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2022-05-05 | Blow-up solutions of damped Klein-Gordon equation on the Heisenberg group | Inthisnote,weprovetheblow-upofsolutionsofthesemilineardamped Klein-Gordon
equation in a finite time for arbitrary positive initial energy on the
Heisenberg group. This work complements the paper [21] by the first author and
Tokmagambetov, where the global in time well-posedness was proved for the small
energy solutions. | 2205.02705v1 |
2022-05-06 | Quaternion-based attitude stabilization via discrete-time IDA-PBC | In this paper, we propose a new sampled-data controller for stabilization of
the attitude dynamics at a desired constant configuration. The design is based
on discrete-time interconnection and damping assignment (IDA) passivity-based
control (PBC) and the recently proposed Hamiltonian representation of
discrete-time nonlinear dynamics. Approximate solutions are provided with
simulations illustrating performances. | 2205.03086v1 |
2022-05-23 | Extended random-phase-approximation study of fragmentation of giant quadrupole resonance in $^{16}$O | The damping of isoscalar giant quadrupole resonance in $^{16}$O is studied
using extended random-phase-approximation approaches derived from the
time-dependent density-matrix theory. It is pointed out that the effects of
ground-state correlations bring strong fragmentation of quadrupole strength
even if the number of two particle--two hole configurations is strongly
limited. | 2205.11654v2 |
2022-06-21 | Nonlinear Compton scattering and nonlinear Breit-Wheeler pair production including the damping of particle states | In the presence of an electromagnetic background plane-wave field, electron,
positron, and photon states are not stable, because electrons and positrons
emit photons and photons decay into electron-positron pairs. This decay of the
particle states leads to an exponential damping term in the probabilities of
single nonlinear Compton scattering and nonlinear Breit-Wheeler pair
production. In this paper we investigate analytically and numerically the
probabilities of nonlinear Compton scattering and nonlinear Breit-Wheeler pair
production including the particle states' decay. For this we first compute
spin- and polarization-resolved expressions of the probabilities, provide some
of their asymptotic behaviors and show that the results of the total
probabilities are independent of the spin and polarization bases. Then, we
present several plots of the total and differential probabilities for different
pulse lengths and for different spin and polarization quantum numbers. We
observe that it is crucial to take into account the damping of the states in
order for the probabilities to stay always below unity and we show that the
damping factors also scale with the intensity and pulse duration of the
background field. In the case of nonlinear Compton scattering we show
numerically that the total probability behaves like a Poissonian distribution
in the regime where the photon recoil is negligible. In all considered cases,
the kinematic conditions are such that the final particles momenta transverse
to the propagation direction of the plane wave are always much smaller than the
particles longitudinal momenta and the main spread of the momentum distribution
on the transverse plane is along the direction of the plane-wave electric
field. | 2206.10345v2 |
2022-06-23 | Nonlinear Landau damping for the 2d Vlasov-Poisson system with massless electrons around Penrose-stable equilibria | In this paper, we prove the nonlinear asymptotic stability of the
Penrose-stable equilibria among solutions of the $2d$ Vlasov-Poisson system
with massless electrons. | 2206.11744v2 |
2022-08-25 | Polynomial energy decay rate of a 2D Piezoelectric beam with magnetic effect on a rectangular domain without geometric conditions | In this paper, we investigate the stability of coupled equations modelling a
2D piezoelectric beam with magnetic effect with only one local viscous damping
on a rectangular domain without geometric conditions. We prove that the energy
of the system decays polynomially with the rate 1/t . | 2208.12012v1 |
2022-10-12 | Backward problem for the 1D ionic Vlasov-Poisson equation | In this paper, we study the backward problem for the one-dimensional
Vlasov-Poisson system with massless electrons, and we show the Landau damping
by fixing the asymptotic behaviour of our solution. | 2210.06123v2 |
2022-10-28 | Oblique Quasi-Kink Modes in Solar Coronal Slabs Embedded in an Asymmetric Magnetic Environment: Resonant Damping, Phase and Group Diagrams | There has been considerable interest in magnetoacoustic waves in static,
straight, field-aligned, one-dimensional equilibria where the exteriors of a
magnetic slab are different between the two sides. We focus on trapped,
transverse fundamental, oblique quasi-kink modes in pressureless setups where
the density varies continuously from a uniform interior (with density
$\rho_{\rm i}$) to a uniform exterior on either side (with density $\rho_{\rm
L}$ or $\rho_{\rm R}$), assuming $\rho_{\rm L}\le\rho_{\rm R}\le\rho_{\rm i}$.
The continuous structuring and oblique propagation make our study new relative
to pertinent studies, and lead to wave damping via the Alfv$\acute{\rm e}$n
resonance. We compute resonantly damped quasi-kink modes as resistive
eigenmodes, and isolate the effects of system asymmetry by varying $\rho_{\rm
i}/\rho_{\rm R}$ from the ``Fully Symmetric'' ($\rho_{\rm i}/\rho_{\rm
R}=\rho_{\rm i}/\rho_{\rm L}$) to the ``Fully Asymmetric'' limit ($\rho_{\rm
i}/\rho_{\rm R}=1$). We find that the damping rates possess a nonmonotonic
$\rho_{\rm i}/\rho_{\rm R}$-dependence as a result of the difference between
the two Alfv$\acute{\rm e}$n continua, and resonant absorption occurs only in
one continuum when $\rho_{\rm i}/\rho_{\rm R}$ is below some threshold. We also
find that the system asymmetry results in two qualitatively different regimes
for the phase and group diagrams. The phase and group trajectories lie
essentially on the same side (different sides) relative to the equilibrium
magnetic field when the configuration is not far from a ``Fully Asymmetric''
(``Fully Symmetric'') one. Our numerical results are understood by making
analytical progress in the thin-boundary limit, and discussed for imaging
observations of axial standing modes and impulsively excited wavetrains. | 2210.16091v1 |
2022-11-02 | Data-driven modeling of Landau damping by physics-informed neural networks | Kinetic approaches are generally accurate in dealing with microscale plasma
physics problems but are computationally expensive for large-scale or
multiscale systems. One of the long-standing problems in plasma physics is the
integration of kinetic physics into fluid models, which is often achieved
through sophisticated analytical closure terms. In this paper, we successfully
construct a multi-moment fluid model with an implicit fluid closure included in
the neural network using machine learning. The multi-moment fluid model is
trained with a small fraction of sparsely sampled data from kinetic simulations
of Landau damping, using the physics-informed neural network (PINN) and the
gradient-enhanced physics-informed neural network (gPINN). The multi-moment
fluid model constructed using either PINN or gPINN reproduces the time
evolution of the electric field energy, including its damping rate, and the
plasma dynamics from the kinetic simulations. In addition, we introduce a
variant of the gPINN architecture, namely, gPINN$p$ to capture the Landau
damping process. Instead of including the gradients of all the equation
residuals, gPINN$p$ only adds the gradient of the pressure equation residual as
one additional constraint. Among the three approaches, the gPINN$p$-constructed
multi-moment fluid model offers the most accurate results. This work sheds
light on the accurate and efficient modeling of large-scale systems, which can
be extended to complex multiscale laboratory, space, and astrophysical plasma
physics problems. | 2211.01021v3 |
2022-11-04 | New Clues About Light Sterile Neutrinos: Preference for Models with Damping Effects in Global Fits | This article reports global fits of short-baseline neutrino data to
oscillation models involving light sterile neutrinos. In the commonly-used 3+1
plane wave model, there is a well-known 4.9$\sigma$ tension between data sets
sensitive to appearance versus disappearance of neutrinos. We find that models
that damp the oscillation prediction for the reactor data sets, especially at
low energy, substantially improve the fits and reduce the tension. We consider
two such scenarios. The first scenario introduces the quantum mechanical
wavepacket effect that accounts for the source size in reactor experiments into
the 3+1 model. We find that inclusion of the wavepacket effect greatly improves
the overall fit compared to a 3$\nu$ model by $\Delta \chi^2/$DOF$=61.1/4$
($7.1\sigma$ improvement) with best-fit $\Delta m^2=1.4$ eV$^2$ and wavepacket
length of 67fm. The internal tension is reduced to 3.4$\sigma$. If reactor-data
only is fit, then the wavepacket preferred length is 91 fm ($>20$ fm at 99\%
CL). The second model introduces oscillations involving sterile flavor and
allows the decay of the heaviest, mostly sterile mass state, $\nu_4$. This
model introduces a damping term similar to the wavepacket effect, but across
all experiments. Compared to a three-neutrino fit, this has a $\Delta
\chi^2/$DOF$=60.6/4$ ($7\sigma$ improvement) with preferred $\Delta m^2=1.4$
eV$^2$ and decay $\Gamma = 0.35$ eV$^2$. The internal tension is reduced to
3.7$\sigma$.
For many years, the reactor event rates have been observed to have structure
that deviates from prediction. Community discussion has focused on an excess
compared to prediction observed at 5 MeV; however, other deviations are
apparent. This structure has $L$ dependence that is well-fit by the damped
models. Before assuming this points to new physics, we urge closer examination
of systematic effects that could lead to this $L$ dependence. | 2211.02610v5 |
2022-12-07 | A recipe for orbital eccentricity damping in the type-I regime for low viscosity 2D-discs | It is known that gap opening depends on the disc's viscosity; however,
eccentricity damping formulas have only been derived at high viscosities,
ignoring partial gap opening. We aim at obtaining a simple formula to model
$e$-damping of the type-I regime in low viscosity discs, where even small
planets may start opening partial. We perform high resolution 2D locally
isothermal hydrodynamical simulations of planets with varying masses on fixed
orbits in discs with varying aspect ratios and viscosities. We determine the
torque and power felt by the planet to derive migration and eccentricity
damping timescales. We first find a lower limit to the gap depths below which
vortices appear; this happens roughly at the transition between type-I and
type-II regimes. For the simulations that remain stable, we obtain a fit to the
observed gap depth in the limit of vanishing eccentricities that is similar to
the one currently used in the literature but is accurate down to
$\alpha=3.16\times 10^{-5}$. We record the $e$-damping efficiency as a function
of the observed gap depth and $e$: when the planet has opened a deep enough
gap, a linear trend is observed independently of $e$; at shallower gaps this
linear trend is preserved at low $e$, while it deviates to more efficient
damping when $e$ is comparable to the disc's scale height. Both trends can be
understood on theoretical grounds and are reproduced by a simple fitting
formula. Our combined fits yield a simple recipe to implement type-I
$e$-damping in $N$-body for partial gap opening planets that is consistent with
high-resolution 2D hydro-simulations. The typical error of the fit is of the
order of a few percent, and lower than the error of type-I torque formulas
widely used in the literature. This will allow a more self-consistent treatment
of planet-disc interactions of the type-I regime for population synthesis
models at low viscosities. | 2212.03608v1 |
2022-12-10 | Linear stabilization for a degenerate wave equation in non divergence form with drift | We consider a degenerate wave equation in one dimension, with drift and in
presence of a leading operator which is not in divergence form. We impose a
homogeneous Dirichlet boundary condition where the degeneracy occurs and a
boundary damping at the other endpoint. We provide some conditions for the
uniform exponential decay of solutions for the associated Cauchy problem. | 2212.05264v1 |
2022-12-31 | On the stability of shear flows in bounded channels, II: non-monotonic shear flows | We give a proof of linear inviscid damping and vorticity depletion for
non-monotonic shear flows with one critical point in a bounded periodic
channel. In particular, we obtain quantitative depletion rates for the
vorticity function without any symmetry assumptions. | 2301.00288v2 |
2023-03-18 | Spin waves in a superconductor | Spin waves that can propagate in normal and superconducting metals are
investigated. Unlike normal metals, the velocity of spin waves becomes
temperature-dependent in a superconductor. The low frequency spin waves survive
within the narrow region below the superconducting transition temperature. At
low temperatures the high frequency waves alone can propagate with an
additional damping due to pair-breaking. | 2303.10468v1 |
2023-04-07 | Echo disappears: momentum term structure and cyclic information in turnover | We extract cyclic information in turnover and find it can explain the
momentum echo. The reversal in recent month momentum is the key factor that
cancels out the recent month momentum and excluding it makes the echo regress
to a damped shape. Both rational and behavioral theories can explain the
reversal. This study is the first explanation of the momentum echo in U.S.
