individual based model with global competition interaction fluctuation effects in pattern formation we present some numerical results obtained from a simple individual based model that describes clustering of organisms caused by competition our aim is to show that even when a deterministic description developed for continuum models predicts no pattern formation an individual based model displays well defined patterns as a consequence of fluctuation effects caused by the discrete nature of the interacting agents

inequality systems and minimax theorems abstract this paper is a comprehensive study of the results about the consistency of inequality systems the minimax theorems are the main tools used in proceeding to this survey most of the known results are quoted and some of them are weakened or generalized to infinite dimensional spaces applications to programming are given

an interacting particle model with compact hierarchical structure abstract we present a model interacting particle system with a population of fixed size in which particles wander randomly in space and pairs interact at a rate determined by a reaction kernel with finite range the pairwise interaction randomly selects one of the particles the victim and instantly transfers it to the position of the other the killer thus maintaining the total number the special feature of the model is that it possesses a closed hierarchical structure in which the statistical moments of the governing master equation lead to closed equations for the reduced distribution functions the concentration pair correlation function and so on in one spatial dimension we show that persistent spatial correlations clusters arise in this model and we characterize the dynamics in terms of analytical properties of the pair correlation function as the range of the reaction kernel is increased the dynamics varies from an ensemble of largely independent random walkers at small range to tightly bound clusters with longer range reaction kernels

numerical solutions of variable order time fractional 1 1 and 1 2 dimensional advection dispersion and diffusion models abstract a numerical scheme based on haar wavelets coupled with finite differences is suggested to study variable order time fractional partial differential equations tfpdes the technique is tested on 1 1 dimensional advection dispersion and 1 2 dimensional advection diffusion equations in the proposed scheme time fractional derivative is firstly approximated by quadrature formula and then finite differences are combined with one and two dimensional haar wavelets with the help of suggested method the tfpdes convert to a system of algebraic equations which is easily solvable also convergence of the proposed scheme has been discussed which is an important part of the present work for validation the obtained results are matched with earlier work and exact solutions computations illustrate that the proposed scheme has better outcomes

a duality theorem for semi infinite convex programs and their finite subprograms in this paper we first establish a general recession condition under which a semi infinite convex program and its formal lagrangian dual have the same value we go on to show that under this condition the following hold first every finite subprogram with enough of the given constraints has the same value as its lagrangian dual second the weak value of the primal program is equal to the optimal value of the primal

the lagrange multiplier rule in set valued optimization the known lagrange multiplier rule is extended to set valued constrained optimization problems using the contingent epiderivative as differentiability notion a necessary optimality condition for weak minimizers is derived which is also a sufficient condition under generalized convexity assumptions

uniform duality in semi infinite convex optimization we study infinite sets of convex functional constraints with possibly a set constraint under general background hypotheses which require closed functions and a closed set but otherwise do not require a slater point for example when the set constraint is not present only the consistency of the conditions is needed

demographic fluctuations in a population of anomalously diffusing individuals the phenomenon of spatial clustering induced by death and reproduction in a population of anomalously diffusing individuals is studied analytically the possibility of social behaviors affecting the migration strategies has been taken into exam in the case that anomalous diffusion is produced by means of a continuous time random walk ctrw in the case of independently diffusing individuals the dynamics appears to coincide with that of dying and reproducing brownian walkers in the strongly social case the dynamics coincides with that of nonmigrating individuals in both limits the growth rate of the fluctuations becomes independent of the hurst exponent of the ctrw the social behaviors that arise when transport in a population is induced by a spatial distribution of random traps have been analyzed

clustering determines who survives for competing brownian and levy walkers the competition between two ecologically similar species that use the same resources and differ from each other only in the type of spatial motion they undergo is studied the latter is assumed to be described either by brownian motion or levy flights competition is taken into account by assuming that individuals reproduce in a density dependent fashion it is observed that no influence of the type of motion occurs when the two species are in a well mixed unstructured state however as soon as the species develop spatial clustering the one forming more concentrated clusters gets a competitive advantage and eliminates the other a similar competitive advantage would occur between walkers of the same type but with different diffusivities if this leads also to different clustering the coexistence of both species is also possible under certain conditions

a meshless method for solving two dimensional variable order time fractional advectiondiffusion equation several physical phenomena such as transformation of pollutants energy particles and many others can be described by the well known convectiondiffusion equation which is a combination of the diffusion and advection equations in this paper this equation is generalized with the concept of variable order fractional derivatives the generalized equation is called variable order time fractional advectiondiffusion equation v otfade an accurate and robust meshless method based on the moving least squares mls approximation and the finite difference scheme is proposed for its numerical solution on two dimensional 2 d arbitrary domains in the time domain the finite difference technique with a weighted scheme and in the space domain the mls approximation are employed to obtain appropriate semi discrete solutions since the newly developed method is a meshless approach it does not require any background mesh structure to obtain semi discrete solutions of the problem under consideration and the numerical solutions are constructed entirely based on a set of scattered nodes the proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere in all such cases the obtained results show that the proposed method is very accurate and robust moreover a remarkable property so called positive scheme for the proposed method is observed in solving concentration transport phenomena the variable order time fractional advectiondiffusion equation in 2 d is defined an accurate and robust meshless method is proposed for its numerical solutions a variable order fractional modeling of air pollution is expressed and investigated it is shown that the proposed method is a positive scheme the proposed method can be extended for other types of variable order fractional problems

