Crucial role of sidewalls in velocity distributions in quasi-2D granular gases

Our experiments and three-dimensional molecular dynamics simulations of particles confined to a vertical monolayer by closely spaced frictional walls (sidewalls) yield velocity distributions with non-Gaussian tails and a peak near zero velocity. Simulations with frictionless sidewalls are not peaked. Thus interactions between particles and their container are an important determinant of the shape of the distribution and should be considered when evaluating experiments on a tightly constrained monolayer of particles.Comment: 4 pages, 4 figures, Added reference, model explanation charified, other minor change

Effective pair potentials for spherical nanoparticles

An effective description for spherical nanoparticles in a fluid of point particles is presented. The points inside the nanoparticles and the point particles are assumed to interact via spherically symmetric additive pair potentials, while the distribution of points inside the nanoparticles is taken to be spherically symmetric and smooth. The resulting effective pair interactions between a nanoparticle and a point particle, as well as between two nanoparticles, are then given by spherically symmetric potentials. If overlap between particles is allowed, the effective potential generally has non-analytic points, but for each effective potential the expressions for different overlapping cases can be written in terms of one analytic auxiliary potential. Effective potentials for hollow nanoparticles (appropriate e.g. for buckyballs) are also considered, and shown to be related to those for solid nanoparticles. Finally, explicit expressions are given for the effective potentials derived from basic pair potentials of power law and exponential form, as well as from the commonly used London-Van der Waals, Morse, Buckingham, and Lennard-Jones potential. The applicability of the latter is demonstrated by comparison with an atomic description of nanoparticles with an internal face centered cubic structure.Comment: 27 pages, 12 figures. Unified description of overlapping and nonoverlapping particles added, as well as a comparison with an idealized atomic descriptio

Mode-coupling theory for multiple-time correlation functions of tagged particle densities and dynamical filters designed for glassy systems

The theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system developed by Van Zon and Schofield [Phys. Rev. E 65, 011106 (2002)] is extended here to include tagged particle densities. Such densities have found an intriguing application as proposed measures of dynamical heterogeneities in structural glasses. The theoretical formalism is based upon projection operator techniques which are used to isolate the slow time evolution of dynamical variables by expanding the slowly-evolving component of arbitrary variables in an infinite basis composed of the products of slow variables of the system. The resulting formally exact mode-coupling expressions for multiple-point and multiple-time correlation functions are made tractable by applying the so-called N-ordering method. This theory is used to derive for moderate densities the leading mode coupling expressions for indicators of relaxation type and domain relaxation, which use dynamical filters that lead to multiple-time correlations of a tagged particle density. The mode coupling expressions for higher order correlation functions are also succesfully tested against simulations of a hard sphere fluid at relatively low density.Comment: 15 pages, 2 figure

Grand canonical ensemble in generalized thermostatistics

We study the grand-canonical ensemble with a fluctuating number of degrees of freedom in the context of generalized thermostatistics. Several choices of grand-canonical entropy functional are considered. The ideal gas is taken as an example.Comment: 14 pages, no figure

Structure and soft magnetic properties of sputter deposited MnZn-ferrite films

In this paper we report the soft magnetic properties of thin films of sputtered MnZn ferrite deposited on thermally oxidized Si substrates. A high deposition temperature, 600¿°C, together with the addition of water vapor to the sputtering gas was found to improve the initial ac permeability, µ. The highest value obtained was approximately 30. For MnZn-ferrite films with much larger grain sizes, as obtained by deposition on a polycrystalline Zn-ferrite substrate, a µ of 100 was obtained. The results are discussed in terms of the so-called nonmagnetic grain boundary model

Multiple-Point and Multiple-Time Correlations Functions in a Hard-Sphere Fluid

A recent mode coupling theory of higher-order correlation functions is tested on a simple hard-sphere fluid system at intermediate densities. Multi-point and multi-time correlation functions of the densities of conserved variables are calculated in the hydrodynamic limit and compared to results obtained from event-based molecular dynamics simulations. It is demonstrated that the mode coupling theory results are in excellent agreement with the simulation results provided that dissipative couplings are included in the vertices appearing in the theory. In contrast, simplified mode coupling theories in which the densities obey Gaussian statistics neglect important contributions to both the multi-point and multi-time correlation functions on all time scales.Comment: Second one in a sequence of two (in the first, the formalism was developed). 12 pages REVTeX. 5 figures (eps). Submitted to Phys.Rev.

Onsager-Machlup theory for nonequilibrium steady states and fluctuation theorems

A generalization of the Onsager-Machlup theory from equilibrium to nonequilibrium steady states and its connection with recent fluctuation theorems are discussed for a dragged particle restricted by a harmonic potential in a heat reservoir. Using a functional integral approach, the probability functional for a path is expressed in terms of a Lagrangian function from which an entropy production rate and dissipation functions are introduced, and nonequilibrium thermodynamic relations like the energy conservation law and the second law of thermodynamics are derived. Using this Lagrangian function we establish two nonequilibrium detailed balance relations, which not only lead to a fluctuation theorem for work but also to one related to energy loss by friction. In addition, we carried out the functional integrals for heat explicitly, leading to the extended fluctuation theorem for heat. We also present a simple argument for this extended fluctuation theorem in the long time limit.Comment: 20 pages, 2 figure

Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases II: Open Systems

We calculate the spectrum of Lyapunov exponents for a point particle moving in a random array of fixed hard disk or hard sphere scatterers, i.e. the disordered Lorentz gas, in a generic nonequilibrium situation. In a large system which is finite in at least some directions, and with absorbing boundary conditions, the moving particle escapes the system with probability one. However, there is a set of zero Lebesgue measure of initial phase points for the moving particle, such that escape never occurs. Typically, this set of points forms a fractal repeller, and the Lyapunov spectrum is calculated here for trajectories on this repeller. For this calculation, we need the solution of the recently introduced extended Boltzmann equation for the nonequilibrium distribution of the radius of curvature matrix and the solution of the standard Boltzmann equation. The escape-rate formalism then gives an explicit result for the Kolmogorov Sinai entropy on the repeller.Comment: submitted to Phys Rev

Theorem on the Distribution of Short-Time Particle Displacements with Physical Applications

The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could have an arbitrary distribution. This class of systems contains canonical equilibrium of a Hamiltonian system as a special case. We prove that for this class of systems the nth order cumulants of the initial short-time displacements behave as the 2n-th power of time for all n>2, rather than exhibiting an nth power scaling. This has direct applications to the initial short-time behavior of the Van Hove self-correlation function, to its non-equilibrium generalizations the Green's functions for mass transport, and to the non-Gaussian parameters used in supercooled liquids and glasses.Comment: A less ambiguous mathematical notation for cumulants was adopted and several passages were reformulated and clarified. 40 pages, 1 figure. Accepted by J. Stat. Phy