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2019-12-13
Distance between Bound Entangled States from Unextendible Product Bases and Separable States
We discuss the use of the Gilbert algorithm to tailor entanglement witnesses for unextendibleproduct basis bound entangled states (UPB BE states). The method relies on the fact that an optimalentanglement witness is given by a plane perpendicular to a line between the reference state, entanglementof which is to be witnessed, and its closest separable state (CSS). The Gilbert algorithm finds anapproximation of CSS. In this article, we investigate if this approximation can be good enough toyield a valid entanglement witness. We compare witnesses found with Gilbert algorithm and those givenby Bandyopadhyay-Ghosh-Roychowdhury (BGR) construction. This comparison allows us to learnabout the amount of entanglement and we find a relationship between it and a feature of the constructionof UPB BE states, namely the size of their central tile. We show that in most studied cases, witnessesfound with the Gilbert algorithm in this work are more optimal than ones obtained by Bandyopadhyay,Ghosh, and Roychowdhury. This result implies the increased tolerance to experimental imperfections ina realization of the state.
1912.06569v2
2020-10-16
Genome organization: experiments and modelling
This is an introduction to the special issue Genome organization: experiments and simulations, published in Chromosome Research, volume 25, issue 1 (2017).
2010.08464v1
2023-10-17
Sparse grid approximation of stochastic parabolic PDEs: The Landau--Lifshitz--Gilbert equation
We show convergence rates for a sparse grid approximation of the distribution of solutions of the stochastic Landau-Lifshitz-Gilbert equation. Beyond being a frequently studied equation in engineering and physics, the stochastic Landau-Lifshitz-Gilbert equation poses many interesting challenges that do not appear simultaneously in previous works on uncertainty quantification: The equation is strongly non-linear, time-dependent, and has a non-convex side constraint. Moreover, the parametrization of the stochastic noise features countably many unbounded parameters and low regularity compared to other elliptic and parabolic problems studied in uncertainty quantification. We use a novel technique to establish uniform holomorphic regularity of the parameter-to-solution map based on a Gronwall-type estimate and the implicit function theorem. This method is very general and based on a set of abstract assumptions. Thus, it can be applied beyond the Landau-Lifshitz-Gilbert equation as well. We demonstrate numerically the feasibility of approximating with sparse grid and show a clear advantage of a multi-level sparse grid scheme.
2310.11225v2
2024-04-04
Resolving Gilbert's Conjecture: Dimensional Dependencies in Hardy Spaces Valued in Clifford Modules
This article provides a thorough investigation into Gilbert's Conjecture, pertaining to Hardy spaces in the upper half-space valued in Clifford modules. We explore the conjecture proposed by Gilbert in 1991, which seeks to extend the classical principle of representing real $L^p$ functions on the real line as boundary values of Hardy holomorphic functions to higher-dimensional Euclidean spaces valued in any Clifford module. We present a complete resolution to this conjecture, demonstrating that its validity is contingent upon the dimension $n$, specifically holding true when \(n \not\equiv 6, 7 \mod 8\) and failing otherwise. The pivotal discovery that Gilbert's conjecture can be reformulated as a set of algebraic conditions is underscored in this work. To navigate these conditions, we employ a novel strategy that leverages the octonions, revealing their instrumental role in addressing issues related to Clifford modules and spinors. This innovative approach not only provides explicit realization through the generalization of the Hilbert transform to the Riesz transform but also establishes a significant advancement in the understanding of Hardy spaces within higher dimensions.
2404.03478v1
1998-02-23
Shell Effects on Rotational Damping in Superdeformed Nuclei
Damping of rotational motion in superdeformed Hg and Dy-region nuclei is studied by means of cranked shell model diagonalization. It is shown that a shell oscillation in single-particle alignments affects significantly properties of rotational damping. Onset properties of damping and damping width for Hg are quite different from those for Dy-region superdeformed nuclei.
9802065v1
2003-08-29
Influence of radiative damping on the optical-frequency susceptibility
Motivated by recent discussions concerning the manner in which damping appears in the electric polarizability, we show that (a) there is a dependence of the nonresonant contribution on the damping and that (b) the damping enters according to the "opposite sign prescription." We also discuss the related question of how the damping rates in the polarizability are related to energy-level decay rates.
0309001v1
2024-03-19
Weakly elliptic damping gives sharp decay
We prove that weakly elliptic damping gives sharp energy decay for the abstract damped wave semigroup, where the damping is not in the functional calculus. In this case, there is no overdamping. We show applications in linearised water waves and Kelvin--Voigt damping.
2403.13067v1
2015-05-15
Reliable Damping of Free Surface Waves in Numerical Simulations
This paper generalizes existing approaches for free-surface wave damping via momentum sinks for flow simulations based on the Navier-Stokes equations. It is shown in 2D flow simulations that, to obtain reliable wave damping, the coefficients in the damping functions must be adjusted to the wave parameters. A scaling law for selecting these damping coefficients is presented, which enables similarity of the damping in model- and full-scale. The influence of the thickness of the damping layer, the wave steepness, the mesh fineness and the choice of the damping coefficients are examined. An efficient approach for estimating the optimal damping setup is presented. Results of 3D ship resistance computations show that the scaling laws apply to such simulations as well, so the damping coefficients should be adjusted for every simulation to ensure convergence of the solution in both model and full scale. Finally, practical recommendations for the setup of reliable damping in flow simulations with regular and irregular free surface waves are given.
1505.04087v2
2019-02-25
Resonant absorption as a damping mechanism for the transverse oscillations of the coronal loops observed by SDO/AIA
Solar coronal loops represent the variety of fast, intermediate, and slow normal mode oscillations. In this study, the transverse oscillations of the loops with a few-minutes period and also with damping caused by the resonant absorption were analyzed using extreme ultraviolet (EUV) images of the Sun. We employed the 171 $\AA$ data recorded by Solar Dynamic Observatory (SDO)/Atmospheric Imaging Assembly (AIA) to analyze the parameters of coronal loop oscillations such as period, damping time, loop length, and loop width. For the loop observed on 11 October 2013, the period and the damping of this loop are obtained to be 19 and 70 minutes, respectively. The damping quality, the ratio of the damping time to the period, is computed about 3.6. The period and damping time for the extracted loop recorded on 22 January 2013 are about 81 and 6.79 minutes, respectively. The damping quality is also computed as 12. It can be concluded that the damping of the transverse oscillations of the loops is in the strong damping regime, so resonant absorption would be the main reason for the damping.
1902.09649v1
2013-05-21
Characterization and Synthesis of Rayleigh Damped Elastodynamic Networks
We consider damped elastodynamic networks where the damping matrix is assumed to be a non-negative linear combination of the stiffness and mass matrices (also known as Rayleigh or proportional damping). We give here a characterization of the frequency response of such networks. We also answer the synthesis question for such networks, i.e., how to construct a Rayleigh damped elastodynamic network with a given frequency response. Our analysis shows that not all damped elastodynamic networks can be realized when the proportionality constants between the damping matrix and the mass and stiffness matrices are fixed.
1305.4961v1
2016-08-08
Damping Functions correct over-dissipation of the Smagorinsky Model
This paper studies the time-averaged energy dissipation rate $\langle \varepsilon_{SMD} (u)\rangle$ for the combination of the Smagorinsky model and damping function. The Smagorinsky model is well known to over-damp. One common correction is to include damping functions that reduce the effects of model viscosity near walls. Mathematical analysis is given here that allows evaluation of $\langle \varepsilon_{SMD} (u)\rangle $ for any damping function. Moreover, the analysis motivates a modified van Driest damping. It is proven that the combination of the Smagorinsky with this modified damping function does not over dissipate and is also consistent with Kolmogorov phenomenology.
1608.02655v2
2012-01-27
Full and Half Gilbert Tessellations with Rectangular Cells
We investigate the ray-length distributions for two different rectangular versions of Gilbert's tessellation. In the full rectangular version, lines extend either horizontally (with east- and west-growing rays) or vertically (north- and south-growing rays) from seed points which form a Poisson point process, each ray stopping when another ray is met. In the half rectangular version, east and south growing rays do not interact with west and north rays. For the half rectangular tessellation we compute analytically, via recursion, a series expansion for the ray-length distribution, whilst for the full rectangular version we develop an accurate simulation technique, based in part on the stopping-set theory of Zuyev, to accomplish the same. We demonstrate the remarkable fact that plots of the two distributions appear to be identical when the intensity of seeds in the half model is twice that in the full model. Our paper explores this coincidence mindful of the fact that, for one model, our results are from a simulation (with inherent sampling error). We go on to develop further analytic theory for the half-Gilbert model using stopping-set ideas once again, with some novel features. Using our theory, we obtain exact expressions for the first and second moment of ray length in the half-Gilbert model. For all practical purposes, these results can be applied to the full-Gilbert model as much better approximations than those provided by Mackissack and Miles.
1201.5780v1
2021-06-08
On numerical aspects of parameter identification for the Landau-Lifshitz-Gilbert equation in Magnetic Particle Imaging
The Landau-Lifshitz-Gilbert equation yields a mathematical model to describe the evolution of the magnetization of a magnetic material, particularly in response to an external applied magnetic field. It allows one to take into account various physical effects, such as the exchange within the magnetic material itself. In particular, the Landau-Lifshitz-Gilbert equation encodes relaxation effects, i.e., it describes the time-delayed alignment of the magnetization field with an external magnetic field. These relaxation effects are an important aspect in magnetic particle imaging, particularly in the calibration process. In this article, we address the data-driven modeling of the system function in magnetic particle imaging, where the Landau-Lifshitz-Gilbert equation serves as the basic tool to include relaxation effects in the model. We formulate the respective parameter identification problem both in the all-at-once and the reduced setting, present reconstruction algorithms that yield a regularized solution and discuss numerical experiments. Apart from that, we propose a practical numerical solver to the nonlinear Landau-Lifshitz-Gilbert equation, not via the classical finite element method, but through solving only linear PDEs in an inverse problem framework.
2106.07625v1
2000-09-11
Numerical Studies on Locally Damped Structures
In the JLC/NLC X-band linear collider, it is essential to reduce the long-range dipole wakefields in the accelerator structure to prevent beam break up (BBU) and emittance degradation. The two methods of reducing the long-range wakefields are detuning and damping. Detuning reduces the wakefields rapidly as the dipole modes de-cohere but, with a finite number of modes, the wakefield will grow again as the modes re-cohere. In contrast, damping suppresses the wakefields at a longer distance. There are two principal damping schemes: synchronous damping using HOM manifolds such as that used in the RDDS1 structure and local damping similar to that used in the CLIC structure. In a locally damped scheme, one can obtain almost any Q value, however, the damping can have significant effects on the accelerating mode. In this paper, we present a medium local-damping scheme where the wakefields are controlled to meet the BBU requirement while minimizing the degradations of the fundamental rf parameters. We will address the load design and pulse heating issues associated with the medium damping scheme.
0009039v1
2015-03-13
A one-step optimal energy decay formula for indirectly nonlinearly damped hyperbolic systems coupled by velocities
In this paper, we consider the energy decay of a damped hyperbolic system of wave-wave type which is coupled through the velocities. We are interested in the asymptotic properties of the solutions of this system in the case of indirect nonlinear damping, i.e. when only one equation is directly damped by a nonlinear damping. We prove that the total energy of the whole system decays as fast as the damped single equation. Moreover, we give a one-step general explicit decay formula for arbitrary nonlinearity. Our results shows that the damping properties are fully transferred from the damped equation to the undamped one by the coupling in velocities, different from the case of couplings through displacements as shown in \cite{AB01, ACK01, AB02, AL12} for the linear damping case, and in \cite{AB07} for the nonlinear damping case. The proofs of our results are based on multiplier techniques, weighted nonlinear integral inequalities and the optimal-weight convexity method of \cite{AB05, AB10}.
1503.04126v1
2015-08-21
Radiative damping in wave guide based FMR measured via analysis of perpendicular standing spin waves in sputtered Permalloy films
The damping $\alpha$ of the spinwave resonances in 75 nm, 120 nm, and 200nm -thick Permalloy films is measured via vector-network-analyzer ferromagnetic-resonance (VNA-FMR) in the out-of-plane geometry. Inductive coupling between the sample and the waveguide leads to an additional radiative damping term. The radiative contribution to the over-all damping is determined by measuring perpendicular standing spin waves (PSSWs) in the Permalloy films, and the results are compared to a simple analytical model. The damping of the PSSWs can be fully explained by three contributions to the damping: The intrinsic damping, the eddy-current damping, and the radiative damping. No other contributions were observed. Furthermore, a method to determine the radiative damping in FMR measurements with a single resonance is suggested.
1508.05265v1
2022-09-28
Tunable nonlinear damping in parametric regime
Nonlinear damping plays a significant role in several area of physics and it is becoming increasingly important to understand its underlying mechanism. However, microscopic origin of nonlinear damping is still a debatable topic. Here, we probe and report nonlinear damping in a highly tunable MoS2 nano mechanical drum resonator using electrical homodyne actuation and detection technique. In our experiment, we achieve 2:1 internal resonance by tuning resonance frequency and observe enhanced non-linear damping. We probe the effect of non-linear damping by characterizing parametric gain. Geometry and tunability of the device allow us to reduce the effect of other prominent Duffing non-linearity to probe the non-linear damping effectively. The enhanced non-linear damping in the vicinity of internal resonance is also observed in direct drive, supporting possible origin of non-linear damping. Our experiment demonstrates, a highly tunable 2D material based nanoresonator offers an excellent platform to study the nonlinear physics and exploit nonlinear damping in parametric regime.
2209.14120v1
2005-11-07
The Effects of Alfven Waves and Radiation Pressure in Dusty Winds of Late-Type Stars. II. Dust-Cyclotron Damping
There are in the literature several theories to explain the mass loss in stellar winds. In particular, for late-type stars, some authors have proposed a wind model driven by an outward-directed flux of damped Alfven waves. The winds of these stars present great amounts of dust particles that, if charged, can give rise to new wave modes or modify the pre-existing ones. In this work, we study how the dust can affect the propagation of Alfven waves in these winds taking into account a specific damping mechanism, dust-cyclotron damping. This damping affects the Alfven wave propagation near the dust-cyclotron frequency. Hence, if we assume a dust size distribution, the damping occurs over a broad band of wave frequencies. In this work, we present a model of Alfven wave-driven winds using the dust-cyclotron damping mechanism. On the basis of coronal holes in the Sun, which present a superradial expansion, our model also assumes a diverging geometry for the magnetic field. Thus, the mass, momentum, and energy equations are obtained and then solved in a self-consistent approach. Our results of wind velocity and temperature profiles for a typical K5 supergiant star shows compatibility with observations. We also show that, considering the presence of charged dust particles, the wave flux is less damped due to the dust-cyclotron damping than it would be if we consider some other damping mechanisms studied in the literature, such as nonlinear damping, resonant surface damping, and turbulent damping.
0511192v2
2013-09-11
Initial versus tangent stiffness-based Rayleigh damping in inelastic time history seismic analyses
In the inelastic time history analyses of structures in seismic motion, part of the seismic energy that is imparted to the structure is absorbed by the inelastic structural model, and Rayleigh damping is commonly used in practice as an additional energy dissipation source. It has been acknowledged that Rayleigh damping models lack physical consistency and that, in turn, it must be carefully used to avoid encountering unintended consequences as the appearance of artificial damping. There are concerns raised by the mass proportional part of Rayleigh damping, but they are not considered in this paper. As far as the stiffness proportional part of Rayleigh damping is concerned, either the initial structural stiffness or the updated tangent stiffness can be used. The objective of this paper is to provide a comprehensive comparison of these two types of Rayleigh damping models so that a practitioner (i) can objectively choose the type of Rayleigh damping model that best fits her/his needs and (ii) is provided with useful analytical tools to design Rayleigh damping model with good control on the damping ratios throughout inelastic analysis. To that end, a review of the literature dedicated to Rayleigh damping within these last two decades is first presented; then, practical tools to control the modal damping ratios throughout the time history analysis are developed; a simple example is finally used to illustrate the differences resulting from the use of either initial or tangent stiffness-based Rayleigh damping model.
