publicationDate
stringlengths
1
2.79k
title
stringlengths
1
36.5k
abstract
stringlengths
1
37.3k
id
stringlengths
9
47
2013-05-21
Characterization and Synthesis of Rayleigh Damped Elastodynamic Networks
We consider damped elastodynamic networks where the damping matrix is assumed to be a non-negative linear combination of the stiffness and mass matrices (also known as Rayleigh or proportional damping). We give here a characterization of the frequency response of such networks. We also answer the synthesis question for such networks, i.e., how to construct a Rayleigh damped elastodynamic network with a given frequency response. Our analysis shows that not all damped elastodynamic networks can be realized when the proportionality constants between the damping matrix and the mass and stiffness matrices are fixed.
1305.4961v1
2016-08-08
Damping Functions correct over-dissipation of the Smagorinsky Model
This paper studies the time-averaged energy dissipation rate $\langle \varepsilon_{SMD} (u)\rangle$ for the combination of the Smagorinsky model and damping function. The Smagorinsky model is well known to over-damp. One common correction is to include damping functions that reduce the effects of model viscosity near walls. Mathematical analysis is given here that allows evaluation of $\langle \varepsilon_{SMD} (u)\rangle $ for any damping function. Moreover, the analysis motivates a modified van Driest damping. It is proven that the combination of the Smagorinsky with this modified damping function does not over dissipate and is also consistent with Kolmogorov phenomenology.
1608.02655v2
2015-02-26
Efficient modelling of particle collisions using a non-linear viscoelastic contact force
In this paper the normal collision of spherical particles is investigated. The particle interaction is modelled in a macroscopic way using the Hertzian contact force with additional linear damping. The goal of the work is to develop an efficient approximate solution of sufficient accuracy for this problem which can be used in soft-sphere collision models for Discrete Element Methods and for particle transport in viscous fluids. First, by the choice of appropriate units, the number of governing parameters of the collision process is reduced to one, which is a simple combination of known material parameters as well as initial conditions. It provides a dimensionless parameter that characterizes all such collisions up to dynamic similitude. Next, a rigorous calculation of the collision time and restitution coefficient from the governing equations, in the form of a series expansion in this parameter is provided. Such a calculation based on first principles is particularly interesting from a theoretical perspective. Since the governing equations present some technical difficulties, the methods employed are also of interest from the point of view of the analytical technique. Using further approximations, compact expressions for the restitution coefficient and the collision time are then provided. These are used to implement an approximate algebraic rule for computing the desired stiffness and damping in the framework of the adaptive collision model (Kempe & Fr\"{o}hlich, J. Fluid Mech., 709: 445-489, 2012). Numerical tests with binary as well as multiple particle collisions are reported to illustrate the accuracy of the proposed method and its superiority in terms of numerical efficiency.
1502.07728v2
2018-12-10
H$_2$/HD molecular data for analysis of quasar spectra in search of varying constants
Absorption lines of H$_2$ and HD molecules observed at high redshift in the line of sight towards quasars are a test ground to search for variation of the proton-to-electron mass ratio $\mu$. For this purpose, results from astronomical observations are compared with a compilation of molecular data of the highest accuracy, obtained in laboratory studies as well as in first-principles calculations. Aims: A comprehensive line list is compiled for H$_2$ and HD absorption lines in the Lyman ($B^1\Sigma_u^+$ - $X^1\Sigma_g^+$) and Werner ($C^1\Pi_u$ - $X^1\Sigma_g^+$) band systems up to the Lyman cutoff at 912 Angstroms. Molecular parameters listed for each line $i$ are the transition wavelength $\lambda_i$, the line oscillator strength $f_i$, the radiative damping parameter of the excited state $\Gamma_i$, and the sensitivity coefficient $K_i$ for a variation of the proton-to-electron mass ratio. Methods: The transition wavelengths $\lambda_i$ for the H$_2$ and HD molecules are determined by a variety of advanced high-precision spectroscopic experiments involving narrowband vacuum ultraviolet lasers, Fourier-transform spectrometers, and synchrotron radiation sources. Results for the line oscillator strengths $f_i$, damping parameters $\Gamma_i$, and sensitivity coefficients $K_i$ are obtained in theoretical quantum chemical calculations. Results: A new list of molecular data is compiled for future analyses of cold clouds of hydrogen absorbers, specifically for studies of $\mu$-variation from quasar data. The list is applied in a refit of quasar absorption spectra of B0642$-$5038 and J1237$+$0647 yielding constraints on a variation of the proton-to-electron mass ratio $\Delta\mu/\mu$ consistent with previous analyses.
1812.03628v2
2019-12-24
Modified Drude model for small gold nanoparticles surface plasmon resonance based on the role of classical confinement
We study the effect of restoration force caused by the limited size of a small metallic nanoparticle (MNP) on its linear response to the electric field of incident light. In a semi-classical phenomenological Drude-like model for small MNP, we consider restoration force caused by the displacement of conduction electrons with respect to the ionic background taking into account a free coefficient as a function of diameter of NP in the force term obtained by the idealistic Thomson model in order to adjust the classical approach. All important mechanisms of the energy dissipation such as electron-electron, electron-phonon and electron-NP surface scatterings and radiation are included in the model. In addition a correction term added to the damping factor of mentioned mechanisms in order to rectify the deficiencies of theoretical approaches. To determine the free parameters, the experimental data of extinction cross section of gold NPs with different sizes doped in the glass are used and a good agreement between experimental data and our model is observed. It is shown that by decreasing the diameter of NP, the restoration force becomes larger and classical confinement effect becomes more dominant in the interaction. According to experimental data, the best fitted parameter for the coefficient of restoration force is a third order negative powers function of diameter. The fitted function for the correction damping factor is proportional to the inverse squared wavelength and third order power series of NP diameter. The real and imaginary parts of permittivity for different sizes of gold NPs are presented and it is seen that the imaginary part is more sensitive to the diameter variations. Increase in the NP diameter causes increase in the real part of permittivity and decrease in the imaginary part.
1912.11245v1
2022-01-03
Solid-like to Liquid-like Behavior of Cu Diffusion in Superionic Cu2X (X=S, Se): An Inelastic Neutron Scattering and Ab-Initio Molecular Dynamics Investigation
Cu2Se and Cu2S are excellent model systems of superionic conductors with large diffusion coefficients that have been reported to exhibit different solid-liquid-like Cu-ion diffusion. In this paper, we clarify the atomic dynamics of these compounds with temperature-dependent ab-initio molecular dynamics (AIMD) simulations and inelastic neutron scattering (INS) experiments. Using the dynamical structure factor and Van-Hove correlation function, we interrogate the jump-time, hopping length distribution and associated diffusion coefficients. In cubic-Cu2Se at 500 K, we find solid-like diffusion with Cu-jump lengths matching well the first-neighbour Cu-Cu distance of ~3 {\AA} in the crystal, and clearly defined optic phonons involving Cu-vibrations. Above 700 K, the jump-length distribution becomes a broad maximum cantered around 4 {\AA}, spanning the first and second neighbour lattice distances, and a concurrent broadening of the Cu-phonon density of states. Further, above 900 K, the Cu-diffusion becomes close to liquid-like, with distributions of Cu-atoms continuously connecting crystal sites, while the vibrational modes involving Cu motions are highly damped, though still not fully over-damped as in a liquid. At low temperatures, the solid-like diffusion is consistent with previous X-ray diffraction and quasielastic neutron scattering experiments, while the higher-temperature observation of the liquid-like diffusion is in agreement with previous AIMD simulations. We also report AIMD simulations in Cu2S in the hexagonal and cubic superionic phases, and observe similar solid and liquid-like diffusion at low- and high-temperatures, respectively. The calculated ionic-conductivity is in fair agreement with reported experimental values.
2201.00606v1
2024-02-22
Laser patterning of magnonic structure via local crystallization of Yittrium Iron Garnet
The fabrication and integration of high-quality structures of Yttrium Iron Garnet (YIG) is critical for magnonics.Films with excellent properties are obtained only on single crystal Gadolinium Gallium Garnet (GGG) substrates using high-temperature processes. The subsequent realization of magnonic structures via lithography and etching is not straightforward as it requires a tight control of the edge roughness, to avoid magnon scattering, and planarization in case of multilayer devices. In this work we describe a different approach based on local laser annealing of amorphous YIG films, avoiding the need for subjecting the entire sample to high thermal budgets and for physical etching. Starting from amorphous and paramagnetic YIG films grown by pulsed laser deposition at room temperature on GGG, a 405 nm laser is used for patterning arbitrary shaped ferrimagnetic structures by local crystallization. In thick films (160 nm) the laser induced surface corrugation prevents the propagation of spin-wave modes in patterned conduits. For thinner films (80 nm) coherent propagation is observed in 1.2 micron wide conduits displaying an attenuation length of 5 micron which is compatible with a damping coefficient of about 5e-3. Possible routes to achieve damping coefficients compatible with state-of-the art epitaxial YIG films are discussed.
2402.14444v1
2024-03-07
The stochastic Ravine accelerated gradient method with general extrapolation coefficients
In a real Hilbert space domain setting, we study the convergence properties of the stochastic Ravine accelerated gradient method for convex differentiable optimization. We consider the general form of this algorithm where the extrapolation coefficients can vary with each iteration, and where the evaluation of the gradient is subject to random errors. This general treatment models a breadth of practical algorithms and numerical implementations. We show that, under a proper tuning of the extrapolation parameters, and when the error variance associated with the gradient evaluations or the step-size sequences vanish sufficiently fast, the Ravine method provides fast convergence of the values both in expectation and almost surely. We also improve the convergence rates from O(.) to o(.). Moreover, we show almost sure summability property of the gradients, which implies the fast convergence of the gradients towards zero. This property reflects the fact that the high-resolution ODE of the Ravine method includes a Hessian-driven damping term. When the space is also separable, our analysis allows also to establish almost sure weak convergence of the sequence of iterates provided by the algorithm. We finally specialize the analysis to consider different parameter choices, including vanishing and constant (heavy ball method with friction) damping parameter, and present a comprehensive landscape of the tradeoffs in speed and accuracy associated with these parameter choices and statistical properties on the sequence of errors in the gradient computations. We provide a thorough discussion of the similarities and differences with the Nesterov accelerated gradient which satisfies similar asymptotic convergence rates.
2403.04860v2
2012-01-27
Full and Half Gilbert Tessellations with Rectangular Cells
We investigate the ray-length distributions for two different rectangular versions of Gilbert's tessellation. In the full rectangular version, lines extend either horizontally (with east- and west-growing rays) or vertically (north- and south-growing rays) from seed points which form a Poisson point process, each ray stopping when another ray is met. In the half rectangular version, east and south growing rays do not interact with west and north rays. For the half rectangular tessellation we compute analytically, via recursion, a series expansion for the ray-length distribution, whilst for the full rectangular version we develop an accurate simulation technique, based in part on the stopping-set theory of Zuyev, to accomplish the same. We demonstrate the remarkable fact that plots of the two distributions appear to be identical when the intensity of seeds in the half model is twice that in the full model. Our paper explores this coincidence mindful of the fact that, for one model, our results are from a simulation (with inherent sampling error). We go on to develop further analytic theory for the half-Gilbert model using stopping-set ideas once again, with some novel features. Using our theory, we obtain exact expressions for the first and second moment of ray length in the half-Gilbert model. For all practical purposes, these results can be applied to the full-Gilbert model as much better approximations than those provided by Mackissack and Miles.
1201.5780v1
2021-06-08
On numerical aspects of parameter identification for the Landau-Lifshitz-Gilbert equation in Magnetic Particle Imaging
The Landau-Lifshitz-Gilbert equation yields a mathematical model to describe the evolution of the magnetization of a magnetic material, particularly in response to an external applied magnetic field. It allows one to take into account various physical effects, such as the exchange within the magnetic material itself. In particular, the Landau-Lifshitz-Gilbert equation encodes relaxation effects, i.e., it describes the time-delayed alignment of the magnetization field with an external magnetic field. These relaxation effects are an important aspect in magnetic particle imaging, particularly in the calibration process. In this article, we address the data-driven modeling of the system function in magnetic particle imaging, where the Landau-Lifshitz-Gilbert equation serves as the basic tool to include relaxation effects in the model. We formulate the respective parameter identification problem both in the all-at-once and the reduced setting, present reconstruction algorithms that yield a regularized solution and discuss numerical experiments. Apart from that, we propose a practical numerical solver to the nonlinear Landau-Lifshitz-Gilbert equation, not via the classical finite element method, but through solving only linear PDEs in an inverse problem framework.
2106.07625v1
2021-01-28
Fluid-elastic coefficients in single phase cross flow: dimensional analysis, direct and indirect experimental methods
The importance of fluid-elastic forces in tube bundle vibrations can hardly be over-emphasized, in view of their damaging potential. In the last decades, advanced models for representing fluid-elastic coupling have therefore been developed by the community of the domain. Those models are nowadays embedded in the methodologies that are used on a regular basis by both steam generators providers and operators, in order to prevent the risk of a tube failure with adequate safety margins. From an R&D point of view however, the need still remains for more advanced models of fluid-elastic coupling, in order to fully decipher the physics underlying the observed phenomena. As a consequence, new experimental flow-coupling coefficients are also required to specifically feed and validate those more sophisticated models. Recent experiments performed at CEA-Saclay suggest that the fluid stiffness and damping coefficients depend on further dimensionless parameters beyond the reduced velocity. In this work, the problem of data reduction is first revisited, in the light of dimensional analysis. For single-phase flows, it is underlined that the flow-coupling coefficients depend at least on two dimensionless parameters, namely the Reynolds number $Re$ and the Stokes number $Sk$. Therefore, reducing the experimental data in terms of the compound dimensionless quantity $V_r=Re/Sk$ necessarily leads to impoverish results, hence the data dispersion. In a second step, experimental data are presented using the dimensionless numbers $Re$ and $Sk$. We report experiments, for a 3x5 square tube bundle subjected to water transverse flow. The bundle is rigid, except for the central tube which is mounted on a flexible suspension allowing for translation motions in the lift direction.
2101.12021v1
2000-09-11
Numerical Studies on Locally Damped Structures
In the JLC/NLC X-band linear collider, it is essential to reduce the long-range dipole wakefields in the accelerator structure to prevent beam break up (BBU) and emittance degradation. The two methods of reducing the long-range wakefields are detuning and damping. Detuning reduces the wakefields rapidly as the dipole modes de-cohere but, with a finite number of modes, the wakefield will grow again as the modes re-cohere. In contrast, damping suppresses the wakefields at a longer distance. There are two principal damping schemes: synchronous damping using HOM manifolds such as that used in the RDDS1 structure and local damping similar to that used in the CLIC structure. In a locally damped scheme, one can obtain almost any Q value, however, the damping can have significant effects on the accelerating mode. In this paper, we present a medium local-damping scheme where the wakefields are controlled to meet the BBU requirement while minimizing the degradations of the fundamental rf parameters. We will address the load design and pulse heating issues associated with the medium damping scheme.
0009039v1
2015-03-13
A one-step optimal energy decay formula for indirectly nonlinearly damped hyperbolic systems coupled by velocities
In this paper, we consider the energy decay of a damped hyperbolic system of wave-wave type which is coupled through the velocities. We are interested in the asymptotic properties of the solutions of this system in the case of indirect nonlinear damping, i.e. when only one equation is directly damped by a nonlinear damping. We prove that the total energy of the whole system decays as fast as the damped single equation. Moreover, we give a one-step general explicit decay formula for arbitrary nonlinearity. Our results shows that the damping properties are fully transferred from the damped equation to the undamped one by the coupling in velocities, different from the case of couplings through displacements as shown in \cite{AB01, ACK01, AB02, AL12} for the linear damping case, and in \cite{AB07} for the nonlinear damping case. The proofs of our results are based on multiplier techniques, weighted nonlinear integral inequalities and the optimal-weight convexity method of \cite{AB05, AB10}.
1503.04126v1
2015-08-21
Radiative damping in wave guide based FMR measured via analysis of perpendicular standing spin waves in sputtered Permalloy films
The damping $\alpha$ of the spinwave resonances in 75 nm, 120 nm, and 200nm -thick Permalloy films is measured via vector-network-analyzer ferromagnetic-resonance (VNA-FMR) in the out-of-plane geometry. Inductive coupling between the sample and the waveguide leads to an additional radiative damping term. The radiative contribution to the over-all damping is determined by measuring perpendicular standing spin waves (PSSWs) in the Permalloy films, and the results are compared to a simple analytical model. The damping of the PSSWs can be fully explained by three contributions to the damping: The intrinsic damping, the eddy-current damping, and the radiative damping. No other contributions were observed. Furthermore, a method to determine the radiative damping in FMR measurements with a single resonance is suggested.
1508.05265v1
2022-09-28
Tunable nonlinear damping in parametric regime
Nonlinear damping plays a significant role in several area of physics and it is becoming increasingly important to understand its underlying mechanism. However, microscopic origin of nonlinear damping is still a debatable topic. Here, we probe and report nonlinear damping in a highly tunable MoS2 nano mechanical drum resonator using electrical homodyne actuation and detection technique. In our experiment, we achieve 2:1 internal resonance by tuning resonance frequency and observe enhanced non-linear damping. We probe the effect of non-linear damping by characterizing parametric gain. Geometry and tunability of the device allow us to reduce the effect of other prominent Duffing non-linearity to probe the non-linear damping effectively. The enhanced non-linear damping in the vicinity of internal resonance is also observed in direct drive, supporting possible origin of non-linear damping. Our experiment demonstrates, a highly tunable 2D material based nanoresonator offers an excellent platform to study the nonlinear physics and exploit nonlinear damping in parametric regime.
2209.14120v1
2005-11-07
The Effects of Alfven Waves and Radiation Pressure in Dusty Winds of Late-Type Stars. II. Dust-Cyclotron Damping
There are in the literature several theories to explain the mass loss in stellar winds. In particular, for late-type stars, some authors have proposed a wind model driven by an outward-directed flux of damped Alfven waves. The winds of these stars present great amounts of dust particles that, if charged, can give rise to new wave modes or modify the pre-existing ones. In this work, we study how the dust can affect the propagation of Alfven waves in these winds taking into account a specific damping mechanism, dust-cyclotron damping. This damping affects the Alfven wave propagation near the dust-cyclotron frequency. Hence, if we assume a dust size distribution, the damping occurs over a broad band of wave frequencies. In this work, we present a model of Alfven wave-driven winds using the dust-cyclotron damping mechanism. On the basis of coronal holes in the Sun, which present a superradial expansion, our model also assumes a diverging geometry for the magnetic field. Thus, the mass, momentum, and energy equations are obtained and then solved in a self-consistent approach. Our results of wind velocity and temperature profiles for a typical K5 supergiant star shows compatibility with observations. We also show that, considering the presence of charged dust particles, the wave flux is less damped due to the dust-cyclotron damping than it would be if we consider some other damping mechanisms studied in the literature, such as nonlinear damping, resonant surface damping, and turbulent damping.
0511192v2
2013-09-11
Initial versus tangent stiffness-based Rayleigh damping in inelastic time history seismic analyses
In the inelastic time history analyses of structures in seismic motion, part of the seismic energy that is imparted to the structure is absorbed by the inelastic structural model, and Rayleigh damping is commonly used in practice as an additional energy dissipation source. It has been acknowledged that Rayleigh damping models lack physical consistency and that, in turn, it must be carefully used to avoid encountering unintended consequences as the appearance of artificial damping. There are concerns raised by the mass proportional part of Rayleigh damping, but they are not considered in this paper. As far as the stiffness proportional part of Rayleigh damping is concerned, either the initial structural stiffness or the updated tangent stiffness can be used. The objective of this paper is to provide a comprehensive comparison of these two types of Rayleigh damping models so that a practitioner (i) can objectively choose the type of Rayleigh damping model that best fits her/his needs and (ii) is provided with useful analytical tools to design Rayleigh damping model with good control on the damping ratios throughout inelastic analysis. To that end, a review of the literature dedicated to Rayleigh damping within these last two decades is first presented; then, practical tools to control the modal damping ratios throughout the time history analysis are developed; a simple example is finally used to illustrate the differences resulting from the use of either initial or tangent stiffness-based Rayleigh damping model.
1309.2741v1
2017-07-14
Damping of gravitational waves by matter
We develop a unified description, via the Boltzmann equation, of damping of gravitational waves by matter, incorporating collisions. We identify two physically distinct damping mechanisms -- collisional and Landau damping. We first consider damping in flat spacetime, and then generalize the results to allow for cosmological expansion. In the first regime, maximal collisional damping of a gravitational wave, independent of the details of the collisions in the matter is, as we show, significant only when its wavelength is comparable to the size of the horizon. Thus damping by intergalactic or interstellar matter for all but primordial gravitational radiation can be neglected. Although collisions in matter lead to a shear viscosity, they also act to erase anisotropic stresses, thus suppressing the damping of gravitational waves. Damping of primordial gravitational waves remains possible. We generalize Weinberg's calculation of gravitational wave damping, now including collisions and particles of finite mass, and interpret the collisionless limit in terms of Landau damping. While Landau damping of gravitational waves cannot occur in flat spacetime, the expansion of the universe allows such damping by spreading the frequency of a gravitational wave of given wavevector.
1707.05192v2
2003-04-10
Electron-Ion Recombination Rate Coefficients and Photoionization Cross Sections for Astrophysically Abundant Elements. VII. Relativistic calculations for O VI and O VII for UV and X-ray modeling
Aimed at ionization balance and spectral analysis of UV and X-ray sources, we present self-consistent sets of photoionization cross sections, recombination cross sections, and rate coefficients for Li-like O VI and He-like O VII. Relativistic fine structure is considered through the Breit-Pauli R-matrix (BPRM) method in the close coupling approximation, implementing the unified treatment for total electron-ion recombination subsuming both radiative and di-electronic recombination processes. Self-consistency is ensured by using an identical wavefunction expansion for the inverse processes of photoionization and photo-recombination. Radiation damping of resonances, important for H-like and He-like core ions, is included. Compared to previous LS coupling results without radiative decay of low-n (<= 10) resonances, the presents results show significant reduction in O VI recombination rates at high temperatures. In addition to the total rates, level-specific photoionization cross sections and recombination rates are presented for all fine structure levels n (lSLJ) up to n <= 10, to enable accurate computation of recombination-cascade matrices and spectral formation of prominent UV and X-ray lines such as the 1032,1038 A doublet of O VI, and the `triplet' forbidden, intercombination, and resonance X-ray lines of O VII at 22.1, 21.8, and 21.6 \ang respectively. Altogether, atomic parameters for 98 levels of O VI and 116 fine structure levels of O VII are theoretically computed. These data should provide a reasonably complete set of photoionization and recombination rates in collisional or radiative equilibrium.
0304204v1
2013-07-25
Relaxation of Bose-Einstein Condensates of Magnons in Magneto-Textural Traps in Superfluid $^3$He-B
In superfluid $^3$He-B externally pumped quantized spin-wave excitations or magnons spontaneously form a Bose-Einstein condensate in a 3-dimensional trap created with the order-parameter texture and a shallow minimum in the polarizing field. The condensation is manifested by coherent precession of the magnetization with a common frequency in a large volume. The trap shape is controlled by the profile of the applied magnetic field and by the condensate itself via the spin-orbit interaction. The trapping potential can be experimentally determined with the spectroscopy of the magnon levels in the trap. We have measured the decay of the ground state condensates after switching off the pumping in the temperature range $(0.14\div 0.2)T_{\mathrm{c}}$. Two contributions to the relaxation are identified: (1) spin-diffusion with the diffusion coefficient proportional to the density of thermal quasiparticles and (2) the approximately temperature-independent radiation damping caused by the losses in the NMR pick-up circuit. The measured dependence of the relaxation on the shape of the trapping potential is in a good agreement with our calculations based on the magnetic field profile and the magnon-modified texture. Our values for the spin diffusion coefficient at low temperatures agree with the theoretical prediction and earlier measurements at temperatures above $0.5T_{\mathrm{c}}$.
1307.6782v2
2014-01-07
Spectral parameter power series for polynomial pencils of Sturm-Liouville operators and Zakharov-Shabat systems
A spectral parameter power series (SPPS) representation for solutions of Sturm-Liouville equations of the form $$(pu')'+qu=u\sum_{k=1}^{N}\lambda^{k}r_{k}$$ is obtained. It allows one to write a general solution of the equation as a power series in terms of the spectral parameter $\lambda$. The coefficients of the series are given in terms of recursive integrals involving a particular solution of the equation $(pu_{0}')'+qu_{0}=0$. The convenient form of the solution provides an efficient numerical method for solving corresponding initial value, boundary value and spectral problems. A special case of the considered Sturm-Liouville equation arises in relation with the Zakharov-Shabat system. We derive an SPPS representation for its general solution and consider other applications as the one-dimensional Dirac system and the equation describing a damped string. Several numerical examples illustrate the efficiency and the accuracy of the numerical method based on the SPPS representations which besides its natural advantages like the simplicity in implementation and accuracy is applicable to the problems admitting complex coefficients, spectral parameter dependent boundary conditions and complex spectrum.
