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The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probability measures with finite second moment. A variational…
Combining analytical and numerical methods, we study within the framework of the homogeneous non-linear Boltzmann equation, a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the new…
A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…
Everett's concept of relative state is used to introduce a geometric phase that depends nontrivially on entanglement in a pure quantum state. We show that this phase can be measured in multiparticle interferometry. A correlation-dependent…
We show that (in contrast to a rather common opinion) QM is not a complete theory. This is a statistical approximation of classical statistical mechanics on the {\it infinite dimensional phase space.} Such an approximation is based on the…
We extend the Van der Waals equation of state to a universal form and find that the van der Waals equation of state is a special condition of this form. Then a good form of the equation of state for a balanced liquid-gas coexistence…
We introduce three stochastic cooperative models for particle deposition and evaporation relevant to ionic self-assembly of nanoparticles with applications in surface fabrication and nanomedicine. We present a method for mapping a…
We introduce isotonic conditional laws (ICL) which extend the classical notion of conditional laws by the additional requirement that there exists an isotonic relationship between the random variable of interest and the conditioning random…
Point processes are an essential tool when we are interested in where in time or space events occur. The basic starting point for point processes is usually the Poisson process. Over the years, Stein's method has been developed with a great…
Since the particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle…
A thermodynamics for systems at a stationary states is formulated. It is based upon the assumption of the existence of local equilibrium in phase space which enables one to interpret the probability density ans its conjugated nonequilibrium…
We are interested in a kinetic equation intended to describe the interaction of particles with their environment. The environment is modeled by a collection of local vibrational degrees of freedom. We establish the existence of weak…
A mathematical model has been developed to simulate the kinetic and thermal behaviour of a porous solid pellet undergoing chemical reaction with a gas. The model describes the chemical reaction itself, the transfer of the gaseous species…
The hierarchy of moment equations derived from the nonlinear Boltzmann equation is solved for a gas of Maxwell molecules undergoing a stationary Poiseuille flow induced by an external force in a pipe. The solution is obtained as a…
We consider thermodynamics of the van der Waals fluid of quantum systems. We derive general relations of thermodynamic functions and parameters of any ideal gas and the corresponding van der Waals fluid. This provides unambiguous…
Concepts of everyday use like energy, heat, and temperature have acquired a precise meaning after the development of thermodynamics. Thermodynamics provides the basis for understanding how heat and work are related and with the general…
It is widely believed that theory is useful in physics because it describes simple systems and that strictly empirical phenomenological approaches are necessary for complex biological and social systems. Here we prove based upon an analysis…
Various strong coupling theories of the one-component plasma have successfully predicted the thermodynamic and structural properties by separating the Coulomb potential into short- and long-ranged parts in {\itshape ad hoc} ways. Moreover,…
The internally electrodynamic (IED) particle model was derived based on overall experimental observations, with the IED process itself being built directly on three experimental facts, a) electric charges present with all material…
Following a recently introduced approach to approximate Lie symmetries of differential equations which is consistent with the principles of perturbative analysis of differential equations containing small terms, we analyze the case of…