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We present here the proof for an alternative procedure to convert a Push Down
Automata (PDA) into a Context Free Grammar (CFG). The procedure involves
intermediate conversion to a single state PDA. In view of the authors, this
conversion is conceptually intuitive and can serve as a teaching aid for the
relevant topics.
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Observations of two unclassified Low Mass X-ray Binaries, X1543-624 and
X1556-605, are presented. In the 2-10 keV band the first of the two sources is
a factor two stronger than the other. Both sources do not show X-ray bursts,
dips or eclipses in their X-ray light curves. We find that both spectra are
described by a two-component model consisting of emission from a cool accretion
disk plus a Comptonized blackbody with kTbb ~ 1.5 keV in a low opacity plasma.
The spectrum of X1543-624 hardens from the first to the second observation,
when the source slowly moves from right to left in the colour-colour diagram.
The spectrum of X1556-605 can also be described by a model consisting of a
blackbody plus an unsaturated Comptonization with electron energy kTe ~ 4 keV.
In the first observation, X1543-624 shows evidence of a Fe K emission line at
6.4 keV. Moreover in both observations, the source spectrum exhibits an
emission feature around 0.7 keV, which is interpreted as due to the
superposition of the K edge absorption features of O and Ne elements with
uncommon relative abundances with respect to the solar one (O/O(sun) ~0.3,
Ne/Ne(sun) ~ 2.5). In the spectrum of X1556-605 no emission lines are observed.
We discuss these results and their implications on the source classification
and the accretion geometry on the compact object.
|
This paper exploits the gravitational magnification of SNe Ia to measure
properties of dark matter haloes. The magnification of individual SNe Ia can be
computed using observed properties of foreground galaxies and dark matter halo
models. We model the dark matter haloes of the galaxies as truncated singular
isothermal spheres with velocity dispersion and truncation radius obeying
luminosity dependent scaling laws. A homogeneously selected sample of 175 SNe
Ia from the first 3-years of the Supernova Legacy Survey (SNLS) in the redshift
range 0.2 < z < 1 is used to constrain models of the dark matter haloes
associated with foreground galaxies. The best-fitting velocity dispersion
scaling law agrees well with galaxy-galaxy lensing measurements. We further
find that the normalisation of the velocity dispersion of passive and star
forming galaxies are consistent with empirical Faber-Jackson and Tully-Fisher
relations, respectively. If we make no assumption on the normalisation of these
relations, we find that the data prefer gravitational lensing at the 92 per
cent confidence level. Using recent models of dust extinction we deduce that
the impact of this effect on our results is very small. We also investigate the
brightness scatter of SNe Ia due to gravitational lensing. The gravitational
lensing scatter is approximately proportional to the SN Ia redshift. We find
the constant of proportionality to be B = 0.055 +0.039 -0.041 mag (B < 0.12 mag
at the 95 per cent confidence level). If this model is correct, the
contribution from lensing to the intrinsic brightness scatter of SNe Ia is
small for the SNLS sample.
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We present optical and near-IR spectroscopic observations of the luminous
blue variable SN 2009ip during its remarkable photometric evolution of 2012.
The spectra sample three key points in the SN 2009ip lightcurve, corresponding
to its initial brightening in August (2012-A) and its dramatic rebrightening in
early October (2012-B). Based on line fluxes and velocities measured in our
spectra, we find a surprisingly low I(H-alpha)/I(H-beta) ~ 1.3-1.4 in the
2012-B spectra. Such a ratio implies either a rare Case B recombination
scenario where H-alpha, but not H-beta, is optically thick, or an extremely
high density for the circumstellar material of n_e > 10^13 cm^(-3) The H-alpha
line intensity yields a minimum radiating surface area of >~20,000 AU^2 in
H-alpha at the peak of SN 2009ip's photometric evolution. Combined with the
nature of this object's spectral evolution in 2012, a high circumstellar
density and large radiating surface area imply the presence of a thin disk
geometry around the central star (and, consequently, a possible binary
companion), suggesting that the observed 2012-B rebrightening of SN 2009ip can
be attributed to the illumination of the disk's inner rim by fast-moving ejecta
produced by the underlying events of 2012-A.
|
We present a detailed study of structural, magnetic and thermodynamic
properties of a series of Heusler alloys Fe2-xMnxCrAl (x=0, 0.25, 0.5, 0.75 and
1). Structural investigation of this series is carried out using high
resolution synchrotron X-ray diffraction. Results suggest that with increasing
Mn concentration, the L21 structure of Fe2CrAl is destabilized. The DC
magnetization results show a decrement in paramagnetic (PM) to ferromagnetic
(FM) phase transition temperature (TC) with increasing Mn concentration. From
the systematic analysis of magnetic memory effect, heat capacity, time
dependent magnetization, and DC field dependent AC susceptibility studies it is
observed that, Fe2CrAl exhibits cluster glass(CG)-like transition approximately
at 3.9 K (Tf2). The alloys, Fe1.75Mn0.25CrAl and Fe1.5Mn0.5CrAl exhibit double
CG-like transitions near Tf1~22 K, Tf2~4.2 K and Tf1~30.4 K, Tf2~9.5 K
respectively, however, in Fe1.25Mn0.75CrAl, a single CG-like transition is
noted at Tf2~11.5 K below TC. Interestingly, FeMnCrAl shows the absence of long
ranged magnetic ordering and this alloy undergoes three CG-like transitions at
~ 22 K (Tf*), 16.6 K (Tf1) and 11 K (Tf2). At high temperatures, a detailed
analysis of temperature response of inverse DC susceptibility clearly reveals
the observation of Griffiths phase (GP) above 300 K (T*) in Fe2CrAl and this
phase persists with Mn concentration with a decrement in T*.
|
In a single j-shell calculation we consider the effects of several different
interactions on the values of Gamow-Teller (B(GT)'s) and magnetic moments. The
interactions used are MBZE, J=0 pairing, J_{max} pairing and half and half.
|
Investigation of the interfacial electronic properties of
N,N'-bis(n-octyl)-(1,7&1,6)-dicyanoperylene-3,4:9,10-bisdicarboximide
(PDI8-CN2) organic semiconductor films grown on silicon dioxide is performed by
polarization-resolved second harmonic generation optical spectroscopy, pointing
out a spatial region where charge carriers distribution in the semiconductor
lacks inversion symmetry. By developing a model for nonlinear susceptibility in
the framework of Debye-Huckel screening theory, we show that the experimental
findings can be interpreted as resulting from the presence of a net charge
localized at the silicon dioxide, accompanied by a non-uniform charge
distribution in the organic semiconductor. Photoluminescence analysis further
reinforces this scenario. Reduction-oxidation reactions involving PDI8-CN2 and
water molecules are invoked as physical origin of the localized charge. The
work outlines a sensitive tool to probe the total charge localized at buried
semiconductor/dielectric interfaces in organic thin-film transistors without
resorting to invasive contact-based analyses.
|
We propose defect lines as a useful tool to study bulk perturbations of
conformal field theories, in particular to analyse the induced renormalisation
group flows of boundary conditions. As a concrete example we investigate bulk
perturbations of N=2 supersymmetric minimal models. To these perturbations we
associate a special class of defects between the respective UV and IR theories,
whose fusion with boundary conditions indeed reproduces the behaviour of the
latter under the corresponding RG flows. v2: Some explanations added in section
4, minor changes.
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We present a simple but general framework for constructing quantum circuits
that implement the multiply-controlled unitary $\text{Select}(H) \equiv
\sum_\ell |\ell\rangle\langle\ell|\otimes H_\ell$, where $H = \sum_\ell H_\ell$
is the Jordan-Wigner transform of an arbitrary second-quantised fermionic
Hamiltonian. $\text{Select}(H)$ is one of the main subroutines of several
quantum algorithms, including state-of-the-art techniques for Hamiltonian
simulation. If each term in the second-quantised Hamiltonian involves at most
$k$ spin-orbitals and $k$ is a constant independent of the total number of
spin-orbitals $n$ (as is the case for the majority of quantum chemistry and
condensed matter models considered in the literature, for which $k$ is
typically 2 or 4), our implementation of $\text{Select}(H)$ requires no ancilla
qubits and uses $\mathcal{O}(n)$ Clifford+T gates, with the Clifford gates
applied in $\mathcal{O}(\log^2 n)$ layers and the $T$ gates in $O(\log n)$
layers. This achieves an exponential improvement in both Clifford- and T-depth
over previous work, while maintaining linear gate count and reducing the number
of ancillae to zero.
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We promote the idea of multi-component Dark Matter (DM) to explain results
from both direct and indirect detection experiments. In these models as
contribution of each DM candidate to relic abundance is summed up to meet
WMAP/Planck measurements of $\Omega_{\rm DM}$, these candidates have larger
annihilation cross-sections compared to the single-component DM models. This
results in larger $\gamma$-ray flux in indirect detection experiments of DM. We
illustrate this fact by introducing an extra scalar to the popular single real
scalar DM model. We also present detailed calculations for the vacuum stability
bounds, perturbative unitarity and triviality constraints on this model. As
direct detection experimental results still show some conflict, we kept our
options open, discussing different scenarios with different DM mass zones. In
the framework of our model we make an interesting observation: The existing
direct detection experiments like CDMS II, CoGeNT, CRESST II, XENON 100 or LUX
together with the observation of excess low energy $\gamma$-ray from Galactic
Centre and Fermi Bubble by FGST already have the capability to distinguish
between different DM halo profiles.
|
Majorana bound states (MBS) are well-established in the clean limit in chains
of ferromagnetically aligned impurities deposited on conventional
superconductors with finite spin-orbit coupling. Here we show that these MBS
are very robust against disorder. By performing self-consistent calculations we
find that the MBS are protected as long as the surrounding superconductor show
no large signs of inhomogeneity. We find that longer chains offer more
stability against disorder for the MBS, albeit the minigap decreases, as do
increasing strengths of spin-orbit coupling and superconductivity.
|
We show the correspondence between left invariant flat projective structures
on Lie groups and certain prehomogeneous vector spaces. Moreover by using the
classification theory of prehomogeneous vector spaces, we classify complex Lie
groups admitting irreducible left invariant flat complex projective structures.
