Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Road-User and Property Taxes on Selected Motor Vehicles 1987

This report provides basic information for 1987 from each State on road-user tax.es and property taxes levied on a selected group of vehicles, The intent is neither to weigh the merits of any of the taxes being reviewed nor to recommend any tax policy, but to supply the means to measure and compare the annual payments that would be made for each of 14 carefully selected vehicles in each State, By arranging these payments in a uniform manner, a useful research and planning tool is made available to highway administrators, legislators and others who are concerned with highways and with vehicles and their use

The timetable constrained distance minimization problem

Abstract. We define the timetable constrained distance minimization problem (TCDMP) which is a sports scheduling problem applicable for tournaments where the total travel distance must be minimized. The problem consists of finding an optimal home-away assignment when the opponents of each team in each time slot are given. We present an integer programming, a constraint programming formulation and describe two alternative solution methods: a hybrid integer programming/constraint programming approach and a branch and price algorithm. We test all four solution methods on benchmark problems and compare the performance. Furthermore, we present a new heuristic solution method called the circular traveling salesman approach (CTSA) for solving the traveling tournament problem. The solution method is able to obtain high quality solutions almost instantaneously, and by applying the TCDMP, we show how the solutions can be further improved

Road-User and Property Taxes on Selected Motor Vehicles 1982

This report provides basic information for 1982 from each State on road--user tax.es and property taxes levied on a selected group of vehicles. The intent is neither to weigh the merits of any of the taxes being reviewed nor to recommend any tax poHcy9 but to supply the means to measure and compare the annual payments that would be made for each of 15 carefully selected vehicles in each State, By arranging these payments in a uniform manner, a useful research and planning tool is made available to highway administrators, legislators, and others who are concerned with highways and with vehicles and their use