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1996-05-06 | A Keck HIRES Investigation of the Metal Abundances and Kinematics of Three Damped Lya Systems Toward Q2206-199 | We present high resolution, high SNR spectra of the QSO Q2206-199 obtained
with HIRES on the 10m W.M. Keck Telescope. Our analysis focuses on the two
previously identified damped \lya systems found at $z=1.920$ and $z=2.076$. For
each system, we measure accurate abundances. The $z=1.920$ system exhibits the
highest metallicity we have measured for a damped \lya system. We report the
first confident ($>5 \sigma$) detection of Ti in a QSO absorption line system.
By contrast the $z=2.076$ system is the most metal poor we have analyzed,
showing absorption features for only the strongest transitions. We find no
positive evidence for the presence of dust in either system. The two damped
systems exhibit significantly different kinematic characteristics, yet we
contend the two systems are consistent with one physical description: that of a
thick, rotating disk.
We investigate a very strong Mg II system at $z=0.752$ which is very likely
yet a third damped \lya system. The very weak Mn II and Ti II transitions have
been positively measured and imply $\log \N{HI} > 19.0$. We analyze the
abundance ratios [Mn/Fe] and [Ti/Fe] and their values are inconsistent with
dust depletion, yet consistent with the abundance pattern detected for halo
stars in the Galaxy (see Lu et al. 1996a).
Finally, we identify a C IV system at $z=2.014$ that shows a very narrow
feature in Si IV and C IV absorption. The corresponding $b$ values (5.5 \kms
and 8.9 \kms for Si IV and C IV) for this component suggest a temperature of
$4.7 \sci{4} \rm K$. Because collisional ionization can explain the observed
abundances only for $T > 8 \sci{4} \rm K$, we contend these ions must have
formed through a different physical process (e.g. photoionization). | 9605021v2 |
1996-09-09 | The Population of Damped Lyman-alpha and Lyman Limit Systems in the Cold Dark Matter Model | Lyman limit and damped Lyman-alpha absorption systems probe the distribution
of collapsed, cold gas at high redshift. Numerical simulations that incorporate
gravity and gas dynamics can predict the abundance of such absorbers in
cosmological models. We develop a semi-analytical method to correct the
numerical predictions for the contribution of unresolved low mass halos, and we
apply this method to the Katz et al. (1996) simulation of the standard cold
dark matter model ($\Omega=1$, $h=0.5$, $\Omega_b=0.05$, $\sigma_8=0.7$). Using
this simulation and higher resolution simulations of individual low mass
systems, we determine the relation between a halo's circular velocity $v_c$ and
its cross section for producing Lyman limit or damped absorption. We combine
this relation with the Press-Schechter formula for the abundance of halos to
compute the number of absorbers per unit redshift. The resolution correction
increases the predicted abundances by about a factor of two at z=2, 3, and 4,
bringing the predicted number of damped absorbers into quite good agreement
with observations. Roughly half of the systems reside in halos with circular
velocities $v_c>100\kms$ and half in halos with $35\kms<v_c<100\kms$. Halos
with $v_c>150\kms$ typically harbor two or more systems capable of producing
damped absorption. Even with the resolution correction, the predicted abundance
of Lyman limit systems is a factor of three below observational estimates,
signifying either a failure of standard CDM or a failure of these simulations
to resolve the systems responsible for most Lyman limit absorption. By
comparing simulations with and without star formation, we find that depletion
of the gas supply by star formation affects absorption line statistics at
$z>=2$ only for column densities exceeding $N_{HI}=10^{22} cm^{-2}$. | 9609072v1 |
1998-05-22 | Protogalactic Disk Models of Damped Lya Kinematics | We present new observational results on the kinematics of the damped lya
systems. Our full sample is now comprised of 31 low-ion profiles and exhibits
similar characteristics to the sample from Paper I. The primary exception is
that the new distribution of velocity widths includes values out to a maximum
of nearly 300 km/s, approx 100 km/s greater than the previous maximum. These
high velocity width systems will significantly leverage models introduced to
explain the damped lya systems. Comparing the characteristics from low-redshift
and high-redshift sub-samples, we find no evidence for significant evolution in
the kinematic properties of protogalaxies from z = 2.0 - 3.3.
The new observations give greater statistical significance to the main
conclusions of our first paper. In particular, those models inconsistent with
the damped lya observations in Paper I are ruled out at even higher levels of
confidence. At the same time, the observations are consistent with a population
of rapidly rotating, thick disks (the TRD model) at high redshift.
Buoyed by the success of the TRD model, we investigate it more closely by
considering more realistic disk properties. Our goal is to demonstrate the
statistical power of the damped lya observations by investigating the
robustness of the TRD model. In particular, we study the effects of warping,
realistic rotation curves, and photoionization on the kinematics of disks in
the TRD model. The principal results are: (1) disk warping has only minimal
effect on the kinematic results, primarily influencing the effective disk
thickness, (2) the TRD model is robust to more realistic rotation curves; (3)
the effects of photoionization require thicker disks to give consistent
velocity width distributions. [abridged] | 9805293v1 |
2000-05-05 | UVES observations of QSO 0000-2620: oxygen and zinc abundances in the Damped Ly-alpha galaxy at z_abs=3.3901 | Observations of the QSO 0000-2620 with UVES spectrograph at the 8.2m ESO
KUEYEN telescope are used for abundance analysis of the damped Ly-alpha system
at z_{abs}=3.3901. Several Oxygen lines are identified in the Ly_alpha forest
and a measure for the oxygen abundance is obtained at [O/H]=-1.85 +/- 0.1 by
means of the unsaturated OI 925 A and OI 950 A lines. This represents the most
accurate O measurement in a damped Ly_alpha galaxy so far. We have also
detected ZnII 2026 A and CrII 2056, 2062 A redshifted at about 8900 A and found
abundances [Zn/H] = -2.07 +/- 0.1 and [Cr/H]=-1.99 +/- 0.1. Furthermore,
previous measurements of Fe, Si, Ni and N have been refined yielding
[Fe/H]=-2.04 +/- 0.1, [Si/H]=-1.90 +/- 0.1, [Ni/H]=-2.27 +/- 0.1, and
[N/H]=-2.68 +/- 0.1. The abundance of the non-refractory element zinc is the
lowest among the damped Ly-alpha systems showing that the associated
intervening galaxy is indeed in the early stages of its chemical evolution. The
fact that the Zn abundance is identical to that of the refractory elements Fe
and Cr suggests that dust grains have not formed yet. In this Damped Ly-alpha
system the observed [O,S,Si/Zn,Fe,Cr] ratios, in whatever combination are
taken, are close to solar (i.e 0.1-0.2 dex) and do not show the
[alpha-element/Fe] enhancement observed in Milky Way stars of comparable
metallicity. The observed behavior supports a galaxy evolution model
characterized by either episodic or low star formation rate rather than a
Milky-Way-type evolutionary model. | 0005098v1 |
2002-02-06 | The UCSD HIRES/KeckI Damped Lya Abundance Database III. An Empirical Study of Photoionization in the Damped Lya System Toward GB1759+7539 | We investigate the ionization state of the damped Lya system at z=2.62 toward
GB1759+7539 through an analysis of ionic ratios sensitive to photoionization:
ArI/SII, FeIII/FeII, NII/NI, AlIII/AlII. Approximately half of the metals arise
in a mostly neutral velocity component with HI/H > 0.9, based on FeIII/FeII <
0.013. In contrast, the remaining half exhibits FeIII/FeII~0.3 indicative of a
partially ionized medium with HI/H~0.5. These conclusions are supported by the
observed NII/NI, AlIII/AlII, and ArI/SII ratios.
We assess ionization corrections for the observed column densities through
photoionization models derived from the CLOUDY software package. In the neutral
gas, the ionization corrections are negligible except for ArI. However for the
partially ionized gas, element abundance ratios differ from the ionic ratios by
0.1-0.3 dex for (SiII, SII, NiII, AlII)/FeII ratios and more for (NI,
ArI)/FeII. Independent of the shape of the photoionizing spectrum and
assumptions on the number of ionization phases, these ionization corrections
have minimal impact (<0.1dex) on the total metallicity inferred for this damped
Lya system. Measurements on the relative elemental abundances of the partially
ionized gas, however, have a greater than ~0.15 dex uncertainty which hides the
effects of nucleosynthesis and dust depletion.
We caution the reader that this damped system is unusual for a number of
reasons (e.g. a very low ArI/SII ratio) and we believe its ionization
properties are special but not unique. Nevertheless, it clearly shows the value
of examining photoionization diagnostics like FeIII/FeII in a larger sample of
systems. | 0202140v1 |
2009-09-26 | Damped and sub-damped Lyman-? absorbers in z > 4 QSOs | We present the results of a survey for damped (DLA, log N(H I) > 20.3) and
sub-damped Lyman-? systems (19.5 < log N(H I) < 20.3) at z > 2.55 along the
lines-of-sight to 77 quasars with emission redshifts in the range 4 < zem <
6.3. Intermediate resolution (R ? 4300) spectra have been obtained with the
Echellette Spectrograph and Imager (ESI) mounted on the Keck telescope. A total
of 100 systems with log N(H I) > 19.5 are detected of which 40 systems are
damped Lyman-? systems for an absorption length of ?X = 378. About half of the
lines of sight of this homogeneous survey have never been investigated for
DLAs. We study the evolution with redshift of the cosmological density of the
neutral gas and find, consis- tently with previous studies at similar
resolution, that ?DLA,H I decreases at z > 3.5. The overall cosmological
evolution of ?HI shows a peak around this redshift. The H I column density
distribution for log N(H I) ? 20.3 is ?tted, consistently with previous
surveys, with a single power-law of index ? ? -1.8$\pm$0.25. This power-law
overpredicts data at the high-end and a second, much steeper, power-law (or a
gamma function) is needed. There is a flattening of the function at lower H I
column densities with an index of ? ? ?1.4 for the column density range log N(H
I) = 19.5?21. The fraction of H I mass in sub-DLAs is of the order of 30%. The
H column density distribution does not evolve strongly from z ? 2.5 to z ? 4.5. | 0909.4839v2 |
2009-10-28 | Nonlinear envelope equation and nonlinear Landau damping rate for a driven electron plasma wave | In this paper, we provide a theoretical description, and calculate, the
nonlinear frequency shift, group velocity and collionless damping rate, $\nu$,
of a driven electron plasma wave (EPW). All these quantities, whose physical
content will be discussed, are identified as terms of an envelope equation
allowing one to predict how efficiently an EPW may be externally driven. This
envelope equation is derived directly from Gauss law and from the investigation
of the nonlinear electron motion, provided that the time and space rates of
variation of the EPW amplitude, $E_p$, are small compared to the plasma
frequency or the inverse of the Debye length. $\nu$ arises within the EPW
envelope equation as more complicated an operator than a plain damping rate,
and may only be viewed as such because $(\nu E_p)/E_p$ remains nearly constant
before abruptly dropping to zero. We provide a practical analytic formula for
$\nu$ and show, without resorting to complex contour deformation, that in the
limit $E_p \to 0$, $\nu$ is nothing but the Landau damping rate. We then term
$\nu$ the "nonlinear Landau damping rate" of the driven plasma wave. As for the
nonlinear frequency shift of the EPW, it is also derived theoretically and
found to assume values significantly different from previously published ones,
assuming that the wave is freely propagating. Moreover, we find no limitation
in $k \lambda_D$, $k$ being the plasma wavenumber and $\lambda_D$ the Debye
length, for a solution to the dispertion relation to exist, and want to stress
here the importance of specifying how an EPW is generated to discuss its
properties. Our theoretical predictions are in excellent agreement with results
inferred from Vlasov simulations of stimulated Raman scattering (SRS), and an
application of our theory to the study of SRS is presented. | 0910.5289v1 |
2011-05-19 | Tidal dissipation compared to seismic dissipation: in small bodies, in earths, and in superearths | While the seismic quality factor and phase lag are defined solely by the bulk
properties of the mantle, their tidal counterparts are determined both by the
bulk properties and self-gravitation of a body as a whole. For a qualitative
estimate, we model the body with a homogeneous sphere and express the tidal
phase lag through the lag in a sample of material. Although simplistic, our
model is sufficient to understand that the lags are not identical. The
difference emerges because self-gravitation pulls the tidal bulge down. At low
frequencies, this reduces strain and makes tidal damping less efficient in
larger bodies. At high frequencies, competition between self-gravitation and
rheology becomes more complex, though for sufficiently large superearths the
same rule works: the larger the body, the weaker tidal damping in it. Being
negligible for small terrestrial planets and moons, the difference between the
seismic and tidal lagging (and likewise between the seismic and tidal damping)
becomes very considerable for superearths. In those, it is much lower than what
one might expect from using a seismic quality factor. The tidal damping rate
deviates from the seismic damping rate especially in the zero-frequency limit,
and this difference takes place for bodies of any size. So the equal in
magnitude but opposite in sign tidal torques, exerted on one another by the
primary and the secondary, go smoothly through zero as the secondary crosses
the synchronous orbit. We describe the mantle rheology with the Andrade model,
allowing it to lean towards the Maxwell model at the lowest frequencies. To
implement this additional flexibility, we reformulate the Andrade model by
endowing it with a free parameter which is the ratio of the anelastic timescale
to the viscoelastic Maxwell time of the mantle. Some uncertainty in this
parameter's frequency-dependence does not influence our principal conclusions. | 1105.3936v12 |
2014-10-07 | The Effect of Nonlinear Landau Damping on Ultrarelativistic Beam Plasma Instabilities | Very-high energy gamma-rays from extragalactic sources pair-produce off of
the extragalactic background light, yielding an electron-positron pair beam.