1309.2741v1
2017-07-14
Damping of gravitational waves by matter
We develop a unified description, via the Boltzmann equation, of damping of gravitational waves by matter, incorporating collisions. We identify two physically distinct damping mechanisms -- collisional and Landau damping. We first consider damping in flat spacetime, and then generalize the results to allow for cosmological expansion. In the first regime, maximal collisional damping of a gravitational wave, independent of the details of the collisions in the matter is, as we show, significant only when its wavelength is comparable to the size of the horizon. Thus damping by intergalactic or interstellar matter for all but primordial gravitational radiation can be neglected. Although collisions in matter lead to a shear viscosity, they also act to erase anisotropic stresses, thus suppressing the damping of gravitational waves. Damping of primordial gravitational waves remains possible. We generalize Weinberg's calculation of gravitational wave damping, now including collisions and particles of finite mass, and interpret the collisionless limit in terms of Landau damping. While Landau damping of gravitational waves cannot occur in flat spacetime, the expansion of the universe allows such damping by spreading the frequency of a gravitational wave of given wavevector.
1707.05192v2
2024-03-13
The q-ary Gilbert-Varshamov bound can be improved for all but finitely many positive integers q
For any positive integer $q\geq 2$ and any real number $\delta\in(0,1)$, let $\alpha_q(n,\delta n)$ denote the maximum size of a subset of $\mathbb{Z}_q^n$ with minimum Hamming distance at least $\delta n$, where $\mathbb{Z}_q=\{0,1,\dotsc,q-1\}$ and $n\in\mathbb{N}$. The asymptotic rate function is defined by $ R_q(\delta) = \limsup_{n\rightarrow\infty}\frac{1}{n}\log_q\alpha_q(n,\delta n).$ The famous $q$-ary asymptotic Gilbert-Varshamov bound, obtained in the 1950s, states that \[ R_q(\delta) \geq 1 - \delta\log_q(q-1)-\delta\log_q\frac{1}{\delta}-(1-\delta)\log_q\frac{1}{1-\delta} \stackrel{\mathrm{def}}{=}R_\mathrm{GV}(\delta,q) \] for all positive integers $q\geq 2$ and $0<\delta<1-q^{-1}$. In the case that $q$ is an even power of a prime with $q\geq 49$, the $q$-ary Gilbert-Varshamov bound was firstly improved by using algebraic geometry codes in the works of Tsfasman, Vladut, and Zink and of Ihara in the 1980s. These algebraic geometry codes have been modified to improve the $q$-ary Gilbert-Varshamov bound $R_\mathrm{GV}(\delta,q)$ at a specific tangent point $\delta=\delta_0\in (0,1)$ of the curve $R_\mathrm{GV}(\delta,q)$ for each given integer $q\geq 46$. However, the $q$-ary Gilbert-Varshamov bound $R_\mathrm{GV}(\delta,q)$ at $\delta=1/2$, i.e., $R_\mathrm{GV}(1/2,q)$, remains the largest known lower bound of $R_q(1/2)$ for infinitely many positive integers $q$ which is a generic prime and which is a generic non-prime-power integer. In this paper, by using codes from geometry of numbers introduced by Lenstra in the 1980s, we prove that the $q$-ary Gilbert-Varshamov bound $R_\mathrm{GV}(\delta,q)$ with $\delta\in(0,1)$ can be improved for all but finitely many positive integers $q$. It is shown that the growth defined by $\eta(\delta)= \liminf_{q\rightarrow\infty}\frac{1}{\log q}\log[1-\delta-R_q(\delta)]^{-1}$ for every $\delta\in(0,1)$ has actually a nontrivial lower bound.
2403.08727v2
2002-06-27
Initial-amplitude dependence in weakly damped oscillators
A pedagogically instructive experimental procedure is suggested for distinguishing between different damping terms in a weakly damped oscillator, which highclights the connection between non-linear damping and initial-amplitude dependence. The most common damping terms such as contact friction, air resistance, viscous drag, and electromagnetic damping have velocity dependences of the form constant, v, or v^2. The corresponding energy dependences of the form \sqrt{E}, E, or E\sqrt{E} in the energy loss equation give rise to characteristic dependence of the amplitude decay slope on the initial amplitude.
0206086v1
2006-05-22
The entanglement of damped noon-state and its performance in phase measurement
The state evolution of the initial optical \textit{noon} state is investigated. The residue entanglement of the state is calculated after it is damped by amplitude and phase damping. The relative entropy of entanglement of the damped state is exactly obtained. The performance of direct application of the damped \textit{noon} state is compared with that of firstly distilling the docoherence damped state then applying it in measurement.
0605184v1
2007-10-04
Channel-Adapted Quantum Error Correction for the Amplitude Damping Channel
We consider error correction procedures designed specifically for the amplitude damping channel. We analyze amplitude damping errors in the stabilizer formalism. This analysis allows a generalization of the [4,1] `approximate' amplitude damping code of quant-ph/9704002. We present this generalization as a class of [2(M+1),M] codes and present quantum circuits for encoding and recovery operations. We also present a [7,3] amplitude damping code based on the classical Hamming code. All of these are stabilizer codes whose encoding and recovery operations can be completely described with Clifford group operations. Finally, we describe optimization options in which recovery operations may be further adapted according to the damping probability gamma.
0710.1052v1
2010-03-24
Dynamical shift condition for unequal mass black hole binaries
Certain numerical frameworks used for the evolution of binary black holes make use of a gamma driver, which includes a damping factor. Such simulations typically use a constant value for damping. However, it has been found that very specific values of the damping factor are needed for the calculation of unequal mass binaries. We examine carefully the role this damping plays, and provide two explicit, non-constant forms for the damping to be used with mass-ratios further from one. Our analysis of the resultant waveforms compares well against the constant damping case.
1003.4681v1
2011-11-30
Local phase damping of single qubits sets an upper bound on the phase damping rate of entangled states
I derive an inequality in which the phase damping rates of single qubits set an upper bound for the phase damping rate of entangled states of many qubits. The derivation is based on two assumptions: first, that the phase damping can be described by a dissipator in Lindblad form and, second, that the phase damping preserves the population of qubit states in a given basis.
1111.7152v2
2012-05-11
Quantum dynamics of the damped harmonic oscillator
The quantum theory of the damped harmonic oscillator has been a subject of continual investigation since the 1930s. The obstacle to quantization created by the dissipation of energy is usually dealt with by including a discrete set of additional harmonic oscillators as a reservoir. But a discrete reservoir cannot directly yield dynamics such as Ohmic damping (proportional to velocity) of the oscillator of interest. By using a continuum of oscillators as a reservoir, we canonically quantize the harmonic oscillator with Ohmic damping and also with general damping behaviour. The dynamics of a damped oscillator is determined by an arbitrary effective susceptibility that obeys Kramers-Kronig relations. This approach offers an alternative description of nano-mechanical oscillators and opto-mechanical systems.
1205.2545v1
2014-02-28
Escape rate for the power-law distribution in low-to-intermediate damping
Escape rate in the low-to-intermediate damping connecting the low damping with the intermediate damping is established for the power-law distribution on the basis of flux over population theory. We extend the escape rate in the low damping to the low-to-intermediate damping, and get an expression for the power-law distribution. Then we apply the escape rate for the power-law distribution to the experimental study of the excited-state isomerization, and show a good agreement with the experimental value. The extra current and the improvement of the absorbing boundary condition are discussed.
1402.7194v2
2015-03-21
On damping created by heterogeneous yielding in the numerical analysis of nonlinear reinforced concrete frame elements
In the dynamic analysis of structural engineering systems, it is common practice to introduce damping models to reproduce experimentally observed features. These models, for instance Rayleigh damping, account for the damping sources in the system altogether and often lack physical basis. We report on an alternative path for reproducing damping coming from material nonlinear response through the consideration of the heterogeneous character of material mechanical properties. The parameterization of that heterogeneity is performed through a stochastic model. It is shown that such a variability creates the patterns in the concrete cyclic response that are classically regarded as source of damping.
1503.07122v1
2016-01-20
Introduction to Landau Damping
The mechanism of Landau damping is observed in various systems from plasma oscillations to accelerators. Despite its widespread use, some confusion has been created, partly because of the different mechanisms producing the damping but also due to the mathematical subtleties treating the effects. In this article the origin of Landau damping is demonstrated for the damping of plasma oscillations. In the second part it is applied to the damping of coherent oscillations in particle accelerators. The physical origin, the mathematical treatment leading to the concept of stability diagrams and the applications are discussed.
1601.05227v1
2018-07-25
Regularity and asymptotic behaviour for a damped plate-membrane transmission problem
We consider a transmission problem where a structurally damped plate equation is coupled with a damped or undamped wave equation by transmission conditions. We show that exponential stability holds in the damped-damped situation and polynomial stability (but no exponential stability) holds in the damped-undamped case. Additionally, we show that the solutions first defined by the weak formulation, in fact have higher Sobolev space regularity.
1807.09730v1
2021-08-04
Nonlinear fluid damping of elastically mounted pitching wings in quiescent water
We experimentally study the nonlinear fluid damping of a rigid but elastically mounted pitching wing in the absence of a freestream flow. The dynamics of the elastic mount are simulated using a cyber-physical system. We perturb the wing and measure the fluid damping coefficient from damped oscillations over a large range of pitching frequencies, pitching amplitudes, pivot locations and sweep angles. A universal fluid damping scaling is proposed to incorporate all these parameters. Flow fields obtained using particle image velocimetry are analyzed to explain the nonlinear behaviors of the fluid damping.
2108.02090v1
2002-11-03
Damping of coupled phonon--plasmon modes
The effect of free carriers on dispersion and damping of coupled phonon-plasmon modes is considered in the long-wave approximation. The electron and phonon scattering rate as well as Landau damping are taken into account.
0211040v1
2002-02-01
On "the authentic damping mechanism" of the phonon damping model
Some general features of the phonon damping model are presented. It is concluded that the fits performed within this model have no physical content.
0202006v1
2010-12-20
Global attractors for the one dimensional wave equation with displacement dependent damping
We study the long-time behavior of solutions of the one dimensional wave equation with nonlinear damping coefficient. We prove that if the damping coefficient function is strictly positive near the origin then this equation possesses a global attractor.
1012.4455v1
2018-01-28
Observations of excitation and damping of transversal oscillation in coronal loops by AIA/SDO
The excitation and damping of transversal coronal loop oscillations and quantitative relation between damping time, damping quality (damping time per period), oscillation amplitude, dissipation mechanism and the wake phenomena are investigated. The observed time series data with the \textit{Atmospheric Imaging Assembly} (AIA) telescope on NASA's \textit{Solar Dynamics Observatory} (SDO) satellite on 2015 March 2, consisting of 400 consecutive images with 12 seconds cadence in the 171 $ \rm{{\AA}}$ pass band is analyzed for evidence of transversal oscillations along the coronal loops by Lomb-Scargle periodgram. In this analysis signatures of transversal coronal loop oscillations that are damped rapidly were found with dominant oscillation periods in the range of $\rm{P=12.25-15.80}$ minutes. Also, damping times and damping qualities of transversal coronal loop oscillations at dominant oscillation periods are estimated in the range of $ \rm{\tau_d=11.76-21.46}$ minutes and $ \rm{\tau_d/P=0.86-1.49}$, respectively. The observational results of this analysis show that damping qualities decrease slowly with increasing the amplitude of oscillation, but periods of oscillations are not sensitive function of amplitude of oscillations. The order of magnitude of the damping qualities and damping times are in good agreement with previous findings and the theoretical prediction for damping of kink mode oscillations by dissipation mechanism. Furthermore, oscillation of loop segments attenuate with time roughly as $t^{-\alpha}$ that magnitude values of $\alpha$ for 30 different segments change from 0.51 to 0.75.
1801.09217v1
1999-11-16
Probing supernovae ejecta by Halpha damping wings
It is predicted that H$\alpha$ emission line at the early nebular epoch of type II-P supernovae may display robust observational effects of damping wings. This is illustrated by Monte-Carlo simulations. The strength of damping wing effects may be used to constrain parameters of the line-emitting zone. An anomalous redshift, width and red wing of H$\alpha$ revealed by SN 1997D on day 150 are explained in terms of damping wing effects.
9911300v1
2009-01-23
Rheological Interpretation of Rayleigh Damping
Damping is defined through various terms such as energy loss per cycle (for cyclic tests), logarithmic decrement (for vibration tests), complex modulus, rise-time or spectrum ratio (for wave propagation analysis), etc. For numerical modeling purposes, another type of damping is frequently used : it is called Rayleigh damping. It is a very convenient way of accounting for damping in numerical models, although the physical or rheological meaning of this approach is not clear. A rheological model is proposed to be related to classical Rayleigh damping : it is a generalized Maxwell model with three parameters. For moderate damping (<25%), this model perfectly coincide with Rayleigh damping approach since internal friction has the same expression in both cases and dispersive phenomena are negligible. This is illustrated by finite element (Rayleigh damping) and analytical (generalized Maxwell model) results in a simple one-dimensional case.
0901.3717v1
2009-05-20
Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation
We determine the general form of the asymptotics for Dirichlet eigenvalues of the one-dimensional linear damped wave operator. As a consequence, we obtain that given a spectrum corresponding to a constant damping term this determines the damping term in a unique fashion. We also derive a trace formula for this problem.
0905.3242v1
2015-05-06
Remarks on the asymptotic behavior of the solution of an abstract damped wave equation
We study an abstract damped wave equation. We prove that the solution of the damped wave equation becomes closer to the solution of a heat type equation as time tend to infinity. As an application of our approach, we also study the asymptotic behavior of the damped wave equation in Euclidean space under the geometric control condition.
1505.01794v2
2017-01-18
Two types of spurious damping forces potentially modeled in numerical seismic nonlinear response history analysis
The purpose of this paper is to provide practitioners with further insight into spurious damping forces that can be generated in nonlinear seismic response history analyses (RHA). The term 'spurious' is used to refer to damping forces that are not present in an elastic system and appear as nonlinearities develop: such damping forces are not necessarily intended and appear as a result of modifications in the structural properties as it yields or damages due to the seismic action. In this paper, two types of spurious damping forces are characterized. Each type has often been treated separately in the literature, but each has been qualified as 'spurious', somehow blurring their differences. Consequently, in an effort to clarify the consequences of choosing a particular viscous damping model for nonlinear RHA, this paper shows that damping models that avoid spurious damping forces of one type do not necessarily avoid damping forces of the other type.
1701.05092v1
2017-02-02
Exponential stability for a coupled system of damped-undamped plate equations
We consider the transmission problem for a coupled system of undamped and structurally damped plate equations in two sufficiently smooth and bounded subdomains. It is shown that, independently of the size of the damped part, the damping is strong enough to produce uniform exponential decay of the energy of the coupled system.
1702.00637v1
2017-09-11
Comparison of damping mechanisms for transverse waves in solar coronal loops
We present a method to assess the plausibility of alternative mechanisms to explain the damping of magnetohydrodynamic (MHD) transverse waves in solar coronal loops. The considered mechanisms are resonant absorption of kink waves in the Alfv\'en continuum, phase-mixing of Alfv\'en waves, and wave leakage. Our methods make use of Bayesian inference and model comparison techniques. We first infer the values for the physical parameters that control the wave damping, under the assumption of a particular mechanism, for typically observed damping time-scales. Then, the computation of marginal likelihoods and Bayes factors enable us to quantify the relative plausibility between the alternative mechanisms. We find that, in general, the evidence is not large enough to support a single particular damping mechanism as the most plausible one. Resonant absorption and wave leakage offer the most probable explanations in strong damping regimes, while phase mixing is the best candidate for weak/moderate damping. When applied to a selection of 89 observed transverse loop oscillations, with their corresponding measurements of damping times scales and taking into account data uncertainties, we find that only in a few cases positive evidence for a given damping mechanism is available.
