91 research outputs found
A rigorous implementation of the Jeans--Landau--Teller approximation
Rigorous bounds on the rate of energy exchanges between vibrational and
translational degrees of freedom are established in simple classical models of
diatomic molecules. The results are in agreement with an elementary
approximation introduced by Landau and Teller. The method is perturbative
theory ``beyond all orders'', with diagrammatic techniques (tree expansions) to
organize and manipulate terms, and look for compensations, like in recent
studies on KAM theorem homoclinic splitting.Comment: 23 pages, postscrip
An improved \eps expansion for three-dimensional turbulence: summation of nearest dimensional singularities
An improved \eps expansion in the -dimensional () stochastic
theory of turbulence is constructed by taking into account pole singularities
at in coefficients of the \eps expansion of universal quantities.
Effectiveness of the method is illustrated by a two-loop calculation of the
Kolmogorov constant in three dimensions.Comment: 4 page
Aging in an infinite-range Hamiltonian system of coupled rotators
We analyze numerically the out-of-equilibrium relaxation dynamics of a
long-range Hamiltonian system of fully coupled rotators. For a particular
family of initial conditions, this system is known to enter a particular regime
in which the dynamic behavior does not agree with thermodynamic predictions.
Moreover, there is evidence that in the thermodynamic limit, when
is taken prior to , the system will never attain true equilibrium.
By analyzing the scaling properties of the two-time autocorrelation function we
find that, in that regime, a very complex dynamics unfolds in which {\em aging}
phenomena appear. The scaling law strongly suggests that the system behaves in
a complex way, relaxing towards equilibrium through intricate trajectories. The
present results are obtained for conservative dynamics, where there is no
thermal bath in contact with the system. This is the first time that aging is
observed in such Hamiltonian systems.Comment: Figs. 2-4 modified, minor changes in text. To appear in Phys. Rev.
Large-Eddy Simulations of Fluid and Magnetohydrodynamic Turbulence Using Renormalized Parameters
In this paper a procedure for large-eddy simulation (LES) has been devised
for fluid and magnetohydrodynamic turbulence in Fourier space using the
renormalized parameters. The parameters calculated using field theory have been
taken from recent papers by Verma [Phys. Rev. E, 2001; Phys. Plasmas, 2001]. We
have carried out LES on grid. These results match quite well with direct
numerical simulations of . We show that proper choice of parameter is
necessary in LES.Comment: 12 pages, 4 figures: Proper figures inserte
Considering Fluctuation Energy as a Measure of Gyrokinetic Turbulence
In gyrokinetic theory there are two quadratic measures of fluctuation energy,
left invariant under nonlinear interactions, that constrain the turbulence. The
recent work of Plunk and Tatsuno [Phys. Rev. Lett. 106, 165003 (2011)] reported
on the novel consequences that this constraint has on the direction and
locality of spectral energy transfer. This paper builds on that work. We
provide detailed analysis in support of the results of Plunk and Tatsuno but
also significantly broaden the scope and use additional methods to address the
problem of energy transfer. The perspective taken here is that the fluctuation
energies are not merely formal invariants of an idealized model
(two-dimensional gyrokinetics) but are general measures of gyrokinetic
turbulence, i.e. quantities that can be used to predict the behavior of the
turbulence. Though many open questions remain, this paper collects evidence in
favor of this perspective by demonstrating in several contexts that constrained
spectral energy transfer governs the dynamics.Comment: Final version as published. Some cosmetic changes and update of
reference
First passage and arrival time densities for L\'evy flights and the failure of the method of images
We discuss the first passage time problem in the semi-infinite interval, for
homogeneous stochastic Markov processes with L{\'e}vy stable jump length
distributions (),
namely, L{\'e}vy flights (LFs). In particular, we demonstrate that the method
of images leads to a result, which violates a theorem due to Sparre Andersen,
according to which an arbitrary continuous and symmetric jump length
distribution produces a first passage time density (FPTD) governed by the
universal long-time decay . Conversely, we show that for LFs the
direct definition known from Gaussian processes in fact defines the probability
density of first arrival, which for LFs differs from the FPTD. Our findings are
corroborated by numerical results.Comment: 8 pages, 3 figures, iopart.cls style, accepted to J. Phys. A (Lett
- …