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2010-06-25
Molecular Dynamics at Low Time Resolution
The internal dynamics of macro-molecular systems is characterized by widely separated time scales, ranging from fraction of ps to ns. In ordinary molecular dynamics simulations, the elementary time step dt used to integrate the equation of motion needs to be chosen much smaller of the shortest time scale, in order not to cut-off important physical effects. We show that, in systems obeying the over-damped Langevin Eq., the fast molecular dynamics which occurs at time scales smaller than dt can be analytically integrated out and gives raise to a time-dependent correction to the diffusion coefficient, which we rigorously compute. The resulting effective Langevin equation describes by construction the same long-time dynamics, but has a lower time resolution power, hence it can be integrated using larger time steps dt. We illustrate and validate this method by studying the diffusion of a point-particle in a one-dimensional toy-model and the denaturation of a protein.
1006.5045v1
2010-07-15
Universal Quantum Viscosity in a Unitary Fermi Gas
A Fermi gas of atoms with resonant interactions is predicted to obey universal hydrodynamics, where the shear viscosity and other transport coefficients are universal functions of the density and temperature. At low temperatures, the viscosity has a universal quantum scale $\hbar n$ where $n$ is the density, while at high temperatures the natural scale is $p_T^3/\hbar^2$ where $p_T$ is the thermal momentum. We employ breathing mode damping to measure the shear viscosity at low temperature. At high temperature $T$, we employ anisotropic expansion of the cloud to find the viscosity, which exhibits precise $T^{3/2}$ scaling. In both experiments, universal hydrodynamic equations including friction and heating are used to extract the viscosity. We estimate the ratio of the shear viscosity to the entropy density and compare to that of a perfect fluid.
1007.2625v2
2010-07-26
Phase-Field Reaction-Pathway Kinetics of Martensitic Transformations in a Model Fe3Ni Alloy
A three-dimensional phase-field approach to martensitic transformations that uses reaction pathways in place of a Landau potential is introduced and applied to a model of Fe3Ni. Pathway branching involves an unbounded set of variants through duplication and rotations by the rotation point groups of the austenite and martensite phases. Path properties, including potential energy and elastic tensors, are calibrated by molecular statics. Acoustic waves are dealt with via a splitting technique between elastic and dissipative behaviors in a large-deformation framework. The sole free parameter of the model is the damping coefficient associated to transformations, tuned by comparisons with molecular dynamics simulations. Good quantitative agreement is then obtained between both methods.
1007.4515v1
2010-08-07
Fermi acceleration and suppression of Fermi acceleration in a time-dependent Lorentz Gas
We study some dynamical properties of a Lorentz gas. We have considered both the static and time dependent boundary. For the static case we have shown that the system has a chaotic component characterized with a positive Lyapunov Exponent. For the time-dependent perturbation we describe the model using a four-dimensional nonlinear map. The behaviour of the average velocity is considered in two situations (i) non-dissipative and (ii) dissipative. Our results show that the unlimited energy growth is observed for the non-dissipative case. However, when dissipation, via damping coefficients, is introduced the senary changes and the unlimited engergy growth is suppressed. The behaviour of the average velocity is described using scaling approach.
1008.1344v2
2010-11-01
Terahertz surface plasmons in optically pumped graphene structures
We analyze the surface plasmons (SPs) propagating along the optically pumped single-graphene layer (SGL) and multiple-graphene layer (MGL) structures. It is shown that at sufficiently strong optical pumping when the real part of dynamic conductivity of SGL and MGL structures becomes negative in the terahertz (THz) range of frequencies due to the interband population inversion, the damping of the THz SPs can give way to their amplification. This effect can be used in graphene-based THz lasers and other devices. Due to relatively small SP group velocity, the absolute value of their absorption coefficient (SP gain) can be large, substantially exceeding that of the optically pumped structures with the dielectric waveguide. The comparison of the SGL and MGL structures shows that to maximize the SP gain the number of GL layers should be properly choosen.
1011.0238v1
2010-11-01
In-flight dissipation as a mechanism to suppress Fermi acceleration
Some dynamical properties of time-dependent driven elliptical-shaped billiard are studied. It was shown that for the conservative time-dependent dynamics the model exhibits the Fermi acceleration [Phys. Rev. Lett. 100, 014103 (2008)]. On the other hand, it was observed that damping coefficients upon collisions suppress such phenomenon [Phys. Rev. Lett. 104, 224101 (2010)]. Here, we consider a dissipative model under the presence of in-flight dissipation due to a drag force which is assumed to be proportional to the square of the particle's velocity. Our results reinforce that dissipation leads to a phase transition from unlimited to limited energy growth. The behaviour of the average velocity is described using scaling arguments.
1011.0419v1
2010-12-29
Dependence of boundary lubrication on the misfit angle between the sliding surfaces
Using molecular dynamics based on Langevin equations with a coordinate- and velocity-dependent damping coefficient, we study the frictional properties of a thin layer of "soft" lubricant (where the interaction within the lubricant is weaker than the lubricant-substrate interaction) confined between two solids. At low driving velocities the system demonstrates stick-slip motion. The lubricant may or may not be melted during sliding, thus exhibiting either the "liquid sliding" (LS) or the "layer over layer sliding" (LoLS) regimes. The LoLS regime mainly operates at low sliding velocities. We investigate the dependence of friction properties on the misfit angle between the sliding surfaces and calculate the distribution of static frictional thresholds for a contact of polycrystalline surfaces.
1012.5922v1
2010-12-31
Structural optimization of the Ziegler's pendulum: singularities and exact optimal solutions
Structural optimization of non-conservative systems with respect to stability criteria is a research area with important applications in fluid-structure interactions, friction-induced instabilities, and civil engineering. In contrast to optimization of conservative systems where rigorously proven optimal solutions in buckling problems have been found, for non-conservative optimization problems only numerically optimized designs were reported. The proof of optimality in the non-conservative optimization problems is a mathematical challenge related to multiple eigenvalues, singularities on the stability domain, and non-convexity of the merit functional. We present a study of the optimal mass distribution in a classical Ziegler's pendulum where local and global extrema can be found explicitly. In particular, for the undamped case, the two maxima of the critical flutter load correspond to a vanishing mass either in a joint or at the free end of the pendulum; in the minimum, the ratio of the masses is equal to the ratio of the stiffness coefficients. The role of the singularities on the stability boundary in the optimization is highlighted and extension to the damped case as well as to the case of higher degrees of freedom is discussed.
1101.0246v1
2011-01-24
Boundary crisis and suppression of Fermi acceleration in a dissipative two dimensional non-integrable time-dependent billiard
Some dynamical properties for a dissipative time-dependent oval-shaped billiard are studied. The system is described in terms of a four-dimensional nonlinear mapping. Dissipation is introduced via inelastic collisions of the particle with the boundary, thus implying that the particle has a fractional loss of energy upon collision. The dissipation causes profound modifications in the dynamics of the particle as well as in the phase space of the non dissipative system. In particular, inelastic collisions can be assumed as an efficient mechanism to suppress Fermi acceleration of the particle. The dissipation also creates attractors in the system, including chaotic. We show that a slightly modification of the intensity of the damping coefficient yields a drastic and sudden destruction of the chaotic attractor, thus leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with its own basin of attraction and confirmed that inelastic collisions do indeed suppress Fermi acceleration in two-dimensional time dependent billiards.
1101.4593v1
2011-04-14
Phenomenological modeling of long range noncontact friction in micro- and nanoresonators
Motivated by the results of an experiment using atomic force microscopy performed by Gotsmann and Fuchs [Phys. Rev. Lett. {\bf 86}, 2597 (2001)], where a strong energy loss due to the tip-sample interaction was measured, we investigate the potential implications of this energy loss channel to the quality factor of suspended micro- and nanoresonators. Because the observed tip-sample dissipation remains without a satisfactory theoretical explanation, two phenomenological models are proposed to generalize the experimental observations. A minimal phenomenological model simply extends for larger separations the range of validity of the power law found experimentally for the damping coefficient. A more elaborate phenomenological model assumes that the noncontact friction is a consequence of the Casimir force acting between the closely spaced surfaces. Both models provide quantitative results for the noncontact friction between any two objects which are then used to estimate the energy loss for suspended bar micro- and nanoresonators. Its is concluded that the energy loss due to the unknown mechanism has the potential to seriously restrict the quality factor of both micro- and nanoresonators.
1104.2832v2
2011-05-03
Nonequilibrium chiral fluid dynamics including dissipation and noise
We present a consistent theoretical approach for the study of nonequilibrium effects in chiral fluid dynamics within the framework of the linear sigma model with constituent quarks. Treating the quarks as an equilibrated heat bath we use the influence functional formalism to obtain a Langevin equation for the sigma field. This allows us to calculate the explicit form of the damping coefficient and the noise correlators. For a selfconsistent derivation of both the dynamics of the sigma field and the quark fluid we have to employ the 2PI (two-particle irreducible) effective action formalism. The energy dissipation from the field to the fluid is treated in the exact formalism of the 2PI effective action where a conserved energy-momentum tensor can be constructed. We derive its form and comment on approximations generating additional terms in the energy-momentum balance of the entire system.
1105.0622v1
2011-05-05
Long-range three-body atom-diatom potential for doublet Li${}_3$
An accurate long-range {\em ab initio} potential energy surface has been calculated for the ground state ${}^2A'$ lithium trimer in the frozen diatom approximation using all electron RCCSD(T). The {\em ab initio} energies are corrected for basis set superposition error and extrapolated to the complete basis limit. Molecular van der Waals dispersion coefficients and three-body dispersion damping terms for the atom-diatomic dissociation limit are presented from a linear least squares fit and shown to be an essentially exact representation of the {\em ab initio} surface at large range.
1105.1090v2
2011-05-12
Searching for Perfect Fluids: Quantum Viscosity in a Universal Fermi Gas
We measure the shear viscosity in a two-component Fermi gas of atoms, tuned to a broad s-wave collisional (Feshbach) resonance. At resonance, the atoms strongly interact and exhibit universal behavior, where the equilibrium thermodynamic properties and the transport coefficients are universal functions of the density $n$ and temperature $T$. We present a new calibration of the temperature as a function of global energy, which is directly measured from the cloud profiles. Using the calibration, the trap-averaged shear viscosity in units of $\hbar\,n$ is determined as a function of the reduced temperature at the trap center, from nearly the ground state to the unitary two-body regime. Low temperature data is obtained from the damping rate of the radial breathing mode, while high temperature data is obtained from hydrodynamic expansion measurements. We also show that the best fit to the high temperature expansion data is obtained for a vanishing bulk viscosity. The measured trap-averaged entropy per particle and shear viscosity are used to estimate the ratio of the shear viscosity to the entropy density, which is compared that conjectured for a perfect fluid.