1709.03347v1
2019-03-25
Distributed Inter-Area Oscillation Damping Control for Power Systems by Using Wind Generators and Load Aggregators
This paper investigates the potential of wind turbine generators (WTGs) and load aggregators (LAs) to provide supplementary damping control services for low frequency inter-area oscillations (LFOs) through the additional distributed damping control units (DCUs) proposed in their controllers. In order to provide a scalable methodology for the increasing number of WTGs and LAs, a novel distributed control framework is proposed to coordinate damping controllers. Firstly, a distributed algorithm is designed to reconstruct the system Jacobian matrix for each damping bus (buses with damping controllers). Thus, the critical LFO can be identified locally at each damping bus by applying eigen-analysis to the obtained system Jacobian matrix. Then, if the damping ratio of the critical LFO is less than a preset threshold, the control parameters of DCUs will be tuned in a distributed and coordinated manner to improve the damping ratio and minimize the total control cost at the same time. The proposed control framework is tested in a modified IEEE 39-bus test system. The simulation results with and without the proposed control framework are compared to demonstrate the effectiveness of the proposed framework.
1903.10135v1
2019-08-19
Spectral determinant for the damped wave equation on an interval
We evaluate the spectral determinant for the damped wave equation on an interval of length $T$ with Dirichlet boundary conditions, proving that it does not depend on the damping. This is achieved by analysing the square of the damped wave operator using the general result by Burghelea, Friedlander, and Kappeler on the determinant for a differential operator with matrix coefficients.
1908.06862v1
2020-10-12
Decays rates for Kelvin-Voigt damped wave equations II: the geometric control condition
We study in this article decay rates for Kelvin-Voigt damped wave equations under a geometric control condition. We prove that when the damping coefficient is sufficiently smooth ($C^1$ vanishing nicely) we show that exponential decay follows from geometric control conditions (see~\cite{BuCh, Te12} for similar results under stronger assumptions on the damping function).
2010.05614v2
2020-12-05
On Periodical Damping Ratio of a Controlled Dynamical System with Parametric Resonances
This report provides an interpretation on the periodically varying damping ratio of a dynamical system with direct control of oscillation or vibration damping. The principal parametric resonance of the system and a new type of parametric resonance, named "zero-th order" parametric resonance, are investigated by using the method of multiple scales to find approximate, analytical solutions of the system, which provide an interpretation on such damping variations.
2012.02932v1
2021-06-09
Grammage of cosmic rays in the proximity of supernova remnants embedded in a partially ionized medium
We investigate the damping of Alfv\'en waves generated by the cosmic ray resonant streaming instability in the context of the cosmic ray escape and propagation in the proximity of supernova remnants. We consider ion-neutral damping, turbulent damping and non linear Landau damping in the warm ionized and warm neutral phases of the interstellar medium. For the ion-neutral damping, up-to-date damping coefficients are used. We investigate in particular whether the self-confinement of cosmic rays nearby sources can appreciably affect the grammage. We show that the ion-neutral damping and the turbulent damping effectively limit the residence time of cosmic rays in the source proximity, so that the grammage accumulated near sources is found to be negligible. Contrary to previous results, this also happens in the most extreme scenario where ion-neutral damping is less effective, namely in a medium with only neutral helium and fully ionized hydrogen. Therefore, the standard picture, in which CR secondaries are produced during the whole time spent by cosmic rays throughout the Galactic disk, need not to be deeply revisited.
2106.04948v1
2021-06-22
Sharp decay rate for the damped wave equation with convex-shaped damping
We revisit the damped wave equation on two-dimensional torus where the damped region does not satisfy the geometric control condition. We show that if the damping vanishes as a H\"older function $|x|^{\beta}$, and in addition, the boundary of the damped region is strictly convex, the wave is stable at rate $t^{-1+\frac{2}{2\beta+7}}$, which is better than the known optimal decay rate $t^{-1+\frac{1}{\beta+3}}$ for strip-shaped dampings of the same H\"older regularity. Moreover, we show by example that the decay rate is optimal. This illustrates the fact that the energy decay rate depends not only on the order of vanishing of the damping, but also on the shape of the damped region. The main ingredient of the proof is the averaging method (normal form reduction) developed by Hitrick and Sj\"ostrand (\cite{Hi1}\cite{Sj}).
2106.11782v3
2021-08-09
Effect of stepwise adjustment of Damping factor upon PageRank
The effect of adjusting damping factor {\alpha}, from a small initial value {\alpha}0 to the final desired {\alpha}f value, upon then iterations needed for PageRank computation is observed. Adjustment of the damping factor is done in one or more steps. Results show no improvement in performance over a fixed damping factor based PageRank.
2108.04150v1
2021-08-17
Asymptotic behaviour of the wave equation with nonlocal weak damping, anti-damping and critical nonlinearity
In this paper we prove the existence of the global attractor for the wave equation with nonlocal weak damping, nonlocal anti-damping and critical nonlinearity.
2108.07395v2
2023-02-23
Buckling Metamaterials for Extreme Vibration Damping
Damping mechanical resonances is a formidable challenge in an increasing number of applications. Many of the passive damping methods rely on using low stiffness dissipative elements, complex mechanical structures or electrical systems, while active vibration damping systems typically add an additional layer of complexity. However, in many cases, the reduced stiffness or additional complexity and mass render these vibration damping methods unfeasible. Here, we introduce a method for passive vibration damping by allowing buckling of the primary load path, which sets an upper limit for vibration transmission: the transmitted acceleration saturates at a maximum value, no matter what the input acceleration is. This nonlinear mechanism leads to an extreme damping coefficient tan delta ~0.23 in our metal metamaterial|orders of magnitude larger than the linear damping of traditional lightweight structural materials. We demonstrate this principle experimentally and numerically in free-standing rubber and metal mechanical metamaterials over a range of accelerations, and show that bi-directional buckling can further improve its performance. Buckling metamaterials pave the way towards extreme vibration damping without mass or stiffness penalty, and as such could be applicable in a multitude of high-tech applications, including aerospace structures, vehicles and sensitive instruments.
2302.11968v1
1997-11-20
Symmetric matrices and quantum codes
This paper has been withdrawn since a Gilbert-Varshamov bound for general quantum codes has already appeared in Ekert and Macchiavello, Prys. Rev. Lett. 77, p. 2585, and a Gilbert-Varshamov bound for stabilizer codes connected with orthogonal geometry, or equivalently, with symmetric matrices as in this paper, has been proved by Calredbank, Rains, Shor and Sloane, Phys. Rev. Lett. 78, p. 405. I would like to thank Robert Calderbank for pointing out these references to me.
9711026v2
1994-06-09
Black Holes from Blue Spectra
Blue primordial power spectra with a spectral index $n>1$ can lead to a significant production of primordial black holes in the very early Universe. The evaporation of these objects leads to a number of observational consequences and a model independent upper limit of $n \approx 1.4$. In some cases this limit is strengthened to $n=1.3$. Such limits may be employed to define the boundary to the region of parameter space consistent with generalized inflationary predictions. [To appear in Proceedings of the CASE WESTERN CMB WORKSHOP, April 22-24 1994. Figures available on request from J.H.Gilbert@qmw.ac.uk]
9406028v1
1995-06-14
Inversions in astronomy and the SOLA method
This paper was presented at the Institute for Mathematics and its Applications workshop "Inverse problems in wave propagation" and will appear in the series IMA volumes (Springer). A brief overview of applications of inversions within astronomy is presented and also an inventory of techniques commonly in use. Most of this paper is focussed on the method of Subtractive Optimally Localized Averages (SOLA) which is an adaptation of the Backus and Gilbert method. This method was originally developed for use in helioseismology where the Backus and Gilbert method is computationally too slow. Since then it has also been applied to the problem of reverberation mapping of active galactic nuclei and the differences between this inverse problem and the ones of helioseismology are also discussed.