stock markets. | 2304.03437v1 |
2023-04-26 | Plasma echoes in graphene | Plasma echo is a dramatic manifestation of plasma damping process
reversibility. In this paper we calculate temporal and spatial plasma echoes in
graphene in the acoustic plasmon regime when echoes dominate over plasmon
emission. We show an extremely strong spatial echo response and discuss how
electron collisions reduce the echo. We also discuss differences between
various electron dispersions, and differences between semiclassical and quantum
model of echoes. | 2304.13440v1 |
2023-06-01 | JWST Measurements of Neutral Hydrogen Fractions and Ionized Bubble Sizes at $z=7-12$ Obtained with Ly$α$ Damping Wing Absorptions in 26 Bright Continuum Galaxies | We present volume-averaged neutral hydrogen fractions $x_{\rm \HI}$ and
ionized bubble radii $R_{\rm b}$ measured with Ly$\alpha$ damping wing
absorption of galaxies at the epoch of reionization. We combine JWST/NIRSpec
spectra taken by CEERS, GO-1433, DDT-2750, and JADES programs, and obtain a
sample containing 26 bright UV-continuum ($M_{\rm UV}<-18.5~{\rm mag}$)
galaxies at $7<z<12$. We construct 4 composite spectra binned by redshift, and
find the clear evolution of softening break towards high redshift at the
rest-frame $1216$ {\AA}, suggesting the increase of Ly$\alpha$ damping wing
absorption. We estimate Ly$\alpha$ damping wing absorption in the galaxy
spectra with realistic templates including Ly$\alpha$ emission and
circum-galactic medium absorptions. Assuming the standard inside-out
reionization picture having an ionized bubble with radius $R_b$ around a galaxy
embedded in the intergalactic medium with $x_{\rm \HI}$, we obtain $x_{\rm
\HI}$ ($R_{\rm b}$) values generally increasing (decreasing) from $x_{\rm
\HI}={0.54}^{+0.13}_{-0.54}$ to ${0.94}^{+0.06}_{-0.41}$ ($\log R_{\rm
b}={1.89}^{+0.49}_{-1.54}$ to ${-0.72}^{+1.57}_{-0.28}$ comoving Mpc) at
redshift $7.12^{+0.06}_{-0.08}$ to $10.28^{+1.12}_{-1.40}$. The redshift
evolution of $x_{\rm \HI}$ indicates a moderately late reionization history
consistent with the one previously suggested from the electron scattering of
cosmic microwave background and the evolution of UV luminosity function with an
escape fraction $f_{\rm esc}\sim 0.2$. Our ${R_{\rm b}}$ measurements suggest
that bubble sizes could be up to a few dex larger than the cosmic average
values estimated by analytic calculations for a given $x_{\rm \HI}$, while our
$R_{\rm b}$ measurements are roughly comparable with the values for merged
ionized bubbles around bright galaxies predicted by recent numerical
simulations. | 2306.00487v2 |
2023-06-20 | New results on controllability and stability for degenerate Euler-Bernoulli type equations | In this paper we study the controllability and the stability for a degenerate
beam equation in divergence form via the energy method. The equation is clamped
at the left end and controlled by applying a shearing force or a damping at the
right end. | 2306.11851v3 |
2023-07-18 | Nonlinear feedback, double bracket dissipation and port control of Lie-Poisson systems | Methods from controlled Lagrangians, double bracket dissipation and
interconnection and damping assignment -- passivity based control (IDA-PBC) are
used to construct nonlinear feedback controls which (asymptotically) stabilize
previously unstable equilibria of Lie-Poisson Hamiltonian systems. The results
are applied to find an asymptotically stabilizing control for the rotor driven
satellite, and a stabilizing control for Hall magnetohydrodynamic flow. | 2307.09235v1 |
2023-08-01 | Aerodynamics of the square-back Ahmed body under rainfall conditions | We report an experimental investigation about the aerodynamics of a
simplified road vehicle, the so-called square-back Ahmed body, under rainfall
conditions. A particular emphasis is put on the evolution of the body base
pressure distribution with respect to the operating conditions. It is found
that rainfall significantly damps both mean base pressure drag and wake
dynamics in comparison to dry conditions. | 2308.00276v1 |
2023-09-11 | Study of damped oscillating structures from charged and neutral K-meson electromagnetic form factors data | The damped oscillating structures (OS) were recently revealed in the proton
"effective" form factor (FF) data. For the time being they can be neither
confirmed nor disproved by investigations of timelike data on the individual
proton electric and proton magnetic FFs because their precision and reliability
(especially of the proton electric FF data) has not achieved required level for
this aim. On the other hand, conjectures that the OS are direct manifestations
of the quark-gluon structure of the proton indicate that they must not be
specific only for the proton and neutron, but that they should be present also
for other hadrons. This opens a plausibility to find damped oscillatory
structures also from the EM FFs data of such hadrons, for which adequate EM FFs
data exist, by using the same procedure as for the proton. Consequently in this
paper damped oscillatory structures are investigated in the EM FFs data of the
charged and neutral $K$-mesons to be extracted from the corresponding
production cross sections, $\sigma^{bare}_{tot}(e^+e^-\to K^+ K^-)$ measured
from the threshold up to 64 GeV$^2$ and $\sigma^{bare}_{tot}(e^+e^-\to K_s
K_L)$ measured from the threshold up to 9.5 GeV$^2$ of the total c.m. energy
squared. The following results have been obtained. If the charged and neutral
K-meson EM FFs timelike data are described by the three parametric formula by
means of which OS have been revealed from the "effective" proton FF data then
OS appear. If physically well founded Unitary and Analytic model of the K-meson
EM structure is used for a description of the charged K-meson EM FFs data, no
OS are visible. However, in the case of the neutral K-meson EM FF data one
cannot make a definite decision. The overall results indicate that OS obtained
from the "effective" proton FF data are likely an artefact of the three
parametric formula which does not describe these data well. | 2309.05354v1 |
2023-10-31 | Variational principle for a damped, quadratically interacting particle chain with nonconservative forcing | A method for designing variational principles for the dynamics of a possibly
dissipative and non-conservatively forced chain of particles is demonstrated.
Some qualitative features of the formulation are discussed. | 2311.00106v2 |
2024-01-30 | Linear stability analysis of the Couette flow for the 2D Euler-Poisson system | This paper is concerned with the linear stability analysis for the Couette
flow of the Euler-Poisson system for both ionic fluid and electronic fluid in
the domain $\bb{T}\times\bb{R}$. We establish the upper and lower bounds of the
linearized solutions of the Euler-Poisson system near Couette flow. In
particular, the inviscid damping for the solenoidal component of the velocity
is obtained. | 2401.17102v1 |
2024-03-21 | Non-resonant invariant foliations of quasi-periodically forced systems | We show the existence and uniqueness of invariant foliations about invariant
tori in analytic discrete-time dynamical systems. The parametrisation method is
used prove the result. Our theory is a foundational block of data-driven model
order reduction, that can only be carried out using invariant foliations. The
theory is illustrated by two mechanical examples, where instantaneous
frequencies and damping ratios are calculated about the invariant tori. | 2403.14771v1 |
2024-04-03 | Comment on "Machine learning conservation laws from differential equations" | In lieu of abstract, first paragraph reads: Six months after the author
derived a constant of motion for a 1D damped harmonic oscillator [1], a similar
result appeared by Liu, Madhavan, and Tegmark [2, 3], without citing the
author. However, their derivation contained six serious errors, causing both
their method and result to be incorrect. In this Comment, those errors are
reviewed. | 2404.02896v1 |
2007-03-01 | Stellar Kinematics in the Complicated Inner Spheroid of M31: Discovery of Substructure Along the Southeastern Minor Axis and its Relationship to the Giant Southern Stream | We present the discovery of a kinematically-cold stellar population along the
SE minor axis of the Andromeda galaxy (M31) that is likely the forward
continuation of M31's giant southern stream. This discovery was made in the
course of an on-going spectroscopic survey of red giant branch (RGB) stars in
M31 using the DEIMOS instrument on the Keck II 10-m telescope. Stellar
kinematics are investigated in eight fields located 9-30 kpc from M31's center
(in projection). A likelihood method based on photometric and spectroscopic
diagnostics is used to isolate confirmed M31 RGB stars from foreground Milky
Way dwarf stars: for the first time, this is done without using radial velocity
as a selection criterion, allowing an unbiased study of M31's stellar
kinematics. The radial velocity distribution of the 1013 M31 RGB stars shows
evidence for the presence of two components. The broad (hot) component has a
velocity dispersion of 129 km/s and presumably represents M31's virialized
spheroid. A significant fraction (19%) of the population is in a narrow (cold)
component centered near M31's systemic velocity with a velocity dispersion that
decreases with increasing radial distance, from 55.5 km/s at R_proj=12 kpc to
10.6 km/s at R_proj=18 kpc. The spatial and velocity distribution of the cold
component matches that of the "Southeast shelf" predicted by the Fardal et al.
(2007) orbital model of the progenitor of the giant southern stream. The
metallicity distribution of the cold component matches that of the giant
southern stream, but is about 0.2 dex more metal rich on average than that of
the hot spheroidal component. We discuss the implications of our discovery on
the interpretation of the intermediate-age spheroid population found in this
region in recent ultra-deep HST imaging studies. | 0703029v3 |
2017-02-26 | Limits on the ultra-bright Fast Radio Burst population from the CHIME Pathfinder | We present results from a new incoherent-beam Fast Radio Burst (FRB) search
on the Canadian Hydrogen Intensity Mapping Experiment (CHIME) Pathfinder. Its
large instantaneous field of view (FoV) and relative thermal insensitivity
allow us to probe the ultra-bright tail of the FRB distribution, and to test a
recent claim that this distribution's slope, $\alpha\equiv-\frac{\partial \log
N}{\partial \log S}$, is quite small. A 256-input incoherent beamformer was
deployed on the CHIME Pathfinder for this purpose. If the FRB distribution were
described by a single power-law with $\alpha=0.7$, we would expect an FRB
detection every few days, making this the fastest survey on sky at present. We
collected 1268 hours of data, amounting to one of the largest exposures of any
FRB survey, with over 2.4\,$\times$\,10$^5$\,deg$^2$\,hrs. Having seen no
bursts, we have constrained the rate of extremely bright events to
$<\!13$\,sky$^{-1}$\,day$^{-1}$ above $\sim$\,220$\sqrt{(\tau/\rm ms)}$ Jy\,ms
for $\tau$ between 1.3 and 100\,ms, at 400--800\,MHz. The non-detection also
allows us to rule out $\alpha\lesssim0.9$ with 95$\%$ confidence, after
marginalizing over uncertainties in the GBT rate at 700--900\,MHz, though we
show that for a cosmological population and a large dynamic range in flux
density, $\alpha$ is brightness-dependent. Since FRBs now extend to large
enough distances that non-Euclidean effects are significant, there is still
expected to be a dearth of faint events and relative excess of bright events.
Nevertheless we have constrained the allowed number of ultra-intense FRBs.
While this does not have significant implications for deeper, large-FoV surveys
like full CHIME and APERTIF, it does have important consequences for other
wide-field, small dish experiments. | 1702.08040v2 |
2019-04-01 | Astro2020 Science White Paper: Construction of an L* Galaxy: the Transformative Power of Wide Fields for Revealing the Past, Present and Future of the Great Andromeda System | The Great Andromeda Galaxy (M31) is the nexus of the near-far galaxy
evolution connection and a principal data point for near-field cosmology. Due
to its proximity (780 kpc), M31 can be resolved into individual stars like the
Milky Way (MW). Unlike the MW, we have the advantage of a global view of M31,
enabling M31 to be observed with techniques that also apply to more distant
galaxies. Moreover, recent evidence suggests that M31 may have survived a major
merger within the last several Gyr, shaping the morphology of its stellar halo
and triggering a starburst, while leaving the stellar disk largely intact. The
MW and M31 thus provide complementary opportunities for in-depth studies of the
disks, halos, and satellites of L* galaxies.
Our understanding of the M31 system will be transformed in the 2020s if they
include wide field facilities for both photometry (HST-like sensitivity and
resolution) and spectroscopy (10-m class telescope, >1 sq. deg. field, highly
multiplexed, R~ 3000 to 6000). We focus here on the power of these facilities
to constrain the past, present, and future merger history of M31, via
chemo-dynamical analyses and star formation histories of phase-mixed stars
accreted at early times, as well as stars in surviving tidal debris features,
M31's extended disk, and intact satellite galaxies that will eventually be
tidally incorporated into the halo. This will yield an unprecedented view of
the hierarchical formation of the M31 system and the subhalos that built it
into the L* galaxy we observe today. | 1904.01074v1 |
2021-09-28 | Diving Beneath the Sea of Stellar Activity: Chromatic Radial Velocities of the Young AU Mic Planetary System | We present updated radial-velocity (RV) analyses of the AU Mic system. AU Mic
is a young (22 Myr) early M dwarf known to host two transiting planets -
$P_{b}\sim8.46$ days, $R_{b}=4.38_{-0.18}^{+0.18}\ R_{\oplus}$,
$P_{c}\sim18.86$ days, $R_{c}=3.51_{-0.16}^{+0.16}\ R_{\oplus}$. With visible
RVs from CARMENES-VIS, CHIRON, HARPS, HIRES, {\sc
{\textsc{Minerva}}}-Australis, and TRES, as well as near-infrared (NIR) RVs
from CARMENES-NIR, CSHELL, IRD, iSHELL, NIRSPEC, and SPIRou, we provide a
$5\sigma$ upper limit to the mass of AU Mic c of $M_{c}\leq20.13\ M_{\oplus}$
and present a refined mass of AU Mic b of $M_{b}=20.12_{-1.57}^{+1.72}\
M_{\oplus}$. Used in our analyses is a new RV modeling toolkit to exploit the
wavelength dependence of stellar activity present in our RVs via
wavelength-dependent Gaussian processes. By obtaining near-simultaneous visible
and near-infrared RVs, we also compute the temporal evolution of RV-``color''
and introduce a regressional method to aid in isolating Keplerian from stellar
activity signals when modeling RVs in future works. Using a multi-wavelength
Gaussian process model, we demonstrate the ability to recover injected planets
at $5\sigma$ significance with semi-amplitudes down to $\approx$
10\,m\,s$^{-1}$ with a known ephemeris, more than an order of magnitude below
the stellar activity amplitude. However, we find that the accuracy of the
recovered semi-amplitudes is $\sim$50\% for such signals with our model. | 2109.13996v1 |
2022-03-04 | Scaling K2. V. Statistical Validation of 60 New Exoplanets From K2 Campaigns 2-18 | The NASA K2 mission, salvaged from the hardware failures of the Kepler
telescope, has continued Kepler's planet-hunting success. It has revealed
nearly 500 transiting planets around the ecliptic plane, many of which are the
subject of further study, and over 1000 additional candidates. Here we present
the results of an ongoing project to follow-up and statistically validate new
K2 planets, in particular to identify promising new targets for further
characterization. By analyzing the reconnaissance spectra, high-resolution
imaging, centroid variations, and statistical likelihood of the signals of 91
candidates, we validate 60 new planets in 46 systems. These include: a number
of planets amenable to transmission spectroscopy (K2-384 f, K2-387 b, K2-390 b,
K2-403 b, and K2-398 c), emission spectroscopy (K2-371 b, K2-370 b, and K2-399
b), and both (K2-405 b and K2-406 b); several systems with planets in or close
to mean motion resonances (K2-381, K2-398) including a compact, TRAPPIST-1-like
system of five small planets orbiting a mid-M dwarf (K2-384); an ultra-short
period sub-Saturn in the hot Saturn desert (K2-399 b); and a super-Earth
orbiting a moderately bright (V=11.93), metal-poor ([Fe/H]=-0.579+/-0.080) host
star (K2-408 b). In total we validate planets around 4 F stars, 26 G stars, 13
K stars, and 3 M dwarfs. In addition, we provide a list of 37 vetted planet
candidates that should be prioritized for future follow-up observation in order
to be confirmed or validated. | 2203.02087v2 |
2007-03-08 | Tensor Microwave Background Fluctuations for Large Multipole Order | We present approximate formulas for the tensor BB, EE, TT, and TE multipole
coefficients for large multipole order l. The error in using the approximate
formula for the BB multipole coefficients is less than cosmic variance for
l>10. These approximate formulas make various qualitative properties of the
calculated multipole coefficients transparent: specifically, they show that,
whatever values are chosen for cosmological parameters, the tensor EE multipole
coefficients will always be larger than the BB coefficients for all l>15, and
that these coefficients will approach each other for l<<100. These
approximations also make clear how these multipole coefficients depend on
cosmological parameters. | 0703179v2 |
1997-11-18 | The fourth virial coefficient of anyons | We have computed by a Monte Carlo method the fourth virial coefficient of
free anyons, as a function of the statistics angle theta. It can be fitted by a
four term Fourier series, in which two coefficients are fixed by the known
perturbative results at the boson and fermion points. We compute partition
functions by means of path integrals, which we represent diagrammatically in
such a way that the connected diagrams give the cluster coefficients. This
provides a general proof that all cluster and virial coefficients are finite.
We give explicit polynomial approximations for all path integral contributions
to all cluster coefficients, implying that only the second virial coefficient
is statistics dependent, as is the case for two-dimensional exclusion
statistics. The assumption leading to these approximations is that the tree
diagrams dominate and factorize. | 9711169v1 |
2006-04-04 | Modified Sonine approximation for the Navier-Stokes transport coefficients of a granular gas | Motivated by the disagreement found at high dissipation between simulation
data for the heat flux transport coefficients and the expressions derived from
the Boltzmann equation by the standard first Sonine approximation [Brey et al.,
Phys. Rev. E 70, 051301 (2004); J. Phys.: Condens. Matter 17, S2489 (2005)], we
implement in this paper a modified version of the first Sonine approximation in
which the Maxwell-Boltzmann weight function is replaced by the homogeneous
cooling state distribution. The structure of the transport coefficients is
common in both approximations, the distinction appearing in the coefficient of
the fourth cumulant $a_2$. Comparison with computer simulations shows that the
modified approximation significantly improves the estimates for the heat flux
transport coefficients at strong dissipation. In addition, the slight
discrepancies between simulation and the standard first Sonine estimates for
the shear viscosity and the self-diffusion coefficient are also partially
corrected by the modified approximation. Finally, the extension of the modified
first Sonine approximation to the transport coefficients of the Enskog kinetic
theory is presented. | 0604079v2 |
1992-03-02 | Can fusion coefficients be calculated from the depth rule ? | The depth rule is a level truncation of tensor product coefficients expected
to be sufficient for the evaluation of fusion coefficients. We reformulate the
depth rule in a precise way, and show how, in principle, it can be used to
calculate fusion coefficients. However, we argue that the computation of the
depth itself, in terms of which the constraints on tensor product coefficients
is formulated, is problematic. Indeed, the elements of the basis of states
convenient for calculating tensor product coefficients do not have a
well-defined depth! We proceed by showing how one can calculate the depth in an
`approximate' way and derive accurate lower bounds for the minimum level at
which a coupling appears. It turns out that this method yields exact results
for $\widehat{su}(3)$ and constitutes an efficient and simple algorithm for
computing $\widehat{su}(3)$ fusion coefficients. | 9203004v2 |
2004-04-21 | Li Coefficients for Automorphic L-Functions | Xian-Jin Li gave a criterion for the Riemann hypothesis in terms of the
positivity of a set of coefficients lambda_n, indexed by the integers. We
define similar coefficients attached to principal automorphic L-functions over
GL(N). We relate these coefficients to values of Weil's quadratic functional
for the associated automorphic representation, and deduce a Riemann hypothesis
criterion in terms of positivity of the real parts of these coefficients. We
determine asymptotics of the coefficients, both unconditionally and on the
Riemann hypothesis, as n increases. We show the existence of an entire function
of exponential type that interpolates the generalized Li coefficients at
integer values. | 0404394v4 |
2007-08-25 | Quiver coefficients of Dynkin type | We study the Grothendieck classes of quiver cycles, i.e. invariant closed
subvarieties of the representation space of a quiver. For quivers without
oriented loops we show that the class of a quiver cycle is determined by quiver
coefficients, which generalize the earlier studied quiver coefficients for
equioriented quivers of type A. We conjecture that quiver coefficients satisfy
positivity and finiteness properties. Our main result is a formula for the
quiver coefficients for orbit closures of Dynkin type with rational
singularities, which confirms the finiteness conjecture. This formula is based
on Reineke's desingularization of such orbit closures. For quivers of type A3,
we give positive combinatorial formulas for the quiver coefficients, which
confirm the full conjecture. We also interpret quiver coefficients as formulas
for degeneracy loci defined by quivers of vector bundle maps. | 0708.3418v1 |
2009-03-23 | Shear Viscosity to Entropy Density Ratio in Six Derivative Gravity | We calculate shear viscosity to entropy density ratio in presence of four
derivative (with coefficient $\alpha'$) and six derivative (with coefficient
$\alpha'^2$) terms in bulk action. In general, there can be three possible four
derivative terms and ten possible six derivative terms in the Lagrangian. Among
them two four derivative and eight six derivative terms are ambiguous, i.e.,
these terms can be removed from the action by suitable field redefinitions.
Rest are unambiguous. According to the AdS/CFT correspondence all the
unambiguous coefficients (coefficients of unambiguous terms) can be fixed in
terms of field theory parameters. Therefore, any measurable quantities of
boundary theory, for example shear viscosity to entropy density ratio, when
calculated holographically can be expressed in terms of unambiguous
coefficients in the bulk theory (or equivalently in terms of boundary
parameters). We calculate $\eta/s$ for generic six derivative gravity and find
that apparently it depends on few ambiguous coefficients at order $\alpha'^2$.
We calculate six derivative corrections to central charges $a$ and $c$ and
express $\eta/s$ in terms of these central charges and unambiguous coefficients
in the bulk theory. | 0903.3925v2 |
2009-05-25 | "Clumpiness" Mixing in Complex Networks | Three measures of clumpiness of complex networks are introduced. The measures
quantify how most central nodes of a network are clumped together. The
assortativity coefficient defined in a previous study measures a similar
characteristic, but accounts only for the clumpiness of the central nodes that
are directly connected to each other. The clumpiness coefficient defined in the
present paper also takes into account the cases where central nodes are
separated by a few links. The definition is based on the node degrees and the
distances between pairs of nodes. The clumpiness coefficient together with the
assortativity coefficient can define four classes of network. Numerical
calculations demonstrate that the classification scheme successfully
categorizes 30 real-world networks into the four classes: clumped assortative,
clumped disassortative, loose assortative and loose disassortative networks.
The clumpiness coefficient also differentiates the Erdos-Renyi model from the
Barabasi-Albert model, which the assortativity coefficient could not
differentiate. In addition, the bounds of the clumpiness coefficient as well as
the relationships between the three measures of clumpiness are discussed. | 0905.4096v1 |
2009-06-30 | Construction of operator product expansion coefficients via consistency conditions | In this thesis an iterative scheme for the construction of operator product
expansion (OPE) coefficients is applied to determine low order coefficients in
perturbation theory for a specific toy model. We use the approach to quantum
field theory proposed by S. Hollands [arXiv:0802.2198], which is centered
around the OPE and a number of axioms on the corresponding OPE coefficients.
This framework is reviewed in the first part of the thesis.
In the second part we apply an algorithm for the perturbative construction of
OPE coefficients to a toy model: Euclidean $\varphi^6$-theory in 3-dimensions.
Using a recently found formulation in terms of vertex operators and a
diagrammatic notation in terms of trees [arXiv:0906.5313v1], coefficients up to
second order are constructed, some general features of coefficients at
arbitrary order are presented and an exemplary comparison to the corresponding
customary method of computation is given. | 0906.5468v1 |
2009-08-22 | Generalization of Fibonomial Coefficients | Following Lucas and then other Fibonacci people Kwasniewski had introduced
and had started ten years ago the open investigation of the overall F-nomial
coefficients which encompass among others Binomial, Gaussian and Fibonomial
coefficients with a new unified combinatorial interpretation expressed in terms
of cobweb posets' partitions and tilings of discrete hyperboxes. In this paper,
we deal with special subfamily of T-nomial coefficients.