1401.1520v1
2016-11-29
Derivation of a generalized Schrödinger equation from the theory of scale relativity
Using Nottale's theory of scale relativity relying on a fractal space-time, we derive a generalized Schr\"odinger equation taking into account the interaction of the system with the external environment. This equation describes the irreversible evolution of the system towards a static quantum state. We first interpret the scale-covariant equation of dynamics stemming from Nottale's theory as a hydrodynamic viscous Burgers equation for a potential flow involving a complex velocity field and an imaginary viscosity. We show that the Schr\"odinger equation can be directly obtained from this equation by performing a Cole-Hopf transformation equivalent to the WKB transformation. We then introduce a friction force proportional and opposite to the complex velocity in the scale-covariant equation of dynamics in a way that preserves the local conservation of the normalization condition. We find that the resulting generalized Schr\"odinger equation, or the corresponding fluid equations obtained from the Madelung transformation, involve not only a damping term but also an effective thermal term. The friction coefficient and the temperature are related to the real and imaginary parts of the complex friction coefficient in the scale-covariant equation of dynamics. This may be viewed as a form of fluctuation-dissipation theorem. We show that our generalized Schr\"odinger equation satisfies an $H$-theorem for the quantum Boltzmann free energy. As a result, the probability distribution relaxes towards an equilibrium state which can be viewed as a Boltzmann distribution including a quantum potential. We propose to apply this generalized Schr\"odinger equation to dark matter halos in the Universe, possibly made of self-gravitating Bose-Einstein condensates.
1612.02323v1
2016-12-08
Robust identification of harmonic oscillator parameters using the adjoint Fokker-Planck equation
We present a model-based output-only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators. In this context, suitable models of the oscillator's damping and stiffness properties are postulated, guided by physical understanding of the oscillatory phenomena. The temporal dynamics and the probability density function of the oscillation amplitude are described by a Langevin equation and its associated Fokker-Planck equation, respectively. One method consists in fitting the postulated analytical drift and diffusion coefficients with their estimated values, obtained from data processing by taking the short-time limit of the first two transition moments. However, this limit estimation loses robustness in some situations - for instance when the data is band-pass filtered to isolate the spectral contents of the oscillatory phenomena of interest. In this paper, we use a robust alternative where the adjoint Fokker-Planck equation is solved to compute Kramers-Moyal coefficients exactly, and an iterative optimisation yields the parameters that best fit the observed statistics simultaneously in a wide range of amplitudes and time scales. The method is illustrated with a stochastic Van der Pol oscillator serving as a prototypical model of thermoacoustic instabilities in practical combustors, where system identification is highly relevant to control.
1612.02579v1
2017-06-19
Derivation of a generalized Schrödinger equation for dark matter halos from the theory of scale relativity
Using Nottale's theory of scale relativity, we derive a generalized Schr\"odinger equation applying to dark matter halos. This equation involves a logarithmic nonlinearity associated with an effective temperature and a source of dissipation. Fundamentally, this wave equation arises from the nondifferentiability of the trajectories of the dark matter particles whose origin may be due to ordinary quantum mechanics, classical ergodic (or almost ergodic) chaos, or to the fractal nature of spacetime at the cosmic scale. The generalized Schr\"odinger equation involves a coefficient ${\cal D}$, possibly different from $\hbar/2m$, whose value for dark matter halos is ${\cal D}=1.02\times 10^{23}\, {\rm m^2/s}$. We suggest that the cold dark matter crisis may be solved by the fractal (nondifferentiable) structure of spacetime at the cosmic scale, or by the chaotic motion of the particles on a very long timescale, instead of ordinary quantum mechanics. The equilibrium states of the generalized Schr\"odinger equation correspond to configurations with a core-halo structure. The quantumlike potential generates a solitonic core that solves the cusp problem of the classical cold dark matter model. The logarithmic nonlinearity accounts for the presence of an isothermal halo that leads to flat rotation curves. The damping term ensures that the system relaxes towards an equilibrium state. This property is guaranteed by an $H$-theorem satisfied by a Boltzmann-like free energy functional. In our approach, the temperature and the friction arise from a single formalism. They correspond to the real and imaginary parts of the complex friction coefficient present in the scale covariant equation of dynamics that is at the basis of Nottale's theory of scale relativity.
1706.05900v2
2017-06-21
Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations
Fractional diffusion equations (FDEs) are a mathematical tool used for describing some special diffusion phenomena arising in many different applications like porous media and computational finance. In this paper, we focus on a two-dimensional space-FDE problem discretized by means of a second order finite difference scheme obtained as combination of the Crank-Nicolson scheme and the so-called weighted and shifted Gr\"unwald formula. By fully exploiting the Toeplitz-like structure of the resulting linear system, we provide a detailed spectral analysis of the coefficient matrix at each time step, both in the case of constant and variable diffusion coefficients. Such a spectral analysis has a very crucial role, since it can be used for designing fast and robust iterative solvers. In particular, we employ the obtained spectral information to define a Galerkin multigrid method based on the classical linear interpolation as grid transfer operator and damped-Jacobi as smoother, and to prove the linear convergence rate of the corresponding two-grid method. The theoretical analysis suggests that the proposed grid transfer operator is strong enough for working also with the V-cycle method and the geometric multigrid. On this basis, we introduce two computationally favourable variants of the proposed multigrid method and we use them as preconditioners for Krylov methods. Several numerical results confirm that the resulting preconditioning strategies still keep a linear convergence rate.
1706.06844v1
2018-02-03
Origin of the size-dependence of the equilibrium van der Waals binding between nanostructures
Nanostructures can be bound together at equilibrium by the van der Waals (vdW) effect, a small but ubiquitous many-body attraction that presents challenges to density functional theory. How does the binding energy depend upon the size or number of atoms in one of a pair of identical nanostructures? To answer this question, we treat each nanostructure properly as a whole object, not as a collection of atoms. Our calculations start from an accurate static dipole polarizability for each considered nanostructure, and an accurate equilibrium center-to-center distance for the pair (the latter from experiment, or from the vdW-DF-cx functional). We consider the competition in each term $-C_{2k}/d^{2k}$ ($k=3, 4, 5$) of the long-range vdW series for the interaction energy, between the size dependence of the vdW coefficient $C_{2k}$ and that of the $2k$-th power of the center-to-center distance $d$. The damping of these vdW terms can be negligible, but in any case it does not affect the size dependence for a given term in the absence of non-vdW binding. To our surprise, the vdW energy can be size-independent for quasi-spherical nanoclusters bound to one another by vdW interaction, even with strong nonadditivity of the vdW coefficient, as demonstrated for fullerenes. We also show that, for low-dimensional systems, the vdW interaction yields the strongest size-dependence, in stark contrast to that of fullerenes. We illustrate this with parallel planar polycyclic aromatic hydrocarbons. Other cases are between, as shown by sodium clusters.
1802.00975v1
2018-04-12
System-size dependence of the viscous attenuation of anisotropic flow in p+Pb and Pb+Pb collisions at LHC energies
The elliptic and triangular flow coefficients ($\mathrm{v_n, \, n=2,3}$) measured in Pb+Pb ($\sqrt{s_{_{\rm NN}}} = 2.76$ TeV) and p+Pb ($\sqrt{s_{_{\rm NN}}} = 5.02$ TeV) collisions, are studied as a function of initial-state eccentricity ($\varepsilon_n$), and dimensionless size characterized by the cube root of the mid-rapidity charged hadron multiplicity density $\mathrm{\left< N_{ch} \right>^{1/3}}$. The results indicate that the influence of eccentricity ($\mathrm{v_n} \propto \varepsilon_n$) observed for large $\mathrm{\left< N_{ch} \right>}$, is superseded by the effects of viscous attenuation for small $\mathrm{\left< N_{ch} \right>}$, irrespective of the colliding species. Strikingly similar acoustic scaling patterns of exponential viscous modulation, with a damping rate proportional to $\mathrm{n^2}$ and inversely proportional to the dimensionless size, are observed for the eccentricity-scaled coefficients for the two sets of colliding species. The resulting scaling parameters suggest that, contrary to current predilections, the patterns of viscous attenuation, as well as the specific shear viscosity $\left<\frac{\eta}{s}(\text{T})\right>$ for the matter created in p+Pb and Pb+Pb collisions, are comparable.
1804.04618v3
2019-03-04
Role of geometrical cues in neuronal growth
Geometrical cues play an essential role in neuronal growth. Here, we quantify axonal growth on surfaces with controlled geometries and report a general stochastic approach that quantitatively describes the motion of growth cones. We show that axons display a strong directional alignment on micro-patterned surfaces when the periodicity of the patterns matches the dimension of the growth cone. The growth cone dynamics on surfaces with uniform geometry is described by a linear Langevin equation with both deterministic and stochastic contributions. In contrast, axonal growth on surfaces with periodic patterns is characterized by a system of two generalized Langevin equations with both linear and quadratic velocity dependence and stochastic noise. We combine experimental data with theoretical analysis to measure the key parameters of the growth cone motion: angular distributions, correlation functions, diffusion coefficients, characteristics speeds and damping coefficients. We demonstrate that axonal dynamics displays a cross-over from an Ornstein-Uhlenbeck process to a non-linear stochastic regime when the geometrical periodicity of the pattern approaches the linear dimension of the growth cone. Growth alignment is determined by surface geometry, which is fully quantified by the deterministic part of the Langevin equation. These results provide new insight into the role of curvature sensing proteins and their interactions with geometrical cues.
1903.01337v2
2019-05-07
On the reduction of required motions in the dynamic analysis using an optimization-based spectral matching
This study aims to show the efficiency of a proposed spectral matching technique for the reduction of required ground motions in the dynamic time history analysis. In this non-stationary spectral matching approach, unconstrained optimization is employed to adjust the signal to match a target spectrum. Adjustment factors of discrete wavelet transform (DWT) coefficients associated with the signals are then considered as decision variables and the Levenberg-Marquardt algorithm is employed to find the optimum values of DWT coefficients. This matching algorithm turns out to be quite effective in the spectral matching objective, where matching at multiple damping ratios can be readily achieved. First, the efficiency of the spectral matching procedure is investigated in a case study earthquake record and then compared with two conventional spectral matching methods. Results show considerable improvement in the matching accuracy which is accompanied by minimal changes in shaking characteristics of the original signal. In addition, it is shown that earthquake records matched with the proposed method can noticeably reduce the essential number of ground motions that are normally required for the dynamic analysis of a case study model. In this regard, it has been found that we can reduce the number of required motions by more than 80% when matched motions are selected to be used as the seismic inputs for the dynamic analysis.
1905.02394v4
2019-06-11
Anomalous diffusion for neuronal growth on surfaces with controlled geometries
Geometrical cues are known to play a very important role in neuronal growth and the formation of neuronal networks. Here, we present a detailed analysis of axonal growth and dynamics for neuronal cells cultured on patterned polydimethylsiloxane surfaces. We use fluorescence microscopy to image neurons, quantify their dynamics, and demonstrate that the substrate geometrical patterns cause strong directional alignment of axons. We quantify axonal growth and report a general stochastic approach that quantitatively describes the motion of growth cones. The growth cone dynamics is described by Langevin and Fokker-Planck equations with both deterministic and stochastic contributions. We show that the deterministic terms contain both the angular and speed dependence of axonal growth, and that these two contributions can be separated. Growth alignment is determined by surface geometry, and it is quantified by the deterministic part of the Langevin equation. We combine experimental data with theoretical analysis to measure the key parameters of the growth cone motion: speed and angular distributions, correlation functions, diffusion coefficients, characteristics speeds and damping coefficients. We demonstrate that axonal dynamics displays a cross-over from Brownian motion (Ornstein-Uhlenbeck process) at earlier times to anomalous dynamics (superdiffusion) at later times. The superdiffusive regime is characterized by non-Gaussian speed distributions and power law dependence of the axonal mean square length and the velocity correlation functions. These results demonstrate the importance of geometrical cues in guiding axonal growth, and could lead to new methods for bioengineering novel substrates for controlling neuronal growth and regeneration.
