integral equation theory for fluids ordered by an external field separable interactions the structural and thermodynamical properties of classical fluids orientationally ordered by an external field are investigated by means of integral equation theories a general theoretical framework for handling these theories is developed and detailed for the particular case of separable interactions between fluid particles this approach is then illustrated for the case of two off lattice models the ferromagnetic heisenberg model and a simple liquid crystal model for which the numerical solution of integral equations such as the percus yevick the hypernetted chain and the reference hypernetted chain closure equations are presented and compared with monte carlo simulation results and the analytical solution of the mean spherical approximation the zero field case is also examined and the spontaneous ordering is analyzed in detail mainly in what concerns the appearance of infinite wavelength singularity in the ornstein zernike equation and the relation with the one body closure equations and the long range orientational ordering that occurs in particular it is shown that the wertheim one body closure equation appears as a sum rule compatible with the ornstein zernike equation the relation between the elastic constant and the long range tail of the pair correlation function is made explicit in particular the long range behavior of the various terms in the expansion of the pair correlation function is depicted the numerical investigation of the two models shows that it is not possible to discriminate between the four integral equations as to which one would be the most accurate in all cases the general trends in the thermodynamical and structural properties seem to indicate that the percus yevick approximation is generally better in the strong ordering case whereas the reference hypernetted chain approximation might be better suited to the study of the isotropic phase and the low ordering regimes

orthogonal polynomial approach to fluids with internal degrees of freedom the case of nonpolar polarizable molecules the molecules of real liquids have internal degrees of freedom that may couple with the external ones of position and orientation so that they affect and are affected by the microscopic liquid structure for cases where the internal coordinates possess a boltzmann like distribution a procedure is described whereby such coordinates can be incorporated into the conventional formulation of classical liquid theory with no approximations beyond some reliable closure relation familiar from simple liquids the basis of the procedure is expansions in appropriate orthogonal polynomials of the internal coordinates this program is successfully carried out for a classical model of nonpolar polarizable molecules treated as drude oscillators generalizing published solutions of the mean spherical approximation for the same model

integral equation and simulation studies of the heisenberg spin fluid in an external magnetic field we develop a general method to study inhomogeneous liquids in an external field using orthogonal polynomials tailored to the one body density the procedure makes integral equation calculations of these systems no more difficult than those of ordinary homogeneous molecular fluids we apply this method to the ferromagnetic heisenberg spin fluid in an external magnetic field using both the reference hypernetted chain closure and a reference version of the zerah hansen closure with no further approximations the calculation includes a mapping of the two phase region for several values of the external magnetic field comparison with monte carlo simulation data shows the integral equation procedure yielding nearly exact results in particular for nonzero external fields s1063 651x 98 15109 7

travelling wavefronts in the diffusive single species model with allee effect and distributed delay in this paper we consider the diffusive single species model with allee effect and distributed delay time special attention is paid to the existence of travelling wavefront solutions first we shall show that such fronts exist when the convolution kernel assumes the strong generic delay kernel and the delay is sufficiently small then in the non local spatial terms which account for the drift of individuals to their present position from their possible positions at previous times we shall show that such fronts still exist for the weak generic delay kernel and small delay the approach used in this paper is the geometric singular perturbation theory

traveling waves for competitive lotka volterra systems with spatial diffusions and spatio temporal delays abstract this paper is concerned with the existence of traveling waves for reaction diffusion equations with spatio temporal delays our approach is to use the cross iteration technique and schauder s fixed point theorem the iterative technique can be established for a class of integral operators when the reaction terms satisfy new monotonicity conditions which is different from those in previous works the results can be well applied to a two species competitive lotka volterra system with more general kernel functions in order to overcome the difficulty of spatio temporal delays we need to use a basic result from a pde textbook existence of traveling waves which connect the trivial equilibrium and the positive equilibrium indicates that there is a transition zone moving the steady state with no species to the steady state with the coexistence of two species our results can extend some existing ones for two species diffusion competitive lotka volterra systems