As a result, direct sums of special linear Lie algebras sl(2) \oplus sl(m_1)
\oplus \cdots \oplus sl(m_k) admit left invariant flat complex projective
structures if the equality 4 + m_1^2 + \cdots + m_k^2 -k - 4 m_1 m_2 \cdots m_k
= 0 holds. These contain sl(2), sl(2) \oplus sl(3)$, sl(2) \oplus sl(3) \oplus
sl(11) for example.
|
Talk given at the 6th Philosophy-and-Physics-Workshop ``Epistemological
Aspects of the Role of Mathematics in Physical Science'', FEST, Heidelberg,
Feb. 1993
|
We use photoemission spectroscopy to discover the first topological magnet in
three dimensions, the material Co$_2$MnGa.
|
The world is going through one of the most dangerous pandemics of all time
with the rapid spread of the novel coronavirus (COVID-19). According to the
World Health Organisation, the most effective way to thwart the transmission of
coronavirus is to wear medical face masks. Monitoring the use of face masks in
public places has been a challenge because manual monitoring could be unsafe.
This paper proposes an architecture for detecting medical face masks for
deployment on resource-constrained endpoints having extremely low memory
footprints. A small development board with an ARM Cortex-M7 microcontroller
clocked at 480 Mhz and having just 496 KB of framebuffer RAM, has been used for
the deployment of the model. Using the TensorFlow Lite framework, the model is
quantized to further reduce its size. The proposed model is 138 KB post
quantization and runs at the inference speed of 30 FPS.
|
We show that if an ample line bundle L on a nonsingular toric 3-fold
satisfies h^0(L+2K)=0, then L is normally generated. As an application, we show
that the anti-canonical divisor on a nonsingular toric Fano 4-fold is normally
generated.
|
A theory of sketches for arithmetic universes (AUs) is developed.
A restricted notion of sketch, called here "context", is defined with the
property that every non-strict model is uniquely isomorphic to a strict model.
This allows us to reconcile the syntactic, dealt with strictly using universal
algebra, with the semantic, in which non-strict models must be considered.
For any context T, a concrete construction is given of the AU AU<T> freely
generated by it.
A 2-category Con of contexts is defined, with a full and faithful 2-functor
to the 2-category of AUs and strict AU-functors, given by T |-> AU<T>. It has
finite pie limits, and also all pullbacks of a certain class of "extension"
maps. Every object, morphism or 2-cell of Con is a finite structure.
|
Given a finite group $\Gamma$ and a virtual character $\wt$ on it, we
construct a Fock space and associated vertex operators in terms of
representation ring of wreath products $\Gamma\sim S_n$. We recover the
character tables of wreath products $\Gamma\sim S_n$ by vertex operator
calculus. When $\Gamma$ is a finite subgroup of $SU_2$, our construction yields
a group theoretic realization of the basic representations of the affine and
toroidal Lie algebras of $ADE$ type, which can be regarded as a new form of
McKay correspondence.
|
In 2016, the Center for Planetary Science proposed a hypothesis arguing a
comet and/or its hydrogen cloud were a strong candidate for the source of the
Wow! Signal. From 27 November 2016 to 24 February 2017, the Center for
Planetary Science conducted 200 observations in the radio spectrum to validate
the hypothesis. The investigation discovered that comet 266/P Christensen
emitted a radio signal at 1420.25 MHz. The results of this investigation,
therefore, conclude that cometary spectra are detectable at 1420 MHz and, more
importantly, that the 1977 Wow! Signal was a natural phenomenon from a Solar
System body.
|
Many real networks in nature and society share two generic properties: they
are scale-free and they display a high degree of clustering. We show that these
two features are the consequence of a hierarchical organization, implying that
small groups of nodes organize in a hierarchical manner into increasingly large
groups, while maintaining a scale-free topology. In hierarchical networks the
degree of clustering characterizing the different groups follows a strict
scaling law, which can be used to identify the presence of a hierarchical
organization in real networks. We find that several real networks, such as the
World Wide Web, actor network, the Internet at the domain level and the
semantic web obey this scaling law, indicating that hierarchy is a fundamental
characteristic of many complex systems.
|
IrTe2, a layered compound with a triangular iridium lattice, exhibits a
structural phase transition at approximately 250 K. This transition is
characterized by the formation of Ir-Ir bonds along the b-axis. We found that
the breaking of Ir-Ir bonds that occurs in Ir1-xPtxTe2 results in the
appearance of a structural critical point in the T = 0 limit at xc = 0.035.
Although both IrTe2 and PtTe2 are paramagnetic metals, superconductivity at Tc
= 3.1 K is induced by the bond breaking in a narrow range of x > xc in
Ir1-xPtxTe2. This result indicates that structural fluctuations can be involved
in the emergence of superconductivity.
|
The paper reviews two prominent approaches for the measurement of
technological complexity: the method of reflection and the assessment of
technologies' combinatorial difficulty. It discusses their central underlying
assumptions and identifies potential problems related to these. A new measure
of structural complexity is introduced as an alternative. The paper also puts
forward four stylized facts of technological complexity that serve as
benchmarks in an empirical evaluation of five complexity measures (increasing
development over time, larger R&D efforts, more collaborative R&D, spatial
concentration). The evaluation utilizes European patent data for the years 1980
to 2013 and finds the new measure of structural complexity to mirror the four
stylized facts as good as or better than traditional measures.
|
A finite EI category is a small category with finitely many morphisms such
that every endomorphism is an isomorphism. They include finite groups, finite
posets and free categories of finite quivers as special cases. In this paper we
consider the representation types of finite EI categories, describe some
criteria for finite representation type, and use them to classify the
representation types of several classes of finite EI categories with extra
properties.
|
Cracks in clay are significant in geotechnical and geoenvironmental
engineering (e.g., embankment erosion and stability of landfill cover systems).
This article studies the mechanism of nucleation and growth of cracks in clay
at the nanoscale through full-scale molecular dynamics simulations. The clay
adopted is pyrophyllite, and the force field is CLAYFF. The crack formation in
a pyrophyllite clay layer is evaluated under uniaxial tension and simple shear.
The numerical results show that cracks in the nanoscale pyrophyllite clay layer
are brittle and strain-rate dependent. Small strain rate results in low
ultimate tensile/shear strength. As strain rate increases, clay crack shifts
from a single-crack pattern to a multiple-crack one. The cracking mechanism is
investigated from bond breakage analysis at the atomic scale. It is found that
the first bond breakage occurs in the silicon-surface oxygen bond. As a crack
propagates, the relative percentage of broken silicon-surface oxygen bonds is
the smallest compared to other types of metal-oxygen interactions,
demonstrating that the atomic interaction between silicon and surface oxygen
atoms is the strongest. To understand the propagation of cracks, we also study
the stress intensity factor and energy release rate of pyrophyllite and their
size dependence at the atomic scale.
|
I examine a possible spectral distortion of the Cosmic Microwave Background
(CMB) due to its absorption by galactic and intergalactic dust. I show that
even subtle intergalactic opacity of $1 \times 10^{-7}\, \mathrm{mag}\, h\,
\mathrm{Gpc}^{-1}$ at the CMB wavelengths in the local Universe causes
non-negligible CMB absorption and decline of the CMB intensity because the
opacity steeply increases with redshift. The CMB should be distorted even
during the epoch of the Universe defined by redshifts $z < 10$. For this epoch,
the maximum spectral distortion of the CMB is at least $20 \times 10^{-22}
\,\mathrm{Wm}^{-2}\, \mathrm{Hz}^{-1}\, \mathrm{sr}^{-1}$ at 300 GHz being well
above the sensitivity of the COBE/FIRAS, WMAP or Planck flux measurements. If
dust mass is considered to be redshift dependent with noticeable dust abundance
at redshifts 2-4, the predicted CMB distortion is even higher. The CMB would be
distorted also in a perfectly transparent universe due to dust in galaxies but
this effect is lower by one order than that due to intergalactic opacity. The
fact that the distortion of the CMB by dust is not observed is intriguing and
questions either opacity and extinction law measurements or validity of the
current model of the Universe.
|
The negative evolution found in X--ray clusters of galaxies limits the amount
of available hot gas for the inverse Compton scattering of the Cosmic Microwave
Background (the Sunyaev--Zel'dovich effect). Using a parametrisation of the
X-ray luminosity function and its evolution in terms of a coalescence model (as
presented in the analysis of a flux limited X-ray cluster sample by Edge et al.
1990), as well as a simple virialised structure for the clusters (which
requires a gas to total mass fraction $\approxgt 0.1$ in order to reproduce
observed properties of nearby clusters) we show that the Compton distortion $y$
parameter is about two orders of magnitude below the current FIRAS upper
limits. Concerning the anisotropies imprinted on arcmin scales they are
dominated by the hottest undetected objects. We show that they are negligible
(${\Delta T\over T}\approxlt 10^{-7}$) at wavelengths $\lambda\approxgt 1$~mm.
At shorter wavelengths they become more important (${\Delta T\over T}\sim
10^{-6}$ at $\lambda\sim 0.3$~mm), but in fact most clusters will produce an
isolated and detectable feature in sky maps. After removal of these signals,
the fluctuations imprinted by the remaining clusters on the residual radiation
are still much smaller. The conclusion is that X-ray clusters can be ignored as
sources of Cosmic Microwave Background fluctuations.
|
Learning with non-modular losses is an important problem when sets of
predictions are made simultaneously. The main tools for constructing convex
surrogate loss functions for set prediction are margin rescaling and slack
rescaling. In this work, we show that these strategies lead to tight convex
surrogates iff the underlying loss function is increasing in the number of
incorrect predictions. However, gradient or cutting-plane computation for these
functions is NP-hard for non-supermodular loss functions. We propose instead a
novel surrogate loss function for submodular losses, the Lov\'asz hinge, which
leads to O(p log p) complexity with O(p) oracle accesses to the loss function
to compute a gradient or cutting-plane. We prove that the Lov\'asz hinge is
convex and yields an extension. As a result, we have developed the first
tractable convex surrogates in the literature for submodular losses. We
demonstrate the utility of this novel convex surrogate through several set
prediction tasks, including on the PASCAL VOC and Microsoft COCO datasets.
|
In order to characterize the common feature of the general Lorentz violation
models that the local speed of light is variable at ultrahigh energy scale, we
introduced a parameter n to characterize the variation of the speed of light
between inertial systems. And in order not to violate some fundamental
principles and experiments' results, some constraints were imposed on n. Then a
coordinate transformation with the parameter n, which meets the symmetry of
inertial systems, was naturally obtained. But just to satisfy the symmetry of
inertial systems, the expression for n cannot be determined. Inspired by the
idea of DSR model, we then discussed a specific expression for n that makes the
particle's energy have a limit rather than be infinite derived from the Lorentz
model. We found that the modified dispersion relation corresponding to the
specific expression for n is deeply associated with the general formula of
dispersion relation from the DSR. The motivation of introducing such a
parameter n was also discussed. Finally, we discussed the possible LIV effects
from astrophysical observations in GRB events and photon annihilation events.
Using the data from GRB 190114C we investigated the special dispersion relation
obtained in this paper and found that it appears to fit these data better than
the two models corresponding to the first or second order approximation of the
general formula of dispersion relation. And similar to the other Lorentz
violation models corresponding to the subluminal case, the modified dispersion
relation obtained in this paper can also result in increasing the energy
threshold of photon annihilation reaction, which is expected to be verified by
the future energetic photons events.
|
An analysis of single-electron orbits in combined coaxial wiggler and axial
guide magnetic fields is presented. Solutions of the equations of motion are
developed in a form convenient for computing orbital velocity components and
trajectories in the radially dependent wiggler. Simple analytical solutions are
obtained in the radially-uniform-wiggler approximation and a formula for the
derivative of the axial velocity $v_{\|}$ with respect to Lorentz factor
$\gamma$ is derived. Results of numerical computations are presented and the
characteristics of the equilibrium orbits are discussed. The third spatial
harmonic of the coaxial wiggler field gives rise to group $III$ orbits which
are characterized by a strong negative mass regime.
|
The conductance confined at the interface of complex oxide heterostructures
provides new opportunities to explore nanoelectronic as well as nanoionic
devices. Herein we show that metallic interfaces can be realized in
SrTiO3-based heterostructures with various insulating overlayers of amorphous
LaAlO3, SrTiO3 and yttria-stabilized zirconia films. On the other hand, samples
of amorphous La7/8Sr1/8MnO3 films on SrTiO3 substrates remain insulating. The
interfacial conductivity results from the formation of oxygen vacancies near
the interface, suggesting that the redox reactions on the surface of SrTiO3
substrates play an important role.
|
In this paper, we investigate the thermodynamic properties of black holes in
the framework of rainbow gravity. By considering rainbow functions in the
metric of Schwarzschild and Reissner-Nordstr\"{o}m black holes, remnant and
critical masses are found to exist. Demanding the universality of logarithmic
corrections to the semi-classical area law for the entropy leads to
constraining the form of the rainbow functions. The mass output and the
radiation rate for these constrained form of rainbow functions have been
computed for different values of the rainbow parameter $\eta$ and have striking
similarity to those derived from the generalized uncertainty principle.
|
The Glazman-Povzner-Wienholtz theorem states that the completeness of a
manifold, when combined with the semiboundedness of the Schr\"odinger operator
$-\Delta + q$ and suitable local regularity assumptions on $q$, guarantees its
essential self-adjointness. Our aim is to extend this result to Schr\"odinger
operators on graphs. We first obtain the corresponding theorem for
Schr\"odinger operators on metric graphs, allowing in particular distributional
potentials $q\in H^{-1}_{\rm loc}$. Moreover, we exploit recently discovered
connections between Schr\"odinger operators on metric graphs and weighted
graphs in order to prove a discrete version of the Glazman-Povzner-Wienholtz
theorem.
|
We employ dynamical density-matrix renormalization group (DDMRG) and
field-theory methods to determine the frequency-dependent optical conductivity
in one-dimensional extended, half-filled Hubbard models. The field-theory
approach is applicable to the regime of `small' Mott gaps which is the most
difficult to access by DDMRG. For very large Mott gaps the DDMRG recovers
analytical results obtained previously by means of strong-coupling techniques.
We focus on exciton formation at energies below the onset of the absorption
continuum. As a consequence of spin-charge separation, these Mott-Hubbard
excitons are bound states of spinless, charged excitations (`holon-antiholon'
pairs). We also determine exciton binding energies and sizes. In contrast to
simple band insulators, we observe that excitons exist in the Mott-insulating
phase only for a sufficiently strong intersite Coulomb repulsion. Furthermore,
our results show that the exciton binding energy and size are not related in a
simple way to the strength of the Coulomb interaction.
|
We formulate a class of minimal tori in S^3 in terms of classical mechanics,
reveal a curious property of the Clifford torus, and note that the question of
periodicity can be made more explicit in a simple way.
|
We present the results of targeted observations and a survey of 1612-, 1665-,
and 1667-MHz circumstellar OH maser emission from asymptotic giant branch (AGB)
stars and red supergiants (RSGs) in the Small Magellanic Cloud (SMC), using the
Parkes and Australia Telescope Compact Array radio telescopes. No clear OH
maser emission has been detected in any of our observations targeting luminous,
long-period, large-amplitude variable stars, which have been confirmed
spectroscopically and photometrically to be mid- to late-M spectral type. These
observations have probed 3 - 4 times deeper than any OH maser survey in the
SMC. Using a bootstrapping method with LMC and Galactic OH/IR star samples and
our SMC observation upper limits, we have calculated the likelihood of not
detecting maser emission in any of the two sources considered to be the top
maser candidates to be less than 0.05%, assuming a similar pumping mechanism as
the LMC and Galactic OH/IR sources. We have performed a population comparison
of the Magellanic Clouds and used Spitzer IRAC and MIPS photometry to confirm
that we have observed all high luminosity SMC sources that are expected to
exhibit maser emission. We suspect that, compared to the OH/IR stars in the
Galaxy and LMC, the reduction in metallicity may curtail the dusty wind phase
at the end of the evolution of the most massive cool stars. We also suspect
that the conditions in the circumstellar envelope change beyond a simple
scaling of abundances and wind speed with metallicity.
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Let F be a p-adic field, and Gn one of the groups GL(n, F), GSO(2n-1, F),
GSp(2n, F), or GSO(2(n - 1), F). Using the mirabolic subgroup or analogues of
it, and related "derivative" functors, we give an asymptotic expansion of
functions in the Whittaker model of generic representations of Gn, with respect
to a minimal set of characters of subgroups of the maximal torus. Denoting by
Zn the center of Gn, and by Nn the unipotent radical of its standard Borel
subgroup, we characterize generic representations occurring in L2(ZnNn\Gn) in
terms of these characters. This is related to a conjecture of Lapid and Mao for
general split groups, asserting that the generic representations occurring in
L2(ZnNn\Gn) are the generic discrete series; we prove it for the group Gn.
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The large deviations of an infinite moving average process with exponentially
light tails are very similar to those of an i.i.d. sequence as long as the
coefficients decay fast enough. If they do not, the large deviations change
dramatically. We study this phenomenon in the context of functional large,
moderate and huge deviation principles.
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We construct braid group actions on coideal subalgebras of quantized
enveloping algebras which appear in the theory of quantum symmetric pairs. In
particular, we construct an action of the semidirect product of Z^n and the
classical braid group in n strands on the coideal subalgebra corresponding to
the symmetric pair (sl_{2n}(C), sp_{2n}(C)). This proves a conjecture by Molev
and Ragoucy. We expect similar actions to exist for all symmetric Lie algebras.
The given actions are inspired by Lusztig's braid group action on quantized
enveloping algebras and are defined explicitly on generators. Braid group and
algebra relations are verified with the help of the package Quagroup within the
computer algebra program GAP.
|
Ionization front instabilities have long been of interest for their suspected
role in a variety of phenomena in the galaxy, from the formation of bright rims
and 'elephant trunks' in nebulae to triggered star formation in molecular
clouds. Numerical treatments of these instabilities have historically been
limited in both dimensionality and input physics, leaving important questions
about their true evolution unanswered. We present the first three-dimensional
radiation hydrodynamical calculations of both R-type and D-type ionization
front instabilities in galactic environments (i.e., solar metallicity gas).
Consistent with linear stability analyses of planar D-type fronts, our models
exhibit many short-wavelength perturbations growing at early times that later
evolve into fewer large-wavelength structures. The simulations demonstrate that
both self-consistent radiative transfer and three-dimensional flow introduce
significant morphological differences to unstable modes when compared to
earlier two-dimensional approximate models. We find that the amplitude of the
instabilities in the nonlinear regime is primarily determined by the efficiency
of cooling within the shocked neutral shell. Strong radiative cooling leads to
long, extended structures with pronounced clumping while weaker cooling leads
to saturated modes that devolve into turbulent flows. These results suggest
that expanding H II regions may either promote or provide turbulent support
against the formation of later generations of stars, with potential
consequences for star formation rates in the galaxy today.
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We present a domain decomposition approach for the computation of the
electromagnetic field within periodic structures. We use a Schwarz method with
transparent boundary conditions at the interfaces of the domains. Transparent
boundary conditions are approximated by the perfectly matched layer method
(PML). To cope with Wood anomalies appearing in periodic structures an adaptive
strategy to determine optimal PML parameters is developed. We focus on the
application to typical EUV lithography line masks. Light propagation within the
multi-layer stack of the EUV mask is treated analytically. This results in a
drastic reduction of the computational costs and allows for the simulation of
next generation lithography masks on a standard personal computer.
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Hand pose estimation from monocular depth images is an important and
challenging problem for human-computer interaction. Recently deep convolutional
networks (ConvNet) with sophisticated design have been employed to address it,
but the improvement over traditional methods is not so apparent. To promote the
performance of directly 3D coordinate regression, we propose a tree-structured
Region Ensemble Network (REN), which partitions the convolution outputs into
regions and integrates the results from multiple regressors on each regions.
Compared with multi-model ensemble, our model is completely end-to-end
training. The experimental results demonstrate that our approach achieves the
best performance among state-of-the-arts on two public datasets.
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We examine through numerical calculation the collision of counter-propagating
trains of optically spaced electron/positron microbunches in a 1 TeV collider
scenario for a dielectric laser accelerator (DLA). A time-dependent envelope
equation is derived for arbitrary number of bunches in the classical limit,
with inclusion of the radiation reaction force (RRF). Example parameters are
examined based on a constrained luminosity relation that takes into account the
bunch charge for optimal efficiency, material damage limits, and power
constraints. We find that for initially identical counter-propagating Gaussian
bunch trains the periodic temporal structure leads to a peak in luminosity with
number of bunches. For longer bunch trains, the enhancement then decreases
inversely with number of bunches. The corresponding fractional energy loss of
the beam is found to be of order 1.75\%, which is reduced to 0.35\% when the
nonlinear radial dependence of the transverse force is included, with an
average beamstrahlung parameter of 0.075, an important result considering that
beamstrahlung losses are a critical concern for future TeV colliders.
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We show that the edit distance between two run-length encoded strings of
compressed lengths $m$ and $n$ respectively, can be computed in
$\mathcal{O}(mn\log(mn))$ time. This improves the previous record by a factor
of $\mathcal{O}(n/\log(mn))$. The running time of our algorithm is within
subpolynomial factors of being optimal, subject to the standard SETH-hardness
assumption. This effectively closes a line of algorithmic research first
started in 1993.
