Related papers: Kinetic equations: computation
The relativistic kinetic equations for the two domains separated by the hypersurface with both space- and time-like parts are derived. The particle exchange between the domains separated by the time-like boundaries generates source terms…
A variety of computational models have been developed to describe active matter at different length and time scales. The diversity of the methods and the challenges in modeling active matter---ranging from molecular motors and cytoskeletal…
We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…
We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex quantum system. A typical quantum complex system is…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
It is shown that mathematical physics differential equations have properties that allow describing processes such as the structures emergence, discrete transitions, quantum jumps. The peculiarity is that such properties are hidden. They do…
Classes of kinetic differential equations are delineated which do have a quadratic first integral, and classes which can not have one. Example reactions corresponding to the obtained kinetic differential equations are shown, and a few…
The general theory of a complex system of nonlinear chemical reactions is a primary language of chemistry that includes chemical engineering and cellular biochemistry. Its significance as an analytical framework, however, has not been fully…
Statistical properties of evolving random graphs are analyzed using kinetic theory. Treating the linking process dynamically, structural characteristics such as links, paths, cycles, and components are obtained analytically using the rate…
The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated round-off errors. For such…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
A dilute gas of hard disks confined between two straight parallel lines is considered. The distance between the two boundaries is in between one and two particle diameters, so that the system is quasi-one-dimensional. A Boltzmann-like…
The configuration space of a mechanical linkage, consisting of rigid bodies moving in space constrained by joints, is defined by algebraic conditions. If these equations do not define a complete intersection, then the dimension of the…
Extended Thermodynamics is a very important theory: for example, it predicts hyperbolicity, finite speeds of propagation waves as well as continuous dependence on initial data. Therefore, it constitutes a significative improvement of…
The distinction between a theory's kinematics and its dynamics, that is, between the space of physical states it posits and its law of evolution, is central to the conceptual framework of many physicists. A change to the kinematics of a…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
Different dynamics, described by kinetic equation and clipping method is shown as well as a role of approximate resonances in wave turbulence theory. Applications of clipping method are sketched for gravity-capillary and drift waves. Brief…
The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…
Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…
The relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this…