Schelling's Segregation Model: Parameters, scaling, and aggregation

Thomas Schelling proposed a simple spatial model to illustrate how, even with relatively mild assumptions on each individual's nearest neighbor preferences, an integrated city would likely unravel to a segregated city, even if all individuals prefer integration. This agent based lattice model has become quite influential amongst social scientists, demographers, and economists. Aggregation relates to individuals coming together to form groups and Schelling equated global aggregation with segregation. Many authors assumed that the segregation which Schelling observed in simulations on very small cities persists for larger, realistic size cities. We describe how different measures could be used to quantify the segregation and unlock its dependence on city size, disparate neighbor comfortability threshold, and population density. We identify distinct scales of global aggregation, and show that the striking global aggregation Schelling observed is strictly a small city phenomenon. We also discover several scaling laws for the aggregation measures. Along the way we prove that as the Schelling model evolves, the total perimeter of the interface between the different agents decreases, which provides a useful analytical tool to study the evolution.clusters, segregation, simulation, statistics

Vortex crystals

Vortex crystals is one name in use for the subject of vortex patterns that move without change of shape or size. Most of what is known pertains to the case of arrays of parallel line vortices moving so as to produce an essentially two-dimensional flow. The possible patterns of points indicating the intersections of these vortices with a plane perpendicular to them have been studied for almost 150 years. Analog experiments have been devised, and experiments with vortices in a variety of fluids have been performed. Some of the states observed are understood analytically. Others have been found computationally to high precision. Our degree of understanding of these patterns varies considerably. Surprising connections to the zeros of 'special functions' arising in classical mathematical physics have been revealed. Vortex motion on two-dimensional manifolds, such as the sphere, the cylinder (periodic strip) and torus (periodic parallelogram) has also been studied, because of the potential applications, and some results are available regarding the problem of vortex crystals in such geometries. Although a large amount of material is available for review, some results are reported here for the first time. The subject seems pregnant with possibilities for further development.published or submitted for publicationis peer reviewe

Regimes of charged particle dynamics in current sheets: the machine learning approach

Current sheets are spatially localized almost-1D structures with intense plasma currents. They play a key role in storing the magnetic field energy and they separate different plasma populations in planetary magnetospheres, the solar wind, and the solar corona. Current sheets are primary regions for the magnetic field line reconnection responsible for plasma heating and charged particle acceleration. One of the most interesting and widely observed type of 1D current sheets is the rotational discontinuity, that can be force-free or include plasma compression. Theoretical models of such 1D current sheets are based on the assumption of adiabatic motion of ions, i.e. ion adiabatic invariants are conserved. We focus on three current sheet configurations, widely observed in the Earth magnetopause and magnetotail and in the near-Earth solar wind. Magnetic field in such current sheets is supported by currents carried by transient ions, which exist only when there is a sufficient number of invariants. In this paper, we apply a novel machine learning approach, AI Poincar'e, to determine parametrical domains where adiabatic invariants are conserved. For all three current sheet configurations, these domains are quite narrow and do not cover the entire parametrical range of observed current sheets. We discuss possible interpretation of obtained results indicating that 1D current sheets are dynamical rather than static plasma equilibria

Can the \u201cMaximum Power Principle\u201d Be Applied to Pulsed Dielectric Barrier Discharge?

In this paper, we report a qualitative model of operation and energy release in pulsed dielectric barrier discharges (DBDs). We demonstrate that pulsed DBDs operate according to the \u201cmaximum power principle\u201d and explain the relevant physical processes. Compared to experimental data, the proposed model allows an accurate estimation of the discharge pulse energy as a function of dielectric properties, electrode size, and pulse parameters (shape and voltage amplitude)

Tailored mixing inside a translating droplet

Tailored mixing inside individual droplets could be useful to ensure that reactions within microscopic discrete fluid volumes, which are used as microreactors in ``digital microfluidic'' applications, take place in a controlled fashion. In this article we consider a translating spherical liquid drop to which we impose a time periodic rigid-body rotation. Such a rotation not only induces mixing via chaotic advection, which operates through the stretching and folding of material lines, but also offers the possibility of tuning the mixing by controlling the location and size of the mixing region. Tuned mixing is achieved by judiciously adjusting the amplitude and frequency of the rotation, which are determined by using a resonance condition and following the evolution of adiabatic invariants. As the size of the mixing region is increased, complete mixing within the drop is obtained

Morphological Changes in Compressible Foams

71 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.We introduce a model free energy, assuming the bubbles in the foam to come in just two sizes and calculate its global minimum for different values of the parameters. We then consider the transition in more detail and show how some subtle factors of the foam's structure and the parameters of the numerical simulations influence the properties of the transformation and the statistics of the foam in the nonuniform state.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD