Dynamics of Nonequilibrium Deposition with Diffusional Relaxation

Models of adhesion of extended particles on linear and planar substrates are of interest in interpreting surface deposition in colloid, polymer, and certain biological systems. An introduction is presented to recent theoretical advances in modeling these processes. Effects of diffusional relaxation are surveyed in detail, including results obtained by analytical, large-scale numerical, mean-field and scaling approaches.Comment: Review article to appear in Annual Reviews in Computational Physics; 24 pages in plain TeX + 4 PostScript figure

The Forest Service: A Study in Public Land Management. By Glen O. Robinson

  This report will provide an overview of climate modeling from a mathematical perspective, particularly with respect to the use of partial differential equations. A visit to the Swedish Meterological and Hydrological Institute's Rossby Center for climate research in Norrkoping, Sweden, is at the foundation of our investigations. An introduction and a brief history section will be followed by a description of the Navier-Stokes equations, which are at the heart of climate-related mathematics, as well as a survey of many of the popular approximations and modeling techniques in use by climate researchers today. Subsequently, a boundary value problem based on the one dimensional compressible Euler equations will be discussed from an analytical as well as a numerical point of view, especially with concern to the well-posedness of the same.

An Agent-Based Model of Collective Emotions in Online Communities

We develop a agent-based framework to model the emergence of collective emotions, which is applied to online communities. Agents individual emotions are described by their valence and arousal. Using the concept of Brownian agents, these variables change according to a stochastic dynamics, which also considers the feedback from online communication. Agents generate emotional information, which is stored and distributed in a field modeling the online medium. This field affects the emotional states of agents in a non-linear manner. We derive conditions for the emergence of collective emotions, observable in a bimodal valence distribution. Dependent on a saturated or a superlinear feedback between the information field and the agent's arousal, we further identify scenarios where collective emotions only appear once or in a repeated manner. The analytical results are illustrated by agent-based computer simulations. Our framework provides testable hypotheses about the emergence of collective emotions, which can be verified by data from online communities.Comment: European Physical Journal B (in press), version 2 with extended introduction, clarification

An improved optimistic three-stage model for the spread of HIV amongst injecting intravenous drug users

We start off this paper with a brief introduction to modeling Human Immunodeficiency Virus (HIV) and Acquired Immune Deficiency Syndrome (AIDS) amongst sharing, injecting drug users (IDUs). Then we describe the mathematical model which we shall use which extends an existing model of the spread of HIV and AIDS amongst IDUs by incorporating loss of HIV infectivity over time. This is followed by the derivation of a key epidemiological parameter, the basic reproduction number R0. Next we give some analytical equilibrium, local and global stability results. We show that if R0 &gte 1 then the disease will always die out. For R0 > 1 there is the disease-free equilibrium (DFE) and a unique endemic equilibrium. The DFE is unstable. An approximation argument shows that we expect the endemic equilibrium to be locally stable. We next discuss a more realistic version of the model, relaxing the assumption that the number of addicts remains constant and obtain some results for this model. The subsequent section gives simulations for both models confirming that if R0 &gte 1 then the disease will die out and if R0 > 1 then if it is initially present the disease will tend to the unique endemic equilibrium. The simulation results are compared with the original model with no loss of HIV infectivity. Next the implications of these results for control strategies are considered. A brief summary concludes the paper

Development of the algorithm for aircraft control at inaccurate measurement of the state vector and variable accuracy parameter

A parametric method of the synthesis of control in the closed circuit, taking into account explicitly generalized error of the inertial module, is presented. The law of control in the form of analytical formulas is typically assigned to the control program and does not change during flight of an unmanned aerial vehicle. This decreases the capabilities of the autonomous flight control system to overcome control errors, which occur for various reasons. To verify assumptions about a possibility of improving the accuracy of an aerial vehicle control by the data of the strapdown inertial navigation system on a certain time interval of autonomous operation, the calculation experiment was conducted with the use of the developed software complex, simulating operation of the automatic flight control system. Parametrization of the law of control is considered as the main contribution (the outcome). Introduction of the parameter made it possible to decrease a negative impact of measurement errors and other disturbing factors on accuracy of reaching by the point of flight destination. Through computer modeling, it was shown that it is possible to decrease the impact of a generalized measurement error on generation of values of control functions by changing the value of the parameter. Analytical expressions for the estimation of accuracy of automatic control at the known generalized error of the inertial module and limited disturbing influences were obtained. After analyzing the influence of these factors on accuracy of the object control, a set of recommendations on selection of a variable parameter of synthesis of control depending on precision level of the sensors, used in the inertial module of measuring sensors, was generated.Розглянуто розв’язання термінальної задачі управління та синтезований параметризований закон управління в аналітичному вигляді, який залежить від змінного параметра глибини прогнозу. Досліджено особливості впливу величини параметра управління на точність досягнення кінцевої точки, дані рекомендації з вибору параметра для нівелювання помилки інерційних вимірювань. Синтез управління здійснюється методом переслідування ведучої точки за інформацією, отриманою інтегруванням вимірювань фактичного прискорення і містить помилку, характерну для акселерометрів