The evaporation of a liquid slab into vacuum is studied by numerical solutions of the Enskog–Vlasov equation for a fluid of spherical molecules interacting by Sutherland potential. The equation provides a simplified description of the microscopic behavior of the fluid but it has the capability of handling both the liquid and vapor phase, thus eliminating the necessity of postulating ad hoc models for boundary conditions at the vapor-liquid interface. This work focuses on obtaining the structure of the vapor-liquid interface in nonequilibrium conditions as well as the distribution function of evaporating molecules. The results show that the molecules crossing a properly defined vapor-liquid boundary have an almost Maxwellian distribution function and that the vapor phase is reasonably well described by the Boltzmann equation with diffusive boundary condition.

This paper proposes a systems approach to social sciences based on mathematical framework derived from a generalization of the mathematical kinetic theory and on theoretical tools of game theory. Social systems are modeled as a living evolutionary ensemble composed by many individuals, who express specific strategies, cooperate, compete and might aggregate into groups which pursue a common interest. A critical analysis on the complexity features of social system is developed and a differential structure is derived to provide a general framework toward modeling.

This paper presents a new approach to behavioral-social dynamics of pedestrian crowds by suitable development of methods of the kinetic theory. It is shown how heterogeneous individual behaviors can modify the collective dynamics, as well as how local unusual behaviors can propagate in the crowd. The main feature of this approach is a detailed analysis of the interactions between dynamics and social behaviors.

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This paper provides an overview and critical analysis on the modeling and applications of the dynamics of human crowds, where social interactions can have an important influence on the behavioral dynamics of the crowd viewed as a living, hence complex, system. The analysis looks at real physical situations where safety problems might arise in some specific circumstances. The approach is based on the methods of the kinetic theory of active particles. Computational applications enlighten the role of human behaviors.2010 Mathematics Subject Classification Primary: 82D99, 91A15; Secondary: 91D10.

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