The main aim of this note is to develop the theory of T-nomial coefficients
with the help of generating functions. The binomial-like theorem for T-nomials
is delivered here and some consequences of it are drawn. A new combinatorial
interpretation of T-nomial coefficients is provided and compared with the
Konvalina way of objects' selections from weighted boxes. A brief summary of
already known properties of T-nomial coefficients is served. | 0908.3248v1 |
2010-01-02 | A note on dilation coefficient, plane-width, and resolution coefficient of graphs | In this note we study and compare three graph invariants related to the
'compactness' of graph drawing in the plane: the dilation coefficient, defined
as the smallest possible quotient between the longest and the shortest edge
length; the plane-width, which is the smallest possible quotient between the
largest distance between any two points and the shortest length of an edge; and
the resolution coefficient, the smallest possible quotient between the longest
edge length and the smallest distance between any two points. These three
invariants coincide for complete graphs.
We show that graphs with large dilation coefficient or plane-width have a
vertex with large valence but there exist cubic graphs with arbitrarily large
resolution coefficient. Surprisingly enough, the one-dimensional analogues of
these three invariants allow us to revisit the three well known graph
parameters: the circular chromatic number, the chromatic number, and the
bandwidth. We also examine the connection between bounded resolution
coefficient and minor-closed graph classes. | 1001.0330v1 |
2010-05-25 | Measuring small absorptions exploiting photo-thermal self-phase modulation | We present a method for the measurement of small optical absorption
coefficients. The method exploits the deformation of cavity Airy peaks that
occur if the cavity contains an absorbing material with a non-zero
thermo-refractive coefficient dn/dT or a non-zero expansion coefficient ath .
Light absorption leads to a local temperature change and to an
intensity-dependent phase shift, i.e. to a photo-thermal self-phase modulation.
The absorption coefficient is derived from a comparison of time-resolved
measurements with a numerical time-domain simulation applying a Markov-chain
Monte-Carlo (MCMC) algorithm. We apply our method to the absorption coefficient
of lithium niobate (LN) doped with 7mol% magnesium oxide (MgO) and derive a
value of alphaLN = (5.9 +/- 0.9) *10^-4/cm . Our method should also apply to
materials with much lower absorption coefficients. Based on our modelling we
estimate that with cavity finesse values of the order 10^4, absorption
coefficients of as low as 10^-8 /cm can be measured. | 1005.4490v1 |
2010-07-05 | Fusion of Daubechies Wavelet Coefficients for Human Face Recognition | In this paper fusion of visual and thermal images in wavelet transformed
domain has been presented. Here, Daubechies wavelet transform, called as D2,
coefficients from visual and corresponding coefficients computed in the same
manner from thermal images are combined to get fused coefficients. After
decomposition up to fifth level (Level 5) fusion of coefficients is done.
Inverse Daubechies wavelet transform of those coefficients gives us fused face
images. The main advantage of using wavelet transform is that it is well-suited
to manage different image resolution and allows the image decomposition in
different kinds of coefficients, while preserving the image information. Fused
images thus found are passed through Principal Component Analysis (PCA) for
reduction of dimensions and then those reduced fused images are classified
using a multi-layer perceptron. For experiments IRIS Thermal/Visual Face
Database was used. Experimental results show that the performance of the
approach presented here achieves maximum success rate of 100% in many cases. | 1007.0621v1 |
2010-12-08 | Littlewood-Richardson coefficients for reflection groups | In this paper we explicitly compute all Littlewood-Richardson coefficients
for semisimple or Kac-Moody groups G, that is, the structure coefficients of
the cohomology algebra H^*(G/P), where P is a parabolic subgroup of G. These
coefficients are of importance in enumerative geometry, algebraic combinatorics
and representation theory. Our formula for the Littlewood-Richardson
coefficients is given in terms of the Cartan matrix and the Weyl group of G.
However, if some off-diagonal entries of the Cartan matrix are 0 or -1, the
formula may contain negative summands. On the other hand, if the Cartan matrix
satisfies $a_{ij}a_{ji}\ge 4$ for all $i,j$, then each summand in our formula
is nonnegative that implies nonnegativity of all Littlewood-Richardson
coefficients. We extend this and other results to the structure coefficients of
the T-equivariant cohomology of flag varieties G/P and Bott-Samelson varieties
Gamma_\ii(G). | 1012.1714v5 |
2012-06-08 | Spin-dependent Seebeck coefficients of Ni_{80}Fe_{20} and Co in nanopillar spin valves | We have experimentally determined the spin-dependent Seebeck coefficient of
permalloy (Ni_{80}Fe_{20}) and cobalt (Co) using nanopillar spin valve devices.
The devices were specifically designed to completely separate heat related
effects from charge related effects. A pure heat current through the nanopillar
spin valve, a stack of two ferromagnetic layers (F) separated by a non-magnetic
layer (N), leads to a thermovoltage proportional to the spin-dependent Seebeck
coefficient S_{S}=S_{\uparrow}-S_{\downarrow} of the ferromagnet, where
S_{\uparrow} and S_{\downarrow} are the Seebeck coefficient for spin-up and
spin-down electrons. By using a three-dimensional finite-element model (3D-FEM)
based on spin-dependent thermoelectric theory, whose input material parameters
were measured in separate devices, we were able to accurately determine a
spin-dependent Seebeck coefficient of -1.8 microvolt/Kelvin and -4.5
microvolt/Kelvin for cobalt and permalloy, respectively corresponding to a
Seebeck coefficient polarization P_{S}=S_{S}/S_{F} of 0.08 and 0.25, where
S_{F} is the Seebeck coefficient of the ferromagnet. The results are in
agreement with earlier theoretical work in Co/Cu multilayers and spin-dependent
Seebeck and spin-dependent Peltier measurements in Ni_{80}Fe_{20}/Cu spin valve
structures. | 1206.1659v1 |
2012-09-07 | Recovering Missing Coefficients in DCT-Transformed Images | A general method for recovering missing DCT coefficients in DCT-transformed
images is presented in this work. We model the DCT coefficients recovery
problem as an optimization problem and recover all missing DCT coefficients via
linear programming. The visual quality of the recovered image gradually
decreases as the number of missing DCT coefficients increases. For some images,
the quality is surprisingly good even when more than 10 most significant DCT
coefficients are missing. When only the DC coefficient is missing, the proposed
algorithm outperforms existing methods according to experimental results
conducted on 200 test images. The proposed recovery method can be used for
cryptanalysis of DCT based selective encryption schemes and other applications. | 1209.1673v1 |
2013-07-28 | Measures of dependence between random vectors and tests of independence. Literature review | Simple correlation coefficients between two variables have been generalized
to measure association between two matrices in many ways. Coefficients such as
the RV coefficient, the distance covariance (dCov) coefficient and kernel based
coefficients have been adopted by different research communities. Scientists
use these coefficients to test whether two random vectors are linked. If they
are, it is important to uncover what patterns exist in these associations.
We discuss the topic of measures of dependence between random vectors and
tests of independence and show links between different approaches. We document
some of the interesting rediscoveries and lack of interconnection between
bodies of literature. After providing definitions of the coefficients and
associated tests, we present the recent improvements that enhance their
statistical properties and ease of interpretation. We summarize multi-table
approaches and provide scenarii where the indices can provide useful summaries
of heterogeneous multi-block data.
We illustrate these different strategies on several examples of real data and
suggest directions for future research. | 1307.7383v3 |
2013-10-23 | The Concept of Heterogeneous Scattering Coefficients and Its Application in Inverse Medium Scattering | This work investigates the scattering coefficients for inverse medium
scattering problems. It shows some fundamental properties of the coefficients
such as symmetry and tensorial properties. The relationship between the
scattering coefficients and the far-field pattern is also derived. Furthermore,
the sensitivity of the scattering coefficients with respect to changes in the
permittivity and permeability distributions is investigated. In the linearized
case, explicit formulas for reconstructing permittivity and permeability
distributions from the scattering coefficients is proposed. They relate the
exponentially ill-posed character of the inverse medium scattering problem at a
fixed frequency to the exponential decay of the scattering coefficients.
Moreover, they show the stability of the reconstruction from multifrequency
measurements. This provides a new direction for solving inverse medium
scattering problems. | 1310.6096v1 |
2014-01-25 | Relativistic many-body calculations of van der Waals coefficients for Yb-Li and Yb-Rb dimers | We derive the relativistic formulas for the van der Waals coefficients of
Yb-alkali dimers that correlate to ground and excited separated-atom limits. We
calculate $C_6$ and $C_8$ coefficients of particular experimental interest. We
also derive a semi-empirical formula that expresses the $C_8$ coefficient of
heteronuclear $A+B$ dimers in terms of the $C_6$ and $C_8$ coefficients of
homonuclear dimers and the static dipole and quadrupole polarizabilities of the
atomic states $A$ and $B$. We report results of calculation of the $C_6$
coefficients for the Yb-Rb $^3/!P_1^o+5s\, ^2/!S_{1/2}$ and $^1/!S_0+5p\,
^2/!P^o_{1/2}$ dimers, and the $C_8$ coefficients for the Yb-Li $^1/!S_0+2s\,
^2/!S_{1/2}$ and Yb-Rb $^1/!S_0+5s\, ^2/!S_{1/2}$ dimers. Uncertainties are
estimated for all predicted properties. | 1401.6585v1 |
2014-07-01 | Polynomial Interpretations over the Natural, Rational and Real Numbers Revisited | Polynomial interpretations are a useful technique for proving termination of
term rewrite systems. They come in various flavors: polynomial interpretations
with real, rational and integer coefficients. As to their relationship with
respect to termination proving power, Lucas managed to prove in 2006 that there
are rewrite systems that can be shown polynomially terminating by polynomial
interpretations with real (algebraic) coefficients, but cannot be shown
polynomially terminating using polynomials with rational coefficients only. He
also proved the corresponding statement regarding the use of rational
coefficients versus integer coefficients. In this article we extend these
results, thereby giving the full picture of the relationship between the
aforementioned variants of polynomial interpretations. In particular, we show
that polynomial interpretations with real or rational coefficients do not
subsume polynomial interpretations with integer coefficients. Our results hold
also for incremental termination proofs with polynomial interpretations. | 1407.0406v2 |
2014-09-03 | Reduction of the resonance error in numerical homogenisation II: correctors and extrapolation | This paper is the companion article of [Gloria, M3AS, 21 (2011), No. 3, pp
1601-1630]. One common drawback among numerical homogenization methods is the
presence of the so-called resonance error, which roughly speaking is a function
of the ratio $\frac{\varepsilon}{\rho}$, where $\rho$ is a typical macroscopic
lengthscale and $\varepsilon$ is the typical size of the heterogeneities. In
the present work, we make a systematic use of regularization and extrapolation
to reduce this resonance error at the level of the approximation of homogenized
coefficients and correctors for general non-necessarily symmetric stationary
ergodic coefficients. We quantify this reduction for the class of periodic
coefficients, for the Kozlov subclass of almost periodic coefficients, and for
the subclass of random coefficients that satisfy a spectral gap estimate (e.g.
Poisson random inclusions). We also report on a systematic numerical study in
dimension 2, which demonstrates the efficiency of the method and the sharpness
of the analysis. Last, we combine this approach to numerical homogenization
methods, prove the asymptotic consistency in the case of locally stationary
ergodic coefficients and give quantitative estimates in the case of periodic
coefficients. | 1409.1155v1 |
2014-11-20 | Local Adaptive Grouped Regularization and its Oracle Properties for Varying Coefficient Regression | Varying coefficient regression is a flexible technique for modeling data
where the coefficients are functions of some effect-modifying parameter, often
time or location in a certain domain. While there are a number of methods for
variable selection in a varying coefficient regression model, the existing
methods are mostly for global selection, which includes or excludes each
covariate over the entire domain. Presented here is a new local adaptive
grouped regularization (LAGR) method for local variable selection in spatially
varying coefficient linear and generalized linear regression. LAGR selects the
covariates that are associated with the response at any point in space, and
simultaneously estimates the coefficients of those covariates by tailoring the
adaptive group Lasso toward a local regression model with locally linear
coefficient estimates. Oracle properties of the proposed method are established
under local linear regression and local generalized linear regression. The
finite sample properties of LAGR are assessed in a simulation study and for
illustration, the Boston housing price data set is analyzed. | 1411.5725v1 |
2015-04-13 | Cohomology with twisted coefficients of the classifying space of a fusion system | We study the cohomology with twisted coefficients of the geometric
realization of a linking system associated to a saturated fusion system
$\mathcal{F}$. More precisely, we extend a result due to Broto, Levi and Oliver
to twisted coefficients. We generalize the notion of $\mathcal{F}$-stable
elements to $\mathcal{F}^c$-stable elements in a setting of cohomology with
twisted coefficients by an action of the fundamental group.% or, in other word,
with locally constant coefficients. We then study the problem of inducing an
idempotent from an $\mathcal{F}$-characteristic $(S,S)$-biset and we show that,
if the coefficient module is nilpotent, then the cohomology of the geometric
realization of a linking system can be computed by $\mathcal{F}^c$-stable
elements. As a corollary, we show that for any coefficient module, the
cohomology of the classifying space of a $p$-local finite group can be computed
by these $\mathcal{F}^c$-stable elements. | 1504.03191v4 |
2015-12-11 | Rectangular Kronecker coefficients and plethysms in geometric complexity theory | We prove that in the geometric complexity theory program the vanishing of
rectangular Kronecker coefficients cannot be used to prove superpolynomial
determinantal complexity lower bounds for the permanent polynomial.