1105.2496v1
2011-05-21
Stochastic population oscillations in spatial predator-prey models
It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic models yield long-lived, but ultimately decaying erratic population oscillations, which can be understood through a resonant amplification mechanism for density fluctuations. In Monte Carlo simulations of spatial stochastic predator-prey systems, one observes striking complex spatio-temporal structures. These spreading activity fronts induce persistent correlations between predators and prey. In the presence of local particle density restrictions (finite prey carrying capacity), there exists an extinction threshold for the predator population. The accompanying continuous non-equilibrium phase transition is governed by the directed-percolation universality class. We employ field-theoretic methods based on the Doi-Peliti representation of the master equation for stochastic particle interaction models to (i) map the ensuing action in the vicinity of the absorbing state phase transition to Reggeon field theory, and (ii) to quantitatively address fluctuation-induced renormalizations of the population oscillation frequency, damping, and diffusion coefficients in the species coexistence phase.
1105.4242v1
2011-06-17
Sequential vibrational resonance in multistable systems
The phenomenon of sequential vibrational resonance existed in a multistable system that is excited by both high- and low-frequency signals is reported. By the method of direct separation of motions, the theoretical investigation on vibrational resonance is conducted in both cases of underdamped and overdamped, and the analytical predictions are in good agreement with the numerical simulations. In view of the theoretical results, the zero-order Bessel function related to the high-frequency signal is included in the renormalized resonant frequency, and which leads to the appearance of the sequential vibrational resonance. In the case of underdamped system with small damping coefficient, the resonance occurs in a series of discrete parameter regions. The sequential vibrational resonance is different from the traditional multiple vibrational resonance, because its appearance is much more regular. The results in this work may be helpful in the field of signal processing electronics, especially for dealing with the very-low-frequency signal.
1106.3431v1
2011-10-27
Existence of global strong solutions for the shallow-water equations with large initial data
This work is devoted to the study of a viscous shallow-water system with friction and capillarity term. We prove in this paper the existence of global strong solutions for this system with some choice of large initial data when $N\geq 2$ in critical spaces for the scaling of the equations. More precisely, we introduce as in \cite{Hprepa} a new unknown,\textit{a effective velocity} $v=u+\mu\n\ln h$ ($u$ is the classical velocity and $h$ the depth variation of the fluid) with $\mu$ the viscosity coefficient which simplifies the system and allow us to cancel out the coupling between the velocity $u$ and the depth variation $h$. We obtain then the existence of global strong solution if $m_{0}=h_{0}v_{0}$ is small in $B^{\N-1}_{2,1}$ and $(h_{0}-1)$ large in $B^{\N}_{2,1}$. In particular it implies that the classical momentum $m_{0}^{'}=h_{0} u_{0}$ can be large in $B^{\N-1}_{2,1}$, but small when we project $m_{0}^{'}$ on the divergence field. These solutions are in some sense \textit{purely compressible}. We would like to point out that the friction term term has a fundamental role in our work inasmuch as coupling with the pressure term it creates a damping effect on the effective velocity.
1110.6100v1
2011-10-28
Nonlinear instability of solutions in parabolic and hyperbolic diffusion
We consider semilinear evolution equations of the form $a(t)\partial_{tt}u + b(t) \partial_t u + Lu = f(x,u)$ and $b(t) \partial_t u + Lu = f(x,u),$ with possibly unbounded $a(t)$ and possibly sign-changing damping coefficient $b(t)$, and determine precise conditions for which linear instability of the steady state solutions implies nonlinear instability. More specifically, we prove that linear instability with an eigenfunction of fixed sign gives rise to nonlinear instability by either exponential growth or finite-time blow-up. We then discuss a few examples to which our main theorem is immediately applicable, including evolution equations with supercritical and exponential nonlinearities.
1110.6240v3
2011-11-09
Numerical stability of the Z4c formulation of general relativity
We study numerical stability of different approaches to the discretization of a conformal decomposition of the Z4 formulation of general relativity. We demonstrate that in the linear, constant coefficient regime a novel discretization for tensors is formally numerically stable with a method of lines time-integrator. We then perform a full set of apples with apples tests on the non-linear system, and thus present numerical evidence that both the new and standard discretizations are, in some sense, numerically stable in the non-linear regime. The results of the Z4c numerical tests are compared with those of BSSNOK evolutions. We typically do not employ the Z4c constraint damping scheme and find that in the robust stability and gauge wave tests the Z4c evolutions result in lower constraint violation at the same resolution as the BSSNOK evolutions. In the gauge wave tests we find that the Z4c evolutions maintain the desired convergence factor over many more light-crossing times than the BSSNOK tests. The difference in the remaining tests is marginal.
1111.2177v1
2012-01-30
Non-contact Friction and Relaxational Dynamics of Surface Defects
Motion of cantilever near sample surfaces exhibits additional friction even before two bodies come into mechanical contact. Called non-contact friction (NCF), this friction is of great practical importance to the ultrasensitive force detection measurements. Observed large NCF of a micron-scale cantilever found anomalously large damping that exceeds theoretical predictions by 8-11 orders of magnitude. This finding points to contribution beyond fluctuating electromagnetic fields within van der Waals approach. Recent experiments reported by Saitoh et al. (Phys. Rev. Lett. 105, 236103 (2010)) also found nontrivial distance dependence of NCF. Motivated by these observations, we propose a mechanism based on the coupling of cantilever to the relaxation dynamics of surface defects. We assume that the surface defects couple to the cantilever tip via spin-spin coupling and their spin relaxation dynamics gives rise to the backaction terms and modifies both the friction coefficient and the spring constant. We explain the magnitude, as well as the distance dependence of the friction due to these backaction terms. Reasonable agreement is found with the experiments.
1201.6378v1
2012-02-09
Casimir-Polder interaction of fullerene molecules with surfaces
We calculate the thermal Casimir--Polder potential of C60 and C70 fullerene molecules near gold and silicon nitride surfaces, motivated by their relevance for molecular matter wave interference experiments. We obtain the coefficients governing the asymptotic power laws of the interaction in the thermal, retarded and nonretarded distance regimes and evaluate the full potential numerically. The interaction is found to be dominated by electronic transitions, and hence independent of the internal temperature of the molecules. The contributions from phonon transitions, which are affected by the molecular temperature, give rise to only a small correction. Moreover, we find that the sizeable molecular line widths of thermal fullerenes may modify the nonretarded interaction, depending on the model used. Detailed measurements of the nonretarded potential of fullerene thus allow one to distinguish between different theories of incorporating damping.
1202.1982v1
2012-04-30
New integrability case for the Riccati equation
A new integrability condition of the Riccati equation $dy/dx=a(x)+b(x)y+c(x)y^{2}$ is presented. By introducing an auxiliary equation depending on a generating function $f(x)$, the general solution of the Riccati equation can be obtained if the coefficients $a(x)$, $b(x)$, $c(x)$, and the function $f(x)$ satisfy a particular constraint. The validity and reliability of the method are tested by obtaining the general solutions of some Riccati type differential equations. Some applications of the integrability conditions for the case of the damped harmonic oscillator with time dependent frequency, and for solitonic wave, are briefly discussed.
1204.6546v1
2012-06-23
Superlattice formed by quantum-dot sheets: density of states and IR absorption
Low-energy continuous states of electron in heterosrtucture with periodically placed quantum-dot sheets are studied theoretically. The Green's function of electron is governed by the Dyson equation with the self-energy function which is determined the boundary conditions at quantum-dot sheets with weak damping in low-energy region. The parameters of superlattice formed by quantum-dot sheets are determined using of the short-range model of quantum dot. The density of states and spectral dependencies of the anisotropic absorption coefficient under mid-IR transitions from doped quantum dots into miniband states of superlattice strongly depend on dot concentration and on period of sheets. These dependencies can be used for characterization of the multi-layer structure and they determine parameters of different optoelectronic devices exploiting vertical transport of carriers through quantum-dot sheets.
1206.5418v1
2012-07-27
Spin transition rates in nanowire superlattices: Rashba spin-orbit coupling effects
We investigate the influence of Rashba spin-orbit coupling in a parabolic nanowire modulated by longitudinal periodic potential. The modulation potential can be obtained from realistically grown supperlattices (SLs). Our study shows that the Rashba spin-orbit interaction induces the level crossing point in the parabolic nanowire SLs. We estimate large anticrossing width (approximately 117 $\mu eV$) between singlet-triplet states. We study the phonon and electromagnetic field mediated spin transition rates in the parabolic nanowire SLs. We report that the phonon mediated spin transition rate is several order of magnitude larger than the electromagnetic field mediated spin transition rate. Based on the Feynman disentangling technique, we find the exact spin transition probability. For the case wave vector $k=0$, we report that the transition probability can be tuned in the form of resonance at fixed time interval. For the general case ($k\neq 0$), we solve the Riccati equation and find that the arbitrary values of $k$ induces the damping in the transition probability. At large value of Rashba spin-orbit coupling coefficients for ($k\neq 0$), spin transition probability freezes.
1207.6580v2
2012-09-24
Non-stationary Magnetic Microstructures in Stellar Thin Accretion Discs
We examine the morphology of magnetic structures in thin plasma accretion discs, generalizing a stationary ideal MHD model to the time-dependent visco-resistive case. Our analysis deals with small scale perturbations to a central dipole-like magnetic field, which give rise -- as in the ideal case -- to the periodic modulation of magnetic flux surfaces along the radial direction, corresponding to the formation of a toroidal current channels sequence. These microstructures suffer an exponential damping in time because of the non-zero resistivity coefficient, allowing us to define a configuration lifetime which mainly depends on the midplane temperature and on the length scale of the structure itself. By means of this lifetime we show that the microstructures can exist within the inner region of stellar discs in a precise range of temperatures, and that their duration is consistent with local transient processes (minutes to hours).
1209.5227v2
2013-03-22
Scattering Rates For Leptogenesis: Damping of Lepton Flavour Coherence and Production of Singlet Neutrinos
Using the Closed-Time-Path approach, we perform a systematic leading order calculation of the relaxation rate of flavour correlations of left-handed Standard Model leptons. This quantity is of pivotal relevance for flavoured Leptogenesis in the Early Universe, and we find it to be 5.19*10^-3 T at T=10^7 GeV and 4.83*10^-3 T at T=10^13 GeV. These values apply to the Standard Model with a Higgs-boson mass of 125 GeV. The dependence of the numerical coefficient on the temperature T is due to the renormalisation group running. The leading linear and logarithmic dependencies of the flavour relaxation rate on the gauge and top-quark couplings are extracted, such that the results presented in this work can readily be applied to extensions of the Standard Model. We also derive the production rate of light (compared to the temperature) sterile right-handed neutrinos, a calculation that relies on the same methods. We confirm most details of earlier results, but find a substantially larger contribution from the t-channel exchange of fermions.
