The paper is concerned with Nash equilibrium solutions for the LighthillWhitham model of traffic flow, where each driver chooses his own departure time in order to minimize the sum of a departure cost and an arrival cost. Estimates are provided on how much the Nash solution may change, depending on the cost functions and on the flux function of the conservation law. It is shown that this equili...

A game-theoretic model of scrip (artificial currency) systems is analyzed. It is shown that relative entropy can be used to characterize the distribution of agent wealth when all agents use threshold strategies—that is, they volunteer to do work iff they have below a threshold amount of money. Monotonicity of agents’ bestreply functions is used to show that scrip systems have pure strategy equi...

A chemical equilibrium study was performed to investigate the effect of growth parameters on the constitution in ZrC films grown by chemical vapor deposition (CVD). The equilibrium analysis of the Zr–C–H system demonstrated that ZrC (fcc) deposition is favorable and that a certain minimum amount of hydrogen should prevent co-deposition of elemental carbon over a wide range of temperature, press...

Low analyzes the equilibrium performance of the recently developed eXplicit Control Protocol (XCP) by applying the derived window-based dynamical model. However, Low’s window-based dynamic model is too complicated to be used easily. In our previous works, a simple rate-based model is proposed for analyzing XCP’s equilibrium performance. Most results that appeared in Low’s paper can be easily re...

This paper presents alternative methods to compute the equilibrium condition immediately following a disturbance to an electric power system. The first uses the brute force method of simply integrating the dynamic model until it reaches steady state. The second uses the straightforward analytical choice of setting all time derivatives of the dynamic model to zero and solving the remaining algeb...

A statistical approach to market equilibrium and efficiency analysis is proposed in this paper. One factor that governs the exchange decisions of traders in a market, named willingness price, is highlighted and constitutes the whole theory. The supply and demand functions are formulated as the distributions of corresponding willing exchange over the willingness price. The laws of supply and dem...

-Equilibrium distributions of collections of discrete dislocations are analyzed, with the dislocations modelled as line defects in a linear elastic medium. The dislocated equilibrium configuration is determined by finding a minimum potential energy configuration, with respect to variations in the dislocation positions, for a fixed number and type of dislocations. Numerical results are presented...