Moreover, we prove the positivity of rectangular Kronecker coefficients for a
large class of partitions where the side lengths of the rectangle are at least
quadratic in the length of the partition. We also compare rectangular Kronecker
coefficients with their corresponding plethysm coefficients, which leads to a
new lower bound for rectangular Kronecker coefficients. Moreover, we prove that
the saturation of the rectangular Kronecker semigroup is trivial, we show that
the rectangular Kronecker positivity stretching factor is 2 for a long first
row, and we completely classify the positivity of rectangular limit Kronecker
coefficients that were introduced by Manivel in 2011. | 1512.03798v2 |
2016-01-28 | Virial coefficients from unified statistical thermodynamics of quantum gases trapped under generic power law potential in $d$ dimension and the equivalence of trapped quantum gases | From the unified statistical thermodynamics of quantum gases, the virial
coefficients of ideal Bose and Fermi gases which are trapped under generic
power law potential are derived systematically. From the general result of
virial coefficients, one can produce the known results in $d=3$ and $d=2$. But
more importantly we found that, the virial coefficients of bosons and fermions
become equal (except the the second virial coefficient, where the sign is
different) when we trap the gases under harmonic potential in $d=1$. This
result suggests the equivalence between Bose and Fermi gases which is already
established for $d=1$ by M M Faruk (J Stat Phys, DOI
10.1007/s10955-015-1344-4). Surprisingly our investigation also shows that the
virial coefficients of two dimensional free quantum gases are identical to the
virial coefficients of one dimensional harmonically trapped quantum gases. | 1601.07946v2 |
2016-06-22 | A Moran coefficient-based mixed effects approach to investigate spatially varying relationships | This study develops a spatially varying coefficient model by extending the
random effects eigenvector spatial filtering model. The developed model has the
following properties: its coefficients are interpretable in terms of the Moran
coefficient; each of its coefficients can have a different degree of spatial
smoothness; and it yields a variant of a Bayesian spatially varying coefficient
model. Also, parameter estimation of the model can be executed with a
relatively small computationally burden. Results of a Monte Carlo simulation
reveal that our model outperforms a conventional eigenvector spatial filtering
(ESF) model and geographically weighted regression (GWR) models in terms of the
accuracy of the coefficient estimates and computational time. We empirically
apply our model to the hedonic land price analysis of flood risk in Japan. | 1606.06885v2 |
2016-09-06 | Stochastic homogenization of linear elliptic equations: Higher-order error estimates in weak norms via second-order correctors | We are concerned with the homogenization of second-order linear elliptic
equations with random coefficient fields. For symmetric coefficient fields with
only short-range correlations, quantified through a logarithmic Sobolev
inequality for the ensemble, we prove that when measured in weak spatial norms,
the solution to the homogenized equation provides a higher-order approximation
of the solution to the equation with oscillating coefficients. In the case of
nonsymmetric coefficient fields, we provide a higher-order approximation (in
weak spatial norms) of the solution to the equation with oscillating
coefficients in terms of solutions to constant-coefficient equations. In both
settings, we also provide optimal error estimates for the two-scale expansion
truncated at second order. Our results rely on novel estimates on the
second-order homogenization corrector, which we establish via sensitivity
estimates for the second-order corrector and a large-scale $L^p$ theory for
elliptic equations with random coefficients. Our results also cover the case of
elliptic systems. | 1609.01528v2 |
2016-10-27 | Influence of multiorbitals and anisotropic Coulomb interactions on isotope effect coefficient in doped Fe-based superconductors | The present work describes the theoretical analysis of isotope effect
coefficient as a function of transition temperature in two orbital per site
model Hamiltonian in iron based superconducting system. The expression of
isotope effect coefficient has been computed numerically and self-consistently
by employing Green's function technique within the BCS-mean-field
approximation. It is observed that the isotope effect coefficient increases
with the increase of the hybridization while with the increase in Coulomb
interaction it starts decreasing. On increasing the carrier density per site in
two orbital per site iron pnictide system, isotope effect coefficient
($\alpha$) exhibits large values (much higher than BCS limit) at lower
temperatures. While in the underdoped case, isotope effect coefficient shows
minimum value in superconducting states of the iron based systems. Furthermore,
it has been found that the large value of the isotope effect coefficient is the
indication of the fact that the contribution of phonon alone is inadequate as
the origin of superconductivity in these systems. Finally, the obtained
theoretical results have been compared with experimental and existing
theoretical observations in iron based superconductors. | 1610.08888v1 |
2016-11-18 | Large Values of the Clustering Coefficient | A prominent parameter in the context of network analysis, originally proposed
by Watts and Strogatz (Collective dynamics of `small-world' networks, Nature
393 (1998) 440-442), is the clustering coefficient of a graph $G$. It is
defined as the arithmetic mean of the clustering coefficients of its vertices,
where the clustering coefficient of a vertex $u$ of $G$ is the relative density
$m(G[N_G(u)])/{d_G(u)\choose 2}$ of its neighborhood if $d_G(u)$ is at least
$2$, and $0$ otherwise. It is unknown which graphs maximize the clustering
coefficient among all connected graphs of given order and size.
We determine the maximum clustering coefficients among all connected regular
graphs of a given order, as well as among all connected subcubic graphs of a
given order. In both cases, we characterize all extremal graphs. Furthermore,
we determine the maximum increase of the clustering coefficient caused by
adding a single edge. | 1611.06135v1 |
2017-10-24 | Lower Error Bounds for Strong Approximation of Scalar SDEs with non-Lipschitzian Coefficients | We study pathwise approximation of scalar stochastic differential equations
at a single time point or globally in time by means of methods that are based
on finitely many observations of the driving Brownian motion. We prove lower
error bounds in terms of the average number of evaluations of the driving
Brownian motion that hold for every such method under rather mild assumptions
on the coefficients of the equation. The underlying simple idea of our analysis
is as follows: the lower error bounds known for equations with coefficients
that have sufficient regularity globally in space should still apply in the
case of coefficients that have this regularity in space only locally, in a
small neighborhood of the initial value. Our results apply to a huge variety of
equations with coefficients that are not globally Lipschitz continuous in space
including Cox-Ingersoll-Ross processes, equations with superlinearly growing
coefficients, and equations with discontinuous coefficients. In many of these
cases the resulting lower error bounds even turn out to be sharp. | 1710.08707v1 |
2018-02-13 | A theoretical guideline for designing an effective adaptive particle swarm | In this paper we theoretically investigate underlying assumptions that have
been used for designing adaptive particle swarm optimization algorithms in the
past years. We relate these assumptions to the movement patterns of particles
controlled by coefficient values (inertia weight and acceleration coefficient)
and introduce three factors, namely the autocorrelation of the particle
positions, the average movement distance of the particle in each iteration, and
the focus of the search, that describe these movement patterns. We show how
these factors represent movement patterns of a particle within a swarm and how
they are affected by particle coefficients (i.e., inertia weight and
acceleration coefficients). We derive equations that provide exact coefficient
values to guarantee achieving a desired movement pattern defined by these three
factors within a swarm. We then relate these movements to the searching
capability of particles and provide guideline for designing potentially
successful adaptive methods to control coefficients in particle swarm. Finally,
we propose a new simple time adaptive particle swarm and compare its results
with previous adaptive particle swarm approaches. Our experiments show that the
theoretical findings indeed provide a beneficial guideline for successful
adaptation of the coefficients in the particle swarm optimization algorithm. | 1802.04855v1 |
2018-03-02 | Stability and error analysis for the Helmholtz equation with variable coefficients | We discuss the stability theory and numerical analysis of the Helmholtz
equation with variable and possibly non-smooth or oscillatory coefficients.
