Relaxation times for Hamiltonian systems

Usually, the relaxation times of a gas are estimated in the frame of the Boltzmann equation. In this paper, instead, we deal with the relaxation problem in the frame of the dynamical theory of Hamiltonian systems, in which the definition itself of a relaxation time is an open question. We introduce a lower bound for the relaxation time, and give a general theorem for estimating it. Then we give an application to a concrete model of an interacting gas, in which the lower bound turns out to be of the order of magnitude of the relaxation times observed in dilute gases.Comment: 26 page

Correcting cold wire measurements in isotropic turbulence with a DNS database

We estimate the effect of the finite spatial resolution of a cold wire for scalar measurements, using a database from direct numerical simulations (DNS). These are for homogeneous isotropic turbulence at low Taylor-microscale Reynolds number (≃ 42) and Schmidt number unity. Correction factors for the scalar variance, scalar mean dissipation rate, and mixed velocity-scalar derivative skewness are evaluated, for a sensor length of up to 15 times the Batchelor length scale. The largest attenuation effect is found on the dissipation rate, followed by the scalar variance. The mixed skewness,which is affected the least, is overestimated

Boundary effects on the dynamics of chains of coupled oscillators

We study the dynamics of a chain of coupled particles subjected to a restoring force (Klein-Gordon lattice) in the cases of either periodic or Dirichlet boundary conditions. Precisely, we prove that, when the initial data are of small amplitude and have long wavelength, the main part of the solution is interpolated by a solution of the nonlinear Schr\"odinger equation, which in turn has the property that its Fourier coefficients decay exponentially. The first order correction to the solution has Fourier coefficients that decay exponentially in the periodic case, but only as a power in the Dirichlet case. In particular our result allows one to explain the numerical computations of the paper \cite{BMP07}

Gyrokinetic Large Eddy Simulations

The Large Eddy Simulation (LES) approach is adapted to the study of plasma microturbulence in a fully three-dimensional gyrokinetic system. Ion temperature gradient driven turbulence is studied with the {\sc GENE} code for both a standard resolution and a reduced resolution with a model for the sub-grid scale turbulence. A simple dissipative model for representing the effect of the sub-grid scales on the resolved scales is proposed and tested. Once calibrated, the model appears to be able to reproduce most of the features of the free energy spectra for various values of the ion temperature gradient

An improved \eps expansion for three-dimensional turbulence: summation of nearest dimensional singularities

An improved \eps expansion in the $d$-dimensional ($d > 2$) stochastic theory of turbulence is constructed by taking into account pole singularities at $d \to 2$ 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

Free energy cascade in gyrokinetic turbulence

In gyrokinetic theory, the quadratic nonlinearity is known to play an important role in the dynamics by redistributing (in a conservative fashion) the free energy between the various active scales. In the present study, the free energy transfer is analyzed for the case of ion temperature gradient driven turbulence. It is shown that it shares many properties with the energy transfer in fluid turbulence. In particular, one finds a forward (from large to small scales), extremely local, and self-similar cascade of free energy in the plane perpendicular to the background magnetic field. These findings shed light on some fundamental properties of plasma turbulence, and encourage the development of large eddy simulation techniques for gyrokinetics.Comment: 4 pages, 2 Postscript figure

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

Discrete Matter, Far Fields, and Dark Matter

We show that in cosmology the gravitational action of the far away matter has quite relevant effects, if retardation of the forces and discreteness of matter (with its spatial correlation) are taken into account. The expansion rate is found to be determined by the density of the far away matter, i.e., by the density of matter at remote times. This leads to the introduction of an effective density, which has to be five times larger than the present one, if the present expansion rate is to be accounted for. The force per unit mass on a test particle is found to be of the order of 0.2cH_0. The corresponding contribution to the virial of the forces for a cluster of galaxies is also discussed, and it is shown that it fits the observations if a decorrelation property of the forces at two separated points is assumed. So it appears that the gravitational effects of the far away matter may have the same order of magnitude as the corresponding local effects of dark matter.Comment: 16 pages, 1 figure. LaTex documen

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 $64^3$ grid. These results match quite well with direct numerical simulations of $128^3$. 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