9506084v1
1997-11-11
No Need for MACHOS in the Halo
A simple interpretation of the more than dozen microlensing events seen in the direction of the LMC is a halo population of MACHOs which accounts for about half of the mass of the Galaxy. Such an interpretation is not without its problems, and we show that current microlensing data can, with some advantage, be explained by dark components of the disk and spheroid, whose total mass is only about 10% of the mass of the Galaxy.
9711110v1
2006-02-11
Likelihood Functions for Galaxy Cluster Surveys
Galaxy cluster surveys offer great promise for measuring cosmological parameters, but survey analysis methods have not been widely studied. Using methods developed decades ago for galaxy clustering studies, it is shown that nearly exact likelihood functions can be written down for galaxy cluster surveys. The sparse sampling of the density field by galaxy clusters allows simplifications that are not possible for galaxy surveys. An application to counts in cells is explicitly tested using cluster catalogs from numerical simulations and it is found that the calculated probability distributions are very accurate at masses above several times 10^{14}h^{-1} solar masses at z=0 and lower masses at higher redshift.
0602251v3
2000-03-25
Thermokinetic approach of the generalized Landau-Lifshitz-Gilbert equation with spin polarized current
In order to describe the recently observed effect of current induced magnetization reversal in magnetic nanostructures, the thermokinetic theory is applied to a metallic ferromagnet in contact with a reservoir of spin polarized conduction electrons. The spin flip relaxation of the conduction electrons is described thermodynamically as a chemical reaction. The diffusion equation of the chemical potential (or the giant magnetoresistance) and the usual Landau-Lifshitz-Gilbert (LLG) equation are derived from the entropy variation. The expression of the conservation laws of the magnetic moments, including spin dependent scattering processes, leads then to the generalized LLG equation with spin polarized current. The equation is applied to the measurements obtained on single magnetic Ni nanowires.
0003409v1
2004-05-26
Nonequilibrium Extension of the Landau-Lifshitz-Gilbert Equation for Magnetic Systems
Using the invariant operator method for an effective Hamiltonian including the radiation-spin interaction, we describe the quantum theory for magnetization dynamics when the spin system evolves nonadiabatically and out of equilibrium, $d \hat{\rho}/dt \neq 0$. It is shown that the vector parameter of the invariant operator and the magnetization defined with respect to the density operator, both satisfying the quantum Liouville equation, still obey the Landau-Lifshitz-Gilbert equation.
0405599v1
2006-10-16
Properties of Codes with the Rank Metric
In this paper, we study properties of rank metric codes in general and maximum rank distance (MRD) codes in particular. For codes with the rank metric, we first establish Gilbert and sphere-packing bounds, and then obtain the asymptotic forms of these two bounds and the Singleton bound. Based on the asymptotic bounds, we observe that asymptotically Gilbert-Varsharmov bound is exceeded by MRD codes and sphere-packing bound cannot be attained. We also establish bounds on the rank covering radius of maximal codes, and show that all MRD codes are maximal codes and all the MRD codes known so far achieve the maximum rank covering radius.
0610099v2
1994-08-26
On the Dirichlet problem for harmonic maps with prescribed singularities
Let $\M$ be a classical Riemannian globally symmetric space of rank one and non-compact type. We prove the existence and uniqueness of solutions to the Dirichlet problem for harmonic maps into $\M$ with prescribed singularities along a closed submanifold of the domain. This generalizes our previous work where such maps into the hyperbolic plane were constructed. This problem, in the case where $\M$ is the complex-hyperbolic plane, has applications to equilibrium configurations of co-axially rotating charged black holes in General Relativity.
9408005v1
1997-08-15
One-Loop Minimization Conditions in the Minimal Supersymmetric Standard Model
We study, in the Minimal Supersymmetric Standard Model, the electroweak symmetry breaking conditions obtained from the one-loop effective potential. Novel model-independent lower and upper bounds on $\tan \beta$, involving the other free parameters of the model, are inferred and determined analytically. We discuss briefly some of the related issues and give an outlook for further applications.
9708368v1
2004-05-31
On a Penrose Inequality with Charge
We construct a time-symmetric asymptotically flat initial data set to the Einstein-Maxwell Equations which satisfies the inequality: m - 1/2(R + Q^2/R) < 0, where m is the total mass, R=sqrt(A/4) is the area radius of the outermost horizon and Q is the total charge. This yields a counter-example to a natural extension of the Penrose Inequality to charged black holes.
0405602v3
2004-07-26
Automorphisms of free groups have asymptotically periodic dynamics
We show that every automorphism $\alpha$ of a free group $F_k$ of finite rank $k$ has {\it asymptotically periodic} dynamics on $F_k$ and its boundary $\partial F_k$: there exists a positive power $\alpha^q$ such that every element of the compactum $F_k \cup \partial F_k$ converges to a fixed point under iteration of $\alpha^q$.
0407437v2
2004-12-30
The Construction of a Partially Regular Solution to the Landau-Lifshitz-Gilbert Equation in $\mathbb{R}^2$
We establish a framework to construct a global solution in the space of finite energy to a general form of the Landau-Lifshitz-Gilbert equation in $\mathbb{R}^2$. Our characterization yields a partially regular solution, smooth away from a 2-dimensional locally finite Hausdorff measure set. This construction relies on approximation by discretization, using the special geometry to express an equivalent system whose highest order terms are linear and the translation of the machinery of linear estimates on the fundamental solution from the continuous setting into the discrete setting. This method is quite general and accommodates more general geometries involving targets that are compact smooth hypersurfaces.
0412534v1
2002-01-13
Inverse Cascade Regime in Shell Models of 2-Dimensional Turbulence
We consider shell models that display an inverse energy cascade similar to 2-dimensional turbulence (together with a direct cascade of an enstrophy-like invariant). Previous attempts to construct such models ended negatively, stating that shell models give rise to a "quasi-equilibrium" situation with equipartition of the energy among the shells. We show analytically that the quasi-equilibrium state predicts its own disappearance upon changing the model parameters in favor of the establishment of an inverse cascade regime with K41 scaling. The latter regime is found where predicted, offering a useful model to study inverse cascades.
0201020v1
2002-04-23
Algebraic decay in hierarchical graphs
We study the algebraic decay of the survival probability in open hierarchical graphs. We present a model of a persistent random walk on a hierarchical graph and study the spectral properties of the Frobenius-Perron operator. Using a perturbative scheme, we derive the exponent of the classical algebraic decay in terms of two parameters of the model. One parameter defines the geometrical relation between the length scales on the graph, and the other relates to the probabilities for the random walker to go from one level of the hierarchy to another. The scattering resonances of the corresponding hierarchical quantum graphs are also studied. The width distribution shows the scaling behavior $P(\Gamma) \sim 1/\Gamma$.
0204056v1
2004-03-11
Statistics of active vs. passive advections in magnetohydrodynamic turbulence
Active turbulent advection is considered in the context of magneto-hydrodynamics. In this case, an auxiliary passive field bears no apparent connection to the active field. The scaling properties of the two fields are different. In the framework of a shell model, we show that the two-point structure function of the passive field has a unique zero mode, characterizing the scaling of this field only. In other words, the existence of statistical invariants for the decaying passive field carries no information on the scaling properties of the active field.
0403017v1
2006-01-19
Drift of particles in self-similar systems and its Liouvillian interpretation
We study the dynamics of classical particles in different classes of spatially extended self-similar systems, consisting of (i) a self-similar Lorentz billiard channel, (ii) a self-similar graph, and (iii) a master equation. In all three systems the particles typically drift at constant velocity and spread ballistically. These transport properties are analyzed in terms of the spectral properties of the operator evolving the probability densities. For systems (i) and (ii), we explain the drift from the properties of the Pollicott-Ruelle resonance spectrum and corresponding eigenvectors
0601042v1
1997-11-20
Quantum self-dual codes and symmetric matrices
This paper has been withdrawn since a Gilbert-Varshamov bound for general quantum codes has already appeared in Ekert and Macchiavello, Prys. Rev. Lett. 77, p. 2585, and a Gilbert-Varshamov bound for stabilizer codes connected with orthogonal geometry, or equivalently, with symmetric matrices as in this paper, has been proved by Calredbank, Rains, Shor and Sloane, Phys. Rev. Lett. 78, p. 405. I would like to thank Robert Calderbank for pointing out these references to me.