1906.05679v1
2019-11-01
Free and forced wave propagation in beam lattice metamaterials with viscoelastic resonators
Beam lattice materials are characterized by a periodic microstructure realizing a geometrically regular pattern of elementary cells. In these microstructured materials, the dispersion properties governing the free dynamic propagation of elastic waves can be studied by formulating parametric lagrangian models and applying the Floquet-Bloch theory. Within this framework, governing the wave propagation by means of spectral design techniques and/or energy dissipation mechanisms is a major issue of theoretical and applied interest. Specifically, the wave propagation can be inhibited by purposely designing the microstructural parameters to open band gaps in the material spectrum at target center frequencies. Based on these motivations, a general dynamic formulation for determining the dispersion properties of beam lattice metamaterials, equipped with local resonators is presented. The mechanism of local resonance is realized by tuning periodic auxiliary masses, viscoelastically coupled with the beam lattice microstructure. As peculiar aspect, the viscoelastic coupling is derived by a mechanical formulation based on the Boltzmann superposition integral, whose kernel is approximated by a Prony series. Consequently, the free propagation of damped waves is governed by a linear homogeneous system of integral-differential equations of motion. Therefore, differential equations of motion with frequency-dependent coefficients are obtained by applying the bilateral Laplace transform. The corresponding complex-valued branches characterizing the dispersion spectrum are determined and parametrically analyzed. Particularly, the spectra corresponding to Taylor series approximations of the equation coefficients are investigated.
1911.00455v1
2020-11-18
The theory of cosmic-ray scattering on pre-existing MHD modes meets data
We present a comprehensive study about the phenomenological implications of the theory describing Galactic cosmic-ray scattering onto magnetosonic and Alfv\'enic fluctuations in the $\mathrm{GeV} - \mathrm{PeV}$ domain. We compute a set of diffusion coefficients from first principles, for different values of the Alfv\'enic Mach number and other relevant parameters associated to both the Galactic halo and the extended disk, taking into account the different damping mechanisms of turbulent fluctuations acting in these environments. We confirm that the scattering rate associated to Alfv\'enic turbulence is highly suppressed if the anisotropy of the cascade is taken into account. On the other hand, we highlight that magnetosonic modes play a dominant role in Galactic confinement of cosmic rays up to $\mathrm{PeV}$ energies. We implement the diffusion coefficients in the numerical framework of the {\tt DRAGON} code, and simulate the equilibrium spectrum of different primary and secondary cosmic-ray species. We show that, for reasonable choices of the parameters under consideration, all primary and secondary fluxes at high energy (above a rigidity of $\simeq 200 \, \mathrm{GV}$) are correctly reproduced within our framework, in both normalization and slope.
2011.09197v2
2021-02-03
On Geometric Fourier Particle In Cell Methods
In this article we describe a unifying framework for variational electromagnetic particle schemes of spectral type, and we propose a novel spectral Particle-In-Cell (PIC) scheme that preserves a discrete Hamiltonian structure. Our work is based on a new abstract variational derivation of particle schemes which builds on a de Rham complex where Low's Lagrangian is discretized using a particle approximation of the distribution function. In this framework, which extends the recent Finite Element based Geometric Electromagnetic PIC (GEMPIC) method to a variety of field solvers, the discretization of the electromagnetic potentials and fields is represented by a de Rham sequence of compatible spaces, and the particle-field coupling procedure is described by approximation operators that commute with the differential operators in the sequence. In particular, for spectral Maxwell solvers the choice of truncated $L^2$ projections using continuous Fourier transform coefficients for the commuting approximation operators yields the gridless Particle-in-Fourier method, whereas spectral Particle-in-Cell methods are obtained by using discrete Fourier transform coefficients computed from a grid. By introducing a new sequence of spectral pseudo-differential approximation operators, we then obtain a novel variational spectral PIC method with discrete Hamiltonian structure that we call Fourier-GEMPIC. Fully discrete schemes are then derived using a Hamiltonian splitting procedure, leading to explicit time steps that preserve the Gauss laws and the discrete Poisson bracket associated with the Hamiltonian structure. These explicit steps share many similarities with standard spectral PIC methods. As arbitrary filters are allowed in our framework, we also discuss aliasing errors and study a natural back-filtering procedure to mitigate the damping caused by anti-aliasing smoothing particle shapes.
2102.02106v1
2021-02-10
Axion Quasiparticles for Axion Dark Matter Detection
It has been suggested that certain antiferromagnetic topological insulators contain axion quasiparticles (AQs), and that such materials could be used to detect axion dark matter (DM). The AQ is a longitudinal antiferromagnetic spin fluctuation coupled to the electromagnetic Chern-Simons term, which, in the presence of an applied magnetic field, leads to mass mixing between the AQ and the electric field. The electromagnetic boundary conditions and transmission and reflection coefficients are computed. A model for including losses into this system is presented, and the resulting linewidth is computed. It is shown how transmission spectroscopy can be used to measure the resonant frequencies and damping coefficients of the material, and demonstrate conclusively the existence of the AQ. The dispersion relation and boundary conditions permit resonant conversion of axion DM into THz photons in a material volume that is independent of the resonant frequency, which is tuneable via an applied magnetic field. A parameter study for axion DM detection is performed, computing boost amplitudes and bandwidths using realistic material properties including loss. The proposal could allow for detection of axion DM in the mass range between 1 and 10 meV using current and near future technology.
2102.05366v2
2021-05-16
A Realizable Filtered Intrusive Polynomial Moment Method
Intrusive uncertainty quantification methods for hyperbolic problems exhibit spurious oscillations at shocks, which leads to a significant reduction of the overall approximation quality. Furthermore, a challenging task is to preserve hyperbolicity of the gPC moment system. An intrusive method which guarantees hyperbolicity is the intrusive polynomial moment (IPM) method, which performs the gPC expansion on the entropy variables. The method, while still being subject to oscillations, requires solving a convex optimization problem in every spatial cell and every time step. The aim of this work is to mitigate oscillations in the IPM solution by applying filters. Filters reduce oscillations by damping high order gPC coefficients. Naive filtering, however, may lead to unrealizable moments, which means that the IPM optimization problem does not have a solution and the method breaks down. In this paper, we propose and analyze two separate strategies to guarantee the existence of a solution to the IPM problem. First, we propose a filter which maintains realizability by being constructed from an underlying Fokker-Planck equation. Second, we regularize the IPM optimization problem to be able to cope with non-realizable gPC coefficients. Consequently, standard filters can be applied to the regularized IPM method. We demonstrate numerical results for the two strategies by investigating the Euler equations with uncertain shock structures in one- and two-dimensional spatial settings. We are able to show a significant reduction of spurious oscillations by the proposed filters.
2105.07473v1
2021-10-04
Probing three-state Potts nematic fluctuations by ultrasound attenuation
Motivated by recent studies of three-state Potts nematic states in magic-angle twisted bilayer graphene and doped-Bi$_2$Se$_3$, we analyze the impact of critical nematic fluctuations on the low energy properties of phonons. In this study we propose how to identify the three-state Potts nematic fluctuations by ultrasound attenuation. The Gaussian fluctuation analysis shows that the Landau damping term becomes isotropic due to fluctuations of the $C_{3}$-breaking bond-order, and the nemato-elastic coupling is also shown to be isotropic. These two features lead to an isotropic divergence of the transverse sound attenuation coefficient and an isotropic lattice softening, in contrast to the case of the $C_4$-breaking bond-order which shows the strong anisotropy. Moreover, we use a mean-field approximation and discuss the impurity effects. The transition temperature takes its maximum near the filling of the van-Hove singularity, and the large density of states favors the nematic phase transition. It turns out that the phase transition is of weak first-order in the wide range of filling and, with increasing the impurity scattering, the first order transition line at low temperatures gradually shifts towards the second-order line, rendering the transition a weak first-order in a wider range of parameters. Furthermore, it is confirmed that the enhancement of the ultrasound attenuation coefficient will be clearly observed in experiments in the case of a weak first-order phase transition.
2110.01308v4
2022-11-09
Gravitational wave constraints on spatial covariant gravities
The direct discovery of gravitational waves (GWs) from the coalescence of compact binary components by the LIGO/Virgo/KAGRA Collaboration provides an unprecedented opportunity for exploring the underlying theory of gravity that drives the coalescence process in the strong and highly dynamical field regime of gravity. In this paper, we consider the observational effects of spatial covariant gravities on the propagation of GWs in the cosmological background and obtain the observational constraints on coupling coefficients in the action of spatial covariant gravities from GW observations. We first decompose the GWs into the left- and right-hand circular polarization modes and derive the effects of the spatial covariant gravities on the propagation equation of GWs. We find that these effects can be divided into three classes: 1) frequency-independent effects on GW speed and friction, 2) parity-violating amplitude and velocity birefringences, and 3) a Lorentz-violating damping rate and dispersion of GWs. With these effects, we calculate the corresponding modified waveform of GWs generated by the coalescence of compact binaries. By comparing these new effects with the publicly available posterior samples or results from various tests of gravities with LIGO/Virgo/KAGRA data in the literature, we derive the observational constraints on coupling coefficients of the spatial covariant gravities. These results represent the most comprehensive constraints on the spatial covariant gravities in the literature.
2211.04711v2
2023-09-08
Minimum-dissipation model for large-eddy simulation in OpenFoam -A study on channel flow, periodic hills and flow over cylinder
The minimum-dissipation model is applied to turbulent channel flows up to $Re_\tau = 2000$, flow past a circular cylinder at $Re=3900$, and flow over periodic hills at $Re=10595$. Numerical simulations are performed in OpenFOAM which is based on finite volume methods for discretizing partial differential equations. We use both symmetry-preserving discretizations and standard second-order accurate discretization methods in OpenFOAM on structured meshes. The results are compared to DNS and experimental data. The results of channel flow mainly demonstrate the static QR model performs equally well as the dynamic models while reducing the computational cost. The model constant $C=0.024$ gives the most accurate prediction, and the contribution of the sub-grid model decreases with the increase of the mesh resolution and becomes very small (less than 0.2 molecular viscosity) if the fine meshes are used. Furthermore, the QR model is able to predict the mean and rms velocity accurately up to $Re_\tau = 2000$ without a wall damping function. The symmetry-preserving discretization outperforms the standard OpenFOAM discretization at $Re_\tau=1000$. The results for the flow over a cylinder show that mean velocity, drag coefficient, and lift coefficient are in good agreement with the experimental data. The symmetry-preserving scheme with the QR model predicts the best results. The various comparisons carried out for flows over periodic hills demonstrate the need to use the symmetry-preserving discretization or central difference schemes in OpenFOAM in combination with the minimum dissipation model. The model constant of $C=0.024$ is again the best one.
2309.04415v1
2023-11-02
Minimum-dissipation model for large-eddy simulation using symmetry-preserving discretization in OpenFOAM
The minimum-dissipation model is applied to channel flow up to $Re_\tau = 2000$, flow past a circular cylinder at $Re=3900$, and flow over periodic hills at $Re=10595$. Numerical simulations were performed in OpenFOAM which is based on the finite volume methods. We used both symmetry-preserving and standard second-order accurate discretization methods in OpenFOAM on structured meshes. The results are compared to DNS and experimental data. The results of channel flow demonstrate a static QR model performs equally well as the dynamic models while reducing the computational cost. The model constant of $C=0.024$ gives the most accurate prediction, and the contribution of the sub-grid model decreases with the increase of the mesh resolution and becomes very small (less than 0.2 molecular viscosity) if a fine mesh is used. Furthermore, the QR model is able to predict the mean and rms velocity accurately up to $Re_\tau = 2000$ without a wall damping function. The symmetry-preserving discretization outperforms the standard OpenFOAM discretization at $Re_\tau=1000$. The results for the flow over a cylinder show that the mean velocity, drag coefficient, and lift coefficient are in good agreement with the experimental data and the central difference schemes conjugated with the QR model predict better results. The various comparisons carried out for flows over periodic hills demonstrate the need to use central difference schemes in OpenFOAM in combination with the minimum dissipation model. The best model constant is again $C=0.024$. The single wind turbine simulation shows that the QR model is capable of predicting accurate results in complex rotating scenarios.