1303.5498v1
2013-06-18
Spinor dynamics in an antiferromagnetic spin-1 thermal Bose gas
We present experimental observations of coherent spin-population oscillations in a cold thermal, Bose gas of spin-1 sodium-23 atoms. The population oscillations in a multi-spatial-mode thermal gas have the same behavior as those observed in a single-spatial-mode antiferromagnetic spinor Bose Einstein condensate. We demonstrate this by showing that the two situations are described by the same dynamical equations, with a factor of two change in the spin-dependent interaction coefficient, which results from the change to particles with distinguishable momentum states in the thermal gas. We compare this theory to the measured spin population evolution after times up to a few hundreds of ms, finding quantitative agreement with the amplitude and period. We also measure the damping time of the oscillations as a function of magnetic field.
1306.4255v1
2013-06-19
Soliton dynamics in an extended nonlinear Schrodinger equation with a spatial counterpart of the stimulated Raman scattering
Dynamics of solitons is considered in the framework of the extended nonlinear Schrodinger equation (NLSE), which is derived from a system of Zakharov's type for the interaction between high- and low-frequency (HF and LF) waves, in which the LF field is subject to diffusive damping. The model may apply to the propagation of HF waves in plasmas. The resulting NLSE includes a pseudo-stimulated-Raman-scattering (PSRS) term, i.e., a spatial-domain counterpart of the SRS term which is well known as an ingredient of the temporal-domain NLSE in optics. Also included is inhomogeneity of the spatial second-order diffraction (SOD). It is shown that the wavenumber downshift of solitons, caused by the PSRS, may be compensated by an upshift provided by the SOD whose coefficient is a linear function of the coordinate. An analytical solution for solitons is obtained in an approximate form. Analytical and numerical results agree well, including the predicted balance between the PSRS and the linearly inhomogeneous SOD.
1306.4550v1
2013-09-18
On an auto-controlled global existence scheme of the incompressible Navier Stokes equation
We propose a global scheme for the incompressible Navier Stokes equation, where at each time step a damping potential term is introduced via a time dilation transformation of the equation itself. This leads a global upper bounds of the value function and its spatial derivatives. The regularity is limited only by the regularity of the viscosity coefficient function and by the regularity and polynomial decay of the data. On an analytical level the scheme proposed is an alternative to schemes with external control functions.
1309.4824v11
2013-10-21
Cosmic ray propagation in galactic turbulence
We revisit propagation of galactic cosmic rays (CRs) in light of recent advances in CR diffusion theory in realistic interstellar turbulence. We use a tested model of turbulence in which it has been shown that fast modes dominate scattering of CRs. As a result, propagation becomes inhomogeneous and environment dependent. By adopting the formalism of the nonlinear theory developed by Yan & Lazarian, we calculate the diffusion of CRs self-consistently from first principles. We assume a two- phase model for the Galaxy to account for different damping mechanisms of the fast modes, and we find that the energy dependence of the diffusion coefficient is mainly affected by medium properties. We show that it gives a correct framework to interpret some of the recent CR puzzles.
1310.5732v2
2013-10-23
Spectroscopic investigation of local mechanical impedance of living cells
The mechanical properties of PC12 living cells have been studied at the nanoscale with a Force Feedback Microscope using two experimental approaches. Firstly, the local mechanical impedance of the cell membrane has been mapped simultaneously to the cell morphology at constant force. As the force of the interaction is gradually increased, we observed the appearance of the sub-membrane cytoskeleton. We shall compare the results obtained with this method with the measurement of other existing techniques. Secondly, a spectroscopic investigation has been performed varying the indentation of the tip in the cell membrane and consequently the force applied on it. In contrast with conventional dynamic atomic force microscopy techniques, here the small oscillation amplitude of the tip is not necessarily imposed at the cantilever first eigenmode. This allows the user to arbitrarily choose the excitation frequency in developing spectroscopic AFM techniques. The mechanical response of the PC12 cell membrane is found to be frequency dependent in the 1 kHz - 10 kHz range. The damping coefficient is reproducibly observed to decrease when the excitation frequency is increased.
1310.6201v1
2013-11-21
Note on the super inflation in loop quantum cosmology
Phenomenological effect of the super-inflation in loop quantum cosmology (LQC) is discussed. We investigate the case that the Universe is filled with the interacting field between massive scalar field and radiation. Considering the damping coefficient $\Gamma$ as a constant, the changes of the scale factor during super-inflation with four different initial conditions are discussed, and we find that the changes of the scale factor depends on the initial values of energy density of the scalar field and radiation at the bounce point. But no matter which initial condition is chosen, the radiation always dominated at the late time. Moreover, we investigate whether the super-inflation can provide enough e-folding number. For the super-inflation starts from the quantum bounce point, the initial value of Hubble parameter $H(t_i)\sim0$, then it is possible to solve the flatness problem and horizon problem. As an example, following the method of \cite{Amoros-prd} to calculate particle horizon on the condition that the radiation dominated at bounce point, and we find that the Universe has had enough time to be homogeneous and isotopic.
1311.5325v1
2013-12-10
Delaying the waterfall transition in warm hybrid inflation
We analyze the dynamics and observational predictions of supersymmetric hybrid inflation in the warm regime, where dissipative effects are mediated by the waterfall fields and their subsequent decay into light degrees of freedom. This produces a quasi-thermal radiation bath with a slowly-varying temperature during inflation and further damps the inflaton's motion, thus prolonging inflation. As in the standard supercooled scenario, inflation ends when the waterfall fields become tachyonic and can no longer sustain a nearly constant vacuum energy, but the interaction with the radiation bath makes the waterfall fields effectively heavier and delays the phase transition to the supersymmetric minimum. In this work, we analyze for the first time the effects of finite temperature corrections and SUSY mass splittings on the quantum effective potential and the resulting dissipation coefficient. We show, in particular, that dissipation can significantly delay the onset of the tachyonic instability to yield 50-60 e-folds of inflation and an observationally consistent primordial spectrum, which is not possible in the standard supercooled regime when inflation is driven by radiative corrections.
1312.2961v1
2013-12-11
Modelling of the optical properties of silver with use of six fitting parameters
We propose a realistic model of the optical properties of silver, in which inter-band transition with a threshold energy of ~ 4 eV is described phenomenologically by an ensemble of oscillators with same damping constant and a certain distribution of resonant frequencies in the interband transition threshold to infinity. The contribution of the conduction electrons in the dielectric function is determined by the Drude formula. The proposed model actually contains the features of both the Drude-Lorentz model (Raki\'c et al. 1998) and Tauc-Lorentz model (Jian-Hong Qiu et al. 2005). However, unlike these works proposed model contains only six fitting parameters, with the square root of the mean square deviation of the absorption coefficient and refractive index of silver from the experimental values in the range of 0.6 nm - 6.0 nm being of the order of 0.05.
1312.3100v1
2014-02-17
Spatio-temporal dynamics of an active, polar, viscoelastic ring
Constitutive equations for a one-dimensional, active, polar, viscoelastic liquid are derived by treating the strain field as a slow hydrodynamic variable. Taking into account the couplings between strain and polarity allowed by symmetry, the hydrodynamics of an active, polar, viscoelastic body include an evolution equation for the polarity field that generalizes the damped Kuramoto-Sivashinsky equation. Beyond thresholds of the active coupling coefficients between the polarity and the stress or the strain rate, bifurcations of the homogeneous state lead first to stationary waves, then to propagating waves of the strain, stress and polarity fields. I argue that these results are relevant to living matter, and may explain rotating actomyosin rings in cells and mechanical waves in epithelial cell monolayers.
1402.3987v1
2014-05-14
An exactly solvable $\mathcal{PT}$-symmetric dimer from a Hamiltonian system of nonlinear oscillators with gain and loss
We show that a pair of coupled nonlinear oscillators, of which one oscillator has positive and the other one negative damping of equal rate, can form a Hamiltonian system. Small-amplitude oscillations in this system are governed by a $\mathcal{PT}$-symmetric nonlinear Schr\"odinger dimer with linear and cubic coupling. The dimer also represents a Hamiltonian system and is found to be exactly solvable in elementary functions. We show that the nonlinearity softens the $\mathcal{PT}$-symmetry breaking transition in the nonlinearly-coupled dimer: stable periodic and quasiperiodic states with large enough amplitudes persist for an arbitrarily large value of the gain-loss coefficient.
1405.3588v2
2014-07-02
Basins of attraction in forced systems with time-varying dissipation
We consider dissipative periodically forced systems and investigate cases in which having information as to how the system behaves for constant dissipation may be used when dissipation varies in time before settling at a constant final value. First, we consider situations where one is interested in the basins of attraction for damping coefficients varying linearly between two given values over many different time intervals: we outline a method to reduce the computation time required to estimate numerically the relative areas of the basins and discuss its range of applicability. Second, we observe that sometimes very slight changes in the time interval may produce abrupt large variations in the relative areas of the basins of attraction of the surviving attractors: we show how comparing the contracted phase space at a time after the final value of dissipation has been reached with the basins of attraction corresponding to that value of constant dissipation can explain the presence of such variations. Both procedures are illustrated by application to a pendulum with periodically oscillating support.
1407.0556v1
2014-09-24
Scaling laws for the bifurcation-escape rate in a nanomechanical resonator
We report on experimental and theoretical studies of the fluctuation-induced escape time from a metastable state of a nanomechanical Duffing resonator in cryogenic environment. By tuning in situ the non-linear coefficient $\gamma$ we could explore a wide range of the parameter space around the bifurcation point, where the metastable state becomes unstable. We measured in a relaxation process the distribution of the escape times. We have been able to verify its exponential distribution and extract the escape rate $\Gamma$. We investigated the scaling of $\Gamma$ with respect to the distance to the bifurcation point and $\gamma$, finding an unprecedented quantitative agreement with the theoretical description of the stochastic problem. Simple power scaling laws turn out to hold in a large region of the parameter's space, as anticipated by recent theoretical predictions. These unique findings, implemented in a model dynamical system, are relevant to all systems experiencing under-damped saddle-node bifurcation.