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We study an incompressible viscous flow around an obstacle with an
oscillating boundary that moves by a translational periodic motion, and we show
existence of strong time-periodic solutions for small data in different
configurations: If the mean velocity of the body is zero, existence of
time-periodic solutions is provided within a framework of Sobolev functions
with isotropic pointwise decay. If the mean velocity is non-zero, this
framework can be adapted, but the spatial behavior of flow requires a setting
of anisotropically weighted spaces. In the latter case, we also establish
existence of solutions within an alternative framework of homogeneous Sobolev
spaces. These results are based on the time-periodic maximal regularity of the
associated linearizations, which is derived from suitable R-bounds for the
Stokes and Oseen resolvent problems. The pointwise estimates are deduced from
the associated time-periodic fundamental solutions.
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The multiple-scale perturbation theory, well known for long-waves, is
extended to the study of the far-field behaviour of short-waves, commonly
called ripples. It is proved that the Benjamin-Bona-Mahony- Peregrine equation
can propagates short-waves. This result contradict the Benjamin hypothesis that
short-waves tends not to propagate in this model and close a part of the old
controversy between Korteweg-de Vries and Benjamin-Bona-Mahony-Peregrine
equations. We shown that a nonlinear (quadratic) Klein-Gordon type equation
substitutes in a short-wave analysis the ubiquitous Korteweg-de Vries equation
of long-wave approach. Moreover the kink solutions of phi-4 and sine-Gordon
equations are understood as an all orders asymptotic behaviour of short-waves.
It is proved that the antikink solution of phi-4 model which was never obtained
perturbatively can be obtained by perturbation expansion in the wave-number k
in the short-wave limit.
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Simulation is a powerful tool to easily generate annotated data, and a highly
desirable feature, especially in those domains where learning models need large
training datasets. Machine learning and deep learning solutions, have proven to
be extremely data-hungry and sometimes, the available real-world data are not
sufficient to effectively model the given task. Despite the initial skepticism
of a portion of the scientific community, the potential of simulation has been
largely confirmed in many application areas, and the recent developments in
terms of rendering and virtualization engines, have shown a good ability also
in representing complex scenes. This includes environmental factors, such as
weather conditions and surface reflectance, as well as human-related events,
like human actions and behaviors. We present a human crowd simulator, called
UniCrowd, and its associated validation pipeline. We show how the simulator can
generate annotated data, suitable for computer vision tasks, in particular for
detection and segmentation, as well as the related applications, as crowd
counting, human pose estimation, trajectory analysis and prediction, and
anomaly detection.
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The release of openly available, robust natural language generation
algorithms (NLG) has spurred much public attention and debate. One reason lies
in the algorithms' purported ability to generate human-like text across various
domains. Empirical evidence using incentivized tasks to assess whether people
(a) can distinguish and (b) prefer algorithm-generated versus human-written
text is lacking. We conducted two experiments assessing behavioral reactions to
the state-of-the-art Natural Language Generation algorithm GPT-2 (Ntotal =
830). Using the identical starting lines of human poems, GPT-2 produced samples
of poems. From these samples, either a random poem was chosen
(Human-out-of-the-loop) or the best one was selected (Human-in-the-loop) and in
turn matched with a human-written poem. In a new incentivized version of the
Turing Test, participants failed to reliably detect the
algorithmically-generated poems in the Human-in-the-loop treatment, yet
succeeded in the Human-out-of-the-loop treatment. Further, people reveal a
slight aversion to algorithm-generated poetry, independent on whether
participants were informed about the algorithmic origin of the poem
(Transparency) or not (Opacity). We discuss what these results convey about the
performance of NLG algorithms to produce human-like text and propose
methodologies to study such learning algorithms in human-agent experimental
settings.
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PURPOSE: Establishing and obtaining consistent quantitative indices of
retinal thickness from a variety of clinically used Spectral-Domain Optical
Coherence Tomography scanners. DESIGN: Retinal images from five Spectral-Domain
Optical Coherence Tomography scanners were used to determine total retinal
thickness with scanner-specific correction factors establishing consistency of
thickness measurement across devices. PARTICIPANTS: 55 Fovea-centered
Spectral-Domain Optical Coherence Tomography volumes from eleven subjects were
analyzed, obtained from Cirrus HD-OCT, RS-3000, Heidelberg Spectralis, RTVue
and Topcon2000, seven subjects with retinal diseases and four normal controls.
METHOD: The Iowa Reference Algorithm measured total retinal thickness.
Nonlinear model of total retinal thickness measurement comparisons was derived
and used for device-specific comparisons. Bland-Altman plots and pairwise
predictive equations yielded pairwise scanner-specific differences. Mendel test
determined whether measurement biases were constant for each scanner pair.
RESULTS: Mendel test revealed that all pairwise scanner differences of total
retinal thickness were constant across the cohort (p=0.992). Individual
measurements can thus be bias-corrected and the Iowa Reference Algorithm serve
as a scanner-agnostic independent standard of total retinal thickness across
the five tested SD-OCT scanners. CONCLUSIONS: Combination of the Iowa Reference
Algorithm with scanner-specific bias correction yields cross-scanner
consistency of total retinal thickness measurements, facilitating
scanning-device independent quantitative assessment of total retinal thickness,
longitudinal follow-up quantification without requiring patients to be imaged
on the same scanner model, and allowing for multi-center studies with
heterogeneous device utilization when using the Iowa Reference Algorithm.
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We report the significance of the double Stokes Mueller polarimetry (DSMP)
technique, to characterize a large size (3 X 3 X 5mm) KTP (Potassium titanyl
phosphate) crystal. The crystal undergoes second harmonic generation with type
II phase matching. The study of standard KTP crystal using the DSMP technique
helps to validate the efficiency of this technique. We were able to extract the
crystal's double Mueller matrix, the relative contribution of the
susceptibility tensor components, the phase difference between the
susceptibility tensor components, etc. We could determine the crystal axes
orientation using this optical technique, which was not possible through a
single crystal X-Ray diffraction technique for such a large size crystal for
which both optic axes and crystallographic axes are the same. Axes direction
determined from polarization microscope measurements and Laue diffraction
measurements on KTP crystal is compared with those obtained from DSMP
measurements.
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Formal verification techniques such as model checking, are becoming popular
in hardware design. SAT-based model checking techniques such as IC3/PDR, have
gained a significant success in hardware industry. In this paper, we present a
new framework for SAT-based safety model checking, named Complementary
Approximate Reachability (CAR). CAR is based on standard reachability analysis,
but instead of maintaining a single sequence of reachable- state sets, CAR
maintains two sequences of over- and under- approximate reachable-state sets,
checking safety and unsafety at the same time. To construct the two sequences,
CAR uses standard Boolean-reasoning algorithms, based on satisfiability
solving, one to find a satisfying cube of a satisfiable Boolean formula, and
one to provide a minimal unsatisfiable core of an unsatisfiable Boolean
formula. We applied CAR to 548 hardware model-checking instances, and compared
its performance with IC3/PDR. Our results show that CAR is able to solve 42
instances that cannot be solved by IC3/PDR. When evaluated against a portfolio
that includes IC3/PDR and other approaches, CAR is able to solve 21 instances
that the other approaches cannot solve. We conclude that CAR should be
considered as a valuable member of any algorithmic portfolio for safety model
checking.
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In this paper, we investigate the exact controllability properties of an
advection-diffusion equation on a bounded domain, using time- and
space-dependent velocity fields as the control parameters. This partial
differential equation (PDE) is the Kolmogorov forward equation for a reflected
diffusion process that models the spatiotemporal evolution of a swarm of
agents. We prove that if a target probability density has bounded first-order
weak derivatives and is uniformly bounded from below by a positive constant,
then it can be reached in finite time using control inputs that are bounded in
space and time. We then extend this controllability result to a class of
advection-diffusion-reaction PDEs that corresponds to a hybrid-switching
diffusion process (HSDP), in which case the reaction parameters are
additionally incorporated as the control inputs. Our proof for controllability
of the advection-diffusion equation is constructive and is based on linear
operator semigroup theoretic arguments and spectral properties of the
multiplicatively perturbed Neumann Laplacian. For the HSDP, we first
constructively prove controllability of the associated continuous-time Markov
chain (CTMC) system, in which the state space is finite. Then we show that our
controllability results for the advection-diffusion equation and the CTMC can
be combined to establish controllability of the forward equation of the HSDP.
Lastly, we provide constructive solutions to the problem of asymptotically
stabilizing an HSDP to a target non-negative stationary distribution using
time-independent state feedback laws, which correspond to spatially-dependent
coefficients of the associated system of PDEs.
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In this study, we introduce a unique approach that employs time-resolved
Schlieren imaging to capture and visualize the dynamic changes of a thin liquid
(mixture of water, soap and glycerin) film in ultrasonic wave field with high
spatial and temporal resolution. By placing a soap film spanning a wire frame
vertically in the path of light, we harnessed the vibrations induced by the
ultrasonic waves, resulting in remarkable Schlieren imaging patterns. The
investigation not only uncovers an unexpected branch flow phenomenon within the
film, challenging existing assumptions, but also reveals a fascinating
interplay between vortex flow and branch flow. The experiments have revealed a
captivating spectrum of dynamic phenomena within the thin liquid films. The
observation of small-scale capillary waves, large-scale standing waves,
traveling waves, and the intricate fusion of capillary-gravity wave patterns
underscores the rich complexity inherent in the interaction between the films
and the holographic ultrasonic wave field. These diverse states of film
dynamics provide a comprehensive understanding of the intricate interplay
between various wave modes and fluid behavior, further enhancing comprehension
of this fascinating phenomenon. The ability to visualize the pressure field
opens up new avenues for optimizing acoustic levitation techniques,
investigating particle behavior, and exploring potential applications in
materials science and bioengineering.
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We prove the existence of the arithmetic degree for dominant rational
self-maps at any point whose orbit is generic. As a corollary, we prove the
same existence for \'etale morphisms on quasi-projective varieties and any
points on it. We apply the proof of this fact to dynamical Lang-Siegel problem.
Namely, we prove that local height function associated with zero-dimensional
subscheme grows slowly along orbits of a rational map under reasonable
assumption. Also if local height function associated with any proper closed
subscheme grows fast on a subset of an orbit of a self-morphism, we prove that
such subset has Banach density zero under some assumptions.
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The negative ion density and temperature are the two fundamental parameters
that are necessary to quantify the properties of electronegative discharges.
However, determining these parameters by means of electrostatic probes can be
quite challenging because of the inherent inaccuracies involved in determining
the electron/ion saturation currents, electron temperatures and plasma
potential, which relies on charge particle collection by the probe surface; as
well as on the sheath models that are originally developed for an ideal
collision-less plasma. This paper briefly reviews the various limitations
associated with these underlying methods and suggests useful means to correct
the anomaly associated in determining the negative ion parameters based on
electrostatic probes.
