A Network Simulation of High-congestion Road-traffic Flows in Cities with Marine Container Terminals

Port cities where marine cargo terminals are located are generally near urban areas characterized by high-congestion road traffic. Changes in cargo traffic volumes into a marine terminal, or in the surrounding traffic arteries, which carry this traffic, can significantly affect the terminal's operations. Conversely, activity at the terminal can have an impact on the traffic levels and congestion for a considerable distance from the terminal. This paper demonstrates a methodology useful for studying the impact of road traffic flows on marine container terminals located in highly congested areas. This model was developed at the request of the Virginia Center for World Trade and was used to answer three planning questions in the port of Hampton Roads, Virginia, USA-what would be the impact of: opening a new section of interstate highway, a projected doubling of container traffic at one terminal, and a daily unit train in the vicinity of another terminal. The problem was made more challenging by limited data-collection funds. None the less, the model was deemed valid by a panel of traffic experts and officials from several major state and private agencies involved in marine traffic management. The model results were subsequently a factor in two major decisions related to terminal management.     

Bases,spanning sets,and the axiom of choice

Two theorems are proved: First that the statement “there exists a field F such that for every vector space over F, every generating set contains a basis” implies the axiom of choice. This generalizes theorems of Halpern, Blass, and Keremedis. Secondly, we prove that the assertion that every vector space over ?₂ has a basis implies that every well‐ordered collection of two‐element sets has a choice function. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Symplectic Yang–Mills theory,Ricci tensor,and connections

A Yang–Mills theory in a purely symplectic framework is developed. The corresponding Euler–Lagrange equations are derived and first integrals are given. We relate the results to the work of Bourgeois and Cahen on preferred symplectic connections.     

Zeta regularized determinants for conic manifolds

We study (relative) zeta regularized determinants of Laplace type operators on compact conic manifolds. We establish gluing formulae for relative zeta regularized determinants. For arbitrary self-adjoint extensions of the Laplace-Beltrami operator, we express the relative ζ-determinants for these as a ratio of the determinants of certain finite matrices. For the self-adjoint extensions corresponding to Dirichlet and Neumann conditions, the formula is particularly simple and elegant.     

Differential algebraic equations with after-effect

In this paper, we are concerned with the solution of delay differential algebraic equations. These are differential algebraic equations with after-effect, or constrained delay differential equations. The general semi-explicit form of the problem consists of a set of delay differential equations combined with a set of constraints that may involve retarded arguments. Even simply stated problems of this type can give rise to difficult analytical and numerical problems. The more tractable examples can be shown to be equivalent to systems of delay or neutral delay differential equations. Our purpose is to highlight some of the complexities and obstacles that can arise when solving these problems, and to indicate problems that require further research.     

Epitaxy: the motion picture

The engineering of many modern electronic devices demands control over a crystal down to the thickness of a single layer of atoms—and future demands will be even more challenging. Such control is achieved by the method of crystal growth known as epitaxy, and that makes this method the subject of intense study. More than that, recent advances are revolutionizing our knowledge of how surfaces grow. In fact, growing surfaces show a beautifully rich variety of phenomena, many of which are only now beginning to be uncovered. In the past few years many surface imaging techniques have been used to give us a close look at how crystals grow—while they are growing. The purpose of this article will be to illustrate some of the ways real surfaces grow and change as revealed by some of the latest in situ microscopic imaging technologies.

It is often said that crystal growth is more of an art than a science. Here we will show that it is emphatically both.     

A self-organizing network in the weak-coupling limit

We prove the existence of spatially localized ground states of the diffusive Haken model. This model describes a self-organizing network whose elements are arranged on a d-dimensional lattice with short-range diffusive coupling. The network evolves according to a competitive gradient dynamics in which the effects of diffusion are counteracted by a localizing potential that incorporates an additional global coupling term. In the absence of diffusive coupling, the ground states of the system are strictly localized, i.e. only one lattice site is excited. For sufficiently small non-zero diffusive coupling , it is shown analytically that localized ground states persist in the network with the excitations exponentially decaying in space. Numerical results establish that localization occurs for arbitrary values of in one dimension but vanishes beyond a critical coupling _c(d), when d> 1. The one-dimensional localized states are interpreted in terms of instanton solutions of a continuum version of the model.