ترغب بنشر مسار تعليمي؟ اضغط هنا

Effects of confinement and vaccination on an epidemic outburst: a statistical mechanics approach

122   0   0.0 ( 0 )
 نشر من قبل Javier Rodriguez-Laguna
 تاريخ النشر 2021
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

This work describes a simple agent model for the spread of an epidemic outburst, with special emphasis on mobility and geographical considerations, which we characterize via statistical mechanics and numerical simulations. As the mobility is decreased, a percolation phase transition is found separating a free-propagation phase in which the outburst spreads without finding spatial barriers and a localized phase in which the outburst dies off. Interestingly, the number of infected agents is subject to maximal fluctuations at the transition point, building upon the unpredictability of the evolution of an epidemic outburst. Our model also lends itself to test with vaccination schedules. Indeed, it has been suggested that if a vaccine is available but scarce it is convenient to select carefully the vaccination program to maximize the chances of halting the outburst. We discuss and evaluate several schemes, with special interest on how the percolation transition point can be shifted, allowing for higher mobility without epidemiological impact.



قيم البحث

اقرأ أيضاً

101 - Vassili Ivanov , Yan Zeng , 2004
We propose a statistical mechanics model for DNA melting in which base stacking and pairing are explicitly introduced as distinct degrees of freedom. Unlike previous approaches, this model describes thermal denaturation of DNA secondary structure in the whole experimentally accessible temperature range. Base pairing is described through a zipper model, base stacking through an Ising model. We present experimental data on the unstacking transition, obtained exploiting the observation that at moderately low pH this transition is moved down to experimentally accessible temperatures. These measurements confirm that the Ising model approach is indeed a good description of base stacking. On the other hand, comparison with the experiments points to the limitations of the simple zipper model description of base pairing.
We study the derivation of macroscopic traffic models from car-following vehicle dynamics by means of hydrodynamic limits of an Enskog-type kinetic description. We consider the superposition of Follow-the-Leader (FTL) interactions and relaxation towa rds a traffic-dependent Optimal Velocity (OV) and we show that the resulting macroscopic models depend on the relative frequency between these two microscopic processes. If FTL interactions dominate then one gets an inhomogeneous Aw-Rascle-Zhang model, whose (pseudo) pressure and stability of the uniform flow are precisely defined by some features of the microscopic FTL and OV dynamics. Conversely, if the rate of OV relaxation is comparable to that of FTL interactions then one gets a Lighthill-Whitham-Richards model ruled only by the OV function. We further confirm these findings by means of numerical simulations of the particle system and the macroscopic models. Unlike other formally analogous results, our approach builds the macroscopic models as physical limits of particle dynamics rather than assessing the convergence of microscopic to macroscopic solutions under suitable numerical discretisations.
We provide here an explicit example of Khinchins idea that the validity of equilibrium statistical mechanics in high dimensional systems does not depend on the details of the dynamics. This point of view is supported by extensive numerical simulation of the one-dimensional Toda chain, an integrable non-linear Hamiltonian system where all Lyapunov exponents are zero by definition. We study the relaxation to equilibrium starting from very atypical initial conditions and focusing on energy equipartion among Fourier modes, as done in the original Fermi-Pasta-Ulam-Tsingou numerical experiment. We find evidence that in the general case, i.e., not in the perturbative regime where Toda and Fourier modes are close to each other, there is a fast reaching of thermal equilibrium in terms of a single temperature. We also find that equilibrium fluctuations, in particular the behaviour of specific heat as function of temperature, are in agreement with analytic predictions drawn from the ordinary Gibbs ensemble, still having no conflict with the established validity of the Generalized Gibbs Ensemble for the Toda model. Our results suggest thus that even an integrable Hamiltonian system reaches thermalization on the constant energy hypersurface, provided that the considered observables do not strongly depend on one or few of the conserved quantities. This suggests that dynamical chaos is irrelevant for thermalization in the large-$N$ limit, where any macroscopic observable reads of as a collective variable with respect to the coordinate which diagonalize the Hamiltonian. The possibility for our results to be relevant for the problem of thermalization in generic quantum systems, i.e., non-integrable ones, is commented at the end.
We propose a new look at the heat bath for two Brownian particles, in which the heat bath as a `system is both perturbed and sensed by the Brownian particles. Non-local thermal fluctuation give rise to bath-mediated static forces between the particle s. Based on the general sum-rule of the linear response theory, we derive an explicit relation linking these forces to the friction kernel describing the particles dynamics. The relation is analytically confirmed in the case of two solvable models and could be experimentally challenged. Our results point out that the inclusion of the environment as a part of the whole system is important for micron- or nano-scale physics.
109 - Veit Elser 2016
These lectures were prepared for the 2014 PCMI graduate summer school and were designed to be a lightweight introduction to statistical mechanics for mathematicians. The applications feature some of the themes of the summer school: sphere packings and tilings.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا