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2023-07-12
|
Exponential stability of damped Euler-Bernoulli beam controlled by boundary springs and dampers
|
In this paper, the vibration model of an elastic beam, governed by the damped
Euler-Bernoulli equation
$\rho(x)u_{tt}+\mu(x)u_{t}$$+\left(r(x)u_{xx}\right)_{xx}=0$, subject to the
clamped boundary conditions $u(0,t)=u_x(0,t)=0$ at $x=0$, and the boundary
conditions $\left(-r(x)u_{xx}\right)_{x=\ell}=k_r u_x(\ell,t)+k_a
u_{xt}(\ell,t)$, $\left(-\left(r(x)u_{xx}\right)_{x}\right )_{x=\ell}$$=- k_d
u(\ell,t)-k_v u_{t}(\ell,t)$ at $x=\ell$, is analyzed. The boundary conditions
at $x=\ell$ correspond to linear combinations of damping moments caused by
rotation and angular velocity and also, of forces caused by displacement and
velocity, respectively. The system stability analysis based on well-known
Lyapunov approach is developed. Under the natural assumptions guaranteeing the
existence of a regular weak solution, uniform exponential decay estimate for
the energy of the system is derived. The decay rate constant in this estimate
depends only on the physical and geometric parameters of the beam, including
the viscous external damping coefficient $\mu(x) \ge 0$, and the boundary
springs $k_r,k_d \ge 0$ and dampers $k_a,k_v \ge 0$. Some numerical examples
are given to illustrate the role of the damping coefficient and the boundary
dampers.
|
2307.06170v2
|
2023-08-03
|
Flavor-wave theory with quasiparticle damping at finite temperatures: Application to chiral edge modes in the Kitaev model
|
We propose a theoretical framework to investigate elementary excitations at
finite temperatures within a localized electron model that describes the
interactions between multiple degrees of freedom, such as quantum spin models
and Kugel-Khomskii models. Thus far, their excitation structures have been
mainly examined using the linear flavor-wave theory, an SU($N$) generalization
of the linear spin-wave theory. These techniques introduce noninteracting
bosonic quasiparticles as elementary excitations from the ground state, thereby
elucidating numerous physical phenomena, including excitation spectra and
transport properties characterized by topologically nontrivial band structures.
Nevertheless, the interactions between quasiparticles cannot be ignored in
systems exemplified by $S=1/2$ quantum spin models, where strong quantum
fluctuations are present. Recent studies have investigated the effects of
quasiparticle damping at zero temperature in such models. In our study,
extending this approach to the flavor-wave theory for general localized
electron models, we construct a comprehensive method to calculate excitation
spectra with the quasiparticle damping at finite temperatures. We apply our
method to the Kitaev model under magnetic fields, a typical example of models
with topologically nontrivial magnon bands. Our calculations reveal that chiral
edge modes undergo significant damping in weak magnetic fields, amplifying the
damping rate by the temperature increase. This effect is caused by collisions
with thermally excited quasiparticles. Since our approach starts from a general
Hamiltonian, it will be widely applicable to other localized systems, such as
spin-orbital coupled systems derived from multi-orbital Hubbard models in the
strong correlation limit.
|
2308.01711v1
|
2024-02-13
|
Investigating the Effect of Noise on the Training Performance of Hybrid Quantum Neural Networks
|
In this paper, we conduct a comprehensively analyze the influence of
different quantum noise gates, including Phase Flip, Bit Flip, Phase Damping,
Amplitude Damping, and the Depolarizing Channel, on the performance of HyQNNs.
Our results reveal distinct and significant effects on HyQNNs training and
validation accuracies across different probabilities of noise. For instance,
the Phase Flip gate introduces phase errors, and we observe that HyQNNs exhibit
resilience at higher probability (p = 1.0), adapting effectively to consistent
noise patterns, whereas at intermediate probabilities, the performance
declines. Bit Flip errors, represented by the PauliX gate, impact HyQNNs in a
similar way to that Phase Flip error gate. The HyQNNs, can adapt such kind of
errors at maximum probability (p = 1.0). Unlike Phase and Bit Flip error gates,
Phase Damping and Amplitude Damping gates disrupt quantum information, with
HyQNNs demonstrating resilience at lower probabilities but facing challenges at
higher probabilities. Amplitude Damping error gate, in particular, poses
efficiency and accuracy issues at higher probabilities however with lowest
probability (p = 0.1),it has the least effect and the HyQNNs, however not very
effectively, but still tends to learn. The Depolarizing Channel proves most
detrimental to HyQNNs performance, with limited or no training improvements.
There was no training potential observed regardless of the probability of this
noise gate. These findings underscore the critical need for advanced quantum
error mitigation and resilience strategies in the design and training of
HyQNNs, especially in environments prone to depolarizing noise. This paper
quantitatively investigate that understanding the impact of quantum noise gates
is essential for harnessing the full potential of quantum computing in
practical applications.
|
2402.08523v1
|
2024-03-03
|
Magnonic $\varphi$ Josephson Junctions and Synchronized Precession
|
There has been a growing interest in non-Hermitian physics. One of its main
goals is to engineer dissipation and to explore ensuing functionality. In
magnonics, the effect of dissipation due to local damping on magnon transport
has been explored. However, the effects of non-local damping on the magnonic
analog of the Josephson effect remain missing, despite that non-local damping
is inevitable and has been playing a central role in magnonics. Here, we
uncover theoretically that a surprisingly rich dynamics can emerge in magnetic
junctions due to intrinsic non-local damping, using analytical and numerical
methods. In particular, under microwave pumping, we show that coherent spin
precession in the right and left insulating ferromagnet (FM) of the junction
becomes synchronized by non-local damping and thereby a magnonic analog of the
$\varphi$ Josephson junction emerges, where $\varphi$ stands here for the
relative precession phase of right and left FM in the stationary limit.
Remarkably, $\varphi$ decreases monotonically from $ \pi$ to $\pi/2$ as the
magnon-magnon interaction, arising from spin anisotropies, increases. Moreover,
we also find a magnonic diode effect giving rise to rectification of magnon
currents. Our predictions are readily testable with current device and
measurement technologies at room temperatures.
|
2403.01625v1
|
1997-01-17
|
Evidence for Rotation in the Galaxy at z=3.15 Responsible for a Damped Lyman-alpha Absorption System in the Spectrum of Q2233+1310
|
Proof of the existence of a significant population of normal disk galaxies at
redshift z>2 would have profound implications for theories of structure
formation and evolution. We present evidence based on Keck HIRES observations
that the damped Lyman-alpha absorber at z=3.15 toward the quasar Q2233+1310 may
well be such an example. Djorgovski et al have recently detected the
Lyman-alpha emission from the absorber, which we assume is at the systemic
redshift of the absorbing galaxy. By examining the profiles of the metal
absorption lines arising from the absorbing galaxy in relation to its systemic
redshift, we find strong kinematical evidence for rotation. Therefore the
absorber is likely to be a disk galaxy. The inferred circular velocity for the
galaxy is >200 km/s. With a separation of ~17 kpc between the galaxy and the
quasar sightline, the implied dynamic mass for the galaxy is >1.6x10(11) solar
mass. The metallicity of the galaxy is found to be [Fe/H]=-1.4, typical of
damped Lyman-alpha galaxies at such redshifts. However, in another damped
galactic rotation is evident. In the latter case, the damped Lyman-alpha
absorber occurs near the background quasar in redshift so its properties may be
influenced by the background quasar. These represent the only two cases at
present for which the technique used here may be applied. Future applications
of the same technique to a large sample of damped Lyman-alpha galaxies may
allow us to determine if a significant population of disk galaxies already
existed only a few billion years after the Big Bang.
|
9701116v2
|
1997-04-11
|
The Metallicity of High Redshift Galaxies: The Abundance of Zinc in 34 Damped Lyman Alpha Systems from z = 0.7 to 3.4
|
We report new observations of ZnII and CrII absorption lines in 10 damped
\lya systems (DLAs), mostly at redshift $z_{abs} \simgt 2.5$ . By combining
these results with those from our earlier survey (Pettini et al. 1994) and
other recent data, we construct a sample of 34 measurements (or upper limits)
of the Zn abundance relative to hydrogen [Zn/H]; the sample includes more than
one third of the total number of DLAs known.
The plot of the abundance of Zn as a function of redshift reinforces the two
main findings of our previous study. (1) Damped \lya systems are mostly
metal-poor, at all redshifts sampled; the column density weighted mean for the
whole data set is [Zn/H] $= -1.13 \pm 0.38$ (on a logarithmic scale), or
approximately 1/13 of solar. (2) There is a large spread, by up to two orders
of magnitude, in the metallicities we measure at essentially the same
redshifts. We propose that damped \lya systems are drawn from a varied
population of galaxies of different morphological types and at different stages
of chemical evolution, supporting the idea of a protracted epoch of galaxy
formation.
At redshifts $z \simgt 2$ the typical metallicity of the damped \lya systems
is in agreement with expectations based on the consumption of HI gas implied by
the recent measurements of $\Omega_{DLA}$ by Storrie-Lombardi et al. (1996a),
and with the metal ejection rates in the universe at these epochs deduced by
Madau (1996) from the ultraviolet luminosities of high redshift galaxies
revealed by deep imaging surveys. There are indications in our data for an
increase in the mean metallicity of the damped \lya systems from $z > 3$ to
$\approx 2$, consistent with the rise in the comoving star formation rate
indicated by the relative numbers of $U$ and $B$ drop-outs in the Hubble Deep
Field. Although such comparisons are still tentative, it appears that these
different avenues for exploring the early evolution of galaxies give a broadly
consistent picture.
|
9704102v1
|
1997-04-17
|
On the Kinematics of the Damped Lyman Alpha Protogalaxies
|
We present the first results of an ongoing program to investigate the
kinematic characteristics of high redshift damped lya systems. Because damped
lya systems are widely believed to be the progenitors of current massive
galaxies, an analysis of their kinematic history allows a direct test of galaxy
formation scenarios.
We have collected a kinematically unbiased sample of 17 high S/N ratio, high
resolution damped lya spectra taken with HIRES on the 10m W.M. Keck Telescope.
Our study focuses on the unsaturated, low-ion transitions of these systems
which reveal their kinematic traits. The profiles exhibit a nearly uniform
distribution of velocity widths ranging from 20 - 200 km/s and a relatively
high degree of asymmetry. In an attempt to explain these characteristics, we
introduce several physical models, which have previously been attributed to
damped lya systems, including rapidly rotating cold disks, slowly rotating hot
disks, massive isothermal halos, and a hydrodynamic spherical accretion model.
Using standard Monte Carlo techniques, we run sightlines through these model
systems to derive simulated low-ion profiles. Comparing statistical measures of
the simulated profiles with the observed profiles, we determine that the
rapidly rotating cold disk model is the only tested model consistent with the
data at high confidence levels. A Relative Likelihood Test of the rapidly
rotating cold disk model indicates the disks must have large rotation speeds; v
> 180 km/s at the 99% c.l. In turn, we demonstrate that the Cold Dark Matter
Model, as developed by Kauffmann (1996), is inconsistent with the damped lya
data at very high c.l. This is because the CDM Model does not predict a large
enough fraction of rapidly rotating disks at z approx 2.5.
|
9704169v2
|
2000-11-20
|
H-alpha Imaging with HST+NICMOS of An Elusive Damped Ly-alpha Cloud at z=0.6
|
Despite previous intensive ground-based imaging and spectroscopic campaigns
and wide-band HST imaging of the z=0.927 QSO 3C336 field, the galaxy that hosts
the damped Ly-alpha system along this line-of-sight has eluded detection. We
present a deep narrow-band H-alpha image of the field of this z=0.656 damped
Ly-alpha absorber, obtained through the F108N filter of NICMOS 1 onboard the
Hubble Space Telescope. The goal of this project was to detect any H-alpha
emission 10 times closer than previous studies to unveil the damped absorber.
We do not detect H-alpha emission between 0.05'' and 6'' (0.24 and 30 $h^{-1}$
kpc) from the QSO, with a 3-sigma flux limit of $3.70 \times 10^{-17} h^{-2}$
erg/s/cm^2 for an unresolved source, corresponding to a star formation rate
(SFR) of $0.3 h^{-2}$ M_sun/yr. This leads to a 3-sigma upper limit of 0.15
M_sun/yr/kpc^2 on the SFR density, or a maximum SFR of 1.87 M_sun/yr assuming a
disk of 4 kpc in diameter. This result adds to the number of low redshift
damped Ly-alpha absorbers that are not associated with the central regions of
Milky-Way-like disks. Damped Ly-alpha absorption can arise from high density
concentrations in a variety of galactic environments including some that,
despite their high local HI densities, are not conducive to widespread star
formation.
|
0011374v2
|
2005-08-17
|
The SDSS Damped Lya Survey: Data Release 3
|
We present the results from a damped Lya survey of the Sloan Digital Sky
Survey, Data Release 3 based on over 500 new damped Lya systems at z>2.2. We
measure the HI column density distribution f(N) and its zeroth and first
moments (the incidence l(X) and gas mass-density O_dla of damped Lya systems,
respectively) as a function of redshift. The key results include: (1) the f(N)
distribution is well fit by a Gamma-function with `break' column density log
N_g=10^21.5 and `faint-end' slope alpha=-1.8; (2) the shape of the f(N)
distributions do not show evolution with redshift; (3) l(X) and O_dla decrease
by 35% and 50% during ~1Gyr between redshift z=[3.,3.5] to z=[2.2,2.5]; and (4)
l(X) and O_dla in the lowest SDSS redshift bin (z=2.2) are consistent with the
current values. We investigate systematic errors in damped Lya analysis and
identify only one important effect: we measure 40 +/- 20% higher O_dla values
toward a subset of brighter quasars than toward a faint subset. This effect
runs contrary to the bias associated with dust obscuration and suggests that
gravitational lensing may be important. Comparing the results against models of
galaxy formation, we find all of the models significantly underpredict l(X) at
z=3 and only SPH models with significant feedback may reproduce O_dla at high
redshift. We argue that the Lyman limit systems contribute ~1/3 of the
universe's HI atoms at all redshifts z=2 to 5 and that the f(N) distribution
for N(HI)<10^20 has an inflection with slope >-1. We advocate a new mass
density definition -- the mass density of predominantly neutral gas O_neut --
to be contrasted with the mass density of gas associated with HI atoms. We
contend the damped Lya systems contribute >80% of O_neut at all redshifts and
therefore are the main reservoirs for star formation. [abridged]
|
0508361v1
|
2010-03-11
|
Damping of MHD turbulence in partially ionized gas and the observed difference of velocities of neutrals and ions
|
Theoretical and observational studies on the turbulence of the interstellar
medium developed fast in the past decades. The theory of supersonic magnetized
turbulence, as well as the understanding of projection effects of observed
quantities, are still in progress. In this work we explore the characterization
of the turbulent cascade and its damping from observational spectral line
profiles. We address the difference of ion and neutral velocities by clarifying
the nature of the turbulence damping in the partially ionized. We provide
theoretical arguments in favor of the explanation of the larger Doppler
broadening of lines arising from neutral species compared to ions as arising
from the turbulence damping of ions at larger scales. Also, we compute a number
of MHD numerical simulations for different turbulent regimes and explicit
turbulent damping, and compare both the 3-dimensional distributions of velocity
and the synthetic line profile distributions. From the numerical simulations,
we place constraints on the precision with which one can measure the 3D
dispersion depending on the turbulence sonic Mach number. We show that no
universal correspondence between the 3D velocity dispersions measured in the
turbulent volume and minima of the 2D velocity dispersions available through
observations exist. For instance, for subsonic turbulence the correspondence is
poor at scales much smaller than the turbulence injection scale, while for
supersonic turbulence the correspondence is poor for the scales comparable with
the injection scale. We provide a physical explanation of the existence of such
a 2D-3D correspondence and discuss the uncertainties in evaluating the damping
scale of ions that can be obtained from observations. However, we show that the
statistics of velocity dispersion from observed line profiles can provide the
spectral index and the energy transfer rate of turbulence. Also, comparing two
similar simulations with different viscous coefficients it was possible to
constrain the turbulent cut-off scale. This may especially prove useful since
it is believed that ambipolar diffusion may be one of the dominant dissipative
mechanism in star-forming regions. In this case, the determination of the
ambipolar diffusion scale may be used as a complementary method for the
determination of magnetic field intensity in collapsing cores. We discuss the
implications of our findings in terms of a new approach to magnetic field
measurement proposed by Li & Houde (2008).
|
1003.2346v1
|
2011-09-07
|
Weakly collisional Landau damping and three-dimensional Bernstein-Greene-Kruskal modes: New results on old problems
|
Landau damping and Bernstein-Greene-Kruskal (BGK) modes are among the most
fundamental concepts in plasma physics. While the former describes the
surprising damping of linear plasma waves in a collisionless plasma, the latter
describes exact undamped nonlinear solutions of the Vlasov equation. There does
exist a relationship between the two: Landau damping can be described as the
phase-mixing of undamped eigenmodes, the so-called Case-Van Kampen modes, which
can be viewed as BGK modes in the linear limit. While these concepts have been
around for a long time, unexpected new results are still being discovered. For
Landau damping, we show that the textbook picture of phase-mixing is altered
profoundly in the presence of collision. In particular, the continuous spectrum
of Case-Van Kampen modes is eliminated and replaced by a discrete spectrum,
even in the limit of zero collision. Furthermore, we show that these discrete
eigenmodes form a complete set of solutions. Landau-damped solutions are then
recovered as true eigenmodes (which they are not in the collisionless theory).
