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2016-10-11
|
Converse theorems and the local Langlands correspondence in families
|
We prove a descent criterion for certain families of smooth representations
of GL_n(F) (F a p-adic field) in terms of the gamma factors of pairs
constructed in previous work of the second author. We then use this descent
criterion, together with a theory of gamma factors for families of
representations of the Weil group W_F (developed previously by both authors),
to prove a series of conjectures, due to the first author, that give a complete
description of the integral Bernstein center in terms of Galois theory and the
local Langlands correspondence. An immediate consequence is the conjectural
"local Langlands correspondence in families" of Emerton and Helm.
|
1610.03277v1
|
2016-10-14
|
An alternative view on dissipation in turbulent flows
|
An original experimental setup has been elaborated in order to get a better
view of turbulent flows in a von Karman geometry. The availability of a very
fast camera allowed to follow in time the evolution of the flows. A surprising
finding is that the development of smaller whorls ceases earlier than expected
and the aspect of the flows remains the same above Reynolds number of a few
thousand. This fact provides an explanation of the constancy of the reduced
dissipation in the same range without the need of singularity. Its cause could
be in relation with the same type of behavior observed in a rotating frame.
|
1610.05356v2
|
2017-03-02
|
Small Superposition Dimension and Active Set Construction for Multivariate Integration Under Modest Error Demand
|
Constructing active sets is a key part of the Multivariate Decomposition
Method. An algorithm for constructing optimal or quasi-optimal active sets is
proposed in the paper. By numerical experiments, it is shown that the new
method can provide sets that are significantly smaller than the sets
constructed by the already existing method. The experiments also show that the
superposition dimension could surprisingly be very small, at most 3, when the
error demand is not smaller than $10^{-3}$ and the weights decay sufficiently
fast.
|
1703.00985v1
|
2017-03-03
|
Heat conduction and the nonequilibrium stationary states of stochastic energy exchange processes
|
I revisit the exactly solvable Kipnis--Marchioro--Presutti model of heat
conduction [J. Stat. Phys. 27 65 (1982)] and describe, for one-dimensional
systems of arbitrary sizes whose ends are in contact with thermal baths at
different temperatures, a systematic characterization of their non-equilibrium
stationary states. These arguments avoid resorting to the analysis of a dual
process and yield a straightforward derivation of Fourier's law, as well as
higher-order static correlations, such as the covariant matrix. The
transposition of these results to families of gradient models generalizing the
KMP model is established and specific cases are examined.
|
1703.01240v1
|
2017-03-04
|
Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound
|
It was shown by Massey that linear complementary dual (LCD for short) codes
are asymptotically good. In 2004, Sendrier proved that LCD codes meet the
asymptotic Gilbert-Varshamov (GV for short) bound. Until now, the GV bound
still remains to be the best asymptotical lower bound for LCD codes. In this
paper, we show that an algebraic geometry code over a finite field of even
characteristic is equivalent to an LCD code and consequently there exists a
family of LCD codes that are equivalent to algebraic geometry codes and exceed
the asymptotical GV bound.
|
1703.01441v1
|
2017-03-17
|
A finite element approximation for the stochastic Landau--Lifshitz--Gilbert equation with multi-dimensional noise
|
We propose an unconditionally convergent linear finite element scheme for the
stochastic Landau--Lifshitz--Gilbert (LLG) equation with multi-dimensional
noise. By using the Doss-Sussmann technique, we first transform the stochastic
LLG equation into a partial differential equation that depends on the solution
of the auxiliary equation for the diffusion part. The resulting equation has
solutions absolutely continuous with respect to time. We then propose a
convergent $\theta$-linear scheme for the numerical solution of the
reformulated equation. As a consequence, we are able to show the existence of
weak martingale solutions to the stochastic LLG equation.
|
1703.05901v1
|
2017-04-12
|
The homology of principally directed ordered groupoids
|
We present some homological properties of a relation $\beta$ on ordered
groupoids that generalises the minimum group congruence for inverse semigroups.
When $\beta$ is a transitive relation on an ordered groupoid $G$, the quotient
$G / \beta$ is again an ordered groupoid, and construct a pair of adjoint
functors between the module categories of $G$ and of $G / \beta$. As a
consequence, we show that the homology of $G$ is completely determined by that
of $G / \beta$, generalising a result of Loganathan for inverse semigroups.
|
1704.03689v1
|
2017-06-15
|
Absence of correlations in the energy exchanges of an exactly solvable model of heat transport with many degrees of freedom
|
A process based on the exactly solvable Kipnis--Marchioro--Presutti model of
heat conduction [J. Stat. Phys. 27 65 (1982)] is described whereby lattice
cells share their energies among many identical degrees of freedom while, in
each cell, only two of them are associated with energy exchanges connecting
neighbouring cells. It is shown that, up to dimensional constants, the heat
conductivity is half the interaction rate, regardless of the degrees of
freedom. Moreover, as this number becomes large, correlations between the
energy variables involved in the exchanges vanish. In this regime, the process
thus boils down to the time-evolution of the local temperatures which is
prescribed by the discrete heat equation.
|
1706.04849v1
|
2017-11-29
|
On the local converse theorem and the descent theorem in families
|
We prove an analogue of Jacquet's conjecture on the local converse theorem
for \ell-adic families of co-Whittaker representations of GL_n(F), where F is a
finite extension of Q_p and \ell does not equal p. We also prove an analogue of
Jacquet's conjecture for a descent theorem, which asks for the smallest
collection of gamma factors determining the subring of definition of an
\ell-adic family. These two theorems are closely related to the local Langlands
correspondence in \ell-adic families.
|
1711.11159v1
|
2018-06-23
|
List Decodability of Symbol-Pair Codes
|
We investigate the list decodability of symbol-pair codes in the present
paper. Firstly, we show that list decodability of every symbol-pair code does
not exceed the Gilbert-Varshamov bound. On the other hand, we are able to prove
that with high probability, a random symbol-pair code can be list decoded up to
the Gilbert-Varshamov bound. Our second result of this paper is to derive the
Johnson-type bound, i.e., a lower bound on list decoding radius in terms of
minimum distance. Finally, we present a list decoding algorithm of Reed-Solomon
codes beyond the Johnson-type bound.
|
1806.08992v1
|
2018-07-05
|
Volumetric performance capture from minimal camera viewpoints
|
We present a convolutional autoencoder that enables high fidelity volumetric
reconstructions of human performance to be captured from multi-view video
comprising only a small set of camera views. Our method yields similar
end-to-end reconstruction error to that of a probabilistic visual hull computed
using significantly more (double or more) viewpoints. We use a deep prior
implicitly learned by the autoencoder trained over a dataset of view-ablated
multi-view video footage of a wide range of subjects and actions. This opens up
the possibility of high-end volumetric performance capture in on-set and
prosumer scenarios where time or cost prohibit a high witness camera count.
|
1807.01950v2
|
2018-10-26
|
Immobilization of convex bodies in $R^n$
|
We extend to arbitrary finite $n$ the notion of immobilization of a convex
body $O$ in $R^n$ by a finite set of points $P$ in the boundary of $O$. Because
of its importance for this problem, necessary and sufficient conditions are
found for the immobilization of an $n$-simplex. A fairly complete geometric
description of these conditions is given: as $n$ increases from $n = 2$, some
qualitative difference in the nature of the sets $P$ emerges.
|
1810.11381v1
|
2019-01-14
|
Groupoids and the algebra of rewriting in group presentations
|
Presentations of groups by rewriting systems (that is, by monoid
presentations), have been fruitfully studied by encoding the rewriting system
in a $2$--complex -- the Squier complex -- whose fundamental groupoid then
describes the derivation of consequences of the rewrite rules. We describe a
reduced form of the Squier complex, investigate the structure of its
fundamental groupoid, and show that key properties of the presentation are
still encoded in the reduced form.
|
1901.04348v1
|
2019-05-27
|
Tuning Free Rank-Sparse Bayesian Matrix and Tensor Completion with Global-Local Priors
|
Matrix and tensor completion are frameworks for a wide range of problems,
including collaborative filtering, missing data, and image reconstruction.
Missing entries are estimated by leveraging an assumption that the matrix or
tensor is low-rank. Most existing Bayesian techniques encourage rank-sparsity
by modelling factorized matrices and tensors with Normal-Gamma priors. However,
the Horseshoe prior and other "global-local" formulations provide
tuning-parameter-free solutions which may better achieve simultaneous
rank-sparsity and missing-value recovery. We find these global-local priors
outperform commonly used alternatives in simulations and in a collaborative
filtering task predicting board game ratings.
|
1905.11496v1
|
2019-06-26
|
Fairness criteria through the lens of directed acyclic graphical models
|
A substantial portion of the literature on fairness in algorithms proposes,
analyzes, and operationalizes simple formulaic criteria for assessing fairness.