2311.01360v1
2023-11-03
Room-Temperature CsPbBr$_3$ Mixed Polaritons States
Light-matter interactions are known to lead to the formation of polariton states through what is called strong coupling, leading to the formation of two hybrid states usually tagged as Upper and Lower Polaritons. Here, we consider a similar interaction between excitons and photons in the realm of strong interactions, with the difference that it enables us to obtain a mixed-polariton state. In this case, the energy of this mixed state is found between the energies of the exciton state and the cavity mode, resulting in an imaginary coupling coefficient related to a specific class of singular points. These mixed states are often considered unobservable, although they are predicted well when the dressed states of a two-level atom are considered. However, intense light confinement can be obtained by using a Bound State in the Continuum, reducing the damping rates, and enabling the observation of mixed states resulting from the correct kind of exceptional point giving place to strong coupling. In this study, using the Transfer Matrix Method, we simulated cavities made of porous silicon coupled with CsPbBr3 perovskite quantum dots to numerically observe the mixed states as well as experimentally, by fabricating appropriate samples. The dispersion relation of the mixed states is fitted using the same equation as that used for strong coupling but considering a complex coupling coefficient, which is directly related to the appropriate type of exceptional point.
2311.02252v2
1998-05-22
Analytic description of the r-mode instability in uniform density stars
We present an analytic description of the $r$-mode instability in newly-born neutron stars, using the approximation of uniform density. Our computation is consistently accurate to second order in the angular velocity of the star. We obtain formulae for the growth-time of the instability due to gravitational-wave emission, for both current and mass multipole radiation and for the damping timescale, due to viscosity. The $l=m=2$ current-multipole radiation dominates the timescale of the instability. We estimate the deviation of the second order accurate results from the lowest order approximation and show that the uncertainty in the equation of state has only a small effect on the onset of the $r$-mode instability. The viscosity coefficients and the cooling process in newly-born neutron stars are, at present, uncertain and our analytic formaulae enables a quick check of such effects on the development of the instability.
9805297v1
2004-06-21
Resolution and accuracy of resonances in R-matrix cross sections
We investigate the effect of resonances in photoionization and recombination cross sections computed using the R-matrix method. Photoionization and recombination rates derived from high-resolution cross sections for oxygen ions are compared with earlier works with less resolution and accuracy, such as in the widely used Opacity Project data. We find significant differences in photoionization rates for O II metastable states, averaged over Planck functions corresponding to ionizing radiation fields, with respect to the intrinsic accuracy of the calculations and improved resolution. Furthermore, for highly charged ions other physical effects are also important. Recombination rate coefficients, averaged over a Maxwellian distribution, are extremely sensitive to the position and resolution of near-threshold resonances, and radiation damping, in (e + O VII) --> O VI + hnu. Surprisingly however, the effect on the monochromatic and the mean Rosseland and Planck bound-free opacities is relatively small, but may be potentially significant.
0406472v1
2006-07-01
Exotic bulk viscosity and its influence on neutron star r-modes
We investigate the effect of exotic matter in particular, hyperon matter on neutron star properties such as equation of state (EoS), mass-radius relationship and bulk viscosity. Here we construct equations of state within the framework of a relativistic field theoretical model. As hyperons are produced abundantly in dense matter, hyperon-hyperon interaction becomes important and is included in this model. Hyperon-hyperon interaction gives rise to a softer EoS which results in a smaller maximum mass neutron star compared with the case without the interaction. Next we compute the coefficient of bulk viscosity and the corresponding damping time scale due to the non-leptonic weak process including $\Lambda$ hyperons. Further, we investigate the role of the bulk viscosity on gravitational radiation driven r-mode instability in a neutron star of given mass and temperature and find that the instability is effectively suppressed.
0607005v2
2006-07-11
Collisional Particle Disks
We present a new, simple, fast algorithm to numerically evolve disks of inelastically colliding particles surrounding a central star. Our algorithm adds negligible computational cost to the fastest existing collisionless N-body codes, and can be used to simulate, for the first time, the interaction of planets with disks over many viscous times. Though the algorithm is implemented in two dimensions-i.e., the motions of bodies need only be tracked in a plane-it captures the behavior of fully three-dimensional disks in which collisions maintain inclinations that are comparable to random eccentricities. We subject the algorithm to a battery of tests for the case of an isolated, narrow, circular ring. Numerical simulations agree with analytic theory with regards to how particles' random velocities equilibrate; how the ring viscously spreads; and how energy dissipation, angular momentum transport, and material transport are connected. We derive and measure the critical value of the coefficient of restitution above which viscous stirring dominates inelastic damping and the particles' velocity dispersion runs away.
0607241v1
2007-01-19
Revised Primordial Helium Abundance Based on New Atomic Data
We have derived a primordial helium abundance of Yp = 0.2477 +- 0.0029, based on new atomic physics computations of the recombination coefficients of He I and of the collisional excitation of the H I Balmer lines together with observations and photoionization models of metal-poor extragalactic H II regions. The new atomic data increase our previous determination of Yp by 0.0086, a very significant amount. By combining our Yp result with the predictions made by the standard Big Bang nucleosynthesis model, we find a baryon-to-photon ratio, \eta, in excellent agreement both with the \eta value derived by the primordial deuterium abundance value observed in damped Lyman-\alpha systems and with the one obtained from the WMAP observations.
0701580v2
1995-07-03
Fundamental steps of group velocity for slow surface polariton under the quantum hall effect conditions
A new type of collective electromagnetic excitations, namely surface polaritons (SP) --- in a 2D electronic layer in a high magnetic field under Quantum Hall Effect (QHE) conditions is predicted. We have found the spectrum, damping, and polarization of the SP in a wide range of frequencies $\omega$ and wavevectors $\bf k$. It is shown that near the Cyclotron Resonance (CR) ($\omega\sim\Omega=\displaystyle eB/mc$) the phase velocity of the SP is drastically slowed down and the group velocity undergoes fundamental steps defined by the Fine Structure Constant $\alpha=e^2/\hbar c$. In the vicinity of a CR subharmonic ($\omega\sim 2 \Omega$) the negative (anomalous) dispersion of the SP occurs. The relaxation of electrons in the 2D layer gives rise to a new dissipative collective threshold-type mode of the SP. We suggest a method for calculating the kinetic coefficients for the 2D electronic layer under QHE condition, using the Wigner distribution function formalism and determine their spatial and frequency dispersion. Using this method we have calculated the line-shape of the CR and the d.c. conductance under the QHE condition, which are in good agreement with experimental data.
9507001v1
1996-04-26
Macroscopic Quantum Tunneling of a Fluxon in a Long Josephson Junction
Macroscopic quantum tunneling (MQT) for a single fluxon moving along a long Josephson junction is studied theoretically. To introduce a fluxon-pinning force, we consider inhomogeneities made by modifying thickness of an insulating layer locally. Two different situations are studied: one is the quantum tunneling from a metastable state caused by a single inhomogeneity, and the other is the quantum tunneling in a two-state system made by two inhomogeneities. In the quantum tunneling from a metastable state, the decay rate is estimated within the WKB approximation. Dissipation effects on a fluxon dynamics are taken into account by the Caldeira-Leggett theory. We propose a device to observe quantum tunneling of a fluxon experimentally. Required experimental resolutions to observe MQT of a fluxon seem attainable within the presently available micro-fabrication technique. For the two-state system, we study quantum resonance between two stable states, i.e., macroscopic quantum coherence (MQC). From the estimate for dissipation coefficients due to quasiparticle tunneling, the observation of MQC appears to be possible within the Caldeira-Leggett theory.
9604160v2
1997-09-03
Shaping an ultracold atomic soliton in a travelling wave laser beam
An ultracold wave packet of bosonic atoms loaded into a travelling laser wave may form a many-atom soliton.This is disturbed by a homogeneous force field, for example by the inevitable gravitation. The wave packet is accelerated and therefore the laser frequency appears to be chirped in the rest frame of the atoms. We derive the effective nonlinear Schr\"odinger equation. It shows a time dependent nonlinearity coefficient which amounts to a damping or antidamping, respectively. The accelerated packet solution remains a soliton which changes its shape adiabatically. Similarly, an active shaping can be obtained in the force-free case by chirping the laser frequency thus representing a way of coherent control of the soliton form. The experimental consequences are discussed.
9709038v1
1997-10-20
Row-switched states in two-dimensional underdamped Josephson junction arrays
When magnetic flux moves across layered or granular superconductor structures, the passage of vortices can take place along channels which develop finite voltage, while the rest of the material remains in the zero-voltage state. We present analytical studies of an example of such mixed dynamics: the row-switched (RS) states in underdamped two-dimensional Josephson arrays, driven by a uniform DC current under external magnetic field but neglecting self-fields. The governing equations are cast into a compact differential-algebraic system which describes the dynamics of an assembly of Josephson oscillators coupled through the mesh current. We carry out a formal perturbation expansion, and obtain the DC and AC spatial distributions of the junction phases and induced circulating currents. We also estimate the interval of the driving current in which a given RS state is stable. All these analytical predictions compare well with our numerics. We then combine these results to deduce the parameter region (in the damping coefficient versus magnetic field plane) where RS states can exist.
9710204v1
1998-04-21
Inelastic collapse of a randomly forced particle
We consider a randomly forced particle moving in a finite region, which rebounds inelastically with coefficient of restitution r on collision with the boundaries. We show that there is a transition at a critical value of r, r_c\equiv e^{-\pi/\sqrt{3}}, above which the dynamics is ergodic but beneath which the particle undergoes inelastic collapse, coming to rest after an infinite number of collisions in a finite time. The value of r_c is argued to be independent of the size of the region or the presence of a viscous damping term in the equation of motion.
9804229v1
1999-02-25
Mobility of Bloch Walls via the Collective Coordinate Method
We have studied the problem of the dissipative motion of Bloch walls considering a totally anisotropic one dimensional spin chain in the presence of a magnetic field. Using the so-called "collective coordinate method" we construct an effective Hamiltonian for the Bloch wall coupled to the magnetic excitations of the system. It allows us to analyze the Brownian motion of the wall in terms of the reflection coefficient of the effective potential felt by the excitations due to the existence of the wall. We find that for finite values of the external field the wall mobility is also finite. The spectrum of the potential at large fields is investigated and the dependence of the damping constant on temperature is evaluated. As a result we find the temperature and magnetic field dependence of the wall mobility.
9902330v1
2004-02-21
Effect of backing thickness on determination of the phase in neutron reflectometry by variation of backing
The determination of density profiles with knowing the phase information of complex reflection coefficient for neutron specularly reflected from a film, yields unique results. Recently it has been shown that the phase can be determined by using controlled variation of the scattering length density of the fronting (incident) and/or backing (substrate) medium instead of reference layers of finite thickness. This method is applicable under the simplifying assumption that the backing is infinitely thick (semi-infinite substrate). By this assumption the reflected beams from the end side of the backing is neglected, which appears reasonable since in most cases absorption will damp out the neutron current before it has reached the end side. But for weakly absorbing backing, the reflection from the end side may be considerable. So backing must be considered as a thick matter. We show that for this kind of backing, using method of variation of the backing, as an example of variation of the surroundings, leads to completely wrong answer in determination of the phase.
0402541v1
2004-03-23
Phase transitions induced by noise cross-correlations
A general approach to consider spatially extended stochastic systems with correlations between additive and multiplicative noises subject to nonlinear damping is developed. Within modified cumulant expansion method, we derive an effective Fokker-Planck equation whose stationary solutions describe a character of ordered state. We find that fluctuation cross-correlations lead to a symmetry breaking of the distribution function even in the case of the zero-dimensional system. In general case, continuous, discontinuous and reentrant noise induced phase transitions take place. It is appeared the cross-correlations play a role of bias field which can induce a chain of phase transitions being different in nature. Within mean field approach, we give an intuitive explanation of the system behavior through an effective potential of thermodynamic type. This potential is written in the form of an expansion with coefficients defined by temperature, intensity of spatial coupling, auto- and cross-correlation times and intensities of both additive and multiplicative noises.
0403583v2
2004-12-13
Field-tuned quantum critical point of antiferromagnetic metals
A magnetic field applied to a three-dimensional antiferromagnetic metal can destroy the long-range order and thereby induce a quantum critical point. Such field-induced quantum critical behavior is the focus of many recent experiments. We investigate theoretically the quantum critical behavior of clean antiferromagnetic metals subject to a static, spatially uniform external magnetic field. The external field does not only suppress (or induce in some systems) antiferromagnetism but also influences the dynamics of the order parameter by inducing spin precession. This leads to an exactly marginal correction to spin-fluctuation theory. We investigate how the interplay of precession and damping determines the specific heat, magnetization, magnetocaloric effect, susceptibility and scattering rates. We point out that the precession can change the sign of the leading \sqrt{T} correction to the specific heat coefficient c(T)/T and can induce a characteristic maximum in c(T)/T for certain parameters. We argue that the susceptibility \chi =\partial M/\partial B is the thermodynamic quantity which shows the most significant change upon approaching the quantum critical point and which gives experimental access to the (dangerously irrelevant) spin-spin interactions.