This pair beam is unstable to various plasma instabilities, especially the
"oblique" instability, which can be the dominant cooling mechanism for the
beam. However, recently, it has been claimed that nonlinear Landau damping
renders it physically irrelevant by reducing the effective damping rate to a
low level. Here, we show with numerical calculations that the effective damping
rate is $8\times 10^{-4}$ of the growth rate of the linear instability, which
is sufficient for the "oblique" instability to be the dominant cooling
mechanism of these pair beams. In particular, we show that previous estimates
of this rate ignored the exponential cutoff in the scattering amplitude at
large wavenumber and assumed that the damping of scattered waves entirely
depends on collisions, ignoring collisionless processes. We find that the total
wave energy eventually grows to approximate equipartition with the beam by
increasingly depositing energy into long wavelength modes. As we have not
included the effect of nonlinear wave-wave interactions on these long
wavelength modes, this scenario represents the "worst-case" scenario for the
oblique instability. As it continues to drain energy from the beam at a faster
rate than other processes, we conclude that the "oblique" instability is
sufficiently strong to make it the physically dominant cooling mechanism for
high-energy pair beams in the intergalactic medium. | 1410.3797v2 |
2014-10-17 | Hunting down systematics in baryon acoustic oscillations after cosmic high noon | Future dark energy experiments will require better and more accurate
theoretical predictions for the baryonic acoustic oscillations (BAO) signature
in the spectrum of cosmological perturbations. Here, we use large N-body
simulations of the \LambdaCDM Planck cosmology to study any possible systematic
shifts and damping in BAO due to the impact of nonlinear gravitational growth
of structure, scale dependent and non-local bias, and redshift-space
distortions. The effect of cosmic variance is largely reduced by dividing the
tracer power spectrum by that from a BAO-free simulation starting with the same
phases. This permits us to study with unprecedented accuracy (better than 0.02%
for dark matter and 0.07% for low-bias halos) small shifts of the pristine BAO
wavenumbers towards larger k, and non-linear damping of BAO wiggles in the
power spectrum of dark matter and halo populations in the redshift range z=0-1.
For dark matter, we provide an accurate parametrization of the evolution of
\alpha as a function of the linear growth factor D(z). For halo samples, with
bias ranging from 1.2 to 2.8, we measure a typical BAO shift of ~0.25%,
observed in real-space, which does not show an appreciable evolution with
redshift within the uncertainties. Moreover, we report a constant shift as a
function of halo bias. We find a different evolution of the damping of the
acoustic feature in all halo samples as compared to dark matter with haloes
suffering less damping, and also find some weak dependence on bias. A larger
BAO shift and damping is measured in redshift-space which can be well explained
by linear theory due to redshift-space distortions. A clear modulation in phase
with the acoustic scale is observed in the scale-dependent halo bias due to the
presence of the baryonic acoustic oscillations. | 1410.4684v2 |
2017-01-24 | Influence of interlayer coupling on the spin torque driven excitations in a spin torque oscillator | The influence of dynamic interlayer interactions on the spin torque driven
and damped excitations are illustrated for a three layer macrospin model system
that corresponds to a standard spin-torque oscillator. The free layer and a
synthetic antiferromagnetic (SyF) pinned layer of the spin-torque oscillator
are in-plane magnetized. In order to understand experimental results, numerical
simulations have been performed considering three types of interlayer
interactions: exchange interaction between the two magnetic layers of the SyF,
mutual spin torque between the top layer of the SyF and the free layer and
dipolar interaction between all three magnetic layers. It will be shown that
the dynamic dipolar coupling plays a predominant role. First, it leads to a
hybridization of the free layer and the SyF linear modes and through this gives
rise to a strong field dependence of the critical current. In particular, there
is a field range of enhanced damping in which much higher current is required
to drive the modes into steady state. This results in a gap in the excitation
spectrum. Second, the dynamic dipolar interaction is also responsible for the
non-linear interaction between the current driven steady state mode and the
damped modes of the system. Here one can distinguish: (i) a resonant
interaction that leads to a kink in the frequency-field and frequency-current
dispersions accompanied by a small hysteresis and a reduction of the linewidth
of the steady state mode and (ii) a non-resonant interaction that leads to a
strong frequency redshift of the damped mode. The results underline the strong
impact of interlayer coupling on the excitation spectra of spin-torque
oscillators and illustrate in a simple three mode model system how in the
non-linear regime the steady state and damped modes influence each other. | 1701.06787v1 |
2017-04-07 | Global Alfven Eigenmodes in the H-1 heliac | Recent upgrades in H-1 power supplies have enabled the operation of the H-1
experiment at higher heating powers than previously attainable. A heating power
scan in mixed hydrogen/helium plasmas reveals a change in mode activity with
increasing heating power. At low power (<50 kW) modes with beta-induced Alfven
eigenmode (BAE) frequency scaling are observed. At higher power modes
consistent with an analysis of nonconventional Global Alfven Eigenmodes (GAEs)
are observed, the subject of this work. We have computed the mode continuum,
and identified GAE structures using the ideal MHD solver CKA and the
gyrokinetic code EUTERPE. An analytic model for ICRH-heated minority ions is
used to estimate the fast ion temperature from the hydrogen species. Linear
growth rate scans using a local flux surface stability calculation, LGRO, are
performed. These studies demonstrate growth from circulating particles whose
speed is significantly less than the Alfven speed, and are resonant with the
mode through harmonics of the Fourier decomposition of the strongly-shaped
heliac magnetic field. They reveal drive is possible with a small, hot
energetic tail of the hydrogen species. Local linear growth rate scans are also
complemented with global calculations from CKA and EUTERPE. These qualitatively
confirm the findings from the LGRO study, and show that the inclusion of finite
Larmor radius effects can reduce the growth rate by a factor of three, but do
not affect marginal stability. Finally, a study of damping of the global mode
with the thermal plasma is conducted, computing continuum, and the damping
arising from parallel electric fields. We find that continuum damping is of
order 0.1% for the configuration studied. The inclusion of resistivity lifts
the damping to 19%. Such large damping is consistent with experimental
observations that in absence of drive the mode decays rapidly (~0.1 ms). | 1704.02089v1 |
2017-11-30 | Scalar dark matter interpretation of the DAMPE data with U(1) gauge interactions | Recently, DAMPE experiment released the new measurement of the total cosmic
$e^+e^-$ flux between 25 GeV and 4.6 TeV which indicates a spectral softening
at around 0.9 TeV and a tentative peak at around 1.4 TeV. We utilize the scalar
dark matter (DM) annihilation scenario to explain the DAMPE peak by extending
$G_{SM}\equiv SU(3)_C \times SU(2)_L \times U(1)_Y$ with additional $U(1)$
gauge symmetries while keeping anomaly free to generate $\chi \chi \to Z^\prime
Z^\prime \to \ell\bar{\ell}\ell^\prime\overline{\ell^\prime}$, where $\chi,
Z^\prime, \ell^{(^\prime)}$ denote the scalar DM, the new gauge boson and
$\ell^{(^\prime)}=e,\mu,\tau$, respectively, with $m_\chi \sim m_{Z^\prime}
\sim 2 \times 1.5$ (TeV). We first illustrate that the minimal framework
$G_{SM} \times U(1)_{Y^\prime}$ with the above mass choices can explain the
DAMPE excess but has been excluded by LHC constraints from the $Z^\prime$
searches. Then we study a non-minimal framework $G_{SM} \times U(1)_{Y^\prime}
\times U(1)_{Y^{\prime \prime}}$ in which $U(1)_{Y^{\prime \prime}}$ mixes with
$U(1)_{Y^\prime}$. We show that such a framework can interpret the DAMPE data
while passing other constraints including the DM relic abundance, DM direct
detection and collider bounds. We also investigate the predicted $e^+e^-$
spectrum in this framework and find that the mass splitting $\Delta m = m_\chi
- m_{Z'}$ should be less than about 17 GeV to produce the peak-like structure. | 1711.11452v2 |
2017-12-14 | Scalar dark matter explanation of the DAMPE data in the minimal Left-Right symmetric model | Left-Right symmetric model (LRSM) has been an attractive extension of the
Standard Model (SM) which can address the origin of parity violation in the SM
electroweak (EW) interactions, generate tiny neutrino masses, accommodate dark