1409.6971v3
2014-09-30
Numerical Simulation of Two Dimentional sine-Gordon Solitons Using the Modified Cubic B-Spline Differential Quadrature Method
In this article, a numerical simulation of two dimensional nonlinear sine-Gordon equation with Neumann boundary condition is obtained by using a composite scheme referred to as a modified cubic B spline differential quadrature method. The modified cubic B-spline serves as a basis function in the differential quadrature method to compute the weighting coefficients. Thus, the sine-Gordon equation is converted into a system of second order ordinary differential equations (ODEs). We solve the resulting system of ODEs by an optimal five stage and fourth-order strong stability preserving Runge Kutta scheme. Both damped and undamped cases are considered for the numerical simulation with Josephson current density function with value minus one. The computed results are found to be in good agreement with the exact solutions and other numerical results available in literature.
1410.0058v1
2014-11-12
Semi-active Suspension Control using Modern Methodology: Comprehensive Comparison Study
Semi-active suspensions have drawn particular attention due to their superior performance over the other types of suspensions. One of their advantages is that their damping coefficient can be controlled without the need for any external source of power. In this study, three control approaches are implemented on a quarter-car model using MATLAB/Simulink. The investigated control methodologies are Acceleration Driven Damper, Power Driven Damper, and H_infinity Robust Control. The three controllers are known as comfort-oriented approaches. H_infinity Robust Control is an advanced method that guarantees transient performance and rejects external disturbances. It is shown that H_infinity with the proposed modification, has the best performance although its relatively high cost of computation could be potentially considered as a drawback.
1411.3305v1
2015-03-19
Quasinormal modes of test fields around regular black holes
We study scalar, electromagnetic and gravitational test fields in the Hayward, Bardeen and Ay\'on-Beato-Garc\'ia regular black hole spacetimes and demonstrate that the test fields are stable in all these spacetimes. Using the sixth order WKB approximation of the linear "axial" perturbative scheme, we determine dependence of the quasinormal mode (QNM) frequencies on the characteristic parameters of the test fields and the spacetime charge parameters of the regular black holes. We give also the greybody factors, namely the transmission and reflection coefficients of scattered scalar, electromagnetic and gravitational waves. We show that damping of the QNMs in regular black hole spacetimes is suppressed in comparison to the case of Schwarzschild black holes, and increasing charge parameter of the regular black holes increases reflection and decreases transmission factor of incident waves for each of the test fields.
1503.05737v2
2015-04-03
Role of attractive forces in determining the equilibrium structure and dynamics of simple liquids
Molecular Dynamics simulations of a Lennard-Jones system with different range of attraction show that the attractive forces modify the radial distribution of the particles. For condensed liquids only, the forces within the the first coordination shell (FCS) are important, but for gases and moderate condensed fluids, even the attractive forces outside the FCS play a role. The changes in the distribution caused by neglecting the attractive forces, lead to a too high pressure. The weak long-range attractions damp the dynamics and the diffusion of the particles in gas-, super critical fluid- and in liquid states. The values of self-diffusion coefficients (SDC) agree qualitatively with a modified Cohen-Turnbull model. The SDC-s along the critical isotherm show no anomaly at the critical point in agreement with experimental data.
1504.00809v1
2015-06-08
Another derivation of generalized Langevin equations
The formal derivation of Langevin equations (and, equivalently Fokker-Planck equations) with projection operator techniques of Mori, Zwanzig, Kawasaki and others apparently not has widely found its way into textbooks. It has been reproduced dozens of times on the fly with many references to the literature and without adding much substantially new. Here we follow the tradition, but strive to produce a self-contained text. Furthermore, we address questions that naturally arise in the derivation. Among other things the meaning of the divergence of the Poisson brackets is explained, and the role of nonlinear damping coefficients is clarified. The derivation relies on classical mechanics, and encompasses everything one can construct from point particles and potentials: solids, liquids, liquid crystals, conductors, polymers, systems with spin-like degrees of freedom ... Einstein relations and Onsager reciprocity relations come for free.
1506.02650v2
2015-06-09
Sensitivity analysis for shape optimization of a focusing acoustic lens in lithotripsy
We are interested in shape sensitivity analysis for an optimization problem arising in medical applications of high intensity focused ultrasound. The goal is to find the optimal shape of a focusing acoustic lens so that the desired acoustic pressure at a kidney stone is achieved. Coupling of the silicone acoustic lens and nonlinearly acoustic fluid region is modeled by the Westervelt equation with nonlinear strong damping and piecewise constant coefficients. We follow the variational approach to calculating the shape derivative of the cost functional which does not require computing the shape derivative of the state variable; however assumptions of certain spatial regularity of the primal and the adjoint state are needed to obtain the derivative, in particular for its strong form according to the Delfour-Hadamard-Zol\' esio Structure Theorem.
1506.02781v1
2015-06-26
Dimer with gain and loss: Integrability and $\mathcal{PT}$-symmetry restoration
A $\mathcal{PT}$-symmetric nonlinear Schr\"odinger dimer is a two-site discrete nonlinear Schr\"odinger equation with one site losing and the other one gaining energy at the same rate. In this paper, two four-parameter families of cubic $\mathcal{PT}$-symmetric dimers are constructed as gain-loss extensions of their conservative, Hamiltonian, counterparts. We prove that all these damped-driven equations define completely integrable Hamiltonian systems. The second aim of our study is to identify nonlinearities that give rise to the spontaneous $\mathcal{PT}$-symmetry restoration. When the symmetry of the underlying linear dimer is broken and an unstable small perturbation starts to grow, the nonlinear coupling of the required type diverts progressively large amounts of energy from the gaining to the losing site. As a result, the exponential growth is saturated and all trajectories remain trapped in a finite part of the phase space regardless of the value of the gain-loss coefficient.
1506.08229v2
2015-07-09
Background field method in the gradient flow
In perturbative consideration of the Yang--Mills gradient flow, it is useful to introduce a gauge non-covariant term ("gauge-fixing term") to the flow equation that gives rise to a Gaussian damping factor also for gauge degrees of freedom. In the present paper, we consider a modified form of the gauge-fixing term that manifestly preserves covariance under the background gauge transformation. It is shown that our gauge-fixing term does not affect gauge-invariant quantities as the conventional gauge-fixing term. The formulation thus allows a background gauge covariant perturbative expansion of the flow equation that provides, in particular, a very efficient computational method of expansion coefficients in the small flow time expansion. The formulation can be generalized to systems containing fermions.
1507.02360v3
2015-07-16
Fast Convergence of an Inertial Gradient-like System with Vanishing Viscosity
In a real Hilbert space $\mathcal H$, we study the fast convergence properties as $t \to + \infty$ of the trajectories of the second-order evolution equation $$ \ddot{x}(t) + \frac{\alpha}{t} \dot{x}(t) + \nabla \Phi (x(t)) = 0, $$ where $\nabla \Phi$ is the gradient of a convex continuously differentiable function $\Phi : \mathcal H \rightarrow \mathbb R$, and $\alpha$ is a positive parameter. In this inertial system, the viscous damping coefficient $\frac{\alpha}{t}$ vanishes asymptotically in a moderate way. For $\alpha > 3$, we show that any trajectory converges weakly to a minimizer of $\Phi$, just assuming that the set of minimizers is nonempty. The strong convergence is established in various practical situations. These results complement the $\mathcal O(t^{-2})$ rate of convergence for the values obtained by Su, Boyd and Cand\`es. Time discretization of this system, and some of its variants, provides new fast converging algorithms, expanding the field of rapid methods for structured convex minimization introduced by Nesterov, and further developed by Beck and Teboulle. This study also complements recent advances due to Chambolle and Dossal.
1507.04782v1
2015-07-29
Gravitational, shear and matter waves in Kantowski-Sachs cosmologies
A general treatment of vorticity-free, perfect fluid perturbations of Kantowski-Sachs models with a positive cosmological constant are considered within the framework of the 1+1+2 covariant decomposition of spacetime. The dynamics is encompassed in six evolution equations for six harmonic coefficients, describing gravito-magnetic, kinematic and matter perturbations, while a set of algebraic expressions determine the rest of the variables. The six equations further decouple into a set of four equations sourced by the perfect fluid, representing forced oscillations and two uncoupled damped oscillator equations. The two gravitational degrees of freedom are represented by pairs of gravito-magnetic perturbations. In contrast with the Friedmann case one of them is coupled to the matter density perturbations, becoming decoupled only in the geometrical optics limit. In this approximation, the even and odd tensorial perturbations of the Weyl tensor evolve as gravitational waves on the anisotropic Kantowski-Sachs background, while the modes describing the shear and the matter density gradient are out of phase dephased by $\pi /2$ and share the same speed of sound.
1507.08300v2
2015-08-14
Reactive collisions of polar molecules in quasi-two-dimensional traps
We investigate collisions of polar molecules in quasi-2D traps in the presence of an external electric field perpendicular to the collision plane. We use the quantum-defect model characterized by two dimensionless parameters: $y$ and $s$. The first of them is related to the probability of the reaction at short distances, whereas the latter one defines the wave function phase at short distances. For $y$ close to unity we obtain universal collision rates determined by the quantum reflection process from the long-range part of the interaction potential that depends only on the van der Waals coefficient, dipole-dipole interaction and the trap frequency. For small short-range reaction probabilities collision rates are highly nonuniversal and trap induced shape resonances are visible. For high dipole moments we observe the damping of reactive collisions, which can stabilize the ultracold gas of polar molecules. The calculations were performed with help of multichannel wave funcion propagation by imposing short-range boundary condition derived from the quantum-defect model.
1508.03443v1
2015-11-06
Curvature and torsion effects in the spin-current driven domain wall motion
The domain wall motion along a helix-shaped nanowire is studied for the case of spin-current driving via Bazaliy-Zhang-Li mechanism. The analysis is based on collective variable approach. Two new effects are ascertained: (i) the curvature results in appearance of the Walker limit for a uniaxial wire, (ii) the torsion results in effective shift of the nonadiabatic spin torque parameter $\beta$. The latter effect changes considerably the domain wall velocity and can result in negative domain wall mobility. This effect can be also used for an experimental determination of the nonadiabatic parameter $\beta$ and damping coefficient $\alpha$.
1511.02193v1
2015-11-15
Fluid friction and wall viscosity of the 1D blood flow model
We study the behavior of the pulse waves of water into a flexible tube for application to blood flow simulations. In pulse waves both fluid friction and wall viscosity are damping factors, and difficult to evaluate separately. In this paper, the coefficients of fluid friction and wall viscosity are estimated by fitting a nonlinear 1D flow model to experimental data. In the experimental setup, a distensible tube is connected to a piston pump at one end and closed at another end. The pressure and wall displacements are measured simultaneously. A good agreement between model predictions and experiments was achieved. For amplitude decrease, the effect of wall viscosity on the pulse wave has been shown as important as that of fluid viscosity.