wave front solutions of a diffusive delay model for populations of daphnia magna abstract in this paper we consider a diffusional food limited population model incorporating a discrete time delay for the case when the delay is small we show that monotone travelling front solutions exist connecting the two uniform steady states of the model the effect of a larger delay is studied numerically suggesting that in this case travelling fronts still exist but lose their monotonicity

multidimensional rovella like attractors in a joint work with a castro v pinheiro both from federal univ of bahia and m j pacifico federal university of rio de janeiro we construct a multidimensional flow exhibiting a rovella like attractor a compact transitive invariant set with an equilibrium accumulated by regular orbits and a partially hyperbolic splitting of the tangent bundle with a multidimensional non uniformly expanding direction moreover this attractor has a physical measure with full support which is a u gibbs state as in the 3 dimensional rovella attractor this example is not robust this introduces a class of multidimensional dynamics where benedicks carleson arguments can be applied to get persistent non uniform expansion

global stability of wavefronts with minimal speeds for nonlocal dispersal equations with degenerate nonlinearity abstract this paper is concerned with the global stability of wavefronts with minimal speeds for degenerate nonlocal dispersal equations by the method of super and subsolutions and a squeezing technique the wavefront with minimal speed is proved to be globally asymptotically stable with phase shift

travelling wave and global attractivity in a competition diffusion system with nonlocal delays in this paper we are concerned with a two competition model described by a reaction diffusion system with nonlocal delays which account for the drift of individuals to their present position from their possible positions at previous times by using the iterative technique recently developed in wang et al 2006 14 the sufficient conditions are established for the existence of travelling wave solutions connecting the semi trivial steady state to the coexistence steady state of the considered system when the domain is bounded we investigate the global attractivity of the coexistence steady state of the system under homogeneous neumann boundary conditions as well the approach used is the upper lower solutions and monotone iteration technique

entire solutions in bistable reaction diffusion equations with nonlocal delayed nonlinearity this paper is concerned with entire solutions for bistable reaction diffusion equations with nonlocal delay in one dimensional spatial domain here the entire solutions are defined in the whole space and for all time t r assuming that the equation has an increasing traveling wave solution with nonzero wave speed and using the comparison argument we prove the existence of entire solutions which behave as two traveling wave solutions coming from both ends of the x axis and annihilating at a finite time furthermore we show that such an entire solution is unique up to space time translations and is liapunov stable a key idea is to characterize the asymptotic behavior of the solutions as t in terms of appropriate subsolutions and supersolutions in order to illustrate our main results two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are considered

stability of steady states and existence of travelling waves in a vector disease model in this paper a host vector model is considered for a disease without immunity in which the current density of infectious vectors is related to the number of infectious hosts at earlier times spatial spread in a region is modelled in the partial integro differential equation by a diffusion term for the general model we first study the stability of the steady states using the contracting convex sets technique when the spatial variable is one dimensional and the delay kernel assumes some special form we establish the existence of travelling wave solutions by using the linear chain trick and the geometric singular perturbation method

spreading speed and wavefronts for parabolic functional differential equations with spatio temporal delays the existence of traveling wavefronts and the spreading speed for a kind of general reaction diffusion system with spatio temporal delays are investigated we obtain the conclusion that there is c 0 being the asymptotic speed of spread and the minimal speed for the system some more delicate analysis techniques have been developed to make the forms of the kernel function g t x and the function f more flexible in our paper a pair of super solution and sub solution have been constructed in order that the existence of traveling wavefronts can be guaranteed there is a biological model as an example in this article which is coincident with this system

traveling wavefronts for a time delayed non newtonian filtration equation abstract this paper is concerned with traveling wavefronts for the evolutionary p laplacian with time delay we first establish some necessary and sufficient conditions for the existence of monotone nondecreasing and nonincreasing traveling wavefronts which correspond to definite wave speeds c 1 and c 2 respectively moreover special attention is also paid to the asymptotic behavior of traveling fronts connecting two uniform steady states