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This paper presents a brief review and latest results of the work that has
been carried out by the Planetary Science community in order to understand that
role of the geotechnical properties of granular asteroids (commonly known as
"rubble-pile" asteroids) in their formation, evolution and possible disruption.
As such, we will touch in aspects of the theoretical and numerical tools that
have been used with this objective and how the obtained results compare to the
observed asteroids.
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Autocatalytic chemical networks play a predominant role in a large number of
natural systems such as in metabolic pathways and in ecological networks.
Despite recent efforts, the precise impact of thermodynamic constraints on
these networks remains elusive. In this work, we present a theoretical
framework that allows determining bounds on the thermodynamic affinity and on
the concentrations of autocatalysts in mass-action autocatalytic networks.
These bounds can be obtained solely from the stoichiometry of the underlying
chemical reaction network, and are independent from the numerical values of
kinetic parameters. This property holds in the specific regime where all the
fluxes of the network are tightly coupled and maximal. Our method is applicable
to large networks, and can be used to complement constraints-based modeling
methods of metabolic networks, which typically do not provide predictions about
thermodynamic properties or concentration ranges of metabolites
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The Painleve expansion for the second Painleve equation (PII) and fourth
Painleve equation (PIV) have two branches. The singular manifold method
therefore requires two singular manifolds. The double singular manifold method
is used to derive Miura transformations from PII and PIV to modified Painleve
type equations for which auto-Backlund transformations are obtained. These
auto-Backlund transformations can be used to obtain discrete equations.
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We study the effect of the intrinsic (Rashba or Dresselhaus) spin-orbit
interaction in superconductor--nanowire--superconductor (SNS) weak links in the
presence of a spin-splitting field that can result either from an intrinsic
exchange field or the Zeeman effect of an applied field. We solve the full
non-linear Usadel equations numerically and analyze the resulting supercurrent
through the weak link and the behavior of the density of states in the center
of the wire. We point out how the presence of the spin-orbit interaction gives
rise to a long-range spin triplet supercurrent, which remains finite even in
the limit of very large exchange fields. In particular, we show how rotating
the field leads to a sequence of transitions between the 0 and $\pi$ states as
a function of the angle between the exchange field and the spin-orbit field.
Simultaneously, the triplet pairing leads to a zero-energy peak in the density
of states. We proceed by solving the linearized Usadel equations, showing the
correspondence to the solutions of the full equations and detail the emergence
of the long-range supercurrent components. Our studies are relevant for
on-going investigations of supercurrent in semiconductor nanowires in the limit
of several channels and in the presence of disorder.
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We have studied solar-like oscillations in ~800 red-giant stars using Kepler
long-cadence photometry. The sample includes stars ranging in evolution from
the lower part of the red-giant branch to the Helium main sequence. We
investigate the relation between the large frequency separation (Delta nu) and
the frequency of maximum power (nu_max) and show that it is different for red
giants than for main-sequence stars, which is consistent with evolutionary
models and scaling relations. The distributions of nu_max and Delta nu are in
qualitative agreement with a simple stellar population model of the Kepler
field, including the first evidence for a secondary clump population
characterized by M ~> 2 M_sun and nu_max ~ 40-110 muHz. We measured the small
frequency separations delta nu_02 and delta nu_01 in over 400 stars and delta
nu_03 in over 40. We present C-D diagrams for l=1, 2 and 3 and show that the
frequency separation ratios delta nu_02/Delta nu and delta nu_01/Delta nu have
opposite trends as a function of Delta nu. The data show a narrowing of the l=1
ridge towards lower nu_max, in agreement with models predicting more efficient
mode trapping in stars with higher luminosity. We investigate the offset
epsilon in the asymptotic relation and find a clear correlation with Delta nu,
demonstrating that it is related to fundamental stellar parameters. Finally, we
present the first amplitude-nu_max relation for Kepler red giants. We observe a
lack of low-amplitude stars for nu_max ~> 110 muHz and find that, for a given
nu_max between 40-110 muHz, stars with lower Delta nu (and consequently higher
mass) tend to show lower amplitudes than stars with higher Delta nu.
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Gradient Inversion Attacks invert the transmitted gradients in Federated
Learning (FL) systems to reconstruct the sensitive data of local clients and
have raised considerable privacy concerns. A majority of gradient inversion
methods rely heavily on explicit prior knowledge (e.g., a well pre-trained
generative model), which is often unavailable in realistic scenarios. To
alleviate this issue, researchers have proposed to leverage the implicit prior
knowledge of an over-parameterized network. However, they only utilize a fixed
neural architecture for all the attack settings. This would hinder the adaptive
use of implicit architectural priors and consequently limit the
generalizability. In this paper, we further exploit such implicit prior
knowledge by proposing Gradient Inversion via Neural Architecture Search
(GI-NAS), which adaptively searches the network and captures the implicit
priors behind neural architectures. Extensive experiments verify that our
proposed GI-NAS can achieve superior attack performance compared to
state-of-the-art gradient inversion methods, even under more practical settings
with high-resolution images, large-sized batches, and advanced defense
strategies.
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We present in this work an exact renormalization group (RG) treatment of a
one-dimensional $p$-wave superconductor. The model proposed by Kitaev consists
of a chain of spinless fermions with a $p$-wave gap. It is a paradigmatic model
of great actual interest since it presents a weak pairing superconducting phase
that has Majorana fermions at the ends of the chain. Those are predicted to be
useful for quantum computation. The RG allows to obtain the phase diagram of
the model and to study the quantum phase transition from the weak to the strong
pairing phase. It yields the attractors of these phases and the critical
exponents of the weak to strong pairing transition. We show that the weak
pairing phase of the model is governed by a chaotic attractor being non-trivial
from both its topological and RG properties. In the strong pairing phase the RG
flow is towards a conventional strong coupling fixed point. Finally, we propose
an alternative way for obtaining $p$-wave superconductivity in a
one-dimensional system without spin-orbit interaction.
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The aim of this paper is to provide some new criteria for the Stieltjes
moment problem. We first give a Tauberian type criterion for moment
indeterminacy that is expressed purely in terms of the asymptotic behavior of
the moment sequence (and its extension to imaginary lines). Under an additional
assumption this provides a converse to the classical Carleman's criterion, thus
yielding an equivalent condition for moment determinacy. We also provide a
criterion for moment determinacy that only involves the large asymptotic
behavior of the distribution (or of the density if it exists), which can be
thought of as an Abelian counterpart to the previous Tauberian type result.
This latter criterion generalizes Hardy's condition for determinacy, and under
some further assumptions yields a converse to the Pedersen's refinement of the
celebrated Krein's theorem. The proofs utilize non-classical Tauberian results
for moment sequences that are analogues to the ones developed in Feigin and
Yashchin, and, Balkema et al. for the bi-lateral Laplace transforms in the
context of asymptotically parabolic functions. We illustrate our results by
studying the time-dependent moment problem for the law of log-L\'evy processes
viewed as a generalization of the log-normal distribution. Along the way, we
derive the large asymptotic behavior of the density of spectrally-negative
L\'evy processes having a Gaussian component, which may be of independent
interest.
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In this work, we study the long time behaviors, including asymptotic
contractivity and dissipativity, of the solutions to several numerical methods
for fractional ordinary differential equations (F-ODEs). The existing algebraic
contractivity and dissipativity rates of the solutions to the scalar F-ODEs are
first improved. In order to study the long time behavior of numerical solutions
to fractional backward differential formulas (F-BDFs), two crucial analytical
techniques are developed, with the first one for the discrete version of the
fractional generalization of the traditional Leibniz rule, and the other for
the algebraic decay rate of the solution to a linear Volterra difference
equation. By mens of these auxiliary tools and some natural conditions, the
solutions to F-BDFs are shown to be contractive and dissipative, and also
preserve the exact contractivity rate of the continuous solutions. Two typical
F-BDFs, based on the Grunwald-Letnikov formula and L1 method respectively, are
studied. For high order F-BDFs, including some second order F-BDFs and
$3-\alpha$ order method, their numerical contractivity and dissipativity are
also developed under some slightly stronger conditions. Numerical experiments
are presented to validate the long time qualitative characteristics of the
solutions to F-BDFs, revealing very different decay rates of the numerical
solutions in terms of the the initial values between F-ODEs and integer ODEs
and demonstrating the superiority of the structure-preserving numerical
methods.
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We investigate the control problem of harmonic map heat flow by means of an
external magnetic field. In contrast to the situation of a parabolic system
with internal or boundary control, the magnetic field acts as the coefficients
of the lower order terms of the equation. We show that for initial data whose
image stays in a hemisphere, with one control acting on a subset of the domain
plus a spatial-independent control acting on the whole domain, the state of the
system can be steered to any ground state, i.e. any given unit vector, within
any short time. To achieve this, in the first step a spatial independent
control is applied to steer the solution into a small neighborhood of the peak
of the hemisphere. Then under stereographic projection, the original system is
reduced to an internal parabolic control system with initial data sufficiently
close to $0$ such that the existing method for local controllability can be
applied. The key process in this step is to give an explicit solution of an
underdetermined algebraic system such that the affine type control can be
converted into an internal control.
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The aim of this Tutorial is to give a pedagogical introduction into
realizations of Majorana fermions, usually termed as Majorana bound states
(MBS), in condensed matter systems with magnetic textures. We begin by
considering the Kitaev chain model of 'spinless' fermions and show how two
'half' fermions can appear at chain ends due to interactions. By considering
this model and its two-dimensional generalization, we emphasize intricate
relation between topological superconductivity and possible realizations of
MBS. We further discuss how 'spinless' fermions can be realized in more
physical systems, e.g., by employing the spin-momentum locking. Next, we
demonstrate how magnetic textures can be used to induce synthetic or fictitious
spin-orbit interactions, and, thus, stabilize MBS. We describe a general
approach that works for arbitrary textures and apply it to skyrmions. We show
how MBS can be stabilized by elongated skyrmions, certain higher order
skyrmions, and chains of skyrmions. We also discuss how braiding operations can
be performed with MBS stabilized on magnetic skyrmions. This Tutorial is aimed
at students at graduate level.
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We find Baikov-Gazizov-Ibragimov approximate point symmetries of the
second-order Boussinesq ODE, and we find the higher-order approximate
symmetries corresponding to the unstable point symmetries (the point symmetries
that disappear fron the classification of the BGI approximate point symmetries)
of the unperturbed equation. Approximate local symmetries are used to construct
a general approximate solution of the Boussinesq ODE. We use approximate
integrating factors to find a general approximate solution of the
Benjamin-Bona-Mahony ODE reduction.