9711047v2
2001-06-06
Constraints on Eavesdropping on the BB84 Protocol
An undetected eavesdropping attack must produce count rate statistics that are indistinguishable from those that would arise in the absence of such an attack. In principle this constraint should force a reduction in the amount of information available to the eavesdropper. In this paper we illustrate, by considering a particular class of eavesdropping attacks, how the general analysis of this problem may proceed.
0106034v2
2007-09-14
A complete proof of The Graceful Tree Conjecture using the concept of Edge Degree
We show the Graceful Tree Conjecture holds.
0709.2201v9
2007-09-24
An extension of a result concerning convex geometric graphs
We show a general result known as the Erdos_Sos Conjecture: if $E(G)>{1/2}(k-1)n$ where $G$ has order $n$ then $G$ contains every tree of order $k+1$ as a subgraph.
0709.3590v5
2008-06-13
Heat conduction and Fourier's law by consecutive local mixing and thermalization
We present a first-principles study of heat conduction in a class of models which exhibit a new multi-step local thermalization mechanism which gives rise to Fourier's law. Local thermalization in our models occurs as the result of binary collisions among locally confined gas particles. We explore the conditions under which relaxation to local equilibrium, which involves no energy exchange, takes place on time scales shorter than that of the binary collisions which induce local thermalization. The role of this mechanism in multi-phase material systems such as aerogels is discussed.
0806.2193v1
2009-08-05
Persistence effects in deterministic diffusion
In systems which exhibit deterministic diffusion, the gross parameter dependence of the diffusion coefficient can often be understood in terms of random walk models. Provided the decay of correlations is fast enough, one can ignore memory effects and approximate the diffusion coefficient according to dimensional arguments. By successively including the effects of one and two steps of memory on this approximation, we examine the effects of ``persistence'' on the diffusion coefficients of extended two-dimensional billiard tables and show how to properly account for these effects, using walks in which a particle undergoes jumps in different directions with probabilities that depend on where they came from.
0908.0600v1
2009-08-10
Diffusion coefficients for multi-step persistent random walks on lattices
We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which enables us to obtain explicit expressions for the diffusion coefficients of walks with two-step memory on different classes of one-, two- and higher-dimensional lattices.
0908.1271v1
2010-04-09
Strict inequalities of critical probabilities on Gilbert's continuum percolation graph
Any infinite graph has site and bond percolation critical probabilities satisfying $p_c^{site}\geq p_c^{bond}$. The strict version of this inequality holds for many, but not all, infinite graphs. In this paper, the class of graphs for which the strict inequality holds is extended to a continuum percolation model. In Gilbert's graph with supercritical density on the Euclidean plane, there is almost surely a unique infinite connected component. We show that on this component $p_c^{site} > p_c^{bond}$. This also holds in higher dimensions.
1004.1596v2
2010-04-15
Rank of mapping tori and companion matrices
Given $f$ in $GL(d,Z)$, it is decidable whether its mapping torus (the semi-direct product of $Z^d$ with $Z$) may be generated by two elements or not; if so, one can classify generating pairs up to Nielsen equivalence. If $f$ has infinite order, the mapping torus of $f^n$ cannot be generated by two elements for $n$ large enough; equivalently, $f^n$ is not conjugate to a companion matrix in $GL(d,Z)$ if $n$ is large.
1004.2649v1
2010-04-30
Limit theory for planar Gilbert tessellations
A Gilbert tessellation arises by letting linear segments (cracks) in the plane unfold in time with constant speed, starting from a homogeneous Poisson point process of germs in randomly chosen directions. Whenever a growing edge hits an already existing one, it stops growing in this direction. The resulting process tessellates the plane. The purpose of the present paper is to establish law of large numbers, variance asymptotics and a central limit theorem for geometric functionals of such tessellations. The main tool applied is the stabilization theory for geometric functionals.
1005.0023v1
2010-06-24
Periodic solutions for the Landau-Lifshitz-Gilbert equation
Ferromagnetic materials tend to develop very complex magnetization patterns whose time evolution is modeled by the so-called Landau-Lifshitz-Gilbert equation (LLG). In this paper, we construct time-periodic solutions for LLG in the regime of soft and small ferromagnetic particles which satisfy a certain shape condition. Roughly speaking, it is assumed that the length of the particle is greater than its hight and its width. The approach is based on a perturbation argument and the spectral analysis of the corresponding linearized problem as well as the theory of sectorial operators.
1006.4765v1
2010-12-19
A counterexample to a Penrose inequality conjectured by Gibbons
We show that the Brill-Lindquist initial data provides a counterexample to a Riemannian Penrose inequality with charge conjectured by G. Gibbons. The observation illustrates a sub-additive characteristic of the area radii for the individual connected components of an outermost horizon as a lower bound of the ADM mass.
1012.4190v2
2011-11-27
A two-stage approach to relaxation in billiard systems of locally confined hard spheres
We consider the three-dimensional dynamics of systems of many interacting hard spheres, each individually confined to a dispersive environment, and show that the macroscopic limit of such systems is characterized by a coefficient of heat conduction whose value reduces to a dimensional formula in the limit of vanishingly small rate of interaction. It is argued that this limit arises from an effective loss of memory. Similarities with the diffusion of a tagged particle in binary mixtures are emphasized.
1111.6272v1
2012-01-12
Coil-helix transition in poly(L-glutamic acid) : Evidence for a 3-state non-cooperative process
A careful analysis of measurements of circular dichroism of poly(L-glutamic acid) (PGA) shows that the data can be very accurately described by introducing a third state for the PGA configuration, in addition to the helix and coil ones, and considering a simple equilibrium between these three states, without cooperativity. The third state is more conspicuous when high molecular weight polyethyleneglycol (PEG) is added. Excluded volume effects shown by differences in presence of short and long PEG chains indicate a direct interaction of PEG and PGA rather than an osmotic effect.
1201.2566v1
2012-03-20
Vortex dynamics in the presence of excess energy for the Landau-Lifschitz-Gilbert equation
We study the Landau-Lifshitz-Gilbert equation for the dynamics of a magnetic vortex system. We present a PDE-based method for proving vortex dynamics that does not rely on strong well-preparedness of the initial data and allows for instantaneous changes in the strength of the gyrovector force due to bubbling events. The main tools are estimates of the Hodge decomposition of the supercurrent and an analysis of the defect measure of weak convergence of the stress energy tensor. Ginzburg-Landau equations with mixed dynamics in the presence of excess energy are also discussed.
1203.4426v1
2012-12-22
Cumulative Distance Enumerators of Random Codes and their Thresholds
Cumulative weight enumerators of random linear codes are introduced, their asymptotic properties are studied, and very sharp thresholds are exhibited; as a consequence, it is shown that the asymptotic Gilbert-Varshamov bound is a very sharp threshold point for the density of the linear codes whose relative distance is greater than a given positive number. For arbitrary random codes, similar settings and results are exhibited; in particular, the very sharp threshold point for the density of the codes whose relative distance is greater than a given positive number is located at half the asymptotic Gilbert-Varshamov bound.
1212.5679v1
2013-01-23
The Importance of Continuous Value Based Project Management in the Context of Requirements Engineering
Despite several scientific achievements in the last years, there are still a lot of IT projects that fail. Researchers found that one out of five IT-projects run out of time, budget or value. Major reasons for this failure are unexpected economic risk factors that emerge during the runtime of projects. In order to be able to identify emerging risks early and to counteract reasonably, financial methods for a continuous IT-project-steering are necessary, which as of today to the best of our knowledge are missing within scientific literature.