For BGK modes, our interest is motivated by recent discoveries of electrostatic
solitary waves in magnetospheric plasmas. While one-dimensional BGK theory is
quite mature, there appear to be no exact three-dimensional solutions in the
literature (except for the limiting case when the magnetic field is
sufficiently strong so that one can apply the guiding-center approximation). We
show, in fact, that two- and three-dimensional solutions that depend only on
energy do not exist. However, if solutions depend on both energy and angular
momentum, we can construct exact three-dimensional solutions for the
unmagnetized case, and two-dimensional solutions for the case with a finite
magnetic field. The latter are shown to be exact, fully electromagnetic
solutions of the steady-state Vlasov-Poisson-Amp\`ere system.
|
1109.1353v1
|
2012-11-06
|
Torsional Alfvén waves in solar partially ionized plasma: effects of neutral helium and stratification
|
Ion-neutral collisions may lead to the damping of Alfven waves in
chromospheric and prominence plasmas. Neutral helium atoms enhance the damping
in certain temperature interval, where the ratio of neutral helium and neutral
hydrogen atoms is increased. Therefore, the height-dependence of ionization
degrees of hydrogen and helium may influence the damping rate of Alfven waves.
We aim to study the effect of neutral helium in the damping of Alfven waves in
stratified partially ionized plasma of the solar chromosphere. We consider a
magnetic flux tube, which is expanded up to 1000 km height and then becomes
vertical due to merging with neighboring tubes, and study the dynamics of
linear torsional Alfven waves in the presence of neutral hydrogen and neutral
helium atoms. We start with three-fluid description of plasma and consequently
derive single-fluid magnetohydrodynamic (MHD) equations for torsional Alfven
waves. Thin flux tube approximation allows to obtain the dispersion relation of
the waves in the lower part of tubes, while the spatial dependence of
steady-state Alfven waves is governed by Bessel type equation in the upper part
of tubes. Consecutive derivation of single-fluid MHD equations results in a new
Cowling diffusion coefficient in the presence of neutral helium which is
different from previously used one. We found that shorter-period (< 5 s)
torsional Alfven waves damp quickly in the chromospheric network due to
ion-neutral collision. On the other hand, longer-period (> 5 s) waves do not
reach the transition region as they become evanescent at lower heights in the
network cores. Propagation of torsional Alfven waves through the chromosphere
into the solar corona should be considered with caution: low-frequency waves
are evanescent due to the stratification, while high-frequency waves are damped
due to ion neutral collisions.
|
1211.1348v2
|
2013-05-16
|
Application of vibration-transit theory to distinct dynamic response for a monatomic liquid
|
We examine the distinct part of the density autocorrelation function Fd(q,t),
also called the intermediate scattering function, from the point of view of the
vibration-transit (V-T) theory of monatomic liquid dynamics. A similar study
has been reported for the self part, and we study the self and distinct parts
separately because their damping processes are not simply related. We begin
with the perfect vibrational system, which provides precise definitions of the
liquid correlations, and provides the vibrational approximation Fdvib(q,t) at
all q and t. Two independent liquid correlations are defined, motional and
structural, and these are decorrelated sequentially, with a crossover time
tc(q). This is done by two independent decorrelation processes: the first,
vibrational dephasing, is naturally present in Fdvib(q,t) and operates to damp
the motional correlation; the second, transit-induced decorrelation, is invoked
to enhance the damping of motional correlation, and then to damp the structural
correlation. A microscopic model is made for the "transit drift", the averaged
transit motion that damps motional correlation on 0 < t < tc(q). Following the
previously developed self-decorrelation theory, a microscopic model is also
made for the "transit random walk," which damps the structural correlation on t
> tc(q). The complete model incorporates a property common to both self and
distinct decorrelation: simple exponential decay following a delay period,
where the delay is tc(q, the time required for the random walk to emerge from
the drift. Our final result is an accurate expression for Fd(q,t) for all q
through the first peak in Sd(q). The theory is calibrated and tested using
molecular dynamics (MD) calculations for liquid Na at 395K; however, the theory
itself does not depend on MD, and we consider other means for calibrating it.
|
1305.3954v2
|
2013-09-16
|
Two-atom system as a nano-antenna for mode switching and light routing
|
We determine how a system composed of two nonidentical two-level atoms with
different resonance frequencies and different damping rates could work as a
nano-antenna for controlled mode switching and light routing. We calculate the
angular distribution of the emitted field detected in a far-field zone of the
system including the direct interatomic interactions and arbitrary linear
dimensions of the system. The calculation is carried out in terms of the
symmetric and antisymmetric modes of the two atom system. We find that as long
as the atoms are identical, the emission cannot be switched between the
symmetric and antisymmetric modes. The switching may occur when the atoms are
non-identical and the emission can then be routed to different modes by
changing the relative ratio of the atomic frequencies, or damping rates or by a
proper tuning of the laser frequency to the atomic resonance frequencies. It is
shown that in the case of atoms of different resonance frequencies but equal
damping rates, the light routing is independent of the frequency of the driving
laser field. It depends only on the sign of the detuning between the atomic
resonance frequencies. In the case of atoms of different damping rates, the
emission can be switched between different modes by changing the laser
frequency from the blue to red detuned from the atomic resonance. The effect of
the interatomic interactions is also considered and it is found that in the
case of unequal resonance frequencies of the atoms, the interactions slightly
modify the visibility of the intensity pattern. The case of unequal damping
rates of the atoms is affected rather more drastically, the light routing
becoming asymmetric under the dipole-dipole interaction with the enhanced
intensities of the modes turned towards the atom of smaller damping rate.
|
1309.3924v1
|
2015-04-01
|
Landau damping of Gardner solitons in a dusty bi-ion plasma
|
The effects of linear Landau damping on the nonlinear propagation of
dust-acoustic solitary waves (DASWs) are studied in a collisionless
unmagnetized dusty plasma with two species of positive ions. The extremely
massive, micron-seized, cold and negatively charged dust particles are
described by fluid equations, whereas the two species of positive ions, namely
the cold (heavy) and hot (light) ions are described by the kinetic Vlasov
equations. Following Ott and Sudan [Phys. Fluids {\bf 12}, 2388 (1969)], and by
considering lower and higher-order perturbations, the evolution of DASWs with
Landau damping is shown to be governed by Korteweg-de Vries (KdV), modified KdV
(mKdV) or Gardner (KdV-mKdV)-like equations. The properties of the phase
velocity and the Landau damping rate of DASWs are studied for different values
of the ratios of the temperatures $(\sigma)$ and the number densities $(\mu)$
of hot and cold ions as well the cold to hot ion mass ratio $m$. The
distinctive features of the decay rates of the amplitudes of the KdV, mKdV and
Gardner solitons with a small effect of Landau damping are also studied in
different parameter regimes. It is found that the Gardner soliton points to
lower wave amplitudes than the KdV and mKdV solitons. The results may be useful
for understanding the localization of solitary pulses and associated wave
damping (collisionless) in laboratory and space plasmas (e.g., the F-ring of
Saturn) in which the number density of free electrons is much smaller than that
of ions and the heavy, micron seized dust grains are highly charged.
|
1504.00089v2
|
2017-07-18
|
Explanations of the DAMPE high energy electron/positron spectrum in the dark matter annihilation and pulsar scenarios
|
Many studies have shown that either the nearby astrophysical source or dark
matter (DM) annihilation/decay is required to explain the origin of high energy
cosmic ray (CR) $e^\pm$, which are measured by many experiments, such as PAMELA
and AMS-02. Recently, the Dark Matter Particle Explorer (DAMPE) collaboration
has reported its first result of the total CR $e^\pm$ spectrum from $25
\,\mathrm{GeV}$ to $4.6 \,\mathrm{TeV}$ with high precision. In this work, we
study the DM annihilation and pulsar interpretations of the DAMPE high energy
$e^\pm$ spectrum. In the DM scenario, the leptonic annihilation channels to
$\tau^+\tau^-$, $4\mu$, $4\tau$, and mixed charged lepton final states can well
fit the DAMPE result, while the $\mu^+\mu^-$ channel has been excluded. In
addition, we find that the mixed charged leptons channel would lead to a sharp
drop at $\sim$ $\mathrm{TeV}$. However, these DM explanations are almost
excluded by the observations of gamma-ray and CMB, unless some complicated DM
models are introduced. In the pulsar scenario, we analyze 21 nearby known
pulsars and assume that one of them is the primary source of high energy CR
$e^\pm$.Considering the constraint from the Fermi-LAT observation of the
$e^\pm$ anisotropy, we find that two pulsars are possible to explain the DAMPE
data. Our results show that it is difficult to distinguish between the DM
annihilation and single pulsar explanations of high energy $e^\pm$ with the
current DAMPE result.
|
1707.05664v2
|
2018-06-27
|
In-flight performance of the DAMPE silicon tracker
|
DAMPE (DArk Matter Particle Explorer) is a spaceborne high-energy cosmic ray
and gamma-ray detector, successfully launched in December 2015. It is designed
to probe astroparticle physics in the broad energy range from few GeV to 100
TeV. The scientific goals of DAMPE include the identification of possible
signatures of Dark Matter annihilation or decay, the study of the origin and
propagation mechanisms of cosmic-ray particles, and gamma-ray astronomy. DAMPE
consists of four sub-detectors: a plastic scintillator strip detector, a
Silicon-Tungsten tracKer-converter (STK), a BGO calorimeter and a neutron
detector. The STK is composed of six double layers of single-sided silicon
micro-strip detectors interleaved with three layers of tungsten for photon
conversions into electron-positron pairs. The STK is a crucial component of
DAMPE, allowing to determine the direction of incoming photons, to reconstruct
tracks of cosmic rays and to estimate their absolute charge (Z). We present the
in-flight performance of the STK based on two years of in-flight DAMPE data,
which includes the noise behavior, signal response, thermal and mechanical
stability, alignment and position resolution.
|
1806.10355v1
|
2018-10-30
|
Effect of Landau damping on ion acoustic solitary waves in a multi-species collisionless unmagnetized plasma consisting of nonthermal and isothermal electrons
|
A Korteweg-de Vries (KdV) equation including the effect of Landau damping is
derived to study the propagation of weakly nonlinear and weakly dispersive ion
acoustic waves in a collisionless unmagnetized plasma consisting of warm
adiabatic ions and two different species of electrons at different
temperatures. The hotter energetic electron species follows the nonthermal
velocity distribution of Cairns et al. [Geophys. Res. Lett. 22, 2709 (1995)]
whereas the cooler electron species obeys the Boltzmann distribution. It is
found that the coefficient of the nonlinear term of this KdV like evolution
equation vanishes along different family of curves in different parameter
planes. In this context, a modified KdV (MKdV) equation including the effect of
Landau damping effectively describes the nonlinear behaviour of ion acoustic
waves. It has also been observed that the coefficients of the nonlinear terms
of the KdV and MKdV like evolution equations including the effect of Landau
damping, are simultaneously equal to zero along a family of curves in the
parameter plane. In this situation, we have derived a further modified KdV
(FMKdV) equation including the effect of Landau damping to describe the
nonlinear behaviour of ion acoustic waves. In fact, different modified KdV like
evolution equations including the effect of Landau damping have been derived to
describe the nonlinear behaviour of ion acoustic waves in different region of
parameter space. The method of Ott & Sudan [Phys. Fluids 12, 2388 (1969)] has
been applied to obtain the solitary wave solution of the evolution equation
having the nonlinear term $(\phi^{(1)})^{r}\frac{\partial \phi^{(1)}}{\partial
\xi}$, where $\phi^{(1)}$ is the first order perturbed electrostatic potential
and $r =1,2,3$. We have found that the amplitude of the solitary wave solution
decreases with time for all $r =1,2,3$.
|
1810.12739v1
|
2019-03-28
|
Improving convergence of volume penalised fluid-solid interactions
|
We analyse and improve the volume-penalty method, a simple and versatile way
to model objects in fluid flows. The volume-penalty method is a kind of
fictitious-domain method that approximates no-slip boundary conditions with
rapid linear damping inside the object. The method can then simulate complex,
moving objects in general numerical solvers without specialised algorithms or
boundary-conforming grids. Volume penalisation pays for this simplicity by
introducing an equation-level error, the $\textit{model error}$, that is
related to the damping time $\eta \ll 1$. While the model error has been proven
to vanish as the damping time tends to zero, previous work suggests convergence
at a slow rate of $\mathcal{O}(\eta^{1/2})$. The stiffness of the damping
implies conventional volume penalisation only achieves first order numerical
accuracy. We analyse the volume-penalty method using multiple-scales
matched-asymptotics with a signed-distance coordinate system valid for
arbitrary smooth geometries. We show the dominant model error stems from a
displacement length that is proportional to a Reynolds number $\text{Re}$
dependent boundary layer of size $\mathcal{O}(\eta^{1/2}\text{Re}^{-1/2})$. The
relative size of the displacement length and damping time leads to multiple
error regimes. Our key finding derives a simple smoothing prescription for the
damping that eliminates the displacement length and reduces the model error to
$\mathcal{O}(\eta)$ in all regimes. This translates to second order numerical
accuracy. We validate our findings in several comprehensive benchmark problems
and finally combine Richardson extrapolation of the model error with our
correction to further improve convergence to $\mathcal{O}(\eta^{2})$.
|
1903.11914v4
|
2019-06-12
|
Study of Alfven Eigenmodes stability in plasma with multiple NBI driven energetic particle specie
|
The aim of this study is to analyze the destabilization of Alfven Eigenmodes
(AE) by multiple energetic particles (EP) species in DIII-D and LHD discharges.
