描述传染病动力学的随机格子气模型

Epidemic growth and Griffiths effects on an emergent network of excited atoms

Whether it be physical, biological or social processes, complex systems exhibit dynamics that are exceedingly difficult to understand or predict from underlying principles. Here we report a striking correspondence between the collective excitation dynamics of a laser driven ultracold gas of Rydberg atoms and the spreading of diseases, which in turn opens up a highly controllable experimental platform for studying non-equilibrium dynamics on complex networks. We find that the competition between facilitated excitation and spontaneous decay results in a fast growth of the number of excitations t…

相互作用疾病的动力学

Dynamics of interacting diseases

目前的传染病建模允许研究复杂和现实的情况，从人口到个人的描述水平。然而，大多数流行病模型都假设传播过程发生在单一层面上（无论是单一种群、元种群系统还是接触网络）。特别是，只有我们超越一个病原体一个网络的办法，才能解决相互依存的传染现象。在本文中，我们提出了一个框架，允许描述两个并发疾病的传播动力学。具体来说，我们分析了两种疾病的流行阈值为不同的情况下，还计算了时间演变特征的展开动态。结果表明，有一些区域的参数空间中，一种疾病的爆发是有条件的其他疾病的流行水平。此外，我们表明，SIS计划，在某些情况下，有限的和不消失的流行病阈值发现，即使在热力学极限的无标度网络。对于SIR情景，现象学更丰富，并且出现了额外的相互依赖性。我们还发现，SIS和SIR模型的次级阈值是不同的，这直接导致两种疾病之间的相互作用。因此，我们的工作解决了一个重要的问题，并为更全面地描述相互作用的疾病的动力学铺平了道路。

描述理想气体中大质量活塞标度极限的流体动力学方程解的稳定性

Stability of Solutions of Hydrodynamic Equations Describing the Scaling Limit of a Massive Piston in an Ideal gas

研究了一类奇异Vlasov型流体动力方程定常解的稳定性。这个方程是（在适当的假设下）作为一个系统的哈密顿演化的流体动力学标度极限推导出来的，该系统由一个浸没在盒子中的点粒子的理想气体中的大质量活塞组成。我们找到了全局稳定性的显式准则以及一类对于密集参数值线性不稳定的解。我们提出的证据（但没有证据），当机械系统的初始条件“接近”静止稳定的解决方案的HE然后它保持接近这些解决方案的时间是长的相比，方程已经推导出来。另一方面，如果粒子系统的初始状态接近于HE的不稳定的固定解，则机械运动在很长一段时间内遵循该方程的扰动解：我们发现这种近似的线性稳定的周期解。

复杂网络的谱分析与慢传播动力学

Spectral analysis and slow spreading dynamics on complex networks

易感-感染-易感（SIS）模型是描述信息/传染病传播现象的最简单的无记忆系统之一。淬火无序对动力学行为的影响最近被比较淬火平均场（QMF）近似的无标度网络。QMF通过邻接矩阵的谱分解分析，可以考虑稳态下活性的拓扑异质性和聚类效应。因此，它可以提供对可能的稀有区域效应的预测，从而对慢动力学的发生。我比较QMF SIS的结果与各种大尺寸图上的模拟。特别是，我表明，Erd \H os-Rényi图这种方法正确预测的流行阈值和稀有区域的影响。如果图是碎片的，或者如果我们在边缘上应用强的、指数抑制的加权方案，格里菲斯阶段就会出现。后一个模型描述了面对面实验中的连接时间分布。在广义Barabási-Albert型网络与老化连接的情况下，强烈的稀有区域效应和格里菲斯相动力学的数值证据。

Influence of individual nodes for continuous-time Susceptible-Infected-Susceptible dynamics on synthetic and real-world networks

In the study of epidemic dynamics a fundamental question is whether a pathogen initially affecting only one individual will give rise to a limited outbreak or to a widespread pandemic. The answer to this question crucially depends not only on the parameters describing the infection and recovery processes but also on where, in the network of interactions, the infection starts from. We study the dependence on the location of the initial seed for the Susceptible-Infected-Susceptible epidemic dynamics in continuous time on networks. We first derive analytical predictions for the dependence on the …

布朗气体的引力坍缩

Gravitational collapse of a Brownian gas

我们研究了一个描述自引力布朗粒子气体动力学的模型。该模型也可以应用于细菌群体的趋化性。在这里，我们专注于在足够低的温度/能量下获得的崩溃阶段和崩溃后制度的奇异时间中心密度发散。几个分析结果说明了数值模拟。

Exact Hydrodynamic Description of Active Lattice Gases

We introduce a class of lattice gas models of active matter systems whose hydrodynamic description can be derived exactly. We illustrate our approach by considering two systems exhibiting two of the most studied collective behaviours in active matter: the motility-induced phase separation and the transition to collective motion. In both cases, we derive coupled partial differential equation describing the dynamics of the local density and polarization fields and show how they quantitatively predict the emerging properties of the macroscopic lattice gases.

Phase transition in a phonon gas with pair correlation

The phase transition to the state of a phonon gas with pairwise correlations of interacting phonons with opposite momenta is studies. A method for describing such phonon systems within the framework of the self-consistent field model is developed and their thermodynamic characteristics are calculated. It is shown that a phonon gas with pair correlations can exist in a state of unstable thermodynamic equilibrium. The possibility of experimental observation of a solid in such a phase is discussed.