Two of these criteria, Equalized Odds and Calibration by Group, have gained
significant attention for their simplicity and intuitive appeal, but also for
their incompatibility. This chapter provides a perspective on the meaning and
consequences of these and other fairness criteria using graphical models which
reveals Equalized Odds and related criteria to be ultimately misleading. An
assessment of various graphical models suggests that fairness criteria should
ultimately be case-specific and sensitive to the nature of the information the
algorithm processes.
|
1906.11333v1
|
2020-01-14
|
Neural Architecture Search for Deep Image Prior
|
We present a neural architecture search (NAS) technique to enhance the
performance of unsupervised image de-noising, in-painting and super-resolution
under the recently proposed Deep Image Prior (DIP). We show that evolutionary
search can automatically optimize the encoder-decoder (E-D) structure and
meta-parameters of the DIP network, which serves as a content-specific prior to
regularize these single image restoration tasks. Our binary representation
encodes the design space for an asymmetric E-D network that typically converges
to yield a content-specific DIP within 10-20 generations using a population
size of 500. The optimized architectures consistently improve upon the visual
quality of classical DIP for a diverse range of photographic and artistic
content.
|
2001.04776v1
|
2020-07-18
|
Finslerian convolution metrics and their special classes
|
Here, it is introduced a concept of convolution metric in Finslerian
Geometry. This convolution metric is a kind of function obtained by a given
mathematical operation between two Finslerian metrics. Some basic properties of
the Finslerian convolution metrics are studied. Then it is characterized
Finslerian convolution metrics which are of type Riemannian, Minkowskian as
well as Randers. Furthermore, some examples of the Finslerian convolutions are
given.
|
2007.14803v3
|
2020-09-14
|
What mathematical billiards teach us about statistical physics?
|
We survey applications of the theory of hyperbolic (and to a lesser extent
non hyperbolic) billiards to some fundamental problems of statistical physics
and their mathematically rigorous derivations in the framework of classical
Hamiltonian systems.
|
2009.06284v2
|
2020-11-29
|
Applications of the Backus-Gilbert method to linear and some non linear equations
|
We investigate the use of a functional analytical version of the
Backus-Gilbert Method as a reconstruction strategy to get specific information
about the solution of linear and slightly non-linear systems with Frech\'et
derivable operators. Some a priori error estimates are shown and tested for two
classes of problems: a nonlinear moment problem and a linear elliptic Cauchy
problem. For this second class of problems a special version of the
Green-formula is developed in order to analyze the involved adjoint equations.
|
2011.14407v1
|
2021-11-30
|
Global weak solutions for the Landau-Lifshitz-Gilbert-Vlasov-Maxwell system coupled via emergent electromagnetic fields
|
Motivated by recent models of current driven magnetization dynamics, we
examine the coupling of the Landau-Lifshitz-Gilbert equation and classical
electron transport governed by the Vlasov-Maxwell system. The interaction is
based on space-time gyro-coupling in the form of emergent electromagnetic
fields of quantized helicity that add up to the conventional Maxwell fields. We
construct global weak solutions of the coupled system in the framework of
frustrated magnets with competing first and second order gradient interactions
known to host topological solitons such as magnetic skyrmions and hopfions.
|
2111.15482v1
|
2022-04-02
|
Introduction to the Artificial Intelligence that can be applied to the Network Automation Journey
|
The computer network world is changing and the NetDevOps approach has brought
the dynamics of applications and systems into the field of communication
infrastructure. Businesses are changing and businesses are faced with
difficulties related to the diversity of hardware and software that make up
those infrastructures. The "Intent-Based Networking - Concepts and Definitions"
document describes the different parts of the ecosystem that could be involved
in NetDevOps. The recognize, generate intent, translate and refine features
need a new way to implement algorithms. This is where artificial intelligence
comes in.
|
2204.00800v1
|
2022-05-24
|
Theory of the Energy Variance in a Quantum Bit
|
We define a new quantum Hermitian operator (namely, the energy variance
operator) which is simply duplicated from the statistical definition of energy
variance in classical physics. Its expectation value yields the standard
deviation of the energy about the mean value of this latter. We show by use of
an exact Hamiltonian description that this standard deviation is due to the
high-frequeny energy oscillations which are usually discarded in the rotating
wave aproximation. We check the present theory by recovering the duration of an
abrupt quantum jump that has been described in a recent experiment.
|
2205.12763v1
|
2022-07-11
|
Quasilinear rough evolution equations
|
We investigate the abstract Cauchy problem for a quasilinear parabolic
equation in a Banach space of the form \( du_t -L_t(u_t)u_t dt = N_t(u_t)dt +
F(u_t)\cdot d\mathbf X_t \), where \( \mathbf X\) is a \( \gamma\)-H\"older
rough path for \( \gamma\in(1/3,1/2)\). We explore the mild formulation that
combines functional analysis techniques and controlled rough paths theory which
entail the local well-posedness of such equations. We apply our results to the
stochastic Landau-Lifshitz-Gilbert and Shigesada-Kawasaki-Teramoto equation. In
this framework we obtain a random dynamical system associated to the
Landau-Lifshitz-Gilbert equation.
|
2207.04787v1
|
2022-08-01
|
A Pansiot-type subword complexity theorem for automorphisms of free groups
|
Inspired by Pansiot's work on substitutions, we prove a similar theorem for
automorphisms of a free group F of finite rank: if a right-infinite word
represents an attracting fixed point of an automorphism of F, the subword
complexity of X is equivalent to n, n log log n, n log n, or n^2. The proof
uses combinatorial arguments analogue to Pansiot's as well as train tracks. We
also define the recurrence complexity of X, and we apply it to laminations. In
particular, we show that attracting laminations have complexity equivalent to
n, n log log n, n log n, or n^2 (to n if the automorphism is fully
irreducible).
|
2208.00676v1
|
2022-08-13
|
May the force be with you
|
Modern methods in dimensionality reduction are dominated by nonlinear
attraction-repulsion force-based methods (this includes t-SNE, UMAP,
ForceAtlas2, LargeVis, and many more). The purpose of this paper is to
demonstrate that all such methods, by design, come with an additional feature
that is being automatically computed along the way, namely the vector field
associated with these forces. We show how this vector field gives additional
high-quality information and propose a general refinement strategy based on
ideas from Morse theory. The efficiency of these ideas is illustrated
specifically using t-SNE on synthetic and real-life data sets.
|
2208.06676v1
|
2022-10-26
|
Linearized frequency domain Landau-Lifshitz-Gilbert equation formulation
|
We present a general finite element linearized Landau-Lifshitz-Gilbert
equation (LLGE) solver for magnetic systems under weak time-harmonic excitation
field. The linearized LLGE is obtained by assuming a small deviation around the
equilibrium state of the magnetic system. Inserting such expansion into LLGE
and keeping only first order terms gives the linearized LLGE, which gives a
frequency domain solution for the complex magnetization amplitudes under an
external time-harmonic applied field of a given frequency. We solve the linear
system with an iterative solver using generalized minimal residual method. We
construct a preconditioner matrix to effectively solve the linear system. The
validity, effectiveness, speed, and scalability of the linear solver are
demonstrated via numerical examples.
|
2210.14525v1
|
2022-11-10
|
Secure Aggregation Is Not All You Need: Mitigating Privacy Attacks with Noise Tolerance in Federated Learning
|
Federated learning is a collaborative method that aims to preserve data
privacy while creating AI models. Current approaches to federated learning tend
to rely heavily on secure aggregation protocols to preserve data privacy.
However, to some degree, such protocols assume that the entity orchestrating
the federated learning process (i.e., the server) is not fully malicious or
dishonest. We investigate vulnerabilities to secure aggregation that could
arise if the server is fully malicious and attempts to obtain access to
private, potentially sensitive data. Furthermore, we provide a method to
further defend against such a malicious server, and demonstrate effectiveness
against known attacks that reconstruct data in a federated learning setting.
|
2211.06324v1
|
2022-12-22
|
Theory and construction of Quasi-Monte Carlo rules for option pricing and density estimation
|
In this paper we propose and analyse a method for estimating three quantities
related to an Asian option: the fair price, the cumulative distribution
function, and the probability density. The method involves preintegration with
respect to one well chosen integration variable to obtain a smooth function of
the remaining variables, followed by the application of a tailored lattice
Quasi-Monte Carlo rule to integrate over the remaining variables.
|
2212.11493v2
|
2022-12-22
|
Novel Bottomonium Results
|
We present the latest results from the use of the Backus-Gilbert method for
reconstructing the spectra of NRQCD bottomonium mesons using anisotropic
FASTSUM ensembles at non-zero temperature. We focus in particular on results
from the $\eta_b$, $\Upsilon$, $\chi_{b1}$ and $h_b$ generated from
Tikhonov-regularized Backus-Gilbert coefficient sets. We extend previous work
on the Laplace shifting theorem as a means of resolution improvement and
present new results from its use. We conclude with a discussion of the
limitations of the improvement routine and elucidate a connection with
Parisi-Lepage statistical scaling.
|
2212.12016v1
|
2022-12-30
|
Asymptotic stability of 2-domain walls for the Landau-Lifshitz-Gilbert equation in a nanowire with Dzyaloshinskii-Moriya interaction
|
We consider a ferromagnetic nanowire, with an energy functional $E$ with
easy-axis in the direction $e_1$, and which takes into account the
Dzyaloshinskii-Moriya interaction. We consider configurations of the
magnetization which are perturbations of two well separated domain wall, and
study their evolution under the Landau-Lifshitz-Gilbert flow associated to E.
Our main result is that, if the two walls have opposite speed, these
configurations are asymptotically stable, up to gauges intrinsic to the
invariances of the energy $E$. Our analysis builds on the framework developed
in [4], taking advantage that it is amenable to space localisation.
|
2212.14589v1
|
2023-01-12
|
Time Domain Verification of Differential Transmission Line Modeling Methods
|
The advantages and limitations of time-domain pseudo-random binary sequence
(PRBS) excitation methods for system identification of individual modes within
a multi-conductor transmission system are discussed. We develop the
modifications necessary to standard frequency-domain transmission-line models
to match time-domain experimental data from several types of transmission
systems. We show a variety of experimental results showing very good to
excellent agreement with our model's predictions, up to approximately 10 GHz.
|
2301.05281v1
|
2023-01-17
|
Power Supply Compensation for Capacitive Loads
|
As ASIC supply voltages approach one volt, the source-impedance goals for
power distribution networks are driven ever lower as well. One approach to
achieving these goals is to add decoupling capacitors of various values until
the desired impedance profile is obtained. An unintended consequence of this
approach can be reduced power supply stability and even oscillation. In this
paper, we present a case study of a system design which encountered these
problems and we describe how these problems were resolved. Time-domain and
frequency-domain analysis techniques are discussed and measured data is
presented.
|
2301.09580v1
|
2023-01-17
|
Applications of Optimization Routines in Signal Integrity Analysis
|
Signal integrity analysis often involves the development of design guidelines
through manual manipulation of circuit parameters and judicious interpretation
of results. Such an approach can result in significant effort and sub-optimal
conclusions. Optimization routines have been well proven to aid analysis across
a variety of common tasks. In addition, there are several non-traditional
applications where optimization can be useful. This paper begins by describing
the basics of optimization followed by two specific case studies where
non-traditional optimization provides significant improvements in both analysis
efficiency and channel performance.
|
2301.10157v1
|
2023-01-17
|
High Speed Parallel Signal Crosstalk Cancellation Concept
|
High performance computing (HPC) systems make extensive use of high speed
electrical interconnects, in routing signals among processing elements, or
between processing elements and memory. Increasing bandwidth demands result in
high density, parallel I/O exposed to crosstalk due to tightly coupled
transmission lines. The crosstalk cancellation signaling concept discussed in
this paper utilizes the known, predictable theory of coupled transmission lines
to cancel crosstalk from neighboring traces with carefully chosen resistive
cross-terminations between them. Through simulation and analysis of practical
bus architectures, we explore the merits of crosstalk cancellation which could
be used in dense interconnect HPC (or other) applications.
|
2301.10170v1
|
2023-04-05
|
Elimination and Factorization
|
If a matrix $A$ has rank $r$, then its row echelon form (from elimination)
contains the identity matrix in its first $r$ independent columns. How do we
\emph{interpret the matrix} $F$ that appears in the remaining columns of that
echelon form\,? $F$ multiplies those first $r$ independent columns of $A$ to
give its $n-r$ dependent columns. Then $F$ reveals bases for the row space and
the nullspace of the original matrix $A$. And $F$ is the key to the column-row
factorization $\boldsymbol{A}=\boldsymbol{CR}$.
|
2304.02659v1
|
2023-04-25
|
Jet: Multilevel Graph Partitioning on Graphics Processing Units
|
The multilevel heuristic is the dominant strategy for high-quality sequential
and parallel graph partitioning. Partition refinement is a key step of
multilevel graph partitioning. In this work, we present Jet, a new parallel
algorithm for partition refinement specifically designed for Graphics
Processing Units (GPUs). We combine Jet with GPU-aware coarsening to develop a
$k$-way graph partitioner, the Jet partitioner. The new partitioner achieves
superior quality compared to state-of-the-art shared memory partitioners on a
large collection of test graphs.
|
2304.13194v2
|
2023-05-16
|
QHDL: a Low-Level Circuit Description Language for Quantum Computing
|
This paper proposes a descriptive language called QHDL, akin to VHDL, to
program gate-based quantum computing systems. Unlike other popular quantum
programming languages, QHDL targets low-level quantum computing programming and
aims to provide a common framework for programming FPGAs and gate-based quantum
computing systems. The paper presents an initial implementation and design
principles of the QHDL framework, including a compiler and quantum computer
simulator. We discuss the challenges of low-level integration of streaming
models and quantum computing for programming FPGAs and gate-based quantum
computing systems.
|
2305.09419v1
|
2023-05-21
|
An Alternative Derivation of the Landau-Lifshitz-Gilbert Equation for Saturated Ferromagnets
|
The Landau-Lifshitz-Gilbert equation for rigid and saturated ferromagnets is
derived using a two-continuum model constructed by H.F. Tiersten for elastic
and saturated ferromagnets. The relevant basic laws of physics are applied
systematically to the two continua or their combination. The exchange
interaction is introduced into the model through surface distributed magnetic
couples. This leads to a continuum theory with magnetization gradients in the
stored energy density. The saturation condition of the magnetization functions
as constraints on the energy density and has implications in the constitutive
relations.
|
2305.18232v1
|
2023-06-25
|
Gilbert's conjecture and A new way to octonionic analytic functions from the clifford analysis
|
In this article we will give a affirmative answer to Gilbert's conjecture on
Hardy spaces of Clifford analytic functions in upper half-space of
$\mathbb{R}^8$. It depends on a explicit construction of Spinor space
$\mathcal{R}_8$ and Clifford algebra $Cl_8$ by octonion algbra. What's more ,
it gives us an associative way to octonionic analytic function theory. And the
similar question has been discussed in Octonionic Hardy space in upper-half
space, some classical results about octonionic analytic functions have been
reformulated, too.
|
2306.14164v1
|
2023-06-28
|
Stochastic Landau-Lifshitz-Gilbert equations for frustrated magnets under fluctuating currents
|
We examine a stochastic Landau-Lifshitz-Gilbert equation for a frustrated
ferromagnet with competing first and second order exchange interactions exposed
to deterministic and random spin transfer torques in form of transport noise.
We prove the existence and pathwise uniqueness of weak martingale solutions in
the energy space. The result ensures the persistence of topological patterns,
occurring in such magnetic systems, under the influence of a fluctuating spin
current.
|
2306.15843v1
|
2023-07-28
|
MDS, Hermitian Almost MDS, and Gilbert-Varshamov Quantum Codes from Generalized Monomial-Cartesian Codes
|
We construct new stabilizer quantum error-correcting codes from generalized
monomial-Cartesian codes. Our construction uses an explicitly defined twist
vector, and we present formulas for the minimum distance and dimension.
Generalized monomial-Cartesian codes arise from polynomials in $m$ variables.