0412284v1
2005-10-13
Statistical-mechanical description of classical test-particle dynamics in the presence of an external force field: modelling noise and damping from first principles
Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly coupled to a large heat-bath in thermal equilibrium. Both subsystems are subject to an external force field. From the (time-non-local) generalized master equation a Fokker-Planck-type equation follows as a "quasi-Markovian" approximation. The kinetic operator thus defined is shown to be ill-defined; in specific, it does not preserve the positivity of the test-particle distribution function $f(\mathbf{x}, \mathbf{v}; t)$. Adopting an alternative approach, previously proposed for quantum open systems, is proposed to lead to a correct kinetic operator, which yields all the expected properties. A set of explicit expressions for the diffusion and drift coefficients are obtained, allowing for modelling macroscopic diffusion and dynamical friction phenomena, in terms of an external field and intrinsic physical parameters.
0510359v2
2006-04-13
Dissipative magneto-optic solitons
Magneto-optic behaviour is a specific, non-reciprocal example of gyrotropic behaviour. When coupled to photo-induced Faraday rotation it is possible to discriminate this effect from the background of other nonlinear effects Non-reciprocal behaviour is characteristic of artificial gyrotropy and can be used in optical isolators and a range of coherence and quantum problems. This is all in sharp contrast to natural gyrotropy, like optical activity. it is also important to go beyond third-order, Kerr, optical nonlinearity and move towards a saturable model of terms in the polarisation. In this spirit, this chapter seeks to determinate the influence of a magneto-optic presence upon an optically nonlinear material that is modelled by a cubic-quintic form of polarisation. In addition, the coefficients of the envelope equation will be made complex, to take into account both linear and nonlinear damping and cubic gain processes. The emphasis is upon the simulation outcomes, however, rather the applications.
0604355v1
2006-12-07
Dynamics of a metastable state nonlinearly coupled to a heat bath driven by an external noise
Based on a system-reservoir model, where the system is nonlinearly coupled to a heat bath and the heat bath is modulated by an external stationary Gaussian noise, we derive the generalized Langevin equation with space dependent friction and multiplicative noise and construct the corresponding Fokker-Planck equation, valid for short correlation time, with space dependent diffusion coefficient to study the escape rate from a metastable state in the moderate to large damping regime. By considering the dynamics in a model cubic potential we analyze the result numerically which are in good agreement with the theoretical prediction. It has been shown numerically that the enhancement of rate is possible by properly tuning the correlation time of the external noise.
0612193v2
2002-12-03
d-Dimensional Black Hole Entropy Spectrum from Quasi-Normal Modes
Starting from recent observations\cite{hod,dreyer1} about quasi-normal modes, we use semi-classical arguments to derive the Bekenstein-Hawking entropy spectrum for $d$-dimensional spherically symmetric black holes. We find that the entropy spectrum is equally spaced: $S_{BH}=k \ln(m_0)n$, where $m_0$ is a fixed integer that must be derived from the microscopic theory. As shown in \cite{dreyer1},4-$d$ loop quantum gravity yields precisely such a spectrum with $m_0=3$ providing the Immirzi parameter is chosen appropriately. For $d$-dimensional black holes of radius $R_H(M)$, our analysis requires the existence of a unique quasinormal mode frequency in the large damping limit $\omega^{(d)}(M) = \alpha^{(d)}c/ R_H(M)$ with coefficient $\alpha^{(d)} = {(d-3)/over 4\pi} \ln(m_0)$, where $m_0$ is an integer and $\Gamma^{(d-2)}$ is the volume of the unit $d-2$ sphere.
0212014v2
2003-12-17
A Post-Newtonian diagnostic of quasi-equilibrium binary configurations of compact objects
Using equations of motion accurate to the third post-Newtonian (3PN) order (O(v/c)^6 beyond Newtonian gravity), we derive expressions for the total energy E and angular momentum J of the orbits of compact binary systems (black holes or neutron stars) for arbitrary orbital eccentricity. We also incorporate finite-size contributions such as spin-orbit and spin-spin coupling, and rotational and tidal distortions, calculated to the lowest order of approximation, but we exclude the effects of gravitational radiation damping. We describe how these formulae may be used as an accurate diagnostic of the physical content of quasi-equilibrium configurations of compact binary systems of black holes and neutron stars generated using numerical relativity. As an example, we show that quasi-equilibrium configurations of corotating neutron stars recently reported by Miller et al. can be fit by our diagnostic to better than one per cent with a circular orbit and with physically reasonable tidal coefficients.
0312082v3
1994-07-29
Standard Model Baryogenesis
Simply on CP arguments, we argue against a Standard Model explanation of baryogenesis via the charge transport mechanism. A CP-asymmetry is found in the reflection coefficients of quarks hitting the electroweak phase boundary created during a first order phase transition. The problem is analyzed both in an academic zero temperature case and in the realistic finite temperature one. At finite temperature, a crucial role is played by the damping rate of quasi-quarks in a hot plasma, which induces loss of spatial coherence and suppresses reflection on the boundary even at tree-level. The resulting baryon asymmetry is many orders of magnitude below what observation requires. We comment as well on related works.
9407403v2
2000-02-25
A New Source for Electroweak Baryogenesis in the MSSM
One of the most experimentally testable explanations for the origin of the baryon asymmetry of the universe is that it was created during the electroweak phase transition, in the minimal supersymmetric standard model. Previous efforts have focused on the current for the difference of the two Higgsino fields, $H_1-H_2$, as the source of biasing sphalerons to create the baryon asymmetry. We point out that the current for the orthogonal linear combination, $H_1+H_2$, is larger by several orders of magnitude. Although this increases the efficiency of electroweak baryogenesis, we nevertheless find that large CP-violating angles $\ge 0.15$ are required to get a large enough baryon asymmetry.
0002272v2
2000-06-15
Development of the electroweak phase transition and baryogenesis
We investigate the evolution of the electroweak phase transition, using a one-Higgs effective potential that can be regarded as an approximation for the Minimal Supersymmetric Standard Model. The phase transition occurs in a small interval around a temperature T_t below the critical one. We calculate this temperature as a function of the parameters of the potential and of a damping coefficient related to the viscosity of the plasma. The parameters that are relevant for baryogenesis, such as the velocity and thickness of the walls of bubbles and the value of the Higgs field inside them, change significantly in the range of temperatures where the first-order phase transition can occur. However, we find that in the likely interval for T_t there is no significant variation of these parameters. Furthermore, the temperature T_t is in general not far below the temperature at which bubbles begin to nucleate.
0006177v2
2001-03-09
Transport theory for a two-flavor color superconductor
QCD with two light quark flavors at high baryonic density and low temperature is a color superconductor. The diquark condensate partially breaks the SU(3) gauge symmetry down to an SU(2) subgroup. We study thermal fluctuations of the superconductor for temperatures below the gap. These are described by a simple transport equation, linked to a quasiparticle behavior of the thermal excitations of the condensate. When solved in the collisionless limit and close to equilibrium, it gives rise to the ``hard superconducting loop'' (HSL) effective theory for the unbroken SU(2) gauge fields with momenta smaller than the gap. This theory describes Debye screening and Landau damping of the gauge fields in the presence of the diquark condensate. We also explain how our effective theory follows to one-loop order from quantum field theory. Our approach provides a convenient starting point for the computation of transport coefficients of the two-flavor color superconductor.
0103092v2
2002-05-18
Perturbative and non-perturbative aspects of the non-abelian Boltzmann-Langevin equation
We study the Boltzmann-Langevin equation which describes the dynamics of hot Yang-Mills fields with typical momenta of order of the magnetic screening scale g^2 T. It is transformed into a path integral and Feynman rules are obtained. We find that the leading log Langevin equation can be systematically improved in a well behaved expansion in log(1/g)^-1. The result by Arnold and Yaffe that the leading log Langevin equation is still valid at next-to-leading-log order is confirmed. We also confirm their result for the next-to-leading-log damping coefficient, or color conductivity, which is shown to be gauge fixing independent for a certain class of gauges. The frequency scale g^2T does not contribute to this result, but it does contribute, by power counting, to the transverse gauge field propagator. Going beyond a perturbative expansion we find 1-loop ultraviolet divergences which cannot be removed by renormalizing the parameters in the Boltzmann-Langevin equation.
0205202v2
2003-07-05
Hard Loops, Soft Loops, and High Density Effective Field Theory
We study several issues related to the use of effective field theories in QCD at large baryon density. We show that the power counting is complicated by the appearance of two scales inside loop integrals. Hard dense loops involve the large scale $\mu^2$ and lead to phenomena such as screening and damping at the scale $g\mu$. Soft loops only involve small scales and lead to superfluidity and non-Fermi liquid behavior at exponentially small scales. Four-fermion operators in the effective theory are suppressed by powers of $1/\mu$, but they get enhanced by hard loops. As a consequence their contribution to the pairing gap is only suppressed by powers of the coupling constant, and not powers of $1/\mu$. We determine the coefficients of four-fermion operators in the effective theory by matching quark-quark scattering amplitudes. Finally, we introduce a perturbative scheme for computing corrections to the gap parameter in the superfluid phase
0307074v1
2004-02-04
Infrared Behavior of High-Temperature QCD
The damping rate \gamma_t(p) of on-shell transverse gluons with ultrasoft momentum p is calculated in the context of next-to-leading-order hard-thermal-loop-summed perturbation of high-temperature QCD. It is obtained in an expansion to second order in p. The first coefficient is recovered but that of order p^2 is found divergent in the infrared. Divergences from light-like momenta do also occur but are circumvented. Our result and method are critically discussed, particularly regarding a Ward identity obtained in the literature. When enforcing the equality between \gamma_t(0) and \gamma_l(0), a rough estimate of the magnetic mass is obtained. Carrying a similar calculation in the context of scalar quantum electrodynamics shows that the early ultrasoft-momentum expansion we make has little to do with the infrared sensitivity of the result.
0402041v1
2004-06-04
Shear Viscosity in a CFL Quark Star
We compute the mean free path and shear viscosity in the color-flavor locked (CFL) phase of dense quark matter at low temperature T, when the contributions of mesons, quarks and gluons to the transport coefficients are Boltzmann suppressed. CFL quark matter displays superfluid properties, and transport phenomena in such cold regime are dominated by phonon-phonon scattering. We study superfluid phonons within thermal field theory and compute the mean free path associated to their most relevant collision processes. Small-angle processes turn out to be more efficient in slowing transport phenomena in the CFL matter, while the mean free path relevant for the shear viscosity is less sensitive to collinear scattering due to the presence of zero modes in the Boltzmann equation. In analogy with superfluid He4, we find the same T power law for the superfluid phonon damping rate and mean free path. Our results are relevant for the study of rotational properties of compact stars, and correct wrong estimates existing in the literature.
0406058v3
2005-01-11
Fermionic dispersion relations in ultradegenerate relativistic plasmas beyond leading logarithmic order
We determine the dispersion relations of fermionic quasiparticles in ultradegenerate plasmas by a complete evaluation of the on-shell hard-dense-loop-resummed one-loop fermion self energy for momenta of the order of the Fermi momentum and above. In the case of zero temperature, we calculate the nonanalytic terms in the vicinity of the Fermi surface beyond the known logarithmic approximation, which turn out to involve fractional higher powers in the energy variable. For nonzero temperature (but much smaller than the chemical potential), we obtain the analogous expansion in closed form, which is then analytic but involves polylogarithms. These expansions are compared with a full numerical evaluation of the resulting group velocities and damping coefficients.
0501089v2
1994-07-19
On the Macroscopic Limit of Nuclear Dissipation
The Landau-Vlasov equation is applied to a slab of width $L$. This geometry is introduced to simulate somehow the finiteness of real nuclei but to allow for analytical solutions, nevertheless. We focus on the damping of low frequency surface modes and discuss their friction coefficient. For this quantity we study the macroscopic limit as defined by $L\to \infty$. We demonstrate that the same result can be obtained for finite $L$ by applying an appropriate frequency smoothing, if only the smearing interval is sufficiently large. The apparent, but important consequences are discussed which this result will have for the understanding of the nature of dissipation in real nuclei.
