Related papers: Multi-particle dynamical systems and polynomials
A new approach for integration of motion in many-body systems of interacting polyatomic molecules is proposed. It is based on splitting time propagation of pseudo-variables in a modified phase space, while the real translational and…
In this paper we obtain the global dynamics and phase portraits of quadratic and cubic quasi-homogeneous but non-homogeneous systems. We first prove that all planar quadratic and cubic quasi-homogeneous but non-homogeneous polynomial…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.
We discuss numerical aspects related to a new class of nonlinear Stochastic Differential Equations in the sense of McKean, which are supposed to represent non conservative nonlinear Partial Differential equations (PDEs). We propose an…
We consider a stochastic particle system in which a finite number of particles interact with one another via a common energy tank. Interaction rate for each particle is proportional to the square root of its kinetic energy, as is consistent…
In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…
Electric circuits are usually described by charge- and flux-oriented modified nodal analysis. In this paper, we derive models as port-Hamiltonian systems on several levels: overall systems, multiply coupled systems and systems within…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…
Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…
Gravitational and electromagnetic interactions are Hamiltonian systems with forces between pairs of particles. We propose an alternative: Hamiltonian dynamics with triplet interactions between point particles. Our system has a potential…
Multiparticle collision dynamics is a modern coarse-grained simulation technique to treat the hydrodynamics of Newtonian fluids by solving the Navier-Stokes equations. Naturally, it also includes thermal noise. Initially it has been applied…
We consider systems of n particles that move with constant velocity between collisions. Their total momentum but not necessarily their kinetic energy is preserved at collisions. As there are no further constraints, these systems are…
Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is…
We present an overview of our studies on the nonequilibrium dynamics of quantum systems that have many interacting particles. Our emphasis is on systems that show strong level repulsion, referred to as chaotic systems. We discuss how full…
Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" symmetries can be reduced to classical symmetric systems of…
The exact equations of motion for microscopic density of classical particles number with account of inter-particle interactions and external field in closed form are derived. An integral equation for equilibrium distributions of the…
Within the frames of the analytical mechanics the method of the description of dynamics of nonequilibrium systems of potentially interacting elements is develops. The method is based on an opportunity of representation of nonequilibrium…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
We consider Lotka-Volterra systems in three dimensions depending on three real parameters. By using elementary algebraic methods we classify the Darboux polynomials (also known as second integrals) for such systems for various values of the…
The long time dynamics of polymeric materials has been extensively studied in the past through various experimental techniques and computer simulations. While computer simulations typically treat generic, simplified models, experiments deal…