traveling waves for nonlinear cellular neural networks with distributed delays abstract in this paper we will establish the existence and nonexistence of traveling waves for nonlinear cellular neural networks with finite or infinite distributed delays the dynamics of each given cell depends on itself and its nearest m left or l right neighborhood cells where delays exist in self feedback and left or right neighborhood interactions our approach is to use schauder s fixed point theorem coupled with upper and lower solutions of the integral equation in a suitable banach space further we obtain the exponential asymptotic behavior in the negative infinity and the existence of traveling waves for the minimal wave speed by the limiting argument our results improve and cover some previous works

invasion traveling wave solutions of a predator prey system abstract this paper is concerned with the traveling wave solutions of a predator prey system in which intra specific conflictions are involved by using the comparison principle and the asymptotic speed of spreading the existence nonexistence and minimal wave speed of non negative traveling wave solutions are established such a traveling wave solution can model the spatial temporal process where the predator invades the territory of the prey and they eventually coexist

the dynamics of the henon map the purpose of this paper is to develop machinery which is suitable for a study of the long time behavior of systems such as the henon map with expansion combined with strong contraction our study is modeled on the treatment of the one dimensional system x 1 ax 2 and we study the perturbation of a from the value a 2 and b small a surprising number of complications arise when b 0 the computer simulations give some indication of the complicated structure of the attractor but it can safely be stated that the real difficulties do not show up the central aim of the paper is to introduce what we consider the relevant concepts and techniques needed to study mappings such as the henon one

on the existence of traveling waves for delayed reaction diffusion equations abstract we study the existence of traveling wave solutions for reaction diffusion equations with nonlocal delay where reaction terms are not necessarily monotone the existence of traveling wave solutions for reaction diffusion equations with nonlocal delays is obtained by combining upper and lower solutions for associated integral equations and the schauder fixed point theorem the smoothness of upper and lower solutions is not required in this paper

possible new strange attractors with spiral structure we define a class of three dimensional differential equations which might present strange attractors of a new kind this is illustrated by numerical observations on an explicit example

absolutely continuous invariant measures for one parameter families of one dimensional maps given a one parameter familyf x of maps of the interval 0 1 we consider the set of parameter values for whichf has an invariant measure absolutely continuous with respect to lebesgue measure we show that this set has positive measure for two classes of maps i f x f x where 0 4 andf x is a functionc3 near the quadratic mapx 1 x and ii f x f x mod 1 wheref isc3 f 0 f 1 0 andf has a unique nondegenerate critical point in 0 1

asymptotic behavior and traveling wave solutions for parabolic functional differential equations on presente une generalisation de la theorie des equations kpp et de diffusion bistables non lineaires on montre que des solutions onde de propagation existent pour des equations fonctionnelles paraboliques non lineaires

wavefronts and global stability in a time delayed population model with stage structure we formulate and study a one dimensional single species diffusive delay population model the time delay is the time taken from birth to maturity without diffusion the delay differential model extends the well known logistic differential equation by allowing delayed constant birth processes and instantaneous quadratically regulated death processes this delayed model is known to have simple global dynamics similar to that of the logistic equation through the use of a sub supersolution pair method we show that the diffusive delay model continues to generate simple global dynamics this has the important biological implication that quadratically regulated death processes dramatically simplify the growth dynamics we also consider the possibility of travelling wavefront solutions of the scalar equation for the mature population connecting the zero solution of that equation with the positive steady state our main finding here is that our fronts appear to be all monotone regardless of the size of the delay this is in sharp contrast to the frequently reported findings that delay causes a loss of monotonicity with the front developing a prominent hump in some other delay models

traveling waves for monotone or non monotone equations with nonlocal delays in a cylinder abstract this paper is devoted to the study of mono stable and bistable traveling waves for monotone or non monotone equations with nonlocal time delays in a cylinder when the time delay is finite the existence of the traveling wave solutions is established by appealing to the theory of monotone semi flows for the monotone equation and the fixed point theory coupled with upper lower solutions method for the non monotone equation when the time delay is infinite the finite delay approximations method is used to obtain the existence of the traveling waves

