On the Second Law of thermodynamics and the piston problem

The piston problem is investigated in the case where the length of the cylinder is infinite (on both sides) and the ratio $m/M$ is a very small parameter, where $m$ is the mass of one particle of the gaz and $M$ is the mass of the piston. Introducing initial conditions such that the stochastic motion of the piston remains in the average at the origin (no drift), it is shown that the time evolution of the fluids, analytically derived from Liouville equation, agrees with the Second Law of thermodynamics. We thus have a non equilibrium microscopical model whose evolution can be explicitly shown to obey the two laws of thermodynamics.Comment: 29 pages, 9 figures submitted to Journal of Statistical Physics (2003

Design of a low-noise aeroacoustic wind tunnel facility at Brunel University

This paper represents the design principle of a quiet, low turbulence and moderately high speed aeroacoustic wind tunnel which was recently commissioned at Brunel University. A new hemi-anechoic chamber was purposely built to facilitate aeroacoustic measurements. The wind tunnel can achieve a maximum speed of about 80 ms-1. The turbulence intensity of the free jet in the potential core is between 0.1–0.2%. The noise characteristic of the aeroacoustic wind tunnel was validated by three case studies. All of which can demonstrate a very low background noise produced by the bare jet in comparison to the noise radiated from the cylinder rod/flat plate/airfoil in the air stream.The constructions of the aeroacoustic wind tunnel and the hemi-anechoic chamber are financially supported by the School of Engineering and Design at Brunel University

Influence of anisotropic next-nearest-neighbor hopping on diagonal charge-striped phases

We consider the model of strongly-correlated system of electrons described by an extended Falicov-Kimball Hamiltonian where the stability of some axial and diagonal striped phases was proved. Introducing a next-nearest-neighbor hopping, small enough not to destroy the striped structure, we examine rigorously how the presence of the next-nearest-neighbor hopping anisotropy reduces the $\pi/2$-rotation degeneracy of the diagonal-striped phase. The effect appears to be similar to that in the case of anisotropy of the nearest-neighbor hopping: the stripes are oriented in the direction of the weaker next-nearest-neighbor hopping.Comment: 9 pages, 3 figures, 1 tabl

Finite-Dimensional Calculus

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement in finite terms Rota's "finite operator calculus".Comment: 26 pages. Added material on Krawtchouk polynomials. Additional references include

Lower bound for the segregation energy in the Falicov-Kimball model

In this work, a lower bound for the ground state energy of the Falicov-Kimball model for intermediate densities is derived. The explicit derivation is important in the proof of the conjecture of segregation of the two kinds of fermions in the Falicov-Kimball model, for sufficiently large interactions. This bound is given by a bulk term, plus a term proportional to the boundary of the region devoid of classical particles. A detailed proof is presented for density n=1/2, where the coefficient 10^(-13) is obtained for the boundary term, in two dimensions. With suitable modifications the method can also be used to obtain a coefficient for all densities.Comment: 8 pages, 2 figure

Observing biogeochemical cycles at global scales with profiling floats and gliders: prospects for a global array

Chemical and biological sensor technologies have advanced rapidly in the past five years. Sensors that require low power and operate for multiple years are now available for oxygen, nitrate, and a variety of bio-optical properties that serve as proxies for important components of the carbon cycle (e.g., particulate organic carbon). These sensors have all been deployed successfully for long periods, in some cases more than three years, on platforms such as profiling floats or gliders. Technologies for pH, pCO2, and particulate inorganic carbon are maturing rapidly as well. These sensors could serve as the enabling technology for a global biogeochemical observing system that might operate on a scale comparable to the current Argo array. Here, we review the scientific motivation and the prospects for a global observing system for ocean biogeochemistry

Segregation and charge-density-wave order in the spinless Falicov-Kimball model

The spinless Falicov-Kimball model is solved exactly in the limit of infinite-dimensions on both the hypercubic and Bethe lattices. The competition between segregation, which is present for large U, and charge-density-wave order, which is prevalent at moderate U, is examined in detail. We find a rich phase diagram which displays both of these phases. The model also shows nonanalytic behavior in the charge-density-wave transition temperature when U is large enough to generate a correlation-induced gap in the single-particle density of states.Comment: 10 pages, 10 figure