When $m=1$ our codes are MDS, and when $m=2$ and our lower bound for the
minimum distance is $3$ the codes are at least Hermitian Almost MDS. For an
infinite family of parameters when $m=2$ we prove that our codes beat the
Gilbert-Varshamov bound. We also present many examples of our codes that are
better than any known code in the literature.
|
2307.15488v1
|
2023-09-06
|
Optimal Control of the 2D Landau-Lifshitz-Gilbert Equation with Control Energy in Effective Magnetic Field
|
The optimal control of magnetization dynamics in a ferromagnetic sample at a
microscopic scale is studied. The dynamics of this model is governed by the
Landau-Lifshitz-Gilbert equation on a two-dimensional bounded domain with the
external magnetic field (the control) applied through the effective field. We
prove the global existence and uniqueness of a regular solution in $\mathbb
S^2$ under a smallness condition on control and initial data. We establish the
existence of optimal control and derive a first-order necessary optimality
condition using the Fr\'echet derivative of the control-to-state operator and
adjoint problem approach.
|
2309.02786v1
|
2023-09-22
|
Relaxed optimal control for the stochastic Landau-Lifshitz-Gilbert equation
|
We consider the stochastic Landau-Lifshitz-Gilbert equation, perturbed by a
real-valued Wiener process. We add an external control to the effective field
as an attempt to drive the magnetization to a desired state and also to control
thermal fluctuations. We use the theory of Young measures to relax the given
control problem along with the associated cost. We consider a control operator
that can depend (possibly non-linearly) on both the control and the associated
solution. Moreover, we consider a fairly general associated cost functional
without any special convexity assumption. We use certain compactness arguments,
along with the Jakubowski version of the Skorohod Theorem to show that the
relaxed problem admits an optimal control.
|
2309.12556v1
|
2023-11-29
|
Bayesian interpretation of Backus-Gilbert methods
|
The extraction of spectral densities from Euclidean correlators evaluated on
the lattice is an important problem, as these quantities encode physical
information on scattering amplitudes, finite-volume spectra, inclusive decay
rates, and transport coefficients. In this contribution, we show that the
Bayesian approach to this "inverse" problem, based on Gaussian processes, can
be reformulated in a way that yields a solution equivalent, up to statistical
uncertainties, to the one obtained in a Backus-Gilbert approach. After
discussing this equivalence, we point out its implications for a reliable
determination of spectral densities from lattice simulations.
|
2311.18125v1
|
2024-01-14
|
Multilevel Metamodels: A Novel Approach to Enhance Efficiency and Generalizability in Monte Carlo Simulation Studies
|
Metamodels, or the regression analysis of Monte Carlo simulation (MCS)
results, provide a powerful tool to summarize MCS findings. However, an as of
yet unexplored approach is the use of multilevel metamodels (MLMM) that better
account for the dependent data structure of MCS results that arises from
fitting multiple models to the same simulated data set. In this study, we
articulate the theoretical rationale for the MLMM and illustrate how it can
dramatically improve efficiency over the traditional regression approach,
better account for complex MCS designs, and provide new insights into the
generalizability of MCS findings.
|
2401.07294v2
|
2024-02-29
|
Evaluating the Gilbert-Varshamov Bound for Constrained Systems
|
We revisit the well-known Gilbert-Varshamov (GV) bound for constrained
systems. In 1991, Kolesnik and Krachkovsky showed that GV bound can be
determined via the solution of some optimization problem. Later, Marcus and
Roth (1992) modified the optimization problem and improved the GV bound in many
instances. In this work, we provide explicit numerical procedures to solve
these two optimization problems and hence, compute the bounds. We then show the
procedures can be further simplified when we plot the respective curves. In the
case where the graph presentation comprise a single state, we provide explicit
formulas for both bounds.
|
2402.18869v1
|
1992-06-18
|
Wormholes and Supersymmetry
|
Revisions: reference added to: G. Gilbert, {\sl Nucl.Phys.} {\bf B328}, 159
(1989)
|
9206072v2
|
1993-05-26
|
Musings on Magnus
|
The object of this paper is to describe a simple method for proving that
certain groups are residually torsion-free nilpotent, to describe some new
parafree groups and to raise some new problems in honour of the memory of
Wilhelm Magnus.
|
9305201v1
|
2001-10-17
|
Expected number of distinct part sizes in a random integer composition
|
The asymptotics, as $n\to\infty$, for the expected number of distinct part
sizes in a random composition of an integer n is obtained.
|
0110189v1
|
2003-12-29
|
Non-hopfian relatively free groups
|
To solve problems of Gilbert Baumslag and Hanna Neumann, posed in the 1960's,
we construct a nontrivial variety of groups all of whose noncyclic free groups
are non-hopfian.
|
0312491v1
|
2005-10-26
|
Winning rate in the full-information best choice problem
|
Following a long-standing suggestion by Gilbert and Mosteller, we derive an
explicit formula for the asymptotic winning rate in the full-information
problem of the best choice.
|
0510568v3
|
2007-12-20
|
The dark matter as a light gravitino (II)
|
We address the question of gravitino dark matter in the context of gauge
mediated supersymmetry breaking models.
|
0712.3465v1
|
2014-02-25
|
Du-Hwang Characteristic Area: Catch-22
|
The paper is devoted to description of two interconnected mistakes generated
by the gap in the Du and Hwang approach to Gilbert-Pollack Steiner ratio
conjecture.
|
1402.6079v1
|
2016-06-01
|
Existence of arbitrarily smooth solutions of the LLG equation in 3D with natural boundary conditions
|
We prove that the Landau-Lifshitz-Gilbert equation in three space dimensions
with homogeneous Neumann boundary conditions admits arbitrarily smooth
solutions, given that the initial data is sufficiently close to a constant
function.
|
1606.00086v1
|
2018-10-28
|
Asymptotic Gilbert-Varshamov bound on Frequency Hopping Sequences
|
Given a $q$-ary frequency hopping sequence set of length $n$ and size $M$
with Hamming correlation $H$, one can obtain a $q$-ary (nonlinear) cyclic code
of length $n$ and size $nM$ with Hamming distance $n-H$. Thus, every upper
bound on the size of a code from coding theory gives an upper bound on the size
of a frequency hopping sequence set. Indeed, all upper bounds from coding
theory have been converted to upper bounds on frequency hopping sequence sets
(\cite{Ding09}). On the other hand, a lower bound from coding theory does not
automatically produce a lower bound for frequency hopping sequence sets. In
particular, the most important lower bound--the Gilbert-Varshamov bound in
coding theory has not been transformed to frequency hopping sequence sets. The
purpose of this paper is to convert the Gilbert-Varshamov bound in coding
theory to frequency hopping sequence sets by establishing a connection between
a special family of cyclic codes (which are called hopping cyclic codes in this
paper) and frequency hopping sequence sets. We provide two proofs of the
Gilbert-Varshamov bound. One is based on probabilistic method that requires
advanced tool--martingale. This proof covers the whole rate region. The other
proof is purely elementary but only covers part of the rate region.
|
1810.11757v2
|
2020-05-26
|
Reidemeister Moves in Gauss Diagrams
|
We provide a simple algorithm for recognizing and performing Reidemeister
moves in a Gauss diagram.
|
2005.12957v1
|
2021-05-26
|
Lee Weight for Nonbinary Quantum Error Correction
|
We propose the quantum Lee weight for quantum errors, provide a
Gilbert-Varshamov type bound, and a code construction for the proposed weight.
|
2105.12354v1
|
2021-09-19
|
Compactness of isospectral conformal Finslerian metrics set on a 3-manifold
|
Let F be a Finslerian metric on an n-dimensional closed manifold M. In this
work, we study problems about compactness of isospectral sets of conformal
Finslerian metrics when n=3.
|
2110.06338v2
|
2001-05-31
|
Lower bound for the quantum capacity of a discrete memoryless quantum channel
|
We generalize the random coding argument of stabilizer codes and derive a
lower bound on the quantum capacity of an arbitrary discrete memoryless quantum
channel. For the depolarizing channel, our lower bound coincides with that
obtained by Bennett et al. We also slightly improve the quantum
Gilbert-Varshamov bound for general stabilizer codes, and establish an analogue
of the quantum Gilbert-Varshamov bound for linear stabilizer codes. Our proof
is restricted to the binary quantum channels, but its extension of to l-adic
channels is straightforward.
|
0105151v4
|
2007-08-30
|
Asymptotic improvement of the Gilbert-Varshamov bound for linear codes
|
The Gilbert-Varshamov bound states that the maximum size A_2(n,d) of a binary
code of length n and minimum distance d satisfies A_2(n,d) >= 2^n/V(n,d-1)
where V(n,d) stands for the volume of a Hamming ball of radius d. Recently
Jiang and Vardy showed that for binary non-linear codes this bound can be
improved to A_2(n,d) >= cn2^n/V(n,d-1) for c a constant and d/n <= 0.499. In
this paper we show that certain asymptotic families of linear binary [n,n/2]
random double circulant codes satisfy the same improved Gilbert-Varshamov
bound.
|
0708.4164v1
|
2007-09-26
|
Finite Element Formalism for Micromagnetism
|
The aim of this work is to present the details of the finite element approach
we developed for solving the Landau-Lifschitz-Gilbert equations in order to be
able to treat problems involving complex geometries. There are several
possibilities to solve the complex Landau-Lifschitz-Gilbert equations
numerically. Our method is based on a Galerkin-type finite element approach. We
start with the dynamic Landau-Lifschitz-Gilbert equations, the associated
boundary condition and the constraint on the magnetization norm. We derive the
weak form required by the finite element method. This weak form is afterwards
integrated on the domain of calculus. We compared the results obtained with our
finite element approach with the ones obtained by a finite difference method.