1511.04729v1
2016-01-10
Classic Calculations of Static Properties of the Nucleons reexamined
Classic calculations of the magnetic moments mu_p and mu_n of the nucleons using the traditional exponential kernel show instability with respect to variations of the Borel mass as well as arbitrariness with respect to the choice of the onset of perturbative QCD. The use of a polynomial kernel, the coefficients of which are determined by the masses of the nucleon resonances stabilizes the calculation and provides much better damping of the unknown contribution of the nucleon continuum. The method is also applied to the evaluation of the coupling gA of proton to the axial current and to the strong part of the neutron-proton mass difference Delta M_np. All these quantities depend sensitively on the value of the 4-quark condensate < 0 | qqqq | 0 > and the value < 0 | qqqq | 0 > ~ 1.5< 0 | qq | 0 >^2 reproduces the experimental results.
1601.02247v2
2016-01-28
Dynamic system classifier
Stochastic differential equations describe well many physical, biological and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and classify complex dynamical systems is proposed within a Bayesian framework. To this end, we develop a dynamic system classifier (DSC). The DSC first abstracts training data of a system in terms of time dependent coefficients of the descriptive stochastic differential equation. Thereby the DSC identifies unique correlation structures within the training data. For definiteness we restrict the presentation of DSC to oscillation processes with a time dependent frequency {\omega}(t) and damping factor {\gamma}(t). Although real systems might be more complex, this simple oscillator captures many characteristic features. The {\omega} and {\gamma} timelines represent the abstract system characterization and permit the construction of efficient signal classifiers. Numerical experiments show that such classifiers perform well even in the low signal-to-noise regime.
1601.07901v2
2016-05-11
Electromagnetic properties of a double layer graphene system with electron-hole pairing
We study electromagnetic properties of a double layer graphene system in which electrons from one layer are coupled with holes from the other layer. The gauge invariant linear response functions are obtained. The frequency dependences of the transmission, reflection and absorption coefficients are computed. We predict a peak in the reflection and absorption at the frequency equals to the gap in the quasiparticle spectrum. It is shown that the electron-hole pairing results in an essential modification of the spectrum of surface TM plasmons. We find that the optical TM mode splits into a low frequency undamped branch and a high frequency damped branch. At zero temperature the lower branch disappears. It is established that the pairing does not influence the acoustic TM mode. It is also shown that the pairing opens the frequency window in the subgap range for the surface TE wave.
1605.03307v1
2016-08-02
Nonperturbative quasi-classical theory of the nonlinear electrodynamic response of graphene
An electromagnetic response of a single graphene layer to a uniform, arbitrarily strong electric field $E(t)$ is calculated by solving the kinetic Boltzmann equation within the relaxation-time approximation. The theory is valid at low (microwave, terahertz, infrared) frequencies satisfying the condition $\hbar\omega\lesssim 2E_F$, where $E_F$ is the Fermi energy. We investigate the saturable absorption and higher harmonics generation effects, as well as the transmission, reflection and absorption of radiation incident on the graphene layer, as a function of the frequency and power of the incident radiation and of the ratio of the radiative to scattering damping rates. We show that the optical bistability effect, predicted in Phys. Rev. B 90, 125425 (2014) on the basis of a perturbative approach, disappears when the problem is solved exactly. We show that, under the action of a high-power radiation ($\gtrsim 100$ kW/cm$^2$) both the reflection and absorption coefficients strongly decrease and the layer becomes transparent.
1608.00877v2
2016-09-23
Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.
1609.07250v1
2016-11-25
Random and quasi-coherent aspects in particle motion and their effects on transport and turbulence evolution
The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not strongly perturbed. The trajectories are, in these conditions, random sequences of large jumps and trapping or eddying events. Trapping determines quasi-coherent trajectory structures, which have a micro-confinement effect that is reflected in the transport coefficients. They determine non-Gaussian statistics and flows associated to an average velocity. Trajectory structures also influence the test modes on turbulent plasmas. Nonlinear damping and generation of zonal flow modes is found in drift turbulence in uniform magnetic field. The coupling of test particle and test mode studies permitted to evaluate the self-consistent evolution of the drift turbulence in an iterated approach. The results show an important nonlinear effect of ion diffusion, which can prevent the transition to the nonlinear regime at small drive of the instability. At larger drive, quasi-coherent trajectory structures appear and they have complex effects on turbulence.
1611.08521v1
2017-01-07
A quantitative description of Nernst effect in high-temperature superconductors
A quantitative vortex-fluid model for flux-flow resistivity $\rho$ and Nernst signal $e_N$ in high-temperature superconductors (HTSC) is proposed. Two kinds of vortices, magnetic and thermal, are considered, and the damping viscosity $\eta$ is modeled by extending the Bardeen-Stephen model to include the contributions of flux pinning at low temperature and in weak magnetic fields, and vortex-vortex collisions in strong magnetic fields. Remarkably accurate descriptions for both Nernst signal of six samples and flux flow resistivity are achieved over a wide range of temperature $T$ and magnetic field $B$. A discrepancy of three orders of magnitude between data and Anderson's model of Nernst signal is pointed out and revised using experimental values of $\eta$ from magnetoresistance. Furthermore, a two-step procedure is developed to reliably extract, from the Nernst signal, a set of physical parameters characterizing the vortex dynamics, which yields predictions of local superfluid density $n_s$, the Kosterlitz coefficient $b$ of thermal vortices, and upper critical field and temperature. Application of the model and systematic measurement of relevant physical quantities from Nernst signal in other HTSC samples are discussed.
1701.01832v1
2017-01-23
Understanding stability diagram of perpendicular magnetic tunnel junctions
Perpendicular magnetic tunnel junctions (MTJ) with a bottom pinned reference layer and a composite free layer (FL) are investigated. Different thicknesses of the FL were tested to obtain an optimal balance between tunneling magnetoresistance (TMR) ratio and perpendicular magnetic anisotropy. After annealing at 400 $^\circ$C, the TMR ratio for 1.5 nm thick CoFeB sublayer reached 180 % at room temperature and 280 % at 20 K with an MgO tunnel barrier thickness corresponding to the resistance area product RA = 10 Ohm$\mathrm{\mu}$m$^2$. The voltage vs. magnetic field stability diagrams measured in pillar-shaped MTJs with 130 nm diameter indicate the competition between spin transfer torque (STT), voltage controlled magnetic anisotropy (VCMA) and temperature effects in the switching process. An extended stability phase diagram model that takes into account all three parameters and the effective damping measured independently using broadband ferromagnetic resonance technique enabled the determination of both STT and VCMA coefficients that are responsible for the FL magnetization switching.
1701.06411v1
2017-01-27
Evaluating the Friction of Rotary Joints in Molecular Machines
A computationally-efficient method for evaluating friction in molecular rotary bearings is presented. This method estimates drag from fluctuations in molecular dynamics simulations via the fluctuation-dissipation theorem. This is effective even for simulation times short compared to a bearing's energy damping time and for rotation speeds comparable to or below typical thermal values. We apply this method to two molecular rotary bearings of similar size at 300K: previously studied nested (9,9)/(14,14) double-walled carbon nanotubes and a hypothetical rotary joint consisting of single acetylenic bonds in a rigid diamondoid housing. The acetylenic joint has a rotational frictional drag coefficient of $2 \times 10^{-35}\,\mbox{kg m${}^2$/s}$. The friction for the nested nanotubes is 120 times larger, comparable to values reported by previous studies. This fluctuation-based method could evaluate dissipation in a variety of molecular systems with similarly rigid and symmetric bearings.
1701.08202v2
2017-04-01
Homogenization for a Class of Generalized Langevin Equations with an Application to Thermophoresis
We study a class of systems whose dynamics are described by generalized Langevin equations with state-dependent coefficients. We find that in the limit, in which all the characteristic time scales vanish at the same rate, the position variable of the system converges to a homogenized process, described by an equation containing additional drift terms induced by the noise. The convergence results are obtained using the main result in \cite{hottovy2015smoluchowski}, whose version is proven here under a weaker spectral assumption on the damping matrix. We apply our results to study thermophoresis of a Brownian particle in a non-equilibrium heat bath.
1704.00134v2
2017-04-03
Parametrization of the Tkatchenko-Scheffler dispersion correction scheme for popular exchange-correlation density functionals: effect on the description of liquid water
We present a list of optimized damping range parameters $s_R$ to be used with the Tkatchenko-Scheffler van der Waals dispersion-correction scheme [Phys. Rev. Lett. 102, 073005 (2009)]. The optimal $s_R$ are obtained for seven popular generalized-gradient approximation exchange-correlation density functionals: PBE, RPBE, revPBE, PBEsol, BLYP, AM05 and PW91. The optimization is carried out in the standard way by minimizing the mean absolute error of the S22 test set, where the reference interaction energies are taken from coupled-cluster calculations. With the optimized range parameters, we assess the impact of van der Waals corrections on the ability of these functionals to accurately describe structural and thermodynamic properties of liquid water: radial distribution functions, self-diffusion coefficients and standard molar entropies.
1704.00761v2
2017-04-13
Stochastic Gradient Descent as Approximate Bayesian Inference
Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an approximate Bayesian posterior inference algorithm. Specifically, we show how to adjust the tuning parameters of constant SGD to best match the stationary distribution to a posterior, minimizing the Kullback-Leibler divergence between these two distributions. (2) We demonstrate that constant SGD gives rise to a new variational EM algorithm that optimizes hyperparameters in complex probabilistic models. (3) We also propose SGD with momentum for sampling and show how to adjust the damping coefficient accordingly. (4) We analyze MCMC algorithms. For Langevin Dynamics and Stochastic Gradient Fisher Scoring, we quantify the approximation errors due to finite learning rates. Finally (5), we use the stochastic process perspective to give a short proof of why Polyak averaging is optimal. Based on this idea, we propose a scalable approximate MCMC algorithm, the Averaged Stochastic Gradient Sampler.
