The inelastic hard dimer gas: a non-spherical model for granular matter

We study a two-dimensional gas of inelastic smooth hard dimers. Since the collisions between dimers are dissipative, being characterized by a coefficient of restitution $\alpha<1$, and no external driving force is present, the energy of the system decreases in time and no stationary state is achieved. However, the resulting non equilibrium state of the system displays several interesting properties in close analogy with systems of inelastic hard spheres, whose relaxational dynamics has been thoroughly explored. We generalise to inelastic systems a recently method introduced [G.Ciccotti and G.Kalibaeva, J. Stat. Phys. {\bf 115}, 701 (2004)] to study the dynamics of rigid elastic bodies made up of different spheres hold together by rigid bonds. Each dimer consists of two hard disks of diameter $d$, whose centers are separated by a fixed distance $a$. By describing the rigid bonds by means of holonomic constraints and deriving the appropriate collision rules between dimers, we reduce the dynamics to a set of equations which can be solved by means of event driven simulation. After deriving the algorithm we study the decay of the total kinetic energy, and of the ratio between the rotational and the translational kinetic energy of inelastic dimers. We show numerically that the celebrated Haff's homogeneous cooling law $t^{-2}$, describing how the kinetic energy of an inelastic hard sphere system with constant coefficient of restitution decreases in time, holds even in the case of these non spherical particles. We fully characterize this homogeneous decay process in terms of appropriate decay constants and confirm numerically the scaling behavior of the velocity distributions.Comment: 21 pages, 6 figures and 2 tables, submitted to JC

Time-averaged MSD of Brownian motion

We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking experiments. For Brownian motion, we derive an exact formula for the Laplace transform of the probability density of the TAMSD by mapping the original problem onto chains of coupled harmonic oscillators. From this formula, we deduce the first four cumulant moments of the TAMSD, the asymptotic behavior of the probability density and its accurate approximation by a generalized Gamma distribution

The Ehrenfest urn revisited: Playing the game on a realistic fluid model

The Ehrenfest urn process, also known as the dogs and fleas model, is realistically simulated by molecular dynamics of the Lennard-Jones fluid. The key variable is Delta z, i.e. the absolute value of the difference between the number of particles in one half of the simulation box and in the other half. This is a pure-jump stochastic process induced, under coarse graining, by the deterministic time evolution of the atomic coordinates. We discuss the Markov hypothesis by analyzing the statistical properties of the jumps and of the waiting times between jumps. In the limit of a vanishing integration time-step, the distribution of waiting times becomes closer to an exponential and, therefore, the continuous-time jump stochastic process is Markovian. The random variable Delta z behaves as a Markov chain and, in the gas phase, the observed transition probabilities follow the predictions of the Ehrenfest theory.Comment: Accepted by Physical Review E on 4 May 200

Generalized Master Equations for Non-Poisson Dynamics on Networks

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Consequently, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that the equation reduces to the standard rate equations when the underlying process is Poisson and that the stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature

The effect of discrete vs. continuous-valued ratings on reputation and ranking systems

When users rate objects, a sophisticated algorithm that takes into account ability or reputation may produce a fairer or more accurate aggregation of ratings than the straightforward arithmetic average. Recently a number of authors have proposed different co-determination algorithms where estimates of user and object reputation are refined iteratively together, permitting accurate measures of both to be derived directly from the rating data. However, simulations demonstrating these methods' efficacy assumed a continuum of rating values, consistent with typical physical modelling practice, whereas in most actual rating systems only a limited range of discrete values (such as a 5-star system) is employed. We perform a comparative test of several co-determination algorithms with different scales of discrete ratings and show that this seemingly minor modification in fact has a significant impact on algorithms' performance. Paradoxically, where rating resolution is low, increased noise in users' ratings may even improve the overall performance of the system.Comment: 6 pages, 2 figure

Towards operational use of aircraft‐derived observations: a case study at London Heathrow airport

Mode-Selective Enhanced Surveillance (Mode-S EHS) aircraft reports can be collected at a low-cost, and are readily available around busy airports. The new work presented here demonstrates that observations derived from Mode-S EHS reports can be used to study the evolution of temperature inversions since the data have a high spatial and temporal frequency. This is illustrated by a case study centred around London Heathrow airport for the period 4 to 5 January 2015. Using Mode-S EHS reports from multiple aircraft and after applying quality control criteria, vertical temperature profiles are constructed by aggregating these reports at discrete intervals between the surface and 3000m. To improve these derived temperatures, four smoothing methods using low-pass filters are evaluated. The effect of smoothing reduces the variance in the aircraft derived temperature by approximately half. After smoothing, the temperature variance between the altitudes 3000m and 1000m is 1K to 2K; and below 1000m it is 2K to 4K. While the differences between the four smoothing methods are small, exponential smoothing is favoured because it uses all available Mode-S EHS reports. The resulting vertical profiles may be useful in operational meteorology for identifying elevated temperature inversions above 1000m. However, below 1000m they are less useful because of the reduced precision of the reported Mach number. A better source of in situ temperature observations would be for aircraft to use the meteorological reporting function of their automatic dependent surveillance (ADS) system

Asymmetry Dependence of the Nuclear Caloric Curve

A basic feature of the nuclear equation of state is not yet understood: the dependence of the nuclear caloric curve on the neutron-proton asymmetry. Predictions of theoretical models differ on the magnitude and even the sign of this dependence. In this work, the nuclear caloric curve is examined for fully reconstructed quasi-projectiles around mass A=50. The caloric curve extracted with the momentum quadrupole fluctuation thermometer shows that the temperature varies linearly with quasi-projectile asymmetry (N-Z)/A. An increase in asymmetry of 0.15 units corresponds to a decrease in temperature on the order of 1 MeV. These results also highlight the importance of a full quasi-projectile reconstruction in the study of thermodynamic properties of hot nuclei

Random Walks on Stochastic Temporal Networks

In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic model for temporal networks in which we summarize the temporal and structural organization of a system using a matrix of waiting-time distributions. We show that random walks on stochastic temporal networks can be described exactly by an integro-differential master equation and derive an analytical expression for its asymptotic steady state. We also discuss how our work might be useful to help build centrality measures for temporal networks.Comment: Chapter in Temporal Networks (Petter Holme and Jari Saramaki editors). Springer. Berlin, Heidelberg 2013. The book chapter contains minor corrections and modifications. This chapter is based on arXiv:1112.3324, which contains additional calculations and numerical simulation