We use the reduced MHD equations to describe the linear evolution of the
poloidal flux and the toroidal component of the vorticity in a full 3D system,
coupled with equations of density and parallel velocity moments for the
energetic particles species, including the effect of the acoustic modes,
diamagnetic currents and helical couplings. We add the Landau damping and
resonant destabilization effects using a closure relation. The simulations with
multiple NBI lines show three different regimes: the non damped regime where
the multi beam AEs growth rate is larger compared to the growth rate of the AEs
destabilized by the individual NBI lines, the interaction regime where the
multi beam AEs growth rate is smaller than the single NBI AEs and the damped
regime where the AEs are suppressed. Operations in the damped regime requires
EP species with different density profile flatness or gradient locations. In
addition, the AEs growth rate in the interaction regime is further reduced if
the combined NBI lines have similar beam temperatures and the beta of the NBI
line with flatter EP density profile increases. Then, optimization trends are
identified in DIII-D high poloidal beta and LHD low density / magnetic field
discharges with multiple NBI lines as well as the configuration requirements to
operate in the damped and interaction regimes. DIII-D simulations show a
decrease of the n=2 to 6 AEs growth rate and n=1 AE are stabilized in the LHD
case. The helical coupling effects in LHD simulations lead to a transition from
the interaction to the damped regime of the n=2,-8,12 helical family.
|
1906.05701v1
|
2019-11-05
|
Observation of Nanoscale Opto-Mechanical Molecular Damping; Origin of Spectroscopic Contrast in Photo Induced Force Microscopy
|
We experimentally investigated the contrast mechanism of infrared
photoinduced force microscopy (PiFM) for recording vibrational resonances.
Extensive experiments have demonstrated that spectroscopic contrast in PiFM is
mediated by opto-mechanical damping of the cantilever oscillation as the
optical wavelength is scanned through optical resonance. To our knowledge, this
is the first time opto-mechanical damping has been observed in the AFM. We
hypothesize that this damping force is a consequence of the dissipative
interaction between the sample and the vibrating tip; the modulated light
source in PiFM modulates the effective damping constant of the 2nd eigenmode of
the cantilever which in turn generate side-band signals producing the PiFM
signal at the 1st eigenmode. A series of experiments have eliminated other
mechanisms of contrast. By tracking the frequency shift of the PiFM signal at
the 1st cantilever eigenmode as the excitation wavenumber is tuned through a
mid-infrared absorption band, we showed that the near-field optical interaction
is attractive. By using a vibrating piezoelectric crystal to mimic sample
thermal expansion in a PiFM operating in mixing mode, we determined that the
minimum thermal expansion our system can detect is 30 pm limited by system
noise. We have confirmed that van der Waal mediated thermal-expansion forces
have negligible effect on PiFM signals by detecting the resonant response of a
4-methylbenzenethiol mono molecular layer deposited on template-stripped gold,
where thermal expansion was expected to be < 3 pm, i.e., 10 times lower than
our system noise level. Finally, the basic theory for dissipative tip-sample
interactions was introduced to model the photoinduced opto-mechanical damping.
Theoretical simulations are in excellent agreement with experiment.
|
1911.05190v1
|
2020-06-08
|
Stochastic re-acceleration and magnetic-field damping in Tycho's supernova remnant
|
A number of studies suggest that shock acceleration with particle feedback
and very efficient magnetic-field amplification combined with Alfv\'{e}nic
drift are needed to explain the rather soft radio spectrum and the narrow rims
observed for Tycho's SNR. We show that the broadband spectrum of Tycho's SNR
can alternatively be well explained when accounting for stochastic acceleration
as a secondary process. The re-acceleration of particles in the turbulent
region immediately downstream of the shock should be efficient enough to impact
particle spectra over several decades in energy. The so-called Alfv\'{e}nic
drift and particle feedback on the shock structure are not required in this
scenario. Additionally, we investigate whether synchrotron losses or
magnetic-field damping play a more profound role in the formation of the
non-thermal filaments. We solve the full particle transport equation in
test-particle mode using hydrodynamic simulations of the SNR plasma flow. The
background magnetic field is either computed from the induction equation or
follows analytic profiles, depending on the model considered. Fast-mode waves
in the downstream region provide the diffusion of particles in momentum space.
We show that the broadband spectrum of Tycho can be well explained if
magnetic-field damping and stochastic re-acceleration of particles are taken
into account. Although not as efficient as standard DSA, stochastic
acceleration leaves its imprint on the particle spectra, which is especially
notable in the emission at radio wavelengths. We find a lower limit for the
post-shock magnetic-field strength $\sim330\,\mathrm{\mu G}$, implying
efficient amplification even for the magnetic-field damping scenario. For the
formation of the filaments in the radio range magnetic-field damping is
necessary, while the X-ray filaments are shaped by both the synchrotron losses
and magnetic-field damping.
|
2006.04832v1
|
2021-02-23
|
Influence of Ion-Neutral Damping on the Cosmic-Ray Streaming Instability: Magnetohydrodynamic Particle-in-cell Simulations
|
We explore the physics of the gyro-resonant cosmic ray streaming instability
(CRSI) including the effects of ion-neutral (IN) damping. This is the main
damping mechanism in (partially-ionized) atomic and molecular gas, which are
the primary components of the interstellar medium (ISM) by mass. Limitation of
CRSI by IN damping is important in setting the amplitude of Alfv\'en waves that
scatter cosmic rays and control galactic-scale transport. Our study employs the
MHD-PIC hybrid fluid-kinetic numerical technique to follow linear growth as
well as post-linear and saturation phases. During the linear phase of the
instability -- where simulations and analytical theory are in good agreement --
IN damping prevents wave growth at small and large wavelengths, with the
unstable bandwidth lower for higher ion-neutral collision rate $\nu_{\rm in}$.
Purely MHD effects during the post-linear phase extend the wave spectrum
towards larger $k$. In the saturated state, the cosmic ray distribution evolves
toward greater isotropy (lower streaming velocity) by scattering off of Alv\'en
waves excited by the instability. In the absence of low-$k$ waves, CRs with
sufficiently high momentum are not isotropized. The maximum wave amplitude and
rate of isotropization of the distribution function decreases at higher
$\nu_{\rm in}$. When the IN damping rate approaches the maximum growth rate of
CSRI, wave growth and isotropization is suppressed. Implications of our results
for CR transport in partially ionized ISM phases are discussed.
|
2102.11878v3
|
2022-06-17
|
Quantum Dynamics of Magnetic Skyrmions: Consistent Path Integral Formulation
|
We present a path integral formalism for the intrinsic quantum dynamics of
magnetic skyrmions coupled to a thermal background of magnetic fluctuations.
Upon promoting the skyrmion's collective coordinate $\boldsymbol{R}$ to a
dynamic variable and integrating out the magnonic heat bath, we derive the
generalized equation of motion for $\boldsymbol{R}$ with a non-local damping
term that describes a steady-state skyrmion dynamics at finite temperatures.
Being essentially temperature dependent, the intrinsic damping is shown to
originate from the coupling of thermally activated magnon modes to the
adiabatic potential driven by a rigid skyrmion motion, which can be regarded as
another manifestation of emergent electrodynamics inherent to topological
magnetic textures. We further argue that the diagonal components of the damping
term act as the source of dissipation and inertia, while its off-diagonal
components modify the gyrotropic motion of a magnetic skyrmion. By means of
numerical calculations for the lattice spin model of chiral ferromagnets, we
study the temperature behavior of the intrinsic damping as a function of
magnetic field in periodic and confined geometries. The intrinsic damping is
demonstrated to be highly non-local, revealing its quantum-mechanical nature,
that becomes more pronounced with increasing temperature. At high temperatures
when the magnon occupation factors are large, the intrinsic damping is shown to
yield a modified Thiele's equation with the additional non-local dissipative
and mass terms that exhibit an almost linear temperature behavior. Our results
provide a microscopic background for semiclassical magnetization dynamics and
establish a framework for understanding spin caloritronics effects in
topological magnetic textures.
|
2206.08532v2
|
2024-02-05
|
Revisiting the role of cosmic-ray driven Alfvén waves in pre-existing magnetohydrodynamic turbulence. I. Turbulent damping rates and feedback on background fluctuations
|
Alfv\'en waves (AWs) excited by the cosmic-ray (CR) streaming instability
(CRSI) are a fundamental ingredient for CR confinement. The effectiveness of
self-confinement relies on a balance between CRSI growth rate and damping
mechanisms acting on quasi-parallel AWs excited by CRs. One relevant mechanism
is the so-called turbulent damping, in which an AW packet injected in
pre-existing turbulence undergoes a cascade process due to its nonlinear
interaction with fluctuations of the background. The turbulent damping of an AW
packet in pre-existing magnetohydrodynamic turbulence is re-examined, revised,
and extended to include most-recent theories of MHD turbulence that account for
dynamic alignment and reconnection-mediated regime. The case in which the role
of feedback of CR-driven AWs on pre-existing turbulence is important will also
be discussed. Particular attention is given to the nonlinearity parameter
$\chi^w$ that estimates the strength of nonlinear interaction between CR-driven
AWs and background fluctuations. We point out the difference between $\chi^w$
and $\chi^z$ that instead describes the strength of nonlinear interactions
between pre-existing fluctuations. When $\chi^w$ is properly taken into
account, one finds that (i) the turbulent damping rate of quasi-parallel AWs in
anisotropic turbulence depends on the background-fluctuations' amplitude to the
third power, hence is strongly suppressed, and (ii) the dependence on the AW's
wavelength (and thus on the CR gyro-radius from which it is excited) is
different from what has been previously obtained. Finally, (iii) when dynamic
alignment of cascading fluctuations and the possibility of a
reconnection-mediated range is included in the picture, the turbulent damping
rate exhibits novel regimes and breaks. Finally, a criterion for CR-feedback is
derived and simple phenomenological models of CR-modified turbulent scaling are
provided.
|
2402.02901v1
|
2006-10-24
|
Logical contradictions of Landau damping
|
Landau damping/growing at boundary condition of excitation of a harmonic wave
in collisionless ion-electron-neutrals plasma contradicts to the law of energy
conservation of a wave damping/growing in space. There is also no criterion of
a choice either damping or growing solution in difference from always
non-damping in the direction of propagation Vlasov waves. Variety of other
incongruities as consequence of Landau damping is specified also. Absence of
explicit positivity and finiteness of wave solutions for electron distribution
function near singularity point leads to need of imposing additional cutting
off constraints with resulting positivity and finiteness of the electron
distribution function at the singularity points and finiteness of the complex
dispersion integral. Landau damping as a real physical phenomenon of
collisionless damping does not exist. A relation is established for the real
dispersion equation with real waves (see Appendices 2,4) between the averaged
over period wave damping decrement and the collisional energy-exchange term of
kinetic equation. Collisionless Vlasov-Landau damping is explained finally by
the usual wrong use of nonlinearly complex wave functions leading to complex
dispersion equation. All used solution of the complex dispersion equation for
the simultaneously existing collisionless both exponentially damping and
growing nonlinear complex waves is entirely, quantitatively and in its logical
sense, different from the solution of initially real dispersion equation for
real either damping or growing waves and should be discarded (see Appendices
2,4,5,6). Collisionless damping is caused by unreasonable use of wave functions
with complex frequency or complex wave number leading to complex dispersion
relation with unphysical binomial virtual complex roots. Thus finding roots of
the complex dispersion equation has only abstract mathematical interest.
|
0610220v67
|
1999-12-17
|
Infrared Spectroscopy of a Massive Obscured Star Cluster in the Antennae Galaxies (NGC 4038/4039) with NIRSPEC
|
We present infrared spectroscopy of the Antennae Galaxies (NGC 4038/4039)
with NIRSPEC at the W. M. Keck Observatory. We imaged the star clusters in the
vicinity of the southern nucleus (NGC 4039) in 0.39" seeing in K-band using
NIRSPEC's slit-viewing camera. The brightest star cluster revealed in the
near-IR (M_K(0) = -17.9) is insignificant optically, but coincident with the
highest surface brightness peak in the mid-IR (12-18 micron) ISO image
presented by Mirabel et al. (1998). We obtained high signal-to-noise 2.03 -
2.45 micron spectra of the nucleus and the obscured star cluster at R ~ 1900.
The cluster is very young (4 Myr old), massive (16e6 M_sun), and compact
(density ~ 115 M_sun pc^(-3) within a 32 pc half-light radius), assuming a
Salpeter IMF (0.1 - 100 M_sun). Its hot stars have a radiation field
characterized by T_eff ~ 39,000 K, and they ionize a compact H II region with
n_e ~ 1e4 cm^(-3). The stars are deeply embedded in gas and dust (A_V ~ 9-10
mag), and their strong FUV field powers a clumpy photodissociation region with
densities n_H >= 1e5 cm^(-3) on scales of up to 200 pc, radiating L[H_2 1-0
S(1)] = 9600 L_sun.
|
9912369v1
|
2000-09-07
|
Practical Quantum Cryptography: A Comprehensive Analysis (Part One)
|
We perform a comprehensive analysis of practical quantum cryptography (QC)
systems implemented in actual physical environments via either free-space or
fiber-optic cable quantum channels for ground-ground, ground-satellite,
air-satellite and satellite-satellite links. (1) We obtain universal
expressions for the effective secrecy capacity and rate for QC systems taking
into account three important attacks on individual quantum bits, including
explicit closed-form expressions for the requisite amount of privacy
amplification. Our analysis also includes the explicit calculation in detail of
the total cost in bits of continuous authentication, thereby obtaining new
results for actual ciphers of finite length. (2) We perform for the first time
a detailed, explicit analysis of all systems losses due to propagation, errors,
noise, etc. as appropriate to both optical fiber cable- and satellite
communications-based implementations of QC. (3) We calculate for the first time
all system load costs associated to classical communication and computational
constraints that are ancillary to, but essential for carrying out, the pure QC
protocol itself. (4) We introduce an extended family of generalizations of the
Bennett-Brassard (BB84) QC protocol that equally provide unconditional secrecy
but allow for the possibility of optimizing throughput rates against specific
cryptanalytic attacks. (5) We obtain universal predictions for maximal rates
that can be achieved with practical system designs under realistic
environmental conditions. (6) We propose a specific QC system design that
includes the use of a novel method of high-speed photon detection that may be
able to achieve very high throughput rates for actual implementations in
realistic environments.
|
0009027v5
|
2009-08-07
|
The Dominance of Metal-Rich Streams in Stellar Halos: A Comparison Between Substructure in M31 and Lambda-CDM Models
|
Extensive photometric and spectroscopic surveys of the Andromeda galaxy (M31)
have discovered tidal debris features throughout M31's stellar halo. We present
stellar kinematics and metallicities in fields with identified substructure
from our on-going SPLASH survey of M31 red giant branch stars with the DEIMOS
spectrograph on the Keck II 10-m telescope. Radial velocity criteria are used
to isolate members of the kinematically-cold substructures. The substructures
are shown to be metal-rich relative to the rest of the dynamically hot stellar
population in the fields in which they are found. We calculate the mean
metallicity and average surface brightness of the various kinematical
components in each field, and show that, on average, higher surface brightness
features tend to be more metal-rich than lower surface brightness features.
Simulations of stellar halo formation via accretion in a cosmological context
are used to illustrate that the observed trend can be explained as a natural
consequence of the observed dwarf galaxy mass-metallicity relation. A
significant spread in metallicity at a given surface brightness is seen in the
data; we show that this is due to time effects, namely the variation in the
time since accretion of the tidal streams' progenitor onto the host halo. We
show that in this theoretical framework a relationship between the
alpha-enhancement and surface brightness of tidal streams is expected, which
arises from the varying times of accretion of the progenitor satellites onto
the host halo. Thus, measurements of the alpha-enrichment, metallicity, and
surface brightness of tidal debris can be used to reconstruct the luminosity
and time of accretion onto the host halo of the progenitors of tidal streams.
|
0908.1111v1
|
2009-09-25
|
The SPLASH Survey: A Spectroscopic Portrait of Andromeda's Giant Southern Stream
|
The giant southern stream (GSS) is the most prominent tidal debris feature in
M31's stellar halo. The GSS is composed of a relatively metal-rich, high
surface-brightness "core" and a lower metallicity, lower surface brightness
"envelope." We present Keck/DEIMOS spectroscopy of red giant stars in six
fields in the vicinity of M31's GSS and one field on Stream C, an arc-like
feature on M31's SE minor axis at R=60 kpc. Several GSS-related findings and
measurements are presented here. We present the innermost kinematical detection
of the GSS core to date (R=17 kpc). This field also contains the continuation
of a second kinematically cold component originally seen in a GSS core field at
R=21 kpc. The velocity gradients of the GSS and the second component in the
combined data set are parallel over a radial range of 7 kpc, suggesting a
possible bifurcation in the line-of-sight velocities of GSS stars. We also
present the first kinematical detection of substructure in the GSS envelope.
