The quasi-equilibrium or maximum entropy approximation is applied in order to derive constitutive equations from kinetic models of polymer dynamics. It is shown in general and illustrated for an example how canonical distribution functions are obtained from the maximum entropy principle, how...

Dynamic recrystallisation (DRX) is an important aspect for industrial applications in hot metal working. Although DRX has been known for more than thirty years, its mechanisms have never been precisely investigated, in part because it was not readily possible to make local texture measurements....

In this paper a constitutive equation is derived for the surface stress tensor of a simple fluid–fluid interface. The equation is an extension of the linear Boussinesq surface fluid model, and is correct up to second order in the rate of deformation tensor. It is valid for simple fluid–fluid...

In this paper we derive constitutive equations for surface diffusion in a non-isothermal fluid–fluid interface, consisting of a mixture of linear viscoelastic components with fading memory. The constitutive equation contains three main contributions to the total diffusive flux: thermal...

The method of invariant manifold is developed for a derivation of reduced description in kinetic equations of dilute polymeric solutions. It is demonstrated that this reduced description becomes universal in the limit of small Deborah and Weissenberg numbers, and it is represented by the...

Models of complex reactions in thermodynamically isolated systems often demonstrate evolution towards low-dimensional manifolds in the phase space. For this class of models, we suggest a direct method to construct such manifolds, and thereby to reduce the effective dimension of the problem. The...

There are roughly speaking the two extreme types of dynamical density functional theories: one is deterministic without noise and another is fully stochastic with noise. We attempt to interpolate these extreme limiting theories for general reduced description of time evolution by making use of a...

The time-dependence of the occupation probabilities of neighboring wells due to diffusion in one dimension is formulated in terms of a set of generalized rate equations describing transitions between neighboring wells and escape across a final barrier. The equations contain rate coefficients,...

This paper represents the first attempt to bridge the evolutionary theory in economics and the theory of active particles in mathematics. It seeks to present a kinetic model for an evolutionary formalization of socio-economic systems. The derived new mathematical formulation intends to formalize...

Lockdown and vaccination policies have been the major concern in the last year in order to contain the SARS-CoV-2 infection during the COVID-19 pandemic. In this paper we present a model able to evaluate alternative lockdown policies and vaccination strategies. Our approach integrates and...