matter (DM) candidates and provide a natural framework for baryogenesis through
leptogenesis. In this work we utilize the minimal LRSM to study the recently
reported DAMPE results of cosmic $e^+e^-$ spectrum which exhibits a tentative
peak around 1.4 TeV, while satisfying the current neutrino data. We propose to
explain the DAMPE peak with a complex scalar DM $\chi$ in two scenarios: 1)
$\chi\chi^* \to H_1^{++}H_1^{--} \to \ell_i^+\ell_i^+\ell_j^-\ell_j^-$; 2)
$\chi\chi^* \to H_{k}^{++}H_{k}^{--} \to \ell_i^+\ell_i^+\ell_j^-\ell_j^-$
accompanied by $\chi\chi^* \to H_1^+ H_1^- \to \ell_i^+ \nu_{\ell_i} \ell_j^-
\nu_{\ell_j}$ with $\ell_{i,j}=e,\mu,\tau$ and $k=1,2$. We fit the theoretical
prediction on $e^+e^-$ spectrum to relevant experimental data to determine the
scalar mass spectrum favored by the DAMPE excess. We also consider various
constraints from theoretical principles, collider experiments as well as DM
relic density and direct search experiments. We find that there are ample
parameter space which can interpret the DAMPE data while passing the
constraints. Our explanations, on the other hand, usually imply the existence
of other new physics at the energy scale ranging from $10^7 {\rm GeV}$ to
$10^{11} {\rm GeV}$. Collider tests of our explanations are also discussed. | 1712.05351v3 |
2018-02-20 | The chemical connection between damped Lyman-α systems and Local Group dwarf galaxies | Abundances of the volatile elements S and Zn have now been measured in around
80 individual stars in the Sculptor dwarf spheroidal galaxy, covering the
metallicity range $-2.4\leq\text{[Fe/H]}\leq-0.9$. These two elements are of
particular interest as they are not depleted onto dust in gas, and their ratio,
[S/Zn], has thus commonly been used as a proxy for [$\alpha$/Fe] in Damped
Lyman-$\alpha$ systems. The S abundances in Sculptor are similar to other
$\alpha$-elements in this galaxy, consistent with S being mainly created in
core-collapse supernovae, but also having some contribution from supernovae
Type Ia. However, our results show that Zn and Fe do not trace all the same
nucleosynthetic production channels. In particular, (contrary to Fe) Zn is not
significantly produced by supernovae Type Ia. Thus, [S/Zn] cannot be reliably
used as a proxy for [$\alpha$/Fe]. We propose [O/S] as a function of [S/H] as a
possible alternative. At higher metallicities, the values of [S/Zn] measured in
Damped Lyman-$\alpha$ systems are inconsistent with those in local dwarf
galaxies, and are more compatible with the Milky Way disk. Low-metallicity
Damped Lyman-$\alpha$ systems are, however, consistent with the most metal-poor
stars in Local Group dwarf spheroidal galaxies. Assuming that the dust
depletions of S and Zn are negligible, our comparison indicates that the star
formation histories of Damped Lyman-$\alpha$ systems are on average different
from both the Milky Way and the Sculptor dwarf spheroidal galaxy. | 1802.07325v5 |
2019-01-12 | GW170817 implications on the frequency and damping time of f-mode oscillations of neutron stars | Within a minimum model for neutron stars consisting of nucleons, electrons
and muons at $\beta$-equilibrium using about a dozen Equation of States (EOSs)
from microscopic nuclear many-body theories and 40,000 EOSs randomly generated
using an explicitly isospin-dependent parametric EOS model for high-density
neutron-rich nucleonic matter within its currently known uncertainty range, we
study correlations among the f-mode frequency, its damping time and the tidal
deformability as well as the compactness of neutron stars. Except for quark
stars, both the f-mode frequency and damping time of canonical neutron stars
are found to scale with the tidal deformability independent of the EOSs used.
Applying the constraint on the tidal deformability of canonical neutron stars
$\Lambda_{1.4}=190^{+390}_{-120}$ extracted by the LIGO+VIRGO Collaborations
from their improved analyses of the GW170817 event, the f-mode frequency and
its damping time of canonical neutron stars are limited to 1.67 kHz - 2.18 kHz
and 0.155 s - 0.255 s, respectively, providing a useful guidance for the
ongoing search for gravitational waves from the f-mode oscillations of isolated
neutron stars. Moreover, assuming either or both the f-mode frequency and its
damping time will be measured precisely in future observations with advanced
gravitational wave detectors, we discuss how information about the mass and/or
radius as well as the still rather elusive nuclear symmetry energies at
supra-saturation densities may be extracted. | 1901.03779v2 |
2019-01-27 | An introductory guide to fluid models with anisotropic temperatures Part 2 -- Kinetic theory, Padé approximants and Landau fluid closures | In Part 2 of our guide to collisionless fluid models, we concentrate on
Landau fluid closures. These closures were pioneered by Hammett and Perkins and
allow for the rigorous incorporation of collisionless Landau damping into a
fluid framework. It is Landau damping that sharply separates traditional fluid
models and collisionless kinetic theory, and is the main reason why the usual
fluid models do not converge to the kinetic description, even in the
long-wavelength low-frequency limit. We start with a brief introduction to
kinetic theory, where we discuss in detail the plasma dispersion function
$Z(\zeta)$, and the associated plasma response function $R(\zeta)=1+\zeta
Z(\zeta)=-Z'(\zeta)/2$. We then consider a 1D (electrostatic) geometry and make
a significant effort to map all possible Landau fluid closures that can be
constructed at the 4th-order moment level. These closures for parallel moments
have general validity from the largest astrophysical scales down to the Debye
length, and we verify their validity by considering examples of the (proton and
electron) Landau damping of the ion-acoustic mode, and the electron Landau
damping of the Langmuir mode. We proceed by considering 1D closures at
higher-order moments than the 4th-order, and as was concluded in Part 1, this
is not possible without Landau fluid closures. We show that it is possible to
reproduce linear Landau damping in the fluid framework to any desired
precision, thus showing the convergence of the fluid and collisionless kinetic
descriptions. We then consider a 3D (electromagnetic) geometry in the
gyrotropic (long-wavelength low-frequency) limit and map all closures that are
available at the 4th-order moment level. In the Appendix A, we provide
comprehensive tables with Pad\'e approximants of $R(\zeta)$ up to the 8th-pole
order, with many given in an analytic form. | 1901.09360v2 |
2019-01-28 | Revisit of non-linear Landau damping for electrostatic instability driven by blazar-induced pair beams | We revisit the effect of non-linear Landau (NL) damping on the electrostatic
instability of blazar-induced pair beams, using a realistic pair-beam
distribution. We employ a simplified 2D model in ${\bf k}$-space to study the
evolution of the electric-field spectrum and to calculate the relaxation time
of the beam. We demonstrate that the 2D model is an adequate representation of
the 3D physics. We find that non-linear Landau damping, once it operates
efficiently, transports essentially the entire wave energy to small wavenumbers
where wave driving is weak or absent. The relaxation time also strongly depends
on the IGM temperature, $T_\mathrm{IGM}$, and for $T_\mathrm{IGM}\ll10$ eV, and
in the absence of any other damping mechanism, the relaxation time of the pair
beam is longer than the inverse Compton (IC) scattering time. The weak
late-time beam energy losses arise from the accumulation of wave energy at
small $k$, that non-linearly drains the wave energy at the resonant
$\mathbf{k}$ of the pair-beam instability. Any other dissipation process
operating at small $k$ would reduce that wave-energy drain and hence lead to
stronger pair-beam energy losses. As an example, collisions reduce the
relaxation time by an order of magnitude, although their rate is very small.
Other non-linear processes, such as the modulation instability, could provide
additional damping of the non-resonant waves and dramatically reduce the
relaxation time of the pair beam. An accurate description of the spectral
evolution of the electrostatic waves is crucial for calculating the relaxation
time of the pair beam. | 1901.09640v3 |
2019-11-22 | Role of Element-Specific Damping on the Ultrafast, Helicity-Independent All-Optical Switching Dynamics in Amorphous (Gd,Tb)Co Thin Films | Ultrafast control of the magnetization in ps timescales by fs laser pulses
offers an attractive avenue for applications such as fast magnetic devices for
logic and memory. However, ultrafast helicity-independent all-optical switching
(HI-AOS) of the magnetization has thus far only been observed in Gd-based,
ferrimagnetic amorphous (\textit{a}-) rare earth-transition metal
(\textit{a}-RE-TM) systems, and a comprehensive understanding of the reversal
mechanism remains elusive. Here, we report HI-AOS in ferrimagnetic
\textit{a}-Gd$_{22-x}$Tb$_x$Co$_{78}$ thin films, from x = 0 to x = 18, and
elucidate the role of Gd in HI-AOS in \textit{a}-RE-TM alloys and multilayers.
Increasing Tb content results in increasing perpendicular magnetic anisotropy
and coercivity, without modifying magnetization density, and slower
remagnetization rates and higher critical fluences for switching but still
shows picosecond HI-AOS. Simulations of the atomistic spin dynamics based on
the two-temperature model reproduce these results qualitatively and predict
that the lower damping on the RE sublattice arising from the small spin-orbit
coupling of Gd (with $L = 0$) is instrumental for the faster dynamics and lower
critical fluences of the Gd-rich alloys. Annealing
\textit{a}-Gd$_{10}$Tb$_{12}$Co$_{78}$ leads to slower dynamics which we argue
is due to an increase in damping. These simulations strongly indicate that
acounting for element-specific damping is crucial in understanding HI-AOS
phenomena. The results suggest that engineering the element specific damping of
materials can open up new classes of materials that exhibit low-energy,
ultrafast HI-AOS. | 1911.09803v3 |
2020-06-08 | Hysteretic depinning of a particle in a periodic potential: Phase diagram and criticality | We consider a massive particle driven with a constant force in a periodic
potential and subjected to a dissipative friction. As a function of the drive
and damping, the phase diagram of this paradigmatic model is well known to
present a pinned, a sliding, and a bistable regime separated by three distinct
bifurcation lines. In physical terms, the average velocity $v$ of the particle
is nonzero only if either (i) the driving force is large enough to remove any
stable point, forcing the particle to slide, or (ii) there are local minima but
the damping is small enough, below a critical damping, for the inertia to allow
the particle to cross barriers and follow a limit cycle; this regime is
bistable and whether $v > 0$ or $v = 0$ depends on the initial state. In this
paper, we focus on the asymptotes of the critical line separating the bistable
and the pinned regimes. First, we study its behavior near the "triple point"
where the pinned, the bistable, and the sliding dynamical regimes meet. Just
below the critical damping we uncover a critical regime, where the line
approaches the triple point following a power-law behavior. We show that its
exponent is controlled by the normal form of the tilted potential close to its
critical force. Second, in the opposite regime of very low damping, we revisit
existing results by providing a simple method to determine analytically the
exact behavior of the line in the case of a generic potential. The analytical
estimates, accurately confirmed numerically, are obtained by exploiting exact
soliton solutions describing the orbit in a modified tilted potential which can
be mapped to the original tilted washboard potential. Our methods and results
are particularly useful for an accurate description of underdamped nonuniform
oscillators driven near their triple point. | 2006.04912v2 |
2020-09-14 | Large field-like torque in amorphous Ru2Sn3 originated from the intrinsic spin Hall effect | We investigated temperature dependent current driven spin-orbit torques in
magnetron sputtered Ru2Sn3 (4 and 10 nm) /Co20Fe60B20 (5 nm) layered structures
with in-plane magnetic anisotropy. The room temperature damping-like and
field-like spin torque efficiencies of the amorphous Ru2Sn3 films were measured
to be 0.14 +- 0.008 (0.07 +- 0.012) and -0.03 +- 0.006 (-0.20 +- 0.009), for
the 4 (10 nm) films respectively, by utilizing the second harmonic Hall
technique. The large field-like torque in the relatively thicker Ru2Sn3 (10 nm)
thin film is unique compared to the traditional spin Hall materials interfaced
with thick magnetic layers with in-plane magnetic anisotropy which typically
have dominant damping-like and negligible field-like torques. Additionally, the
observed room temperature field-like torque efficiency in Ru2Sn3 (10 nm)/CoFeB
(5 nm) is up to three times larger than the damping-like torque (-0.20 +- 0.009
and 0.07 +- 0.012, respectively) and thirty times larger at 50 K (-0.29 +-
0.014 and 0.009 +- 0.017, respectively). The temperature dependence of the
field-like torques show dominant contributions from the intrinsic spin Hall
effect while the damping-like torques show dominate contributions from the
extrinsic spin Hall effects, skew scattering and side jump. Through macro-spin
calculations, we found that including field-like torques on the order or larger
than the damping-like torque can reduce the switching critical current and
decrease magnetization procession for a perpendicular ferromagnetic layer. | 2009.06711v2 |
2021-01-12 | Phase Retrieval using Expectation Consistent Signal Recovery Algorithm based on Hypernetwork | Phase retrieval (PR) is an important component in modern computational
imaging systems. Many algorithms have been developed over the past
half-century. Recent advances in deep learning have introduced new
possibilities for a robust and fast PR. An emerging technique called deep
unfolding provides a systematic connection between conventional model-based
iterative algorithms and modern data-based deep learning. Unfolded algorithms,
which are powered by data learning, have shown remarkable performance and
convergence speed improvement over original algorithms. Despite their
potential, most existing unfolded algorithms are strictly confined to a fixed
number of iterations when layer-dependent parameters are used. In this study,
we develop a novel framework for deep unfolding to overcome existing
limitations. Our development is based on an unfolded generalized expectation
consistent signal recovery (GEC-SR) algorithm, wherein damping factors are left
for data-driven learning. In particular, we introduce a hypernetwork to
generate the damping factors for GEC-SR. Instead of learning a set of optimal
damping factors directly, the hypernetwork learns how to generate the optimal
damping factors according to the clinical settings, thereby ensuring its
adaptivity to different scenarios. To enable the hypernetwork to adapt to
varying layer numbers, we use a recurrent architecture to develop a dynamic
hypernetwork that generates a damping factor that can vary online across
layers. We also exploit a self-attention mechanism to enhance the robustness of
the hypernetwork. Extensive experiments show that the proposed algorithm
outperforms existing ones in terms of convergence speed and accuracy and still
works well under very harsh settings, even under which many classical PR
algorithms are unstable. | 2101.04348v2 |
2021-06-18 | Sloshing dynamics of liquid tank with built-in buoys for wave energy harvesting | This paper proposes a novel design of liquid tank with built-in buoys for
wave energy harvesting, named the 'sloshing wave energy converter (S-WEC)'.
When the tank is oscillated by external loads (such as ocean waves), internal
liquid sloshing is activated, and the mechanical energy of sloshing waves can
be absorbed by the power take-off (PTO) system attached to these buoys. A
fully-nonlinear numerical model is established based on the boundary element
method for a systematic investigation on dynamic properties of the proposed
S-WEC. A motion decoupling algorithm based on auxiliary functions is developed
to solve the nonlinear interaction of sloshing waves and floating buoys in the
tank. An artificial damping model is introduced to reflect viscous effects of
the sloshing liquid. Physical experiments are carried out on a scaled S-WEC
model to validate the mathematical and numerical methodologies. Natural
frequencies of the S-WEC system are first investigated through spectrum
analyses on motion histories of the buoy and sloshing liquid. The viscous
damping strength is identified through comparisons with experimental
measurements. Effects of the PTO damping on power generation characteristics of
S-WEC is further explored. An optimal PTO damping can be found for each
excitation frequency, leading to the maximisation of both the power generation
and conversion efficiency of the buoy. To determine a constant PTO damping for
engineering design, a practical approach based on diagram analyses is proposed.
Effects of the buoy's geometry on power generation characteristics of the S-WEC
are also investigated. In engineering practice, the present design of S-WEC can
be a promising technical solution of ocean wave energy harvesting, based on its
comprehensive advantages on survivability enhancement, metal corrosion or
fouling organism inhibition, power generation stability and efficiency, and so
on. | 2106.10005v1 |
2005-03-31 | Study of the angular coefficients and corresponding helicity cross sections of the W boson in hadron collisions | We present the Standard Model prediction for the eight angular coefficients
of the W boson, which completely describe its differential cross section in
hadron collisions. These coefficients are ratios of the W helicity cross
sections and the total unpolarized cross section. We also suggest a technique
to experimentally extract the coefficients. | 0503291v1 |
1992-06-08 | su(3)k fusion coefficients | A closed and explicit formula for all $\su{(3)}_k$ fusion coefficients is
presented which, in the limit $k \rightarrow \infty$, turns into a simple and
compact expression for the $su(3)$ tensor product coefficients. The derivation
is based on a new diagrammatic method which gives directly both tensor product
and fusion coefficients. | 9206032v1 |
2005-11-15 | Power series coefficients for probabilities in finite classical groups | It is shown that a wide range of probabilities and limiting probabilities in
finite classical groups have integral coefficients when expanded as a power
series in 1/q. Moreover it is proved that the coefficients of the limiting
probabilities in the general linear and unitary cases are equal modulo 2. The
rate of stabilization of the finite dimensional coefficients as the dimension
increases is discussed. | 0511390v1 |
2007-09-20 | Uniform Convergence of the Spectral Expansion for a Differential Operator with Periodic Matrix Coefficients | In this paper, we obtain asymptotic formulas for eigenvalues and
eigenfunctions of the operator generated by a system of ordinary differential
equations with summable coefficients and the quasiperiodic boundary conditions.
Using these asymptotic formulas, we find conditions on the coefficients for
which the root functions of this operator form a Riesz basis. Then we obtain
the uniformly convergent spectral expansion of the differential operators with
the periodic matrix coefficients | 0709.3190v1 |
2007-11-07 | A Diagrammatic Approach for the Coefficients of the Characteristic Polynomial | In this work we provide a novel approach for computing the coefficients of
the characteristic polynomial of a square matrix. We demonstrate that each
coefficient can be efficiently represented by a set of circle graphs. Thus, one
can employ a diagrammatic approach to determine the coefficients of the
characteristic polynomial. | 0711.1032v1 |
2008-11-12 | Some Probabilistic and Statistical Properties of a Random Coefficient Autoregressive Model | A statistical inference for random coefficient first-order autoregressive
model $[RCAR(1)]$ was investigated by P.M. ROBINSON (1978) in which the
coefficients varying over individuals. In this paper we attempt to generalize
this result to random coefficient autoregressive model of order $p$
$[RCAR(p)]$. The stationarity condition will derived for this model. | 0811.1846v1 |
2009-03-04 | On the Differential Operators with Periodic Matrix Coefficients | In this article we obtain asymptotic formulas for eigenvalues and
eigenfunctions of the operator generated by a system of ordinary differential
equations with summable coefficients and quasiperiodic boundary conditions.
Then using these asymptotic formulas, we find conditions on the coefficients
for which the number of gaps in the spectrum of the self-adjoint differential
operator with the periodic matrix coefficients is finite. | 0903.0776v1 |
2009-04-27 | SO(5) Clebsch-Gordan coefficients involving the 14-dimensional representation | Analytic expressions for the Clebsch-Gordan (CG) coefficients of the SO(5)
group that involve the 14-dimensional representation can be found in an old
paper of M. K. F. Wong. A careful analysis yields that roughly 30% of the
coefficients given in that paper are wrong. The correct analytic expressions
for all SO(5) group CG coefficients containing the 14-dimensional
representation are obtained. | 0904.4200v1 |
2010-01-18 | Coefficients in powers of the log series | We determine the p-exponent in many of the coefficients in the power series
(log(1+x)/x)^t, where t is any integer. In our proof, we introduce a variant of
multinomial coefficients. We also characterize the power series x/log(1+x) by
certain zero coefficients in its powers. | 1001.3068v1 |
2011-04-05 | Comparison of Weibull tail-coefficient estimators | We address the problem of estimating the Weibull tail-coefficient which is
the regular variation exponent of the inverse failure rate function. We propose
a family of estimators of this coefficient and an associate extreme quantile
estimator. Their asymptotic normality are established and their asymptotic
mean-square errors are compared. The results are illustrated on some finite
sample situations. | 1104.0764v1 |
2011-07-05 | Solution of Fokker-Planck equation for a broad class of drift and diffusion coefficients | We consider a Langevin equation with variable drift and diffusion
coefficients separable in time and space and its corresponding Fokker-Planck
equation in the Stratonovich approach. From this Fokker-Planck equation we
obtain a class of exact solutions with the same spatial drift and diffusion
coefficients. Furthermore, we analyze some details of this system by using the
spatial diffusion coefficient $D(x)=\sqrt{D}|x| ^{-% \frac{\theta}{2}}$. | 1107.0959v1 |
2011-07-13 | Identification of the coefficients in the linear Boltzmann equation by a finite number of boundary measurements | In this paper we consider an inverse problem for the time dependent linear
Boltzmann equation. It concerns the identification of the coefficients via a
finite number of measurements on the boundary. We prove that the total
extinction coefficient and the collision kernel can be uniquely determined by
at most k measurements on the boundary, provided that these coefficients belong
to a finite k-dimensional vector space. | 1107.2682v1 |
2012-02-01 | A generalization of the Gaussian formula and a q-analog of Fleck's congruence | The q-binomial coefficients are the polynomial cousins of the traditional
binomial coefficients, and a number of identities for binomial coefficients can
be translated into this polynomial setting. For instance, the familiar
vanishing of the alternating sum across row n of Pascal's triangle is captured
by the so-called Gaussian Formula. In this paper, we find a q-binomial
congruence which synthesizes this result and Fleck's congruence for binomial
coefficients. | 1202.0199v1 |
2012-05-03 | On some binomial coefficients related to the evaluation of tan(nx) | The purpose of this paper is to study some binomial coefficients which are
related to the evaluation of tan(nx). We present a connection between these
binomial coefficients and the coefficients of a family of derivative
polynomials for tangent and secant. | 1205.0735v4 |
2012-08-01 | Applications of Theory of Differential Subordination for Functions with Fixed Initial Coefficient to Univalent Functions | By using the theory of first-order differential subordination for functions
with fixed initial coefficient, several well-known results for subclasses of
univalent functions are improved by restricting the functions to have fixed
second coefficient. The influence of the second coefficient of univalent
functions is evident in the results obtained. | 1208.0148v1 |
2013-11-12 | Strong Rate of Convergence for the Euler-Maruyama Approximation of Stochastic Differential Equations with Irregular Coefficients | We consider the Euler-Maruyama approximation for multi-dimensional stochastic
differential equations with irregular coefficients. We provide the rate of
strong convergence where the possibly discontinuous drift coefficient satisfies
a one-sided Lipschitz condition and the diffusion coefficient is H\"older
continuous. | 1311.2725v2 |
2014-03-08 | Functional equations for double series of Euler-Hurwitz-Barnes type with coefficients | We first survey the known results on functional equations for the double
zeta-function of Euler type and its various generalizations. Then we prove two
new functional equations for double series of Euler-Hurwitz-Barnes type with
complex coefficients. The first one is of general nature, while the second one
is valid when the coefficients are Fourier coefficients of a cusp form. | 1403.1940v1 |
2014-04-09 | $L^p(Ω)$-Difference of One-Dimensional Stochastic Differential Equations with Discontinuous Drift | We consider a one-dimensional stochastic differential equations (SDE) with
irregular coefficients. The purpose of this paper is to estimate the
$L^p(\Omega)$-difference of SDEs using the norm of the difference of
coefficients, where the discontinuous drift coefficient satisfies a one-sided
Lipschitz condition and the diffusion coefficient is bounded, uniformly
elliptic and H\"older continuous. As an application, we consider the stability
problem. | 1404.2358v1 |
2014-05-20 | Convergence of a Metropolized Integrator for Stochastic Differential Equations with Variable Diffusion Coefficient | We present an explicit method for simulating stochastic differential
equations (SDEs) that have variable diffusion coefficients and satisfy the
detailed balance condition with respect to a known equilibrium density. In
Tupper and Yang (2012), we proposed a framework for such systems in which,
instead of a diffusion coefficient and a drift coefficient, a modeller
specifies a diffusion coefficient and a equilibrium density, and then assumes
detailed balance with respect to this equilibrium density. We proposed a
numerical method for such systems that works directly with the diffusion
coefficient and equilibrium density, rather than the drift coefficient, and
uses a Metropolis-Hastings rejection process to preserve the equilibrium
density exactly. Here we show that the method is weakly convergent with order
1/2 for such systems with smooth coefficients. We perform numerical experiments
demonstrating the convergence of the method for systems not covered by our
theorem, including systems with discontinuous diffusion coefficients and
equilibrium densities. | 1405.5264v2 |
2014-07-06 | Deligne categories and reduced Kronecker coefficients | The Kronecker coefficients are the structural constants for the tensor
categories of representations of the symmetric groups; namely, given three
partitions $\lambda, \mu, \tau$ of $n$, the multiplicity of $\lambda$ in $\mu
\otimes \tau$ is called the Kronecker coefficient $g^{\lambda}_{\mu, \tau}$.