The results being in very good agreement, we can state that our approach is
well adapted for 2D micromagnetic systems.
|
0709.4153v1
|
2009-05-07
|
Heat transport in stochastic energy exchange models of locally confined hard spheres
|
We study heat transport in a class of stochastic energy exchange systems that
characterize the interactions of networks of locally trapped hard spheres under
the assumption that neighbouring particles undergo rare binary collisions. Our
results provide an extension to three-dimensional dynamics of previous ones
applying to the dynamics of confined two-dimensional hard disks [Gaspard P &
Gilbert T On the derivation of Fourier's law in stochastic energy exchange
systems J Stat Mech (2008) P11021]. It is remarkable that the heat conductivity
is here again given by the frequency of energy exchanges. Moreover the
expression of the stochastic kernel which specifies the energy exchange
dynamics is simpler in this case and therefore allows for faster and more
extensive numerical computations.
|
0905.1051v1
|
2011-08-15
|
Hydrodynamics of self-alignment interactions with precession and derivation of the Landau-Lifschitz-Gilbert equation
|
We consider a kinetic model of self-propelled particles with alignment
interaction and with precession about the alignment direction. We derive a
hydrodynamic system for the local density and velocity orientation of the
particles. The system consists of the conservative equation for the local
density and a non-conservative equation for the orientation. First, we assume
that the alignment interaction is purely local and derive a first order system.
However, we show that this system may lose its hyperbolicity. Under the
assumption of weakly non-local interaction, we derive diffusive corrections to
the first order system which lead to the combination of a heat flow of the
harmonic map and Landau-Lifschitz-Gilbert dynamics. In the particular case of
zero self-propelling speed, the resulting model reduces to the phenomenological
Landau-Lifschitz-Gilbert equations. Therefore the present theory provides a
kinetic formulation of classical micromagnetization models and spin dynamics.
|
1108.2951v1
|
2011-09-30
|
Magnetization Dynamics, Gyromagnetic Relation, and Inertial Effects
|
The gyromagnetic relation - i.e. the proportionality between the angular
momentum $\vec L$ (defined by an inertial tensor) and the magnetization $\vec
M$ - is evidence of the intimate connections between the magnetic properties
and the inertial properties of ferromagnetic bodies. However, inertia is absent
from the dynamics of a magnetic dipole (the Landau-Lifshitz equation, the
Gilbert equation and the Bloch equation contain only the first derivative of
the magnetization with respect to time). In order to investigate this
paradoxical situation, the lagrangian approach (proposed originally by T. H.
Gilbert) is revisited keeping an arbitrary nonzero inertial tensor. A dynamic
equation generalized to the inertial regime is obtained. It is shown how both
the usual gyromagnetic relation and the well-known Landau-Lifshitz-Gilbert
equation are recovered at the kinetic limit, i.e. for time scales above the
relaxation time $\tau$ of the angular momentum.
|
1109.6782v1
|
2012-08-28
|
Decomposition of modified Landau-Lifshitz-Gilbert equation and corresponding analytic solutions
|
The Suzuki-Trotter decomposition in general allows one to divide the equation
of motion of a dynamical system into smaller parts whose integration are easier
than the original equation. In this study, we first rewrite by employing
feasible approximations the modified Landau-Lifshitz-Gilbert equation for
localized spins in a suitable form for simulations using the Suzuki-Trotter
decomposition. Next we decompose the equation into parts and demonstrate that
the parts are classified into three groups, each of which can be solved
exactly. Since the modified Landau-Lifshitz-Gilbert equation from which we
start is in rather a general form, simulations of spin dynamics in various
systems accompanying only small numerical errors are possible.
|
1208.5545v1
|
2013-11-20
|
Asymptotic Improvement of the Gilbert-Varshamov Bound on the Size of Permutation Codes
|
Given positive integers $n$ and $d$, let $M(n,d)$ denote the maximum size of
a permutation code of length $n$ and minimum Hamming distance $d$. The
Gilbert-Varshamov bound asserts that $M(n,d) \geq n!/V(n,d-1)$ where $V(n,d)$
is the volume of a Hamming sphere of radius $d$ in $\S_n$.
Recently, Gao, Yang, and Ge showed that this bound can be improved by a
factor $\Omega(\log n)$, when $d$ is fixed and $n \to \infty$. Herein, we
consider the situation where the ratio $d/n$ is fixed and improve the
Gilbert-Varshamov bound by a factor that is \emph{linear in $n$}. That is, we
show that if $d/n < 0.5$, then $$ M(n,d)\geq cn\,\frac{n!}{V(n,d-1)} $$ where
$c$ is a positive constant that depends only on $d/n$. To establish this
result, we follow the method of Jiang and Vardy. Namely, we recast the problem
of bounding $M(n,d)$ into a graph-theoretic framework and prove that the
resulting graph is locally sparse.
|
1311.4925v1
|
2016-11-21
|
On the List-Decodability of Random Self-Orthogonal Codes
|
In 2011, Guruswami-H{\aa}stad-Kopparty \cite{Gru} showed that the
list-decodability of random linear codes is as good as that of general random
codes. In the present paper, we further strengthen the result by showing that
the list-decodability of random {\it Euclidean self-orthogonal} codes is as
good as that of general random codes as well, i.e., achieves the classical
Gilbert-Varshamov bound. Specifically, we show that, for any fixed finite field
$\F_q$, error fraction $\delta\in (0,1-1/q)$ satisfying $1-H_q(\delta)\le
\frac12$ and small $\epsilon>0$, with high probability a random Euclidean
self-orthogonal code over $\F_q$ of rate $1-H_q(\delta)-\epsilon$ is $(\delta,
O(1/\epsilon))$-list-decodable. This generalizes the result of linear codes to
Euclidean self-orthogonal codes. In addition, we extend the result to list
decoding {\it symplectic dual-containing} codes by showing that the
list-decodability of random symplectic dual-containing codes achieves the
quantum Gilbert-Varshamov bound as well. This implies that list-decodability of
quantum stabilizer codes can achieve the quantum Gilbert-Varshamov bound.
The counting argument on self-orthogonal codes is an important ingredient to
prove our result.
|
1611.06673v1
|
2017-11-29
|
Linear second-order IMEX-type integrator for the (eddy current) Landau-Lifshitz-Gilbert equation
|
Combining ideas from [Alouges et al. (Numer. Math., 128, 2014)] and
[Praetorius et al. (Comput. Math. Appl., 2017)], we propose a numerical
algorithm for the integration of the nonlinear and time-dependent
Landau-Lifshitz-Gilbert (LLG) equation which is unconditionally convergent,
formally (almost) second-order in time, and requires only the solution of one
linear system per time-step. Only the exchange contribution is integrated
implicitly in time, while the lower-order contributions like the
computationally expensive stray field are treated explicitly in time. Then, we
extend the scheme to the coupled system of the Landau-Lifshitz-Gilbert equation
with the eddy current approximation of Maxwell equations (ELLG). Unlike
existing schemes for this system, the new integrator is unconditionally
convergent, (almost) second-order in time, and requires only the solution of
two linear systems per time-step.
|
1711.10715v1
|
2017-12-28
|
Subquadratic time encodable codes beating the Gilbert-Varshamov bound
|
We construct explicit algebraic geometry codes built from the
Garcia-Stichtenoth function field tower beating the Gilbert-Varshamov bound for
alphabet sizes at least 192. Messages are identied with functions in certain
Riemann-Roch spaces associated with divisors supported on multiple places.
