Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular dynamics simulations

Following the work of Leutheusser [Physica A 127, 667 (1984)], the solution to the Percus-Yevick equation for a seven-dimensional hard-sphere fluid is explicitly found. This allows the derivation of the equation of state for the fluid taking both the virial and the compressibility routes. An analysis of the virial coefficients and the determination of the radius of convergence of the virial series are carried out. Molecular dynamics simulations of the same system are also performed and a comparison between the simulation results for the compressibility factor and theoretical expressions for the same quantity is presented.Comment: 12 pages, 4 figures; v3: Equation (A.19) corrected (see http://dx.doi.org/10.1063/1.2390712

Simple equation of state for hard disks on the hyperbolic plane

A simple equation of state for hard disks on the hyperbolic plane is proposed. It yields the exact second virial coefficient and contains a pole at the highest possible packing. A comparison with another very recent theoretical proposal and simulation data is presented.Comment: 3 pages, 1 figur

Black hole collapse simulated by vacuum fluctuations with a moving semi-transparent mirror

Creation of scalar massless particles in two-dimensional Minkowski space-time--as predicted by the dynamical Casimir effect--is studied for the case of a semitransparent mirror initially at rest, then accelerating for some finite time, along a trajectory that simulates a black hole collapse (defined by Walker, and Carlitz and Willey), and finally moving with constant velocity. When the reflection and transmission coefficients are those in the model proposed by Barton, Calogeracos, and Nicolaevici [r(w)=-i\alpha/(\w+i\alpha) and s(w)=\w/(\w+i\alpha), with $\alpha\geq 0$], the Bogoliubov coefficients on the back side of the mirror can be computed exactly. This allows us to prove that, when $\alpha$ is very large (case of an ideal, perfectly reflecting mirror) a thermal emission of scalar massless particles obeying Bose-Einstein statistics is radiated from the mirror (a black body radiation), in accordance with results previously obtained in the literature. However, when $\alpha$ is finite (semitransparent mirror, a physically realistic situation) the striking result is obtained that the thermal emission of scalar massless particles obeys Fermi-Dirac statistics. We also show here that the reverse change of statistics takes place in a bidimensional fermionic model for massless particles, namely that the Fermi-Dirac statistics for the completely reflecting situation will turn into the Bose-Einstein statistics for a partially reflecting, physical mirror.Comment: 13 pages, no figures, version to appear in Physical Review

On the radial distribution function of a hard-sphere fluid

Two related approaches, one fairly recent [A. Trokhymchuk et al., J. Chem. Phys. 123, 024501 (2005)] and the other one introduced fifteen years ago [S. B. Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991)], for the derivation of analytical forms of the radial distribution function of a fluid of hard spheres are compared. While they share similar starting philosophy, the first one involves the determination of eleven parameters while the second is a simple extension of the solution of the Percus-Yevick equation. It is found that the {second} approach has a better global accuracy and the further asset of counting already with a successful generalization to mixtures of hard spheres and other related systems.Comment: 3 pages, 1 figure; v2: slightly shortened, figure changed, to be published in JC

Demixing can occur in binary hard-sphere mixtures with negative non-additivity

A binary fluid mixture of non-additive hard spheres characterized by a size ratio $\gamma=\sigma_2/\sigma_1<1$ and a non-additivity parameter $\Delta=2\sigma_{12}/(\sigma_1+\sigma_2)-1$ is considered in infinitely many dimensions. From the equation of state in the second virial approximation (which is exact in the limit $d\to\infty$) a demixing transition with a critical consolute point at a packing fraction scaling as $\eta\sim d 2^{-d}$ is found, even for slightly negative non-additivity, if $\Delta>-{1/8}(\ln\gamma)^2$. Arguments concerning the stability of the demixing with respect to freezing are provided.Comment: 4 pages, 2 figures; title changed; final paragraph added; to be published in PRE as a Rapid Communicatio

Optimal Policy Derivation for Transmission Duty-Cycle Constrained LPWAN

Low-power wide-area network (LPWAN) technologies enable Internet of Things (IoT) devices to efficiently and robustly communicate over long distances, thus making them especially suited for industrial environments. However, the stringent regulations on the usage of certain industrial, scientific, and medical bands in many countries in which LPWAN operate limit the amount of time IoT motes can occupy the shared bands. This is particularly challenging in industrial scenarios, where not being able to report some detected events might result in the failure of critical assets. To alleviate this, and by mathematically modeling LPWAN-based IoT motes, we have derived optimal transmission policies that maximize the number of reported events (prioritized by their importance) while still complying with current regulations. The proposed solution has been customized for two widely known LPWAN technologies: 1) LoRa and 2) Sigfox. Analytical results reveal that our solution is feasible and performs remarkably close to the theoretical limit for a wide range of network activity patterns