9407029v1
1997-12-08
Amplitude equations and pattern selection in Faraday waves
A nonlinear theory of pattern selection in parametric surface waves (Faraday waves) is presented that is not restricted to small viscous dissipation. By using a multiple scale asymptotic expansion near threshold, a standing wave amplitude equation is derived from the governing equations. The amplitude equation is of gradient form, and the coefficients of the associated Lyapunov function are computed for regular patterns of various symmetries as a function of a viscous damping parameter gamma. For gamma approximately 1, the selected wave pattern comprises a single standing wave (stripe pattern). For gamma much less than 1, patterns of square symmetry are obtained in the capillary regime (large frequencies). At lower frequencies (the mixed gravity-capillary regime), a sequence of six-fold (hexagonal), eight-fold,... patterns are predicted. For even lower frequencies (gravity waves) a stripe pattern is again selected. Our predictions of the stability regions of the various patterns are in quantitative agreement with recent experiments conducted in large aspect ratio systems.
9712003v1
2003-04-17
Linear theory of nonlocal transport in a magnetized plasma
A system of nonlocal electron-transport equations for small perturbations in a magnetized plasma is derived using the systematic closure procedure of V. Yu. Bychenkov et al., Phys. Rev. Lett. 75, 4405 (1995). Solution to the linearized kinetic equation with a Landau collision operator is obtained in the diffusive approximation. The Fourier components of the longitudinal, oblique, and transversal electron fluxes are found in an explicit form for quasistatic conditions in terms of the generalized forces: the gradients of density and temperature, and the electric field. The full set of nonlocal transport coefficients is given and discussed. Nonlocality of transport enhances electron fluxes across magnetic field above the values given by strongly collisional local theory. Dispersion and damping of magnetohydrodynamic waves in weakly collisional plasmas is discussed. Nonlocal transport theory is applied to the problem of temperature relaxation across the magnetic field in a laser hot spot.
0304063v1
2005-10-20
Probing liquid surface waves, liquid properties and liquid films with light diffraction
Surface waves on liquids act as a dynamical phase grating for incident light. In this article, we revisit the classical method of probing such waves (wavelengths of the order of mm) as well as inherent properties of liquids and liquid films on liquids, using optical diffraction. A combination of simulation and experiment is proposed to trace out the surface wave profiles in various situations (\emph{eg.} for one or more vertical, slightly immersed, electrically driven exciters). Subsequently, the surface tension and the spatial damping coefficient (related to viscosity) of a variety of liquids are measured carefully in order to gauge the efficiency of measuring liquid properties using this optical probe. The final set of results deal with liquid films where dispersion relations, surface and interface modes, interfacial tension and related issues are investigated in some detail, both theoretically and experimentally. On the whole, our observations and analyses seem to support the claim that this simple, low--cost apparatus is capable of providing a wealth of information on liquids and liquid surface waves in a non--destructive way.
0510184v2
2002-04-30
Laser-driven atom moving in a multimode cavity: strong enhancement of cavity-cooling efficiency
Cavity-mediated cooling of the center--of--mass motion of a transversally, coherently pumped atom along the axis of a high--Q cavity is studied. The internal dynamics of the atomic dipole strongly coupled to the cavity field is treated by a non-perturbative quantum mechanical model, while the effect of the cavity on the external motion is described classically in terms of the analytically obtained linear friction and diffusion coefficients. Efficient cavity-induced damping is found which leads to steady-state temperatures well-below the Doppler limit. We reveal a mathematical symmetry between the results here and for a similar system where, instead of the atom, the cavity field is pumped. The cooling process is strongly enhanced in a degenerate multimode cavity. Both the temperature and the number of scattered photons during the characteristic cooling time exhibits a significant reduction with increasing number of modes involved in the dynamics. The residual number of spontaneous emissions in a cooling time for large mode degeneracy can reach and even drop below the limit of a single photon.
0204170v1
2004-07-06
Field quantization in inhomogeneous absorptive dielectrics
The quantization of the electromagnetic field in a three-dimensional inhomogeneous dielectric medium with losses is carried out in the framework of a damped-polariton model with an arbitrary spatial dependence of its parameters. The equations of motion for the canonical variables are solved explicitly by means of Laplace transformations for both positive and negative time. The dielectric susceptibility and the quantum noise-current density are identified in terms of the dynamical variables and parameters of the model. The operators that diagonalize the Hamiltonian are found as linear combinations of the canonical variables, with coefficients depending on the electric susceptibility and the dielectric Green function. The complete time dependence of the electromagnetic field and of the dielectric polarization is determined. Our results provide a microscopic justification of the phenomenological quantization scheme for the electromagnetic field in inhomogeneous dielectrics.
0407045v1
2006-09-15
Photoionization Broadening of the 1S-2S Transition in a Beam of Atomic Hydrogen
We consider the excitation dynamics of the two-photon \sts transition in a beam of atomic hydrogen by 243 nm laser radiation. Specifically, we study the impact of ionization damping on the transition line shape, caused by the possibility of ionization of the 2S level by the same laser field. Using a Monte-Carlo simulation, we calculate the line shape of the \sts transition for the experimental geometry used in the two latest absolute frequency measurements (M. Niering {\it et al.}, PRL 84, 5496 (2000) and M. Fischer {\it et al.}, PRL 92, 230802 (2004)). The calculated line shift and line width are in excellent agreement with the experimentally observed values. From this comparison we can verify the values of the dynamic Stark shift coefficient for the \sts transition for the first time on a level of 15%. We show that the ionization modifies the velocity distribution of the metastable atoms, the line shape of the \sts transition, and has an influence on the derivation of its absolute frequency.
0609114v1
2006-09-21
ε-convertibility of entangled states and extension of Schmidt rank in infinite-dimensional systems
By introducing the concept of $\epsilon$-convertibility, we extend Nielsen's and Vidal's theorems to the entanglement transformation of infinite-dimensional systems. Using an infinite-dimensional version of Vidal's theorem we derive a new stochastic-LOCC (SLOCC) monotone which can be considered as an extension of the Schmidt rank. We show that states with polynomially-damped Schmidt coefficients belong to a higher rank of entanglement class in terms of SLOCC convertibility. For the case of Hilbert spaces of countable, but infinite dimensionality, we show that there are actually an uncountable number of classes of pure non-interconvertible bipartite entangled states.
0609167v4
2007-04-20
Determining factors behind the PageRank log-log plot
We study the relation between PageRank and other parameters of information networks such as in-degree, out-degree, and the fraction of dangling nodes. We model this relation through a stochastic equation inspired by the original definition of PageRank. Further, we use the theory of regular variation to prove that PageRank and in-degree follow power laws with the same exponent. The difference between these two power laws is in a multiple coefficient, which depends mainly on the fraction of dangling nodes, average in-degree, the power law exponent, and damping factor. The out-degree distribution has a minor effect, which we explicitly quantify. Our theoretical predictions show a good agreement with experimental data on three different samples of the Web.
0704.2694v1
2007-05-15
Electrical excitation of shock and soliton-like waves in two-dimensional electron channels
We study electrical excitation of nonlinear plasma waves in heterostructures with two-dimensional electron channels and with split gates, and the propagation of these waves using hydrodynamic equations for electron transport coupled with two-dimensional Poisson equation for self-consistent electric potential. The term related to electron collisions with impurities and phonons as well as the term associated with viscosity are included into the hydrodynamic equations. We demonstrate the formation of shock and soliton-like waves as a result of the evolution of strongly nonuniform initial electron density distribution. It is shown that the shock wave front and the shape of soliton-like pulses pronouncedly depend on the coefficient of viscosity, the thickness of the gate layer and the nonuniformity of the donor distribution along the channel. The electron collisions result in damping of the shock and soliton-like waves, while they do not markedly affect the thickness of the shock wave front.
0705.2111v1
2007-07-27
Oscillatory D'yakonov-Perel' spin dynamics in two dimensional electron gases
Optical pump-probe measurements of spin-dynamics at temperatures down to 1.5K are described for a series of (001)-oriented GaAs/AlGaAs quantum well samples containing high mobility two-dimensional electron gases (2DEGs). For well widths ranging from 5 nm to 20 nm and 2DEG sheet densities from 1.75x1011cm-2 to 3.5x1011cm-2 the evolution of a small injected spin population is found to be a damped oscillation rather than exponential relaxation, consistent with the quasi-collision-free regime of D'yakonov-Perel spin dynamics. A Monte Carlo simulation method is used to extract the spin-orbit-induced electron spin precession frequency |W(kF)| and electron momentum scattering time tp* at the Fermi wavevector. The spin decay time passes through a minimum at a temperature corresponding to the transition from collision-free to collision-dominated regimes and tp* is found to be close to the ensemble momentum scattering time tp obtained from Hall measurements of electron mobility. The values of |W(kF)| give the Dresselhaus (BIA) coefficient of spin-orbit interaction as a function of electron confinement energy in the quantum show, qualitatively, the behaviour expected from k.p theory.
0707.4180v1
2008-01-07
Field Theoretic Description of Ultrarelativistic Electron-Positron Plasmas
Ultrarelativistic electron-positron plasmas can be produced in high-intensity laser fields and play a role in various astrophysical situations. Their properties can be calculated using QED at finite temperature. Here we will use perturbative QED at finite temperature for calculating various important properties, such as the equation of state, dispersion relations of collective plasma modes of photons and electrons, Debye screening, damping rates, mean free paths, collision times, transport coefficients, and particle production rates, of ultrarelativistic electron-positron plasmas. In particular, we will focus on electron-positron plasmas produced with ultra-strong lasers.
0801.0956v2
2008-05-20
Probability of metastable configurations in spherical three-dimensional Yukawa crystals
Recently the occurrence probabilities of ground- and metastable states of three-dimensional Yukawa clusters with 27 and 31 particles have been analyzed in dusty plasma experiments [Block et al., Physics of Plasmas 15, 040701 (2008)]. There it was found that, in many cases, the ground state appeared substantially less frequently than excited states. Here we analyze this question theoretically by means of molecular dynamics (MD) and Monte Carlo simulations and an analytical method based on the canonical partition function. We confirm that metastable states can occur with a significantly higher probability than the ground state. The results strongly depend on the screening parameter of the Yukawa interaction and the damping coefficient used in the MD simulations. The analytical method allows one to gain insight into the mechanisms being responsible for the occurrence probabilities of metastable states in strongly correlated finite systems.
0805.3016v1
2008-05-29
Dispersion enhancement and damping by buoyancy driven flows in 2D networks of capillaries
The influence of a small relative density difference on the displacement of two miscible liquids is studied experimentally in transparent 2D networks of micro channels. Both stable displacements in which the denser fluid enters at the bottom of the cell and displaces the lighter one and unstable displacements in which the lighter fluid is injected at the bottom and displaces the denser one are realized. Except at the lowest mean flow velocity U, the average $C(x,t)$ of the relative concentration satisfies a convection-dispersion equation. The dispersion coefficient is studied as function of the relative magnitude of fluid velocity and of the velocity of buoyancy driven fluid motion. A model is suggested and its applicability to previous results obtained in 3D media is discussed.
0805.4564v1
2008-06-12
Vortex dynamics in trapped Bose-Einstein condensate
We perform numerical simulations of vortex motion in a trapped Bose-Einstein condensate by solving the two-dimensional Gross-Pitaevskii Equation in the presence of a simple phenomenological model of interaction between the condensate and the finite temperature thermal cloud. At zero temperature, the trajectories of a single, off - centred vortex precessing in the condensate, and of a vortex - antivortex pair orbiting within the trap, excite acoustic emission. At finite temperatures the vortices move to the edge of the condensate and vanish. By fitting the finite -temperature trajectories, we relate the phenomenological damping parameter to the friction coefficients $\alpha$ and $\alpha^{'}$, which are used to describe the interaction between quantised vortices and the normal fluid in superfluid helium.
0806.2077v2
2008-06-12
Diversity-induced resonance in a system of globally coupled linear oscillators
The purpose of this paper to analyze in some detail the arguably simplest case of diversity-induced reseonance: that of a system of globally-coupled linear oscillators subjected to a periodic forcing. Diversity appears as the parameters characterizing each oscillator, namely its mass, internal frequency and damping coefficient are drawn from a probability distribution. The main ingredients for the diversity-induced-resonance phenomenon are present in this system as the oscillators display a variability in the individual responses but are induced, by the coupling, to synchronize their responses. A steady state solution for this model is obtained. We also determine the conditions under which it is possible to find a resonance effect.
0806.2106v1
2008-08-05
From Equilibrium to Transport Properties of Strongly Correlated Fermi Liquids
We summarize recent results regarding the equilibrium and non-equilibrium behavior of cold dilute atomic gases in the limit in which the two body scattering length a goes to infinity. In this limit the system is described by a Galilean invariant (non-relativistic) conformal field theory. We discuss the low energy effective lagrangian appropriate to the limit a->infinity, and compute low energy coefficients using an epsilon-expansion. We also show how to combine the effective lagrangian with kinetic theory in order to compute the shear viscosity, and compare the kinetic theory predictions to experimental results extracted from the damping of collective modes in trapped Fermi gases.
