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2020-09-17
|
Temperature Dependent Non-linear Damping in Palladium Nano-mechanical Resonators
|
Advances in nano-fabrication techniques has made it feasible to observe
damping phenomena beyond the linear regime in nano-mechanical systems. In this
work, we report cubic non-linear damping in palladium nano-mechanical
resonators. Nano-scale palladium beams exposed to a $H_2$ atmosphere become
softer and display enhanced Duffing non-linearity as well as non-linear damping
at ultra low temperatures. The damping is highest at the lowest temperatures of
$\sim 110\: mK$ and decreases when warmed up-to $\sim 1\textrm{ }K$. We
experimentally demonstrate for the first time a temperature dependent
non-linear damping in a nano-mechanical system below 1 K. It is consistent with
a predicted two phonon mediated non-linear Akhiezer scenario for ballistic
phonons with mean free path comparable to the beam thickness. This opens up new
possibilities to engineer non-linear phenomena at low temperatures.
|
2009.08324v1
|
2020-09-22
|
Sharp exponential decay rates for anisotropically damped waves
|
In this article, we study energy decay of the damped wave equation on compact
Riemannian manifolds where the damping coefficient is anisotropic and modeled
by a pseudodifferential operator of order zero. We prove that the energy of
solutions decays at an exponential rate if and only if the damping coefficient
satisfies an anisotropic analogue of the classical geometric control condition,
along with a unique continuation hypothesis. Furthermore, we compute an
explicit formula for the optimal decay rate in terms of the spectral abscissa
and the long-time averages of the principal symbol of the damping over
geodesics, in analogy to the work of Lebeau for the isotropic case. We also
construct genuinely anisotropic dampings which satisfy our hypotheses on the
flat torus.
|
2009.10832v2
|
2020-12-25
|
Information constraint in open quantum systems
|
We propose an effect called information constraint which is characterized by
the existence of different decay rates of signal strengths propagating along
opposite directions. It is an intrinsic property of a type of open quantum
system, which does not rely on boundary conditions. We define the value of
information constraint ($I_C$) as the ratio of different decay rates and derive
the analytical representation of $I_C$ for general quadratic Lindbladian
systems. Based on information constraint, we can provide a simple and elegant
explanation of chiral and helical damping, and get the local maximum points of
relative particle number for the periodical boundary system, consistent with
numerical calculations. Inspired by information constraint, we propose and
prove the correspondence between edge modes and damping modes. A new damping
mode called Dirac damping is constructed, and chiral/helical damping can be
regarded as a special case of Dirac damping.
|
2012.13583v3
|
2021-04-29
|
Non-linear damping of standing kink waves computed with Elsasser variables
|
In a previous paper, we computed the energy density and the non-linear energy
cascade rate for transverse kink waves using Elsasser variables. In this paper,
we focus on the standing kink waves, which are impulsively excited in coronal
loops by external perturbations. We present an analytical calculation to
compute the damping time due to the non-linear development of the
Kelvin-Helmholtz instability. The main result is that the damping time is
inversely proportional to the oscillation amplitude. We compare the damping
times from our formula with the results of numerical simulations and
observations. In both cases we find a reasonably good match. The comparison
with the simulations show that the non-linear damping dominates in the high
amplitude regime, while the low amplitude regime shows damping by resonant
absorption. In the comparison with the observations, we find a power law
inversely proportional to the amplitude $\eta^{-1}$ as an outer envelope for
our Monte Carlo data points.
|
2104.14331v1
|
2021-05-31
|
Revisiting the Plasmon Radiation Damping of Gold Nanorods
|
Noble metal nanoparticles have been utilized for a vast amount of optical
applications. For the applications that used metal nanoparticles as nanosensors
and optical labeling, larger radiation damping is preferred (higher optical
signal). To get a deeper knowledge about the radiation damping of noble metal
nanoparticles, we used gold nanorods with different geometry factors (aspect
ratios) as the model system to study. We investigated theoretically how the
radiation damping of a nanorod depends on the material, and shape of the
particle. Surprisingly, a simple analytical equation describes radiation
damping very accurately and allow to disentangle the maximal radiation damping
parameter for gold nanorod with resonance energy E_res around 1.81 eV (685 nm).
We found very good agreement with theoretical predictions and experimental data
obtained by single-particle spectroscopy. Our results and approaches may pave
the way for designing and optimizing gold nanostructure with higher optical
signal and better sensing performance.
|
2105.14873v1
|
2021-06-23
|
Bayesian evidence for a nonlinear damping model for coronal loop oscillations
|
Recent observational and theoretical studies indicate that the damping of
solar coronal loop oscillations depends on the oscillation amplitude. We
consider two mechanisms, linear resonant absorption and a nonlinear damping
model. We confront theoretical predictions from these models with observed data
in the plane of observables defined by the damping ratio and the oscillation
amplitude. The structure of the Bayesian evidence in this plane displays a
clear separation between the regions where each model is more plausible
relative to the other. There is qualitative agreement between the regions of
high marginal likelihood and Bayes factor for the nonlinear damping model and
the arrangement of observed data. A quantitative application to 101 loop
oscillation cases observed with SDO/AIA results in the marginal likelihood for
the nonlinear model being larger in the majority of them. The cases with
conclusive evidence for the nonlinear damping model outnumber considerably
those in favor of linear resonant absorption.
|
2106.12243v1
|
2021-07-13
|
Convergence of iterates for first-order optimization algorithms with inertia and Hessian driven damping
|
In a Hilbert space setting, for convex optimization, we show the convergence
of the iterates to optimal solutions for a class of accelerated first-order
algorithms. They can be interpreted as discrete temporal versions of an
inertial dynamic involving both viscous damping and Hessian-driven damping. The
asymptotically vanishing viscous damping is linked to the accelerated gradient
method of Nesterov while the Hessian driven damping makes it possible to
significantly attenuate the oscillations. By treating the Hessian-driven
damping as the time derivative of the gradient term, this gives, in discretized
form, first-order algorithms. These results complement the previous work of the
authors where it was shown the fast convergence of the values, and the fast
convergence towards zero of the gradients.
|
2107.05943v1
|
2021-12-13
|
Effect of interfacial damping on high-frequency surface wave resonance on a nanostrip-bonded substrate
|
Since surface acoustic waves (SAW) are often generated on substrates to which
nanostrips are periodically attached, it is very important to consider the
effect of interface between the deposited strip and the substrate surface,
which is an unavoidable issue in manufacturing. In this paper, we propose a
theoretical model that takes into account the interface damping and calculate
the dispersion relationships both for frequency and attenuation of SAW
resonance. This results show that the interface damping has an insignificant
effect on resonance frequency, but, interestingly, attenuation of the SAW can
decrease significantly in the high frequency region as the interface damping
increases. Using picosecond ultrasound spectroscopy, we confirm the validity of
our theory; the experimental results show similar trends both for resonant
frequency and attenuation in the SAW resonance. Furthermore, the resonant
behavior of the SAW is simulated using the finite element method, and the
intrinsic cause of interface damping on the vibrating system is discussed.
These findings strongly indicate the necessity of considering interfacial
damping in the design of SAW devices.
|
2112.06367v1
|
2021-12-13
|
Cosmic ray streaming in the turbulent interstellar medium
|
We study the streaming instability of GeV$-100~$GeV cosmic rays (CRs) and its
damping in the turbulent interstellar medium (ISM). We find that the damping of
streaming instability is dominated by ion-neutral collisional damping in weakly
ionized molecular clouds, turbulent damping in the highly ionized warm medium,
and nonlinear Landau damping in the Galactic halo. Only in the Galactic halo,
is the streaming speed of CRs close to the Alfv\'{e}n speed. Alfv\'{e}nic
turbulence plays an important role in both suppressing the streaming
instability and regulating the diffusion of streaming CRs via magnetic field
line tangling, with the effective mean free path of streaming CRs in the
observer frame determined by the Alfv\'{e}nic scale in super-Alfv\'{e}nic
turbulence. The resulting diffusion coefficient is sensitive to Alfv\'{e}n Mach
number, which has a large range of values in the multi-phase ISM.
Super-Alfv\'{e}nic turbulence contributes to additional confinement of
streaming CRs, irrespective of the dominant damping mechanism.
|
2112.06941v2
|
2022-05-27
|
Scalar field damping at high temperatures
|
The motion of a scalar field that interacts with a hot plasma, like the
inflaton during reheating, is damped, which is a dissipative process. At high
temperatures the damping can be described by a local term in the effective
equation of motion. The damping coefficient is sensitive to multiple
scattering. In the loop expansion its computation would require an all-order
resummation. Instead we solve an effective Boltzmann equation, similarly to the
computation of transport coefficients. For an interaction with another scalar
field we obtain a simple relation between the damping coefficient and the bulk
viscosity, so that one can make use of known results for the latter. The
numerical prefactor of the damping coefficient turns out to be rather large, of
order $ 10 ^ 4 $.
|
2205.14166v2
|
2022-09-13
|
Latest results from the DAMPE space mission
|
The DArk Matter Particle Explorer (DAMPE) is a space-based particle detector
launched on December 17th, 2015 from the Jiuquan Satellite Launch Center
(China). The main goals of the DAMPE mission are the study of galactic cosmic
rays (CR), the electron-positron energy spectrum, gamma-ray astronomy, and
indirect dark matter search. Among its sub-detectors, the deep calorimeter
makes DAMPE able to measure electrons and gamma-ray spectra up to 10 TeV, and
CR nuclei spectra up to hundreds of TeV, with unprecedented energy resolution.
This high-energy region is important in order to search for electron-positron
sources, for dark matter signatures in space, and to clarify CR acceleration
and propagation mechanisms inside our galaxy. A general overview of the DAMPE
experiment will be presented in this work, along with its main results and
ongoing activities.
|
2209.06014v1
|
2022-10-25
|
Microscopic structure of electromagnetic whistler wave damping by kinetic mechanisms in hot magnetized Vlasov plasmas
|
The kinetic damping mechanism of low frequency transverse perturbations
propagating parallel to the magnetic field in a magnetized warm electron plasma
is simulated by means of electromagnetic (EM) Vlasov simulations. The
short-time-scale damping of the electron magnetohydrodynamic whistler
perturbations and underlying physics of finite electron temperature effect on
its real frequency are recovered rather deterministically, and analyzed. The
damping arises from an interplay between a global (prevailing over entire
phase-space) and the more familiar resonant-electron-specific kinetic damping
mechanisms, both of which preserve entropy but operate distinctly by leaving
their characteristic signatures on an initially coherent finite amplitude
modification of the warm electron equilibrium distribution. The net damping
results from a deterministic thermalization, or phase-mixing process, largely
supplementing the resonant acceleration of electrons at shorter time scales,
relevant to short-lived turbulent EM fluctuations. A kinetic model for the
evolving initial transverse EM perturbation is presented and applied to
signatures of the whistler wave phase-mixing process in simulations.
|
2210.13764v1
|
2022-12-02
|
Equivalence between the energy decay of fractional damped Klein-Gordon equations and geometric conditions for damping coefficients
|
We consider damped $s$-fractional Klein--Gordon equations on $\mathbb{R}^d$,
where $s$ denotes the order of the fractional Laplacian. In the one-dimensional
case $d = 1$, Green (2020) established that the exponential decay for $s \geq
2$ and the polynomial decay of order $s/(4-2s)$ hold if and only if the damping
coefficient function satisfies the so-called geometric control condition. In
this note, we show that the $o(1)$ energy decay is also equivalent to these
conditions in the case $d=1$. Furthermore, we extend this result to the
higher-dimensional case: the logarithmic decay, the $o(1)$ decay, and the
thickness of the damping coefficient are equivalent for $s \geq 2$. In
addition, we also prove that the exponential decay holds for $0 < s < 2$ if and
only if the damping coefficient function has a positive lower bound, so in
particular, we cannot expect the exponential decay under the geometric control
condition.
|
2212.01029v4
|
2023-01-13
|
An artificially-damped Fourier method for dispersive evolution equations
|
Computing solutions to partial differential equations using the fast Fourier
transform can lead to unwanted oscillatory behavior. Due to the periodic nature
of the discrete Fourier transform, waves that leave the computational domain on
one side reappear on the other and for dispersive equations these are typically
high-velocity, high-frequency waves. However, the fast Fourier transform is a
very efficient numerical tool and it is important to find a way to damp these
oscillations so that this transform can still be used. In this paper, we
accurately model solutions to four nonlinear partial differential equations on
an infinite domain by considering a finite interval and implementing two
damping methods outside of that interval: one that solves the heat equation and
one that simulates rapid exponential decay. Heat equation-based damping is best
suited for small-amplitude, high-frequency oscillations while exponential decay
is used to damp traveling waves and high-amplitude oscillations. We demonstrate
significant improvements in the runtime of well-studied numerical methods when
adding in the damping method.
|
2301.05789v1
|
2023-03-07
|
Stabilization of the wave equation on larger-dimension tori with rough dampings
|
This paper deals with uniform stabilization of the damped wave equation. When
the manifold is compact and the damping is continuous, the geometric control
condition is known to be necessary and sufficient. In the case where the
damping is a sum of characteristic functions of polygons on a two-dimensional
torus, a result by Burq-G\'erard states that stabilization occurs if and only
if every geodesic intersects the interior of the damped region or razes damped
polygons on both sides. We give a natural generalization of their result to a
sufficient condition on tori of any dimension $d \geq 3$. In some particular
cases, we show that this sufficient condition can be weakened.
|
2303.03733v4
|
2023-07-10
|
The Characteristic Shape of Damping Wings During Reionization
|
Spectroscopic analysis of Ly$\alpha$ damping wings of bright sources at $z>6$
is a promising way to measure the reionization history of the universe.
However, the theoretical interpretation of the damping wings is challenging due
to the inhomogeneous nature of the reionization process and the proximity
effect of bright sources. In this Letter, we analyze the damping wings arising
from the neutral patches in the radiative transfer cosmological simulation
suite Cosmic Reionization on Computers (CROC). We find that the damping wing
profile remains a tight function of volume-weighted neutral fraction $\left<
x_{\rm HI} \right>_{\rm v}$, especially when $\left< x_{\rm HI} \right>_{\rm
v}>0.5$, despite the patchy nature of reionization and the proximity effect.
This small scatter indicates that with a well-measured damping wing profile, we
could constrain the volume-weighted neutral fraction as precise as $\Delta
\left< x_{\rm HI} \right>_{\rm v} \lesssim 0.1$ in the first half of
reionization.
|
2307.04797v1
|
2023-07-17
|
Dissipation in solids under oscillatory shear: Role of damping scheme and sample thickness
|
We study dissipation as a function of sample thickness in solids under global
oscillatory shear applied to the top layer of the sample. Two types of damping
mechanism are considered: Langevin and Dissipative Particle Dynamics (DPD). In
the regime of low driving frequency, and under strain-controlled conditions, we
observe that for Langevin damping, dissipation increases with sample thickness,
while for DPD damping, it decreases. Under force-controlled conditions,
dissipation increases with sample thickness for both damping schemes. These
results can be physically understood by treating the solid as a one-dimensional
harmonic chain in the quasi-static limit, for which explicit equations (scaling
relations) describing dissipation as a function of chain length (sample
thickness) are provided. The consequences of these results, in particular
regarding the choice of damping scheme in computer simulations, are discussed.
|
2307.08413v1
|
2023-08-17
|
A low-rank algorithm for strongly damped wave equations with visco-elastic damping and mass terms
|
Damped wave equations have been used in many real-world fields. In this
paper, we study a low-rank solution of the strongly damped wave equation with
the damping term, visco-elastic damping term and mass term. Firstly, a
second-order finite difference method is employed for spatial discretization.
Then, we receive a second-order matrix differential system. Next, we transform
it into an equivalent first-order matrix differential system, and split the
transformed system into three subproblems. Applying a Strang splitting to these
subproblems and combining a dynamical low-rank approach, we obtain a low-rank
algorithm. Numerical experiments are reported to demonstrate that the proposed
low-rank algorithm is robust and accurate, and has second-order convergence
rate in time.
|
2308.08888v2
|
2023-10-30
|
Optimal backward uniqueness and polynomial stability of second order equations with unbounded damping
|
For general second order evolution equations, we prove an optimal condition
on the degree of unboundedness of the damping, that rules out finite-time
extinction. We show that control estimates give energy decay rates that
explicitly depend on the degree of unboundedness, and establish a dilation
method to turn existing control estimates for one propagator into those for
another in the functional calculus. As corollaries, we prove Schr\"odinger
observability gives decay for unbounded damping, weak monotonicity in damping,
and quantitative unique continuation and optimal propagation for fractional
Laplacians. As applications, we establish a variety of novel and explicit
energy decay results to systems with unbounded damping, including singular
damping, linearised gravity water waves and Euler--Bernoulli plates.
|
2310.19911v1
|
2024-03-12
|
Modulational instability of nonuniformly damped, broad-banded waves: applications to waves in sea-ice
|
This paper sets out to explore the modulational (or Benjamin-Feir)
instability of a monochromatic wave propagating in the presence of damping such
as that induced by sea-ice on the ocean surface. The fundamental wave motion is
modelled using the spatial Zakharov equation, to which either uniform or
non-uniform (frequency dependent) damping is added. By means of mode truncation
the spatial analogue of the classical Benjamin-Feir instability can be studied
analytically using dynamical systems techniques. The formulation readily yields
the free surface envelope, giving insight into the physical implications of
damping on the modulational instability. The evolution of an initially unstable
mode is also studied numerically by integrating the damped, spatial Zakharov
equation, in order to complement the analytical theory. This sheds light on the
effects of damping on spectral broadening arising from this instability.
|
2403.07425v1
|
1994-05-12
|
Black Hole Relics and Inflation: Limits on Blue Perturbation Spectra
|
Blue primordial power spectra have spectral index $n>1$ and arise naturally
in the recently proposed hybrid inflationary scenario. An observational upper
limit on {\em n} is derived by normalizing the spectrum at the quadrupole scale
and considering the possible overproduction of Planck mass relics formed in the
final stage of primordial black hole evaporation. In the inflationary Universe
with the maximum reheating temperature compatible with the observed quadrupole
anisotropy, the upper limit is $n=1.4$, but it is slightly weaker for lower
reheat temperatures. This limit applies over 57 decades of mass and is
therefore insensitive to cosmic variance and any gravitational wave
contribution to the quadrupole anisotropy. It is also independent of the dark
matter content of the Universe and therefore the bias parameter. In some
circumstances, there may be an extended dust-like phase between the end of
inflation and reheating. In this case, primordial black holes form more
abundantly and the upper limit is $n=1.3$.
|
9405027v1
|
1995-02-01
|
Spectra and Statistics of Cosmic String Perturbations on the Microwave Background: A Monte Carlo Approach
|
Using Monte Carlo simulations of perturbations induced by cosmic strings on
the microwave background, we demonstrate the scale invariance of string
fluctuation patterns. By comparing string-induced fluctuation patterns with
gaussian random phase ones, we show that the non-gaussian signatures of the
string patterns are detectable by tests based on the moments of the
distributions only for angular scales smaller than a few arcminutes and for
maps based on the gradient of temperature fluctuations. However, we find that
tests of the gaussianity of the moments fail when we include a reasonable
amount of instrumental noise in a pattern. Signal to noise ratios of $3.3$ or
greater completely suppress a string pattern's non-gaussian features even at
the highest resolutions.
|
9502004v2
|
1999-04-16
|
The Sunyaev-Zeldovich Effect as Microwave Foreground and Probe of Cosmology
|
The Sunyaev-Zel'dovich (SZ) effect from clusters of galaxies should yield a
significant signal in cosmic microwave background(CMB) experiments at small
angular scales ($\ell \ga 1000$). Experiments with sufficient frequency
coverage should be able to remove much of this signal in order to recover the
primary anisotropy. The SZ signal is interesting in its own right; the
amplitude and angular dependence are sensitive to both cosmology and the
evolution of the gas. Combining CMB measurements with planned non-targeted SZ
surveys could isolate the cosmological effects, providing CMB experiments with
a low-redshift test of cosmology as a consistency check. Improvements in the
determination of the angular diameter distance as a function of redshift from
SZ and X-ray observations of a large sample of clusters will also provide a
probe of cosmology.
|
9904220v1
|
2000-12-05
|
Near-IR Spectroscopy and Population Synthesis of Super Star Clusters in NGC 1569
|
We present H- and K-band NIRSPEC spectroscopy of super star clusters (SSCs)
in the irregular starburst galaxy NGC 1569, obtained at the Keck Observatory.
We fit these photospheric spectra to NextGen model atmospheres to obtain
effective spectral types of clusters, and find that the information in both H-
and K-band spectra is necessary to remove degeneracy in the fits. The light of
SSC B is unambiguously dominated by K0 supergiants (T_eff=4400 +- 100 K, log
g=0.5 +- 0.5). The double cluster SSC A has higher T_eff (G5) and less tightly
constrained surface gravity (log g=1.3 +- 1.3), consistent with a mixed stellar
population dominated by blue Wolf-Rayet stars and red supergiants. We predict
the time evolution of infrared spectra of SSCs using Starburst99 population
synthesis models coupled with empirical stellar spectral libraries (at solar
metallicity). The resulting model sequence allows us to assign ages of 15-18
Myr for SSC B and 18-21 Myr for SSC A.
|
0012089v1
|
2001-05-14
|
Understanding Cluster Gas Evolution and Fine-Scale CMB Anisotropy with Deep Sunyaev-Zel'dovich Effect Surveys
|
We investigate the impact of gas evolution on the expected yields from deep
Sunyaev-Zel'dovich (SZ) effect surveys as well as on the expected SZ effect
contribution to fine scale anisotropy in the Cosmic Microwave Background. The
approximate yields from SZ effect surveys are remarkably insensitive to gas
evolution, even though the observable properties of the resulting clusters can
be markedly different. The CMB angular power spectrum at high multipoles due to
the SZ effect from clusters is quite sensitive to gas evolution. We show that
moderate resolution SZ effect imaging of clusters found in deep SZ effect
surveys should allow a good understanding of gas evolution in galaxy clusters,
independent of the details of the nature of the gas evolution. Such an
understanding will be necessary before precise cosmological constraints can be
set from yields of large cluster surveys.
|
0105229v1
|
2001-05-22
|
Constraints on Omega_m, Omega_L, and Sigma_8, from Galaxy Cluster Redshift Distributions
|
We show that the counts of galaxy clusters in future deep cluster surveys can
place strong constraints on the matter density, Omega_m, the vacuum energy
density, Omega_L, and the normalization of the matter power spectrum, sigma_8.
Degeneracies between these parameters are different from those in studies of
either high--redshift type Ia Supernovae (SNe), or cosmic microwave background
(CMB) anisotropies. Using a mass threshold for cluster detection expected to be
typical for upcoming SZE surveys, we find that constraints on Omega_m and
sigma_8 at the level of roughly 5% or better can be expected, assuming redshift
information is known at least to z=0.5 and in the absence of significant
systematic errors. Without information past this redshift, Omega_L is
constrained to 25%. With complete redshift information, deep (M_{lim}=
10^{14}h^{-1}{M_sun}), relatively small solid angle (roughly 12 {deg}^2)
surveys can further constrain Omega_L to an accuracy of 15%, while large solid
angle surveys with ground-based large-format bolometer arrays could measure
Omega_L to a precision of 4% or better.
|
0105396v2
|
2002-05-27
|
Radio Point Sources and the Thermal SZ Power Spectrum
|
Radio point sources are strongly correlated with clusters of galaxies, so a
significant fraction of the thermal Sunyaev-Zel'dovich (SZ) effect signal could
be affected by point source contamination. Based on empirical estimates of the
radio galaxy population, it is shown that the rms temperature fluctuations of
the thermal SZ effect could be underestimated by as much as 30% at an observing
frequency of 30 GHz at l>1000. The effect is larger at higher multipoles. If
the recent report of excess power at small angular scales is to be explained by
the thermal SZ effect, then radio point sources at an observing frequency of 30
GHz must be a surprisingly weak contaminant of the SZ effect for low-mass
clusters.
|
0205467v2
|
2002-07-29
|
Measuring Cluster Peculiar Velocities and Temperatures at cm and mm Wavelengths
|
We present a detailed investigation of issues related to the measurement of
peculiar velocities and temperatures using Sunyaev-Zel'dovich (SZ) effects. We
estimate the accuracy to which peculiar velocities and gas temperatures of
distant galaxy clusters could be measured. With uK sensitivity on arcminute
scales at several frequencies it will be possible to measure peculiar
velocities to an accuracy of about 130 km/s and gas temperatures to better than
1 keV. The limiting factor for the accuracy of the measured peculiar velocity
is the presence of bulk motions within the galaxy cluster, even for apparently
relaxed clusters. The accuracy of the temperature is mainly limited by noise.
These results are independent of redshift. Such constraints can best be
achieved with only three frequencies: one in the Rayleigh-Jeans region (<40
GHz), one near 150 GHz, and the third at 300 GHz or higher. Measurements at the
null of the thermal SZ effect are of marginal utility, other than as a
foreground/background monitor.
|
0207600v2
|
2002-07-29
|
CMB-Normalized Predictions for Sunyaev-Zel'dovich effect fluctuations
|
We predict the level of small-scale anisotropy in the cosmic microwave
background (CMB) due to the Sunyaev--Zel'dovich (SZ) effect for the ensemble of
cosmological models that are consistent with current measurements of
large-scale CMB anisotropy. We argue that the recently reported detections of
the small-scale (arcminutes) CMB anisotropy are only marginally consistent with
being the SZ effect when cosmological models are calibrated to the existing
primary CMB data on large scales. The discrepancy is at more than 2-2.5 sigma,
and is mainly due to a lower sigma_8 <0.8 favored by the primary CMB and a
higher sigma_8 > 1 favored by the SZ effect. A degeneracy between the optical
depth to Thomson scattering and the CMB-derived value of sigma_8 suggests that
the discrepancy is reduced if the universe was reionized very early, at a
redshift of about 25.
|
0207633v1
|
2002-08-08
|
Cosmology with the Sunyaev-Zel'dovich Effect
|
The Sunyaev-Zel'dovich effect (SZE) provides a unique way to map the
large-scale structure of the universe as traced by massive clusters of
galaxies. As a spectral distortion of the cosmic microwave background, the SZE
is insensitive to the redshift of the galaxy cluster, making it well-suited for
studies of clusters at all redshifts, and especially at reasonably high
redshifts (z > 1) where the abundance of clusters is critically dependent on
the underlying cosmology. Recent high signal-to-noise detections of the SZE
have enabled interesting constraints on the Hubble constant and the matter
density of the universe using small samples of galaxy clusters. Upcoming SZE
surveys are expected to find hundreds to thousands of new galaxy clusters, with
a mass selection function that is remarkably uniform with redshift. In this
review we provide an overview of the SZE and its use for cosmological studies
with emphasis on the cosmology that can, in principle, be extracted from SZE
survey yields. We discuss the observational and theoretical challenges that
must be met before precise cosmological constraints can be extracted from the
survey yields.
|
0208192v1
|
2002-09-25
|
External Shear in Quadruply Imaged Lens Systems
|
We use publicly available N-body simulations and semi-analytic models of
galaxy formation to estimate the levels of external shear due to structure near
the lens in gravitational lens systems. We also describe two selection effects,
specific to four-image systems, that enhance the probability of observing
systems to have higher external shear. Ignoring additional contributions from
"cosmic shear" and assuming that lens galaxies are not significantly flattened,
we find that the mean shear at the position of a quadruple lens galaxy is 0.11,
the rms shear is roughly 0.15, and there is roughly a 45% likelihood of
external shear greater than 0.1. This is much larger than previous estimates
and in good agreement with typical measured external shear. The higher shear
primarily stems from the tendency of early-type galaxies, which are the
majority of lenses, to reside in overdense regions.
|
0209532v2
|
2003-05-21
|
A Method for Mapping the Temperature Profile of X-ray Clusters Through Radio Observations
|
Many of the most luminous extragalactic radio sources are located at the
centers of X-ray clusters, and so their radiation must be scattered by the
surrounding hot gas. We show that radio observations of the highly-polarized
scattered radiation (which depends on the electron density distribution) in
combination with the thermal Sunyaev-Zeldovich effect (which measures the
electron pressure distribution), can be used to determine the radial profile of
the electron temperature within the host cluster. The sensitivity levels
expected from current instruments will allow radio measurements of
mass-weighted cluster temperature profiles to better than roughly 1 keV
accuracy, as long as the central radio source is steady over several million
years. Variable or beamed sources will leave observable signatures in the
scattered emission. For clusters with a central point source brighter than
about 1 mJy, the scattered polarization signal is stronger than competing
effects due to the cosmic microwave background.
|
0305417v1
|
2006-09-26
|
Reconstructing the Thomson Optical Depth due to Patchy Reionization with 21-cm Fluctuation Maps
|
Large fluctuations in the electron column density can occur during the
reionization process. We investigate the possibility of deriving the electron
density fluctuations through detailed mapping of the redshifted 21-cm emission
from the neutral medium during reionization. We find that the
electron-scattering optical depth and 21-cm differential brightness temperature
are strongly anti-correlated, allowing optical depth estimates based entirely
on redshifted 21-cm measurements. This should help isolate the CMB polarization
fluctuations that are due to reionization, allowing both cleaning of the patchy
reionization polarization signal as a contaminating source of confusion to
other signals and a measurement of the primordial quadrupole that would be
measured at various locations in the universe at the epoch of reionization.
This latter application in principle allows mapping of the primordial density
field at z~1100 over a large fraction of the Hubble volume.
|
0609689v2
|
1998-07-06
|
Field Driven Thermostated System : A Non-Linear Multi-Baker Map
|
In this paper, we discuss a simple model for a field driven, thermostated
random walk that is constructed by a suitable generalization of a multi-baker
map. The map is a usual multi-baker, but perturbed by a thermostated external
field that has many of the properties of the fields used in systems with
Gaussian thermostats. For small values of the driving field, the map is
hyperbolic and has a unique SRB measure that we solve analytically to first
order in the field parameter. We then compute the positive and negative
Lyapunov exponents to second order and discuss their relation to the transport
properties. For higher values of the parameter, this system becomes
non-hyperbolic and posseses an attractive fixed point.
|
9807011v2
|
2006-01-19
|
Fluctuation theorem for constrained equilibrium systems
|
We discuss the fluctuation properties of equilibrium chaotic systems with
constraints such as iso-kinetic and Nos\'e-Hoover thermostats. Although the
dynamics of these systems does not typically preserve phase-space volumes, the
average phase-space contraction rate vanishes, so that the stationary states
are smooth. Nevertheless finite-time averages of the phase-space contraction
rate have non-trivial fluctuations which we show satisfy a simple version of
the Gallavotti-Cohen fluctuation theorem, complementary to the usual
fluctuation theorem for non-equilibrium stationary states, and appropriate to
constrained equilibrium states. Moreover we show these fluctuations are
distributed according to a Gaussian curve for long-enough times. Three
different systems are considered here, namely (i) a fluid composed of particles
interacting with Lennard-Jones potentials; (ii) a harmonic oscillator with
Nos\'e-Hoover thermostatting; (iii) a simple hyperbolic two-dimensional map.
|
0601435v1
|
2003-06-12
|
ATLAS Data Challenge 1
|
In 2002 the ATLAS experiment started a series of Data Challenges (DC) of
which the goals are the validation of the Computing Model, of the complete
software suite, of the data model, and to ensure the correctness of the
technical choices to be made. A major feature of the first Data Challenge (DC1)
was the preparation and the deployment of the software required for the
production of large event samples for the High Level Trigger (HLT) and physics
communities, and the production of those samples as a world-wide distributed
activity. The first phase of DC1 was run during summer 2002, and involved 39
institutes in 18 countries. More than 10 million physics events and 30 million
single particle events were fully simulated. Over a period of about 40 calendar
days 71000 CPU-days were used producing 30 Tbytes of data in about 35000
partitions. In the second phase the next processing step was performed with the
participation of 56 institutes in 21 countries (~ 4000 processors used in
parallel). The basic elements of the ATLAS Monte Carlo production system are
described. We also present how the software suite was validated and the
participating sites were certified. These productions were already partly
performed by using different flavours of Grid middleware at ~ 20 sites.
|
0306052v1
|
2004-06-21
|
Long Nonbinary Codes Exceeding the Gilbert - Varshamov Bound for any Fixed Distance
|
Let A(q,n,d) denote the maximum size of a q-ary code of length n and distance
d. We study the minimum asymptotic redundancy \rho(q,n,d)=n-log_q A(q,n,d) as n
grows while q and d are fixed. For any d and q<=d-1, long algebraic codes are
designed that improve on the BCH codes and have the lowest asymptotic
redundancy \rho(q,n,d) <= ((d-3)+1/(d-2)) log_q n known to date. Prior to this
work, codes of fixed distance that asymptotically surpass BCH codes and the
Gilbert-Varshamov bound were designed only for distances 4,5 and 6.
|
0406039v3
|
2006-08-19
|
Algorithmic linear dimension reduction in the l_1 norm for sparse vectors
|
This paper develops a new method for recovering m-sparse signals that is
simultaneously uniform and quick. We present a reconstruction algorithm whose
run time, O(m log^2(m) log^2(d)), is sublinear in the length d of the signal.
The reconstruction error is within a logarithmic factor (in m) of the optimal
m-term approximation error in l_1. In particular, the algorithm recovers
m-sparse signals perfectly and noisy signals are recovered with polylogarithmic
distortion. Our algorithm makes O(m log^2 (d)) measurements, which is within a
logarithmic factor of optimal. We also present a small-space implementation of
the algorithm. These sketching techniques and the corresponding reconstruction
algorithms provide an algorithmic dimension reduction in the l_1 norm. In
particular, vectors of support m in dimension d can be linearly embedded into
O(m log^2 d) dimensions with polylogarithmic distortion. We can reconstruct a
vector from its low-dimensional sketch in time O(m log^2(m) log^2(d)).
Furthermore, this reconstruction is stable and robust under small
perturbations.
|
0608079v1
|
2007-03-06
|
LIBOPT - An environment for testing solvers on heterogeneous collections of problems - Version 1.0
|
The Libopt environment is both a methodology and a set of tools that can be
used for testing, comparing, and profiling solvers on problems belonging to
various collections. These collections can be heterogeneous in the sense that
their problems can have common features that differ from one collection to the
other. Libopt brings a unified view on this composite world by offering, for
example, the possibility to run any solver on any problem compatible with it,
using the same Unix/Linux command. The environment also provides tools for
comparing the results obtained by solvers on a specified set of problems. Most
of the scripts going with the Libopt environment have been written in Perl.
|
0703025v1
|
1995-09-19
|
Harmonic Maps with Prescribed Singularities on Unbounded Domains
|
The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and
axially symmetric case to a harmonic map with prescribed singularities
$\p\colon\R^3\sm\Sigma\to\H^{k+1}_\C$ into the $(k+1)$-dimensional complex
hyperbolic space. In this paper, we prove the existence and uniqueness of
harmonic maps with prescribed singularities $\p\colon\R^n\sm\Sigma\to\H$, where
$\Sigma$ is an unbounded smooth closed submanifold of $\R^n$ of codimension at
least $2$, and $\H$ is a real, complex, or quaternionic hyperbolic space. As a
corollary, we prove the existence of solutions to the reduced stationary and
axially symmetric Einstein/Abelian-Yang-Mills Equations.
|
9509003v1
|
1994-12-12
|
N-Black Hole Stationary and Axially Symmetric Solutions of the Einstein-Maxwell Equations
|
The Einstein/Maxwell equations reduce in the stationary and axially symmetric
case to a harmonic map with prescribed singularities phi: R^3\Sigma -> H^2_C,
where Sigma is a subset of the axis of symmetry, and H^2_C is the complex
hyperbolic plane. Motivated by this problem, we prove the existence and
uniqueness of harmonic maps with prescribed singularities phi: R^n\Sigma -> H,
where Sigma is a submanifold of R^n of co-dimension at least 2, and H is a
classical Riemannian globally symmetric space of noncompact type and rank one.
This result, when applied to the black hole problem, yields solutions which can
be interpreted as equilibrium configurations of multiple co-axially rotating
charged black holes held apart by singular struts.
|
9412036v2
|
1997-11-17
|
Novel Electroweak Symmetry Breaking Conditions From Quantum Effects In The MSSM
|
We present, in the context of the Minimal Supersymmetric Standard Model, a
detailed one-loop analytic study of the minimization conditions of the
effective potential in the Higgs sector.
Special emphasis is put on the role played by $Str M^4$ in the determination
of the electroweak symmetry breaking conditions, where first and second order
derivatives of the effective potential are systematically taken into account.
Novel, necessary (and sufficient in the Higgs sector) model-independent
constraints, are thus obtained analytically, leading to new theoretical lower
and upper bounds on $\tan \beta$. Although fully model-independent, these
bounds are found to be much more restrictive than the existing model-dependent
ones! A first illustration is given in the context of a SUGRA-GUT motivated
scenario.
|
9711356v1
|
1999-01-08
|
On the fourth adjoint Contractions of divisorial and fiber types
|
In this paper, we will list up all the cases for the ray contractions of
divisorial and fiber types for smooth projective varieties of dimension five.
These are obtained as a corollary from the lists of n-dimensional k-th adjoint
contractions f: X -> Y of the same types for k=1,2,3 and 4 (n> or =5). The
lists for k=1,2 and 3 have previously been obtained in [Na], Proposition 1.2
and Theorem 1.3. The main task will be to have such a list for k=4, where one
case in the list fails to show that a positive-dimensional general fiber F of f
is irreducible when n>5. This assertion will, however, be proven when n=5 with
an essential aid of 3-dimensional Minimal Model Program in [Mo2]. (We do not
show the existence of cases.)
|
9901033v2
|
2004-04-19
|
Asymptotic Improvement of the Gilbert-Varshamov Bound on the Size of Binary Codes
|
Given positive integers $n$ and $d$, let $A_2(n,d)$ denote the maximum size
of a binary code of length $n$ and minimum distance $d$. The well-known
Gilbert-Varshamov bound asserts that $A_2(n,d) \geq 2^n/V(n,d-1)$, where
$V(n,d) = \sum_{i=0}^{d} {n \choose i}$ is the volume of a Hamming sphere of
radius $d$. We show that, in fact, there exists a positive constant $c$ such
that $$ A_2(n,d) \geq c \frac{2^n}{V(n,d-1)} \log_2 V(n,d-1) $$ whenever $d/n
\le 0.499$. The result follows by recasting the Gilbert- Varshamov bound into a
graph-theoretic framework and using the fact that the corresponding graph is
locally sparse. Generalizations and extensions of this result are briefly
discussed.
|
0404325v1
|
2005-11-03
|
On the automorphism group of generalized Baumslag-Solitar groups
|
A generalized Baumslag-Solitar group (GBS group) is a finitely generated
group $G$ which acts on a tree with all edge and vertex stabilizers infinite
cyclic. We show that Out(G) either contains non-abelian free groups or is
virtually nilpotent of class at most 2. It has torsion only at finitely many
primes.
One may decide algorithmically whether Out(G) is virtually nilpotent or not.
If it is, one may decide whether it is virtually abelian, or finitely
generated. The isomorphism problem is solvable among GBS groups with Out(G)
virtually nilpotent.
If $G$ is unimodular (virtually $F_n \times Z$), then Out(G) is commensurable
with a semi-direct product $Z^k \rtimes Out(H)$ with $H$ virtually free.
|
0511083v1
|
2001-07-08
|
Statistically Preserved Structures in Shell Models of Passive Scalar Advection
|
It was conjectured recently that Statiscally Preserved Structures underlie
the statistical physics of turbulent transport processes. We analyze here in
detail the time-dependent (non compact) linear operator that governs the
dynamics of correlation functions in the case of shell models of passive scalar
advection. The problem is generic in the sense that the driving velocity field
is neither Gaussian nor $\delta$-correlated in time. We show how to naturally
discuss the dynamics in terms of an effective compact operator that displays
"zero modes" which determine the anomalous scaling of the correlation
functions. Since shell models have neither Lagrangian structure nor "shape
dynamics" this example differs significantly from standard passive scalar
advection. Nevertheless with the necessary modifications the generality and
efficacy of the concept of Statistically Preserved Structures are further
exemplified. In passing we point out a bonus of the present approach, in
providing analytic predictions for the time-dependent correlation functions in
decaying turbulent transport.
|
0107016v1
|
2001-11-13
|
Statistically Preserved Structures and Anomalous Scaling in Turbulent Active Scalar Advection
|
The anomalous scaling of correlation functions in the turbulent statistics of
active scalars (like temperature in turbulent convection) is understood in
terms of an auxiliary passive scalar which is advected by the same turbulent
velocity field. While the odd-order correlation functions of the active and
passive fields differ, we propose that the even-order correlation functions are
the same to leading order (up to a trivial multiplicative factor). The leading
correlation functions are statistically preserved structures of the passive
scalar decaying problem, and therefore universality of the scaling exponents of
the even-order correlations of the active scalar is demonstrated.
|
0111030v1
|
2003-03-27
|
On the parametric dependences of a class of non-linear singular maps
|
We discuss a two-parameter family of maps that generalize piecewise linear,
expanding maps of the circle. One parameter measures the effect of a
non-linearity which bends the branches of the linear map. The second parameter
rotates points by a fixed angle. For small values of the nonlinearity
parameter, we compute the invariant measure and show that it has a singular
density to first order in the nonlinearity parameter. Its Fourier modes have
forms similar to the Weierstrass function. We discuss the consequences of this
singularity on the Lyapunov exponents and on the transport properties of the
corresponding multibaker map. For larger non-linearities, the map becomes
non-hyperbolic and exhibits a series of period-adding bifurcations.
|
0303062v1
|
2001-06-06
|
The Secrecy Capacity of Practical Quantum Cryptography
|
Quantum cryptography has attracted much recent attention due to its potential
for providing secret communications that cannot be decrypted by any amount of
computational effort. This is the first analysis of the secrecy of a practical
implementation of the BB84 protocol that simultaneously takes into account and
presents the {\it full} set of complete analytical expressions for effects due
to the presence of pulses containing multiple photons in the attenuated output
of the laser, the finite length of individual blocks of key material, losses
due to error correction, privacy amplification, continuous authentication,
errors in polarization detection, the efficiency of the detectors, and
attenuation processes in the transmission medium. The analysis addresses
eavesdropping attacks on individual photons rather than collective attacks in
general. Of particular importance is the first derivation of the necessary and
sufficient amount of privacy amplification compression to ensure secrecy
against the loss of key material which occurs when an eavesdropper makes
optimized individual attacks on pulses containing multiple photons. It is shown
that only a fraction of the information in the multiple photon pulses is
actually lost to the eavesdropper.
|
0106033v1
|
2005-11-17
|
Quantum Computer Condition: Stability, Classical Computation and Norms
|
The Quantum Computer Condition (QCC) provides a rigorous and completely
general framework for carrying out analyses of questions pertaining to
fault-tolerance in quantum computers. In this paper we apply the QCC to the
problem of fluctuations and systematic errors in the values of characteristic
parameters in realistic systems. We show that fault-tolerant quantum
computation is possible despite variations in these parameters. We also use the
QCC to explicitly show that reliable classical computation can be carried out
using as input the results of fault-tolerant, but imperfect, quantum
computation. Finally, we consider the advantages and disadvantages of the
superoperator and diamond norms in connection with application of the QCC to
various quantum information-theoretic problems.
|
0511177v1
|
2006-12-19
|
On the use of photonic N00N states for practical quantum interferometry
|
The performance of photonic $N00N$ states, propagating in an attenuating
medium, is analyzed with respect to phase estimation. It is shown that, for
$N00N$ states propagating through a lossy medium, the Heisenberg limit is never
achieved. It is also shown that, for a given value of $N$, a signal comprised
of an attenuated separable state of $N$ photons will actually produce a better
phase estimate than will a signal comprised of an equally attenuated $N00N$
state, unless the transmittance of the medium is very high. This is a
consequence of the need to utilize measurement operators appropriate to the
different signal states. The result is that, for most practical applications in
realistic scenarios with attenuation, the resolution of $N00N$ state-based
phase estimation not only does not achieve the Heisenberg Limit, but is
actually worse than the Standard Quantum Limit. It is demonstrated that this
performance deficit becomes more pronounced as the number, $N$, of photons in
the signal increases.
|
0612156v1
|
2007-05-22
|
Analysis of evidence of Mars life
|
Gillevinia straata, the scientific name [1, 2] recognizing the first
extraterrestrial living form ever nomenclated, as well as the existence of a
new biological kingdom, Jakobia, in a new biosphere -Marciana- of what now has
become the living system Solaria, is grounded on old evidence reinterpreted in
the light of newly acquired facts. The present exposition provides a summary
overview of all these grounds, outlined here as follows. A more detailed paper
is being prepared for publication.
|
0705.3176v3
|
2007-06-26
|
Feedback in the Antennae Galaxies (NGC 4038/9): I. High-Resolution Infrared Spectroscopy of Winds from Super Star Clusters
|
We present high-resolution (R ~ 24,600) near-IR spectroscopy of the youngest
super star clusters (SSCs) in the prototypical starburst merger, the Antennae
Galaxies. These SSCs are young (3-7 Myr old) and massive (10^5 - 10^7 M_sun for
a Kroupa IMF) and their spectra are characterized by broad, extended Br-gamma
emission, so we refer to them as emission-line clusters (ELCs) to distinguish
them from older SSCs. The Brgamma lines of most ELCs have supersonic widths
(60-110 km/s FWHM) and non-Gaussian wings whose velocities exceed the clusters'
escape velocities. This high-velocity unbound gas is flowing out in winds that
are powered by the clusters' massive O and W-R stars over the course of at
least several crossing times. The large sizes of some ELCs relative to those of
older SSCs may be due to expansion caused by these outflows; many of the ELCs
may not survive as bound stellar systems, but rather dissipate rapidly into the
field population. The observed tendency of older ELCs to be more compact than
young ones is consistent with the preferential survival of the most
concentrated clusters at a given age.
|
0706.3935v1
|
2007-06-29
|
Reliable Final Computational Results from Faulty Quantum Computation
|
In this paper we extend both standard fault tolerance theory and Kitaev's
model for quantum computation, combining them so as to yield quantitative
results that reveal the interplay between the two. Our analysis establishes a
methodology that allows us to quantitatively determine design parameters for a
quantum computer, the values of which ensure that an overall computation of
interest yields a correct *final result* with some prescribed probability of
success, as opposed to merely ensuring that the desired *final quantum state*
is obtained. As a specific example of the practical application of our
approach, we explicitly calculate the number of levels of error correction
concatenation needed to achieve a correct final result for the overall
computation with some prescribed success probability. Since our methodology
allows one to determine parameters required in order to achieve the correct
final result for the overall quantum computation, as opposed to merely ensuring
that the desired final quantum state is produced, our method enables the
determination of complete quantum computational resource requirements
associated to the actual solution of practical problems.
|
0707.0008v1
|
2007-08-24
|
Quantum Sensor Miniaturization
|
The classical bound on image resolution defined by the Rayleigh limit can be
beaten by exploiting the properties of quantum mechanical entanglement. If
entangled photons are used as signal states, the best possible resolution is
instead given by the Heisenberg limit, an improvement proportional to the
number of entangled photons in the signal. In this paper we present a novel
application of entanglement by showing that the resolution obtained by an
imaging system utilizing separable photons can be achieved by an imaging system
making use of entangled photons, but with the advantage of a smaller aperture,
thus resulting in a smaller and lighter system. This can be especially valuable
in satellite imaging where weight and size play a vital role.
|
0708.3403v1
|
2007-09-02
|
A Universal Operator Theoretic Framework for Quantum Fault Tolerance
|
In this paper we introduce a universal operator theoretic framework for
quantum fault tolerance. This incorporates a top-down approach that implements
a system-level criterion based on specification of the full system dynamics,
applied at every level of error correction concatenation. This leads to more
accurate determinations of error thresholds than could previously be obtained.
This is demonstrated both formally and with an explicit numerical example. The
basis for our approach is the Quantum Computer Condition (QCC), an inequality
governing the evolution of a quantum computer. We show that all known coding
schemes are actually special cases of the QCC. We demonstrate this by
introducing a new, operator theoretic form of entanglement assisted quantum
error correction, which incorporates as special cases all known error
correcting protocols, and is itself a special case of the QCC.
|
0709.0128v3
|
2007-10-25
|
Ordering in red abalone nacre
|
Red abalone nacre is an intensely studied biomineral, and yet its formation
mechanism remains poorly understood. Here we report quantitative measurements
probing the degree of order of the aragonite tablets in nacre, and show that
order develops over a distance of about 50 microns. These observations indicate
that the orientational order of aragonite tablets in nacre is established
gradually and dynamically, and we show that a model of controlled assembly
based on suppression of the crystal growth rate along a specific direction,
when growth is confined in a layered structure, yields a tablet pattern
consistent with those revealed by detailed experimental measurements. This work
provides strong evidence that the organism s control of crystal orientation in
nacre occurs via regulation of crystal nucleation and growth as opposed to
direct templation or heteroepitaxial growth on organic molecules on the organic
matrix sheets.
|
0710.4573v1
|
2007-11-01
|
Interaction effects in mixed-valent Kondo insulators
|
We study theoretically the class of mixed-valent Kondo insulators, employing
a recently developed local moment approach to heavy Fermion systems using the
asymmetric periodic Anderson model (PAM). Novel features in spectra and
transport, observable experimentally but lying outside the scope of the
symmetric PAM or the Kondo lattice model, emerge naturally within the present
theory. We argue in particular that a shoulder-like feature in the optical
conductivity, that is distinct from the usual mid-infrared or direct gap peak
and has been observed experimentally in mixed-valent compounds such as
CeOs4Sb12 and YbAl3, is of intrinsic origin. Detailed comparison is made
between the resultant theory and transport/optical experiments on the
filled-skutterudite compound CeOs4Sb12, and good agreement is obtained.
|
0711.0121v1
|
2008-01-31
|
Counting growth types of automorphisms of free groups
|
Given an automorphism of a free group $F_n$, we consider the following
invariants: $e$ is the number of exponential strata (an upper bound for the
number of different exponential growth rates of conjugacy classes); $d$ is the
maximal degree of polynomial growth of conjugacy classes; $R$ is the rank of
the fixed subgroup. We determine precisely which triples $(e,d,R)$ may be
realized by an automorphism of $F_n$. In particular, the inequality $e\le
(3n-2)/4}$ (due to Levitt-Lustig) always holds. In an appendix, we show that
any conjugacy class grows like a polynomial times an exponential under
iteration of the automorphism.
|
0801.4844v2
|
2008-02-29
|
Heat conduction and Fourier's law in a class of many particle dispersing billiards
|
We consider the motion of many confined billiard balls in interaction and
discuss their transport and chaotic properties. In spite of the absence of mass
transport, due to confinement, energy transport can take place through binary
collisions between neighbouring particles. We explore the conditions under
which relaxation to local equilibrium occurs on time scales much shorter than
that of binary collisions, which characterize the transport of energy, and
subsequent relaxation to local thermal equilibrium. Starting from the
pseudo-Liouville equation for the time evolution of phase-space distributions,
we derive a master equation which governs the energy exchange between the
system constituents. We thus obtain analytical results relating the transport
coefficient of thermal conductivity to the frequency of collision events and
compute these quantities. We also provide estimates of the Lyapunov exponents
and Kolmogorov-Sinai entropy under the assumption of scale separation. The
validity of our results is confirmed by extensive numerical studies.
|
0802.4455v3
|
2008-04-29
|
Combining geometry and combinatorics: A unified approach to sparse signal recovery
|
There are two main algorithmic approaches to sparse signal recovery:
geometric and combinatorial. The geometric approach starts with a geometric
constraint on the measurement matrix and then uses linear programming to decode
information about the signal from its measurements. The combinatorial approach
constructs the measurement matrix and a combinatorial decoding algorithm to
match. We present a unified approach to these two classes of sparse signal
recovery algorithms.
The unifying elements are the adjacency matrices of high-quality unbalanced
expanders. We generalize the notion of Restricted Isometry Property (RIP),
crucial to compressed sensing results for signal recovery, from the Euclidean
norm to the l_p norm for p about 1, and then show that unbalanced expanders are
essentially equivalent to RIP-p matrices.
From known deterministic constructions for such matrices, we obtain new
deterministic measurement matrix constructions and algorithms for signal
recovery which, compared to previous deterministic algorithms, are superior in
either the number of measurements or in noise tolerance.
|
0804.4666v1
|
2008-08-08
|
Heat conductivity from molecular chaos hypothesis in locally confined billiard systems
|
We study the transport properties of a large class of locally confined
Hamiltonian systems, in which neighboring particles interact through hard core
elastic collisions. When these collisions become rare and the systems large, we
derive a Boltzmann-like equation for the evolution of the probability
densities. We solve this equation in the linear regime and compute the heat
conductivity from a Green-Kubo formula. The validity of our approach is
demonstated by comparing our predictions to the results of numerical
simulations performed on a new class of high-dimensional defocusing chaotic
billiards.
|
0808.1179v2
|
2008-09-23
|
On the derivation of Fourier's law in stochastic energy exchange systems
|
We present a detailed derivation of Fourier's law in a class of stochastic
energy exchange systems that naturally characterize two-dimensional mechanical
systems of locally confined particles in interaction. The stochastic systems
consist of an array of energy variables which can be partially exchanged among
nearest neighbours at variable rates. We provide two independent derivations of
the thermal conductivity and prove this quantity is identical to the frequency
of energy exchanges. The first derivation relies on the diffusion of the
Helfand moment, which is determined solely by static averages. The second
approach relies on a gradient expansion of the probability measure around a
non-equilibrium stationary state. The linear part of the heat current is
determined by local thermal equilibrium distributions which solve a
Boltzmann-like equation. A numerical scheme is presented with computations of
the conductivity along our two methods. The results are in excellent agreement
with our theory.
|
0809.3967v2
|
2008-10-19
|
Coding Theorems for Repeat Multiple Accumulate Codes
|
In this paper the ensemble of codes formed by a serial concatenation of a
repetition code with multiple accumulators connected through random
interleavers is considered. Based on finite length weight enumerators for these
codes, asymptotic expressions for the minimum distance and an arbitrary number
of accumulators larger than one are derived using the uniform interleaver
approach. In accordance with earlier results in the literature, it is first
shown that the minimum distance of repeat-accumulate codes can grow, at best,
sublinearly with block length. Then, for repeat-accumulate-accumulate codes and
rates of 1/3 or less, it is proved that these codes exhibit asymptotically
linear distance growth with block length, where the gap to the
Gilbert-Varshamov bound can be made vanishingly small by increasing the number
of accumulators beyond two. In order to address larger rates, random puncturing
of a low-rate mother code is introduced. It is shown that in this case the
resulting ensemble of repeat-accumulate-accumulate codes asymptotically
achieves linear distance growth close to the Gilbert-Varshamov bound. This
holds even for very high rate codes.
|
0810.3422v1
|
2008-12-09
|
Statistical properties of time-reversible triangular maps of the square
|
Time reversal symmetric triangular maps of the unit square are introduced
with the property that the time evolution of one of their two variables is
determined by a piecewise expanding map of the unit interval. We study their
statistical properties and establish the conditions under which their
equilibrium measures have a product structure, i.e. factorises in a symmetric
form. When these conditions are not verified, the equilibrium measure does not
have a product form and therefore provides additional information on the
statistical properties of theses maps. This is the case of anti-symmetric cusp
maps, which have an intermittent fixed point and yet have uniform invariant
measures on the unit interval. We construct the invariant density of the
corresponding two-dimensional triangular map and prove that it exhibits a
singularity at the intermittent fixed point.
|
0812.1648v1
|
2009-03-20
|
Fractality of the non-equilibrium stationary states of open volume-preserving systems: I. Tagged particle diffusion
|
Deterministic diffusive systems such as the periodic Lorentz gas, multi-baker
map, as well as spatially periodic systems of interacting particles, have
non-equilibrium stationary states with fractal properties when put in contact
with particle reservoirs at their boundaries. We study the macroscopic limits
of these systems and establish a correspondence between the thermodynamics of
the macroscopic diffusion process and the fractality of the stationary states
that characterize the phase-space statistics. In particular the entropy
production rate is recovered from first principles using a formalism due to
Gaspard [J. Stat. Phys. 88, 1215 (1997)]. This article is the first of two; the
second article considers the influence of a uniform external field on such
systems.
|
0903.3476v1
|
2009-03-20
|
Fractality of the non-equilibrium stationary states of open volume-preserving systems: II. Galton boards
|
Galton boards are models of deterministic diffusion in a uniform external
field, akin to driven periodic Lorentz gases, here considered in the absence of
dissipation mechanism. Assuming a cylindrical geometry with axis along the
direction of the external field, the two-dimensional board becomes a model for
one-dimensional mass transport along the direction of the external field. This
is a purely diffusive process which admits fractal non-equilibrium stationary
states under flux boundary conditions. Analytical results are obtained for the
statistics of multi-baker maps modeling such a non-uniform diffusion process. A
correspondence is established between the local phase-space statistics and
their macroscopic counter-parts. The fractality of the invariant state is shown
to be responsible for the positiveness of the entropy production rate.
|
0903.3849v1
|
2009-07-23
|
On Possible Variation in the Cosmological Baryon Fraction
|
The fraction of matter that is in the form of baryons or dark matter could
have spatial fluctuations in the form of baryon-dark matter isocurvature
fluctuations. We use big bang nucleosynthesis calculations compared with
observed light element abundances as well as galaxy cluster gas fractions to
constrain cosmological variations in the baryon fraction. Light element
abundances constrain spatial variations to be less than 26-27%, while a sample
of "relaxed" galaxy clusters shows spatial variations in gas fractions less
than 8%. Larger spatial variations could cause differential screening of the
primary cosmic microwave background anisotropies, leading to asymmetries in the
fluctuations and ease some tension with the halo-star 7Li abundance.
Fluctuations within our allowed bounds can lead to "B-mode" CMB polarization
anisotropies at a non-negligible level.
|
0907.3919v2
|
2009-08-28
|
Chaos in cylindrical stadium billiards via a generic nonlinear mechanism
|
We describe conditions under which higher-dimensional billiard models in
bounded, convex regions are fully chaotic, generalizing the Bunimovich stadium
to dimensions above two. An example is a three-dimensional stadium bounded by a
cylinder and several planes; the combination of these elements may give rise to
defocusing, allowing large chaotic regions in phase space. By studying families
of marginally-stable periodic orbits that populate the residual part of phase
space, we identify conditions under which a nonlinear instability mechanism
arises in their vicinity. For particular geometries, this mechanism rather
induces stable nonlinear oscillations, including in the form of
whispering-gallery modes.
|
0908.4243v2
|
2009-09-23
|
The Gilbert Arborescence Problem
|
We investigate the problem of designing a minimum cost flow network
interconnecting n sources and a single sink, each with known locations in a
normed space and with associated flow demands. The network may contain any
finite number of additional unprescribed nodes from the space; these are known
as the Steiner points. For concave increasing cost functions, a minimum cost
network of this sort has a tree topology, and hence can be called a Minimum
Gilbert Arborescence (MGA). We characterise the local topological structure of
Steiner points in MGAs, showing, in particular, that for a wide range of
metrics, and for some typical real-world cost-functions, the degree of each
Steiner point is 3.
|
0909.4270v2
|
2010-08-12
|
Magnetization dynamics in the inertial regime: nutation predicted at short time scales
|
The dynamical equation of the magnetization has been reconsidered with
enlarging the phase space of the ferromagnetic degrees of freedom to the
angular momentum. The generalized Landau-Lifshitz-Gilbert equation that
includes inertial terms, and the corresponding Fokker-Planck equation, are then
derived in the framework of mesoscopic non-equilibrium thermodynamics theory. A
typical relaxation time $\tau$ is introduced describing the relaxation of the
magnetization acceleration from the inertial regime towards the precession
regime defined by a constant Larmor frequency. For time scales larger than
$\tau$, the usual Gilbert equation is recovered. For time scales below $\tau$,
nutation and related inertial effects are predicted. The inertial regime offers
new opportunities for the implementation of ultrafast magnetization switching
in magnetic devices.
|
1008.2177v1
|
2010-09-20
|
Diffusive properties of persistent walks on cubic lattices with application to periodic Lorentz gases
|
We calculate the diffusion coefficients of persistent random walks on cubic
and hypercubic lattices, where the direction of a walker at a given step
depends on the memory of one or two previous steps. These results are then
applied to study a billiard model, namely a three-dimensional periodic Lorentz
gas. The geometry of the model is studied in order to find the regimes in which
it exhibits normal diffusion. In this regime, we calculate numerically the
transition probabilities between cells to compare the persistent random-walk
approximation with simulation results for the diffusion coefficient.
|
1009.3922v1
|
2010-11-03
|
Existence of vertical spin stiffness in Landau-Lifshitz-Gilbert equation in ferromagnetic semiconductors
|
We calculate the magnetization torque due to the spin polarization of the
itinerant electrons by deriving the kinetic spin Bloch equations based on the
$s$-$d$ model. We find that the first-order gradient of the magnetization
inhomogeneity gives rise to the current-induced torques, which are consistent
to the previous works. At the second-order gradient, we find an effective
magnetic field perpendicular to the spin stiffness filed. This field is
proportional to the nonadiabatic parameter $\beta$. We show that this vertical
spin stiffness term can significantly modify the domain-wall structure in
ferromagnetic semiconductors and hence should be included in the
Landau-Lifshitz-Gilbert equation in studying the magnetization dynamics.
|
1011.0871v1
|
2011-01-05
|
The Fascinating World of Landau-Lifshitz-Gilbert Equation: An Overview
|
The Landau-Lifshitz-Gilbert (LLG) equation is a fascinating nonlinear
evolution equation both from mathematical and physical points of view. It is
related to the dynamics of several important physical systems such as
ferromagnets, vortex filaments, moving space curves, etc. and has intimate
connections with many of the well known integrable soliton equations, including
nonlinear Schr\"odinger and sine-Gordon equations. It can admit very many
dynamical structures including spin waves, elliptic function waves, solitons,
dromions, vortices, spatio-temporal patterns, chaos, etc. depending on the
physical and spin dimensions and the nature of interactions. An exciting recent
development is that the spin torque effect in nanoferromagnets is described by
a generalization of the LLG equation which forms a basic dynamical equation in
the field of spintronics. This article will briefly review these developments
as a tribute to Robin Bullough who was a great admirer of the LLG equation.
|
1101.1005v1
|
2011-02-05
|
Graph Theory
|
This is a replacement paper. There are 6 chapters. The first two chapters are
introductory. The third chapter is on extremal graph theory. The fourth chapter
is about algebra in graph theory. The fifth chapter is focused on algorithms.
The third section of the fifth chapter deals with computable time. The sixth
chapter has sections on probability and enumeration.
|
1102.1087v11
|
2011-04-28
|
The High-Redshift Neutral Hydrogen Signature of an Anisotropic Matter Power Spectrum
|
An anisotropic power spectrum will have a clear signature in the 21cm
radiation from high-redshift hydrogen. We calculate the expected power spectrum
of the intensity fluctuations in neutral hydrogen from before the epoch of
reionization, and predict the accuracy to which future experiments could
constrain a quadrupole anisotropy in the power spectrum. We find that the
Square Kilometer Array will have marginal detection abilities for this signal
at z~17 if the process of reionization has not yet started; reionization could
enhance the detectability substantially. Pushing to higher redshifts and higher
sensitivity will allow highly precise (percent level) measurements of
anisotropy.
|
1104.5403v3
|
2011-06-30
|
A generalisation of the Gilbert-Varshamov bound and its asymptotic evaluation
|
The Gilbert-Varshamov (GV) lower bound on the maximum cardinality of a q-ary
code of length n with minimum Hamming distance at least d can be obtained by
application of Turan's theorem to the graph with vertex set {0,1,..,q-1}^n in
which two vertices are joined if and only if their Hamming distance is at least
d. We generalize the GV bound by applying Turan's theorem to the graph with
vertex set C^n, where C is a q-ary code of length m and two vertices are joined
if and only if their Hamming distance at least d. We asymptotically evaluate
the resulting bound for n-> \infty and d \delta mn for fixed \delta > 0, and
derive conditions on the distance distribution of C that are necessary and
sufficient for the asymptotic generalized bound to beat the asymptotic GV
bound. By invoking the Delsarte inequalities, we conclude that no improvement
on the asymptotic GV bound is obtained. By using a sharpening of Turan's
theorem due to Caro and Wei, we improve on our bound. It is undecided if there
exists a code C for which the improved bound can beat the asymptotic GV bound.
|
1106.6206v1
|
2011-07-17
|
Probabilistic Methods on Erdos Problems
|
The paper reviews and tries to describe the reference set method, which is a
method of combinatorial optimization that gives upper bounds on parameters.
|
1107.3279v17
|
2011-09-12
|
Externally-driven transmission and collisions of domain walls in ferromagnetic wires
|
Analytical multi-domain solutions to the dynamical (Landau-Lifshitz-Gilbert)
equation of a one-dimensional ferromagnet including an external magnetic field
and spin-polarized electric current are found using the Hirota bilinearization
method. A standard approach to solve the Landau-Lifshitz equation (without the
Gilbert term) is modified in order to treat the dissipative dynamics. I
establish the relations between the spin interaction parameters (the constants
of exchange, anisotropy, dissipation, external-field intensity, and
electric-current intensity) and the domain-wall parameters (width and velocity)
and compare them to the results of the Walker approximation and micromagnetic
simulations. The domain-wall motion driven by a longitudinal external field is
analyzed with especial relevance to the field-induced collision of two domain
walls. I determine the result of such a collision (which is found to be the
elastic one) on the domain-wall parameters below and above the Walker breakdown
(in weak- and strong-field regimes). Single-domain-wall dynamics in the
presence of an external transverse field is studied with relevance to the
challenge of increasing the domain-wall velocity below the breakdown.
|
1109.2465v1
|
2011-10-19
|
Current-induced switching in transport through anisotropic magnetic molecules
|
Anisotropic single-molecule magnets may be thought of as molecular switches,
with possible applications to molecular spintronics. In this paper, we consider
current-induced switching in single-molecule junctions containing an
anisotropic magnetic molecule. We assume that the carriers interact with the
magnetic molecule through the exchange interaction and focus on the regime of
high currents in which the molecular spin dynamics is slow compared to the time
which the electrons spend on the molecule. In this limit, the molecular spin
obeys a non-equilibrium Langevin equation which takes the form of a generalized
Landau-Lifshitz-Gilbert equation and which we derive microscopically by means
of a non-equilibrium Born-Oppenheimer approximation. We exploit this Langevin
equation to identify the relevant switching mechanisms and to derive the
current-induced switching rates. As a byproduct, we also derive S-matrix
expressions for the various torques entering into the Landau-Lifshitz-Gilbert
equation which generalize previous expressions in the literature to
non-equilibrium situations.
|
1110.4270v2
|
2011-10-27
|
George Augustus Linhart - as a "widely unknown" thermodynamicist
|
The name of George Augustus Linhart is in fact "widely unknown". In effect,
he was a Viennese-born USA-American physicist-chemist, partially associated
with the Gilbert Newton Lewis' school of thermodynamics at the University of
California in Berkeley. As a lone small boy, he had arrived (from Austria via
Hamburg) at New York in 1896, but was officially USA-naturalized only in 1912.
He was able to pick up English in the streets of New York and Philadelphia,
when occasionally working as a waiter and/or as a tailor - just to somehow
survive. But, nonetheless, he could successfully graduate a high school in
about one year - and then went to the universities for his further education.
After obtaining his BS from the University of Pennsylvania, he could manage
getting both MA and then PhD from the Yale University, Kent Chemical
Laboratory. George Augustus Linhart was afterwards definitely able to
successfully work out the true foundations of thermodynamics and could thus
outdistance many famous thermodynamicists of his time and even the later ones.
Linhart's view of the Second Law of Thermodynamics was and is extremely
fruitful. The interconnection of Linhart's ideas with those of Gilbert Newton
Lewis, as well as with the modern standpoints are discussed here in detail.
|
1110.6352v1
|
2012-03-29
|
Power Allocation over Two Identical Gilbert-Elliott Channels
|
We study the problem of power allocation over two identical Gilbert-Elliot
communication channels. Our goal is to maximize the expected discounted number
of bits transmitted over an infinite time horizon. This is achieved by choosing
among three possible strategies: (1) betting on channel 1 by allocating all the
power to this channel, which results in high data rate if channel 1 happens to
be in good state, and zero bits transmitted if channel 1 is in bad state (even
if channel 2 is in good state) (2) betting on channel 2 by allocating all the
power to the second channel, and (3) a balanced strategy whereby each channel
is allocated half the total power, with the effect that each channel can
transmit a low data rate if it is in good state. We assume that each channel's
state is only revealed upon transmission of data on that channel. We model this
problem as a partially observable Markov decision processes (MDP), and derive
key threshold properties of the optimal policy. Further, we show that by
formulating and solving a relevant linear program the thresholds can be
determined numerically when system parameters are known.
|
1203.6630v2
|
2012-04-11
|
A short note on spin pumping theory with Landau-Lifshitz-Gilbert equation under quantum fluctuation; necessity for quantization of localized spin
|
We would like to point out the blind spots of the approach combining the spin
pumping theory proposed by Tserkovnyak et al. with the Landau-Lifshitz-Gilbert
equation; this method has been widely used for interpreting vast experimental
results. The essence of the spin pumping effect is the quantum fluctuation.
Thus, localized spin degrees of freedom should be quantized, i.e. be treated as
magnons not as classical variables. Consequently, the precessing ferromagnet
can be regarded as a magnon battery. This point of view will be useful for
further progress of spintronics.
|
1204.2339v1
|
2012-05-22
|
Signature of Phase Transitions in the Disordered Quantum Spin Hall State From the Entanglement Spectrum
|
Of the available classes of insulators which have been shown to contain
topologically non-trivial properties one of the most important is class AII,
which contains systems that possess time-reversal symmetry $T$ with $T^2=-1.$
This class has been the subject of significant attention as it encompasses
non-trivial Z$_2$ topological insulators such as the quantum spin Hall (QSH)
state and the 3D strong topological insulator. One of the defining properties
of this system is the robustness of the state under the addition of disorder
that preserves $T.$ In this letter, we explore the phase diagram of the
disordered QSH state as a function of disorder strength and chemical potential
by examining the entanglement spectrum for disordered class AII symplectic
systems. As for the case of the $T$ breaking Chern insulator we show that there
is a correspondence between the level-spacing statistics of the Hamiltonian and
that of the level spacing statistics of the entanglement spectrum. We observe a
feature in the statistics of the entanglement spectrum that aids the
identification of delocalized states and consequently critical energies across
which phase transitions occur.
|
1205.5071v1
|
2012-07-03
|
The unusual smoothness of the extragalactic unresolved radio background
|
If the radio background is coming from cosmological sources, there should be
some amount of clustering due to the large scale structure in the universe.
Simple models for the expected clustering combined with the recent measurement
by ARCADE-2 of the mean extragalactic temperature lead to predicted clustering
levels that are substantially above upper limits from searches for anisotropy
on arcminute scales using ATCA and the VLA. The rms temperature variations in
the cosmic radio background appear to be more than a factor of 10 smaller (in
temperature) than the fluctuations in the cosmic infrared background. It is
therefore extremely unlikely that this background comes from galaxies, galaxy
clusters, or any sources that trace dark matter halos at z<5, unless typical
sources are smooth on arcminute scales, requiring typical sizes of several Mpc.
|
1207.0856v1
|
2012-10-12
|
Optimal Power Allocation Policy over Two Identical Gilbert-Elliott Channels
|
We study the fundamental problem of optimal power allocation over two
identical Gilbert-Elliott (Binary Markov) communication channels. Our goal is
to maximize the expected discounted number of bits transmitted over an infinite
time span by judiciously choosing one of the four actions for each time slot:
1) allocating power equally to both channels, 2) allocating all the power to
channel 1, 3) allocating all the power to channel 2, and 4) allocating no power
to any of the channels. As the channel state is unknown when power allocation
decision is made, we model this problem as a partially observable Markov
decision process(POMDP), and derive the optimal policy which gives the optimal
action to take under different possible channel states. Two different
structures of the optimal policy are derived analytically and verified by
linear programming simulation. We also illustrate how to construct the optimal
policy by the combination of threshold calculation and linear programming
simulation once system parameters are known.
|
1210.3609v1
|
2013-03-16
|
A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equation
|
We consider a lowest-order finite element discretization of the nonlinear
system of Maxwell's and Landau-Lifshitz-Gilbert equations (MLLG). Two
algorithms are proposed to numerically solve this problem, both of which only
require the solution of at most two linear systems per timestep. One of the
algorithms is fully decoupled in the sense that each timestep consists of the
sequential computation of the magnetization and afterwards the magnetic and
electric field. Under some mild assumptions on the effective field, we show
that both algorithms converge towards weak solutions of the MLLG system.
Numerical experiments for a micromagnetic benchmark problem demonstrate the
performance of the proposed algorithms.
|
1303.4009v1
|
2013-03-17
|
On the Landau-Lifshitz-Gilbert equation with magnetostriction
|
To describe and simulate dynamic micromagnetic phenomena, we consider a
coupled system of the nonlinear Landau-Lifshitz-Gilbert equation and the
conservation of momentum equation. This coupling allows to include
magnetostrictive effects into the simulations. Existence of weak solutions has
recently been shown in [Carbout et al. 2011]. In our contribution, we give an
alternate proof which additionally provides an effective numerical integrator.
The latter is based on lowest-order finite elements in space and a
linear-implicit Euler time-stepping. Despite the nonlinearity, only two linear
systems have to be solved per timestep, and the integrator fully decouples both
equations. Finally, we prove unconditional convergence---at least of a
subsequence---towards, and hence existence of, a weak solution of the coupled
system, as timestep size and spatial mesh-size tend to zero. Numerical
experiments conclude the work and shed new light on the existence of blow-up in
micromagnetic simulations.
|
1303.4060v2
|
2013-03-27
|
Optimal Power Allocation over Multiple Identical Gilbert-Elliott Channels
|
We study the fundamental problem of power allocation over multiple
Gilbert-Elliott communication channels. In a communication system with time
varying channel qualities, it is important to allocate the limited transmission
power to channels that will be in good state. However, it is very challenging
to do so because channel states are usually unknown when the power allocation
decision is made. In this paper, we derive an optimal power allocation policy
that can maximize the expected discounted number of bits transmitted over an
infinite time span by allocating the transmission power only to those channels
that are believed to be good in the coming time slot. We use the concept belief
to represent the probability that a channel will be good and derive an optimal
power allocation policy that establishes a mapping from the channel belief to
an allocation decision.
Specifically, we first model this problem as a partially observable Markov
decision processes (POMDP), and analytically investigate the structure of the
optimal policy. Then a simple threshold-based policy is derived for a
three-channel communication system. By formulating and solving a linear
programming formulation of this power allocation problem, we further verified
the derived structure of the optimal policy.
|
1303.6771v1
|
2013-04-29
|
Generalized Baumslag-Solitar groups: rank and finite index subgroups
|
A generalized Baumslag-Solitar (GBS) group is a finitely generated group
acting on a tree with infinite cyclic edge and vertex stabilizers. We show how
to determine effectively the rank (minimal cardinality of a generating set) of
a GBS group; as a consequence, one can compute the rank of the mapping torus of
a finite order outer automorphism of a free group $F_n$. We also show that the
rank of a finite index subgroup of a GBS group G cannot be smaller than the
rank of G. We determine which GBS groups are large (some finite index subgroup
maps onto $F_2$), and we solve the commensurability problem (deciding whether
two groups have isomorphic finite index subgroups) in a particular family of
GBS groups.
|
1304.7582v2
|
2013-06-02
|
On the Riemannian Penrose inequality with charge and the cosmic censorship conjecture
|
We note an area-charge inequality orignially due to Gibbons: if the outermost
horizon $S$ in an asymptotically flat electrovacuum initial data set is
connected then $|q|\leq r$, where $q$ is the total charge and $r=\sqrt{A/4\pi}$
is the area radius of $S$. A consequence of this inequality is that for
connected black holes the following lower bound on the area holds: $r\geq
m-\sqrt{m^2-q^2}$. In conjunction with the upper bound $r\leq m +
\sqrt{m^2-q^2}$ which is expected to hold always, this implies the natural
generalization of the Riemannian Penrose inequality: $m\geq 1/2(r+q^2/r)$.
|
1306.0206v3
|
2013-08-19
|
A finite element approximation for the stochastic Landau-Lifshitz-Gilbert equation
|
The stochastic Landau--Lifshitz--Gilbert (LLG) equation describes the
behaviour of the magnetization under the influence of the effective field
consisting of random fluctuations. We first reformulate the equation into an
equation the unknown of which is differentiable with respect to the time
variable. We then propose a convergent $\theta$-linear scheme for the numerical
solution of the reformulated equation. As a consequence, we show the existence
of weak martingale solutions to the stochastic LLG equation. A salient feature
of this scheme is that it does not involve a nonlinear system, and that no
condition on time and space steps is required when $\theta\in(\frac{1}{2},1]$.
Numerical results are presented to show the applicability of the method.
|
1308.3912v2
|
2014-01-14
|
Constructions of Pure Asymmetric Quantum Alternant Codes Based on Subclasses of Alternant Codes
|
In this paper, we construct asymmetric quantum error-correcting codes(AQCs)
based on subclasses of Alternant codes. Firstly, We propose a new subclass of
Alternant codes which can attain the classical Gilbert-Varshamov bound to
construct AQCs. It is shown that when $d_x=2$, $Z$-parts of the AQCs can attain
the classical Gilbert-Varshamov bound. Then we construct AQCs based on a famous
subclass of Alternant codes called Goppa codes. As an illustrative example, we
get three $[[55,6,19/4]],[[55,10,19/3]],[[55,15,19/2]]$ AQCs from the well
known $[55,16,19]$ binary Goppa code. At last, we get asymptotically good
binary expansions of asymmetric quantum GRS codes, which are quantum
generalizations of Retter's classical results. All the AQCs constructed in this
paper are pure.
|
1401.3215v2
|
2014-03-19
|
Numerical integration of the stochastic Landau-Lifshitz-Gilbert equation in generic time-discretisation schemes
|
We introduce a numerical method to integrate the stochastic
Landau-Lifshitz-Gilbert equation in spherical coordinates for generic
discretization schemes. This method conserves the magnetization modulus and
ensures the approach to equilibrium under the expected conditions. We test the
algorithm on a benchmark problem: the dynamics of a uniformly magnetized
ellipsoid. We investigate the influence of various parameters, and in
particular, we analyze the efficiency of the numerical integration, in terms of
the number of steps needed to reach a chosen long time with a given accuracy.
|
1403.4822v2
|
2014-05-05
|
Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards
|
We perform numerical measurements of the moments of the position of a tracer
particle in a two-dimensional periodic billiard model (Lorentz gas) with
infinite corridors. This model is known to exhibit a weak form of
super-diffusion, in the sense that there is a logarithmic correction to the
linear growth in time of the mean-squared displacement. We show numerically
that this expected asymptotic behavior is easily overwhelmed by the subleading
linear growth throughout the time-range accessible to numerical simulations. We
compare our simulations to the known analytical results for the variance of the
anomalously-rescaled limiting normal distributions.
|
1405.0975v2
|
2014-05-12
|
Efficient Energy-minimization in Finite-Difference Micromagnetics: Speeding up Hysteresis Computations
|
We implement an efficient energy-minimization algorithm for finite-difference
micromagnetics that proofs especially useful for the computation of hysteresis
loops. Compared to results obtained by time integration of the
Landau-Lifshitz-Gilbert equation, a speedup of up to two orders of magnitude is
gained. The method is implemented in a finite-difference code running on CPUs
as well as GPUs. This setup enables us to compute accurate hysteresis loops of
large systems with a reasonable computational effort. As a benchmark we solve
the {\mu}Mag Standard Problem #1 with a high spatial resolution and compare the
results to the solution of the Landau-Lifshitz-Gilbert equation in terms of
accuracy and computing time.
|
1405.2728v3
|
2014-07-01
|
Transport properties of Lévy walks: an analysis in terms of multistate processes
|
Continuous time random walks combining diffusive and ballistic regimes are
introduced to describe a class of L\'evy walks on lattices. By including
exponentially-distributed waiting times separating the successive jump events
of a walker, we are led to a description of such L\'evy walks in terms of
multistate processes whose time-evolution is shown to obey a set of coupled
delay differential equations. Using simple arguments, we obtain asymptotic
solutions to these equations and rederive the scaling laws for the mean squared
displacement of such processes. Our calculation includes the computation of all
relevant transport coefficients in terms of the parameters of the models.
|
1407.0227v2
|
2014-07-26
|
Magnetization reversal condition for a nanomagnet within a rotating magnetic field
|
The reversal condition of magnetization in a nanomagnet under the effect of
rotating magnetic field generated by a microwave is theoretically studied based
on the Landau-Lifshitz-Gilbert equation. In a rotating frame, the microwave
produces a dc magnetic field pointing in the reversed direction, which
energetically stabilizes the reversed state. We find that the microwave
simultaneously produces a torque preventing the reversal. It is pointed out
that this torque leads to a jump in the reversal field with respect to the
frequency. We derive the equations determining the reversal fields in both the
low- and high-frequency regions from the energy balance equation. The
validities of the formulas are confirmed by a comparison with the numerical
simulation of the Landau-Lifshitz-Gilbert equation.
|
1407.7095v1
|
2014-09-17
|
Aharonov-Bohm Oscillations in a Quasi-Ballistic 3D Topological Insulator Nanowire
|
In three-dimensional topological insulators (3D TI) nanowires, transport
occurs via gapless surface states where the spin is fixed perpendicular to the
momentum[1-6]. Carriers encircling the surface thus acquire a \pi Berry phase,
which is predicted to open up a gap in the lowest-energy 1D surface subband.
Inserting a magnetic flux ({\Phi}) of h/2e through the nanowire should cancel
the Berry phase and restore the gapless 1D mode[7-8]. However, this signature
has been missing in transport experiments reported to date[9-11]. Here, we
report measurements of mechanically-exfoliated 3D TI nanowires which exhibit
Aharonov-Bohm oscillations consistent with topological surface transport. The
use of low-doped, quasi-ballistic devices allows us to observe a minimum
conductance at {\Phi} = 0 and a maximum conductance reaching e^2/h at {\Phi} =
h/2e near the lowest subband (i.e. the Dirac point), as well as the carrier
density dependence of the transport.
|
1409.5095v1
|
2014-10-13
|
[$α$/Fe] Abundances of Four Outer M 31 Halo Stars
|
We present alpha element to iron abundance ratios, [$\alpha$/Fe], for four
stars in the outer stellar halo of the Andromeda Galaxy (M 31). The stars were
identified as high-likelihood field halo stars by Gilbert et al. (2012) and lie
at projected distances between 70 and 140 kpc from M 31's center. These are the
first alpha abundances measured for a halo star in a galaxy beyond the Milky
Way. The stars range in metallicity between [Fe/H]= -2.2 and [Fe/H]= -1.4. The
sample's average [$\alpha$/Fe] ratio is +0.20+/-0.20. The best-fit average
value is elevated above solar which is consistent with rapid chemical
enrichment from Type II supernovae. The mean [$\alpha$/Fe] ratio of our M31
outer halo sample agrees (within the uncertainties) with that of Milky Way
inner/outer halo stars that have a comparable range of [Fe/H].
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1410.3475v1
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