a purification algorithm for semi infinite programming abstract in this paper we present a purification algorithm for semi infinite linear programming starting with a feasible point the algorithm either finds an improved extreme point or concludes with the unboundedness of the problem the method is based on the solution of a sequence of linear programming problems the study of some recession conditions has allowed us to establish a weak assumption for the finite convergence of this algorithm numerical results illustrating the method are given

on convergence of closed convex sets in this paper we introduce a convergence concept for closed convex subsets of a finite dimensional normed vector space this convergence is called c convergence it is defined by appropriate notions of upper and lower limits we compare this convergence with the well known painleve kuratowski convergence and with scalar convergence in fact we show that a sequence an n n c converges to a if and only if the corresponding support functions converge pointwise except at relative boundary points of the domain of the support function of a to the support function of a

fluctuations impact on a pattern forming model of population dynamics with non local interactions a model of interacting random walkers is presented and shown to give rise to patterns consisting in periodic arrangements of fluctuating particle clusters the model represents biological individuals that die or reproduce at rates depending on the number of neighbors within a given distance we evaluate the importance of the discrete and fluctuating character of this particle model on the pattern forming process to this end a deterministic mean field description including a linear stability and a weakly nonlinear analysis is given and compared with the particle model the deterministic approach is shown to reproduce some of the features of the discrete description in particular the existence of a finite wavelength instability stochasticity in the particle dynamics however has strong effects in other important aspects such as the parameter values at which pattern formation occurs or the nature of the homogeneous phase

soc in a population model with global control abstract we study a plant population model introduced recently by wallinga oikos 74 1995 377 it is similar to the contact process simple epidemic directed percolation but instead of using an infection or recovery rate as control parameter the population size is controlled directly and globally by removing excess plants we show that the model is very closely related to directed percolation dp anomalous scaling laws appear in the limit of large populations small densities and long times these laws associated critical exponents and even some non universal parameters can be related to those of dp as in invasion percolation and in other models where the roles of control and order parameters are interchanged the critical value pc of the wetting probability p is obtained in the scaling limit as singular point in the distribution of removal rates we show that a mean field type approximation leads to a model studied by zhang et al j stat phys 58 1990 849 finally we verify the claim of wallinga that family extinction in a marginally surviving population is governed by dp scaling laws and speculate on applications to human mitochondrial dna

evolution on a smooth landscape we study in detail a recently proposed simple discrete model for evolution on smooth landscapes an asymptotic solution of this model for long times is constructed we find that the dynamics of the population is governed by correlation functions that although being formally down by powers ofn the population size nonetheless control the evolution process after a very short transient the long time behavior can be found analytically since only one of these higher order correlators the two point function is relevant we compare and contrast the exact findings derived herein with a previously proposed phenomenological treatment employing mean field theory supplemented with a cutoff at small population density finally we relate our results to the recently studied case of mutation on a totally flat landscape

generalized viscoelastic models their fractional equations with solutions recently fractional calculus fc has encountered much success in the description of complex dynamics in particular fc has proved to be a valuable tool to handle viscoelastic aspects in this paper we construct fractional rheological constitutive equations on the basis of well known mechanical models especially the maxwell the kelvin voigt the zener and the poynting thomson model to this end we introduce a fractional element in addition to the standard purely elastic and purely viscous elements as we proceed to show many of the fractional differential equations which we obtain by this construction method admit closed form analytical solutions in terms of fox h functions of the minag leffler type

competitive brownian and levy walkers population dynamics of individuals undergoing birth and death and diffusing by short or long range two dimensional spatial excursions gaussian jumps or l evy flights is studied competitive interactions are considered in a global case in which birth and death rates are influenced by all individuals in the system and in a nonlocal but finite range case in which interaction affects individuals in a neighborhood we also address the noninteracting case in the global case one single or few cluster configurations are achieved with the spatial distribution of the bugs tied to the type of diffusion in the l evy case long tails appear for some properties characterizing the shape and dynamics of clusters under nonlocal finite range interactions periodic patterns appear with periodicity set by the interaction range this length acts as a cutoff limiting the influence of the long l evy jumps so that spatial configurations under the two types of diffusion become more similar by dividing initially everyone into different families and following their descent it is possible to show that mixing of families and their competition is greatly influenced by the spatial dynamics

persistence of instanton connections in chemical reactions with time dependent rates the evolution of a system of chemical reactions can be studied in the eikonal approximation by means of a hamiltonian dynamical system the fixed points of this dynamical system represent the different states in which the chemical system can be found and the connections among them represent instantons or optimal paths linking these states we study the relation between the phase portrait of the hamiltonian system representing a set of chemical reactions with constant rates and the corresponding system when these rates vary in time we show that the topology of the phase space is robust for small time dependent perturbations in concrete examples and state general results when possible this robustness allows us to apply some of the conclusions on the qualitative behavior of the autonomous system to the time dependent situation

