6,215 research outputs found
Liquid compressibility effects during the collapse of a single cavitating bubble
The effect of liquid compressibility on the dynamics of a single, spherical cavitating bubble is studied.
While it is known that compressibility damps the amplitude of bubble rebounds, the extent to which
this effect is accurately captured by weakly compressible versions of the Rayleigh–Plesset equation is
unclear. To clarify this issue, partial differential equations governing conservation of mass, momentum,
and energy are numerically solved both inside the bubble and in the surrounding compressible
liquid. Radiated pressure waves originating at the unsteady bubble interface are directly captured.
Results obtained with Rayleigh–Plesset type equations accounting for compressibility effects, proposed
by Keller and Miksis [J. Acoust. Soc. Am. 68, 628–633 (1980)], Gilmore, and Tomita and
Shima [Bull. JSME 20, 1453–1460 (1977)], are compared with those resulting from the full model.
For strong collapses, the solution of the latter reveals that an important part of the energy concentrated
during the collapse is used to generate an outgoing pressure wave. For the examples considered in
this research, peak pressures are larger than those predicted by Rayleigh–Plesset type equations,
whereas the amplitudes of the rebounds are smaller
On the derivation of Fourier's law in stochastic energy exchange systems
We present a detailed derivation of Fourier's law in a class of stochastic
energy exchange systems that naturally characterize two-dimensional mechanical
systems of locally confined particles in interaction. The stochastic systems
consist of an array of energy variables which can be partially exchanged among
nearest neighbours at variable rates. We provide two independent derivations of
the thermal conductivity and prove this quantity is identical to the frequency
of energy exchanges. The first derivation relies on the diffusion of the
Helfand moment, which is determined solely by static averages. The second
approach relies on a gradient expansion of the probability measure around a
non-equilibrium stationary state. The linear part of the heat current is
determined by local thermal equilibrium distributions which solve a
Boltzmann-like equation. A numerical scheme is presented with computations of
the conductivity along our two methods. The results are in excellent agreement
with our theory.Comment: 19 pages, 5 figures, to appear in Journal of Statistical Mechanics
(JSTAT
A Solution of the Maxwell-Dirac Equations in 3+1 Dimensions
We investigate a class of localized, stationary, particular numerical
solutions to the Maxwell-Dirac system of classical nonlinear field equations.
The solutions are discrete energy eigenstates bound predominantly by the
self-produced electric field.Comment: 12 pages, revtex, 2 figure
An Extension of the Fluctuation Theorem
Heat fluctuations are studied in a dissipative system with both mechanical
and stochastic components for a simple model: a Brownian particle dragged
through water by a moving potential. An extended stationary state fluctuation
theorem is derived. For infinite time, this reduces to the conventional
fluctuation theorem only for small fluctuations; for large fluctuations, it
gives a much larger ratio of the probabilities of the particle to absorb rather
than supply heat. This persists for finite times and should be observable in
experiments similar to a recent one of Wang et al.Comment: 12 pages, 1 eps figure in color (though intelligible in black and
white
Fluctuations of topological disclination lines in nematics: renormalization of the string model
The fluctuation eigenmode problem of the nematic topological disclination
line with strength is solved for the complete nematic tensor order
parameter. The line tension concept of a defect line is assessed, the line
tension is properly defined. Exact relaxation rates and thermal amplitudes of
the fluctuations are determined. It is shown that within the simple string
model of the defect line the amplitude of its thermal fluctuations is
significantly underestimated due to the neglect of higher radial modes. The
extent of universality of the results concerning other systems possessing line
defects is discussed.Comment: 6 pages, 3 figure
Mean-field calculation of critical parameters and log-periodic characterization of an aperiodic-modulated model
We employ a mean-field approximation to study the Ising model with aperiodic
modulation of its interactions in one spatial direction. Two different values
for the exchange constant, and , are present, according to the
Fibonacci sequence. We calculated the pseudo-critical temperatures for finite
systems and extrapolate them to the thermodynamic limit. We explicitly obtain
the exponents , , and and, from the usual scaling
relations for anisotropic models at the upper critical dimension (assumed to be
4 for the model we treat), we calculate , , , ,
and . Within the framework of a renormalization-group approach, the
Fibonacci sequence is a marginal one and we obtain exponents which depend on
the ratio , as expected. But the scaling relation is obeyed for all values of we studied. We characterize
some thermodynamic functions as log-periodic functions of their arguments, as
expected for aperiodic-modulated models, and obtain precise values for the
exponents from this characterization.Comment: 17 pages, including 9 figures, to appear in Phys. Rev.
Renormalized waves and thermalization of the Klein-Gordon equation: What sound does a nonlinear string make?
We study the thermalization of the classical Klein-Gordon equation under a
u^4 interaction. We numerically show that even in the presence of strong
nonlinearities, the local thermodynamic equilibrium state exhibits a weakly
nonlinear behavior in a renormalized wave basis. The renormalized basis is
defined locally in time by a linear transformation and the requirement of
vanishing wave-wave correlations. We show that the renormalized waves oscillate
around one frequency, and that the frequency dispersion relation undergoes a
nonlinear shift proportional to the mean square field. In addition, the
renormalized waves exhibit a Planck like spectrum. Namely, there is
equipartition of energy in the low frequency modes described by a Boltzmann
distribution, followed by a linear exponential decay in the high frequency
modes.Comment: 13 pages, 13 figure
Synthetic LISA: Simulating Time Delay Interferometry in a Model LISA
We report on three numerical experiments on the implementation of Time-Delay
Interferometry (TDI) for LISA, performed with Synthetic LISA, a C++/Python
package that we developed to simulate the LISA science process at the level of
scientific and technical requirements. Specifically, we study the laser-noise
residuals left by first-generation TDI when the LISA armlengths have a
realistic time dependence; we characterize the armlength-measurements
accuracies that are needed to have effective laser-noise cancellation in both
first- and second-generation TDI; and we estimate the quantization and
telemetry bitdepth needed for the phase measurements. Synthetic LISA generates
synthetic time series of the LISA fundamental noises, as filtered through all
the TDI observables; it also provides a streamlined module to compute the TDI
responses to gravitational waves according to a full model of TDI, including
the motion of the LISA array and the temporal and directional dependence of the
armlengths. We discuss the theoretical model that underlies the simulation, its
implementation, and its use in future investigations on system characterization
and data-analysis prototyping for LISA.Comment: 18 pages, 14 EPS figures, REVTeX 4. Accepted PRD version. See
http://www.vallis.org/syntheticlisa for information on the Synthetic LISA
software packag
Choosing integration points for QCD calculations by numerical integration
I discuss how to sample the space of parton momenta in order to best perform
the numerical integrations that lead to a calculation of three jet cross
sections and similar observables in electron-positron annihilation.Comment: 25 pages with 8 figure
A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
Recent progress in unitarity techniques for one-loop scattering amplitudes
makes a numerical implementation of this method possible. We present a
4-dimensional unitarity method for calculating the cut-constructible part of
amplitudes and implement the method in a numerical procedure. Our technique can
be applied to any one-loop scattering amplitude and offers the possibility that
one-loop calculations can be performed in an automatic fashion, as tree-level
amplitudes are currently done. Instead of individual Feynman diagrams, the
ingredients for our one-loop evaluation are tree-level amplitudes, which are
often already known. To study the practicality of this method we evaluate the
cut-constructible part of the 4, 5 and 6 gluon one-loop amplitudes numerically,
using the analytically known 4, 5 and 6 gluon tree-level amplitudes.
Comparisons with analytic answers are performed to ascertain the numerical
accuracy of the method.Comment: 29 pages with 8 figures; references updated in rsponse to readers'
suggestion
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