We derive thermo-mechanical continuum equations from Molecular Dynamics (MD) equations using the Generalized Mathematical Homogenization (GMH) theory developed by the authors for 0 K applications. GMH constructs an array of atomistic unit cell problems coupled with a thermo-mechanical continuum problem. The unit cell problem derived is a molecular dynamics problem defined for the perturbation f...

Classical model Sdc of Dirac particle SD is constructed. SD is the dynamic system described by the Dirac equation. Its classical analog Sdc is described by a system of ordinary differential equations, containing the quantum constant h̄ as a parameter. Dynamic equations for Sdc are determined by the Dirac equation uniquely. Both dynamic systems SD and Sdc appear to be nonrelativistic. One succeed...

a novel computational fluid dynamics and molecular kinetic theory (cfd-mk) method was developed to simulate the impingement of a nanodroplet onto a solid surface. a numerical solution of the navier–stokes equation using a volume-of-fluid (vof) technique was used to model nanodroplet deformation. dynamic contact angle during droplet impact was obtained by molecular kinetic theory. this dynamic c...

The paper discusses a problem of stochastic optimal control of a linear singledegree-of-freedom system subjected to external sinusoidal and white noise excitations. An external, bounded in magnitude control force is introduced into the system to reduce mean system response energy. The dynamic programming approach is used to derive the corresponding Hamilton-Jacobi-Bellman equation. Hybrid solut...

Topics considered here include: examples of optimal control problems; dynamic programming and the Hamilton-Jacobi-Bellman equation; verification theorems; the Pontryagin Maximum Principle Principle. The examples include many with an economic flavor, but others too (including the Hopf-Lax solution formula for ut + H(Du) = 0 with H convex). There’s much more here than we’ll have time to do in lec...

The focus of this paper is the traffic shaping at the access of an network node. We propose a novel algorithm that dynamically shapes the incoming traffic, based on service curves equations, in order to meet the QoS constraints in terms of buffer size or delay. We first estimate arrival parameters within various time intervals in order to make the incoming traffic fit into a token bucket traffi...

We study centred second-order in time and space discretizations of the inviscid Burgers equation. Although this equation in its continuum formulation supports non-smooth shock wave solutions, the discrete equation generically supports smooth solitary wave solutions. Using backward error analysis we derive the modified equation associated with the numerical scheme. We identify three different eq...

We consider a general class of discrete nonlinear Schrödinger equations (DNLS) on the lattice hZ with mesh size h > 0. In the continuum limit when h → 0, we prove that the limiting dynamics are given by a nonlinear Schrödinger equation (NLS) on R with the fractional Laplacian (− ) as dispersive symbol. In particular, we obtain that fractional powers 1 2 < α < 1 arise from long-range lattice int...

We develop a discrete analogue of the Hamilton–Jacobi theory in the framework of the discrete Hamiltonian mechanics. We first reinterpret the discrete Hamilton–Jacobi equation derived by Elnatanov and Schiff in the language of discrete mechanics. The resulting discrete Hamilton– Jacobi equation is discrete only in time, and is shown to recover the Hamilton–Jacobi equation in the continuous-time...

In this paper we consider the optimal control problem for a insurance company. Our objective is to maximize the expectation of discounted dividends and its terminal value which represents the company liquidation value upon the time of bankruptcy. The surplus of the insurance company is governed by the Brownian motion with a constant drift and a diffusion term. The company can manage its risk ex...