Using the unique continuation principle and the Fredholm alternative, we first
give an existence-uniqueness result for this problem, which holds under rather
general conditions on the coefficients and on the domain. Under additional
assumptions, we derive estimates for the stability constant (i.e., the norm of
the solution operator) in terms of the data (i.e. PDE coefficients and
frequency), and we apply these estimates to obtain a new finite element error
analysis for the Helmholtz equation which is valid at high frequency and with
variable wave speed. The central role played by the stability constant in this
theory leads us to investigate its behaviour with respect to coefficient
variation in detail. We give, via a 1D analysis, an a priori bound with
stability constant growing exponentially in the variance of the coefficients
(wave speed and/or diffusion coefficient). Then, by means a family of analytic
examples (supplemented by numerical experiments), we show that this estimate is
sharp | 1803.00966v2 |
2018-05-06 | Self-diffusion coefficient of the square-well fluid from molecular dynamics within the constant force approach | We present a systematic study of the self-diffusion coefficient for a fluid
of particles interacting via the square-well pair potential by means of
molecular dynamics simulations in the canonical (N,V,T) ensemble. The discrete
nature of the interaction potential is modeled through the constant force
approximation and the self-diffusion coefficients is determined for several
packing fractions at super critical thermodynamic states. The dependence of the
self-diffusion coefficient with the potential range $\lambda$ is analyzed in
the range of $1.1 \leq \lambda \leq 1.5 $. The obtained molecular dynamics
simulations results are in agreement with the self-diffusion coefficient
predicted with the Enskog method. Additionally, we soh that the diffusion
coefficient is very sensitive to the potential range, $\lambda$, at low
densities leading to a density dependence of this coefficient not shared with
other macroscopic properties such as the equation of state. The constant force
approximation used in this work to model the discrete pair potential has shown
to be an excellent scheme to compute the transport properties using standar
computer simulations. Finally, the simulation results presented here are
resourceful to improving theoretical approaches, such as the Enskog method. | 1805.02245v1 |
2018-06-15 | Parametric versus nonparametric: the fitness coefficient | The fitness coefficient, introduced in this paper, results from a competition
between parametric and nonparametric density estimators within the likelihood
of the data. As illustrated on several real datasets, the fitness coefficient
generally agrees with p-values but is easier to compute and interpret. Namely,
the fitness coefficient can be interpreted as the proportion of data coming
from the parametric model. Moreover, the fitness coefficient can be used to
build a semiparamteric compromise which improves inference over the parametric
and nonparametric approaches. From a theoretical perspective, the fitness
coefficient is shown to converge in probability to one if the model is true and
to zero if the model is false. From a practical perspective, the utility of the
fitness coefficient is illustrated on real and simulated datasets. | 1806.05830v1 |
2018-09-22 | On the performance of the Euler-Maruyama scheme for SDEs with discontinuous drift coefficient | Recently a lot of effort has been invested to analyze the $L_p$-error of the
Euler-Maruyama scheme in the case of stochastic differential equations (SDEs)
with a drift coefficient that may have discontinuities in space. For scalar
SDEs with a piecewise Lipschitz drift coefficient and a Lipschitz diffusion
coefficient that is non-zero at the discontinuity points of the drift
coefficient so far only an $L_p$-error rate of at least $1/(2p)-$ has been
proven. In the present paper we show that under the latter conditions on the
coefficients of the SDE the Euler-Maruyama scheme in fact achieves an
$L_p$-error rate of at least $1/2$ for all $p\in [1,\infty)$ as in the case of
SDEs with Lipschitz coefficients. | 1809.08423v1 |
2018-10-10 | Numerical Evaluation of the Relativistic Magnetized Plasma Susceptibility Tensor and Faraday Rotation Coefficients | Polarized models of relativistically hot astrophysical plasmas require
transport coefficients as input: synchrotron absorption and emission
coefficients in each of the four Stokes parameters, as well as three Faraday
rotation coefficients. Approximations are known for all coefficients for a
small set of electron distribution functions, such as the Maxwell-Juttner
relativistic thermal distribution, and a general procedure has been obtained by
Huang & Shcherbakov for an isotropic distribution function. Here we provide an
alternative general procedure, with a full derivation, for calculating
absorption and rotation coefficients for an arbitrary isotropic distribution
function. Our method involves the computation of the full plasma susceptibility
tensor, which in addition to absorption and rotation coefficients may be used
to determine plasma modes and the dispersion relation. We implement the scheme
in a publicly available library with a simple interface, thus allowing for easy
incorporation into radiation transport codes. We also provide a comprehensive
survey of the literature and comparison with earlier results. | 1810.05530v1 |
2018-10-26 | Diving Body Shape Coefficient Setting Based on Moment of Inertia Analysis | In the diving competition rules, FINA specifies the code of different diving
movements and its difficulty coefficient. The rule simply relies on the
complexity of the action to determine the difficulty. In the formulation of the
diving difficulty coefficient, the athlete's body shape has not been fully
considered, so it is difficult to fully guarantee the fairness of the diving
competition. Based on the above problems, this paper analyzes the rules of the
FINA's 10-meter platform diving difficulty coefficient, establishes the
multi-rigid-body model of the human body, obtains the relationship between the
moment of inertia and the completion time of the athletes to complete each
diving action and the athlete's body shape, and determines the index to measure
the athlete's body shape. The Lagrange Interpolation Polynomial is used to
establish the functional relationship between the body shape correction
coefficient and the body shape correction index, and the body shape correction
coefficient corresponding to different body type athletes is determined
accordingly. Finally, a new 10-meter platform diving difficulty coefficient
scheme was developed. | 1811.04750v2 |
2019-02-26 | Numerical approximations for the variable coefficient fractional diffusion equations with non-smooth data | In this article we study the numerical approximation of a variable
coefficient fractional diffusion equation. Using a change of variable, the
variable coefficient fractional diffusion equation is transformed into a
constant coefficient fractional diffusion equation of the same order. The
transformed equation retains the desirable stability property of being an
elliptic equation. A spectral approximation scheme is proposed and analyzed for
the transformed equation, with error estimates for the approximated solution
derived. An approximation to the unknown of the variable coefficient fractional
diffusion equation is then obtained by post processing the computed
approximation to the transformed equation. Error estimates are also presented
for the approximation to the unknown of the variable coefficient equation with
both smooth and non-smooth diffusivity coefficient and right-hand side. Three
numerical experiments are given whose convergence results are in strong
agreement with the theoretically derived estimates. | 1902.10208v1 |
2019-03-26 | The current density and transport coefficients in the fully ionized plasma with q-distributions in nonextensive statistics | We study the current density and transport coefficients in the fully ionized
plasma with the q-distributions in nonextensive statistics and in strong
magnetic field. By using the generalized Boltzmann transport equation in
nonextensive statistics, we derive the current density and the expressions of
the transport coefficients, including the conductivity, the thermoelectric
coefficient, the Hall coefficient, and the Nernst coefficient. It is shown that
these new transport coefficients has been generalized to the nonequilibrium
complex plasmas with q-distributions in nonextensive statistics, which depend
strongly on the q-parameters and when we take the limit q to 1, they perfectly
return to those for the plasma based on a Maxwellian distribution. | 1904.07066v2 |
2019-05-20 | Floquet Problem and Center Manifold Reduction for Ordinary Differential Operators with Periodic Coefficients in Hilbert Spaces | A first order differential equation with a periodic operator coefficient
acting in a pair of Hilbert spaces is considered. This setting models both
elliptic equations with periodic coefficients in a cylinder and parabolic
equations with time periodic coefficients. Our main results are a construction
of a pointwise projector and a spectral splitting of the system into a finite
dimensional system of ordinary differential equations with constant
coefficients and an infinite dimensional part whose solutions have better
properties in a certain sense. This complements the well-known asymptotic
results for periodic hypoelliptic problems in cylinders (Kuchment) and for
elliptic problems in quasicylinders (Nazarov).
As an application we give a center manifold reduction for a class of
non-linear ordinary differential equations in Hilbert spaces with periodic
coefficients. This result generalizes the known case with constant coefficients
(Mielke). | 1905.07890v2 |
2019-09-12 | Multi-rater delta: extending the delta nominal measure of agreement between two raters to many raters | The need to measure the degree of agreement among R raters who independently
classify n subjects within K nominal categories is frequent in many scientific
areas. The most popular measures are Cohen's kappa (R = 2), Fleiss' kappa,
Conger's kappa and Hubert's kappa (R $\geq$ 2) coefficients, which have several
defects. In 2004, the delta coefficient was defined for the case of R = 2,
which did not have the defects of Cohen's kappa coefficient. This article
extends the coefficient delta from R = 2 raters to R $\geq$ 2. The coefficient
multi-rater delta has the same advantages as the coefficient delta with regard
to the type kappa coefficients: i) it is intuitive and easy to interpret,
because it refers to the proportion of replies that are concordant and non
random; ii) the summands which give its value allow the degree of agreement in
each category to be measured accurately, with no need to be collapsed; and iii)
it is not affected by the marginal imbalance. | 1909.05575v2 |
2019-11-26 | Determining Ultra-low Absorption Coefficients of Organic Semiconductors from the Sub-bandgap Photovoltaic External Quantum Efficiency | Energy states below the bandgap of a semiconductor, such as trap states or
charge transfer states in organic donor acceptor blends, can contribute to
light absorption. Due to their low number density or ultrasmall absorption
cross-section, the absorption coefficient of these states is challenging to
measure using conventional transmission reflection spectrophotometry. As an
alternative, the external quantum efficiency (EQE) of photovoltaic devices is
often used as a representative of the absorption coefficient, where the
spectral line shape of the EQE is considered to follow the absorption
coefficient of the active layer material. In this work, it is shown that the
subbandgap EQE is subject to thickness dependent low finesse cavity
interference effects within the device, making this assumption questionable. A
better estimate for the absorption coefficient is obtained when EQE spectra
corresponding to different active layer thicknesses are fitted simultaneously
for one attenuation coefficient using an iterative transfer matrix method. The
principle is demonstrated for two model acceptor-donor systems (PCE12ITIC and
PBTTTPC71BM) and accurate subgap absorption coefficients are determined. This
approach has particular relevance for both understanding sub-gap states and
their utilization in organic optoelectronic devices. | 1911.11485v1 |
2020-02-12 | On the Coefficients of $(\mathbb{Z}/p)^n$-Equivariant Ordinary Cohomology with Coefficients in $\mathbb{Z}/p$ | This note contains a generalization to $p>2$ of the authors' previous
calculations of the coefficients of $(\mathbb{Z}/2)^n$-equivariant ordinary
cohomology with coefficients in the constant $\mathbb{Z}/2$-Mackey functor. The
algberaic results by S.Kriz allow us to calculate the coefficients of the
geometric fixed point spectrum $\Phi^{(\mathbb{Z}/p)^n}H\mathbb{Z}/p$, and more
generally, the $\mathbb{Z}$-graded coefficients of the localization of
$H\mathbb{Z}/p_{(\mathbb{Z}/p)^n}$ by inverting any chosen set of embeddings
$S^0\rightarrow S^{\alpha_i}$ where $\alpha_i$ are non-trivial irreducible
representations. We also calculate the $RO(G)^+$-graded coefficients of
$H\mathbb{Z}/p_{(\mathbb{Z}/p)^n}$, which means the cohomology of a point
indexed by an actual (not virtual) representation. (This is the "non-derived"
part, which has a nice algebraic description.) | 2002.05284v1 |
2020-02-27 | DC Hall coefficient of the strongly correlated Hubbard model | The Hall coefficient is related to the effective carrier density and Fermi
surface topology in noninteracting and weakly interacting systems. In strongly
correlated systems, the relation between the Hall coefficient and
single-particle properties is less clear. Clarifying this relation would give
insight into the nature of transport in strongly correlated materials that lack
well-formed quasiparticles. In this work, we investigate the DC Hall
coefficient of the Hubbard model using determinant quantum Monte Carlo in
conjunction with a recently developed expansion of magneto-transport
coefficients in terms of thermodynamic susceptibilities. At leading order in
the expansion, we observe a change of sign in the Hall coefficient as a
function of temperature and interaction strength, which we relate to a change
in the topology of the apparent Fermi surface. We also combine our Hall
coefficient results with optical conductivity values to evaluate the Hall
angle, as well as effective mobility and effective mass based on Drude theory
of metals. | 2002.12289v2 |
2020-05-20 | Balancing spatial and non-spatial variation in varying coefficient modeling: a remedy for spurious correlation | This study discusses the importance of balancing spatial and non-spatial
variation in spatial regression modeling. Unlike spatially varying coefficients
(SVC) modeling, which is popular in spatial statistics, non-spatially varying
coefficients (NVC) modeling has largely been unexplored in spatial fields.
Nevertheless, as we will explain, consideration of non-spatial variation is
needed not only to improve model accuracy but also to reduce spurious
correlation among varying coefficients, which is a major problem in SVC
modeling. We consider a Moran eigenvector approach modeling spatially and
non-spatially varying coefficients (S&NVC). A Monte Carlo simulation experiment
comparing our S&NVC model with existing SVC models suggests both modeling
accuracy and computational efficiency for our approach. Beyond that, somewhat
surprisingly, our approach identifies true and spurious correlations among
coefficients nearly perfectly, even when usual SVC models suffer from severe
spurious correlations. It implies that S&NVC model should be used even when the
analysis purpose is modeling SVCs. Finally, our S&NVC model is employed to
analyze a residential land price dataset. Its results suggest existence of both
spatial and non-spatial variation in regression coefficients in practice. The
S&NVC model is now implemented in the R package spmoran. | 2005.09981v2 |
2020-07-16 | Viscosity of the magnetized strongly coupled one-component plasma | The viscosity tensor of the magnetized one-component plasma, consisting of
five independent shear viscosity coefficients, a bulk viscosity coefficient,
and a cross coefficient, is computed using equilibrium molecular dynamics
simulations and the Green-Kubo relations. A broad range of Coulomb coupling and
magnetization strength conditions are studied. Magnetization is found to
strongly influence the shear viscosity coefficients when the gyrofrequency
exceeds the Coulomb collision frequency. Three regimes are identified as the
Coulomb coupling strength and magnetization strength are varied. The Green-Kubo
relations are used to separate kinetic and potential energy contributions to
each viscosity coefficient, showing how each contribution depends upon the
magnetization strength. The shear viscosity coefficient associated with the
component of the stress tensor parallel to the magnetic field, and the two
coefficients associated with the component perpendicular to the magnetic field,
are all found to merge to a common value at strong Coulomb coupling. | 2007.08417v1 |
2021-03-08 | The Efficacy of the Method of Four Coefficients to Determine Charge Carrier Scattering | The investigation of the electronic properties of semiconductors is
inherently challenging due to the ensemble averaging of fundamentals to
transport measurements (i.e., resistivity, Hall, and Seebeck coefficient
measurements). Here, we investigate the incorporation of a fourth measurement
of electronic transport, the Nernst coefficient, into the analysis, termed the
method of four-coefficients. This approach yields the Fermi level, effective
mass, scattering exponent, and relaxation time. We begin with a review of the
underlying mathematics and investigate the mapping between the four-dimensional
material property and transport coefficient spaces. We then investigate how the
traditional single parabolic band method yields a single, potentially incorrect
point on the solution sub-space. This uncertainty can be resolved through
Nernst coefficient measurements and we map the span of the ensuing sub-space.