When the first part of each of the partitions is taken to be very large (the
remaining parts being fixed), the values of the appropriate Kronecker
coefficients stabilize; the stable value is called the reduced (or stable)
Kronecker coefficient. These coefficients also generalize the
Littlewood-Richardson coefficients, and have been studied quite extensively.
In this paper, we show that reduced Kronecker coefficients appear naturally
as structure constants of the Deligne categories $\underline{Rep}(S_t)$. This
allows us to interpret various properties of the reduced Kronecker coefficients
as categorical properties of the categories $\underline{Rep}(S_t)$. | 1407.1506v1 |
2014-12-08 | On the optimal estimates and comparison of Gegenbauer expansion coefficients | In this paper, we study optimal estimates and comparison of the coefficients
in the Gegenbauer series expansion. We propose an alternative derivation of the
contour integral representation of the Gegenbauer expansion coefficients which
was recently derived by Cantero and Iserles [SIAM J. Numer. Anal., 50 (2012),
pp.307-327]. With this representation, we show that optimal estimates for the
Gegenbauer expansion coefficients can be derived, which in particular includes
Legendre coefficients as a special case. Further, we apply these estimates to
establish some rigorous and computable bounds for the truncated Gegenbauer
series. In addition, we compare the decay rates of the Chebyshev and Legendre
coefficients. For functions whose singularity is outside or at the endpoints of
the expansion interval, asymptotic behaviour of the ratio of the nth Legendre
coefficient to the nth Chebyshev coefficient is given, which provides us an
illuminating insight for the comparison of the spectral methods based on
Legendre and Chebyshev expansions. | 1412.2525v3 |
2015-04-25 | Improved Vietoris Sine Inequalities for Non-Monotone, Non-Decaying Coefficients | Recently the author established an improvement of the classical Vietoris sine
inequality to include sine polynomials with non-monotone coefficients.
In this paper two further improvements are presented admitting sine
polynomials with non-monotone and non-decaying coefficients.
The extremal sums of the two results have the coefficient sequences {2a, a,
4/3, 1, 6/5, 1, 8/7, 1, ...}, where a = 0.78265..., and {3, 3/2, 7/3, 7/4,
11/5, 11/6, ...}. | 1504.06705v1 |
2015-05-16 | Relation Functions Evaluated from Unique Coefficient Patterns | In this paper, we study polynomials of the form $f(x)=(x^n+x^{n-1}+...+1)^l$
for $l=1,2,3,4$ to generate a pattern titled "unique coefficient pattern".
Namely, we analyze each unique coefficient patterns of $f(x)$ and generate
functions titled "relation functions". The approach that we follow will allow
us to evaluate desired coefficients for such polynomial expansions by simply
using these relation functions. | 1505.04325v1 |
2015-06-05 | Cluster automorphism groups of cluster algebras with coefficients | We study the cluster automorphism group of a skew-symmetric cluster algebra
with geometric coefficients. For this, we introduce the notion of gluing free
cluster algebra, and show that under a weak condition the cluster automorphism
group of a gluing free cluster algebra is a subgroup of the cluster
automorphism group of its principal part cluster algebra (i.e. the
corresponding cluster algebra without coefficients). We show that several
classes of cluster algebras with coefficients are gluing free, for example,
cluster algebras with principal coefficients, cluster algebras with universal
geometric coefficients, and cluster algebras from surfaces (except a 4-gon)
with coefficients from boundaries. Moreover, except four kinds of surfaces, the
cluster automorphism group of a cluster algebra from a surface with
coefficients from boundaries is isomorphic to the cluster automorphism group of
its principal part cluster algebra; for a cluster algebra with principal
coefficients, its cluster automorphism group is isomorphic to the automorphism
group of its initial quiver. | 1506.01942v1 |
2015-07-28 | Some identities involving polynomial coefficients | By polynomial (or extended binomial) coefficients, we mean the coefficients
in the expansion of integral powers, positive and negative, of the polynomial
$1+t +\cdots +t^{m}$; $m\geq 1$ being a fixed integer. We will establish
several identities and summation formul\ae\ parallel to those of the usual
binomial coefficients. | 1507.07968v2 |
2016-03-12 | On alternating sums of binomial coefficients and $q$-binomial coefficients | In this paper we shall evaluate two alternating sums of binomial coefficients
by a combinatorial argument. Moreover, by combining the same combinatorial idea
with partition theoretic techniques, we provide $q$-analogues involving the
$q$-binomial coefficients. | 1603.03881v2 |
2016-04-27 | Series extension: Predicting approximate series coefficients from a finite number of exact coefficients | Given the first 20-100 coefficients of a typical generating function of the
type that arises in many problems of statistical mechanics or enumerative
combinatorics, we show that the method of differential approximants performs
surprisingly well in predicting (approximately) subsequent coefficients. These
can then be used by the ratio method to obtain improved estimates of critical
parameters. In favourable cases, given only the first 20 coefficients, the next
100 coefficients are predicted with useful accuracy. More surprisingly, this is
also the case when the method of differential approximants does not do a useful
job in estimating the critical parameters, such as those cases in which one has
stretched exponential asymptotic behaviour. Nevertheless, the coefficients are
predicted with surprising accuracy. As one consequence, significant computer
time can be saved in enumeration problems where several runs would normally be
made, modulo different primes, and the coefficients constructed from their
values modulo different primes. Another is in the checking of newly calculated
coefficients. We believe that this concept of approximate series extension
opens up a whole new chapter in the method of series analysis. | 1604.08254v1 |
2016-09-26 | A Note On Signs Of Fourier Coefficients Of Two Cusp Forms | Kohnen and Sengupta proved that two cusp forms of different integral weights
with real algebraic Fourier coefficients have infinitely many Fourier
coefficients of the same as well as of opposite sign, up to the action of a
Galois automorphism. Recently Gun, Kohnen and Rath strengthen their result by
comparing the simultaneous sign changes of Fourier coefficients of two cusp
forms with arbitrary real Fourier coefficients. The simultaneous sign changes
of Fourier coefficients of two same integral weight cusp forms follow from an
earlier work of Ram Murty. In this note we compare the signs of the Fourier
coefficients of two cusp forms simultaneously for the congruence subgroup
$\Gamma_0(\mathit{N})$ where the coefficients lie in an arithmetic progression.
Next we consider an analogous question for the particular sparse sequences of
Fourier coefficients of normalized Hecke eigen cusp forms for the full modular
group. | 1609.07938v2 |
2016-11-29 | Stapledon Decompositions and Inequalities for Coefficients of Chromatic Polynomials | We use a polynomial decomposition result by Stapledon to show that the
numerator polynomial of the Ehrhart series of an open polytope is the
difference of two symmetric polynomials with nonnegative integer coefficients.
We obtain a related decomposition for order polytopes and for the numerator
polynomial of the corresponding series for chromatic polynomials. The
nonnegativity of the coefficients in such decompositions provide inequalities
satisfied by the coefficients of chromatic polynomials for any simple graph. | 1611.09728v1 |
2017-09-12 | Langevin Diffusion Coefficients Ratio in STU Model with Higher Derivative Corrections | In this letter, we study Langevin diffusion coefficients for the five
dimensional $\mathcal{N}=2$ STU model in presence of higher derivative
corrections. We obtained effect of black hole charge, corresponding to the
chemical potential, on the Langevin diffusion coefficients ratio. We confirm
universal behavior of transverse to longitudinal ratio of coefficients. | 1709.06846v1 |
2017-09-29 | Equivalence of sparse and Carleson coefficients for general sets | We remark that sparse and Carleson coefficients are equivalent for every
countable collection of Borel sets and hence, in particular, for dyadic
rectangles, the case relevant to the theory of bi-parameter singular integrals.
