Density outbursts in a food web model with a closed nutrient cycle

A spatial three level food web model with a closed nutrient cycle is presented and analyzed via Monte Carlo simulations. The food web consists of three trophic levels. The basal level species (called resources  , R$R$) corresponds to primary producers in real ecosystems. The species at an intermediate level (consumers  , C$C$) relates to herbivores. It feeds on the resources. The consumers themselves constitute food for the top level species (predators  , P$P$), which corresponds to carnivores. The remains of the consumers and predators (detritus  , D$D$) provide nutrient for the resources. The time evolution of the model reveals two asymptotic states: an absorbing one with all species being extinct, and a coexisting one, in which concentrations of all species are non-zero. There are two possible ways for the system to reach the absorbing state. In some cases the densities increase very quickly at the beginning of a simulation and then decline slowly and almost monotonically. In others, well pronounced peaks in the R$R$, C$C$ and D$D$ densities appear regularly before the extinction. Those peaks correspond to density outbursts (waves) traveling through the system. We investigate the mechanisms leading to the waves. In particular, we show that the percolation of the detritus (i.e. the accumulation of nutrients) is necessary for the emergence of the waves. Moreover, our results corroborate the hypothesis that top-level predators play an essential role in maintaining the stability of a food web (top-down control).     

WAVES IN FERROMAGNETIC MEDIA

ABSTRACT

It is shown that small perturbations of equilibrium states in ferromagnetic media give rise to standing and traveling waves that are stable for long times. The evolution of the wave profiles is governed by semilinear heat equations. The mathematical model underlying these results consists of the Landau–Lifshitz equation for the magnetization vector and Maxwell's equations for the electromagnetic field variables. The model belongs to a general class of hyperbolic equations for vector-valued functions, whose asymptotic properties are analyzed rigorously. The results are illustrated with numerical examples.     

Packing circuits in matroids

The purpose of this paper is to characterize all matroids M that satisfy the following minimax relation: for any nonnegative integral weight function w defined on E(M),

Quality inspection scheduling for multi-unit service enterprises

The traveling salesman problem is a classic NP-hard problem used to model many production and scheduling problems. The problem becomes even more difficult when additional salesmen are added to create a multiple traveling salesman problem (MTSP). We consider a variation of this problem where one salesman visits a given set of cities in a series of short trips. This variation is faced by numerous franchise companies that use quality control inspectors to ensure properties are maintaining acceptable facility and service levels. We model an actual franchised hotel chain using traveling quality inspectors to demonstrate the technique. The model is solved using a commercially available genetic algorithm (GA) tool as well as a custom GA program. The custom GA is proven to be an effective method of solving the proposed model.     

Electron Beam Optics System PIC Simulation for MMW TWTs

The basic feature and design method of MMW TWTs electron optics are analyzed in this paper. With the increasing area convergence ratio of the electron gun in TWTs, the initial thermal velocity of electrons at cathode and the non-magnetic shielded effect can no longer be neglected. It brings new challenge for the design and simulation of MMW TWTs electron optics. A method of investigation the beam DC characteristics is described using particle-in-cell (PIC) simulation and incorporate electron beam optics model integrated electron gun with periodic permanent magnetic focusing system. It is valuable for achieving the goal of first-pass design success and the electron optics engineering design and optimization.     

EVANS FUNCTIONS AND ASYMPTOTIC STABILITY OF TRAVELINGWAVE SOLUTIONS

' 61. IntroductionStability Of traveling ~ solutionS haS been one Of the main issues in aPPlied mathematics. In this paper, we are concerned with ~Otic stability of traveling wave solutionsOf the nonlinear system of integral-~ial equationSThe nonlinear systems aze derived from neuronai networkslv--ic]. The noulocal integral termsoften repre86at interactionS between neurons. TheSe systems ado arise from other interestingbackgrounds, such as Phase tr~iohells]. In the system (l.1), x E (--a…     

On the nearest neighbor rule for the traveling salesman problem

Rosenkrantz et al. (SIAM J. Comput. 6 (1977) 563) and Johnson and Papadimitriou (in: E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy Kan, D.B. Shmoys (Eds.), The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, Wiley, Chichester, 1985, pp. 145-180, (Chapter 5)) constructed families of TSP instances with n cities for which the nearest neighbor rule yields a tour-length that is a factor above the length of the optimal tour.We describe two new families of TSP instances, for which the nearest neighbor rule shows the same bad behavior. The instances in the first family are graphical, and the instances in the second family are Euclidean. Our construction and our arguments are extremely simple and suitable for classroom use.     

The traveling salesman problem on a graph and some related integer polyhedra

Given a graphG = (N, E) and a length functionl: E , the Graphical Traveling Salesman Problem is that of finding a minimum length cycle goingat least once through each node ofG. This formulation has advantages over the traditional formulation where each node must be visited exactly once. We give some facet inducing inequalities of the convex hull of the solutions to that problem. In particular, the so-called comb inequalities of Grötschel and Padberg are generalized. Some related integer polyhedra are also investigated. Finally, an efficient algorithm is given whenG is a series-parallel graph.Work was supported in part by NSF grant ECS-8205425.     

Nonlinear low-frequency electrostatic wave dynamics in a two-dimensional quantum plasma

The problem of two-dimensional arbitrary amplitude low-frequency electrostatic oscillation in a quasi-neutral quantum plasma is solved exactly by elementary means. In such quantum plasmas we have treated electrons quantum mechanically and ions classically. The exact analytical solution of the nonlinear system exhibits the formation of dark and black solitons. Numerical simulation also predicts the possible periodic solution of the nonlinear system. Nonlinear analysis reveals that the system does have a bifurcation at a critical Mach number that depends on the angle of propagation of the wave. The small-amplitude limit leads to the formation of weakly nonlinear Kadomstev–Petviashvili solitons.     

Classification of traveling wave solutions to the Green–Naghdi model

In this paper, the Green–Naghdi model is investigated by employing the qualitative method. We classify all traveling wave solutions to this model in specified parameter region of the parameter space. Especially, we study the limiting behavior of all smooth and non-smooth periodic solutions as the parameters tend to some special values. Based on the qualitative results, all exact traveling wave solutions as well as their profiles are also given.