letter to the editor on borwein s paper adjoint process duality we give counterexamples for some statements of borwein and sufficient conditions for the validity of these

flutter analysis of a flag of fractional viscoelastic material we develop a two dimensional model to study the effects of the material viscoelasticity on the dynamics of a flag in flow two periodic states of an elastic flag are firstly identified with different dimensionless bending stiffness a lower frequency state and a higher frequency state the scott blair model and the fractional kelvin voigt model are further used to represent the viscoelasticity of the flag material when the scott blair model is used with the increase of the fractional derivative order the flag flapping frequency of the higher frequency state decreases abruptly and that of the lower frequency state also shows a downward trend when the system parameters are in a certain range an interesting phenomenon is observed where the time needed to achieve the periodic steady state initially increases and then decreases with increasing the phenomenon implies that the flag has a higher energy harvesting speed when approaches 1 when the fractional kelvin voigt model is used the increasing also causes the transition from the higher frequency state to the lower frequency state and quasi periodic states are observed during the transition the fractional kelvin voigt type viscoelasticity produces complex effects on the lower frequency state

duality gaps in semi infinite linear programming an approximation problem this paper builds upon the relationship between the objective function of a semi infinite linear program and its constraints to identify a class of semi infinite linear programs which do not have a duality gap the key idea is to guarantee the approximation of the primal program by a sequence of linear programs where thenth approximating program is to minimize the objective function subject to the firstn constraints the paper goes on to show that any program not in the identified class can be linearly perturbed into it with the optimal value of the perturbed program converging to the optimal value of the original program the results are then extended to the case when an uncountable number of constraints are present by reducing this case to the countable case

continuity and differentiability properties of convex operators this paper provides some theorems on the generic differentiability of convex operators between topological vector spaces these results are applied to give new conditions for subgradients of convex operators to be non empty and well behaved limiting examples are given

a note on d stability of convex problems and limiting lagrangians in this paper we give a criterion for d stability of convex programs and a perturbation result which subsume and generalize some recent results in semi infinite programming and limiting lagrangians

simulation of flexible filaments in a uniform flow by the immersed boundary method an improved version of the immersed boundary ib method is developed for simulating flexible filaments in a uniform flow the proposed ib method is based on an efficient navier stokes solver adopting the fractional step method and a staggered cartesian grid system the fluid motion defined on an eulerian grid and the filament motion defined on a lagrangian grid are independently solved and their interaction force is explicitly calculated using a feedback law a direct numerical method is developed to calculate the filament motion under the constraint of inextensibility when applied to the case of a swinging filament analogous to a rope pendulum the proposed method gave results very similar to those of the analytical solution derived using the perturbation method for a flexible filament flapping in a uniform flow the mechanism by which small vortex processions are produced was investigated the bistable property of the system was observed by altering the filament length and the effects of the boundary condition at the fixed end simply supported or clamped were studied for two side by side filaments in a uniform flow both in phase flapping and out of phase flapping were reproduced in the present simulations a repulsive force was included in the formulation to handle collisions between the free ends of side by side filaments undergoing out of phase flapping

a one phase algorithm for semi infinite linear programming we present an algorithm for solving a large class of semi infinite linear programming problems this algorithm has several advantages it handles feasibility and optimality together it has very weak restrictions on the constraints it allows cuts that are not near the most violated cut and it solves the primal and the dual problems simultaneously we prove the convergence of this algorithm in two steps first we show that the algorithm can find ane optimal solution after finitely many iterations then we use this result to show that it can find an optimal solution in the limit we also estimate how good ane optimal solution is compared to an optimal solution and give an upper bound on the total number of iterations needed for finding ane optimal solution under some assumptions this algorithm is generalized to solve a class of nonlinear semi infinite programming problems applications to convex programming are discussed

adjoint process duality we study convex processes between topological vector spaces with particular emphasis on their adjoints this study is then applied to produce general duality results for classes of convex programs involving processes the use of processes allows one to exploit the symmetry of linear programming and to obtain significantly broader and stronger results

diffusion reproduction processes interesting physics emerges from studying a population of reproducing individuals each can be regarded as a random walker but it can either duplicate or die novel features of the collective behavior are quite surprising if individuals reproduce or die freely the life expectation is proportional to the size of the population and if it is kept constant the center of mass moves in space as if it were a single walker i e the diffusion constant is independent of population s size biology inspired interactions are also considered

weaker conditions for subdifferential calculus of convex functions abstract in this paper we establish new rules for the calculus of the subdifferential mapping of the sum of two convex functions our results are established under conditions which are at an intermediate level of generality among those leading to the hiriart urruty and phelps formula hiriart urruty and phelps 1993 15 involving the approximate subdifferential and the stronger assumption used in the well known moreau rockafellar formula rockafellar 1970 23 moreau 1966 20 which only uses the exact subdifferential we give an application to derive asymptotic optimality conditions for convex optimization

direct theorems in semi infinite convex programming we show that a semi infinite quasi convex program with certain regularity conditions possesses finitely constrained subprograms with the same optimal value this result is applied to various problems