1704.04289v2
2017-05-19
Phenomenology of light- and strange-quark simultaneous production at high energies
This letter presents an extension of EPL116(2017)62001 to light- and strange-quark nonequilibrium chemical phase-space occupancy factors ($\gamma_{q,s}$). The resulting damped trigonometric functionalities relating $\gamma_{q,s}$ to the nucleon-nucleon center-of-mass energies $(\sqrt{s_{NN}})$ looks very similar except different coefficients. The phenomenology of the resulting $\gamma_{q,s}(\sqrt{s_{NN}})$ describes a rapid decrease at $\sqrt{s_{NN}}\lesssim7~$GeV followed by a faster increase up to $\sim20~$GeV. Then, both $\gamma_{q,s}$ become nonsensitive to $\sqrt{s_{NN}}$. Although these differ from $\gamma_{s}(\sqrt{s_{NN}})$ obtained at $\gamma_q(\sqrt{s_{NN}})=1$, various particle ratios including $\mathrm{K}^+/\pi^+$, $\mathrm{K}^-/\pi^-$, $\mathrm{\Lambda}/\pi^-$, $\bar{\mathrm{\Lambda}}/\pi^-$, $\mathrm{\Xi}^+/\pi^+$, and $\mathrm{\Omega}/\pi^-$, can well be reproduced, as well. We conclude that $\gamma_{q,s}(\sqrt{s_{NN}})$ should be instead determined from fits of various particle yields and ratios but not merely from fits to the particle ratio $\mathrm{K}^+/\pi^+$.
1705.06961v1
2017-11-08
An Extended Kalman Filter Enhanced Hilbert-Huang Transform in Oscillation Detection
Hilbert-Huang transform (HHT) has drawn great attention in power system analysis due to its capability to deal with dynamic signal and provide instantaneous characteristics such as frequency, damping, and amplitudes. However, its shortcomings, including mode mixing and end effects, are as significant as its advantages. A preliminary result of an extended Kalman filter (EKF) method to enhance HHT and hopefully to overcome these disadvantages is presented in this paper. The proposal first removes dynamic DC components in signals using empirical mode decomposition. Then an EKF model is applied to extract instant coefficients. Numerical results using simulated and real-world low-frequency oscillation data suggest the proposal can help to overcome the mode mixing and end effects with a properly chosen number of modes.
1711.04644v1
2017-11-15
Probing Split-Ring Resonator Permeabilities with Loop-Gap Resonators
A method is proposed to experimentally determine the effective complex permeability of split-ring resonator (SRR) arrays used in the design of metamaterials at microwave frequencies. We analyze the microwave response of a loop-gap resonator (LGR) whose bore has been partially loaded with one or more SRRs. Our analysis reveals that the resonance frequency, magnetic plasma frequency, and damping constant of the effective permeability of the SRR array can be extracted from fits to the reflection coefficient (S11) of an inductively-coupled LGR. We propose LGR designs that would allow both a one-dimensional array of SRRs and small three-dimensional arrays of SRRs to be characterized. Finally, we demonstrate the method using a toroidal LGR loaded with a single extended SRR of length z.
1711.05819v1
2017-12-01
Some Optimizations on Detecting Gravitational Wave Using Convolutional Neural Network
This work investigates the problem of detecting gravitational wave (GW) events based on simulated damped sinusoid signals contaminated with white Gaussian noise. It is treated as a classification problem with one class for the interesting events. The proposed scheme consists of the following two successive steps: decomposing the data using a wavelet packet, representing the GW signal and noise using the derived decomposition coefficients; and determining the existence of any GW event using a convolutional neural network (CNN) with a logistic regression output layer. The characteristics of this work is its comprehensive investigations on CNN structure, detection window width, data resolution, wavelet packet decomposition and detection window overlap scheme. Extensive simulation experiments show excellent performances for reliable detection of signals with a range of GW model parameters and signal-to-noise ratios. While we use a simple waveform model in this study, we expect the method to be particularly valuable when the potential GW shapes are too complex to be characterized with a template bank.
1712.00356v2
2018-02-12
Dynamics of a magnetic skyrmionium driven by spin waves
The magnetic skyrmionium is a skyrmion-like structure but carries a zero net skyrmion number, which can be used as a building block for non-volatile information processing devices. Here, we study the dynamics of a magnetic skyrmionium driven by propagating spin waves. It is found that the skyrmionium can be effectively driven into motion by spin waves showing tiny skyrmion Hall effect, of which the mobility is much better than that of the skyrmion at the same condition. We also show that the skyrmionium mobility depends on the nanotrack width and damping coefficient, and can be controlled by an external out-of-plane magnetic field. Besides, we demonstrate the skyrmionium motion driven by spin waves is inertial. Our results indicate that the skyrmionium is a promising building block for building spin-wave spintronic devices.
1802.03868v2
2018-02-16
Articulatory information and Multiview Features for Large Vocabulary Continuous Speech Recognition
This paper explores the use of multi-view features and their discriminative transforms in a convolutional deep neural network (CNN) architecture for a continuous large vocabulary speech recognition task. Mel-filterbank energies and perceptually motivated forced damped oscillator coefficient (DOC) features are used after feature-space maximum-likelihood linear regression (fMLLR) transforms, which are combined and fed as a multi-view feature to a single CNN acoustic model. Use of multi-view feature representation demonstrated significant reduction in word error rates (WERs) compared to the use of individual features by themselves. In addition, when articulatory information was used as an additional input to a fused deep neural network (DNN) and CNN acoustic model, it was found to demonstrate further reduction in WER for the Switchboard subset and the CallHome subset (containing partly non-native accented speech) of the NIST 2000 conversational telephone speech test set, reducing the error rate by 12% relative to the baseline in both cases. This work shows that multi-view features in association with articulatory information can improve speech recognition robustness to spontaneous and non-native speech.
1802.05853v1
2018-02-26
A magnetic resonance in high-frequency viscosity of two-dimensional electrons
Two-dimensional (2D) electrons in high-quality nanostructures at low temperatures can form a viscous fluid. We develop a theory of high-frequency magnetotransport in such fluid. The time dispersion of viscosity should be taken into account at the frequencies about and above the rate of electron-electron collisions. We show that the shear viscosity coefficients as functions of magnetic field and frequency have the only resonance at the frequency equal to the doubled cyclotron frequency. We demonstrate that such resonance manifests itself in the plasmon damping. Apparently, the predicted resonance is also responsible for the peaks and features in photoresistance and photovoltage, recently observed on the best-quality GaAs quantum wells. The last fact should considered as an important evidence of forming a viscous electron fluid in such structures.
1802.09179v3
2018-03-14
Langevin equation in systems with also negative temperatures
We discuss how to derive a Langevin equation (LE) in non standard systems, i.e. when the kinetic part of the Hamiltonian is not the usual quadratic function. This generalization allows to consider also cases with negative absolute temperature. We first give some phenomenological arguments suggesting the shape of the viscous drift, replacing the usual linear viscous damping, and its relation with the diffusion coefficient modulating the white noise term. As a second step, we implement a procedure to reconstruct the drift and the diffusion term of the LE from the time-series of the momentum of a heavy particle embedded in a large Hamiltonian system. The results of our reconstruction are in good agreement with the phenomenological arguments. Applying the method to systems with negative temperature, we can observe that also in this case there is a suitable Langevin equation, obtained with a precise protocol, able to reproduce in a proper way the statistical features of the slow variables. In other words, even in this context, systems with negative temperature do not show any pathology.
1803.05317v2
2018-04-07
Chemotaxis effect vs logistic damping on boundedness in the 2-D minimal Keller-Segel model
In this paper, we study chemotaxis effect vs logistic dampening on boundedness for the two-dimensional minimal Keller-Segel model with logistic source in a 2-D smooth and bounded domain. It is well-known that this model allows only for global and uniform-in-time bounded solutions for any chemotactic strength and logistic dampening. Here, we carefully employ a simple and new method to regain its boundedness and, with particular attention to how boundedness depends qualitatively on the coefficient of chemotactic strength and logistic dampening rate. Up to a scaling constant depending only on initial data and the domain, we provide explicit upper bounds for the the solution components of the corresponding initial-boundary value problem. This qualitative boundedness results seems to be the first result in the regard.
1804.02501v1
2018-05-07
Lewis-Riesenfeld quantization and SU(1,1) coherent states for 2D damped harmonic oscillator
In this paper we study a two-dimensional [2D] rotationally symmetric harmonic oscillator with time-dependent frictional force. At the classical level, we solve the equations of motion for a particular case of the time-dependent coefficient of friction. At the quantum level, we use the Lewis-Riesenfeld procedure of invariants to construct exact solutions for the corresponding time-dependent Schr\"{o}dinger equations. The eigenfunctions obtained are in terms of the generalized Laguerre polynomials. By mean of the solutions we verify a generalization version of the Heisenberg's uncertainty relation and derive the generators of the $su(1,1)$ Lie algebra. Based on these generators, we construct the coherent states $\grave{\textrm{a}}$ la Barut-Girardello and $\grave{\textrm{a}}$ la Perelomov and respectively study their properties.
1805.02484v2
2018-05-16
Numerical analysis of the weakly nonlinear Boussinesq system with a freely moving body on the bottom
In this study, the numerical analysis of a specific fluid-solid interaction problem is detailed. The weakly nonlinear Boussinesq system is considered with the addition of a solid object lying on the flat bottom, allowed to move horizontally under the pressure forces created by the waves. We present an accurate finite difference scheme for this physical model, finely tuned to preserve important features of the original coupled system: nonlinear effects for the waves, energy dissipation due to the frictional movement of the solid. The moving bottom case is compared with a system where the same object is fixed to the bottom in order to observe the qualitative and quantitative differences in wave transformation. In particular a loss of wave amplitude is observed. The influence of the friction on the whole system is also measured, indicating differences for small and large coefficients of friction. Overall, hydrodynamic damping effects reminiscent to the dead-water phenomenon can be established.
1805.07216v1
2018-05-21
Squeezed in three dimensions, moving in two: Hydrodynamic theory of 3D incompressible easy-plane polar active fluids
We study the hydrodynamic behavior of three dimensional (3D) incompressible collections of self-propelled entities in contact with a momentum sink in a state with non-zero average velocity, hereafter called 3D easy-plane incompressible polar active fluids. We show that the hydrodynamic model for this system belongs to the same universality class as that of an equilibrium system, namely a special 3D anisotropic magnet. The latter can be further mapped onto yet another equilibrium system, a DNA-lipid mixture in the sliding columnar phase. Through these connections we find a divergent renormalization of the damping coefficients in 3D easy-plane incompressible polar active fluids, and obtain their equal-time velocity correlation functions.
