The Torus-Equivariant Cohomology of Nilpotent Orbits

We consider aspects of the geometry and topology of nilpotent orbits in finite-dimensional complex simple Lie algebras. In particular, we give the equivariant cohomologies of the regular and minimal nilpotent orbits with respect to the action of a maximal compact torus of the overall group in question.Comment: 17 pages. Comments are most welcome. Version 2: A few minor changes were mad

Exploring Cities Using Agent-Based Models and GIS

Cities are faced with many problems such as urban sprawl, congestion, and segregation. They are also constantly changing. Computer modelling is becoming an increasingly important tool when examining how cities operate. Agent based models (ABM) allow for the testing of different hypotheses and theories for urban change, thus leading to a greater understanding of how cities work. This paper presents how ABMs can be developed by their integration with Geographical Information System (GIS). To highlight this, a generic ABM is presented. This is then applied to two model applications: a segregation model and a location model. Both models highlight how different theories can be incorporated into the generic model and demonstrate the importance of space in the modelling process. Cities are faced with many problems such as urban sprawl, congestion, and segregation. They are also constantly changing. Computer modelling is becoming an increasingly important tool when examining how cities operate. Agent based models (ABM) allow for the testing of different hypotheses and theories for urban change, thus leading to a greater understanding of how cities work. This paper presents how ABMs can be developed by their integration with Geographical Information System (GIS). To highlight this, a generic ABM is presented. This is then applied to two model applications: a segregation model and a location model. Both models highlight how different theories can be incorporated into the generic model and demonstrate the importance of space in the modelling process

The Repast Simulation/Modelling System for Geospatial Simulation

The use of simulation/modelling systems can simplify the implementation of agent-based models. Repast is one of the few simulation/modelling software systems that supports the integration of geospatial data especially that of vector-based geometries. This paper provides details about Repast specifically an overview, including its different development languages available to develop agent-based models. Before describing Repast’s core functionality and how models can be developed within it, specific emphasis will be placed on its ability to represent dynamics and incorporate geographical information. Once these elements of the system have been covered, a diverse list of Agent-Based Modelling (ABM) applications using Repast will be presented with particular emphasis on spatial applications utilizing Repast, in particular, those that utilize geospatial data

Path ensembles averages in systems driven far-from-equilibrium

The Kawasaki nonlinear response relation, the transient fluctuation theorem, and the Jarzynski nonequilibrium work relation are all expressions that describe the behavior of a system that has been driven from equilibrium by an external perturbation. In contrast to linear response theory, these expressions are exact no matter the strength of the perturbation, or how far the system has been driven away from equilibrium. In this paper I show that these three relations (and several other closely related results) can all be considered special cases of a single theorem. This expression is explicitly derived for discrete time and space Markovian dynamics, with the additional assumptions that the single time step dynamics preserve the appropriate equilibrium ensemble, and that the energy of the system remains finite.Comment: 6 page

A Play for San Jacinto Night

Mode of access: Internet

Stability of travelling-wave solutions for reaction-diffusion-convection systems

We are concerned with the asymptotic behaviour of classical solutions of systems of the form u_t = Au_xx + f(u, u_x), x in R, t>0, u(x,t) a vector in RN, with u(x,0)= U(x), where A is a positive-definite diagonal matrix and f is a 'bistable' nonlinearity satisfying conditions which guarantee the existence of a comparison principle. Suppose that there is a travelling-front solution w with velocity c, that connects two stable equilibria of f. We show that if U is bounded, uniformly continuously differentiable and such that w(x) - U(x) is small when the modulus of x is large, then there exists y in R such that u(., t) converges to w(.+y-ct) in the C1 norm at an exponential rate as t tends to infinity. Our approach extends an idea developed by Roquejoffre, Terman and Volpert in the convectionless case, where f is independent of u_x.Comment: 23 pages. To appear in Topological Methods in Nonlinear Analysi