The key observation is that a dual refomulation by I. E. Verbitsky for
Carleson coefficients over dyadic cubes holds also for Carleson coefficients
over general sets. We give a simple proof for this reformulation. | 1709.10457v1 |
2018-09-21 | The partition algebra and the plethysm coefficients I: stability and Foulkes' conjecture | We propose a new approach to study plethysm coefficients by using the
Schur-Weyl duality between the symmetric group and the partition algebra. This
allows us to explain the stability properties of plethysm and Kronecker
coefficients in a simple and uniform fashion for the first time. We prove the
strengthened Foulkes' conjecture for stable plethysm coefficients in an
elementary fashion. | 1809.08128v2 |
2018-10-09 | A class of univalent functions with real coefficients | In this paper we study class $\mathcal{S}^+$ of univalent functions $f$ such
that $\frac{z}{f(z)}$ has real and positive coefficients. For such functions we
give estimates of the Fekete-Szeg\H{o} functional and sharp estimates of their
initial coefficients and logarithmic coefficients. Also, we present necessary
and sufficient conditions for $f\in \mathcal{S}^+$ to be starlike of order
$1/2$. | 1810.03839v2 |
2019-07-12 | Tamagawa number formula with coefficients over varieties in positive characteristic | We express the order of the pole and the leading coefficient of the
L-function of a (large class of) -adic coefficients (any prime) over a
quasi-projective variety over a finite field of characteristic p. This is a
generalization of the result of Milne-Ramachandran with coefficients. The new
key ingredient is the use of F-gauges and their equivalence in the derived
category with Raynaud modules proved by Ekedahl. | 1907.05838v1 |
2019-10-21 | Super-congruences involving trininomial coefficients | The aim of this work is to establish congruences $\left(
\operatorname{mod}p^{2}\right) $ involving the trinomial coefficients
$\binom{np-1}{p-1}_{2}$ and $\binom{np-1}{\left( p-1\right)/2}_{2}$ arising
from the expansion of the powers of the polynomial $1+x+x^{2}.$ In main results
we extend some known congruences involving the binomial coefficients
$\binom{np-1}{p-1}$ and $\binom{np-1}{\left( p-1\right) /2}$ and establish
congruences link binomial coefficients and harmonic numbers. | 1910.09262v1 |
2020-01-06 | On resolvent approximations of elliptic differential operators with periodic coefficients | We study resolvent approximations for elliptic differential nonselfadjoint
operators with periodic coefficients in the limit of the small period. The
class of operators covered by our analysis includes uniformly elliptic families
with bounded coefficients and also with unbounded coefficients from the
John-Nirenberg space $BMO$ (bounded mean oscillation). We apply the modified
method of the first approximation with the usage of Steklov's smoothing. | 2001.01701v1 |
2020-02-25 | Upper bounds on Kronecker coefficients with few rows | We present three different upper bounds for Kronecker coefficients
$g(\lambda,\mu,\nu)$ in terms of Kostka numbers, contingency tables and
Littlewood--Richardson coefficients. We then give various examples, asymptotic
applications, and compare them with existing lower bounds. | 2002.10956v2 |
2020-03-13 | Transforming ODEs and PDEs with radical coefficients into rational coefficients | We present an algorithm that transforms, if possible, a given ODE or PDE with
radical function coefficients into one with rational coefficients by means of a
rational change of variables. It also applies to systems of linear ODEs. It is
based on previous work on reparametrization of radical algebraic varieties. | 2003.06301v1 |
2020-04-09 | Magneto-Seebeck coefficient and Nernst coefficient of hot and dense hadron gas | We discuss the thermoelectric effect of hot and dense hadron gas within the
framework of the hadron resonance gas model. Using the relativistic Boltzmann
equation within the relaxation time approximation we estimate the Seebeck
coefficient of the hot and dense hadronic medium with a gradient in temperature
and baryon chemical potential. The hadronic medium in this calculation is
modeled by the hadron resonance gas (HRG) model with hadrons and their
resonances up to a mass cutoff $\Lambda\sim 2.6$ GeV. We also extend the
formalism of the thermoelectric effect for a nonvanishing magnetic field. The
presence of magnetic field also leads to a Hall type thermoelectric coefficient
(Nernst coefficient) for the hot and dense hadronic matter apart from a
magneto-Seebeck coefficient. We find that generically in the presence of a
magnetic field Seebeck coefficient decreases while the Nernst coefficient
increases with the magnetic field. At higher temperature and/or baryon chemical
potential these coefficients approach to their values at vanishing magnetic
field. | 2004.04665v2 |
2020-04-29 | Large Fourier coefficients of half-integer weight modular forms | This article is concerned with the Fourier coefficients of cusp forms (not
necessarily eigenforms) of half-integer weight lying in the plus space. We give
a soft proof that there are infinitely many fundamental discriminants $D$ such
that the Fourier coefficients evaluated at $|D|$ are non-zero. By adapting the
resonance method, we also demonstrate that such Fourier coefficients must take
quite large values. | 2004.14450v1 |
2020-09-23 | A combinatorial correspondence between finite Euclidean geometries and symmetric subsets of $\mathbb{Z}/n\mathbb{Z}$ | $q$-analogues of quantities in mathematics involve perturbations of classical
quantities using the parameter $q$, and revert to the original quantities when
$q$ goes $1$. An important example is the $q$-analogues of binomial
coefficients which give the number of $k$-dimensional subspaces in
$\mathbb{F}_{q}^{n}$. When $q$ goes to $1$, this reverts to the binomial
coefficients which measure the number of $k$-sets in $\left [ n \right ]$.
Dot-analogues of $q$-binomial coefficients were studied by Yoo (2019) in order
to investigate combinatorics of quadratic spaces over finite fields. The number
of $k$-dimensional quadratic spaces of
$(\mathbb{F}_{q}^{n},x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2})$ which are
isometrically isomorphic to
$(\mathbb{F}_{q}^{k},x_{1}^{2}+x_{2}^{2}+\cdots+x_{k}^{2})$ can be also
described as analogous to binomial coefficients, called the dot-binomial
coefficients, $\binom{n}{k}_{d}$.
In this paper, we study a combinatorial correspondence between this finite
Euclidean geometries and symmetric subsets of $\mathbb{Z}/n\mathbb{Z}$. In
addition, we show that dot-binomial coefficients can be expressed in terms of
$q$-binomial coefficients and polynomials, and we prove that dot-binomial
coefficients are polynomials in $q$. Furthermore, we study the properties of
the polynomials given by the dot binomial coefficients $\binom{n}{k}_{d}$. | 2009.11258v2 |
2020-11-21 | Measuring Quadrangle Formation in Complex Networks | The classic clustering coefficient and the lately proposed closure
coefficient quantify the formation of triangles from two different
perspectives, with the focal node at the centre or at the end in an open triad
respectively. As many networks are naturally rich in triangles, they become
standard metrics to describe and analyse networks. However, the advantages of
applying them can be limited in networks, where there are relatively few
triangles but which are rich in quadrangles, such as the protein-protein
interaction networks, the neural networks and the food webs. This yields for
other approaches that would leverage quadrangles in our journey to better
understand local structures and their meaning in different types of networks.
Here we propose two quadrangle coefficients, i.e., the i-quad coefficient and
the o-quad coefficient, to quantify quadrangle formation in networks, and we
further extend them to weighted networks. Through experiments on 16 networks
from six different domains, we first reveal the density distribution of the two
quadrangle coefficients, and then analyse their correlations with node degree.
Finally, we demonstrate that at network-level, adding the average i-quad
coefficient and the average o-quad coefficient leads to significant improvement
in network classification, while at node-level, the i-quad and o-quad
coefficients are useful features to improve link prediction. | 2011.10763v1 |
2021-05-20 | On the $RO(Q)$-graded coefficients of Eilenberg-MacLane spectra | Let $Q$ denote the cyclic group of order two. Using the Tate diagram we
compute the $RO(Q)$-graded coefficients of Eilenberg-MacLane $Q$-spectra and
describe their structure as a module over the coefficients of the
Eilenberg-MacLane spectrum of the Burnside Mackey functor. If the underlying
Mackey functor is a Green functor, we also infer the multiplicative structure
on the $RO(Q)$-graded coefficients. | 2105.09768v2 |
2021-06-09 | A Data-driven Optimization of First-order Regular Perturbation Coefficients for Fiber Nonlinearities | We study the performance of gradient-descent optimization to estimate the
coefficients of the discrete-time first-order regular perturbation (FRP). With
respect to numerically computed coefficients, the optimized coefficients yield
a model that (i) extends the FRP range of validity, and (ii) reduces the
model's complexity. | 2106.05088v2 |
2021-09-05 | Counting irreducible polynomials with prescribed coefficients over a finite field | We continue our study on counting irreducible polynomials over a finite field
with prescribed coefficients. We set up a general combinatorial framework using
generating functions with coefficients from a group algebra which is generated
by equivalent classes of polynomials with prescribed coefficients. Simplified
expressions are derived for some special cases. Our results extend some earlier
results. | 2109.02000v1 |
2022-02-17 | High-Dimensional Time-Varying Coefficient Estimation | In this paper, we develop a novel high-dimensional time-varying coefficient
estimation method, based on high-dimensional Ito diffusion processes. To
account for high-dimensional time-varying coefficients, we first estimate local
(or instantaneous) coefficients using a time-localized Dantzig selection scheme
under a sparsity condition, which results in biased local coefficient
estimators due to the regularization. To handle the bias, we propose a
debiasing scheme, which provides well-performing unbiased local coefficient
estimators. With the unbiased local coefficient estimators, we estimate the
integrated coefficient, and to further account for the sparsity of the
coefficient process, we apply thresholding schemes. We call this Thresholding
dEbiased Dantzig (TED). We establish asymptotic properties of the proposed TED
estimator. In the empirical analysis, we apply the TED procedure to analyzing
high-dimensional factor models using high-frequency data. | 2202.08419v3 |
2022-03-26 | Fourier coefficients of Hilbert modular forms at cusps | The aim of this article is to study the fields generated by the Fourier
coefficients of Hilbert newforms at arbitrary cusps. Precisely, given a
cuspidal Hilbert newform $f$ and a matrix $\sigma$ in (a suitable conjugate of)
the Hilbert modular group, we give a cyclotomic extension of the field
generated by the Fourier coefficients at infinity which contains all the
Fourier coefficients of $f||_k\sigma$. | 2203.14096v1 |
2022-05-07 | Bounds on the Total Coefficient Size of Nullstellensatz Proofs of the Pigeonhole Principle and the Ordering Principle | In this paper, we investigate the total coefficient size of Nullstellensatz
proofs. We show that Nullstellensatz proofs of the pigeonhole principle on $n$
pigeons require total coefficient size $2^{\Omega(n)}$ and that there exist
Nullstellensatz proofs of the ordering principle on $n$ elements with total
coefficient size $2^n - n$. | 2205.03577v1 |
2022-05-09 | Hypothesis testing for varying coefficient models in tail index regression | This study examines the varying coefficient model in tail index regression.
The varying coefficient model is an efficient semiparametric model that avoids
the curse of dimensionality when including large covariates in the model. In
fact, the varying coefficient model is useful in mean, quantile, and other
regressions. The tail index regression is not an exception. However, the
varying coefficient model is flexible, but leaner and simpler models are
preferred for applications. Therefore, it is important to evaluate whether the
estimated coefficient function varies significantly with covariates. If the
effect of the non-linearity of the model is weak, the varying coefficient
structure is reduced to a simpler model, such as a constant or zero.