1805.07930v1
2018-06-12
Complex magnetism and non-Fermi liquid state in the vicinity of the quantum critical point in the CeCo$_{1-x}$Fe$_x$Ge$_3$ series
We report extensive studies on the CeCo$_{1-x}$Fe$_{x}$Ge$_3$ alloys, which show quantum critical point (QCP) due to damping the antiferromagnetic order in CeCoGe$_3$ down to 0 K by doping with the paramagnetic CeFeGe$_3$ compound. The presence of QCP is confirmed by detecting the non-Fermi liquid behavior (NFL) using a wide range of the experimental methods: magnetic susceptibility, specific heat, electrical resistivity, magnetoresistance, and thermoelectric power. In the case of the thermoelectric power we find a clear enhancement of the Seebeck coefficient for $x$ around 0.6, i.e. in the neighborhood of QCP. Finally, the different complementary studies enabled construction of the complex magnetic phase diagram for the CeCo$_{1-x}$Fe$_{x}$Ge$_3$ system, including the energy scale imposed by the crystal electric field splitting of the Ce ground state.
1806.04656v1
2018-08-21
Position Sensor-less and Adaptive Speed Design for Controlling Brush-less DC Motor Drives
This paper proposes a method for direct torque control of Brushless DC (BLDC) motors. Evaluating the trapezium of back-EMF is needed, and is done via a sliding mode observer employing just one measurement of stator current. The effect of the proposed estimation algorithm is reducing the impact of switching noise and consequently eliminating the required filter. Furthermore, to overcome the uncertainties related to BLDC motors, Recursive Least Square (RLS) is regarded as a real-time estimator of inertia and viscous damping coefficients of the BLDC motor. By substituting the estimated load torque in mechanical dynamic equations, the rotor speed can be calculated. Also, to increase the robustness and decrease the rise time of the system, Modified Model Reference Adaptive System (MMRAS) is applied in order to design a new speed controller. Simulation results confirm the validity of this recommended method.
1808.06768v1
2018-09-28
Unifying averaged dynamics of the Fokker-Planck equation for Paul traps
Collective dynamics of a collisional plasma in a Paul trap is governed by the Fokker-Planck equation, which is usually assumed to lead to a unique asymptotic time-periodic solution irrespective of the initial plasma distribution. This uniqueness is, however, hard to prove in general due to analytical difficulties. For the case of small damping and diffusion coefficients, we apply averaging theory to a special solution to this problem, and show that the averaged dynamics can be represented by a remarkably simple 2D phase portrait, which is independent of the applied rf field amplitude. In particular, in the 2D phase portrait, we have two regions of initial conditions. From one region, all solutions are unbounded. From the other region, all solutions go to a stable fixed point, which represents a unique time-periodic solution of the plasma distribution function, and the boundary between these two is a parabola.
1809.10952v2
2018-10-29
Three Mechanisms of Weight Decay Regularization
Weight decay is one of the standard tricks in the neural network toolbox, but the reasons for its regularization effect are poorly understood, and recent results have cast doubt on the traditional interpretation in terms of $L_2$ regularization. Literal weight decay has been shown to outperform $L_2$ regularization for optimizers for which they differ. We empirically investigate weight decay for three optimization algorithms (SGD, Adam, and K-FAC) and a variety of network architectures. We identify three distinct mechanisms by which weight decay exerts a regularization effect, depending on the particular optimization algorithm and architecture: (1) increasing the effective learning rate, (2) approximately regularizing the input-output Jacobian norm, and (3) reducing the effective damping coefficient for second-order optimization. Our results provide insight into how to improve the regularization of neural networks.
1810.12281v1
2018-11-05
Logarithmic estimates for continuity equations
The aim of this short note is twofold. First, we give a sketch of the proof of a recent result proved by the authors in the paper [Colombo, Crippa, and Spirito, Calc. Var. Partial Differential Equations 2015] concerning existence and uniqueness of renormalized solutions of continuity equations with unbounded damping coefficient. Second, we show how the ideas in [Colombo, Crippa, and Spirito, Calc. Var. Partial Differential Equations 2015] can be used to provide an alternative proof of the result in [Clop, Jiang, Mateu, and Orobitg, Calc. Var. Partial Differential Equations 2016], [Desjardins, Comm. Partial Diff. Eq. 1996], and [Mucha, J. Differential Equations 2010] where the usual requirement of boundedness of the divergence of the vector field has been relaxed to various settings of exponentially integrable functions.
1811.02463v1
2018-12-20
Edge modes and Fabry-Perot Plasmonic Resonances in anomalous-Hall Thin Films
We study plasmon propagation on a metallic two-dimensional surface partially coated with a thin film of anomalous-Hall material. The resulting three regions, separated by two sharp interfaces, are characterised by different Hall conductivities but identical normal conductivities. A single bound mode is found, which can localise to either interface and has an asymmetric potential profile across the region. For propagating modes, we calculate the reflection and transmission coefficients through the magnetic region. We find Airy transmission patterns with sharp maxima and minima as a function of the plasmon incidence angle. The system therefore behaves as a high-quality filter.
1812.08798v2
2019-01-01
Gravitational Waves in the Presence of Viscosity
We analyze gravitational waves propagating in an isotropic cosmic fluid endowed with a bulk viscosity $\zeta$ and a shear viscosity $\eta$, assuming these coefficients to vary with fluid density $\rho$ as $\rho^\lambda$, with $\lambda=1/2$ favored by experimental evidence. We give the general governing equation for the gravitational waves, and focus thereafter on two examples. The first concerns waves in the very late universe, close to the Big Rip, where the fate of the comic fluid is dependent highly on the values of the parameters. Our second example considers the very early universe, the lepton era; the motivation for this choice being that the microscopical bulk viscosity as calculated from statistical mechanics is then at maximum. We find that the gravitational waves on such an underlying medium are damped, having a decay constant equal to the inverse of the conformal Hubble parameter. Our results turn out to be in good agreement with other viscosity-based approaches.
1901.00767v3
2019-01-20
Fate of spin polarization in a relativistic fluid: An entropy-current analysis
We derive relativistic hydrodynamic equations with a dynamical spin degree of freedom on the basis of an entropy-current analysis. The first and second laws of local thermodynamics constrain possible structures of the constitutive relations including a spin current and the antisymmetric part of the (canonical) energy-momentum tensor. Solving the obtained hydrodynamic equations within the linear-mode analysis, we find spin-diffusion modes, indicating that spin density is damped out after a characteristic time scale controlled by transport coefficients introduced in the antisymmetric part of the energy-momentum tensor in the entropy-current analysis. This is a consequence of mutual convertibility between spin and orbital angular momentum.
1901.06615v2
2019-01-24
A priori error estimates for the finite element approximation of Westervelt's quasilinear acoustic wave equation
We study the spatial discretization of Westervelt's quasilinear strongly damped wave equation by piecewise linear finite elements. Our approach employs the Banach fixed-point theorem combined with a priori analysis of a linear wave model with variable coefficients. Degeneracy of the semi-discrete Westervelt equation is avoided by relying on the inverse estimates for finite element functions and the stability and approximation properties of the interpolation operator. In this way, we obtain optimal convergence rates in $L^2$-based spatial norms for sufficiently small data and mesh size and an appropriate choice of initial approximations. Numerical experiments in a setting of a 1D channel as well as for a focused-ultrasound problem illustrate our theoretical findings.
1901.08510v3
2019-02-26
Coulomb drag of excitons in Bose-Fermi mixtures
We develop a microscopic theory of the Coulomb drag effect in a hybrid system consisting of spatially separated two-dimensional quantum gases of degenerate electrons and dipolar excitons. We consider both the normal-phase and condensate regimes of the exciton subsystem and investigate the cross-mobility of the system being the kinetic coefficient, which couples the static electric field applied to the electron layer with the particle density current (flux) in the exciton subsystem. We study the temperature dependence of the cross-mobility and its dependence on the interlayer separation. We show that exciton-exciton interaction plays a dramatic role. If the exciton gas is in the normal phase, then the screening of interlayer interaction by the exciton subsystem results in an exponential damping of the cross-mobility with the decrease of temperature, while at low temperatures, the interactions result in a robust bosonic transport due to the emergence of the Bogoliubov quasiparticles.
1902.09721v1
2019-04-23
Generalized Moment Correction for Long-Ranged Electrostatics
Describing long-ranged electrostatics using short-ranged pair potentials is appealing since the computational complexity scales linearly with the number of particles. The foundation of this approach is to mimic the long-ranged medium response by cancelling electric multipoles within a small cutoff sphere. We propose a rigorous and formally exact new method that cancels up to infinitely many multipole moments and is free of operational damping parameters often required in existing theories. Using molecular dynamics simulations of water with and without added salt, we discuss radial distribution functions, Kirkwood-Buff integrals, dielectrics, diffusion coefficients, and angular correlations in relation to existing electrostatic models. We find that the proposed method is an efficient and accurate alternative for handling long-ranged electrostatics as compared to Ewald summation schemes. The methodology and proposed parameterization is applicable also for dipole-dipole interactions.
1904.10335v2
2019-06-02
Analytical prediction of logarithmic Rayleigh scattering in amorphous solids from tensorial heterogeneous elasticity with power-law disorder
The damping or attenuation coefficient of sound waves in solids due to impurities scales with the wavevector to the fourth power, also known as Rayleigh scattering. In amorphous solids, Rayleigh scattering may be enhanced by a logarithmic factor although computer simulations offer conflicting conclusions regarding this enhancement and its microscopic origin. We present a tensorial replica field-theoretic derivation based on heterogeneous or fluctuating elasticity (HE), which shows that long-range (power-law) spatial correlations of the elastic constants, is the origin of the logarithmic enhancement to Rayleigh scattering of phonons in amorphous solids. We also consider the case of zero spatial fluctuations in the elastic constants, and of power-law decaying fluctuations in the internal stresses. Also in this case the logarithmic enhancement to the Rayleigh scattering law can be derived from the proposed tensorial HE framework.
1906.00372v3
2019-05-31
Deterministic and stochastic damage detection via dynamic response analysis
The paper proposes a method of damage detection in elastic materials, which is based on analyzing the time-dependent (dynamic) response of the material excited by an acoustic signal. A case study is presented consisting of experimental measurements and their mathematical analysis. The decisive parameters (wave speed and damping coefficient) of a mathematical model of the acoustic wave are calibrated by comparing the measurement data with the numerically evaluated exact solution predicted by the mathematical model. The calibration is done both deterministically by minimizing the square error over time and stochastically by a Bayesian approach, implemented through the Metropolis-Hastings algorithm. The resulting posterior distribution of the parameters can be used to construct a Bayesian test for damage.
