An anyon model

We construct an infinite-dimensional dynamical Hamiltonian system that can be interpreted as a localized structure (“quasiparticle”) on the plane E ₂. The model is based on the theory of an infinite string in the Minkowski space E _1,3 formulated in terms of the second fundamental forms of the worldsheet. The model phase space H is parameterized by the coordinates, which are interpreted as “internal” (E(2)-invariant) and “external” (elements of T*E ₂) degrees of freedom. The construction is nontrivial because H contains a finite number of constraints entangling these two groups of coordinates. We obtain the expressions for the energy and for the effective mass of the constructed system and the formula relating the proper angular momentum and the energy. We consider a possible interpretation of the proposed construction as an anyon model.     

An oscillatory population model

We consider a simple population model which includes time-dependent parameters prompted by the recent work of Lakshmi [Chaos, Solitons & Fractals 16 (2003) 183]. Time-dependent parameters introduce the possibility of chaos into the dynamics of even simple models. We provide some solutions of the model, compare them with the ones obtained by Lakshmi and discuss their behaviour and properties.     

An integrable SIS model

We provide a demonstration of the integrability of a classical model of an infectious disease which neither kills nor induces autoimmunity by means of the Painlevé analysis and use the Lie theory of transformation groups to present an explicit solution.     

An intelligent agent model

This paper discusses fundamental issues of intelligent agents. Based on a portrayal of agent characteristics a general agent architecture linking aspects of perception, interpretation of natural language, learning and decision-making is provided. Agents built upon this architecture are equipped to handle unknown, open and distributed environments. The paper concludes with a discussion whether or not agents designed in accordance with this architecture exhibit some sort of intelligence.     

一类SIRS传染病模型

This paper considers an SIRS epidemic model that incorporates constant immigration rate, a general population-size dependent contact rate and proportional transfer rate from the infective class to susceptible class. A threshold parameter a is identified. If σ≤1, the disease-free equilibrium is globally stable. If σ＞1, a unique endemic equilibrium is locally asymptotically stable. For two important special cases of mass action incidence and standard incidence,global stability of the endemic equilibrium is proved provided the threshold is larger than unity. Some previous results are extended and improved.     

An optimal software debugging model

This paper deals with the question of optimal debugging times for large-scale computer programs, given certain assumptions concerning the distribution of error within the program, the cost that is incurred whenever a fault occurs, and the cost of debugging. Modeling takes place within the framework of independent Poisson processes describing faults caused by errors. The optimization aim is to minimize the long-run total expected discounted cost. Some general results concerning the optimal polity are presented.This research has been supported by NATO Grant No. RG.86/0024, by the Alexander von Humboldt Foundation, and by the University of Passau, Germany.     

An extended thermal-medium crack model

It is important to investigate the effects of heat conduction of crack interior on thermoelastic fields of a cracked material. In this paper, an extended thermal-medium crack model is proposed to address the influences of the thermal conductivity inside an opening crack on the induced thermoelastic fields. Then the problem of a penny-shaped crack in a transversely isotropic material is investigated under applied mechanical and uniform heat flow loadings. Based on the Hankel transform technique, the governing partial differential equations are transformed to ordinary differential equations, then to a system of coupled dual integral equations. The thermoelastic fields around the penny-shaped crack are obtained explicitly by solving the derived dual integral equations. Numerical results are reported to show the influences of the thermal conductivity of crack interior on partial insulation coefficient, temperature change across crack and thermal stress intensity factor. As compared to the known thermal-medium crack model, the proposed one exhibits more applicability.     

An essay on model theory

Some basic ideas of model theory are presented and a personal outlook on its perspectives is given.     

An ODE traffic network model

We are interested in models for vehicular traffic flow based on partial differential equations and their extensions to networks of roads. In this paper, we simplify a fluidodynamic traffic model and derive a new traffic flow model based on ordinary differential equations (ODEs). This is obtained by spatial discretization of an averaged density evolution and a suitable approximation of the coupling conditions at junctions of the network. We show that the new model inherits similar features of the full model, e.g., traffic jam propagation. We consider optimal control problems controlled by the ODE model and derive the optimality system. We present numerical results on the simulation and optimization of traffic flow in sample networks.     

An economic model of short-rotation forestry

This paper presents an economic model of short-rotation forestry and shows that Lemke's linear complementarity algorithm can be used to compute optimal sustainable harvesting strategies. As an example, we apply our method, using existing data, to calculate optimal harvesting strategies for a plantation consisting of two interdependent species of trees.     

