Clustering, advection and patterns in a model of population dynamics with neighborhood-dependent rates

We introduce a simple model of population dynamics which considers birth and death rates for every individual that depend on the number of particles in its neighborhood. The model shows an inhomogeneous quasistationary pattern with many different clusters of particles. We derive the equation for the macroscopic density of particles, perform a linear stability analysis on it, and show that there is a finite-wavelength instability leading to pattern formation. This is the responsible for the approximate periodicity with which the clusters of particles arrange in the microscopic model. In addition, we consider the population when immersed in a fluid medium and analyze the influence of advection on global properties of the model.Comment: Some typos and some problems with the figures correcte

Quantum Hall transitions: An exact theory based on conformal restriction

We revisit the problem of the plateau transition in the integer quantum Hall effect. Here we develop an analytical approach for this transition, based on the theory of conformal restriction. This is a mathematical theory that was recently developed within the context of the Schramm-Loewner evolution which describes the stochastic geometry of fractal curves and other stochastic geometrical fractal objects in 2D space. Observables elucidating the connection with the plateau transition include the so-called point-contact conductances (PCCs) between points on the boundary of the sample, described within the language of the Chalker-Coddington network model. We show that the disorder-averaged PCCs are characterized by classical probabilities for certain geometric objects in the plane (pictures), occurring with positive statistical weights, that satisfy the crucial restriction property with respect to changes in the shape of the sample with absorbing boundaries. Upon combining this restriction property with the expected conformal invariance at the transition point, we employ the mathematical theory of conformal restriction measures to relate the disorder-averaged PCCs to correlation functions of primary operators in a conformal field theory (of central charge $c=0$). We show how this can be used to calculate these functions in a number of geometries with various boundary conditions. Since our results employ only the conformal restriction property, they are equally applicable to a number of other critical disordered electronic systems in 2D. For most of these systems, we also predict exact values of critical exponents related to the spatial behavior of various disorder-averaged PCCs.Comment: Published versio

Transition Phenomena Induced by Internal Noise and Quasi-absorbing State

We study a simple chemical reaction system and effects of the internal noise. The chemical reaction system causes the same transition phenomenon discussed by Togashi and Kaneko [Phys. Rev. Lett. 86 (2001) 2459; J. Phys. Soc. Jpn. 72 (2003) 62]. By using the simpler model than Togashi-Kaneko's one, we discuss the transition phenomenon by means of a random walk model and an effective model. The discussion makes it clear that quasi-absorbing states, which are produced by the change of the strength of the internal noise, play an important role in the transition phenomenon. Stabilizing the quasi-absorbing states causes bifurcation of the peaks in the stationary probability distribution discontinuously.Comment: 6 pages, 5 figure

Extended Seiberg-Witten Theory and Integrable Hierarchy

The prepotential of the effective N=2 super-Yang-Mills theory perturbed in the ultraviolet by the descendents of the single-trace chiral operators is shown to be a particular tau-function of the quasiclassical Toda hierarchy. In the case of noncommutative U(1) theory (or U(N) theory with 2N-2 fundamental hypermultiplets at the appropriate locus of the moduli space of vacua) or a theory on a single fractional D3 brane at the ADE singularity the hierarchy is the dispersionless Toda chain. We present its explicit solutions. Our results generalize the limit shape analysis of Logan-Schepp and Vershik-Kerov, support the prior work hep-th/0302191 which established the equivalence of these N=2 theories with the topological A string on CP^1 and clarify the origin of the Eguchi-Yang matrix integral. In the higher rank case we find an appropriate variant of the quasiclassical tau-function, show how the Seiberg-Witten curve is deformed by Toda flows, and fix the contact term ambiguity.Comment: 49 page

The experience of enchantment in human-computer interaction

Improving user experience is becoming something of a rallying call in human–computer interaction but experience is not a unitary thing. There are varieties of experiences, good and bad, and we need to characterise these varieties if we are to improve user experience. In this paper we argue that enchantment is a useful concept to facilitate closer relationships between people and technology. But enchantment is a complex concept in need of some clarification. So we explore how enchantment has been used in the discussions of technology and examine experiences of film and cell phones to see how enchantment with technology is possible. Based on these cases, we identify the sensibilities that help designers design for enchantment, including the specific sensuousness of a thing, senses of play, paradox and openness, and the potential for transformation. We use these to analyse digital jewellery in order to suggest how it can be made more enchanting. We conclude by relating enchantment to varieties of experience.</p

Adaptation of Autocatalytic Fluctuations to Diffusive Noise

Evolution of a system of diffusing and proliferating mortal reactants is analyzed in the presence of randomly moving catalysts. While the continuum description of the problem predicts reactant extinction as the average growth rate becomes negative, growth rate fluctuations induced by the discrete nature of the agents are shown to allow for an active phase, where reactants proliferate as their spatial configuration adapts to the fluctuations of the catalysts density. The model is explored by employing field theoretical techniques, numerical simulations and strong coupling analysis. For d<=2, the system is shown to exhibits an active phase at any growth rate, while for d>2 a kinetic phase transition is predicted. The applicability of this model as a prototype for a host of phenomena which exhibit self organization is discussed.Comment: 6 pages 6 figur

Critical curves in conformally invariant statistical systems

We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). We also provide links between this description and the stochastic (Schramm-) Loewner evolution (SLE). The connection appears in the long-time limit of stochastic evolution of various SLE observables related to CFT primary fields. We show how the multifractal spectrum of harmonic measure and other fractal characteristics of critical curves can be obtained.Comment: Published versio

The use of a ward's history in training psychiatric child care workers

The importance of the contribution of historical-cultural factors to an inpatient treatment setting's contemporaneous psycho-social climate has been given little attention in published discussions of ward staff problems and training. This report illustrates some ways in which such historical-cultural forces, embodied in social myths and entrenched traditions, operate. Examples are provided from a ward of disturbed adolescents, where young child care workers struggled as a group with the daily stresses of providing therapeutic milieu support to children ambivalently seeking and resisting external controls for their feelings and impulses. The process of incorporating the analysis of historical-cultural factors in an inservice training program is described.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44275/1/10566_2005_Article_BF01642066.pd