Encoding amounts to evaluating these functions at degree one places. By
exploiting algebraic structures particular to the Garcia-Stichtenoth tower, we
devise an intricate deterministic \omega/2 < 1.19 runtime exponent encoding and
1+\omega/2 < 2.19 expected runtime exponent randomized (unique and list)
decoding algorithms. Here \omega < 2.373 is the matrix multiplication exponent.
If \omega = 2, as widely believed, the encoding and decoding runtimes are
respectively nearly linear and nearly quadratic. Prior to this work, encoding
(resp. decoding) time of code families beating the Gilbert-Varshamov bound were
quadratic (resp. cubic) or worse.
|
1712.10052v2
|
2018-11-15
|
Hilbert-Schmidt distance and entanglement witnessing
|
Gilbert proposed an algorithm for bounding the distance between a given point
and a convex set. In this article we apply the Gilbert's algorithm to get an
upper bound on the Hilbert-Schmidt distance between a given state and the set
of separable states. While Hilbert Schmidt Distance does not form a proper
entanglement measure, it can nevertheless be useful for witnessing
entanglement. We provide here a few methods based on the Gilbert's algorithm
that can reliably qualify a given state as strongly entangled or practically
separable, while being computationally efficient. The method also outputs
successively improved approximations to the Closest Separable State for the
given state. We demonstrate the efficacy of the method with examples.
|
1811.06599v3
|
2020-02-13
|
Age of Information with Gilbert-Elliot Servers and Samplers
|
We study age of information in a status updating system that consists of a
single sampler, i.e., source node, that sends time-sensitive status updates to
a single monitor node through a server node. We first consider a Gilbert-Elliot
service profile at the server node. In this model, service times at the server
node follow a finite state Markov chain with two states: ${bad}$ state $b$ and
${good}$ state $g$ where the server is faster in state $g$. We determine the
time average age experienced by the monitor node and characterize the
age-optimal state transition matrix $P$ with and without an average cost
constraint on the service operation. Next, we consider a Gilbert-Elliot
sampling profile at the source. In this model, the interarrival times follow a
finite state Markov chain with two states: ${bad}$ state $b$ and ${good}$ state
$g$ where samples are more frequent in state $g$. We find the time average age
experienced by the monitor node and characterize the age-optimal state
transition matrix $P$.
|
2002.05711v1
|
2005-08-26
|
Damping of MHD turbulence in Solar Flares
|
(Abridged) We describe the cascade of plasma waves or turbulence injected,
presumably by reconnection, at scales comparable to the size of a solar flare
loop to scales comparable to particle gyroradii, and evaluate their damping by
various mechanisms. We show that the classical viscous damping is unimportant
for magnetically dominated or low beta plasmas and the primary damping
mechanism is the collisionless damping by the background particles. We show
that the damping rate is proportional to the total random momentum density of
the particles. For solar flare conditions this means that in most flares,
except the very large ones, the damping is dominated by thermal background
electrons. For large flares one requires acceleration of essentially all
background electrons into a nonthermal distribution so that the accelerated
electrons can be important in the damping of the waves. In general, damping by
thermal or nonthermal protons is negligible compared to that of electrons
except for quasi-perpendicular propagating waves or for rare proton dominated
flares with strong nuclear gamma-ray line emission. Using the rate for damping
we determine the critical scale below which the damping becomes important and
the spectrum of the turbulence steepens. This critical scale, however, has
strong dependence on the angle of propagation with respect to the magnetic
field direction. The waves can cascade down to very small scales, such as the
gyroradii of the particles at small angles (quasi-parallel propagation) and
possibly near 90 degree (quasi-perpendicular propagation) giving rise to a
highly anisotropic spectral distribution.
|
0508567v1
|
2011-07-27
|
Constraint damping for the Z4c formulation of general relativity
|
One possibility for avoiding constraint violation in numerical relativity
simulations adopting free-evolution schemes is to modify the continuum
evolution equations so that constraint violations are damped away. Gundlach et.
al. demonstrated that such a scheme damps low amplitude, high frequency
constraint violating modes exponentially for the Z4 formulation of General
Relativity. Here we analyze the effect of the damping scheme in numerical
applications on a conformal decomposition of Z4. After reproducing the
theoretically predicted damping rates of constraint violations in the linear
regime, we explore numerical solutions not covered by the theoretical analysis.
In particular we examine the effect of the damping scheme on low-frequency and
on high-amplitude perturbations of flat spacetime as well and on the long-term
dynamics of puncture and compact star initial data in the context of spherical
symmetry. We find that the damping scheme is effective provided that the
constraint violation is resolved on the numerical grid. On grid noise the
combination of artificial dissipation and damping helps to suppress constraint
violations. We find that care must be taken in choosing the damping parameter
in simulations of puncture black holes. Otherwise the damping scheme can cause
undesirable growth of the constraints, and even qualitatively incorrect
evolutions. In the numerical evolution of a compact static star we find that
the choice of the damping parameter is even more delicate, but may lead to a
small decrease of constraint violation. For a large range of values it results
in unphysical behavior.
|
1107.5539v2
|
1999-11-24
|
Damped Lyman alpha absorber and the faint end of the galaxy luminosity function at high redshift
|
We combine predictions for several hierarchical cosmogonies with
observational evidence on damped Lyman alpha systems to establish a
correspondence between the high redshift galaxy population and the properties
of damped Lyman alpha systems. We assume that high redshift galaxies and damped
Lyman alpha systems are hosted by the same dark matter halos and require
consistency between the predicted halo space density, the rate of incidence and
the velocity width distribution of damped Lyman alpha systems, and the observed
galaxy luminosity function at the bright end. We arrive at the following
results: (1) predicted impact parameters between the damped absorption system
and the luminous part of the absorbing galaxy are expected to be very small
(0.3 - 1arcsec) for most galaxies; (2) luminosities of galaxies causing damped
absorption are generally fainter than m_R = 25 and damped Lyman alpha systems
are predicted to sample preferentially the outer regions of galaxies at the
faint end of the galaxy luminosity function at high redshift. Therefore, DLAS
should currently provide the best probe of the progenitors of normal
present-day galaxies.
|
9911447v1
|
2003-03-13
|
An explicit unconditionally stable numerical method for solving damped nonlinear Schrödinger equations with a focusing nonlinearity
|
This paper introduces an extension of the time-splitting sine-spectral (TSSP)
method for solving damped focusing nonlinear Schr\"{o}dinger equations (NLS).
The method is explicit, unconditionally stable and time transversal invariant.
Moreover, it preserves the exact decay rate for the normalization of the wave
function if linear damping terms are added to the NLS. Extensive numerical
tests are presented for cubic focusing nonlinear Schr\"{o}dinger equations in
2d with a linear, cubic or a quintic damping term. Our numerical results show
that quintic or cubic damping always arrests blowup, while linear damping can
arrest blowup only when the damping parameter $\dt$ is larger than a threshold
value $\dt_{\rm th}$. We note that our method can also be applied to solve the
3d Gross-Pitaevskii equation with a quintic damping term to model the dynamics
of a collapsing and exploding Bose-Einstein condensate (BEC).
|
0303158v1
|
2004-11-03
|
Quantum probability applied to the damped harmonic oscillator
|
In this introductory course we sketch the framework of quantum probability in
order to discuss open quantum systems, in particular the damped harmonic
oscillator.
|
0411024v1
|
2006-11-23
|
Path integrals and wavepacket evolution for damped mechanical systems
|
Damped mechanical systems with various forms of damping are quantized using
the path integral formalism. In particular, we obtain the path integral kernel
for the linearly damped harmonic oscillator and a particle in a uniform
gravitational field with linearly or quadratically damped motion. In each case,
we study the evolution of Gaussian wavepackets and discuss the characteristic
features that help us distinguish between different types of damping. For
quadratic damping, we show that the action and equation of motion of such a
system has a connection with the zero dimensional version of a currently
popular scalar field theory. Furthermore we demonstrate that the equation of
motion (for quadratic damping) can be identified as a geodesic equation in a
fictitious two-dimensional space.
|
0611239v1
|
2007-07-05
|
Damping of bulk excitations over an elongated BEC - the role of radial modes
|
We report the measurement of Beliaev damping of bulk excitations in cigar
shaped Bose Einstein condensates of atomic vapor. By using post selection,
excitation line shapes of the total population are compared with those of the
undamped excitations. We find that the damping depends on the initial
excitation energy of the decaying quasi particle, as well as on the excitation
momentum. We model the condensate as an infinite cylinder and calculate the
damping rates of the different radial modes. The derived damping rates are in
good agreement with the experimentally measured ones. The damping rates
strongly depend on the destructive interference between pathways for damping,
due to the quantum many-body nature of both excitation and damping products.
|
0707.0776v1
|
2008-09-22
|
Damping in 2D and 3D dilute Bose gases
|
Damping in 2D and 3D dilute gases is investigated using both the
hydrodynamical approach and the Hartree-Fock-Bogoliubov (HFB) approximation .
We found that the both methods are good for the Beliaev damping at zero
temperature and Landau damping at very low temperature, however, at high
temperature, the hydrodynamical approach overestimates the Landau damping and
the HFB gives a better approximation. This result shows that the comparison of
the theoretical calculation using the hydrodynamical approach and the
experimental data for high temperature done by Vincent Liu (PRL {\bf21} 4056
(1997)) is not proper. For two-dimensional systems, we show that the Beliaev
damping rate is proportional to $k^3$ and the Landau damping rate is
proportional to $ T^2$ for low temperature and to $T$ for high temperature. We
also show that in two dimensions the hydrodynamical approach gives the same
result for zero temperature and for low temperature as HFB, but overestimates
the Landau damping for high temperature.
|
0809.3632v3
|
2008-12-08
|
Landau Damping and Alfven Eigenmodes of Neutron Star Torsion Oscillations
|
Torsion oscillations of the neutron star crust are Landau damped by the
Alfven continuum in the bulk. For strong magnetic fields (in magnetars),
undamped Alfven eigenmodes appear.
|
0812.1570v1
|
2010-09-24
|
Spatial Damping of Propagating Kink Waves in Prominence Threads
|
Transverse oscillations and propagating waves are frequently observed in
threads of solar prominences/filaments and have been interpreted as kink
magnetohydrodynamic (MHD) modes. We investigate the spatial damping of
propagating kink MHD waves in transversely nonuniform and partially ionized
prominence threads. Resonant absorption and ion-neutral collisions (Cowling's
diffusion) are the damping mechanisms taken into account. The dispersion
relation of resonant kink waves in a partially ionized magnetic flux tube is
numerically solved by considering prominence conditions. Analytical expressions
of the wavelength and damping length as functions of the kink mode frequency
are obtained in the Thin Tube and Thin Boundary approximations. For typically
reported periods of thread oscillations, resonant absorption is an efficient
mechanism for the kink mode spatial damping, while ion-neutral collisions have
a minor role. Cowling's diffusion dominates both the propagation and damping
for periods much shorter than those observed. Resonant absorption may explain
the observed spatial damping of kink waves in prominence threads. The
transverse inhomogeneity length scale of the threads can be estimated by
comparing the observed wavelengths and damping lengths with the theoretically
predicted values. However, the ignorance of the form of the density profile in
the transversely nonuniform layer introduces inaccuracies in the determination
of the inhomogeneity length scale.
|
1009.4871v1
|
2012-08-01
|
Artificial Neural Network Based Prediction of Optimal Pseudo-Damping and Meta-Damping in Oscillatory Fractional Order Dynamical Systems
|
This paper investigates typical behaviors like damped oscillations in
fractional order (FO) dynamical systems. Such response occurs due to the
presence of, what is conceived as, pseudo-damping and meta-damping in some
special class of FO systems. Here, approximation of such damped oscillation in
FO systems with the conventional notion of integer order damping and time
constant has been carried out using Genetic Algorithm (GA). Next, a multilayer
feed-forward Artificial Neural Network (ANN) has been trained using the GA
based results to predict the optimal pseudo and meta-damping from knowledge of
the maximum order or number of terms in the FO dynamical system.
|
1208.0318v1
|
2012-08-27
|
Optimization of the damped quantum search
|
The damped quantum search proposed in [A. Mizel, Phys. Rev. Lett., 102 150501
(2009)] was analyzed by calculating the highest possible probability of finding
the target state in each iteration. A new damping parameter that depends on the
number of iterations was obtained, this was compared to the critical damping
parameter for different values of target to database size ratio. The result
shows that the range of the new damping parameter as a function of the target
to database size ratio increases as the number of iterations is increased.
Furthermore, application of the new damping parameter per iteration on the
damped quantum search scheme shows a significant improvement on some target to
database size ratio (i.e. greater than or equal to 50% maximum percentage
difference) over the critically damped quantum search.
|
1208.5475v1
|
2013-04-03
|
Damping the zero-point energy of a harmonic oscillator
|
The physics of quantum electromagnetism in an absorbing medium is that of a
field of damped harmonic oscillators. Yet until recently the damped harmonic
oscillator was not treated with the same kind of formalism used to describe
quantum electrodynamics in a arbitrary medium. Here we use the techniques of
macroscopic QED, based on the Huttner--Barnett reservoir, to describe the
quantum mechanics of a damped oscillator. We calculate the thermal and
zero-point energy of the oscillator for a range of damping values from zero to
infinity. While both the thermal and zero-point energies decrease with damping,
the energy stored in the oscillator at fixed temperature increases with
damping, an effect that may be experimentally observable. As the results follow
from canonical quantization, the uncertainty principle is valid for all damping
levels.
|
1304.0977v2
|
2015-05-28
|
Damping factors for head-tail modes at strong space charge
|
This paper suggests how feedback and Landau damping can be taken into account
for transverse oscillations of bunched beam at strong space charge.
|
1505.07704v1
|
2015-06-18
|
Damping of MHD turbulence in partially ionized plasma: implications for cosmic ray propagation
|
We study the damping from neutral-ion collisions of both incompressible and
compressible magnetohydrodynamic (MHD) turbulence in partially ionized medium.
We start from the linear analysis of MHD waves applying both single-fluid and
two-fluid treatments. The damping rates derived from the linear analysis are
then used in determining the damping scales of MHD turbulence. The physical
connection between the damping scale of MHD turbulence and cutoff boundary of
linear MHD waves is investigated. Our analytical results are shown to be
applicable in a variety of partially ionized interstellar medium (ISM) phases
and solar chromosphere. As a significant astrophysical utility, we introduce
damping effects to propagation of cosmic rays in partially ionized ISM. The
important role of turbulence damping in both transit-time damping and
gyroresonance is identified.
|
1506.05585v1
|
2016-02-04
|
Damping Evaluation for Free Vibration of Spherical Structures in Elastodynamic-Acoustic Interaction
|
This paper discusses the free vibration of elastic spherical structures in
the presence of an externally unbounded acoustic medium. In this vibration,
damping associated with the radiation of energy from the confined solid medium
to the surrounding acoustic medium is observed. Evaluating the coupled system
response (solid displacement and acoustic pressure) and characterizing the
acoustic radiation damping in conjunction with the media properties are the
main objectives of this research. In this work, acoustic damping is
demonstrated for two problems: the thin spherical shell and the solid sphere.
The mathematical approach followed in solving these coupled problems is based
on the Laplace transform method. The linear under-damped harmonic oscillator is
the reference model for damping estimation. The damping evaluation is performed
in frequency as well as in time domains; both investigations lead to identical
damping factor expressions.
|
1604.06738v1
|
2017-09-05
|
Enhancement of space-charge induced damping due to reactive impedances for head-tail modes
|
Landau damping of head-tail modes in bunches due to spreads in the tune shift
can be a deciding factor for beam stability. We demonstrate that the coherent
tune shifts due to reactive impedances can enhance the space-charge induced
damping and change the stability thresholds (here, a reactive impedance implies
the imaginary part of the impedance of both signs). For example, high damping
rates at strong space-charge, or damping of the $k=0$ mode, can be possible. It
is shown and explained, how the negative reactive impedances (causing negative
coherent tune shifts similarly to the effect of space-charge) can enhance the
Landau damping, while the positive coherent tune shifts have an opposite
effect. It is shown that the damping rate is a function of the coherent mode
position in the incoherent spectrum, in accordance with the concept of the
interaction of a collective mode with resonant particles. We present an
analytical model, which allows for quantitative predictions of damping
thresholds for different head-tail modes, for arbitrary space-charge and
coherent tune-shift conditions, as it is verified using particle tracking
simulations.
|
1709.01425v1
|
2018-05-21
|
Critical damping in nonviscously damped linear systems
|
In structural dynamics, energy dissipative mechanisms with non-viscous
damping are characterized by their dependence on the time-history of the
response velocity, mathematically represented by convolution integrals
involving hereditary functions. Combination of damping parameters in the
dissipative model can lead the system to be overdamped in some (or all) modes.
