These three lectures introduce the reader to recent progress on the hydrodynamic limits of the kinetic theory of gases. Lecture 1 outlines the main mathematical results in this direction, and explains in particular how the Euler or NavierStokes equations for compressible as well as incompressible fluids, can be derived from the Boltzmann equation. It also presents the notion of renormalized sol...

In this paper, we develop a macroscopic model for pedestrian flow using the dynamic continuum modeling approach. We consider a two-dimensional walking facility that is represented as a continuum within which pedestrians can move freely in any direction. A pedestrian chooses a route based on his or her memory of the shortest path to the desired destination when the facility is empty and, at the ...

abstract: since the field of micro electromechanical systems (mems) continues to grow, the flow in micro devices have become an area that receives a significant attention. the microscopic flows are usually characterized by the knudsen number (kn). when the characteristic size of the particle decreases down to a value comparable to the mean free path of the molecules, the continuum assumption fa...

We establish the existence and uniqueness of a solution to master equation for mean field game controls with absorption. The arises as continuum limit dynamic exhaustible resources modeling Cournot competition between producers. proof relies on an analysis forward-backward system nonlocal Hamilton-Jacobi/Fokker-Planck equations Dirichlet boundary conditions. In particular, we new priori estimat...

We propose a numerical multiscale method for coupling a conservation law for mass at the continuum scale with a discrete network model that describes the microscale flow in a porous medium. In this work we focus on coupling pressure equations. Evaluating pressure from a detailed network model over a large physical domain is typically computationally very expensive. We assume that over the same ...

We present a systematic discretization scheme for the Kardar-Parisi-Zhang (KPZ) equation, which correctly captures the strong-coupling properties of the continuum model. In particular we show that the scheme contains no finite-time singularities in contrast to conventional schemes. The implications of these results to i) previous numerical integration of the KPZ equation, and ii) the non-trivia...

A new type of backbone robot is presented in this paper. The core idea is to use a cross shape mechanism with the principle of functioning of the scissors linkages, known as a pantograph. Although this continuum arm acts quite similar to tendon-driven robot, this manipulator does not include any tendon in its structure. This design does not suffer from the weaknesses of the continuum design suc...

a nonlocal beam model based on the bernoulli–euler beam theory is presented to investigate the dynamic stability of embedded single-walled carbon nanotubes (swcnts) in thermal environment under combined static and periodic axial loads. the dynamic stability analysis is carried out by including the effects of small-scale parameter, temperature change and elastic medium. the equation of motion is...

In the present study, the dynamic buckling of the graphene sheet coupled by a viscoelastic matrix was studied. In light of the simplicity of Eringen's non-local continuum theory to considering the nanoscale influences, this theory was employed. Equations of motion and boundary conditions were obtained using Mindlin plate theory by taking nonlinear strains of von Kármán and Hamilton's principle ...

We study monotonicity results for optimal policies of various queueing and resource sharing models. The standard approach is to prove, for each speciic model, certain properties of the dynamic programming value function. By concentrating on the events instead of the entire value function we come to a uniied treatment of monotonicity results for symmetric two-dimensional models. Several models f...