Using kinematically identified samples, we show that the envelope debris has a
~0.7 dex lower mean photometric metallicity and possibly higher intrinsic
velocity dispersion than the GSS core. The GSS is also identified in the field
of the M31 dSph satellite And I; the GSS in this field has a metallicity
distribution identical to that of the GSS core. We confirm the presence of two
kinematically cold components in Stream C, and measure intrinsic velocity
dispersions of ~10 and ~4 km/s. This compilation of the kinematical (mean
velocity, intrinsic velocity dispersion) and chemical properties of stars in
the GSS core and envelope, coupled with published surface brightness
measurements and wide-area star-count maps, will improve constraints on the
orbit and internal structure of the dwarf satellite progenitor.
|
0909.4540v1
|
2011-05-28
|
Transmission Control of Two-User Slotted ALOHA Over Gilbert-Elliott Channel: Stability and Delay Analysis
|
In this paper, we consider the problem of calculating the stability region
and average delay of two user slotted ALOHA over a Gilbert-Elliott channel,
where users have channel state information and adapt their transmission
probabilities according to the channel state. Each channel has two states,
namely, the 'good' and 'bad' states. In the 'bad' state, the channel is assumed
to be in deep fade and the transmission fails with probability one, while in
the 'good' state, there is some positive success probability. We calculate the
Stability region with and without Multipacket Reception capability as well as
the average delay without MPR. Our results show that the stability region of
the controlled S-ALOHA is always a superset of the stability region of
uncontrolled S-ALOHA. Moreover, if the channel tends to be in the 'bad' state
for long proportion of time, then the stability region is a convex Polyhedron
strictly containing the TDMA stability region and the optimal transmission
strategy is to transmit with probability one whenever the nodes have packets
and it is shown that this strategy is delay optimal. On the other hand, if the
channel tends to be in the 'good' state more often, then the stability region
is bounded by a convex curve and is strict subset of the TDMA stability region.
We also show that enhancing the physical layer by allowing MPR capability can
significantly enhance the performance while simplifying the MAC Layer design by
the lack of the need of scheduling under some conditions. Furthermore, it is
shown that transmission control not only allows handling higher stable arrival
rates but also leads to lower delay for the same arrival rate compared with
ordinary S-ALOHA.
|
1105.5676v2
|
2012-10-11
|
Global Properties of M31's Stellar Halo from the SPLASH Survey. I. Surface Brightness Profile
|
We present the surface brightness profile of M31's stellar halo out to a
projected radius of 175 kpc. The surface brightness estimates are based on
confirmed samples of M31 red giant branch stars derived from Keck/DEIMOS
spectroscopic observations. A set of empirical spectroscopic and photometric
M31 membership diagnostics is used to identify and reject foreground and
background contaminants. This enables us to trace the stellar halo of M31 to
larger projected distances and fainter surface brightnesses than previous
photometric studies. The surface brightness profile of M31's halo follows a
power-law with index -2.2 +/- 0.2 and extends to a projected distance of at
least ~175 kpc (~ 2/3 of M31's virial radius), with no evidence of a downward
break at large radii. The best-fit elliptical isophotes have b/a=0.94 with the
major axis of the halo aligned along the minor axis of M31's disk, consistent
with a prolate halo, although the data are also consistent with M31's halo
having spherical symmetry. The fact that tidal debris features are
kinematically cold is used to identify substructure in the spectroscopic fields
out to projected radii of 90 kpc, and investigate the effect of this
substructure on the surface brightness profile. The scatter in the surface
brightness profile is reduced when kinematically identified tidal debris
features in M31 are statistically subtracted; the remaining profile indicates a
comparatively diffuse stellar component to M31's stellar halo exists to large
distances. Beyond 90 kpc, kinematically cold tidal debris features can not be
identified due to small number statistics; nevertheless, the significant
field-to-field variation in surface brightness beyond 90 kpc suggests that the
outermost region of M31's halo is also comprised to a significant degree of
stars stripped from accreted objects.
|
1210.3362v2
|
2014-09-12
|
Global Properties of M31's Stellar Halo from the SPLASH Survey: II. Metallicity Profile
|
We present the metallicity distribution of red giant branch (RGB) stars in
M31's stellar halo, derived from photometric metallicity estimates for over
1500 spectroscopically confirmed RGB halo stars. The stellar sample comes from
38 halo fields observed with the Keck/DEIMOS spectrograph, ranging from 9 to
175 kpc in projected distance from M31's center, and includes 52 confirmed M31
halo stars beyond 100 kpc. While a wide range of metallicities is seen
throughout the halo, the metal-rich peak of the metallicity distribution
function becomes significantly less prominent with increasing radius. The
metallicity profile of M31's stellar halo shows a continuous gradient from 9 to
~100 kpc, with a magnitude of -0.01 dex/kpc. The stellar velocity distributions
in each field are used to identify stars that are likely associated with tidal
debris features. The removal of tidal debris features does not significantly
alter the metallicity gradient in M31's halo: a gradient is maintained in
fields spanning 10 to 90 kpc. We analyze the halo metallicity profile, as well
as the relative metallicities of stars associated with tidal debris features
and the underlying halo population, in the context of current simulations of
stellar halo formation. We argue that the large scale gradient in M31's halo
implies M31 accreted at least one relatively massive progenitor in the past,
while the field to field variation seen in the metallicity profile indicates
that multiple smaller progenitors are likely to have contributed substantially
to M31's outer halo.
|
1409.3843v1
|
2016-07-15
|
Solving the stochastic Landau-Lifshitz-Gilbert-Slonczewski equation for monodomain nanomagnets : A survey and analysis of numerical techniques
|
The stochastic Landau-Lifshitz-Gilbert-Slonczewski (s-LLGS) equation is
widely used to study the temporal evolution of the macrospin subject to spin
torque and thermal noise. The numerical simulation of the s-LLGS equation
requires an appropriate choice of stochastic calculus and numerical integration
scheme. In this paper, we comprehensively evaluate the accuracy and complexity
of various numerical techniques to solve the s-LLGS equation. We focus on
implicit midpoint, Heun, and Euler-Heun methods that converge to the
Stratonovich solution of the s-LLGS equation. By performing numerical tests for
both strong (path-wise) and weak (statistical) convergence, we quantify the
accuracy of various numerical schemes used to solve the s-LLGS equation. We
demonstrate a new method intended to solve Stochastic Differential Equations
(SDEs) with small noise (RK4-Heun), and test its capability to handle the
s-LLGS equation. We also discuss the circuit implementation of nanomagnets for
large-scale SPICE-based simulations. We evaluate the efficacy of SPICE in
handling the stochastic dynamics of the multiplicative noise in the s-LLGS
equation. Numerical schemes such as Euler and Gear, typically used by
SPICE-based circuit simulators do not yield the expected outcome when solving
the Stratonovich s-LLGS equation. While the trapezoidal method in SPICE does
solve for the Stratonovich solution, its accuracy is limited by the minimum
time step of integration in SPICE. We implement the s-LLGS equation in both its
cartesian and spherical coordinates form in SPICE and compare the stability and
accuracy of the two implementations. The results in this paper will serve as
guidelines for researchers to understand the tradeoffs between accuracy and
complexity of various numerical methods and the choice of appropriate calculus
to solve the s-LLGS equation.
|
1607.04596v4
|
2016-11-30
|
Low Energy Supergravity Revisited (I)
|
General forms of the K\"ahler and superpotenials that lead to consistent low
energy broken Supersymmetry originating from $N=1$ Supergravity have been
classified and used for model building since more than three decades. We point
out the incompleteness of this classification when hidden sector vacuum
expectation values are of the order of the Planck mass. Focusing in this paper
mainly on the case of minimal K\"ahler potential, we adopt a rigorous approach
that retrieves on the one hand the known forms, and demonstrate on the other
hand the existence of a whole set of new forms for the superpotential of which
we give a complete classification. The latter forms involve a new type of
chiral superfields having the unusual property of belonging neither to the
hidden sector nor to the conventional observable sector. Comparing the obtained
forms with the conventional ones, we argue how new possibilities for model
building can arise, and discuss the gravity mediation of soft as well as
additional hard (but parametrically small) Supersymmetry breaking, in the
presence of the new type of chiral superfields. In the simplest case, we study
the vacuum structure, characterize the masses and couplings of the scalar
components to the hidden and observable sectors and discuss briefly the
physical role they could play. In the generic case, we estimate the magnitude
and possible consequences of the hard breaking of Supersymmetry in terms of the
interplay between hidden and visible sectors mass scales.
|
1611.10327v2
|
2018-08-08
|
Analysis of quasi-Monte Carlo methods for elliptic eigenvalue problems with stochastic coefficients
|
We consider the forward problem of uncertainty quantification for the
generalised Dirichlet eigenvalue problem for a coercive second order partial
differential operator with random coefficients, motivated by problems in
structural mechanics, photonic crystals and neutron diffusion. The PDE
coefficients are assumed to be uniformly bounded random fields, represented as
infinite series parametrised by uniformly distributed i.i.d. random variables.
The expectation of the fundamental eigenvalue of this problem is computed by
(a) truncating the infinite series which define the coefficients; (b)
approximating the resulting truncated problem using lowest order conforming
finite elements and a sparse matrix eigenvalue solver; and (c) approximating
the resulting finite (but high dimensional) integral by a randomly shifted
quasi-Monte Carlo lattice rule, with specially chosen generating vector. We
prove error estimates for the combined error, which depend on the truncation
dimension $s$, the finite element mesh diameter $h$, and the number of
quasi-Monte Carlo samples $N$. Under suitable regularity assumptions, our
bounds are of the particular form $\mathcal{O}(h^2+N^{-1+\delta})$, where
$\delta>0$ is arbitrary and the hidden constant is independent of the
truncation dimension, which needs to grow as $h\to 0$ and $N\to\infty$.
Although the eigenvalue problem is nonlinear, which means it is generally
considered harder than the analogous source problem, in almost all cases we
obtain error bounds that converge at the same rate as the corresponding rate
for the source problem. The proof involves a detailed study of the regularity
of the fundamental eigenvalue as a function of the random parameters. As a key
intermediate result in the analysis, we prove that the spectral gap (between
the fundamental and the second eigenvalues) is uniformly positive over all
realisations of the random problem.
|
1808.02639v3
|
2018-09-24
|
Ionic Tuning of Cobaltites at the Nanoscale
|
Control of materials through custom design of ionic distributions represents
a powerful new approach to develop future technologies ranging from spintronic
logic and memory devices to energy storage. Perovskites have shown particular
promise for ionic devices due to their high ion mobility and sensitivity to
chemical stoichiometry. In this work, we demonstrate a solid-state approach to
control of ionic distributions in (La,Sr)CoO$_{3}$ thin films. Depositing a Gd
capping layer on the perovskite film, oxygen is controllably extracted from the
structure, up-to 0.5 O/u.c. throughout the entire 36 nm thickness. Commensurate
with the oxygen extraction, the Co valence state and saturation magnetization
show a smooth continuous variation. In contrast, magnetoresistance measurements
show no-change in the magnetic anisotropy and a rapid increase in the
resistivity over the same range of oxygen stoichiometry. These results suggest
significant phase separation, with metallic ferromagnetic regions and
oxygen-deficient, insulating, non-ferromagnetic regions, forming percolated
networks. Indeed, X-ray diffraction identifies oxygen-vacancy ordering,
including transformation to a brownmillerite crystal structure. The unexpected
transformation to the brownmillerite phase at ambient temperature is further
confirmed by high-resolution scanning transmission electron microscopy which
shows significant structural - and correspondingly chemical - phase separation.
This work demonstrates room-temperature ionic control of magnetism, electrical
resistivity, and crystalline structure in a 36 nm thick film, presenting new
opportunities for ionic devices that leverage multiple material
functionalities.
|
1809.08728v1
|
2019-04-10
|
The Convergence of Iterative Delegations in Liquid Democracy in a Social Network
|
Liquid democracy is a collective decision making paradigm which lies between
direct and representative democracy. One of its main features is that voters
can delegate their votes in a transitive manner such that: A delegates to B and
B delegates to C leads to A indirectly delegates to C. These delegations can be
effectively empowered by implementing liquid democracy in a social network, so
that voters can delegate their votes to any of their neighbors in the network.
However, it is uncertain that such a delegation process will lead to a stable
state where all voters are satisfied with the people representing them. We
study the stability (w.r.t. voters preferences) of the delegation process in
liquid democracy and model it as a game in which the players are the voters and
the strategies are their possible delegations. We answer several questions on
the equilibria of this process in any social network or in social networks that
correspond to restricted types of graphs.
We show that a Nash-equilibrium may not exist, and that it is even
NP-complete to decide whether one exists or not. This holds even if the social
network is a complete graph or a bounded degree graph. We further show that
this existence problem is W[1]-hard w.r.t. the treewidth of the social network.
Besides these hardness results, we demonstrate that an equilibrium always
exists whatever the preferences of the voters iff the social network is a tree.
We design a dynamic programming procedure to determine some desirable
equilibria (e.g., minimizing the dissatisfaction of the voters) in polynomial
time for tree social networks. Lastly, we study the convergence of delegation
dynamics. Unfortunately, when an equilibrium exists, we show that a best
response dynamics may not converge, even if the social network is a path or a
complete graph.
|
1904.05775v2
|
2019-06-20
|
Ongoing Vaccine and Monoclonal Antibody HIV Prevention Efficacy Trials and Considerations for Sequel Efficacy Trial Designs
|
Four randomized placebo-controlled efficacy trials of a candidate vaccine or
passively infused monoclonal antibody for prevention of HIV-1 infection are
underway (HVTN 702 in South African men and women; HVTN 705 in sub-Saharan
African women; HVTN 703/HPTN 081 in sub-Saharan African women; HVTN 704/HPTN
085 in U.S., Peruvian, Brazilian, and Swiss men or transgender persons who have
sex with men). Several challenges are posed to the optimal design of the sequel
efficacy trials, including: (1) how to account for the evolving mosaic of
effective prevention interventions that may be part of the trial design or
standard of prevention; (2) how to define viable and optimal sequel trial
designs depending on the primary efficacy results and secondary 'correlates of
protection' results of each of the ongoing trials; and (3) how to define the
primary objective of sequel efficacy trials if HIV-1 incidence is expected to
be very low in all study arms such that a standard trial design has a steep
opportunity cost. After summarizing the ongoing trials, I discuss statistical
science considerations for sequel efficacy trial designs, both generally and
specifically to each trial listed above. One conclusion is that the results of
'correlates of protection' analyses, which ascertain how different host
immunological markers and HIV-1 viral features impact HIV-1 risk and prevention
efficacy, have an important influence on sequel trial design. This influence is
especially relevant for the monoclonal antibody trials because of the focused
pre-trial hypothesis that potency and coverage of serum neutralization
constitutes a surrogate endpoint for HIV-1 infection... (see manuscript for the
full abstract)
|
1906.08409v1
|
2019-08-12
|
Elemental Abundances in M31: First Alpha and Iron Abundance Measurements in M31's Giant Stellar Stream
|
We present the first measurements of [Fe/H] and [$\alpha$/Fe] abundances,
obtained using spectral synthesis modeling, for red giant branch stars in M31's
giant stellar stream. The spectroscopic observations, obtained at a projected
distance of 17 kpc from M31's center, yielded 61 stars with [Fe/H]
measurements, including 21 stars with [$\alpha$/Fe] measurements, from 112
targets identified as M31 stars. The [Fe/H] measurements confirm the
expectation from photometric metallicity estimates that stars in this region of
M31's halo are relatively metal-rich compared to stars in the MW's inner halo:
more than half the stars in the field, including those not associated with
kinematically identified substructure, have [Fe/H] abundances $> -1.0$. The
stars in this field are $\alpha$-enhanced at lower metallicities, while
[$\alpha$/Fe] decreases with increasing [Fe/H] above metallicities of [Fe/H]
$\gtrsim -0.9$. Three kinematical components have been previously identified in
this field: the giant stellar stream, a second kinematically cold feature of
unknown origin, and M31's kinematically hot halo. We compare probabilistic
[Fe/H] and [$\alpha$/Fe] distribution functions for each of the components. The
giant stellar stream and the second kinematically cold feature have very
similar abundance distributions, while the halo component is more metal-poor.
