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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 |
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