相关论文: Deterministic Equations of Motion and Phase Orderi…

Dynamical processes can be classified in various ways as deterministic or stochastic, and continuous or discrete time. All these types can be studied by the path-spaces they generate, and stationary measures on that path-space. Such…

We investigate piecewise deterministic Markov processes (PDMP), where the deterministic dynamics follows a scalar conservation law and random jumps in the system are characterized by changes in the flux function. We show under which…

We study a subclass of POMDPs, called Deterministic POMDPs, that is characterized by deterministic actions and observations. These models do not provide the same generality of POMDPs yet they capture a number of interesting and challenging…

Quantifying energy flows at nanometer scales promises to guide future research in a variety of disciplines, from microscopic control and manipulation, to autonomously operating molecular machines. A general understanding of the…

Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…

This paper presents a new mathematical model of vehicular traffic, based on the methods of the generalized kinetic theory, in which the space of microscopic states (position and velocity) of the vehicles is genuinely discrete. While in the…

An autonomous dynamical system is described by a system of second order differential equations whose solution gives the trajectories of the system. The solution is facilitated by the use of first integrals (FIs) that are used to reduce the…

We propose a simple deterministic dynamic equation and reveal the mechanism of large-scale endless evolvement of spatial density inhomogeneity in active nematic. We determine the phase regions analytically. The interplay of density,…

We consider a piecewise deterministic Markov decision process, where the expected exponential utility of total (nonnegative) cost is to be minimized. The cost rate, transition rate and post-jump distributions are under control. The state…

The kinetics of monoatomic steps in diffusion-controlled crystal growth and evaporation processes are investigated analytically using a Green's function approach. Integro-differential equations of motion for the steps are derived; and a…

We consider the dynamics of a collection of particles that interact pairwise and are restricted to move along the real line. Moreover, we focus on the situation in which particles undergo perfectly inelastic collisions when they collide.…

Rapidly oscillating potentials with a vanishing time average have been used for a long time to trap charged particles in source-free regions. It has been argued that the motion of a particle in such a potential can be approximately…

In deterministic theories, one can start from a set of ontological states to formulate the dynamical laws, but these may not be directly observable. Observable are only equivalence classes of states, and these will span a basis of…

We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…

We introduce the concept of a deterministic walk. Confining our attention to the finite state case, we establish hypotheses that ensure that the deterministic walk is transitive, and show that this property is in some sense robust. We also…

Analysis is presented of a system whose dynamics are dramatically simplified by tiny amounts of additive noise. The dynamics divide naturally into two phases. In the slower phase, trajectories are close to an invariant manifold; this allows…

The weak form of the SDOF and MDOF equations of motion are obtained. The original initial conditions problem is transformed into a boundary value problem. The boundary value problem is then solved and transformed back to the initial…

We investigate the physical properties of steady flows in a holographic first-order phase transition model, extending from the thermodynamics at equilibrium to the real-time dynamics far from equilibrium. Through spinodal decomposition or…

We consider the motion of a finite though large number of particles in the whole space R n. Particles move freely until they experience pairwise collisions. We use our recent theory of divergence-controlled positive symmetric tensors in…

Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These…