Although the current sample sizes are small, a comparison of the abundances of
stars in the giant stellar stream field with abundances of M31 halo and dSph
stars from the literature indicate that the progenitor of the stream was likely
more massive, and experienced a higher efficiency of star formation, than M31's
existing dSphs or the dEs NGC147 and NGC185.
|
1908.04429v1
|
2019-08-21
|
Generalized Metric Repair on Graphs
|
Many modern data analysis algorithms either assume or are considerably more
efficient if the distances between the data points satisfy a metric. These
algorithms include metric learning, clustering, and dimension reduction. As
real data sets are noisy, distances often fail to satisfy a metric. For this
reason, Gilbert and Jain and Fan et al. introduced the closely related sparse
metric repair and metric violation distance problems. The goal of these
problems is to repair as few distances as possible to ensure they satisfy a
metric. Three variants were considered, one admitting a polynomial time
algorithm. The other variants were shown to be APX-hard, and an
$O(OPT^{1/3})$-approximation was given, where $OPT$ is the optimal solution
size.
In this paper, we generalize these problems to no longer consider all
distances between the data points. That is, we consider a weighted graph $G$
with corrupted weights $w$, and our goal is to find the smallest number of
weight modifications so that the resulting weighted graph distances satisfy a
metric. This is a natural generalization and is more flexible as it takes into
account different relationships among the data points. As in previous work, we
distinguish among the types of repairs permitted and focus on the increase only
and general versions. We demonstrate the inherent combinatorial structure of
the problem, and give an approximation-preserving reduction from MULTICUT.
Conversely, we show that for any fixed constant $\varsigma$, for the large
class of $\varsigma$-chordal graphs, the problems are fixed parameter
tractable. Call a cycle broken if it contains an edge whose weight is larger
than the sum of all its other edges, and call the amount of this difference its
deficit. We present approximation algorithms, one which depends on the maximum
number of edges in a broken cycle, and one which depends on the number of
distinct deficit values.
|
1908.08411v1
|
2019-09-19
|
Parameterized Complexity of Manipulating Sequential Allocation
|
The sequential allocation protocol is a simple and popular mechanism to
allocate indivisible goods, in which the agents take turns to pick the items
according to a predefined sequence. While this protocol is not strategy-proof,
it has been shown recently that finding a successful manipulation for an agent
is an NP-hard problem (Aziz et al., 2017). Conversely, it is also known that
finding an optimal manipulation can be solved in polynomial time in a few
cases: if there are only two agents or if the manipulator has a binary or a
lexicographic utility function. In this work, we take a parameterized approach
to provide several new complexity results on this manipulation problem. More
precisely, we give a complete picture of its parameterized complexity w.r.t.
the following three parameters: the number $n$ of agents, the number $\mu(a_1)$
of times the manipulator $a_1$ picks in the picking sequence, and the maximum
range $\mathtt{rg}^{\max}$ of an item. This third parameter is a correlation
measure on the preference rankings of the agents. In particular, we show that
the problem of finding an optimal manipulation can be solved in polynomial time
if $n$ or $\mu(a_1)$ is a constant, and that it is fixed-parameter tractable
w.r.t. $\mathtt{rg}^{\max}$ and $n+\mu(a_1)$. Interestingly enough, we show
that w.r.t. the single parameters $n$ and $\mu(a_1)$ it is W[1]-hard. Moreover,
we provide an integer program and a dynamic programming scheme to solve the
manipulation problem and we show that a single manipulator can increase the
utility of her bundle by a multiplicative factor which is at most 2.
|
1909.08920v4
|
2019-11-06
|
Doppler Spectrum Classification with CNNs via Heatmap Location Encoding and a Multi-head Output Layer
|
Spectral Doppler measurements are an important part of the standard
echocardiographic examination. These measurements give important insight into
myocardial motion and blood flow providing clinicians with parameters for
diagnostic decision making. Many of these measurements can currently be
performed automatically with high accuracy, increasing the efficiency of the
diagnostic pipeline. However, full automation is not yet available because the
user must manually select which measurement should be performed on each image.
In this work we develop a convolutional neural network (CNN) to automatically
classify cardiac Doppler spectra into measurement classes. We show how the
multi-modal information in each spectral Doppler recording can be combined
using a meta parameter post-processing mapping scheme and heatmaps to encode
coordinate locations. Additionally, we experiment with several state-of-the-art
network architectures to examine the tradeoff between accuracy and memory usage
for resource-constrained environments. Finally, we propose a confidence metric
using the values in the last fully connected layer of the network. We analyze
example images that fall outside of our proposed classes to show our confidence
metric can prevent many misclassifications. Our algorithm achieves 96% accuracy
on a test set drawn from a separate clinical site, indicating that the proposed
method is suitable for clinical adoption and enabling a fully automatic
pipeline from acquisition to Doppler spectrum measurements.
|
1911.02407v2
|
2020-01-02
|
The Effect of Treatment-Related Deaths and "Sticky" Diagnoses on Recorded Prostate Cancer Mortality
|
Background: Although recorded cancer mortality should include both deaths
from cancer and deaths from cancer treatment, there is evidence suggesting that
the measure may be incomplete. To investigate the completeness of recorded
prostate cancer mortality, we compared other-cause (non-prostate cancer)
mortality in men found and not found to have prostate cancer following a needle
biopsy.
Methods: We linked Medicare claims data to SEER data to analyze survival in
the population of men aged 65+ enrolled in Medicare who resided in a SEER area
and received a needle biopsy in 1993-2001. We compared other-cause mortality in
men found to have prostate cancer (n=53,462) to that in men not found to have
prostate cancer (n=103,659).
Results: The age-race adjusted other-cause mortality rate was 471 per 10,000
person-years in men found to have prostate cancer vs. 468 per 10,000 in men not
found to have prostate cancer (RR = 1.01;95% CI:0.98-1.03). The effect was
modified, however, by age. The RR declined in a stepwise fashion from 1.08 (95%
CI:1.03-1.14) in men age 65-69 to 0.89 (95% CI:0.83-0.95) in men age 85 and
older. If the excess (or deficit) in other-cause mortality were added to the
recorded prostate cancer mortality, prostate cancer mortality would rise 23% in
the youngest age group (from 90 to 111 per 10,000) and would fall 30% in the
oldest age group (from 551 to 388 per 10,000).
Conclusion: Although recorded prostate cancer mortality appears to be an
accurate measure overall, it systematically underestimates the mortality
associated with prostate cancer diagnosis and treatment in younger men and
overestimates it in the very old. We surmise that in younger men
treatment-related deaths are incompletely captured in recorded prostate cancer
mortality, while in older men the diagnosis "sticks"-- once diagnosed, they are
more likely to be said to have died from the disease.
|
2001.00492v1
|
2020-06-09
|
Elemental Abundances in M31: Iron and Alpha Element Abundances in M31's Outer Halo
|
We present [Fe/H] and [$\alpha$/Fe] abundances, derived using spectral
synthesis techniques, for stars in M31's outer stellar halo. The 21 [Fe/H]
measurements and 7 [$\alpha$/Fe] measurements are drawn from fields ranging
from 43 to 165 kpc in projected distance from M31. We combine our measurements
with existing literature measurements, and compare the resulting sample of 23
stars with [Fe/H] and 9 stars with [$\alpha$/Fe] measurements in M31's outer
halo with [$\alpha$/Fe] and [Fe/H] measurements, also derived from spectral
synthesis, in M31's inner stellar halo ($r < $26 kpc) and dSph galaxies. The
stars in M31's outer halo have [$\alpha$/Fe] patterns that are consistent with
the largest of M31's dSph satellites (And I and And VII). These abundances
provide tentative evidence that the [$\alpha$/Fe] abundances of stars in M31's
outer halo are more similar to the abundances of Milky Way halo stars than to
the abundances of stars in M31's inner halo. We also compare the spectral
synthesis-based [Fe/H] measurements of stars in M31's halo with previous
photometric [Fe/H] estimates, as a function of projected distance from M31. The
spectral synthesis-based [Fe/H] measurements are consistent with a large-scale
metallicity gradient previously observed in M31's stellar halo to projected
distances as large as 100 kpc.
|
2006.05430v1
|
2020-11-11
|
Unique Decoding of Explicit $ε$-balanced Codes Near the Gilbert-Varshamov Bound
|
The Gilbert-Varshamov bound (non-constructively) establishes the existence of
binary codes of distance $1/2 -\epsilon$ and rate $\Omega(\epsilon^2)$ (where
an upper bound of $O(\epsilon^2\log(1/\epsilon))$ is known). Ta-Shma [STOC
2017] gave an explicit construction of $\epsilon$-balanced binary codes, where
any two distinct codewords are at a distance between $1/2 -\epsilon/2$ and
$1/2+\epsilon/2$, achieving a near optimal rate of
$\Omega(\epsilon^{2+\beta})$, where $\beta \to 0$ as $\epsilon \to 0$.
We develop unique and list decoding algorithms for (essentially) the family
of codes constructed by Ta-Shma. We prove the following results for
$\epsilon$-balanced codes with block length $N$ and rate
$\Omega(\epsilon^{2+\beta})$ in this family:
- For all $\epsilon, \beta > 0$ there are explicit codes which can be
uniquely decoded up to an error of half the minimum distance in time
$N^{O_{\epsilon, \beta}(1)}$.
- For any fixed constant $\beta$ independent of $\epsilon$, there is an
explicit construction of codes which can be uniquely decoded up to an error of
half the minimum distance in time $(\log(1/\epsilon))^{O(1)} \cdot
N^{O_\beta(1)}$.
- For any $\epsilon > 0$, there are explicit $\epsilon$-balanced codes with
rate $\Omega(\epsilon^{2+\beta})$ which can be list decoded up to error $1/2 -
\epsilon'$ in time $N^{O_{\epsilon,\epsilon',\beta}(1)}$, where $\epsilon',
\beta \to 0$ as $\epsilon \to 0$.
The starting point of our algorithms is the list decoding framework from Alev
et al. [SODA 2020], which uses the Sum-of-Squares SDP hierarchy. The rates
obtained there were quasipolynomial in $\epsilon$. Here, we show how to
overcome the far from optimal rates of this framework obtaining unique decoding
algorithms for explicit binary codes of near optimal rate. These codes are
based on simple modifications of Ta-Shma's construction.
|
2011.05500v1
|
2021-03-30
|
Equivalence between Sobolev spaces of first-order dominating mixed smoothness and unanchored ANOVA spaces on $\mathbb{R}^d$
|
We prove that a variant of the classical Sobolev space of first-order
dominating mixed smoothness is equivalent (under a certain condition) to the
unanchored ANOVA space on $\mathbb{R}^d$, for $d \geq 1$. Both spaces are
Hilbert spaces involving weight functions, which determine the behaviour as
different variables tend to $\pm \infty$, and weight parameters, which
represent the influence of different subsets of variables. The unanchored ANOVA
space on $\mathbb{R}^d$ was initially introduced by Nichols & Kuo in 2014 to
analyse the error of quasi-Monte Carlo (QMC) approximations for integrals on
unbounded domains; whereas the classical Sobolev space of dominating mixed
smoothness was used as the setting in a series of papers by Griebel, Kuo &
Sloan on the smoothing effect of integration, in an effort to develop a
rigorous theory on why QMC methods work so well for certain non-smooth
integrands with kinks or jumps coming from option pricing problems. In this
same setting, Griewank, Kuo, Le\"ovey & Sloan in 2018 subsequently extended
these ideas by developing a practical smoothing by preintegration technique to
approximate integrals of such functions with kinks or jumps.
We first prove the equivalence in one dimension (itself a non-trivial task),
before following a similar, but more complicated, strategy to prove the
equivalence for general dimensions. As a consequence of this equivalence, we
analyse applying QMC combined with a preintegration step to approximate the
fair price of an Asian option, and prove that the error of such an
approximation using $N$ points converges at a rate close to $1/N$.
|
2103.16075v3
|
2021-06-13
|
Advantages of a semi-implicit scheme over a fully implicit scheme for Landau-Lifshitz-Gilbert equation
|
Magnetization dynamics in magnetic materials is modeled by the
Landau-Lifshitz-Gilbert (LLG) equation. In the LLG equation, the length of
magnetization is conserved and the system energy is dissipative. Implicit and
semi-implicit schemes have been used in micromagnetics simulations due to their
unconditional numerical stability. In more details, implicit schemes preserve
the properties of the LLG equation, but solve a nonlinear system of equations
per time step. In contrast, semi-implicit schemes only solve a linear system of
equations, while additional operations are needed to preserve the length of
magnetization. It still remains unclear which one shall be used if both
implicit and semi-implicit schemes are available. In this work, using the
implicit Crank-Nicolson (ICN) scheme as a benchmark, we propose to make this
implicit scheme semi-implicit. It can be proved that both schemes are
second-order accurate in space and time. For the unique solvability of
nonlinear systems of equations in the ICN scheme, we require that the temporal
step size scales quadratically with the spatial mesh size. It is numerically
verified that the convergence of the nonlinear solver becomes slower for larger
temporal step size and multiple magnetization profiles are obtained for
different initial guesses. The linear systems of equations in the semi-implicit
CN (SICN) scheme are unconditionally uniquely solvable, and the condition that
the temporal step size scales linearly with the spatial mesh size is needed in
the convergence of the SICN scheme. In terms of numerical efficiency, the SICN
scheme achieves the same accuracy as the ICN scheme with less computational
time. Based on these results, we conclude that a semi-implicit scheme is
superior to its implicit analog both theoretically and numerically, and we
recommend the semi-implicit scheme in micromagnetics simulations if both
methods are available.
|
2106.06936v1
|
2021-08-06
|
A second-order semi-implicit method for the inertial Landau-Lifshitz-Gilbert equation
|
Recent theoretical and experimental advances show that the inertia of
magnetization emerges at sub-picoseconds and contributes to the ultrafast
magnetization dynamics which cannot be captured intrinsically by the LLG
equation. Therefore, as a generalization, the inertial Landau-Lifshitz-Gilbert
(iLLG) equation is proposed to model the ultrafast magnetization dynamics.
Mathematically, the LLG equation is a nonlinear system of parabolic type with
(possible) degeneracy. However, the iLLG equation is a nonlinear system of
mixed hyperbolic-parabolic type with degeneracy, and exhibits more complicated
structures. It behaves like a hyperbolic system at the sub-picosecond scale
while behaves like a parabolic system at larger timescales. Such hybrid
behaviors impose additional difficulties on designing numerical methods for the
iLLG equation. In this work, we propose a second-order semi-implicit scheme to
solve the iLLG equation. The second temporal derivative of magnetization is
approximated by the standard centered difference scheme and the first
derivative is approximated by the midpoint scheme involving three time steps.
The nonlinear terms are treated semi-implicitly using one-sided interpolation
with the second-order accuracy. At each step, the unconditionally unique
solvability of the unsymmetric linear system of equations in the proposed
method is proved with a detailed discussion on the condition number.
Numerically, the second-order accuracy in both time and space is verified.
Using the proposed method, the inertial effect of ferromagnetics is observed in
micromagnetics simulations at small timescales, in consistency with the
hyperbolic property of the model at sub-picoseconds. For long time simulations,
the results of the iLLG model are in nice agreements with those of the LLG
model, in consistency with the parabolic feature of the iLLG model at larger
timescales.
|
2108.03060v1
|
2021-09-08
|
Flares, Rotation, and Planets of the AU Mic System from TESS Observations
|
AU Mic is a young ($\sim$24 Myr), pre-Main Sequence M~dwarf star that was
observed in the first month of science observations of the Transiting Exoplanet
Survey Satellite (TESS) and re-observed two years later. This target has
photometric variability from a variety of sources that is readily apparent in
the TESS light curves; spots induce modulation in the light curve, flares are
present throughout (manifesting as sharp rises with slow exponential decay
phases), and transits of AU Mic b may be seen by eye as dips in the light
curve. We present a combined analysis of both TESS Sector 1 and Sector 27 AU
Mic light curves including the new 20-second cadence data from TESS Year 3. We
compare flare rates between both observations and analyze the spot evolution,
showing that the activity levels increase slightly from Sector 1 to Sector 27.
Furthermore, the 20-second data collection allows us to detect more flares,
smaller flares, and better resolve flare morphology in white light as compared
to the 2-minute data collection mode. We also refine the parameters for AU Mic
b by fitting three additional transits of AU Mic b from Sector 27 using a model
that includes stellar activity. We show that the transits exhibit clear transit
timing variations (TTVs) with an amplitude of $\sim$80 seconds. We also detect
three transits of a 2.8 $R_\oplus$ planet, AU Mic c, which has a period of
18.86 days.
|
2109.03924v1
|
2021-10-29
|
The TREX Survey: Kinematical Complexity Throughout M33's Stellar Disk and Evidence for a Stellar Halo
|
We present initial results from a large spectroscopic survey of stars
throughout M33's stellar disk. We analyze a sample of 1667 red giant branch
(RGB) stars extending to projected distances of $\sim 11$ kpc from M33's center
($\sim 18$ kpc, or $\sim 10$ scale lengths, in the plane of the disk). The
line-of-sight velocities of RGB stars show the presence of two kinematical
components. One component is consistent with rotation in the plane of M33's HI
disk and has a velocity dispersion ($\sim 19$ km s$^{-1}$) consistent with that
observed in a comparison sample of younger stars, while the second component
has a significantly higher velocity dispersion. A two-component fit to the RGB
velocity distribution finds that the high dispersion component has a velocity
dispersion of $59.3^{+2.6}_{-2.5}$ km s$^{-1}$ and rotates very slowly in the
plane of the disk (consistent with no rotation at the $<1.5\sigma$ level),
which favors interpreting it as a stellar halo rather than a thick disk
population. A spatial analysis indicates that the fraction of RGB stars in the
high-velocity-dispersion component decreases with increasing radius over the
range covered by the spectroscopic sample. Our spectroscopic sample establishes
that a significant high-velocity-dispersion component is present in M33's RGB
population from near M33's center to at least the radius where M33's HI disk
begins to warp at 30$'$ ($\sim 7.5$ kpc) in the plane of the disk. This is the
first detection and spatial characterization of a kinematically hot stellar
component throughout M33's inner regions.
|
2110.15773v1
|
2021-11-23
|
Magnetism in Metastable and Annealed Compositionally Complex Alloys
|
Compositionally complex materials (CCMs) present a potential paradigm shift
in the design of magnetic materials. These alloys exhibit long-range structural
order coupled with limited or no chemical order. As a result, extreme local
environments exist with a large opposing magnetic energy term, which can
manifest large changes in the magnetic behavior. In the current work, the
magnetic properties of (Cr, Mn, Fe, Ni) alloys are presented. These materials
were prepared by room-temperature combinatorial sputtering, resulting in a
range of compositions with a single BCC structural phase and no chemical
ordering. The combinatorial growth technique allows CCMs to be prepared outside
of their thermodynamically stable phase, enabling the exploration of otherwise
inaccessible order. The mixed ferromagnetic and antiferromagnetic interactions
in these alloys causes frustrated magnetic behavior, which results in an
extremely low coercivity (<1 mT), which increases rapidly at 50 K. At low
temperatures, the coercivity achieves values of nearly 500 mT, which is
comparable to some high-anisotropy magnetic materials. Commensurate with the
divergent coercivity is an atypical drop in the temperature dependent
magnetization. These effects are explained by a mixed magnetic phase model,
consisting of ferro-, antiferro , and frustrated magnetic regions, and are
rationalized by simulations. A machine-learning algorithm is employed to
visualize the parameter space and inform the development of subsequent
compositions. Annealing the samples at 600 {\deg}C orders the sample, more-than
doubling the Curie temperature and increasing the saturation magnetization by
as much as 5x. Simultaneously, the large coercivities are suppressed, resulting
in magnetic behavior that is largely temperature independent over a range of
350 K.
|
2111.12188v1
|
2021-11-23
|
Controlling magnetic configuration in soft-hard bilayers probed by polarized neutron reflectometry
|
Hard/soft magnetic bilayer thin films have been widely used in data storage
technologies and permanent magnet applications. The magnetic configuration and
response to temperatures and magnetic fields in these heterostructures are
considered to be highly dependent on the interfacial coupling. However, the
intrinsic properties of each of the layers, such as the saturation
magnetization and layer thickness, also strongly influence the magnetic
configuration. Changing these parameters provides an effective method to tailor
magnetic properties in composite magnets. Here, we use polarized neutron
reflectometry (PNR) to experimentally probe the interfacial magnetic
configurations in hard/soft bilayer thin films: L10-FePt/A1-FePt, [Co/Pd]
/CoPd, [Co/Pt] /FeNi and L10-FePt/Fe, which all have a perpendicular magnetic
anisotropy in the hard layer. These films were designed with different soft and
hard layer thicknesses (t_soft and t_hard) and saturation magnetization
(M_s^soft and M_s^hard), respectively. The influences of an in-plane magnetic
field (H_ip) and temperature (T) are also studied using a L10 FePt/A1-FePt
bilayer sample. Comparing the PNR results to micromagnetic simulations reveals
that the interfacial magnetic configuration is highly dependent on t_soft,
M_s^soft and the external factors (H_ip and T), and has a relatively weak
dependence on t_hard and M_s^hard. Key among these results, for thin t_soft,
the hard and soft layers are rigidly coupled in the out-of-plane direction,
then undergo a transition to relax in-plane. This transition can be delayed to
larger t_soft by decreasing M_s^soft. Understanding the influence of these
parameters on the magnetic configuration is critical to designing functional
composite magnets for applications.
|
2111.12191v1
|
2022-01-18
|
On-demand electrical control of spin qubits
|
Once called a "classically non-describable two-valuedness" by Pauli , the
electron spin is a natural resource for long-lived quantum information since it
is mostly impervious to electric fluctuations and can be replicated in large
arrays using silicon quantum dots, which offer high-fidelity control.
Paradoxically, one of the most convenient control strategies is the integration
of nanoscale magnets to artificially enhance the coupling between spins and
electric field, which in turn hampers the spin's noise immunity and adds
architectural complexity. Here we demonstrate a technique that enables a
\emph{switchable} interaction between spins and orbital motion of electrons in
silicon quantum dots, without the presence of a micromagnet. The naturally weak
effects of the relativistic spin-orbit interaction in silicon are enhanced by
more than three orders of magnitude by controlling the energy quantisation of
electrons in the nanostructure, enhancing the orbital motion. Fast electrical
control is demonstrated in multiple devices and electronic configurations,
highlighting the utility of the technique. Using the electrical drive we
achieve coherence time $T_{2,{\rm Hahn}}\approx50 \mu$s, fast single-qubit
gates with ${T_{\pi/2}=3}$ ns and gate fidelities of 99.93 % probed by
randomised benchmarking. The higher gate speeds and better compatibility with
CMOS manufacturing enabled by on-demand electric control improve the prospects
for realising scalable silicon quantum processors.
|
2201.06679v2
|
2022-04-28
|
Anti-microbial properties of a multi-component alloy
|
High traffic touch surfaces such as doorknobs, countertops, and handrails can
be transmission points for the spread of pathogens, emphasizing the need to
develop materials that actively self-sanitize. Metals are frequently used for
these surfaces due to their durability, but many metals also possess
antimicrobial properties which function through a variety of mechanisms. This
work investigates metallic alloys comprised of several bioactive metals with
the target of achieving broad-spectrum, rapid bioactivity through synergistic
activity. An entropy-motivated stabilization paradigm is proposed to prepare
scalable alloys of copper, silver, nickel and cobalt. Using combinatorial
sputtering, thin-film alloys were prepared on 100 mm wafers with 50%
compositional grading of each element across the wafer. The films were then
annealed and investigated for alloy stability. Bioactivity testing was
performed on both the as-grown alloys and the annealed films using four
microorganisms -- Phi6, MS2, Bacillus subtilis and Escherichia coli -- as
surrogates for human viral and bacterial pathogens. Testing showed that after
30 s of contact with some of the test alloys, Phi6, an enveloped,
single-stranded RNA bacteriophage that serves as a SARS-CoV 2 surrogate, was
reduced up to 6.9 orders of magnitude (>99.9999%). Additionally, the
non-enveloped, double-stranded DNA bacteriophage MS2, and the Gram-negative E.
coli and Gram-positive B. subtilis bacterial strains showed a 5.0, 6.4, and 5.7
log reduction in activity after 30, 20 and 10 minutes, respectively.
Bioactivity in the alloy samples showed a strong dependence on the composition,
with the log reduction scaling directly with the Cu content. Concentration of
Cu by phase separation after annealing improved activity in some of the
samples. The results motivate a variety of themes which can be leveraged to
design ideal bioactive surfaces.
|
2205.00886v1
|
2022-05-11
|
Models of Advance Recording Systems: A Multi-timescale Micromagnetic code for granular thin film magnetic recording systems
|
Micromagnetic modelling provides the ability to simulate large magnetic
systems accurately without the computational cost limitation imposed by
atomistic modelling. Through micromagnetic modelling it is possible to simulate
systems consisting of thousands of grains over a time range of nanoseconds to
years, depending upon the solver used. Here we present the creation and release
of an open-source multi-timescale micromagnetic code combining three key
solvers: Landau-Lifshitz-Gilbert; Landau-Lifshitz-Bloch; Kinetic Monte Carlo.
This code, called MARS (Models of Advanced Recording Systems), is capable of
accurately simulating the magnetisation dynamics in large and structurally
complex single- and multi-layered granular systems. The short timescale
simulations are achieved for systems far from and close to the Curie point via
the implemented Landau-Lifshitz-Gilbert and Landau-Lifshitz-Bloch solvers
respectively. This enables read/write simulations for general perpendicular
magnetic recording and also state of the art heat assisted magnetic recording
(HAMR). The long timescale behaviour is simulated via the Kinetic Monte Carlo
solver, enabling investigations into signal-to-noise ratio and data longevity.
The combination of these solvers opens up the possibility of multi-timescale
simulations within a single software package. For example the entire HAMR
process from initial data writing and data read back to long term data storage
is possible via a single simulation using MARS. The use of atomistic
parameterisation for the material input of MARS enables highly accurate
material descriptions which provide a bridge between atomistic simulation and
real world experimentation. Thus MARS is capable of performing simulations for
all aspects of recording media research and development. This ranges from
material characterisation and optimisation to system design and implementation.
|
2205.05263v1
|
2022-10-11
|
Finite-time singularity formations for the Landau-Lifshitz-Gilbert equation in dimension two
|
We construct finite time blow-up solutions to the Landau-Lifshitz-Gilbert
equation (LLG) from ${\mathbb R}^2$ into $S^2$ \begin{equation*} \begin{cases}
u_t= a(\Delta u+|\nabla u|^2u) -b u\wedge \Delta u &\ \mbox{ in }\ {\mathbb
R}^2\times(0,T), u(\cdot,0) = u_0\in S^2 &\ \mbox{ in }\ {\mathbb R}^2,
\end{cases} \end{equation*} where $a^2+b^2=1,~a > 0,~ b\in {\mathbb R}$. Given
any prescribed $N$ points in $\mathbb{R}^2$ and small $T>0$, we prove that
there exists regular initial data such that the solution blows up precisely at
these points at finite time $t=T$, taking around each point the profile of
sharply scaled degree 1 harmonic map with the type II blow-up speed
\begin{equation*} \| \nabla u\|_{L^\infty } \sim \frac{|\ln(T-t)|^2}{ T-t } \
\mbox{ as } \ t\to T. \end{equation*} The proof is based on the {\em parabolic
inner-outer gluing method}, developed in \cite{17HMF} for Harmonic Map Flow
(HMF). However, a direct consequence of the presence of dispersion is the {\em
lack of maximum principle} for suitable quantities, which makes the analysis
more delicate even at the linearized level. To overcome this difficulty, we
make use of two key technical ingredients: first, for the inner problem we
employ the tool of {\em distorted Fourier transform}, as developed by Krieger,
Miao, Schlag and Tataru \cite{Krieger09Duke,KMS20WM}. Second, the linear theory
for the outer problem is achieved by means of the sub-Gaussian estimate for the
fundamental solution of parabolic system in non-divergence form with
coefficients of Dini mean oscillation in space ($\mathsf{DMO_x}$), which was
proved by Dong, Kim and Lee \cite{dong22-non-divergence} recently.
|
2210.05800v1
|
2023-01-03
|
Measuring Physical and Electrical Parameters in Free-Living Subjects: Motivating an Instrument to Characterize Analytes of Clinical Importance in Blood Samples
|
Significance: A path is described to increase the sensitivity and accuracy of
body-worn devices used to monitor patient health. This path supports improved
health management. A wavelength-choice algorithm developed at Mayo demonstrates
that critical biochemical analytes can be assessed using accurate optical
absorption curves over a wide range of wavelengths. Aim: Combine the
requirements for monitoring cardio/electrical, movement, activity, gait,
tremor, and critical biochemical analytes including hemoglobin makeup in the
context of body-worn sensors. Use the data needed to characterize clinically
important analytes in blood samples to drive instrument requirements. Approach:
Using data and knowledge gained over previously separate research threads, some
providing currently usable results from more than eighty years back, determine
analyte characteristics needed to design sensitive and accurate multiuse
measurement and recording units. Results: Strategies for wavelength selection
are detailed. Fine-grained, broad-spectrum measurement of multiple analytes
transmission, absorption, and anisotropic scattering are needed.
Post-Beer-Lambert, using the propagation of error from small variations, and
utility functions that include costs and systemic error sources, improved
measurements can be performed. Conclusions: The Mayo Double-Integrating Sphere
Spectrophotometer (referred hereafter as MDISS), as described in the companion
report arXiv:2212.08763, produces the data necessary for optimal component
choice. These data can provide for robust enhancement of the sensitivity, cost,
and accuracy of body-worn medical sensors. Keywords: Bio-Analyte,
Spectrophotometry, Body-worn monitor, Propagation of error, Double-Integrating
Sphere, Mt. Everest medical measurements, O2SAT
Please see also arXiv:2212.08763
|
2301.00938v2
|
2023-01-09
|
A Second Earth-Sized Planet in the Habitable Zone of the M Dwarf, TOI-700
|
We report the discovery of TOI-700 e, a 0.95 R$_\oplus$ planet residing in
the Optimistic Habitable Zone (HZ) of its host star. This discovery was enabled
by multiple years of monitoring from NASA's Transiting Exoplanet Survey
Satellite (TESS) mission. The host star, TOI-700 (TIC 150428135), is a nearby
(31.1 pc), inactive, M2.5 dwarf ($V_{mag} = 13.15$). TOI-700 is already known
to host three planets, including the small, HZ planet, TOI-700 d. The new
planet has an orbital period of 27.8 days and, based on its radius (0.95
R$_\oplus$), it is likely rocky. TOI-700 was observed for 21 sectors over Years
1 and 3 of the TESS mission, including 10 sectors at 20-second cadence in Year
3. Using this full set of TESS data and additional follow-up observations, we
identify, validate, and characterize TOI-700 e. This discovery adds another
world to the short list of small, HZ planets transiting nearby and bright host
stars. Such systems, where the stars are bright enough that follow-up
observations are possible to constrain planet masses and atmospheres using
current and future facilities, are incredibly valuable. The presence of
multiple small, HZ planets makes this system even more enticing for follow-up
observations.
|
2301.03617v1
|
2023-01-17
|
Introduction to Non-Invasive Current Estimation (NICE)
|
It is notoriously difficult to measure instantaneous supply current to a
device such as an ASIC, FPGA, or CPU without also affecting the instantaneous
supply voltage and compromising the operation of the device [21]. For decades
designers have relied on rough estimates of dynamic load currents that
stimulate a designed Power Delivery Network (PDN). The consequences of
inaccurate load-current characterization can range from excessive PDN cost and
lengthened development schedules to poor performance or functional failure.
This paper will introduce and describe a method to precisely determine
timedomain current waveforms from a pair of measured timedomain voltage
waveforms. This NonInvasive Current Estimation (NICE) method is based on
established twoport network theory along with component and board modeling
techniques that have been validated through measurements on demonstrative
circuits. This paper will show that the NICE method works for any transient
event that can be captured on a digital oscilloscope. Limitations of the method
and underlying measurements are noted where appropriate. The method is applied
to a simple PDN with an arbitrary load, and the NICE-derived current waveform
is verified against an independent measurement by sense resistor. With careful
component and board modeling, it is possible to calculate current waveforms
with a root mean square error of less than five percent compared to the
reference measurement. Current transients that were previously difficult or
impossible to characterize by any means can now be calculated and displayed
within seconds of an oscilloscope-trigger event by using NICE. ASIC and FPGA
manufacturers can now compute the startup current for their device and publish
the actual waveform, or provide a piecewiselinear SPICE model (PWL source) to
facilitate design and testing of the regulator and PDN required to support
their device.
|
2301.10237v1
|
2023-02-08
|
Weighted Edit Distance Computation: Strings, Trees and Dyck
|
Given two strings of length $n$ over alphabet $\Sigma$, and an upper bound
$k$ on their edit distance, the algorithm of Myers (Algorithmica'86) and Landau
and Vishkin (JCSS'88) computes the unweighted string edit distance in
$\mathcal{O}(n+k^2)$ time. Till date, it remains the fastest algorithm for
exact edit distance computation, and it is optimal under the Strong Exponential
Hypothesis (STOC'15). Over the years, this result has inspired many
developments, including fast approximation algorithms for string edit distance
as well as similar $\tilde{\mathcal{O}}(n+$poly$(k))$-time algorithms for
generalizations to tree and Dyck edit distances. Surprisingly, all these
results hold only for unweighted instances.
While unweighted edit distance is theoretically fundamental, almost all
real-world applications require weighted edit distance, where different weights
are assigned to different edit operations and may vary with the characters
being edited. Given a weight function $w: \Sigma \cup \{\varepsilon \}\times
\Sigma \cup \{\varepsilon \} \rightarrow \mathbb{R}_{\ge 0}$ (such that
$w(a,a)=0$ and $w(a,b)\ge 1$ for all $a,b\in \Sigma \cup \{\varepsilon\}$ with
$a\ne b$), the goal is to find an alignment that minimizes the total weight of
edits. Except for the vanilla $\mathcal{O}(n^2)$-time dynamic-programming
algorithm and its almost trivial $\mathcal{O}(nk)$-time implementation, none of
the aforementioned developments on the unweighted edit distance apply to the
weighted variant. In this paper, we propose the first
$\mathcal{O}(n+$poly$(k))$-time algorithm that computes weighted string edit
distance exactly, thus bridging a fundamental gap between our understanding of
unweighted and weighted edit distance. We then generalize this result to
weighted tree and Dyck edit distances, which lead to a deterministic algorithm
that improves upon the previous work for unweighted tree edit distance.
|
2302.04229v1
|
2023-03-07
|
Multilevel Monte Carlo methods for stochastic convection-diffusion eigenvalue problems
|
We develop new multilevel Monte Carlo (MLMC) methods to estimate the
expectation of the smallest eigenvalue of a stochastic convection-diffusion
operator with random coefficients. The MLMC method is based on a sequence of
finite element (FE) discretizations of the eigenvalue problem on a hierarchy of
increasingly finer meshes. For the discretized, algebraic eigenproblems we use
both the Rayleigh quotient (RQ) iteration and implicitly restarted Arnoldi
(IRA), providing an analysis of the cost in each case. By studying the variance
on each level and adapting classical FE error bounds to the stochastic setting,
we are able to bound the total error of our MLMC estimator and provide a
complexity analysis. As expected, the complexity bound for our MLMC estimator
is superior to plain Monte Carlo. To improve the efficiency of the MLMC
further, we exploit the hierarchy of meshes and use coarser approximations as
starting values for the eigensolvers on finer ones. To improve the stability of
the MLMC method for convection-dominated problems, we employ two additional
strategies. First, we consider the streamline upwind Petrov--Galerkin
formulation of the discrete eigenvalue problem, which allows us to start the
MLMC method on coarser meshes than is possible with standard FEs. Second, we
apply a homotopy method to add stability to the eigensolver for each sample.
Finally, we present a multilevel quasi-Monte Carlo method that replaces Monte
Carlo with a quasi-Monte Carlo (QMC) rule on each level. Due to the faster
convergence of QMC, this improves the overall complexity. We provide detailed
numerical results comparing our different strategies to demonstrate the
practical feasibility of the MLMC method in different use cases. The results
support our complexity analysis and further demonstrate the superiority over
plain Monte Carlo in all cases.
|
2303.03673v2
|
2023-03-09
|
Zonostrophic instabilities in magnetohydrodynamic Kolmogorov flow
|
This paper concerns the stability of Kolmogorov flow u = (0, sin x) in the
infinite (x,y)-plane. A mean magnetic field of strength B0 is introduced and
the MHD linear stability problem studied for modes with wave-number k in the
y-direction, and Bloch wavenumber l in the x-direction. The parameters
governing the problem are Reynolds number 1/nu, magnetic Prandtl number P, and
dimensionless magnetic field strength B0. The mean magnetic field can be taken
to have an arbitrary direction in the (x,y)-plane and a mean x-directed flow U0
can be incorporated.
First the paper considers Kolmogorov flow with y-directed mean magnetic
field, referred to as vertical. Taking l=0, the suppression of the pure
hydrodynamic instability is observed with increasing field strength B0. A
branch of strong-field instabilities occurs for magnetic Prandtl number P less
than unity, as found by A.E. Fraser, I.G. Cresser and P. Garaud (J. Fluid Mech.
949, A43, 2022). Analytical results using eigenvalue perturbation theory in the
limit k->0 support the numerics for both weak- and strong-field instabilities,
and originate in the coupling of large-scale modes with x-wavenumber n=0, to
smaller-scale modes.
The paper considers the case of horizontal or x-directed mean magnetic field.
The unperturbed state consists of steady, wavey magnetic field lines. As the
magnetic field is increased, the purely hydrodynamic instability is suppressed
again, but for stronger fields a new branch of instabilities appears. Allowing
a non-zero Bloch wavenumber l allows further instability, and in some
circumstances when the system is hydrodynamically stable, arbitrarily weak
magnetic fields can give growing modes. Numerical results are presented
together with eigenvalue perturbation theory in the limits k,l->0. The theory
gives analytical approximations for growth rates and thresholds in good
agreement with those computed.
|
2303.05212v1
|
2023-03-30
|
Fate of entanglement in magnetism under Lindbladian or non-Markovian dynamics and conditions for their transition to Landau-Lifshitz-Gilbert classical dynamics
|
It is commonly assumed in spintronics and magnonics that localized spins
within antiferromagnets are in the N\'{e}el ground state (GS), as well as that
such state evolves, when pushed out of equilibrium by current or external
fields, according to the Landau-Lifshitz-Gilbert (LLG) equation viewing
localized spins as classical vectors of fixed length. On the other hand, the
true GS of antiferromagnets is highly entangled, as confirmed by very recent
neutron scattering experiments witnessing their entanglement. Although GS of
ferromagnets is always unentangled, their magnonic low-energy excitation are
superpositions of many-body spin states and, therefore, entangled. In this
study, we initialize quantum Heisenberg ferro- or antiferromagnetic chains
hosing localized spins $S=1/2$, $S=1$ or $S=5/2$ into unentangled pure state
and then evolve them by quantum master equations (QMEs) of Lindblad or
non-Markovian type, derived by coupling localized spins to a bosonic bath (such
as due to phonons) or by using additional ``reaction coordinate'' in the latter
case. The time evolution is initiated by applying an external magnetic field,
and entanglement of time-evolving {\em mixed} quantum states is monitored by
computing its logarithmic negativity. We find that non-Markovian dynamics
maintains some degree of entanglement, which shrinks the length of the vector
of spin expectation values, thereby making the LLG equation inapplicable.
Conversely, Lindbladian (i.e., Markovian) dynamics ensures that entanglement
goes to zero, thereby enabling quantum-to-classical (i.e., to LLG) transition
in all cases -- $S=1/2$, $S=1$ and $S=5/2$ ferromagnet or $S=5/2$
antiferromagnet -- {\em except} for $S=1/2$ and $S=1$ antiferromagnet. We also
investigate the stability of entangled antiferromagnetic GS upon suddenly
coupling it to the bosonic bath.
|
2303.17596v3
|
2024-02-07
|
Item-Level Heterogeneous Treatment Effects of Selective Serotonin Reuptake Inhibitors (SSRIs) on Depression: Implications for Inference, Generalizability, and Identification
|
In analysis of randomized controlled trials (RCTs) with patient-reported
outcome measures (PROMs), Item Response Theory (IRT) models that allow for
heterogeneity in the treatment effect at the item level merit consideration.
These models for ``item-level heterogeneous treatment effects'' (IL-HTE) can
provide more accurate statistical inference, allow researchers to better
generalize their results, and resolve critical identification problems in the
estimation of interaction effects. In this study, we extend the IL-HTE model to
polytomous data and apply the model to determine how the effect of selective
serotonin reuptake inhibitors (SSRIs) on depression varies across the items on
a depression rating scale. We first conduct a Monte Carlo simulation study to
assess the performance of the polytomous IL-HTE model under a range of
conditions. We then apply the IL-HTE model to item-level data from 28 RCTs
measuring the effect of SSRIs on depression using the 17-item Hamilton
Depression Rating Scale (HDRS-17) and estimate potential heterogeneity by
subscale (HDRS-6). Our results show that the IL-HTE model provides more
accurate statistical inference, allows for generalizability of results to
out-of-sample items, and resolves identification problems in the estimation of
interaction effects. Our empirical application shows that while the average
effect of SSRIs on depression is beneficial (i.e., negative) and statistically
significant, there is substantial IL-HTE, with estimates of the standard
deviation of item-level effects nearly as large as the average effect. We show
that this substantial IL-HTE is driven primarily by systematically larger
effects on the HDRS-6 subscale items. The IL-HTE model has the potential to
provide new insights for the inference, generalizability, and identification of
treatment effects in clinical trials using patient reported outcome measures.
|
2402.04487v1
|
1995-02-16
|
Lyman alpha Emission from High-Redshift Galaxies
|
We summarise the results of a deep search for Lyman alpha emission from
star-forming regions associated with damped Lyman alpha absorption systems and
conclude that the Lyman alpha luminosity of high redshift galaxies is generally
less than 10^(42) erg/s . We also present a newly discovered case, in the field
of the QSO Q2059-360, where the emission is unusually strong, possibly because
the damped system is close in redshift to the QSO.
|
9502076v1
|
1995-10-12
|
Limits on diffusive shock acceleration in dense and incompletely ionised media
|
The limits imposed on diffusive shock acceleration by upstream ion-neutral
Alfven wave damping, and by ionisation and Coulomb losses of low energy
particles, are calculated. Analytic solutions are given for the steady upstream
wave excitation problem with ion-neutral damping and the resulting escaping
upstream flux calculated. The time dependent problem is discussed and numerical
solutions presented. Finally the significance of these results for possible
observational tests of shock acceleration in supernova remnants is discussed.
|
9510066v2
|
1995-11-28
|
Damping of GRR instability by direct URCA reactions
|
The role of direct URCA reactions in damping of the gravitational radiation
driven instability is discussed. The temperature at which bulk viscosity
suppresses completely this instability is calculated.
The results are obtained analytically using recent calculations performed in
the case of bulk viscosity due to the modified URCA processes (Lindblom 1995;
Yoshida & Eriguchi 1995).
The bulk viscosity caused by direct URCA reactions is found to reduce
significantly the region of temperatures and rotation frequencies where a
neutron star is subject to GRR instability.
|
9511136v1
|
1997-10-31
|
Abundances in Damped Lyman-alpha Systems and Chemical Evolution of High Redshift Galaxies
|
Recent abundance measurements in damped Lyman-alpha galaxies, supplemented
with unpublished Keck observations, are discussed. The metallicity distribution
with cosmic time is examined for clues about the degree of enrichment, the
onset of initial star formation, and the nature of the galxies. The relative
abundances of the elements are compared with the abundnce pattern in Galactic
halo stars and in the Sun, taking into account of the effects of dust
depletion, in order to gain insight into the stellar processes and the time
scales by which the enrichment occurred.
|
9710370v1
|
1998-05-08
|
Exploring the Damped Lyman-alpha Clouds with AXAF
|
The High Energy Transmission Grating (HETG) Spectrometer on the Advanced
X-ray Astrophysics Facility (AXAF) (scheduled for launch in August, 1998) will
provide a new tool for the study of absorption in the X-ray spectra of high
redshift quasars due to the material along the line of sight. In this paper we
try to explore the possibility of using AXAF HETG to detect resonance
absorption lines from the Damped Lyman-alpha (DLA) clouds.
|
9805110v1
|
1998-05-28
|
Photon Damping of Waves in Accretion Disks
|
MHD turbulence is generally believed to have two important functions in
accretion disks: it transports angular momentum outward, and the energy in its
shortest wavelength modes is dissipated into the heat that the disks radiate.
In this paper we examine a pair of mechanisms which may play an important role
in regulating the amplitude and spectrum of this turbulence: photon diffusion
and viscosity. We demonstrate that in radiation pressure-dominated disks,
photon damping of compressive MHD waves is so rapid that it likely dominates
all other dissipation mechanisms.
|
9805358v1
|
1998-06-11
|
Damping of differential rotation in neutron stars
|
We derive the transport relaxation times for quasiparticle-vortex scattering
processes via nuclear force, relevant for the damping of differential rotation
of superfluids in the quantum liquid core of a neutron star. The proton
scattering off the neutron vortices provides the dominant resistive force on
the vortex lattice at all relevant temperatures in the phase where neutrons
only are in the paired state. If protons are superconducting, a small fraction
of hyperons and resonances in the normal state would be the dominant source of
friction on neutron and proton vortex lattices at the core temperatures $T\ge
10^{7}$ K.
|
9806156v1
|
1999-03-10
|
Elemental abundances at early times: the nature of Damped Lyman-alpha systems
|
The distribution of element abundances with redshift in Damped Ly-alpha (DLA)
systems can be adequately reproduced by the same model reproducing the halo and
disk components of the Milky Way Galaxy at different galactocentric distances:
DLA systems are well represented by normal spiral galaxies in their early
evolutionary stages.
|
9903150v1
|
1999-07-26
|
Are Damped Ly-alpha Systems Large, Galactic Disks ?
|
The hypothesis that the Damped Ly-alpha systems (DLAs) are large, galactic
disks (Milky Way sized) is tested by confronting predictions of models of the
formation and evolution of (large) disk galaxies with observations, in
particular the Zinc abundance distribution with neutral hydrogen column density
found for DLAs. A pronounced mismatch is found strongly hinting that the
majority of DLAs may not be large, galactic disks.
|
9907349v1
|
1999-08-26
|
Oscillator Strengths and Damping Constants for Atomic Lines in the J and H Bands
|
We have built a line list in the near-infrared J and H bands (1.00-1.34,
1.49-1.80 um) by gathering a series of laboratory and computed line lists.
Oscillator strengths and damping constants were computed or obtained by fitting
the solar spectrum.
The line list presented in this paper is, to our knowledge, the most complete
one now available, and supersedes previous lists.
|
9908296v1
|
1999-11-25
|
Probing Solar Convection
|
In the solar convection zone acoustic waves are scattered by turbulent sound
speed fluctuations. In this paper the scattering of waves by convective cells
is treated using Rytov's technique. Particular care is taken to include
diffraction effects which are important especially for high-degree modes that
are confined to the surface layers of the Sun. The scattering leads to damping
of the waves and causes a phase shift. Damping manifests itself in the width of
the spectral peak of p-mode eigenfrequencies. The contribution of scattering to
the line widths is estimated and the sensitivity of the results on the assumed
spectrum of the turbulence is studied. Finally the theoretical predictions are
compared with recently measured line widths of high-degree modes.
|
9911469v1
|
1999-12-14
|
The Gas Reservoir for present day Galaxies : Damped Ly-alpha Absorption Systems
|
We present results from an ongoing search for galaxy counterparts of a
subgroup of Quasar Absorption Line Systems called Damped Ly-alpha Absorbers
(DLAs). DLAs have several characteristics that make them essential in the
process of understanding how galaxies formed in the early universe and evolved
to the galaxies we see today in the local universe.
Finally we compare DLAs with recent findings of a population of starforming
galaxies at high redshifts, so called Lyman-break galaxies.
|
9912268v1
|
2000-06-22
|
Nuclear Reaction Rates in a Plasma: The Effect of Highly Damped Modes
|
The fluctuation-dissipation theorem is used to evaluate the screening factor
of nuclear reactions due to the electromagnetic fluctuations in a plasma. We
show that the commonly used Saltpeter factor is obtained if only fluctuations
near the plasma eigenfrequency are assumed to be important (\omega \sim
\omega_{pe}\ll T (\hbar=k_{B}=1)). By taking into account all the fluctuations,
the highly damped ones, with \omega >\omega_{pe}, as well as those with
\omega\leq\omega_{pe}, we find that nuclear reaction rates are higher than
those obtained using the Saltpeter factor, for many interesting plasmas.
|
0006326v1
|
2000-09-06
|
The Cosmological Evolution of Quasar Damped Lyman-Alpha Systems
|
We present results from an efficient, non-traditional survey to discover
damped Lyman-alpha (DLA) absorption-line systems with neutral hydrogen column
densities N(HI)>2x10^{20} atoms cm^{-2} and redshifts z<1.65. Contrary to
previous studies at higher redshift that showed a decrease in the cosmological
mass density of neutral gas in DLA absorbers, Omega_{DLA}, with time, our
results indicate that Omega_{DLA} is consistent with remaining constant from
redshifts z \approx 4 to z \approx 0.5. There is no evidence that Omega_{DLA}
is approaching the value at z=0. Other interesting results from the survey are
also presented.
|
0009098v1
|
2001-01-13
|
Measuring Feedback in Damped Lyman Alpha Systems
|
We measure feedback (heating rates) in damped Lyman alpha systems from the
cooling rate of the neutral gas. Since cooling occurs through [C II] 158 micron
emission, we infer cooling from C II^{*} 1335.7 absorption lines detected with
HIRES on the Keck I telescope. The inferred heating rates are about 30 times
lower than for the Galaxy ISM. At z = 2.8, the implied star formation rate per
unit area is 10^{-2.4+-0.3} solar masses per kpc^{2} per year, and the the star
formation rate per unit comoving volume is 10^{-0.8+-0.2} solar masses per
Mpc^{3} per year. This is the first measurement of star formation rates in
objects likely to be the progenitors of current galaxies.
|
0101218v1
|
2001-04-18
|
The First Detection of Cobalt in a Damped Lyman Alpha System
|
We present the first ever detection of Cobalt in a Damped Lyman Alpha system
(DLA) at z = 1.92. In addition to providing important clues to the star
formation history of these high redshift galaxies, we discuss how studying the
Co abundance in DLAs may also help to constrain models of stellar
nucleosynthesis in a regime not probed by Galactic stars.
|
0104301v1
|
2001-05-09
|
Nuclear reaction rates and energy in stellar plasmas : The effect of highly damped modes
|
The effects of the highly damped modes in the energy and reaction rates in a
plasma are discussed. These modes, with wavenumbers $k \gg k_{D}$, even being
only weakly excited, with less than $k_{B}T$ per mode, make a significant
contribution to the energy and screening in a plasma. When the de Broglie
wavelength is much less than the distance of closest approach of thermal
electrons, a classical analysis of the plasma can
|
0105153v1
|
2001-07-03
|
The HI Content and Extent of Low Surface Brightness Galaxies - Could LSB Galaxies be Responsible for Damped Ly-alpha Absorption?
|
Low surface brightness galaxies, those galaxies with a central surface
brightness at least one magnitude fainter than the night sky, are often not
included in discussions of extragalactic gas at z < 0.1. In this paper we
review many of the properties of low surface brightness galaxies, including
recent studies which indicate low surface brightness systems may contribute far
more to the local HI luminosity function than previously thought. Additionally,
we use the known (HI) gas properties of low surface brightness galaxies to
consider their possible contribution to nearby damped Lyman-alpha absorbers.
|
0107064v1
|
2001-09-10
|
H_2 molecules in damped systems
|
Damped Lyman alpha systems seen in the spectra of high-z QSOs arise in
high-density neutral gas in which molecular hydrogen (H_2) should be
conspicuous. Systematic searches to detect the H_2 lines redshifted into the
Lyman alpha forest at <3400\AA are now possible thanks to the unique
capabilities of UVES on the VLT. Here we summarise the present status of our on
going programme to search for H_2 in DLAs, discuss the physical conditions in
the systems where H_2 is detected and the implications of non-detections.
|
0109155v1
|
2001-10-23
|
A scaling law of interstellar depletions as a tool for abundance studies of Damped Ly alpha systems
|
An analytical expression is presented that allows dust depletions to be
estimated in different types of interstellar environments, including Damped Ly
alpha systems. The expression is a scaling law of a reference depletion pattern
and takes into account the possibility that the dust chemical composition may
vary as a function of the dust-to-metals ratio and of the intrinsic abundances
of the medium. Preliminary tests and applications of the proposed scaling law
are briefly reported.
|
0110499v1
|
2002-09-23
|
Outflows in Galaxies and Damped Ly-alpha System
|
Although quasar absorbers, and in particular Damped Lyman-alpha systems
(DLAs) have proven a valuable tool to study the early Universe, their exact
nature is so far poorly constrained. It has been suggested that outflows in
galaxies might account for at least part of the DLA population. Observational
evidences and models in support of this hypothesis are reviewed, including
recent observations of Lyman Break Galaxies (LBGs). Observational
counter-arguments and theoretical limitations are also given. Finally,
implications of such a model for the environment of galaxies at high-redshifts
are discussed.
|
0209463v1
|
2004-03-15
|
The Damping Wing of the Gunn-Peterson Absorption and Lyman-Alpha Emitters in the Pre-Reionization Era
|
We use a numerical simulation of cosmological reionization to estimate the
likelihood of detecting Lyman-alpha emitting galaxies during the
pre-reionization era. We show that it is possible to find galaxies even at z~9
that are barely affected by the dumping wing of the Gunn-Peterson absorption
from the neutral IGM outside of their HII regions. The damping wing becomes
rapidly more significant at z>9, but even at z>10 is it not inconceivable
(although quite hard) to see a Lyman-alpha emission line from a star-forming
galaxy.
|
0403345v1
|
2005-05-28
|
Cosmic ray transport in MHD turbulence
|
Recent advances in understanding of magnetohydrodynamic (MHD) turbulence call
for revisions in the picture of cosmic ray transport. In this paper we use
recently obtained scaling laws for MHD modes to obtain the scattering frequency
for cosmic rays. We account for the turbulence cutoff arising from both
collisional and collisionless damping. We obtain the scattering rate and show
that fast modes provide the dominant contribution to cosmic ray scattering for
the typical interstellar conditions in spite of the fact that fast modes are
subjected to damping. We determine how the efficiency of the scattering depends
on the characteristics of ionized media, e.g. plasma $\beta$. We show that
streaming instability is suppressed by the ambient MHD turbulence.
|
0505575v1
|
2005-06-09
|
Phantom damping of matter perturbations
|
Cosmological scaling solutions are particularly important in solving the
coincidence problem of dark energy. We derive the equations of sub-Hubble
linear matter perturbations for a general scalar-field Lagrangian--including
quintessence, tachyon, dilatonic ghost condensate and k-essence--and solve them
analytically for scaling solutions. We find that matter perturbations are
always damped if a phantom field is coupled to dark matter and identify the
cases in which the gravitational potential is constant. This provides an
interesting possibility to place stringent observational constraints on scaling
dark energy models.
|
0506222v1
|
2005-06-22
|
A Damped Ly-alpha Absorption-line System in an Apparent Void at Redshift 2.38
|
We study the contents of an apparent void in the distribution of Ly-alpha
emitting galaxies at redshift 2.38. We show that this void is not empty, but
contains a damped Ly-alpha absorption-line system, seen in absorption against
background QSO 2138-4427. Imaging does not reveal any galaxy associated with
this absorption-line system, but it contains metals (Fe/H ~ -1.3), and its
large velocity range (~ 180 km/s) implies a significant mass.
|
0506525v1
|
2005-08-08
|
Fluorescence in damp air and comments on the radiative life time
|
Photon yields in damp air excited by an electron using a Sr90 $\beta$ source
are compared withthose in dry air. Water vapors considerably reduce the yields,
however, a further study is needed to evaluate the effects on the energy
estimation of ultrahigh-energy cosmic rays. The relation of fluorescence
efficiency to the life time of de-excitation by radiation is discussed.
|
0508183v1
|
2006-08-17
|
Electron thermal conductivity owing to collisions between degenerate electrons
|
We calculate the thermal conductivity of electrons produced by
electron-electron Coulomb scattering in a strongly degenerate electron gas
taking into account the Landau damping of transverse plasmons. The Landau
damping strongly reduces this conductivity in the domain of ultrarelativistic
electrons at temperatures below the electron plasma temperature. In the inner
crust of a neutron star at temperatures T < 1e7 K this thermal conductivity
completely dominates over the electron conductivity due to electron-ion
(electron-phonon) scattering and becomes competitive with the the electron
conductivity due to scattering of electrons by impurity ions.
|
0608371v1
|
2006-09-19
|
Dust, Metals and Diffuse Interstellar Bands in Damped Lyman Alpha Systems
|
Although damped Lyman alpha (DLA) systems are usually considered metal-poor,
it has been suggested that this could be due to observational bias against
metal-enriched absorbers. I review recent surveys to quantify the particular
issue of dust obscuration bias and demonstrate that there is currently no
compelling observational evidence to support a widespread effect due to
extinction. On the other hand, a small sub-set of DLAs may be metal-rich and I
review some recent observations of these metal-rich absorbers and the detection
of diffuse interstellar bands in one DLA at z ~ 0.5.
|
0609530v1
|
2006-11-08
|
Comments on Viscous Damping of Non-Adiabatic MHD Waves in an Unbounded Solar Coronal Plasma by Kumar and Kumar
|
Considering thermal conduction, compressive viscosity and optically thin
radiation as damping mechanisms for MHD waves, we derive a six-order general
dispersion relation. We point out a fundamental flaw in the derivation of
five-order dispersion relation by Kumar and Kumar (2006) who adopt as a basis
vector. The correct definition of the motion in the x-z plane (2-D vector
space) stems from the two independent variables, namely .
|
0611252v2
|
2007-01-10
|
Non-gaussianity in fluctuations from warm inflation
|
The scalar mode density perturbations in a the warm inflationary scenario are
analysed with a view to predicting the amount of non-gaussianity produced by
this scenario. The analysis assumes that the inflaton evolution is strongly
damped by the radiation, with damping terms that are temperature independent.
Entropy fluctuations during warm inflation play a crucial role in generating
non-gaussianity and result in a distinctive signal which should be observable
by the Planck satellite.
|
0701302v2
|
1998-05-22
|
WKB for a damped spin
|
The master equation for a damped spin well known from the theory of
superradiance, is written as a finite-difference equation and solved by a
WKB-like method. The propagator thus obtained looks like the van Vleck
propagator of a certain classical Hamiltonian system with one degree of
freedom. A new interpretation is provided of the temporal broadening of
initially sharp probability distributions as the analogue of the spreading of
the quantum mechanical wave packet.
|
9805018v1
|
1998-11-04
|
Cascades of energy and helicity in the GOY shell model of turbulence
|
The effect of extreme hyperviscous damping, $\nu k_n^p, p=\infty$ is studied
numerically in the GOY shell model of turbulence. It has resently been
demonstrated [Leveque and She, Phys. Rev. Lett, 75,2690 (1995)] that the
inertial range scaling in the GOY model is non-universal and depending on the
viscous damping. The present study shows that the deviation from Kolmogorov
scaling is due to the cascade of the second inviscid invariant. This invariant
is non-positive definite and in this sense analogous to the helicity of 3D
turbulent flow.
|
9811009v1
|
1994-02-04
|
Effects of Disorder in a Dilute Bose Gas
|
We discuss the effects of a weak random external potential on the properties
of the dilute Bose gas at zero temperature. The results recently obtained by
Huang and Meng for the depletion of the condensate and of the superfluid
density are recovered. Results for the shift of the velocity of sound as well
as for its damping due to collisions with the external field are presented. The
damping of phonons is calculated also for dense superfluids. (submitted to
Phys.Rev.B)
|
9402015v1
|
1995-02-10
|
The influence of structure disorder on mean atomic momentum fluctuations and a spin-wave spectrum
|
The relation between atomic momenta fluctuations and density fluctuations is
obtained in frames of mean-field approximation. Using two-time temperature
Green functions within Tyablikov approximation the equations for spin
excitation energy and damping are obtained. The asymptotics of energy and
damping in the long-wave limit are investigated and the anomalous behaviour of
spin-wave stiffness constant is discussed.
|
9502042v1
|
1997-02-13
|
Comment on "Collective Excitations of a Bose-Einstein Condensate in a Magnetic Trap"
|
We calculate the damping rate of collective excitations for a nearly pure
Bose-Einstein condensate regarding the recent experiments in MIT [M.-O. Mews et
al, Phys. Rev. Lett. 77, 988 (1996)]. The decay time of collective excitations
obtained in our theoretical calculations agrees well with their experimental
result. We argue that the damping of collective excitations is due to thermal
contributions rather than interactions between collective modes.
|
9702122v1
|
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