An integro-PDE model with variable motility

This paper is concerned with a nonlocal reaction–diffusion–mutation model. It involves the spatial variable and a trait variable which govern the spatial diffusion of species. By establishing comparison principle and constructing monotone iterative sequence, we have proved the existence of solution to Cauchy problem. Then, based on the quasi-elementary solution, auxiliary equation and method of successive improvement of upper and lower solutions, the solutions are shown to be unique, bounded and globally stable.     

An inventory model with component commonality

Qualitative implications of component commonality in assemble-to-order systems are discussed. We show that in a static model the stocks of product-specific components always increase when other components are combined. As optimal policy for the dynamic version is shown to be myopic, the qualitative results apply there as well.     

An automotive bulk recycling planning model

The automotive recycling infrastructure successfully recovers 75% of the material weight in end-of-life vehicles primarily through ferrous metal separation. However, this industry faces significant challenges as automotive manufacturers increase the use of nonferrous and nonmetallic materials. As the nonferrous content in end-of-life vehicles rises, automotive shredders need to evaluate to what extent to separate nonferrous metals. We propose a recycling planning model for automotive shredders to make short-term tactical decisions regarding to what extent to process and to reprocess materials through multiple passes. In addition, the mixed integer programming model determines whether to combine materials for shipment. In a case study for automotive shredding decisions for the current composition and more polymer-intensive end-of-life vehicles, we use our model to show the sensitivity of the decision to reprocess light nonferrous metal to low and high metal prices. Contrary to observations in practice to mix light and heavy nonferrous metals for shipment, we show multiple scenarios where the model chooses to reprocess and ship separated light and heavy nonferrous metals.     

An adaptive solar radiation numerical model

A numerical model for the evaluation of solar radiation in different locations is presented. The solar radiation model is implemented taking into account the terrain surface using two-dimensional adaptive meshes of triangles that are constructed using a refinement/derefinement procedure in accordance with the variations of terrain surface and albedo. The selected methodology defines the terrain characteristics with a minimum number of points so that the computational cost is reduced for a given accuracy. The model can be used in atmospheric sciences as well as in other fields such as electrical engineering, since it allows the user to find the optimal location for maximum power generation in photovoltaic or solar thermal power plants. For this purpose, the effect of shadows is considered in each time step. The solar radiation is first computed for clear sky conditions considering the different components of the radiation. The real sky radiation is computed daily, starting from the results of clear sky radiation, in terms of the clear sky index. Maps for the clear sky index are obtained from a spatial interpolation of observational data that are available for each day at several points of the region under consideration. Finally, the solar radiation maps for a month are calculated from the daily results. The model can also be applied in solar radiation forecasting with the help of a forecasting meteorological model. This model takes into account the shadows cast, and allows the user to make a better estimation of the amount of solar power generation. Some numerical experiments related to the generation of solar radiation maps in Gran Canaria Island (Canary Islands, Spain) are presented.     

An automaton model of data banks

Translated from Issledovaniya po Prikladnoi Matematike, No. 5, pp. 10–17, 1976.     

An ornstein-uhlenbeck model for random oscillations

We consider the effect of a random "noise" on an n-dimensional simple harmonic oscillator with time-dependent damping. The noise in the system is modelled by incorporating a Brownian motion term in the equation for the velocity process of the simple harmonic oscillator, giving a stochastic differential equation similar to that of an Ornstein-Uhlenbeck proces. Necessary and sufficient conditions for the convergence of the solution of this SDE to an orbit of simple harmonic motion (satisfying the usual ODE) are then obtained     

An analytical model for conflict dynamics

A coherent dynamic conflict model is developed from basic principles. The governing equations have a striking resemblance to the continuity equation in fluid dynamics with an additional term for the response to pressure by the opponent. The salient feature of the model is a moving confrontation line which is an excellent indicator for the evolution of conflict. The developed model also permits investigation of the necessary minimum involvement of a third party actor such as an international organization to establish a status quo between the actors. The model is demonstrated on the Russian–Chechen conflict and the Bosnian war.     

An economic model of pollution prevention

Pollution prevention is modelled with an approach that combines the substitutability of inputs in the twice-differentiable neoclassical production function and the discreteness of linear activity analysis. The polluting firm's emissions, which result from its use of a toxic input, can be reduced by substituting other inputs for the toxic input and&2.urule;or by switching to a nonpolluting process. The strengths of the model are that zero emissions are achievable at a finite marginal cost, the nonconvexity that may occur in conventional activity analysis does not occur in this model, and there is a range of output levels at which polluting and nonpolluting firms in the same industry realistically coexist.