Related papers: Beyond Kinetic Relations
To develop and investigate detailed mathematical models of cellular metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, explicit…
The article provides an overview of some advances in the mathematical understanding of the nature of the kinetic equations of quantum systems of many particles. The fundamental equations of modern mathematical physics are studied, in…
The main purpose of this article is to guide the reader to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important…
Relativity and classical dynamics, as defined so far, form distinct parts of classical physics and are formulated based on independent principles. We propose that the formalism of classical dynamics can be considered as the theoretical…
We introduce one dimensional sets to help describe and constrain the integral curves of an $n$ dimensional dynamical system. These curves provide more information about the system than the zero-dimensional sets (fixed points) do. In fact,…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
In collider experiments, an event is characterized by two distinct yet mutually complementary features: the `global features' and the `local features'. Kinematic information such as the event topology of a hard process, masses, and spins of…
Nonlocal models provide accurate representations of physical phenomena ranging from fracture mechanics to complex subsurface flows, where traditional partial differential equations fail to capture effects caused by long-range forces at the…
Starting from a microscopic approach, we develop a covariant formalism to describe a set of interacting gases. For that purpose, we model the collision term entering the Boltzmann equation for a class of interactions and then integrate this…
The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important…
We develop a diagrammatic approach with local and nonlocal self-energy diagrams, constructed from the local irreducible vertex. This approach includes the local correlations of dynamical mean field theory and long-range correlations beyond.…
Relative fluctuations of observables in discrete stochastic systems are bounded at all times by the mean dynamical activity in the system, quantified by the mean number of jumps. This constitutes a kinetic uncertainty relation that is…
We consider a model of a scalar field, with dispersion relation {\omega}(k), coupled to a random medium of two level atoms. We investigate the dynamics of states with at most one quanta of excitation in the system. In a high frequency…
This paper presents a new approach to the modeling of vehicular traffic flows on road networks based on kinetic equations. While in the literature the problem has been extensively studied by means of macroscopic hydrodynamic models, to date…
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…
In this paper we generalize the kinetic mixing idea to time reparametrization invariant theories, namely, relativistic point particles and cosmology in order to obtain new insights for dark matter and energy. In the first example, two…
The general framework of Entropic Dynamics (ED) is used to construct non-relativistic models of relational quantum mechanics from well known inference principles -- probability, entropy and information geometry. Although only partially…
A human is a thing that moves in space. Like all things that move in space, we can in principle use differential equations to describe their motion as a set of functions that maps time to position (and velocity, acceleration, and so on).…
It is shown that the kinetics of time-reversible chemical reactions having the same equilibrium constant but different initial conditions are closely related to one another by a directly measurable symmetry relation analogous to chemical…
Classical theories of chemical kinetics assume independent reactions in dilute solutions, whose rates are determined by mean concentrations. In condensed matter, strong interactions alter chemical activities and create inhomogeneities that…