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Suzaku observations of the Wolf-Rayet binary WR 140 (WC7pd+O5.5fc) were made
at four different times around periastron passage in 2009 January. The spectra
changed in shape and flux with the phase. As periastron approached, the column
density of the low-energy absorption increased, which indicates that the
emission from the wind-wind collision plasma was absorbed by the dense W-R
wind. The spectra can be mostly fitted with two different components: a warm
component with kT=0.3--0.6 keV and a dominant hot component with kT~3 keV. The
emission measure of the dominant, hot component is not inversely proportional
to the distance between the two stars. This can be explained by the O star wind
colliding before it has reached its terminal velocity, leading to a reduction
in its wind momentum flux. At phases closer to periastron, we discovered a cool
plasma component in a recombining phase, which is less absorbed. This component
may be a relic of the wind-wind collision plasma, which was cooled down by
radiation, and may represent a transitional stage in dust formation.
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Over the last several years, several well-established and prominent
brick-and-mortar retail chains have ceased operations, raising concerns for
something that some have referred to as a retail apocalypse. While the demise
of brick-and-mortar is far from certain, scholars have attempted to model the
likelihood that a retailer is about to fail using different approaches. This
paper examines the failures of Bed Bath and Beyond, J.C. Penney, Rite Aid, and
Sears Holdings in the United States between 2013 and 2022. A model of retail
failure is presented that considers internal and external firm factors using
both annual report and macroeconomic data. The findings suggest that certain
revenue-based financial ratios and the annual average U.S. inflation rates are
statistically significant predictors of failure. Furthermore, the failure model
demonstrated that it can provide a nontrivial early warning signal at least the
year before failure. The paper concludes with a discussion and directions for
future research.
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The Next-to Minimal Supersymmetric Standard Model (NMSSM) with a Type-I
seesaw mechanism extends the NMSSM by three generations of right-handed
neutrino fields to generate neutrino mass. As a byproduct it renders the
lightest sneutrino as a viable DM candidate. Due to the gauge singlet nature of
the DM, its scattering with nucleon is suppressed in most cases to coincide
spontaneously with the latest XENON-1T results. Consequently, broad parameter
spaces in the Higgs sector, especially a light Higgsino mass, are resurrected
as experimentally allowed, which makes the theory well suited to explain the
long standing $b \bar{b}$ excess at LEP-II and the continuously observed
$\gamma \gamma$ excess by CMS collaboration. We show by both analytic formulas
and numerical results that the theory can naturally predict the central values
of the excesses in its broad parameter space, and the explanations are
consistent with the Higgs data of the discovered Higgs boson, $B-$physics and
DM physics measurements, the electroweak precision data as well as the LHC
search for sparticles. Part of the explanations may be tested by future DM
experiments and the SUSY search at the LHC.
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Using event-by-event viscous fluid dynamics to evolve fluctuating initial
density profiles from the Monte-Carlo Glauber model for U+U collisions, we
report a "knee"-like structure in the elliptic flow as a function of collision
centrality, located around the 0.5% most central collisions as measured by the
final charged multiplicity. This knee is due to the preferential selection of
tip-on-tip collision geometries by a high-multiplicity trigger. Such a knee
structure is not seen in the STAR data. This rules out the two-component
MC-Glauber model for initial energy and entropy production. Hence an enrichment
of tip-tip configurations by triggering solely on high-multiplicity in the U+U
collisions does not work. On the other hand, by using the Zero Degree
Calorimeters (ZDCs) coupled with event-shape engineering such a selection is
possible. We identify the selection purity of body-body and tip-tip events in
full-overlap U+U collisions. By additionally constraining the asymmetry of the
ZDC signals we can further increase the probability of selecting tip-tip events
in U+U collisions.
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We envision that quantum spin Hall effect should be observed in
$(111)$-oriented thin films of SnSe and SnTe topological crystalline
insulators. Using a tight-binding approach supported by first-principles
calculations of the band structures we demonstrate that in these films the
energy gaps in the two-dimensional band spectrum depend in an oscillatory
fashion on the layer thickness. These results as well as the calculated
topological invariant indexes and edge state spin polarizations show that for
films ~20-40 monolayers thick a two-dimensional topological insulator phase
appears. In this range of thicknesses in both, SnSe and SnTe, (111)-oriented
films edge states with Dirac cones with opposite spin polarization in their two
branches are obtained. While in the SnTe layers a single Dirac cone appears at
the projection of the G point of the two-dimensional Brillouin zone, in the
SnSe (111)-oriented layers three Dirac cones at M points projections are
predicted.
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Considering the geometry of Reissner-Nordstr\"{o}m (RN) black hole immersed
in magnetic field we have studied the dynamics of neutral and charged
particles. A collision of particles in the inner stable circular orbit is
considered and the conditions for the escape of colliding particles from the
vicinity of black hole are given. The trajectories of the escaping particle are
discussed. Also the velocity required for this escape is calculated. It is
observed that there are more than one stable regions if magnetic field is
present in the accretion disk of black hole so the stability of ISCO increases
in the presence of magnetic field. Effect of magnetic field on the angular
motion of neutral and charged particles is observed graphically.
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We present the first spatially resolved map of stellar proper motions within
the central ($\sim$3.1 $\times$ 2.4 kpc) regions of the Small Magellanic Cloud
(SMC). The data used for this study encompasses four tiles from the ongoing
near-infrared VISTA survey of the Magellanic Clouds system and covers a total
contiguous area on the sky of $\sim$6.81 deg$^2$. Proper motions have been
calculated independently in two dimensions from the spatial offsets in the
$K_s$ filter over time baselines between 22 and 27 months. The reflex motions
of $\sim$33~000 background galaxies are used to calibrate the stellar motions
to an absolute scale. The resulting catalog is composed of more than 690 000
stars which have been selected based on their position in the $(J-K_s, K_s)$
color-magnitude diagram. For the median absolute proper motion of the SMC, we
find ($\mu_{\alpha}\mathrm{cos}(\delta)$, $\mu_{\delta}$) = (1.087 $\pm$ 0.192
(sys.) $\pm$ 0.003 (stat.), $-$1.187 $\pm$ 0.008 (sys.) $\pm$ 0.003 (stat.))
mas yr$^{-1}$, consistent with previous studies. Mapping the proper motions as
a function of position within the SMC reveals a non uniform velocity pattern
indicative of a tidal feature behind the main body of the SMC and a flow of
stars in the South-East moving predominantly along the line-of-sight.
|
We study cross-graph charging schemes for graphs drawn in the plane. These
are charging schemes where charge is moved across vertices of different graphs.
Such methods have been recently applied to obtain various properties of
triangulations that are embedded over a fixed set of points in the plane. We
show how this method can be generalized to obtain results for various other
types of graphs that are embedded in the plane. Specifically, we obtain a new
bound of $O^*(187.53^N)$ (where the $O^*()$ notation hides polynomial factors)
for the maximum number of crossing-free straight-edge graphs that can be
embedded over any specific set of $N$ points in the plane (improving upon the
previous best upper bound $207.85^N$ in Hoffmann et al.). We also derive upper
bounds for numbers of several other types of plane graphs (such as connected
and bi-connected plane graphs), and obtain various bounds on expected
vertex-degrees in graphs that are uniformly chosen from the set of all
crossing-free straight-edge graphs that can be embedded over a specific point
set.
We then show how to apply the cross-graph charging-scheme method for graphs
that allow certain types of crossings. Specifically, we consider graphs with no
set of $k$ pairwise-crossing edges (more commonly known as $k$-quasi-planar
graphs). For $k=3$ and $k=4$, we prove that, for any set $S$ of $N$ points in
the plane, the number of graphs that have a straight-edge $k$-quasi-planar
embedding over $S$ is only exponential in $N$.
|
We suggest to study the $B_{s}$ and its excitations $B_{sJ}$ in the $B_c$
decays. We calculate the $B_c\to B_{sJ}$ and $B_c\to B_{J}$ form factors within
the covariant light-front quark model, where the $B_{sJ}$ and $B_{J}$ denote an
s-wave or p-wave $\bar bs$ and $\bar bd$ meson, respectively. The form factors
at $q^2=0$ are directly computed while their $q^2$-distributions are obtained
by the extrapolation. The derived form factors are then used to study
semileptonic $B_c\to (B_{sJ},B_{J})\bar\ell\nu$ decays, and nonleptonic $B_c\to
B_{sJ}\pi$. Branching fractions and polarizations are predicted in the standard
model. We find that the branching fractions are sizable and might be accessible
at the LHC experiment and future high-energy $e^+e^-$ colliders with a high
luminosity at the $Z$-pole. The future experimental measurements are helpful to
study the nonperturbative QCD dynamics in the presence of a heavy spectator and
also of great value for the spectroscopy study.
|
This is a comment on Phys. Rev. Lett. {\bf 110}, 126405 (2013), showing it
biases the ferromagnetic order more than mean field theories would do. With
over-biases like this, the theoretical method applied in the given context is
called into question.
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Interdisciplinary research has emerged as a hotbed for innovation and a key
approach to addressing complex societal challenges. The increasing dominance of
grant-supported research in shaping scientific advances, coupled with growing
interest in funding interdisciplinary work, raises fundamental questions about
the effectiveness of interdisciplinary grants in fostering high-impact
interdisciplinary research outcomes. Here, we quantify the interdisciplinarity
of both research grants and publications, capturing 350,000 grants from 164
funding agencies across 26 countries and 1.3 million papers that acknowledged
their support from 1985 to 2009. Our analysis uncovers two seemingly
contradictory patterns: Interdisciplinary grants tend to produce
interdisciplinary papers, which are generally associated with high impact.
However, compared to disciplinary grants, interdisciplinary grants on average
yield fewer papers and interdisciplinary papers they support tend to have
substantially reduced impact. We demonstrate that the key to explaining this
paradox lies in the power of disciplinary grants in propelling high-impact
interdisciplinary research. Specifically, our results show that highly
interdisciplinary papers supported by deeply disciplinary grants garner
disproportionately more citations, both within their core disciplines and from
broader fields. Moreover, disciplinary grants, particularly when combined with
other similar grants, are more effective in producing high-impact
interdisciplinary research. Amidst the rapid rise of support for
interdisciplinary work across the sciences, these results highlight the
hitherto unknown role of disciplinary grants in driving crucial
interdisciplinary advances, suggesting that interdisciplinary research requires
deep disciplinary expertise and investments.
|
In this paper, we derive closed-form exact expressions for the main
statistics of the ratio of squared alpha-mu random variables, which are of
interest in many scenarios for future wireless networks where generalized
distributions are more suitable to fit with field data. Importantly, different
from previous proposals, our expressions are general in the sense that are
valid for non constrained arbitrary values of the parameters of the alpha-mu
distribution. Thus, the probability density function, cumulative distribution
function, moment generating function, and higher order moments are given in
terms of both (i) theFox H-function for which we provide a portable and
efficient Wolfram Mathematica code and (ii) easily computable series
expansions. Our expressions can be used straightforwardly in the performance
analysis of a number of wireless communication systems, including either
interference-limited scenarios, spectrum sharing, full-duplex or physical-layer
security networks, for which we present the application of the proposed
framework. Moreover, closed-form expressions for some classical distributions,
derived as special cases from the alpha-mu distribution, are provided as
byproducts. The validity of the proposed expressions is confirmed via Monte
Carlo simulations.
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In our current best cosmological model, the vast majority of matter in the
Universe is dark, consisting of yet undetected, non-baryonic particles that do
not interact electro-magnetically. So far, the only significant evidence for
dark matter has been found in its gravitational interaction, as observed in
galaxy rotation curves or gravitational lensing effects. The inferred dark
matter agglomerations follow almost universal mass density profiles that can be
reproduced well in simulations, but have eluded an explanation from a
theoretical viewpoint. Forgoing standard (astro-)physical methods, I show that
it is possible to derive these profiles from an intriguingly simple
mathematical approach that directly determines the most likely spatial
configuration of a self-gravitating ensemble of collisionless dark matter
particles.
|
A Relay Station (RS) uses a buffer to store and process the received data
packets before forwarding them. Recently, the buffer has been exploited in
one-way relaying to opportunistically schedule the two different links
according to their channel quality. The intuition is that, if the channel to
the destination is poor, then RS stores more data from the source, in order to
use it when the channel to the destination is good. We apply this intuition to
the case of half-duplex two-way relaying, where the interactions among the
buffers and the links become more complex. We investigate the sum-rate
maximization problem in the Time Division Broadcast (TDBC): the users send
signals to the RS in different time slots, the RS decodes and stores messages
in the buffers. For downlink transmission, the RS re-encodes and sends using
the optimal broadcast strategy. The operation in each time slot is not
determined in advance, but depends on the channel state information (CSI). We
derive the decision function for adaptive link selection with respect to CSI
using the Karush-Kuhn-Tucker (KKT) conditions. The thresholds of the decision
function are obtained under Rayleigh fading channel conditions. The numerical
results show that the sum-rate of the adaptive link selection protocol with
buffering is significantly larger compared to the reference protocol with fixed
transmission schedule.
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It has been shown that superconducting vortices with antiferromagnetic cores
arise within Zhang's SO(5) model of high temperature supercondictivity. Similar
phenomena where the symmetry is not restored in the core of the vortex was
discussed by Witten in the case of cosmic strings. It was also suggested that
such strings can form stable vortons, which are closed loops of such vortices.
Motivated by this analogy, in following we will show that loops of such
vortices in the SO(5) model of high T_c superconductivity can exist as
classically stable objects, stabilized by the presence of conserved charges
trapped on the vortex core. These objects carry angular momentum which
counteracts the effect of the string tension that causes the loops to shrink.
The existence of such quasiparticles, which are called vortons, could be
interesting for the physics of high temperature superconductors. We also
speculate that the phase transition between superconducting and
antiferromagnetic phases at zero external magnetic field when the doping
parameter changes is associated with vortons.
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While excitonic instabilities in multiorbital systems recently have come
under scrutiny in a variety of transition-metal compounds, understanding
emergence of these instabilities from strong electronic interactions has
remained a challenge. Here, we present a sign-problem-free determinant quantum
Monte Carlo study of excitonic density orders in a half-filled two-orbital
Hubbard-Kanamori model with broken orbital degeneracy, which accounts for the
role of Hund's coupling in transition-metal compounds. For strong inverted
(negative) Hund's exchange, we find numerical evidence for the emergence of
excitonic density order, with competition between anti-ferro-orbital order and
$\mathbf{Q} = (\pi,\pi)$ excitonic density order as a function of orbital
splitting and Hund's coupling. While inverted Hund's coupling stabilizes a
spin-singlet excitonic density phase for weak orbital splitting, positive
Hund's coupling favors a spin-triplet excitonic density phase.
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Since more than twenty years it is known that deposition of Ag onto
Si(111)-(7\times7) leads under certain conditions to the formation of so-called
"ring-like" clusters, that are particularly stable among small clusters. In
order to resolve their still unknown atomic structure, we performed voltage
dependent scanning tunneling microscopy (STM) measurements providing
interesting information about the electronic properties of clusters which are
linked with their atomic structure. Based on a structural model of Au cluster
on Si(111)-(7\times7) and our STM images, we propose an atomic arrangement for
the two most stable Ag "ring-like" clusters.
|
Dynamical systems can be quantised only if they are Hamiltonian. This prompts
the question from which our talk gets its title. We show how the simple
predator-prey equation and the damped harmonic oscillator can be considered to
be Hamiltonian with respect to an infinite number of non-standard Poisson
brackets. This raises some interesting questions about the nature of
quantisation. Questions which are valid even for flows which possess a
canonical structure.
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Efficiently and accurately simulating partial differential equations (PDEs)
in and around arbitrarily defined geometries, especially with high levels of
adaptivity, has significant implications for different application domains. A
key bottleneck in the above process is the fast construction of a `good'
adaptively-refined mesh. In this work, we present an efficient novel
octree-based adaptive discretization approach capable of carving out
arbitrarily shaped void regions from the parent domain: an essential
requirement for fluid simulations around complex objects. Carving out objects
produces an $\textit{incomplete}$ octree. We develop efficient top-down and
bottom-up traversal methods to perform finite element computations on
$\textit{incomplete}$ octrees. We validate the framework by (a) showing
appropriate convergence analysis and (b) computing the drag coefficient for
flow past a sphere for a wide range of Reynolds numbers ($\mathcal{O}(1-10^6)$)
encompassing the drag crisis regime. Finally, we deploy the framework on a
realistic geometry on a current project to evaluate COVID-19 transmission risk
in classrooms.
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We study the steady plane shear flow of a dense assembly of frictional,
inelastic disks using discrete simulation and prescribing the pressure and the
shear rate. We show that, in the limit of rigid grains, the shear state is
determined by a single dimensionless number, called inertial number I, which
describes the ratio of inertial to pressure forces. Small values of I
correspond to the quasi-static regime of soil mechanics, while large values of
I correspond to the collisional regime of the kinetic theory. Those shear
states are homogeneous, and become intermittent in the quasi-static regime.
When I increases in the intermediate regime, we measure an approximately linear
decrease of the solid fraction from the maximum packing value, and an
approximately linear increase of the effective friction coefficient from the
static internal friction value. From those dilatancy and friction laws, we
deduce the constitutive law for dense granular flows, with a plastic Coulomb
term and a viscous Bagnold term. We also show that the relative velocity
fluctuations follow a scaling law as a function of I. The mechanical
characteristics of the grains (restitution, friction and elasticity) have a
very small influence in this intermediate regime. Then, we explain how the
friction law is related to the angular distribution of contact forces, and why
the local frictional forces have a small contribution to the macroscopic
friction. At the end, as an example of heterogeneous stress distribution, we
describe the shear localization when gravity is added.
|
We report a new theory of dissipative forces acting between colliding
viscoelastic bodies. The impact velocity is assumed not to be large, to avoid
plastic deformations and fragmentation at the impact. The bodies may be of an
arbitrary convex shape and of different materials. We develop a mathematically
rigorous perturbation scheme to solve the continuum mechanics equation that
deals with both displacement and displacement rate fields and accounts for the
dissipation in the bulk of the material. The perturbative solution of this
equation allows to go beyond the previously used quasi-static approximation and
obtain the dissipative force. This force does not suffer from the physical
inconsistencies of the latter approximation and depends on particle deformation
and deformation rate.
|
Bosonization is normally thought of as a purely two-dimensional phenomenon,
and generic field theories with fermions in D>2 are not expected be describable
by local bosonic actions, except in some special cases. We point out that 3D
SU(N) gauge theories on R^{1,1} x S^{1}_{L} with adjoint fermions can be
bosonized in the large N limit. The key feature of such theories is that they
enjoy large N volume independence for arbitrary circle size L. A consequence of
this is a large N equivalence between these 3D gauge theories and certain 2D
gauge theories, which matches a set of correlation functions in the 3D theories
to corresponding observables in the 2D theories. As an example, we focus on a
3D SU(N) gauge theory with one flavor of adjoint Majorana fermions and derive
the large-N equivalent 2D gauge theory. The extra dimension is encoded in the
color degrees of freedom of the 2D theory. We then apply the technique of
non-Abelian bosonization to the 2D theory to obtain an equivalent local theory
written purely in terms of bosonic variables. Hence the bosonized version of
the large N three-dimensional theory turns out to live in two dimensions.
|
We report on the detection of extremely narrow Feshbach resonances by
employing a Mott-insulating state for cesium atoms in a three-dimensional
optical lattice. The Mott insulator protects the atomic ensemble from high
background three-body losses in a magnetic field region where a broad Efimov
resonance otherwise dominates the atom loss in bulk samples. Our technique
reveals three ultra-narrow and previously unobserved Feshbach resonances in
this region with widths below $\approx 10\,\mu$G, measured via
Landau-Zener-type molecule formation and confirmed by theoretical predictions.
For comparatively broader resonances we find a lattice-induced substructure in
the respective atom-loss feature due to the interplay of tunneling and strong
particle interactions. Our results provide a powerful tool to identify and
characterize narrow scattering resonances, particularly in systems with complex
Feshbach spectra. The observed ultra-narrow Feshbach resonances could be
interesting candidates for precision measurements.
|
We begin by reviewing the results on the decay of unstable D-branes in type
II string theory, and the open-closed string duality proposal that arises from
these studies. We then apply this proposal to the study of tachyon driven
cosmology, namely cosmological solutions describing the decay of unstable space
filling D-branes. This naturally gives rise to a time reversal invariant bounce
solution with positive spatial curvature. In the absence of a bulk cosmological
constant the universe always begins with a big bang and ends in a big crunch.