We conclude with an investigation of how sensitive the analysis of transport
coefficients is to experimental error for different sample types. | 2103.04569v1 |
2021-07-27 | Updated Magnetized Transport Coefficients: Impact on Laser-Plasmas with Self-Generated or Applied Magnetic Fields | Errors in the Epperlein & Haines [PoF (1986)] transport coefficients were
recently found at low electron magnetizations, with new magnetic transport
coefficients proposed simultaneously by two teams [Sadler, Walsh & Li, PRL
(2021) and Davies, Wen, Ji & Held, PoP (2021)]; these two separate sets of
updated coefficients are shown in this paper to be in agreement. The importance
of these new coefficients in laser-plasmas with either self-generated or
applied magnetic fields is demonstrated. When an external magnetic field is
applied, the cross-gradient-Nernst term twists the field structure; this
twisting is reduced by the new coefficients in the low magnetization regime.
For plasmas where only self-generated magnetic fields are present, the new
coefficients are found to result in the magnetic field moving with the
Righi-Leduc heat-flow, enhancing the impact of MHD. Simulations of Biermann
Battery magnetic fields around ICF hot-spot perturbations are presented, with
cross-gradient-Nernst transport increasing spike penetration. | 2107.12988v1 |
2021-09-13 | The correlation coefficient between citation metrics and winning a Nobel or Abel Prize | Computing such correlation coefficient would be straightforward had we had
available the rankings given by the prize committee to all scientists in the
pool. In reality we only have citation rankings for all scientists. This means,
however, that we have the ordinal rankings of the prize winners with regard to
citation metrics. I use maximum likelihood method to infer the most probable
correlation coefficient to produce the observed pattern of ordinal ranks of the
prize winners. I get the correlation coefficients of 0.47 and 0.59 between the
composite citation indicator and getting Abel Prize and Fields Medal,
respectively. The correlation coefficient between getting a Nobel Prize and the
Q-factor is 0.65. These coefficients are of the same magnitude as the
correlation coefficient between Elo ratings of the chess players and their
popularity measured as numbers of webpages mentioning the players. | 2109.06329v1 |
2021-09-23 | Scattering by finely-layered obstacles: frequency-explicit bounds and homogenization | We consider the scalar Helmholtz equation with variable, discontinuous
coefficients, modelling transmission of acoustic waves through an anisotropic
penetrable obstacle. We first prove a well-posedness result and a
frequency-explicit bound on the solution operator, with both valid for
sufficiently-large frequency and for a class of coefficients that satisfy
certain monotonicity conditions in one spatial direction, and are only assumed
to be bounded (i.e., $L^\infty$) in the other spatial directions. This class of
coefficients therefore includes coefficients modelling transmission by
penetrable obstacles with a (potentially large) number of layers (in 2-d) or
fibres (in 3-d). Importantly, the frequency-explicit bound holds uniformly for
all coefficients in this class; this uniformity allows us to consider
highly-oscillatory coefficients and study the limiting behaviour when the
period of oscillations goes to zero. In particular, we bound the $H^1$ error
committed by the first-order bulk correction to the homogenized transmission
problem, with this bound explicit in both the period of oscillations of the
coefficients and the frequency of the Helmholtz equation; to our knowledge,
this is the first homogenization result for the Helmholtz equation that is
explicit in these two quantities and valid without the assumption that the
frequency is small. | 2109.11267v2 |
2021-11-16 | Operator Growth and Symmetry-Resolved Coefficient Entropy in Quantum Maps | Operator growth, or operator spreading, describes the process where a
"simple" operator acquires increasing complexity under the Heisenberg time
evolution of a chaotic dynamics, therefore has been a key concept in the study
of quantum chaos in both single-particle and many-body systems. An explicit way
to quantify the complexity of an operator is the Shannon entropy of its
operator coefficients over a chosen set of operator basis, dubbed "coefficient
entropy". However, it remains unclear if the basis-dependency of the
coefficient entropy may result in a false diagnosis of operator growth, or the
lack thereof. In this paper, we examine the validity of coefficient entropy in
the presence of hidden symmetries. Using the quantum cat map as an example, we
show that under a generic choice of operator basis, the coefficient entropy
fails to capture the suppression of operator growth caused by the symmetries.
We further propose "symmetry-resolved coefficient entropy" as the proper
diagnosis of operator complexity, which takes into account robust unknown
symmetries, and demonstrate its effectiveness in the case of quantum cat map. | 2111.08729v1 |
2022-01-13 | Towards a realistic evaluation of transport coefficients in non-equilibrium space plasmas | Recent studies have outlined the interest for the evaluation of transport
coefficients in space plasmas, where the observed velocity distributions of
plasma particles are conditioned not only by the binary collisions, e.g., at
low energies, but also by the energisation of particles from their interaction
with wave turbulence and fluctuations, generating the suprathermal
Kappa-distributed populations. This paper provides a first estimate of the main
transport coefficients based on regularised Kappa distributions (RKDs), which,
unlike standard Kappa distributions (SKDs), enable macroscopic parameterisation
without mathematical divergences or physical inconsistencies. All transport
coefficients derived here, i.e., the diffusion and mobility coefficients,
electric conductivity, thermoelectric coefficient and thermal conductivity, are
finite and well defined for all values of $\kappa > 0$. Moreover, for low
values of $\kappa$ (i.e., below the SKD poles), the transport coefficients can
be orders of magnitudes higher than the corresponding Maxwellian limits,
meaning that significant underestimations can be made if suprathermal electrons
are ignored. | 2201.05157v1 |
2022-03-02 | Fourth cluster and virial coefficients of a unitary Fermi gas for an arbitrary mass ratio | We calculate the fourth cluster coefficients of the homogeneous unitary spin
1/2 Fermi gas as functions of the internal-state mass ratio, over intervals
constrained by the 3- or 4-body Efimov effect. For this we use our 2016
conjecture (validated for equal masses by Hou and Drut in 2020) in a
numerically efficient formulation making the sum over angular momentum converge
faster, which is crucial at large mass ratio. The mean cluster coefficient,
relevant for equal chemical potentials, is not of constant sign and increases
rapidly close to the Efimovian thresholds. We also get the fourth virial
coefficients, which we find to be very poor indicators of interaction-induced
4-body correlations. We obtain analytically for all $n$ the cluster
coefficients of order $n$ + 1 for an infinity-mass impurity fermion, matching
the conjecture for $n=3$. Finally, in a harmonic potential, we predict a
non-monotonic behavior of the 3 + 1 cluster coefficient with trapping
frequency, near mass ratios where this coefficient vanishes in the homogeneous
case. | 2203.00916v2 |
2022-08-11 | Painlevé IV, Chazy II, and Asymptotics for Recurrence Coefficients of Semi-classical Laguerre Polynomials and Their Hankel Determinants | This paper studies the monic semi-classical Laguerre polynomials based on
previous work by Boelen and Van Assche \cite{Boelen}, Filipuk et al.
\cite{Filipuk} and Clarkson and Jordaan \cite{Clarkson}. Filipuk, Van Assche
and Zhang proved that the diagonal recurrence coefficient $\alpha_n(t)$
satisfies the fourth Painlev\'{e} equation. In this paper we show that the
off-diagonal recurrence coefficient $\beta_n(t)$ fulfills the first member of
Chazy II system. We also prove that the sub-leading coefficient of the monic
semi-classical Laguerre polynomials satisfies both the continuous and discrete
Jimbo-Miwa-Okamoto $\sigma$-form of Painlev\'{e} IV. By using Dyson's Coulomb
fluid approach together with the discrete system for $\alpha_n(t)$ and
$\beta_n(t)$, we obtain the large $n$ asymptotic expansions of the recurrence
coefficients and the sub-leading coefficient. The large $n$ asymptotics of the
associate Hankel determinant (including the constant term) is derived from its
integral representation in terms of the sub-leading coefficient. | 2208.05883v1 |
2022-09-07 | Greedy expansions with prescribed coefficients in Hilbert spaces for special classes of dictionaries | Greedy expansions with prescribed coefficients have been introduced by V. N.
Temlyakov in the frame of Banach spaces. The idea is to choose a sequence of
fixed (real) coefficients $\{c_n\}_{n=1}^\infty$ and a fixed set of elements
(dictionary) of the Banach space; then, under suitable conditions on the
coefficients and the dictionary, it is possible to expand all the elements of
the Banach space in series that contain only the fixed coefficients and the
elements of the dictionary. In Hilbert spaces the convergence of greedy
algorithm with prescribed coefficients is characterized, in the sense that
there are necessary and sufficient conditions on the coefficients in order that
the algorithm is convergent for all the dictionaries. This paper is concerned
with the question if such conditions can be weakened for particular classes of
spaces or dictionaries; we prove that this is the case for finite dimensional
spaces, and for some classes of dictionaries related to orthonormal sequences
in infinite dimensional spaces. | 2209.03091v2 |
2022-12-23 | Domain Decomposition Methods for Elliptic Problems with High Contrast Coefficients Revisited | In this paper, we revisit the nonoverlapping domain decomposition methods for
solving elliptic problems with high contrast coefficients. Some interesting
results are discovered. We find that the Dirichlet-Neumann algorithm and
Robin-Robin algorithms may make full use of the ratio of coefficients.
Actually, in the case of two subdomains, we show that their convergence rates
are $O(\epsilon)$, if $\nu_1\ll\nu_2$, where $\epsilon = \nu_1/\nu_2$ and
$\nu_1,\nu_2$ are coefficients of two subdomains. Moreover, in the case of many
subdomains, the condition number bounds of Dirichlet-Neumann algorithm and
Robin-Robin algorithm are $1+\epsilon(1+\log(H/h))^2$ and
$C+\epsilon(1+\log(H/h))^2$, respectively, where $\epsilon$ may be a very small
number in the high contrast coefficients case. Besides, the convergence
behaviours of the Neumann-Neumann algorithm and Dirichlet-Dirichlet algorithm
may be independent of coefficients while they could not benefit from the
discontinuous coefficients. Numerical experiments are preformed to confirm our
theoretical findings. | 2212.12216v1 |
2023-01-17 | Numerical experiments on coefficients of instanton partition functions | We analyze the coefficients of partition functions of Vafa-Witten theory for
the complex projective plane $\mathbb{CP}^2$. We experimentally study the
growth of the coefficients for gauge group $SU(2)$ and $SU(3)$, which are
examples of mock modular forms of depth $1$ and 2 respectively. We also
introduce the notion of ``mock cusp form'', and study an example of weight 3
related to the $SU(3)$ partition function. Numerical experiments on the first
200 coefficients suggest that the coefficients of a mock modular form of weight
$k$ grow as the coefficients of a modular form of weight $k$, that is to say as
$n^{k-1}$. On the other hand the coefficients of the mock cusp form appear to
grow as $n^{3/2}$, which exceeds the growth of classical cusp forms of weight
3. We provide bounds using saddle point analysis, which however largely exceed
the experimental observation. | 2301.06711v2 |
2023-02-22 | Quantum complexity of the Kronecker coefficients | Whether or not the Kronecker coefficients of the symmetric group count some
set of combinatorial objects is a longstanding open question. In this work we
show that a given Kronecker coefficient is proportional to the rank of a
projector that can be measured efficiently using a quantum computer. In other
words a Kronecker coefficient counts the dimension of the vector space spanned
by the accepting witnesses of a QMA verifier, where QMA is the quantum analogue
of NP. This implies that approximating the Kronecker coefficients to within a
given relative error is not harder than a certain natural class of quantum
approximate counting problems that captures the complexity of estimating
thermal properties of quantum many-body systems. A second consequence is that
deciding positivity of Kronecker coefficients is contained in QMA,
complementing a recent NP-hardness result of Ikenmeyer, Mulmuley and Walter. We
obtain similar results for the related problem of approximating row sums of the
character table of the symmetric group. Finally, we discuss an efficient
quantum algorithm that approximates normalized Kronecker coefficients to
inverse-polynomial additive error. | 2302.11454v2 |
2023-05-03 | Combinatorial interpretations of binomial analogues of Fibonacci and q Fibonacci numbers | The Fibonomial and Gaussian binomial coefficients are well known analogues of
the binomial coefficients. A combinatorial interpretation for these analogues
was first presented by Sagan and Savage in 2010. We introduce a slightly
modified interpretation of Fibonomial coefficients. We also prove some
identities involving Gaussian binomial coefficients. Recently Bergeron gave a
similar interpretation of the q Fibonomial coefficients. Inspired from the
model given by Bennett, they obtained a staircase model for the q Fibonomial
coefficients as well. They have provided the proofs for the same using
induction and bijective correspondence techniques. We establish a new model for
q Fibonacci numbers using which we can give a non bijective proof to the
staircase model. We apply this model to prove some identities of q Fibonacci
numbers. Also we will demonstrate some identities related to the q Fibonomial
coefficients using the staircase model. | 2305.01838v1 |
2023-07-21 | Revisiting the gas-phase chemical rate coefficients at high temperatures in CLOUDY | A two-body gas-phase reaction rate coefficient can be given by the usual
Arrhenius-type formula which depends on temperature. The UMIST Database for
Astrochemistry is a widely used database for reaction rate coefficients. They
provide fittings for coefficients valid over a particular range of
temperatures. The permissible upper-temperature limits vary over a wide range:
from 100 K to 41000K. A wide range of temperatures occurs in nature; thus, it
requires evaluating the rate coefficients at temperatures outside the range of
validity. As a result, a simple extrapolation of the rate coefficients can lead
to unphysically large values at high temperatures. These result in unrealistic
predictions. Here we present a solution to prevent the gas-phase reaction
coefficients from diverging at a very high temperature. We implement this into
the spectral synthesis code CLOUDY which operates over a wide range of
temperatures from CMB to 10$^{10}$ K subject to different astrophysical
environments. | 2308.02500v1 |
2023-11-14 | Clustering coefficients for networks with higher order interactions | We introduce a clustering coefficient for nondirected and directed
hypergraphs, which we call the quad clustering coefficient. We determine the
average quad clustering coefficient and its distribution in real-world
hypergraphs and compare its value with those of random hypergraphs drawn from
the configuration model. We find that real-world hypergraphs exhibit a
nonnegligible fraction of nodes with a maximal value of the quad clustering
coefficient, while we do not find such nodes in random hypergraphs.
