Related papers: Beyond Kinetic Relations
We consider a new approach to the description of the collective behavior of complex systems of mathematical biology based on the evolution equations for observables of such systems. This representation of the kinetic evolution seems, in…
We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…
We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various type of reflections, extending our previous work [LLS14] on half-space equations with incoming boundary…
My goal is to study the dynamics of the Universe from a relational perspective based on the happening of events in temporal relation to each other and their respective points of reference. Accordingly, the flow of time was modeled as the…
Analysis of collisions is standardly included in the introductory physics course. In one dimension (1D), there do not seem to be any unusual issues: Typically, the initial velocities of the two colliding objects are specified, and the…
The thermodynamic uncertainty relation expresses a universal trade-off between precision and entropy production, which applies in its original formulation to current observables in steady-state systems. We generalize this relation to…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
In nonequilibrium chemical reaction systems, a fundamental relationship between unbalanced kinetic one-way fluxes and thermodynamic chemical driving forces is believed to exists. However this relation has been rigorously demonstrated only…
The way a relativistic system approaches fluid dynamical behaviour can be understood physically through the signals that will contribute to its linear response to perturbations. What these signals are is captured in the analytic structure…
We present kinetic equations that describe the evolution of O(N)-symmetric real scalar quantum fields out of thermal equilibrium in a systematic nonperturbative approximation scheme. This description starts from the 1/N-expansion of the 2PI…
This contribution presents a concept to dynamic fracture with continuum-kinematics-based peridynamics. Continuum-kinematics-based peridynamics is a geometrically exact formulation of peridynamics, which adds surface- or volumetric-based…
The local analysis is an established approach to the study of singularities and mobility of linkages. Key result of such analyses is a local picture of the finite motion through a configuration. This reveals the finite mobility at that…
We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…
Present-day thermodynamics has long outgrown the initial frames of the heat-engine theory and transmuted into a rather general macroscopic method for studying kinetics of various transfer processes in their inseparable connection with the…
A new type of kinetic models with non-instantaneous binary collisions is considered. Collisions are described by a transport process in the joint state space of a pair of particles. The interactions are of alignment type, where the states…
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…
We propose a formal extension of thermodynamics and kinetic theories to a larger class of entropy functionals. Kinetic equations associated to Boltzmann, Fermi, Bose and Tsallis entropies are recovered as a special case. This formalism…
The kinetic theory of gases, including Granular Gases, is based on the Boltzmann equation. Many properties of the gas, from the characteristics of the velocity distribution function to the transport coefficients may be expressed in terms of…
Kinematic algebras can be realised on geometric spaces and constrain the physical models that can live on these spaces. Different types of kinematic algebras exist and we consider the interplay of these algebras for non-relativistic limits…
Kinetically-constrained models are lattice-gas models that are used for describing glassy systems. By construction, their equilibrium state is trivial and there are no equal-time correlations between the occupancy of different sites. We…