Accordingly, the hypothesis test for model assessment in the varying
coefficient model has been discussed in mean and quantile regression. However,
there are no results in tail index regression. In this study, we investigate
the asymptotic properties of an estimator and provide a hypothesis testing
method for varying coefficient models for tail index regression. | 2205.04176v3 |
2023-01-13 | Li coefficients as norms of functions in a model space | It is known that the nonnegativity of Li coefficients is a necessary and
sufficient condition for the Riemann hypothesis. We show that it is a necessary
and sufficient condition for the Riemann hypothesis that all Li coefficients
are norms of certain concrete functions on the real line. Such conditional
formulas for Li coefficients are understood as a kind of Weil's criterion for
the Riemann hypothesis. | 2301.05779v2 |
2023-07-14 | Computational progress on the unfair 0-1 polynomial Conjecture | Let $c(x)$ be a monic integer polynomial with coefficients $0$ or $1$. Write
$c(x) = a(x) b(x)$ where $a(x)$ and $b(x)$ are monic polynomials with
non-negative real (not necessarily integer) coefficients. The unfair 0--1
polynomial conjecture states that $a(x)$ and $b(x)$ are necessarily integer
polynomials with coefficients $0$ or $1$. Let $a(x)$ be a candidate factor of a
(currently unknown) 0--1 polynomial. We will assume that we know if a
coefficient is $0$, $1$ or strictly between $0$ and $1$, but that we do not
know the precise value of non-integer coefficients. Given this candidate
$a(x)$, this paper gives an algorithm to either find a $b(x)$ and $c(x)$ with
$a(x) b(x) = c(x)$ such that $b(x)$ has non-negative real coefficients and
$c(x)$ has coefficients $0$ or $1$, or (often) shows that no such $c(x)$ and
$b(x)$ exist. Using this algorithm, we consider all candidate factors with
degree less than or equal to 15. With the exception of 975 candidate factors
(out of a possible 7141686 cases), this algorithm shows that there do not exist
$b(x)$ with non-negative real coefficients and $c(x)$ with coefficients $0$ or
$1$ such that $a(x) b(x) = c(x)$. | 2307.07363v1 |
2023-09-27 | Sharp Estimates on Coefficient functionals of Ozaki close-to-convex functions | The goal of this manuscript to establish the best possible estimate on
coefficient functionals like Hermitian-Toeplitz determinant of secoend order
involving logarithmic coefficients, initial logarithmic inverse coefficients
and initial order Schwarzian derivatives of the Ozaki close-to-convex
functions. | 2309.15927v1 |
2023-10-24 | Kronecker coefficients for (dual) symmetric inverse semigroups | We study analogues of Kronecker coefficients for symmetric inverse
semigroups, for dual symmetric inverse semigroups and for the inverse
semigroups of bijections between subquotients of finite sets. In all cases we
reduce the problem of determination of such coefficients to some
group-theoretic and combinatorial problems. For symmetric inverse semigroups,
we provide an explicit formula in terms of the classical Kronecker and
Littlewood--Richardson coefficients for symmetric groups. | 2310.15537v1 |
2023-10-27 | Data-scientific study of Kronecker coefficients | We take a data-scientific approach to study whether Kronecker coefficients
are zero or not. Motivated by principal component analysis and kernel methods,
we define loadings of partitions and use them to describe a sufficient
condition for Kronecker coefficients to be nonzero. The results provide new
methods and perspectives for the study of these coefficients. | 2310.17906v1 |
2023-12-11 | Hilbert Coefficients and Sally Modules: A Survey of Vasconcelos' Contributions | This paper surveys and summarizes Wolmer Vasconcelos' results surrounding
multiplicities, Hilbert coefficients, and their extensions. We particularly
focus on Vasconcelos' results regarding multiplicities and Chern coefficients,
and other invariants which they bound. The Sally module is an important
instrument introduced by Vasconcelos for this study, which naturally relates
Hilbert coefficients to reduction numbers. | 2312.06846v1 |
2024-01-05 | Nonconvex High-Dimensional Time-Varying Coefficient Estimation for Noisy High-Frequency Observations | In this paper, we propose a novel high-dimensional time-varying coefficient
estimator for noisy high-frequency observations. In high-frequency finance, we
often observe that noises dominate a signal of an underlying true process.
Thus, we cannot apply usual regression procedures to analyze noisy
high-frequency observations. To handle this issue, we first employ a smoothing
method for the observed variables. However, the smoothed variables still
contain non-negligible noises. To manage these non-negligible noises and the
high dimensionality, we propose a nonconvex penalized regression method for
each local coefficient. This method produces consistent but biased local
coefficient estimators. To estimate the integrated coefficients, we propose a
debiasing scheme and obtain a debiased integrated coefficient estimator using
debiased local coefficient estimators. Then, to further account for the
sparsity structure of the coefficients, we apply a thresholding scheme to the
debiased integrated coefficient estimator. We call this scheme the Thresholded
dEbiased Nonconvex LASSO (TEN-LASSO) estimator. Furthermore, this paper
establishes the concentration properties of the TEN-LASSO estimator and
discusses a nonconvex optimization algorithm. | 2401.02694v1 |
2014-11-28 | Heat kernel expansions, ambient metrics and conformal invariants | The conformal powers of the Laplacian of a Riemannian metric which are known
as the GJMS-operators admit a combinatorial description in terms of the Taylor
coefficients of a natural second-order one-parameter family $\H(r;g)$ of
self-adjoint elliptic differential operators. $\H(r;g)$ is a non-Laplace-type
perturbation of the conformal Laplacian $P_2(g) = \H(0;g)$. It is defined in
terms of the metric $g$ and covariant derivatives of the curvature of $g$. We
study the heat kernel coefficients $a_{2k}(r;g)$ of $\H(r;g)$ on closed
manifolds. We prove general structural results for the heat kernel coefficients
$a_{2k}(r;g)$ and derive explicit formulas for $a_0(r)$ and $a_2(r)$ in terms
of renormalized volume coefficients. The Taylor coefficients of $a_{2k}(r;g)$
(as functions of $r$) interpolate between the renormalized volume coefficients
of a metric $g$ ($k=0$) and the heat kernel coefficients of the conformal
Laplacian of $g$ ($r=0$). Although $\H(r;g)$ is not conformally covariant,
there is a beautiful formula for the conformal variation of the trace of its
heat kernel. As a consequence, we give a heat equation proof of the conformal
transformation law of the integrated renormalized volume coefficients. By
refining these arguments, we also give a heat equation proof of the conformal
transformation law of the renormalized volume coefficients itself. The Taylor
coefficients of $a_2(r)$ define a sequence of higher-order Riemannian curvature
functionals with extremal properties at Einstein metrics which are analogous to
those of integrated renormalized volume coefficients. Among the various
additional results the reader finds a Polyakov-type formula for the
renormalized volume of a Poincar\'e-Einstein metric in terms of $Q$-curvature
of its conformal infinity and additional holographic terms. | 1411.7851v1 |
2015-06-17 | Global clustering coefficient in scale-free weighted and unweighted networks | In this paper, we present a detailed analysis of the global clustering
coefficient in scale-free graphs. Many observed real-world networks of diverse
nature have a power-law degree distribution. Moreover, the observed degree
distribution usually has an infinite variance. Therefore, we are especially
interested in such degree distributions. In addition, we analyze the clustering
coefficient for both weighted and unweighted graphs.
There are two well-known definitions of the clustering coefficient of a
graph: the global and the average local clustering coefficients. There are
several models proposed in the literature for which the average local
clustering coefficient tends to a positive constant as a graph grows. On the
other hand, there are no models of scale-free networks with an infinite
variance of the degree distribution and with an asymptotically constant global
clustering coefficient. Models with constant global clustering and finite
variance were also proposed. Therefore, in this paper we focus only on the most
interesting case: we analyze the global clustering coefficient for graphs with
an infinite variance of the degree distribution.
For unweighted graphs, we prove that the global clustering coefficient tends
to zero with high probability and we also estimate the largest possible
clustering coefficient for such graphs. On the contrary, for weighted graphs,
the constant global clustering coefficient can be obtained even for the case of
an infinite variance of the degree distribution. | 1507.00925v1 |
2015-10-07 | Linear Bounds between Contraction Coefficients for $f$-Divergences | Data processing inequalities for $f$-divergences can be sharpened using
constants called "contraction coefficients" to produce strong data processing
inequalities. For any discrete source-channel pair, the contraction
coefficients for $f$-divergences are lower bounded by the contraction
coefficient for $\chi^2$-divergence. In this paper, we elucidate that this
lower bound can be achieved by driving the input $f$-divergences of the
contraction coefficients to zero. Then, we establish a linear upper bound on
the contraction coefficients for a certain class of $f$-divergences using the
contraction coefficient for $\chi^2$-divergence, and refine this upper bound
for the salient special case of Kullback-Leibler (KL) divergence. Furthermore,
we present an alternative proof of the fact that the contraction coefficients
for KL and $\chi^2$-divergences are equal for a Gaussian source with an
additive Gaussian noise channel (where the former coefficient can be power
constrained). Finally, we generalize the well-known result that contraction
coefficients of channels (after extremizing over all possible sources) for all
$f$-divergences with non-linear operator convex $f$ are equal. In particular,
we prove that the so called "less noisy" preorder over channels can be
equivalently characterized by any non-linear operator convex $f$-divergence. | 1510.01844v4 |
2021-03-03 | Generalized Collisional Fluid Theory for Multi-Component, Multi-Temperature Plasma Using The Linearized Boltzmann Collision Operator for Scrape-Off Layer/Edge Applications | Grad's method is used on the linearized Boltzmann collision operator to
derive the most general expressions for the collision coefficients for a
multi-component, multi-temperature plasma up to rank-2. In doing so, the
collision coefficients then get expressed as series sum of pure coefficients of
temperature and mass ratios multiplied by the cross-section dependent
Chapman-Cowling integrals. These collisional coefficients are compared to
previously obtained coefficients by Zhdanov et al [Zhdanov V.M., Transport
processes in multi-component plasma, Taylor and Francis (2002)] for 13N-moment
multi-temperature scheme. First, the differences in coefficients are compared
directly, and then the differences in first approximation to viscosity and
friction force are compared. For the 13N-moment multi-temperature coefficients,
it is found that they behave reasonably similarly for small temperature
differences, but display substantial differences in the coefficients when the
temperature differences are high, both for the coefficients and for viscosity
and friction force values. Furthermore, the obtained coefficients are compared
to the 21N-moment single-temperature approximation provided by Zhdanov et al,
and it is seen that the differences are higher than the 13N-moment
multi-temperature coefficients, and have substantial differences even in the
vicinity of equal temperatures, especially for the viscosity and friction force
calculations. | 2103.02455v3 |
2022-01-31 | GenMod: A generative modeling approach for spectral representation of PDEs with random inputs | We propose a method for quantifying uncertainty in high-dimensional PDE
systems with random parameters, where the number of solution evaluations is
small. Parametric PDE solutions are often approximated using a spectral
decomposition based on polynomial chaos expansions. For the class of systems we
consider (i.e., high dimensional with limited solution evaluations) the
coefficients are given by an underdetermined linear system in a regression
formulation. This implies additional assumptions, such as sparsity of the
coefficient vector, are needed to approximate the solution. Here, we present an
approach where we assume the coefficients are close to the range of a
generative model that maps from a low to a high dimensional space of
coefficients. Our approach is inspired be recent work examining how generative
models can be used for compressed sensing in systems with random Gaussian
measurement matrices. Using results from PDE theory on coefficient decay rates,
we construct an explicit generative model that predicts the polynomial chaos
coefficient magnitudes. The algorithm we developed to find the coefficients,
which we call GenMod, is composed of two main steps. First, we predict the