In the presence of a bulk cosmological constant one may get non-singular
cosmological solutions for some special range of initial conditions on the
tachyon.
|
We provide a comprehensive census of the near-Infrared (NIR, 0.8-2.4 $\mu$m)
spectroscopic properties of 102 nearby (z < 0.075) active galactic nuclei
(AGN), selected in the hard X-ray band (14-195 keV) from the Swift-Burst Alert
Telescope (BAT) survey. With the launch of the James Webb Space Telescope this
regime is of increasing importance for dusty and obscured AGN surveys. We
measure black hole masses in 68% (69/102) of the sample using broad emission
lines (34/102) and/or the velocity dispersion of the Ca II triplet or the CO
band-heads (46/102). We find that emission line diagnostics in the NIR are
ineffective at identifying bright, nearby AGN galaxies because ([Fe II]
1.257$\mu$m/Pa$\beta$ and H$_2$ 2.12$\mu$m/Br$\gamma$) identify only 25%
(25/102) as AGN with significant overlap with star forming galaxies and only
20% of Seyfert 2 have detected coronal lines (6/30). We measure the coronal
line emission in Seyfert 2 to be weaker than in Seyfert 1 of the same
bolometric luminosity suggesting obscuration by the nuclear torus. We find that
the correlation between the hard X-ray and the [Si VI] coronal line luminosity
is significantly better than with the [O III] luminosity. Finally, we find 3/29
galaxies (10%) that are optically classified as Seyfert 2 show broad emission
lines in the NIR. These AGN have the lowest levels of obscuration among the
Seyfert 2s in our sample ($\log N_{\rm H} < 22.43$ cm$^{-2}$), and all show
signs of galaxy-scale interactions or mergers suggesting that the optical broad
emission lines are obscured by host galaxy dust.
|
Satellite galaxies are commonly used as tracers to measure the line-of-sight
velocity dispersion ($\sigma_{\rm LOS}$) of the dark matter halo associated
with their central galaxy, and thereby to estimate the halo's mass. Recent
observational dispersion estimates of the Local Group, including the Milky Way
and M31, suggest $\sigma\sim$50 km/s, which is surprisingly low when compared
to the theoretical expectation of $\sigma\sim$100s km/s for systems of their
mass. Does this pose a problem for $\Lambda$CDM? We explore this tension using
the {\small{SURFS}} suite of $N$-body simulations, containing over 10000
(sub)haloes with well tracked orbits. We test how well a central galaxy's host
halo velocity dispersion can be recovered by sampling $\sigma_{\rm LOS}$ of
subhaloes and surrounding haloes. Our results demonstrate that $\sigma_{\rm
LOS}$ is biased mass proxy. We define an optimal window in $v_{\rm LOS}$ and
projected distance ($D_p$) -- $0.5\lesssim D_p/R_{\rm vir}\lesssim1.0$ and
$v_{\rm LOS} \lesssim0.5V_{\rm esc}$, where $R_{\rm vir}$ is the virial radius
and $V_{\rm esc}$ is the escape velocity -- such that the scatter in LOS to
halo dispersion is minimised - $\sigma_{\rm LOS}=(0.5\pm0.1)\sigma_{v,{\rm
H}}$. We argue that this window should be used to measure line-of-sight
dispersions as a proxy for mass, as it minimises scatter in the $\sigma_{\rm
LOS}-M_{\rm vir}$ relation. This bias also naturally explains the results from
\cite{mcconnachie2012a}, who used similar cuts when estimating $\sigma_{\rm
LOS,LG}$, producing a bias of $\sigma_{\rm LG}=(0.44\pm0.14)\sigma_{v,{\rm
H}}$. We conclude that the Local Group's velocity dispersion does not pose a
problem for $\Lambda$CDM and has a mass of $\log M_{\rm LG,
vir}/M_\odot=12.0^{+0.8}_{-2.0}$.
|
A nonmonotonic dependence of the critical Josephson supercurrent on the
injection current through a normal metal/ferromagnet weak link from a single
domain ferromagnetic strip has been observed experimentally in nanofabricated
planar crosslike S-N/F-S Josephson structures. This behavior is explained by
0-pi and pi-0 transitions, which can be caused by the suppression and Zeeman
splitting of the induced superconductivity due to interaction between N and F
layers, and the injection of spin-polarized current into the weak link. A model
considering both effects has been developed. It shows the qualitative agreement
between the experimental results and the theoretical model in terms of spectral
supercurrent-carrying density of states of S-N/F-S structure and the
spin-dependent double-step nonequilibrium quasiparticle distribution.
|
We report on VLBA observations of a gamma-ray bright blazar NRAO 530 at
multiple frequencies (5, 8, 15, 22, 39, 43, and 45 GHz) in 1997 and 1999. These
multi-epoch multi-frequency high-resolution VLBI images exhibit a consistent
core-dominated morphology with a bending jet to the north of the core. The
quasi-simultaneous data observed at five frequencies (5, 8, 15, 22 and 43 GHz)
in February 1997 enable us to estimate the spectra of compact VLBI components
in this highly variable source. Flat spectra are seen in central two components
(A and B), and the most compact component A with the flattest spectral index at
the south end is identified as the core.
|
This paper develops a test for homogeneity in finite mixture models where the
mixing proportions are known a priori (taken to be 0.5) and a common nuisance
parameter is present. Statistical tests based on the notion of Projected
Likelihood Contrasts (PLC) are considered. The PLC is a slight modification of
the usual likelihood ratio statistic or the Wilk's $\Lambda$ and is similar in
spirit to the Rao's score test. Theoretical investigations have been carried
out to understand the large sample statistical properties of these tests.
Simulation studies have been carried out to understand the behavior of the null
distribution of the PLC statistic in the case of Gaussian mixtures with unknown
means (common variance as nuisance parameter) and unknown variances (common
mean as nuisance parameter). The results are in conformity with the theoretical
results obtained. Power functions of these tests have been evaluated based on
simulations from Gaussian mixtures.
|
Observations of jets from young stellar objects reveal the asymmetric
outflows from some sources. A large set of $2.5$D MHD simulations has been
carried out for axisymmetric viscous/diffusive disc accretion to rotating
magnetized stars for the purpose of assessing the conditions where the outflows
or jets are asymmetric relative to the equatorial plane. We consider initial
magnetic fields that are symmetric about the equatorial plane and consist of a
radially distributed field threading the disc (disc-field) and a stellar dipole
field.({\bf 1}). For pure disc-fields the symmetry or asymmetry of the outflows
is affected by the midplane plasma $\beta$ of the disc (where $\beta$ is the
ratio of the plasma pressure to the magnetic pressure). For the low density
discs with small plasma $\beta$ values, outflows are observed to be symmetric
to within $10\%$ over timescales of hundreds of inner disc orbits. For the
denser higher $\beta$ discs, the coupling of the upper and lower coronal
plasmas is broken, and quasi-periodic field motion in the two hemispheres
becomes different. This asymmetry leads to asymmetric episodic outflows. ({\bf
2.}) Accreting stars with a stellar dipole field and no disc-field exhibit
episodic, two component outflows - a magnetospheric wind and an inner disc wind
from somewhat larger radial distances. Both are characterized by similar
velocity profiles but the magnetospheric wind has densities $\gtrsim 10$ times
that of the disc wind. ({\bf 3}.)Adding a disc-field parallel to the stellar
dipole field acts to enhance the magnetospheric winds but suppress the disc
wind. ({\bf 4}.) In contrast, adding a disc-field which is anti-parallel to the
stellar dipole field in the disc acts to suppress the magnetospheric and disc
winds. Our simulations reproduce some key features of observations of
asymmetric outflows of T Tauri stars.
|
We investigate the breathing mode and the stability of a quantum droplet in a
tightly trapped one-dimensional dipolar gas of bosonic atoms. When the droplet
with a flat-top density profile is formed, the breathing mode frequency scales
as the inverse of the number of atoms in the cloud. This is straightforwardly
derived within a phenomenological hydrodynamical approach and confirmed using
both a variational method based on a generalized Gross-Pitaevskii action
functional and the sum-rule approach. We extend our analysis also to the
presence of axial confinement showing the effect of the trap on the density
profile and therefore on the breathing mode frequency scaling. Our analysis
confirms the stability of the quantum droplet against the particles emission
when the flat-top density profile is observed. Our results can be used as a
guide to the experimental investigations of collective modes to detect the
formation of quantum droplets in quasi-one-dimensional dipolar gases.
|
Deep learning has made remarkable achievement in many fields. However,
learning the parameters of neural networks usually demands a large amount of
labeled data. The algorithms of deep learning, therefore, encounter
difficulties when applied to supervised learning where only little data are
available. This specific task is called few-shot learning. To address it, we
propose a novel algorithm for few-shot learning using discrete geometry, in the
sense that the samples in a class are modeled as a reduced simplex. The volume
of the simplex is used for the measurement of class scatter. During testing,
combined with the test sample and the points in the class, a new simplex is
formed. Then the similarity between the test sample and the class can be
quantized with the ratio of volumes of the new simplex to the original class
simplex. Moreover, we present an approach to constructing simplices using local
regions of feature maps yielded by convolutional neural networks. Experiments
on Omniglot and miniImageNet verify the effectiveness of our simplex algorithm
on few-shot learning.
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A $J$-frame is a frame $\mathcal{F}$ for a Krein space $(\mathcal{H}, [\, ,
\,])$ which is compatible with the indefinite inner product $[\, , \, ]$ in the
sense that it induces an indefinite reconstruction formula that resembles those
produced by orthonormal bases in $\mathcal{H}$. With every $J$-frame the
so-called $J$-frame operator is associated, which is a self-adjoint operator in
the Krein space $\mathcal{H}$. The $J$-frame operator plays an essential role
in the indefinite reconstruction formula.
In this paper we characterize the class of $J$-frame operators in a Krein
space by a $2\times 2$ block operator representation. The $J$-frame bounds of
$\mathcal{F}$ are then recovered as the suprema and infima of the numerical
ranges of some uniformly positive operators which are build from the entries of
the $2\times 2$ block representation. Moreover, this $2\times 2$ block
representation is utilized to obtain enclosures for the spectrum of $J$-frame
operators, which finally leads to the construction of a square root. This
square root allows a complete description of all $J$-frames associated with a
given $J$-frame operator.
|
One of the simplest viable models for dark matter is an additional neutral
scalar, stabilised by a $\mathbb{Z}_2$ symmetry. Using the GAMBIT package and
combining results from four independent samplers, we present Bayesian and
frequentist global fits of this model. We vary the singlet mass and coupling
along with 13 nuisance parameters, including nuclear uncertainties relevant for
direct detection, the local dark matter density, and selected quark masses and
couplings. We include the dark matter relic density measured by Planck, direct
searches with LUX, PandaX, SuperCDMS and XENON100, limits on invisible Higgs
decays from the Large Hadron Collider, searches for high-energy neutrinos from
dark matter annihilation in the Sun with IceCube, and searches for gamma rays
from annihilation in dwarf galaxies with the Fermi-LAT. Viable solutions remain
at couplings of order unity, for singlet masses between the Higgs mass and
about 300 GeV, and at masses above $\sim$1 TeV. Only in the latter case can the
scalar singlet constitute all of dark matter. Frequentist analysis shows that
the low-mass resonance region, where the singlet is about half the mass of the
Higgs, can also account for all of dark matter, and remains viable. However,
Bayesian considerations show this region to be rather fine-tuned.
|
Subsets and Splits