Interestingly, these highly clustered nodes can have large degrees and can be
incident to hyperedges of large cardinality. Moreover, highly clustered nodes
are not observed in an analysis based on the pairwise clustering coefficient of
the associated projected graph that has binary interactions, and hence higher
order interactions are required to identify nodes with a large quad clustering
coefficient. | 2311.08563v2 |
2023-11-18 | Asymptotic distributions of the average clustering coefficient and its variant | In network data analysis, summary statistics of a network can provide us with
meaningful insight into the structure of the network. The average clustering
coefficient is one of the most popular and widely used network statistics. In
this paper, we investigate the asymptotic distributions of the average
clustering coefficient and its variant of a heterogeneous Erd\"{o}s-R\'{e}nyi
random graph. We show that the standardized average clustering coefficient
converges in distribution to the standard normal distribution. Interestingly,
the variance of the average clustering coefficient exhibits a phase transition
phenomenon. The sum of weighted triangles is a variant of the average
clustering coefficient. It is recently introduced to detect geometry in a
network. We also derive the asymptotic distribution of the sum weighted
triangles, which does not exhibit a phase transition phenomenon as the average
clustering coefficient. This result signifies the difference between the two
summary statistics. | 2311.10979v1 |
2024-03-04 | Binomial Coefficients and Littlewood--Richardson Coefficients for Interpolation Polynomials | Inhomogeneous versions of Jack and Macdonald polynomials, called
interpolation polynomials, have been introduced by Knop--Sahi (type $A$) and
Okounkov (type $BC$). In this paper, we study binomial coefficients and
Littlewood--Richardson (LR) coefficients for these interpolation polynomials.
We extend to type $BC$ the weighted sum formula for binomial coefficients due
to the second author in type $A$, and obtain a new weighted sum formula for LR
coefficients for both types $A$ and $BC$. We prove that binomial coefficients
are positive and monotone using the weighted sum formula and the combinatorial
formulas due to Okounkov. As an application, we show that the containment
partial order can be characterized in terms of Schur positivity or Jack
positivity. This result is in parallel with the work of
Cuttler--Greene--Skandera, Sra and Khare--Tao, which characterize two other
partial orders, majorization and weak majorization, in terms of evaluation
positivity of Schur functions. | 2403.02490v1 |
2024-01-30 | Multi-view Subspace Clustering via An Adaptive Consensus Graph Filter | Multiview subspace clustering (MVSC) has attracted an increasing amount of
attention in recent years. Most existing MVSC methods first collect
complementary information from different views and consequently derive a
consensus reconstruction coefficient matrix to indicate the subspace structure
of a multi-view data set. In this paper, we initially assume the existence of a
consensus reconstruction coefficient matrix and then use it to build a
consensus graph filter. In each view, the filter is employed for smoothing the
data and designing a regularizer for the reconstruction coefficient matrix.
Finally, the obtained reconstruction coefficient matrices from different views
are used to create constraints for the consensus reconstruction coefficient
matrix. Therefore, in the proposed method, the consensus reconstruction
coefficient matrix, the consensus graph filter, and the reconstruction
coefficient matrices from different views are interdependent. We provide an
optimization algorithm to obtain their optimal values. Extensive experiments on
diverse multi-view data sets demonstrate that our approach outperforms some
state-of-the-art methods. | 2403.08787v1 |
1994-06-27 | Reverberation mapping of active galactic nuclei : The SOLA method for time-series inversion | In this paper a new method is presented to find the transfer function of the
broad-line region in active galactic nuclei. The subtractive optimally
localized averages (SOLA) method is a modified version of the Backus-Gilbert
method and is presented as an alternative to the more often used
maximum-entropy method. The SOLA method has been developed for use in
helioseismology. It has been applied to the solar oscillation frequency
splitting data currently available to deduce the internal rotation rate of the
sun. The original SOLA method is reformulated in the present paper to cope with
the slightly different problem of inverting time series. We use simulations to
test the viability of the method and apply the SOLA method to the real data of
the Seyfert-1 galaxy NGC 5548. We investigate the effects of measurement errors
and how the resolution of the TF critically depends upon both the sampling rate
and the photometric accuracy of the data. A uuencoded compressed postscript
file of the paper which includes the figures is available by anonymous ftp at
ftp://solaris.astro.uu.se/pub/articles/atmos/frank/PijWan.uue | 9406070v1 |
1997-06-20 | Rejection of the Binary Broad-Line Region Interpretation of Double-Peaked Emission Lines in Three Active Galactic Nuclei | It has been suggested that the peculiar double-peaked Balmer lines of certain
broad-line radio galaxies come from individual broad-line regions associated
with the black holes of a supermassive binary. We continue to search for
evidence of the radial velocity variations characteristic of a double-lined
spectroscopic binary that are required in such a model. After spectroscopic
monitoring of three suitable candidates (Arp 102B, 3C 390.3, and 3C 332)
spanning two decades, we find no such long-term systematic changes in radial
velocity. A trend noticed by Gaskell in one of the Balmer-line peaks of 3C
390.3 before 1988 did not continue after that year, invalidating his inferred
orbital period and mass. Instead, we find lower limits on the plausible orbital
periods that would require the assumed supermassive binaries in all three
objects to have total masses in excess of 10^10 solar masses. In the case of 3C
390.3 the total binary mass must exceed 10^11 solar masses to satisfy
additional observational constraints on the inclination angle. Such large
binary black hole masses are difficult to reconcile with other observations and
with theory. In addition, there are peculiar properties of the line profiles
and flux ratios in these objects that are not explained by ordinary broad-line
region cloud models. We therefore doubt that the double-peaked line profiles of
the three objects arise in a pair of broad-line regions. Rather, they are much
more likely to be intimately associated with a single black hole. | 9706222v2 |
1999-08-13 | Infrared Spectroscopy of the High Redshift Radio Galaxy MRC~2025-218 and a Neighboring Extremely Red Galaxy | This paper presents infrared spectra taken with the newly commissioned
NIRSPEC spectrograph on the Keck Telescope of the High Redshift Radio Galaxy
MRC 2025-218 (z=2.630) and an extremely red galaxy (R-K > 6 mag) 9'' away.
These observations represent the deepest infrared spectra of a radio galaxy to
date and have allowed for the detection of Hbeta, OIII (4959/5007), OI (6300),
Halpha, NII (6548/6583) and SII (6716/6713). The Halpha emission is very broad
(FWHM~6000 km/s) and strongly supports AGN unification models linking radio
galaxies and quasars. The line ratios are most consistent with a partially
obscured nuclear region and very high excitation. The OIII (5007) line is
extended several arcseconds and shows high velocity clouds in the extended
emission. The nucleus also appears spectrally double and we argue that the
radio galaxy is undergoing a violent merger process. The red galaxy, by
comparison, is very featureless even though we have a good continuum detection
in the H and K bands. We suggest that this object is a foreground galaxy,
probably at a redshift less than 1.5. | 9908153v1 |
2000-01-11 | 2 micron Spectroscopy within 0.3 arcseconds of SgrA* | We present moderate (R~$\approx$~2,700) and high resolution
(R~$\approx$~22,000) 2.0$-$2.4 \micron\ spectroscopy of the central 0.1 square
arcseconds of the Galaxy obtained with NIRSPEC, the facility near-infrared
spectrometer for the Keck II telescope. The composite spectra do not have any
features attributable to the brightest stars in the central cluster, i.e.\
after background subtraction, W$_{\rm ^{12}CO(2-0)}$~$<$~2~\AA. This stringent
limit leads us to conclude that the majority, if not all, of the stars are
hotter than typical red giants. Coupled with previously reported photometry, we
conclude that the sources are likely OB main sequence stars. In addition, the
continuum slope in the composite spectrum is bluer than that of a red giant and
is similar to that of the nearby hot star, IRS16NW. It is unlikely that they
are late-type giants stripped of their outer envelopes because such sources
would be much fainter than those observed. Given their inferred youth
($\tau_{\rm age}$~$<$~20~\Myr), we suggest the possibility that the stars have
formed within 0.1 pc of the supermassive black hole. We find a newly-identified
broad-line component (V$_{\rm FWHM}$ $\approx$ 1,000 \kms) to the 2.2178
\micron\ [\ion{Fe}{3}] line located within a few arcseconds of Sgr~A$^*$. A
similar component is not seen in the Br-$\gamma$ emission. | 0001171v1 |
2000-02-17 | Discovery of an Obscured Broad Line Region in the High Redshift Radio Galaxy MRC 2025-218 | This paper presents infrared spectra taken with the newly commissioned
NIRSPEC spectrograph on the Keck II Telescope of the High Redshift Radio Galaxy
MRC 2025-218 (z=2.63) These observations represent the deepest infrared spectra
of a radio galaxy to date and have allowed for the detection of Hbeta, [OIII]
(4959/5007), [OI] (6300), Halpha, [NII] (6548/6583) and [SII] (6716/6713). The
Halpha emission is very broad (FWHM = 9300 km/s) and luminous (2.6x10^44
ergs/s) and it is very comparable to the line widths and strengths of radio
loud quasars at the same redshift. This strongly supports AGN unification
models linking radio galaxies and quasars, although we discuss some of the
outstanding differences. The [OIII] (5007) line is extremely strong and has
extended emission with large relative velocities to the nucleus. We also derive
that if the extended emission is due to star formation, each knot has a star
formation rate comparable to a Lyman Break Galaxy at the same redshift. | 0002335v1 |
2000-02-26 | Hot Stars and Cool Clouds: The Photodissociation Region M16 | We present high-resolution spectroscopy and images of a photodissociation
region (PDR) in M16 obtained during commissioning of NIRSPEC on the Keck II
telescope. PDRs play a significant role in regulating star formation, and M16
offers the opportunity to examine the physical processes of a PDR in detail. We
simultaneously observe both the molecular and ionized phases of the PDR and
resolve the spatial and kinematic differences between them. The most prominent
regions of the PDR are viewed edge-on. Fluorescent emission from nearby stars
is the primary excitation source, although collisions also preferentially
populate the lowest vibrational levels of H2. Variations in density-sensitive
emission line ratios demonstrate that the molecular cloud is clumpy, with an
average density n = 3x10^5 cm^(-3). We measure the kinetic temperature of the
molecular region directly and find T_H2 = 930 K. The observed density,
temperature, and UV flux imply a photoelectric heating efficiency of 4%. In the
ionized region, n_i=5x10^3 cm^(-3) and T_HII = 9500 K. In the brightest regions
of the PDR, the recombination line widths include a non-thermal component,
which we attribute to viewing geometry. | 0002491v1 |
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