1906.00797v2
2019-07-21
Supersolutions for parabolic equations with unbounded diffusion and its applications to some classes of parabolic and hyperbolic equations
This paper is concerned with supersolutions to parabolic equations of the form \begin{equation} \partial_t U (x,t)-D(x)\Delta U(x,t)=0, \quad (x,t)\in \mathbb{R}^N \times (0,\infty), \end{equation} where $D\in C(\mathbb{R}^N)$ is positive. Under the behavior of the diffusion coefficient $D$ with polynomial order at spatial infinity, a family of supersolutions with slowly decaying property at spatial infinity is provided. As a first application, weighted $L^2$ type decay estimates for the initial-boundary value problem of the corresponding parabolic equation are proved. The second application is the study of the exterior problem of wave equations with space-dependent damping terms. By using supersolutions provided above, energy estimates with polynomial weight and diffusion phenomena are shown.
1907.08992v1
2019-08-11
A computational study of transient shear banding in soft jammed solids
We have designed 3D numerical simulations of a soft spheres model, with size polidispersity and in athermal conditions, to study the transient shear banding that occurs during yielding of jammed soft solids. We analyze the effects of different types of drag coefficients used in the simulations and compare the results obtained using Lees-Edwards periodic boundary conditions with the case in which the same model solid is confined between two walls. The specific damping mechanism and the different boundary conditions indeed modify the load curves and the velocity profiles in the transient regime. Nevertheless, we find that the presence of a stress-overshoot and of a related transient banding phenomenon for large enough samples are a robust feature for overdamped systems, where their presence do not depend on the specific drag used and on the different boundary conditions.
1908.03943v1
2019-09-10
Diffusion and memory effect in a stochastic processes and the correspondence to an information propagation in a social system
A generalized Langevin equation is suggested to describe a system with memory($u(t,t') = \frac{1}{\Gamma (\nu )}(t - t')^\nu $) as well as with positive and negative damping. The equation can be transformed into the Fokker-Planck equation by using the Kramers-Moyal expansion. The solution of Fokker-Planck equation shows that velocity obeys a Gaussian distribution. The distribution curve will flatten as the memory parameter increases, which indicates that memory can enhance the randomness of the system. There are also some other memory effects behind this distribution, which can be characterized by calculating the transport coefficients, mean square displacement and correlation between the noise and space. These discussions can be paralleled to a social system to understand the propagation of social ideology caused by memory.
1909.04220v1
2019-10-10
Mesoscopic theory for systems with competing interactions near a confining wall
Mesoscopic theory for self-assembling systems near a planar confining surface is developed. Euler- Lagrange (EL) equations and the boundary conditions (BC) for the local volume fraction and the correlation function are derived from the DFT expression for the grand thermodynamic potential. Various levels of approximation can be considered for the obtained equations. The lowest-order nontrivial approximation (GM) resembles the Landau-Brazovskii type theory for a semiinfinite system. Unlike in the original phenomenological theory, however, all coefficients in our equations and BC are expressed in terms of the interaction potential and the thermodynamic state. Analytical solutions of the linearized equations in GM are presented and discussed on a general level and for a particular example of the double-Yukawa potential. We show exponentially damped oscillations of the volume fraction and the correlation function in the direction perpendicular to the confining surface. The correlations show oscillatory decay in directions parallel to this surface too, with the decay length increasing significantly when the system boundary is approached. The framework of our theory allows for a systematic improvement of the accuracy of the results.
1910.04474v2
2019-11-11
Orbit-like trajectory of the vortex core in a magnetic nanodot
In physics, conserved quantities are key to understanding and describing physical phenomena. These conserved quantities are related to Noether's theorem and the Lagrangian description both in classical mechanics and in field theory. In this article we have found the equation of the vortex core trajectory in terms of two conserved physical quantities, namely the energy, $E$, and a vector perpendicular to the orbit plane, $\vec{A} = -\vec{L} + \vec{G} \, |\vec{r}_c|^2/2$ where $\vec{G}$, $\vec{L}$ and $\vec{r}_c$ are the topological gyrovector, the angular momentum and the position of the vortex core, respectively. We find that in the absence of a dissipative term, for small deviations of the vortex core, the trajectory is bounded between two concentric circles. On the contrary, under the action of a dissipative term proportional to the damping coefficient, $\vec{A}$ is no longer conservative and the vortex core moves either towards the center or out of the cylinder, depending on the circularity of the magnetic vortex and the intensity of the magnetic field applied in the plane of the cylinder.
1911.04555v2
2019-12-04
A high-order discontinuous Galerkin method for nonlinear sound waves
We propose a high-order discontinuous Galerkin scheme for nonlinear acoustic waves on polytopic meshes. To model sound propagation with and without losses, we use Westervelt's nonlinear wave equation with and without strong damping. Challenges in the numerical analysis lie in handling the nonlinearity in the model, which involves the derivatives in time of the acoustic velocity potential, and in preventing the equation from degenerating. We rely in our approach on the Banach fixed-point theorem combined with a stability and convergence analysis of a linear wave equation with a variable coefficient in front of the second time derivative. By doing so, we derive an a priori error estimate for Westervelt's equation in a suitable energy norm for the polynomial degree $p \geq 2$. Numerical experiments carried out in two-dimensional settings illustrate the theoretical convergence results. In addition, we demonstrate efficiency of the method in a three-dimensional domain with varying medium parameters, where we use the discontinuous Galerkin approach in a hybrid way.
1912.02281v1
2019-12-05
The blow up of solutions to semilinear wave equations on asymptotically Euclidean manifolds
In this paper, we investigate the problem of blow up and sharp upper bound estimates of the lifespan for the solutions to the semilinear wave equations, posed on asymptotically Euclidean manifolds. Here the metric is assumed to be exponential perturbation of the spherical symmetric, long range asymptotically Euclidean metric. One of the main ingredients in our proof is the construction of (unbounded) positive entire solutions for $\Delta_{g}\phi_\lambda=\lambda^{2}\phi_\lambda$, with certain estimates which are uniform for small parameter $\lambda\in (0,\lambda_0)$. In addition, our argument works equally well for semilinear damped wave equations, when the coefficient of the dissipation term is integrable (without sign condition) and space-independent.
1912.02540v1
2019-12-08
Dynamical Primal-Dual Accelerated Method with Applications to Network Optimization
This paper develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. This paper analyzes critical values for parameters in the proposed method and prove that the rate of convergence in terms of the duality gap function is $O(\tfrac{1}{t^2})$ by choosing suitable parameters. As far as we know, this is the first continuous-time primal-dual accelerated method that can obtain the optimal rate. Then this work applies the proposed method to two network optimization problems, a distributed optimization problem with consensus constraints and a distributed extended monotropic optimization problem, and obtains two variant distributed algorithms. Finally, numerical simulations are given to demonstrate the efficacy of the proposed method.
1912.03690v2
2020-01-08
Assessing different approaches to ab initio calculations of spin wave stiffness
Ab initio calculations of the spin wave stiffness constant $D$ for elemental Fe and Ni performed by different groups in the past have led to values with a considerable spread of 50-100 %. We present results for the stiffness constant $D$ of Fe, Ni, and permalloy Fe$_{0.19}$Ni$_{0.81}$ obtained by three different approaches: (i) by finding the quadratic term coefficient of the power expansion of the spin wave energy dispersion, (ii) by a damped real-space summation of weighted exchange coupling constants, and (iii) by integrating the appropriate expression in reciprocal space. All approaches are implemented by means of the same Korringa-Kohn-Rostoker (KKR) Green function formalism. We demonstrate that if properly converged, all procedures yield comparable values, with uncertainties of 5-10 % remaining. By a careful analysis of the influence of various technical parameters we estimate the margin of errors for the stiffness constants evaluated by different approaches and suggest procedures to minimize the risk of getting incorrect results.
2001.02558v2
2020-02-12
Exact Solution for the Heat Conductance in Harmonic Chains
We present an exact solution for the heat conductance along a harmonic chain connecting two reservoirs at different temperatures. In this model, the end points correspond to Brownian particles with different damping coefficients. Such analytical expression for the heat conductance covers its behavior from mesoscopic to very long one-dimensional quantum chains, and validates the ballistic nature of the heat transport in the latter example. This implies the absence of the Fourier law for classical and quantum harmonic chains. We also provide a thorough analysis of the normal modes of system which helps us to satisfactorily interpret these results.
2002.05195v2
2020-04-17
On Enhanced Dissipation for the Boussinesq Equations
In this article we consider the stability and damping problem for the 2D Boussinesq equations with partial dissipation near a two parameter family of stationary solutions which includes Couette flow and hydrostatic balance. In the first part we show that for the linearized problem in an infinite periodic channel the evolution is asymptotically stable if any diffusion coefficient is non-zero. In particular, this imposes weaker conditions than for example vertical diffusion. Furthermore, we study the interaction of shear flow, hydrostatic balance and partial dissipation. In a second part we adapt the methods used by Bedrossian, Vicol and Wang in the Navier-Stokes problem and combine them with cancellation properties of the Boussinesq equations to establish small data stability and enhanced dissipation results for the nonlinear Boussinesq problem with full dissipation.
2004.08125v1
2020-05-05
Heavy quark diffusion in an overoccupied gluon plasma
We extract the heavy-quark diffusion coefficient \kappa and the resulting momentum broadening <p^2> in a far-from-equilibrium non-Abelian plasma. We find several features in the time dependence of the momentum broadening: a short initial rapid growth of <p^2>, followed by linear growth with time due to Langevin-type dynamics and damped oscillations around this growth at the plasmon frequency. We show that these novel oscillations are not easily explained using perturbative techniques but result from an excess of gluons at low momenta. These oscillation are therefore a gauge invariant confirmation of the infrared enhancement we had previously observed in gauge-fixed correlation functions. We argue that the kinetic theory description of such systems becomes less reliable in the presence of this IR enhancement.
2005.02418v2
2020-09-02
Frustrated bearings
In a bearing state, touching spheres (disks in two dimensions) roll on each other without slip. Here we frustrate a system of touching spheres by imposing two different bearing states on opposite sides and search for the configurations of lowest energy dissipation. If the dissipation between contacts of spheres is viscous (with random damping constants), the angular momentum continuously changes from one bearing state to the other. For Coulomb friction (with random friction coefficients) in two dimensions, a sharp line separates the two bearing states and we show that this line corresponds to the minimum cut. Astonishingly however, in three dimensions, intermediate bearing domains, that are not synchronized with either side, are energetically more favorable than the minimum-cut surface. Instead of a sharp cut, the steady state displays a fragmented structure. This novel type of state of minimum dissipation is characterized by a spanning network of slipless contacts that reaches every sphere. Such a situation becomes possible because in three dimensions bearing states have four degrees of freedom.
2009.01295v1