In the domain of the damping parameters, the thresholds between induced
oscillatory and non--oscillatory motion are called critical damping surfaces
(or manifolds, since we can have a lot of parameters). In this paper a general
method to obtain critical damping surfaces for nonviscously damped systems is
proposed. The approach is based on transforming the algebraic equations which
defined implicitly the critical curves into a system of differential equations.
The derivations are validated with three numerical methods covering single and
multiple degree of freedom systems.
|
1805.08022v1
|
2018-11-01
|
Hereditary effects of exponentially damped oscillators with past histories
|
Hereditary effects of exponentially damped oscillators with past histories
are considered in this paper. Nonviscously damped oscillators involve
hereditary damping forces which depend on time-histories of vibrating motions
via convolution integrals over exponentially decaying functions. As a result,
this kind of oscillators are said to have memory. In this work, initialization
for nonviscously damped oscillators is firstly proposed. Unlike the classical
viscously damped ones, information of the past history of response velocity is
necessary to fully determine the dynamic behaviors of nonviscously damped
oscillators. Then, initialization response of exponentially damped oscillators
is obtained to characterize the hereditary effects on the dynamic response. At
last, stability of initialization response is proved and the hereditary effects
are shown to gradually recede with increasing of time.
|
1811.00216v1
|
2019-08-01
|
The Temperature-dependent Damping of Propagating Slow Magnetoacoustic Waves
|
The rapid damping of slow magnetoacoustic waves in the solar corona has been
extensively studied in previous years. Most studies suggest that thermal
conduction is a dominant contributor to this damping, albeit with a few
exceptions. Employing extreme-ultraviolet (EUV) imaging data from SDO/AIA, we
measure the damping lengths of propagating slow magnetoacoustic waves observed
in several fan-like loop structures using two independent methods. The
dependence of the damping length on temperature has been studied for the first
time. The results do not indicate any apparent decrease in damping length with
temperature, which is in contrast to the existing viewpoint. Comparing with the
corresponding theoretical values calculated from damping due to thermal
conduction, it is inferred that thermal conduction is suppressed in hotter
loops. An alternative interpretation that suggests thermal conduction is not
the dominant damping mechanism, even for short period waves in warm active
region loops, is also presented.
|
1908.00384v1
|
2019-10-14
|
Decay rates for the damped wave equation with finite regularity damping
|
Decay rates for the energy of solutions of the damped wave equation on the
torus are studied. In particular, damping invariant in one direction and equal
to a sum of squares of nonnegative functions with a particular number of
derivatives of regularity is considered. For such damping energy decays at rate
$1/t^{2/3}$. If additional regularity is assumed the decay rate improves. When
such a damping is smooth the energy decays at $1/t^{4/5-\delta}$. The proof
uses a positive commutator argument and relies on a pseudodifferential calculus
for low regularity symbols.
|
1910.06372v3
|
2022-07-01
|
Seismic Response of Yielding Structures Coupled to Rocking Walls with Supplemental Damping
|
Given that the coupling of a framing structure to a strong, rocking wall
enforces a first-mode response, this paper investigates the dynamic response of
a yielding single-degree-of-freedom oscillator coupled to a rocking wall with
supplemental damping (hysteretic or linear viscous) along its sides. The full
nonlinear equations of motion are derived, and the study presents an earthquake
response analysis in term of inelastic spectra. The study shows that for
structures with preyielding period T1<1.0 s the effect of supplemental damping
along the sides of the rocking wall is marginal even when large values of
damping are used. The study uncovers that occasionally the damped response
matches or exceeds the undamped response; however, when this happens, the
exceedance is marginal. The paper concludes that for yielding structures with
strength less than 10% of their weight the use of supplemental damping along
the sides of a rocking wall coupled to a yielding structure is not recommended.
The paper shows that supplemental damping along the sides of the rocking wall
may have some limited beneficial effects for structures with longer preyielding
periods (say T1>1.0 s). Nevertheless, no notable further response reduction is
observed when larger values of hysteretic or viscous damping are used.
|
2207.00641v1
|
2023-03-08
|
Material-Geometry Interplay in Damping of Biomimetic Scale Beams
|
Biomimetic scale-covered substrates are architected meta-structures
exhibiting fascinating emergent nonlinearities via the geometry of collective
scales contacts. In spite of much progress in understanding their elastic
nonlinearity, their dissipative behavior arising from scales sliding is
relatively uninvestigated in the dynamic regime. Recently discovered is the
phenomena of viscous emergence, where dry Coulomb friction between scales can
lead to apparent viscous damping behavior of the overall multi-material
substrate. In contrast to this structural dissipation, material dissipation
common in many polymers has never been considered, especially synergestically
with geometrical factors. This is addressed here for the first time, where
material visco-elasticity is introduced via a simple Kelvin-Voigt model for
brevity and clarity. The results contrast the two damping sources in these
architectured systems: material viscoelasticity, and geometrical frictional
scales contact. It is discovered that although topically similar in effective
damping, viscoelsatic damping follows a different damping envelope than dry
friction, including starkly different effects on damping symmetry and specific
damping capacity.
|
2303.04920v1
|
1998-03-28
|
Landau damping and the echo effect in a confined Bose-Einstein condensate
|
Low energy collective mode of a confined Bose-Einstein condensate should
demonstrate the echo effect in the regime of Landau damping. This echo is a
signature of reversible nature of Landau damping. General expression for the
echo profile is derived in the limit of small amplitudes of the external
pulses. Several universal features of the echo are found. The existence of echo
in other cases of reversible damping -- Fano effect and Caldeira-Leggett model
-- is emphasized. It is suggested to test reversible nature of the damping in
the atomic traps by conducting the echo experiment.
|
9803351v1
|
2000-07-10
|
Dephasing of Electrons on Helium by Collisions with Gas Atoms
|
The damping of quantum effects in the transport properties of electrons
deposited on a surface of liquid helium is studied. It is found that due to
vertical motion of the helium vapour atoms the interference of paths of
duration $t$ is damped by a factor $\exp - (t/\tau_v)^3$. An expression is
derived for the weak-localization lineshape in the case that damping occurs by
a combination of processes with this type of cubic exponential damping and
processes with a simple exponential damping factor.
|
0007160v1
|
1997-10-07
|
Damping rate of plasmons and photons in a degenerate nonrelativistic plasma
|
A calculation is presented of the plasmon and photon damping rates in a dense
nonrelativistic plasma at zero temperature, following the resummation program
of Braaten-Pisarski. At small soft momentum $k$, the damping is dominated by $3
\to 2$ scattering processes corresponding to double longitudinal Landau
damping. The dampings are proportional to $(\alpha/v_{F})^{3/2} k^2/m$, where
$v_{F}$ is the Fermi velocity.
|
9710260v1
|
2002-12-16
|
Influence of damping on the vanishing of the electro-optic effect in chiral isotropic media
|
Using first principles, it is demonstrated that radiative damping alone
cannot lead to a nonvanishing electro-optic effect in a chiral isotropic
medium. This conclusion is in contrast with that obtained by a calculation in
which damping effects are included using the standard phenomenological model.
We show that these predictions differ because the phenomenological damping
equations are valid only in regions where the frequencies of the applied
electromagnetic fields are nearly resonant with the atomic transitions. We also
show that collisional damping can lead to a nonvanishing electrooptic effect,
but with a strength sufficiently weak that it is unlikely to be observable
under realistic laboratory conditions.
|
0212089v1
|
2005-08-28
|
Simultaneous amplitude and phase damping of a kind of Gaussian states and their separability
|
We give out the time evolution solution of simultaneous amplitude and phase
damping for any continuous variable state. For the simultaneous amplitude and
phase damping of a wide class of two- mode entangled Gaussian states, two
analytical conditions of the separability are given. One is the sufficient
condition of separability. The other is the condition of PPT separability where
the Peres-Horodecki criterion is applied. Between the two conditions there may
exist bound entanglement. The simplest example is the simultaneous amplitude
and phase damping of a two-mode squeezed vacuum state. The damped state is
non-Gaussian.
|
0508209v2
|
2007-05-14
|
Identification of the dominant precession damping mechanism in Fe, Co, and Ni by first-principles calculations
|
The Landau-Lifshitz equation reliably describes magnetization dynamics using
a phenomenological treatment of damping. This paper presents first-principles
calculations of the damping parameters for Fe, Co, and Ni that quantitatively
agree with existing ferromagnetic resonance measurements. This agreement
establishes the dominant damping mechanism for these systems and takes a
significant step toward predicting and tailoring the damping constants of new
materials.
|
0705.1990v1
|
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