time whether
$\omega^* = 1$ or $\omega^* < 1$, a task that was not previously known to be
decidable, together with a simple tensor-product strategy that achieves value 1
in the former case. The only previous candidate algorithm for this problem was
the Navascu\'{e}s-Pironio-Ac\'{i}n (also known as noncommutative Sum of Squares
or ncSoS) hierarchy, but no convergence bounds were known.
2. A family of games with three players and with $\omega^* < 1$, where it
takes doubly exponential time for the ncSoS algorithm to witness this (in
contrast with our algorithm which runs in polynomial time).
3. A family of games achieving a bias difference $2(\omega^* - \omega)$
arbitrarily close to the maximum possible value of $1$ (and as a consequence,
achieving an unbounded bias ratio), answering an open question of Bri\"{e}t and
Vidick.
4. Existence of an unsatisfiable phase for random (non-symmetric) XOR games:
that is, we show that there exists a constant $C_k^{\text{unsat}}$ depending
only on the number $k$ of players, such that a random $k$-XOR game over an
alphabet of size $n$ has $\omega^* < 1$ with high probability when the number
of clauses is above $C_k^{\text{unsat}} n$.
5. A lower bound of $\Omega(n \log(n)/\log\log(n))$ on the number of levels
in the ncSoS hierarchy required to detect unsatisfiability for most random
3-XOR games. This is in contrast with the classical case where the $n$-th level
of the sum-of-squares hierarchy is equivalent to brute-force enumeration of all
possible solutions.
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We propose an experiment to test the effects of gravity and acceleration on
quantum entanglement in space-based setups. We show that the entanglement
between excitations of two Bose-Einstein condensates is degraded after one of
them undergoes a change in the gravitational field strength. This prediction
can be tested if the condensates are initially entangled in two separate
satellites while being in the same orbit and then one of them moves to a
different orbit. We show that the effect is observable in a typical orbital
manoeuvre of nanosatellites like CanX4 and CanX5.
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We consider dynamical realization of the democratic type Yukawa coupling
matrices as the Pendelton-Ross infrared fixed points.?Such fixed points of the
Yukawa couplings become possible by introducing many Higgs fields, which are
made superheavy but one massless mode. Explicitly, we consider a strongly
coupled GUT based on $SU(5) \times SU(5)$, where rapid convergence to the
infrared fixed point generates sufficiently large mass hierarchy for quarks and
leptons. Especially, it is found that the remarkable difference between mixing
angles in the quark and lepton sectors may be explained as a simple dynamical
consequence. We also discuss a possible scenario leading to the realistic mass
spectra and mixing angles for quarks and leptons. In this scheme, the Yukawa
couplings not only for top but also for bottom appear close to their
quasi-fixed points at low energy and, therefore, $\tan \beta$ should be large.
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We consider the susceptibility function Psi(z) of a piecewise expanding
unimodal interval map f with unique acim mu, a perturbation X, and an
observable phi. Combining previous results (deduced from spectral properties of
Ruelle transfer operators) with recent work of Breuer-Simon (based on
techniques from the spectral theory of Jacobi matrices and a classical paper of
Agmon), we show that density of the postcritical orbit (a generic condition)
implies that Psi(z) has a strong natural boundary on the unit circle. The
Breuer-Simon method provides uncountably many candidates for the outer
functions of Psi(z), associated to precritical orbits. If the perturbation X is
horizontal, a generic condition (Birkhoff typicality of the postcritical orbit)
implies that the nontangential limit of the Psi(z) as z tends to 1 exists and
coincides with the derivative of the acim with respect to the map (linear
response formula). Applying the Wiener-Wintner theorem, we study the
singularity type of nontangential limits as z tends to e^{i\omega}. An
additional LIL typicality assumption on the postcritical orbit gives stronger
results.
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The nearest neighbor two-point correlation function of the $Z$-invariant
inhomogeneous eight-vertex model in the thermodynamic limit is computed using
the free field representation.
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The topological containment problem is known to be polynomial-time solvable
for any fixed pattern graph $H$, but good characterisations have been found for
only a handful of non-trivial pattern graphs. The complete graph on five
vertices, $K_5$, is one pattern graph for which a characterisation has not been
found. The discovery of such a characterisation would be of particular
interest, due to the Haj\'os Conjecture. One step towards this may be to find a
good characterisation of graphs that do not topologically contain the simpler
pattern graph $K_5^-$, obtained by removing a single edge from $K_5$.
This paper makes progress towards achieving this, by showing that every
4-connected graph must contain a $K_5^-$-subdivision.
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In case of non-dissipative tissue the inverse problem of thermoacoustic
imaging basically consists of two inverse problems. First, a function $\phi$
depending on the \emph{electromagnetic absorption function}, is estimated from
one of three types of projections (spherical, circular or planar) and secondly,
the \emph{electromagnetic absorption function} is estimated from $\phi$. In
case of dissipative tissue, it is no longer possible to calculate explicitly
the projection of $\phi$ from the respective pressure data (measured by point,
planar or line detectors). The goal of this paper is to derive for each of the
three types of pressure data, an integral equation that allows estimating the
respective projection of $\phi$. The advantage of this approach is that all
known reconstruction formulas for $\phi$ from the respective projection can be
exploited.