coefficient signs using Orthogonal Matching Pursuit. Then, we assume the
coefficients are within a sparse deviation from the range of a sign-adjusted
generative model. This allows us to find the coefficients by solving a
nonconvex optimization problem, over the input space of the generative model
and the space of sparse vectors. We obtain theoretical recovery results for a
Lipschitz continuous generative model and for a more specific generative model,
based on coefficient decay rate bounds. We examine three high-dimensional
problems and show that, for all three examples, the generative model approach
outperforms sparsity promoting methods at small sample sizes. | 2201.12973v1 |
2022-07-14 | Homology and cohomology of cubical sets with coefficients in systems of objects | This paper continues the research of the author on the homology of cubical
and semi-cubical sets with coefficients in systems of objects. The main result
is the theorem that the homology of cubical sets with coefficients in
contravariant systems in an Abelian category with exact coproducts is
isomorphic to the left satellites of a colimit functor. This made it possible
to prove a number of the following new assertions, presented in the paper,
about the homology and cohomology of cubical sets with coefficients in systems
of objects. These homology are invariant under morphism between cubical sets
when passing to the direct image of the system of coefficients. There is a
criterion for the invariance of these homologies when passing to the inverse
image. These homology generalize the singular cubical homology with local
coefficients and the homology of semi-cubical sets with coefficients in
contravariant systems. There is a spectral sequence for colimit homologies of
cubical sets with coefficients in contravariant systems. The weak equivalence
of cubical sets induces an isomorphism of homology with local systems. For a
morphism of cubical sets whose inverse fiber morphisms are weak equivalences,
there exists a spectral sequence for homology with local systems converging to
the homology of the domain of this morphism. The homology of small category
with coefficients in a diagram can be calculated as cubical homology. The
Baues-Wirsching cohomologies with coefficients in natural systems are
isomorphic to cubical cohomologies with coefficients in covariant systems. | 2207.07233v6 |
2023-01-02 | Sample-to-sample fluctuations of transport coefficients in the totally asymmetric simple exclusion process with quenched disorder | We consider the totally asymmetric simple exclusion processes on quenched
random energy landscapes. We show that the current and the diffusion
coefficient differ from those for homogeneous environments. Using the
mean-field approximation, we analytically obtain the site density when the
particle density is low or high. As a result, the current and the diffusion
coefficient are described by the dilute limit of particles or holes,
respectively. However, in the intermediate regime, due to the many-body effect,
the current and the diffusion coefficient differ from those for single-particle
dynamics. The current is almost constant and becomes the maximal value in the
intermediate regime. Moreover, the diffusion coefficient decreases with the
particle density in the intermediate regime. We obtain analytical expressions
for the maximal current and the diffusion coefficient based on the renewal
theory. The deepest energy depth plays a central role in determining the
maximal current and the diffusion coefficient. As a result, the maximal current
and the diffusion coefficient depend crucially on the disorder, i.e.,
non-self-averaging. Based on the extreme value theory, we find that
sample-to-sample fluctuations of the maximal current and diffusion coefficient
are characterized by the Weibull distribution. We show that the disorder
averages of the maximal current and the diffusion coefficient converge to zero
as the system size is increased and quantify the degree of the
non-self-averaging effect for the maximal current and the diffusion
coefficient. | 2301.00563v3 |
2024-03-12 | Preconditioners based on Voronoi quantizers of random variable coefficients for stochastic elliptic partial differential equations | A preconditioning strategy is proposed for the iterative solve of large
numbers of linear systems with variable matrix and right-hand side which arise
during the computation of solution statistics of stochastic elliptic partial
differential equations with random variable coefficients sampled by Monte
Carlo. Building on the assumption that a truncated Karhunen-Lo\`{e}ve expansion
of a known transform of the random variable coefficient is known, we introduce
a compact representation of the random coefficient in the form of a Voronoi
quantizer. The number of Voronoi cells, each of which is represented by a
centroidal variable coefficient, is set to the prescribed number $P$ of
preconditioners. Upon sampling the random variable coefficient, the linear
system assembled with a given realization of the coefficient is solved with the
preconditioner whose centroidal variable coefficient is the closest to the
realization. We consider different ways to define and obtain the centroidal
variable coefficients, and we investigate the properties of the induced
preconditioning strategies in terms of average number of solver iterations for
sequential simulations, and of load balancing for parallel simulations. Another
approach, which is based on deterministic grids on the system of stochastic
coordinates of the truncated representation of the random variable coefficient,
is proposed with a stochastic dimension which increases with the number $P$ of
preconditioners. This approach allows to bypass the need for preliminary
computations in order to determine the optimal stochastic dimension of the
truncated approximation of the random variable coefficient for a given number
of preconditioners. | 2403.07824v1 |
2003-01-10 | Hydrodynamics and transport coefficients for Granular Gases | The hydrodynamics of granular gases of viscoelastic particles, whose
collision is described by an impact-velocity dependent coefficient of
restitution, is developed using a modified Chapman-Enskog approach. We derive
the hydrodynamic equations and the according transport coefficients with the
assumption that the shape of the velocity distribution function follows
adiabatically the decaying temperature. We show numerically that this
approximation is justified up to intermediate dissipation. The transport
coefficients and the coefficient of cooling are expressed in terms of the
elastic and dissipative parameters of the particle material and by the gas
parameters. The dependence of these coefficients on temperature differs
qualitatively from that obtained with the simplifying assumption of a constant
coefficient of restitution which was used in previous studies. The approach
formulated for gases of viscoelastic particles may be applied also for other
impact-velocity dependencies of the restitution coefficient. | 0301152v1 |
1992-12-26 | Unimodality of generalized Gaussian coefficients | A combinatorial proof of the unimodality of the generalized q-Gaussian
coefficients based on the explicit formula for Kostka-Foulkes polynomials is
given. | 9212152v1 |
2005-02-19 | When a C*-algebra is a coefficient algebra for a given endomorphism | The paper presents a criterion for a C*-algebra to be a coefficient algebra
associated with a given endomorphism | 0502414v1 |
2008-01-04 | Borg type uniqueness Theorems for periodic Jacobi operators with matrix valued coefficients | We give a simple proof of Borg type uniqueness Theorems for periodic Jacobi
operators with matrix valued coefficients. | 0801.0687v1 |
2008-08-11 | Apery, Bessel, Calabi-Yau and Verrill | A differential equation related to the moments of Bessel functions is shown
to have a solution at infinity with coefficients being squares of binomial
coefficients. | 0808.1480v1 |
2008-12-04 | Quasipolynomial formulas for the Kronecker coefficients indexed by two two-row shapes (extended abstract) | We show that the Kronecker coefficients (the Clebsch-Gordan coefficients of
the symmetric group) indexed by two two-row shapes are given by quadratic
quasipolynomial formulas whose domains are the maximal cells of a fan. Simple
calculations provide explicitly the quasipolynomial formulas and a description
of the associated fan.
These new formulas are obtained from analogous formulas for the corresponding
reduced Kronecker coefficients and a formula recovering the Kronecker
coefficients from the reduced Kronecker coefficients.
As an application, we characterize all the Kronecker coefficients indexed by
two two-row shapes that are equal to zero. This allowed us to disprove a
conjecture of Mulmuley about the behavior of the stretching functions attached
to the Kronecker coefficients. | 0812.0861v1 |
2009-01-11 | Counting Bipartite, k-Colored and Directed Acyclic Multi Graphs Through F-nomial coefficients | F-nomial coefficients encompass among others well-known binomial coefficients
or Gaussian coefficients that count subsets of finite set and subspaces of
finite vector space respectively. Here, the so called F-cobweb tiling sequences
N(a) are considered. For such specific sequences a new interpretation with
respect to Kwasniewski general combinatorial interpretation of F-nomial
coefficients is unearhed.
Namely, for tiling sequences F = N(a)$ the F-nomial coefficients are equal to
the number of labeled special bipartite multigraphs denoted here as
a-multigraphs G(a,n,k).
An explicit relation between the number of k-colored a-multigraphs and multi
N(a)-nomial coefficients is established. We also prove that the unsigned values
of the first row of inversion matrix for N(a) -nomial coefficients considered
here are equal to the numbers of directed acyclic a-multigraphs with n nodes. | 0901.1337v1 |
2010-06-01 | Second-order linear constant coefficient dynamic equations with polynomial forcing on time scales | A general solution for a second-order linear constant coefficient dynamic
equation with polynomial forcing on time scales is given. | 1006.0074v1 |
2010-06-15 | Some congruences for trinomial coefficients | We prove several congruences for trinomial coefficients. | 1006.3025v2 |
2010-08-13 | Flexible Shrinkage Estimation in High-Dimensional Varying Coefficient Models | We consider the problem of simultaneous variable selection and constant
coefficient identification in high-dimensional varying coefficient models based
on B-spline basis expansion. Both objectives can be considered as some type of
model selection problems and we show that they can be achieved by a double
shrinkage strategy. We apply the adaptive group Lasso penalty in models
involving a diverging number of covariates, which can be much larger than the
sample size, but we assume the number of relevant variables is smaller than the
sample size via model sparsity. Such so-called ultra-high dimensional settings
are especially challenging in semiparametric models as we consider here and has
not been dealt with before. Under suitable conditions, we show that consistency
in terms of both variable selection and constant coefficient identification can
be achieved, as well as the oracle property of the constant coefficients. Even
in the case that the zero and constant coefficients are known a priori, our
results appear to be new in that it reduces to semivarying coefficient models
(a.k.a. partially linear varying coefficient models) with a diverging number of
covariates. We also theoretically demonstrate the consistency of a
semiparametric BIC-type criterion in this high-dimensional context, extending
several previous results. The finite sample behavior of the estimator is
evaluated by some Monte Carlo studies. | 1008.2271v1 |
2010-11-26 | Idempotents with polynomial coefficients | We combine Young idempotents in the group algebra of the symmetric group with
the action of the symmetric group on products of Vandermonde determinants to
obtain idempotents with polynomial coefficients. | 1011.5815v1 |
2011-04-29 | Closed string transport coefficients and the membrane paradigm | I discuss a correspondence between a fictitious fluid in the black hole
membrane paradigm and highly excited closed string states according to the
black hole correspondence principle. I calculate the membrane transport
coefficients of an electric NS-NS 2-charged black hole and transport
coefficients of the highly excited closed string states which possess a
Kaluza-Klein number and a winding number. Comparing both the transport
coefficients at the correspondence point, I show that, except for the bulk
viscosity, the membrane transport coefficients are of the same order as the
transport coefficients of the closed string states on the stretched horizon.
Also, I show that, except for the bulk viscosity, both the dimensionless
transport coefficients, which are defined by dividing the transport
coefficients by the entropy density, are exactly equal if the central charge is
6. | 1104.5556v3 |
2011-09-26 | Logarithmic vector-valued modular forms and polynomial-growth estimates of their Fourier coefficients | We establish (Theorem 3.6) polynomial-growth estimates for the
Fourier coefficients of holomorphic logarithmic vector-valued modular forms. | 1109.5740v1 |
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