0808.0734v1
2008-09-09
What can we learn from electromagnetic plasmas about the quark-gluon plasma?
Ultra-relativistic electromagnetic plasmas can be used for improving our understanding of the quark-gluon plasma. In the weakly coupled regime both plasmas can be described by transport theoretical and quantum field theoretical methods leading to similar results for the plasma properties (dielectric tensor, dispersion relations, plasma frequency, Debye screening, transport coefficients, damping and particle production rates). In particular, future experiments with ultra-relativistic electron-positron plasmas in ultra-strong laser fields might open the possibility to test these predictions, e.g. the existence of a new fermionic plasma wave (plasmino). In the strongly coupled regime electromagnetic plasmas such as complex plasmas can be used as models or at least analogies for the quark-gluon plasma possibly produced in relativistic heavy-ion experiments. For example, pair correlation functions can be used to investigate the equation of state and cross section enhancement for parton scattering can be explained.
0809.1507v1
2008-10-06
Ultrarelativistic Electron-Positron Plasma
Ultrarelativistic electron-positron plasmas can be produced in high-intensity laser fields and play a role in various astrophysical situations. Their properties can be calculated using QED at finite temperature. Here we will use perturbative QED at finite temperature for calculating various important properties, such as the equation of state, dispersion relations of collective plasma modes of photons and electrons, Debye screening, damping rates, mean free paths, collision times, transport coefficients, and particle production rates, of ultrarelativistic electron-positron plasmas. In particular, we will focus on electron-positron plasmas produced with ultra-strong lasers.
0810.0909v1
2009-01-27
A simple, low-cost, data-logging pendulum built from a computer mouse
Lessons and homework problems involving a pendulum are often a big part of introductory physics classes and laboratory courses from high school to undergraduate levels. Although laboratory equipment for pendulum experiments is commercially available, it is often expensive and may not be affordable for teachers on fixed budgets, particularly in developing countries. We present a low-cost, easy-to-build rotary sensor pendulum using the existing hardware in a ball-type computer mouse. We demonstrate how this apparatus may be used to measure both the frequency and coefficient of damping of a simple physical pendulum. This easily constructed laboratory equipment makes it possible for all students to have hands-on experience with one of the most important simple physical systems.
0901.4319v1
2009-02-18
Frequency dependence of viscous and viscoelastic dissipation in coated micro-cantilevers from noise measurement
We measure the mechanical thermal noise of soft silicon atomic force microscopy cantilevers. Using an interferometric setup, we have a resolution down to 1E-14 m/rtHz on a wide spectral range (3 Hz to 1E5 Hz). The low frequency behavior depends dramatically on the presence of a reflective coating: almost flat spectrums for uncoated cantilevers versus 1/f like trend for coated ones. The addition of a viscoelastic term in models of the mechanical system can account for this observation. Use of Kramers-Kronig relations validate this approach with a complete determination of the response of the cantilever: a power law with a small coefficient is found for the frequency dependence of viscoelasticity due to the coating, whereas the viscous damping due to the surrounding atmosphere is accurately described by the Sader model.
0902.3134v2
2009-03-10
Phonon-phonon interactions and phonon damping in carbon nanotubes
We formulate and study the effective low-energy quantum theory of interacting long-wavelength acoustic phonons in carbon nanotubes within the framework of continuum elasticity theory. A general and analytical derivation of all three- and four-phonon processes is provided, and the relevant coupling constants are determined in terms of few elastic coefficients. Due to the low dimensionality and the parabolic dispersion, the finite-temperature density of noninteracting flexural phonons diverges, and a nonperturbative approach to their interactions is necessary. Within a mean-field description, we find that a dynamical gap opens. In practice, this gap is thermally smeared, but still has important consequences. Using our theory, we compute the decay rates of acoustic phonons due to phonon-phonon and electron-phonon interactions, implying upper bounds for their quality factor.
0903.1771v2
2009-03-30
Breit-Wigner resonances and the quasinormal modes of anti-de Sitter black holes
The purpose of this short communication is to show that the theory of Breit-Wigner resonances can be used as an efficient numerical tool to compute black hole quasinormal modes. For illustration we focus on the Schwarzschild anti-de Sitter (SAdS) spacetime. The resonance method is better suited to small SAdS black holes than the traditional series expansion method, allowing us to confirm that the damping timescale of small SAdS black holes for scalar and gravitational fields is proportional to r_+^(-2l-2), where r_+ is the horizon radius. The proportionality coefficients are in good agreement with analytic calculations. We also examine the eikonal limit of SAdS quasinormal modes, confirming quantitatively Festuccia and Liu's prediction of the existence of very long-lived modes in asymptotically AdS spacetimes. Our results are particularly relevant for the AdS/CFT correspondence, since long-lived modes presumably dominate the decay timescale of the perturbations.
0903.5311v1
2009-08-21
Aspects of warm-flat directions
Considering the mechanism of dissipative slow-roll that has been used in warm inflation scenario, we show that dissipation may alter usual cosmological scenarios associated with SUSY-flat directions. We mainly consider SUSY-flat directions that have strong interactions with non-flat directions and may cause strong dissipation both in thermal and non-thermal backgrounds. An example is the Affleck-Dine mechanism in which dissipation may create significant (both qualitative and quantitative) discrepancies between the conventional scenario and the dissipative one. We also discuss several mechanisms of generating curvature perturbations in which the dissipative field, which is distinguished from the inflaton field, can be used as the source of cosmological perturbations. Considering the Morikawa-Sasaki dissipative coefficient, the damping caused by the dissipation may be significant for many MSSM flat directions even if the dissipation is far from thermal equilibrium.
0908.3059v4
2009-10-19
Friction force on slow charges moving over supported graphene
We provide a theoretical model that describes the dielectric coupling of a 2D layer of graphene, represented by a polarization function in the Random Phase Approximation, and a semi-infinite 3D substrate, represented by a surface response function in a non-local formulation. We concentrate on the role of the dynamic response of the substrate for low-frequency excitations of the combined graphene-substrate system, which give rise to the stopping force on slowly moving charges above graphene. A comparison of the dielectric loss function with experimental HREELS data for graphene on a SiC substrate is used to estimate the damping rate in graphene and to reveal the importance of phonon excitations in an insulating substrate. A signature of the hybridization between graphene's pi plasmon and the substrate's phonon is found in the stopping force. A friction coefficient that is calculated for slow charges moving above graphene on a metallic substrate shows an interplay between the low-energy single-particle excitations in both systems.
0910.3586v1
2009-11-15
Effect of three-body loss on itinerant ferromagnetism in an atomic Fermi gas
A recent experiment has provided the first evidence for itinerant ferromagnetism in an ultracold atomic gas of fermions with repulsive interactions. However, the gas in this regime is also subject to significant three-body loss. We adopt an extended Hertz-Millis theory to account for the effect of loss on the transition and on the ferromagnetic state. We find that the losses damp quantum fluctuations and thereby significantly increase the critical interaction strength needed to induce ferromagnetism. This effect may resolve a discrepancy between the experiment and previous theoretical predictions of the critical interaction strength. We further illuminate the impact of loss by studying the collective spin excitations in the ferromagnet. Even in the fully polarized state, where loss is completely suppressed, spin waves acquire a decay rate proportional to the three-body loss coefficient.
0911.2839v1
2009-12-18
Gravitational Instability in Presence of Bulk Viscosity: the Jeans Mass and the Quasi-Isotropic Solution
This paper focuses on the analysis of the gravitational instability in presence of bulk viscosity both in Newtonian regime and in the fully-relativistic approach. The standard Jeans Mechanism and the Quasi-Isotropic Solution are treated expressing the bulk-viscosity coefficient $\zeta$ as a power-law of the fluid energy density $\rho$, i.e., $\zeta=\zo\rho^{s}$. In the Newtonian regime, the perturbation evolution is founded to be damped by viscosity and the top-down mechanism of structure fragmentation is suppressed. The value of the Jeans Mass remains unchanged also in presence of viscosity. In the relativistic approach, we get a power-law solution existing only in correspondence to a restricted domain of $\zo$.
0912.3641v1
2010-01-14
A Theoretical Closure for Turbulent Flows Near Walls
This paper proposes a simple new closure principle for turbulent shear flows. The turbulent flow field is divided into an outer and an inner region. The inner region is made up of a log-law region and a wall layer. The wall layer is viewed in terms of the well known inrush-sweep-burst sequence observed since 1967. It is modelled as a transient laminar sub-boundary layer, which obeys the Stokes solution for an impulsively started flat plate. The wall layer may also be modelled with a steady state solution by adding a damping function to the log-law. Closure is achieved by matching the unsteady and steady state solutions at the edge of the wall layer. This procedure in effect feeds information about the transient coherent structures back into the time-averaged solution and determines theoretically the numerical coefficient of the logarithmic law of the wall The method gives a new technique for writing accurate wall functions, valid for all Reynolds numbers, in computer fluid dynamics (CFD) programmes. Keywords: Reynolds equations, modelling, closure technique, wall layer, log-law, CFD.
1001.2353v1
2010-02-23
Bulk viscosity in hyperonic star and r-mode instability
We consider a rotating neutron star with the presence of hyperons in its core, using an equation of state in an effective chiral model within the relativistic mean field approximation. We calculate the hyperonic bulk viscosity coefficient due to nonleptonic weak interactions. By estimating the damping timescales of the dissipative processes, we investigate its role in the suppression of gravitationally driven instabilities in the $r$-mode. We observe that $r$-mode instability remains very much significant for hyperon core temperature of around $10^8 $K, resulting in a comparatively larger instability window. We find that such instability can reduce the angular velocity of the rapidly rotating star considerably upto $\sim0.04 \Omega_K$, with $\Omega_K$ as the Keplerian angular velocity.
1002.4253v1
2010-03-03
Phonon lineshapes in atom-surface scattering
Phonon lineshapes in atom-surface scattering are obtained from a simple stochastic model based on the so-called Caldeira-Leggett Hamiltonian. In this single-bath model, the excited phonon resulting from a creation or annihilation event is coupled to a thermal bath consisting of an infinite number of harmonic oscillators, namely the bath phonons. The diagonalization of the corresponding Hamiltonian leads to a renormalization of the phonon frequencies in terms of the phonon friction or damping coefficient. Moreover, when there are adsorbates on the surface, this single-bath model can be extended to a two-bath model accounting for the effect induced by the adsorbates on the phonon lineshapes as well as their corresponding lineshapes.
1003.0790v2
2010-03-30
Superfluid hyperon bulk viscosity and the r-mode instability of rotating neutron stars
In order to establish whether the unstable r-modes in a rotating neutron star provide a detectable source of gravitational waves, we need to understand the details of the many dissipative processes that tend to counteract the instability. It has been established that the bulk viscosity due to exotic particles, like hyperons, may be particularly important in this respect. However, the effects of hyperon superfluidity have so far not been fully accounted for. While the associated suppression of the reaction rates that give rise to the bulk viscosity has been estimated, superfluid aspects of the fluid dynamics have not been considered. In this paper we determine the r-mode instability window for a neutron star with a $\Sigma^{-}$ hyperon core, using the appropriate multifluid formalism including, for the first time, the effect of the "superfluid" bulk viscosity coefficients. We demonstrate that, even though the extra terms may increase the bulk viscosity damping somewhat, their presence does not affect the qualitative features of the r-mode instability window.
1003.5849v1
2010-05-07
r-modes in low temperature colour-flavour-locked superconducting quark star
We present the first multi-fluid analysis of a dense neutron star core with a deconfined colour-flavour-locked superconducting quark component. Accounting only for the condensate and (finite temperature) phonons, we make progress by taking over results for superfluid $^4$He. The resultant two-fluid model accounts for a number of additional viscosity coefficients (compared to the Navier-Stokes equations) and we show how they enter the dissipation analysis for an oscillating star. We provide simple estimates for the gravitational-wave driven r-mode instability, demonstrating that the various phonon processes that we consider are not effective damping agents. Even though the results are likely of little direct astrophysical importance (since we consider an overly simplistic stellar model) our analysis represents significant technical progress, laying the foundation for more detailed numerical studies and preparing the ground for the inclusion of additional aspects (in particular associated with kaons) of the problem.
1005.1163v1