Related papers: On the general structure of mathematical models fo…
In the realm of Continuum Physics, material bodies are realized as continous media and so-called extensive quantities, such as mass, momentum and energy, are monitored through the fields of their densities, which are related by balance laws…
Historically it happen so that in branches of physics connected with field theory and of physics of material systems (continuous media) the concept of "conservation laws" has a different meaning. In field theory "conservation laws" are…
In this paper we form a general conservation law that unifies a class of physics field theories. For this we first introduce the notion of a general field as a formal sum differential forms on a Minkowski manifold. Thereafter, we employ the…
A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…
Physics relies on mathematical spaces carefully matched to the phenomena under study. Phase space in classical mechanics, Hilbert space in quantum theory, configuration spaces in field theory all provide representations in which physical…
Within the framework of continuum mechanics, the full description Of joint motion of elastic bodies and compressible viscous fluids with taking into account thermal effects is given by the system consisting of the mass, momentum, and energy…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
The discovery of physical laws consistent with empirical observations lies at the heart of (applied) science and engineering. These laws typically take the form of nonlinear differential equations depending on parameters, dynamical systems…
Stable numerical simulations for a hyperbolic system of conservation laws of relaxation type but not in divergence form are obtained by incorporating the physical entropy into the simulations. The entropy balance is utilized as an…
In spite of the large amount of existing neural models in the literature, there is a lack of a systematic review of the possible effect of choosing different initial conditions on the dynamic evolution of neural systems. In this short…
The {\em hydrodynamic} approach to a continuum mechanical description of granular behavior is reviewed and elucidated. By considering energy and momentum conservation simultaneously, the general formalism of {\em hydrodynamics} provides a…
General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and…
We consider a hyperbolic system of three conservation laws in one space variable. The system is a model for fluid flow allowing phase transitions; in this case the state variables are the specific volume, the velocity and the mass density…
We use dynamical systems theory to construct the normal form of the Navier--Stokes equations for the flow of a thin layer of fluid upon a solid substrate. The normal form equations illuminate the fluid dynamics by decoupling the long-term…
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
Since physical theories employ mathematical models to describe and predict physical phenomena, our knowledge depends on the models available to that end. To increase their scope we present a particular type of simplified models, serial…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
We formulate physically-motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to Quantum Mechanics as the only nontrivial consistent theory. Complex numbers and the existence of…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…