Relative Entropy of a Freely Cooling Granular Gas

The time evolution and stationary values of the entropy per particle of a homogeneous freely cooling granular gas, relative to the maximum entropy consistent with the instantaneous translational and rotational temperatures, is analyzed by means of a Sonine approximation involving fourth-degree cumulants. The results show a rich variety of dependencies of the relative entropy on time and on the coefficients of normal and tangential restitution, including a peculiar behavior in the quasi-smooth limit.Comment: 6 pages; 2 figures; contributed paper at the 28th International Symposium on Rarefied Gas Dynamics (Zaragoza, Spain, July 9-13, 2012

Triangle-Well and Ramp Interactions in One-Dimensional Fluids: A Fully Analytic Exact Solution

The exact statistical-mechanical solution for the equilibrium properties, both thermodynamic and structural, of one-dimensional fluids of particles interacting via the triangle-well and the ramp potentials is worked out. In contrast to previous studies, where the radial distribution function $g(r)$ was obtained numerically from the structure factor by Fourier inversion, we provide a fully analytic representation of $g(r)$ up to any desired distance. The solution is employed to perform an extensive study of the equation of state, the excess internal energy per particle, the residual multiparticle entropy, the structure factor, the radial distribution function, and the direct correlation function. In addition, scatter plots of the bridge function versus the indirect correlation function are used to gauge the reliability of the hypernetted-chain, Percus--Yevick, and Martynov--Sarkisov closures. Finally, the Fisher--Widom and Widom lines are obtained in the case of the triangle-well model.Comment: 19 pages, 9 figure

A nonparametric analysis of the Cournot model

An observer makes a number of observations of an industry producing a homogeneous good. Each observation consists of the market price, the output of individual firms and perhaps information on each firm's production cost. We provide various tests (typically, linear programs) with which the observer can determine if the data set is consistent with the hypothesis that firms in this industry are playing a Cournot game at each observation. When cost information is wholly or partially unavailable, these tests could potentially be used to derive cost information on the firms. This paper is a contribution to the literature that aims to characterize (in various contexts) the restrictions that a data set must satisfy for it to be consistent with Nash outcomes in a game. It is also inspired by the seminal result of Afriat (and the subsequent literature) which addresses similar issues in the context of consumer demand, though one important technical difference from most of these results is that the objective functions of firms in a Cournot game are not necessarily quasiconcave

How Do Induced Affective States Bias Emotional Contagion to Faces? A Three-Dimensional Model

Affective states can propagate in a group of people and influence their ability to judge others’ affective states. In the present paper, we present a simple mathematical model to describe this process in a three-dimensional affective space. We obtained data from 67 participants randomly assigned to two experimental groups. Participants watched either an upsetting or uplifting video previously calibrated for this goal. Immediately, participants reported their baseline subjective affect in three dimensions: (1) positivity, (2) negativity, and (3) arousal. In a second phase, participants rated the affect they subjectively judged from 10 target angry faces and ten target happy faces in the same three-dimensional scales. These judgments were used as an index of participant’s affective state after observing the faces. Participants’ affective responses were subsequently mapped onto a simple three-dimensional model of emotional contagion, in which the shortest distance between the baseline self-reported affect and the target judgment was calculated. The results display a double dissociation: negatively induced participants show more emotional contagion to angry than happy faces, while positively induced participants show more emotional contagion to happy than angry faces. In sum, emotional contagion exerted by the videos selectively affected judgments of the affective state of others’ faces. We discuss the directionality of emotional contagion to faces, considering whether negative emotions are more easily propagated than positive ones. Additionally, we comment on the lack of significant correlations between our model and standardized tests of empathy and emotional contagion.DFG, 414044773, Open Access Publizieren 2019 - 2020 / Technische Universität Berli

A methodology for population projections: an application to Spain

This paper looks at projections for the Spanish population by sex and age for the period of 2005 to 2050. These were carried out using forecasts for birth and mortality rates, and migration. These rates are calculated using two main sources of information. First, a multivariate time series model was applied for the series of variables from the 1970 to 2001 period. Second a model was estimated for life expectancy and for a synthetic fertility index. Both sources of information were combined to obtain the forecasts for the rates. Immigration rates are predicted by assuming three possible scenarios based on the maximum proportion that immigrants will represent in the Spanish population. With these variables a structure of ages and sex for the Spanish population is estimated using a cohort component model

FORECAST OF THE EXPECTED NON-EPIDEMIC MORBIDITY OF ACUTE DISEASES USING RESAMPLING METHODS

In epidemiological surveillance it is important that any unusual increase of reported cases be detected as rapidly as possible. Reliable forecasting based on a suitable time series model for an epidemiological indicator is necessary for estimating the expected non-epidemic indicator and to elaborate an alert threshold. Time series analysis of acute diseases often use Gaussian autoregressive integrated moving average models. However, these approaches could be adversely affected by departures from the true underlying distribution. The objective of this paper is to introduce a bootstrap procedure for obtaining prediction intervals in linear models in order to avoid the normality assumption. We present a Monte Carlo study comparing the finite sample properties of the bootstrap prediction intervals with those of alternative methods. Finally, we illustrate the performance of the proposed method with a meningococcal disease incidence series.

Sonine approximation for collisional moments of granular gases of inelastic rough spheres

We consider a dilute granular gas of hard spheres colliding inelastically with coefficients of normal and tangential restitution $\alpha$ and $\beta$, respectively. The basic quantities characterizing the distribution function $f(\mathbf{v},\bm{\omega})$ of linear ($\mathbf{v}$) and angular ($\bm{\omega}$) velocities are the second-degree moments defining the translational ($T^\text{tr}$) and rotational ($T^\text{rot}$) temperatures. The deviation of $f$ from the Maxwellian distribution parameterized by $T^\text{tr}$ and $T^\text{rot}$ can be measured by the cumulants associated with the fourth-degree velocity moments. The main objective of this paper is the evaluation of the collisional rates of change of these second- and fourth-degree moments by means of a Sonine approximation. The results are subsequently applied to the computation of the temperature ratio $T^\text{rot}/T^\text{tr}$ and the cumulants of two paradigmatic states: the homogeneous cooling state and the homogeneous steady state driven by a white-noise stochastic thermostat. It is found in both cases that the Maxwellian approximation for the temperature ratio does not deviate much from the Sonine prediction. On the other hand, non-Maxwellian properties measured by the cumulants cannot be ignored, especially in the homogeneous cooling state for medium and small roughness. In that state, moreover, the cumulant directly related to the translational velocity differs in the quasi-smooth limit $\beta\to -1$ from that of pure smooth spheres ($\beta=-1$). This singular behavior is directly related to the unsteady character of the homogeneous cooling state and thus it is absent in the stochastic thermostat case.Comment: 14 pages, 8 figures; v2: some parts rewritten, new references added; published in a special topic decicated to Carlo Cercignan