1301.5438v1
2013-04-08
On Automorphisms and Subtowers of an asymptotically optimal Tower of Function Fields
In this article we investigate the automorphism group of an asymptotically optimal tower of function fields introduced by Garcia and Stichtenoth. In particular we provide a detailed description of the decomposition group of some rational places. This group acts on the algebraic-geometric standard codes obtained by the Garcia-Stichtenoth tower exceeding the Gilbert-Varshamov bound. The fields fixed by the decomposition groups form an asymptotically optimal non-Galois subtower, which has been first found by Bezerra and Garcia and yields an improvement for computing codes above the Gilbert-Varshamov bound. In this article we also describe its proportionality to the Garcia-Stichtenoth tower and obtain new precise results on its rational places and their Weierstra{\ss} semigroups.
1304.2145v1
2013-05-06
The Moment Generating function for ray lengths in the Half Gilbert Model with Rectangular Cells
In the full rectangular version of Gilbert's tessellation lines extend either horizontally (with east- and west--growing rays) or vertically (north- and south--growing rays) from seed points which form a Poisson point process, each ray stopping when another ray is met. In the half rectangular version, east and south growing rays do not interact with west and north rays. Using techniques developed in our previous paper, we derive an exact expression for the moment generating function for the ray length distribution in the half rectangular model.
1305.1289v1
2013-07-15
Degenerate transition pathways for screw dislocations: implications for migration
In body-centred-cubic (bcc) metals migrating 1/2<111> screw dislocations experience a periodic energy landscape with a triangular symmetry. Atomistic simulations, such as those performed using the nudged-elastic-band (NEB) method, generally predict a transition-pathway energy-barrier with a double-hump; contradicting Ab Initio findings. Examining the trajectories predicted by NEB for a particle in a Peierls energy landscape representative of that obtained for a screw dislocation, reveals an unphysical anomaly caused by the occurrence of monkey saddles in the landscape. The implications for motion of screws with and without stress are discussed.
1307.3848v2
2013-08-17
The Riemannian Penrose Inequality with Charge for Multiple Black Holes
We present a proof of the Riemannian Penrose inequality with charge $r\leq m + \sqrt{m^2-q^2}$, where $A=4\pi r^2$ is the area of the outermost apparent horizon with possibly multiple connected components, $m$ is the total ADM mass, and $q$ the total charge of a strongly asymptotically flat initial data set for the Einstein-Maxwell equations, satisfying the charged dominant energy condition, with no charged matter outside the horizon.
1308.3771v3
2013-08-23
Quotients and subgroups of Baumslag-Solitar groups
We determine all generalized Baumslag-Solitar groups (finitely generated groups acting on a tree with all stabilizers infinite cyclic) which are quotients of a given Baumslag-Solitar group BS(m,n), and (when BS(m,n) is not Hopfian) which of them also admit BS(m,n) as a quotient. We determine for which values of r,s one may embed BS(r,s) into a given BS(m,n), and we characterize finitely generated groups which embed into some BS(n,n).
1308.5122v2
2013-12-17
Limit theory for the Gilbert graph
For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random geometric graph, is investigated as the intensity of the Poisson point process is increased and the distance parameter goes to zero. The asymptotic expectation and covariance structure of a class of length-power functionals are computed. Distributional limit theorems are derived that have a Gaussian, a stable or a compound Poisson limiting distribution. Finally, concentration inequalities are provided using a concentration inequality for the convex distance.
1312.4861v2
2014-03-13
Fibrations of ordered groupoids and the factorization of ordered functors
We investigate canonical factorizations of ordered functors of ordered groupoids through star-surjective functors. Our main construction is a quotient ordered groupoid, depending on an ordered version of the notion of normal subgroupoid, that results is the factorization of an ordered functor as a star-surjective functor followed by a star-injective functor. Any star-injective functor possesses a universal factorization through a covering, by Ehresmann's Maximum Enlargement Theorem. We also show that any ordered functor has a canonical factorization through a functor with the ordered homotopy lifting property.
1403.3254v2
2014-03-16
Interpolating local constants in families
We extend the theory of local constants to l-adic families of representations of GL_n(F) where F is a p-adic field with l not equal to p. We construct zeta integrals and gamma factors for representations coming from the conjectural "local Langlands correspondence in families" of Emerton-Helm, proving a rationality result and functional equation. We also construct a universal gamma factor with coefficients in the integral Bernstein center.
1403.3914v2
2014-06-10
A thin-film limit in the Landau-Lifshitz-Gilbert equation relevant for the formation of Néel walls
We consider an asymptotic regime for two-dimensional ferromagnetic films that is consistent with the formation of transition layers (N\'eel walls). We first establish compactness of S2-valued magnetizations in the energetic regime of N\'eel walls and characterize the set of accumulation points. We then prove that N\'eel walls are asymptotically the unique energy minimizing configurations. We finally study the corresponding dynamical issues, namely the compactness properties of the magnetizations under the flow of the Landau-Lifshitz-Gilbert equation.
1406.2709v1
2014-08-02
Machta-Zwanzig regime of anomalous diffusion in infinite-horizon billiards
We study diffusion on a periodic billiard table with infinite horizon in the limit of narrow corridors. An effective trapping mechanism emerges according to which the process can be modeled by a L\'evy walk combining exponentially-distributed trapping times with free propagation along paths whose precise probabilities we compute. This description yields an approximation of the mean squared displacement of infinite-horizon billiards in terms of two transport coefficients which generalizes to this anomalous regime the Machta-Zwanzig approximation of normal diffusion in finite-horizon billiards [Phys. Rev. Lett. 50, 1959 (1983)].
1408.0349v1
2014-12-11
Gamma factors of pairs and a local converse theorem in families
We prove a GL(n)xGL(n-1) local converse theorem for l-adic families of smooth representations of GL(n,F) where F is a finite extension of Q_p and l is different from p. To do so, we also extend the theory of Rankin-Selberg integrals, first introduced by Jacquet, Piatetski-Shapiro, and Shalika, to the setting of families, continuing previous work of the author.
1412.3500v2
2015-05-28
A Geometric Interpretation of the Boolean Gilbert-Johnson-Keerthi Algorithm
The Gilbert-Johnson-Keerthi (GJK) algorithm is an iterative improvement technique for finding the minimum distance between two convex objects. It can easily be extended to work with concave objects and return the pair of closest points. [4] The key operation of GJK is testing whether a Voronoi region of a simplex contains the origin or not. In this paper we show that, in the context where one is interested only in the Boolean value of whether two convex objects intersect, and not in the actual distance between them, the number of test cases in GJK can be significantly reduced. This results in a simpler and more efficient algorithm that can be used in many computational geometry applications.
1505.07873v1
2016-01-29
Ordered groupoid quotients and congruences on inverse semigroups
We introduce a preorder on an inverse semigroup $S$ associated to any normal inverse subsemigroup $N$, that lies between the natural partial order and Green's ${\mathscr J}$-relation. The corresponding equivalence relation $\simeq_N$ is not necessarily a congruence on $S$, but the quotient set does inherit a natural ordered groupoid structure. We show that this construction permits the factorisation of any inverse semigroup homomorphism into a composition of a quotient map and a star-injective functor, and that this decomposition implies a classification of congruences on $S$. We give an application to the congruence and certain normal inverse subsemigroups associate to an inverse monoid presentation.
1601.08194v1
2016-08-16
Closed inverse subsemigroups of graph inverse semigroups
As part of his study of representations of the polycylic monoids, M.V. Lawson described all the closed inverse submonoids of a polycyclic monoid $P_n$ and classified them up to conjugacy. We show that Lawson's description can be extended to closed inverse subsemigroups of graph inverse semigroups. We then apply B. Schein's theory of cosets in inverse semigroups to the closed inverse subsemigroups of graph inverse semigroups: we give necessary and sufficient conditions for a closed inverse subsemigroup of a graph inverse semigroup to have finite index, and determine the value of the index when it is finite.
1608.04538v1