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Adapting Large Language Models (LLMs) to new tasks through fine-tuning has
been made more efficient by the introduction of Parameter-Efficient Fine-Tuning
(PEFT) techniques, such as LoRA. However, these methods often underperform
compared to full fine-tuning, particularly in scenarios involving complex
datasets. This issue becomes even more pronounced in complex domains,
highlighting the need for improved PEFT approaches that can achieve better
performance. Through a series of experiments, we have uncovered two critical
insights that shed light on the training and parameter inefficiency of LoRA.
Building on these insights, we have developed HydraLoRA, a LoRA framework with
an asymmetric structure that eliminates the need for domain expertise. Our
experiments demonstrate that HydraLoRA outperforms other PEFT approaches, even
those that rely on domain knowledge during the training and inference phases.
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Our recent work demonstrates a correlation between the high-velocity blue
edge, $v_{edge}$, of the iron-peak Fe/Co/Ni $H$-band emission feature and the
optical light curve shape of normal, transitional and sub-luminous type Ia
Supernovae (SNe Ia). We explain this correlation in terms of SN Ia physics.
$v_{edge}$ corresponds to the sharp transition between the complete and
incomplete silicon burning regions in the ejecta. It measures the point in
velocity space where the outer $^{56}$Ni mass fraction, $X_{\rm{Ni}}$, falls to
the order of 0.03-0.10. For a given $^{56}$Ni mass, $M(^{56}Ni)$, $v_{edge}$ is
sensitive to the specific kinetic energy $E_{\rm kin}$($M(^{56}Ni)/M_{WD}$) of
the corresponding region. Combining $v_{edge}$ with light curve parameters
(i.e., s$_{BV}$, $\Delta m_{15,s}$ in $B$ and $V$) allows us to distinguish
between explosion scenarios. The correlation between $v_{edge}$ and light-curve
shape is consistent with explosion models near the Chandrasekhar limit.
However, the available sub-$M_{Ch}$ WD explosion model based on SN 1999by
exhibits velocities which are too large to explain the observations. Finally,
the sub-luminous SN 2015bo exhibits signatures of a dynamical merger of two WDs
demonstrating diversity among explosion scenarios at the faint end of the SNe
Ia population.
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The DArk Matter Particle Explorer (DAMPE) is well suitable for searching for
monochromatic and sharp $\gamma$-ray structures in the GeV$-$TeV range thanks
to its unprecedented high energy resolution. In this work, we search for
$\gamma$-ray line structures using five years of DAMPE data. To improve the
sensitivity, we develop two types of dedicated data sets (including the BgoOnly
data which is the first time to be used in the data analysis for the
calorimeter-based gamma-ray observatories) and adopt the signal-to-noise ratio
optimized regions of interest (ROIs) for different DM density profiles. No line
signals or candidates are found between 10 and 300 GeV in the Galaxy. The
constraints on the velocity-averaged cross section for $\chi\chi \to
\gamma\gamma$ and the decay lifetime for $\chi \to \gamma\nu$, both at 95%
confidence level, have been calculated and the systematic uncertainties have
been taken into account. Comparing to the previous Fermi-LAT results, though
DAMPE has an acceptance smaller by a factor of $\sim 10$, similar constraints
on the DM parameters are achieved and below 100 GeV the lower limits on the
decay lifetime are even stronger by a factor of a few. Our results demonstrate
the potential of high-energy-resolution observations on dark matter detection.
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Images in the $H\alpha$ emission line are presented for 35 nearby objects
observed with the 6-m BTA telescope. Three of them, NGC 3377, NGC 3384, and NGC
3390, are bright E and S0 galaxies, one is an edge-on Sd galaxy UGC 7321, two
are remote globular clusters associated with M 31, and the rest are dwarf
galaxies of morphological types dIr, dTr, dSph, BCD, and Sm. The measured
$H\alpha$ fluxes are used to estimate the integral $(SFR)$ and specific
$(sSFR)$ star formation rates for these galaxies. The values of $\log[sSFR]$
for all these objects lie below a limit of $-0.4$(Gyr$^{-1})$. We note that the
emission disk for the nearest superthin edge-on galaxy UGC 7321 has an
extremely large axis ratio of $a/b = 38.$
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The combustion instability is investigated computationally for a
multi-injector rocket engine using the flamelet progress variable (FPV) model.
A C++ code is developed based on OpenFOAM 4.0 to apply the combustion model.
Flamelet tables are generated for methane/oxygen combustion at the background
pressure of $200$ bar using a 12-species chemical mechanism. A power law is
determined for rescaling the reaction rate for the progress variable to address
the pressure effect. The combustion is also simulated by the one-step-kinetics
(OSK) method for comparison with the FPV approach. A study of combustion
instability shows that a longitudinal mode of $1500$ Hz and a tangential
standing wave of $2500$ Hz are dominant for both approaches. While the
amplitude of the longitudinal mode remains almost the same for both approaches,
the tangential standing wave achieves a larger amplitude in the FPV simulation.
A preliminary study of the resonance in the injectors, which is driven by the
longitudinal-mode oscillation in the combustion chamber, is also presented.
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