The basic partial differential equation PDE models for supply chain networks with re-entrant nodes and their macroscopic are proposed. However, through numerical examples, the basic continuummodels do not performwell for multiple re-entrant systems. Then, a new state equation considering the re-entrant degree of the products is introduced to improve the effectiveness of the basic continuum mode...

over the admissible controls U . Both g and κ · u (u ∈ U) may take positive and negative values. This paper studies the corresponding dynamic programming equation (DPE), a second-order degenerate elliptic partial differential equation of HJB-type with a state constraint boundary condition. Under the controllability condition GU = R and the finiteness of H(q) = supu∈U1{−Gu · q− κ · u}, q ∈ R , w...

The numerical study of continuum-rarefied gas flows is of considerable interest because it can provide fundamental knowledge regarding flow physics. Recently, the nonlinear coupled constitutive method (NCCM) has been derived from the Boltzmann equation and implemented to investigate continuum-rarefied gas flows. In this study, we first report the important and detailed issues in the use of the ...

We study the dynamics of denaturation bubbles in double-stranded DNA. Demonstrating that the associated Fokker-Planck equation is equivalent to a Coulomb problem, we derive expressions for the bubble survival distribution W(t). Below Tm, W(t) is associated with the continuum of scattering states of the repulsive Coulomb potential. At Tm, the Coulomb potential vanishes and W(t) assumes a power-l...

<abstract><p>This contribution presents a concept to dynamic fracture with continuum-kinematics-based peridynamics. Continuum-kinematics-based peridynamics is geometrically exact formulation of peridynamics, which adds surface- or volume-based interactions the classical peridynamic bonds, thus capturing finite deformation kinematics correctly. The surfaces and volumes considered for...

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which a...

The existence of quasi-periodic eigensolutions of a linear second order ordinary differential equation with quasi-periodic coefficient f{a>it, io%t) is investigated numerically and graphically. For sufficiently incommensurate frequencies coi, a>2 a doubly indexed infinite sequence of eigenvalues and eigenmodes is obtained. The equation considered is a model for the magneto-hydrodvnamic "continu...

A coupled continuum-discrete numerical model is presented to study the synthesis of TiC nanosized aggregates during a self-propagating combustion synthesis (SHS) process. The overall model describes the transient of the basic mechanisms governing the SHS process in a two-dimensional micrometer size geometry system. At each time step, the continuum (micrometer scale) model computes the current t...

The discrete Painlevé I equation (dPI) is an integrable difference equation which has the classical first Painlevé equation (PI) as a continuum limit. dPI is believed to be integrable because it is the discrete isomonodromy condition for an associated (single-valued) linear problem. In this paper, we derive higher-order difference equations as isomonodromy conditions that are associated to the ...

in the current study the effect of casimir force and squeezed film damping on the pull-in instability and dynamic behavior of electrostatically actuated nano and micro electromechanical systems is investigated separately. linear elastic membrane theory is used to model the static and dynamic behavior of system for strip, annular and disk geometries. squeezed film damping effect is modeled using...