continuum percolation of simple fluids energetic connectivity criteria abstract during the last few years a number of works in computer simulation have focused on the clustering and percolation properties of simple fluids based on an energetic connectivity criterion proposed long ago by t l hill j chem phys 23 1955 617 this connectivity criterion appears to be the most appropriate in the study of gas liquid phase transition so far integral equation theories have relayed on a velocity averaged version of this criterion we show by using molecular dynamics simulations that this average strongly overestimates percolation densities in the lennard jones fluid making unreliable any prediction based on it additionally we use a recently developed integral equation theory phys rev e 61 2000 r6067 to show how this velocity average can be overcome

existence and nonexistence of monotone traveling waves for the delayed fisher equation abstract in this paper a new approach based on a shooting method in a half line coupled with the technique of upper lower solution pair is used to study the existence and nonexistence of monotone waves for one form of the delayed fisher equation that does not have the quasimonotonicity property a necessary and sufficient condition is provided this new method can be extended to investigate many other nonlocal and non monotone delayed reaction diffusion equations

a reaction diffusion model for a single species with age structure i travelling wavefronts on unbounded domains in this paper we derive the equation for a single species population with two age classes and a fixed maturation period living in a spatially unbounded environment we show that if the mature deat

delay induced traveling wave fronts in reaction diffusion equations of kpp fisher type this paper explores the impact of delay on the existence of traveling wave fronts in reaction diffusion equations of kpp fisher type for two such equations one being local and the other with nonlocal effect arising from the age structure of the population we show that delay can induce slow traveling wave fronts

travelling wave fronts in reaction diffusion systems with spatio temporal delays this paper deals with the existence of travelling wave fronts in reaction diffusion systems with spatio temporal delays our approach is to use monotone iterations and a nonstandard ordering for the set of profiles of the corresponding wave system new iterative techniques are established for a class of integral operators when the reaction term satisfies different monotonicity conditions following this the existence of travelling wave fronts for reaction diffusion systems with spatio temporal delays is established finally we apply the main results to a single species diffusive model with spatio temporal delay and obtain some existence criteria of travelling wave fronts by choosing different kernels

traveling wavefronts for delayed reaction diffusion systems via a fixed point theorem abstract by using schauder s fixed point theorem we prove some existence results for traveling wavefronts of reaction diffusion systems with quasimonotonicity reactions more precisely we reduce the existence of traveling wavefronts to the existence of an admissible pair of supersolution and subsolution which are easy to construct in practice finally to illustrate our main results we study the existence of traveling wavefronts for a delayed predator prey model with diffusion as well as the reaction diffusion system with the well known belousov zhabotinskii reaction and the obtained results improve the existing ones

traveling waves for a nonlocal anisotropic dispersal equation with monostable nonlinearity abstract this paper is concerned with traveling wave solutions of the equation u t j u u f u on r 0 where the dispersion kernel j is nonnegative and the nonlinearity f is monostable type we show that there exists c r such that for any c c there is a nonincreasing traveling wave solution with 1 and lim e 1 where 1 c is the smallest positive solution to c r j z e z d z 1 f 0 furthermore the existence of traveling wave solutions with c c is also established for c 0 we further prove that the traveling wave solution is unique up to translation and is globally asymptotically stable in certain sense

dynamical analysis of a logistic equation with spatio temporal delay this paper is concerned with a logistic equation with spatio temporal delay the local asymptotic behavior of positive constant steady state solution of the equation is considered in particular by using the iterative technique sufficient conditions are established for the existence of traveling wave front solution connecting the zero and the positive constant steady state solution finally numerical simulations supporting the theoretical analysis are also included

hopf bifurcation analysis in a diffusive food chain model with time delay in this paper we consider the direction and stability of time delay induced hopf bifurcation in a three species food chain model with diffusion by means of analyzing eigenvalue spectrum and lyapunov functional we show that the positive equilibrium is asymptotically stable in the absence of time delay but loses its stability via the hopf bifurcation when the time delay increases beyond a threshold using the norm form and the center manifold theory we investigate the stability and direction of the hopf bifurcation the instability of the hopf bifurcation leads to the emergence of spatial patterns numerical calculations are performed to illustrate our theoretical results

infinite modal maps with global chaotic behavior we prove that certain parametrized families of one dimensional maps with infinitely many critical points exhibit global chaotic behavior in a persistent way for a positive lebesgue measure set of parameter values the map is transitive and almost every orbit has positive lyapunov exponent an application of these methods yields a proof of existence and even persistence of global spiral attractors for smooth flows in three dimensions to be given in 5

entire solutions in nonlocal dispersal equations with bistable nonlinearity abstract we consider entire solutions of nonlocal dispersal equations with bistable nonlinearity in one dimensional spatial domain a two dimensional manifold of entire solutions which behave as two traveling wave solutions coming from both directions is established by an increasing traveling wave front with nonzero wave speed furthermore we show that such an entire solution is unique up to space time translations and liapunov stable a key idea is to characterize the asymptotic behaviors of the solutions as t in terms of appropriate subsolutions and supersolutions we have to emphasize that a lack of regularizing effect occurs

travelling waves of a diffusive kermack mckendrick epidemic model with non local delayed transmission we obtain full information about the existence and non existence of travelling wave solutions for a general class of diffusive kermack mckendrick sir models with non local and delayed disease transmission we show that this information is determined by the basic reproduction number of the corresponding ordinary differential model and the minimal wave speed is explicitly determined by the delay such as the latent period and non locality in disease transmission and the spatial movement pattern of the infected individuals the difficulty is the lack of order preserving property of the general system and we obtain the threshold dynamics for spatial spread of the disease by constructing an invariant cone and applying schauder s fixed point theorem

traveling waves in a nonlocal dispersal population model with age structure abstract this paper is concerned with the traveling waves in a single species population model which is derived by considering the nonlocal dispersal and age structure if the birth function is monotone then the existence of traveling wavefront is reduced to the existence of a pair of super and subsolutions without the requirement of smoothness it is proved that the traveling wavefront is strictly increasing and unique up to a translation the asymptotic behavior of traveling wavefronts is also obtained if the birth function is not monotone the existence of traveling wave solution is affirmed by introducing two auxiliary nonlocal dispersal equations with quasi monotonicity

pyramidal traveling fronts in a nonlocal delayed diffusion equation abstract recently there have been great progresses on the study of nonplanar traveling wave solutions of reaction diffusion equations in this paper we study the pyramidal traveling fronts of nonlocal delayed diffusion equation in r n with n 2 by using the comparison principle and establishing super and subsolution since the effect of nonlocal delay we show that nonlocal delayed diffusion equation in n dimensional space has a pyramidal traveling front u t x v x x n s t toward x n axis for each s c 0 in particular two dimensional traveling curved front and three dimensional pyramidal fronts for nonlocal delayed diffusion equation in r 2 and r 3 are also established respectively moreover we also extend our results to generally nonlocal delayed reaction diffusion equation

stability and hopf bifurcation in a diffusive logistic population model with nonlocal delay effect abstract a reaction diffusion model with logistic type growth nonlocal delay effect and dirichlet boundary condition is considered and combined effect of the time delay and nonlocal spatial dispersal provides a more realistic way of modeling the complex spatiotemporal behavior the stability of the positive spatially nonhomogeneous positive equilibrium and associated hopf bifurcation are investigated for the case of near equilibrium bifurcation point and the case of spatially homogeneous dispersal kernel

travelling waves in the nicholson s blowflies equation with spatio temporal delay abstract in this paper nicholson s blowflies equation with diffusion and delay is investigated by taking four different kinds of delay kernels and defining four corresponding characteristic equations the existence of travelling wave solutions for nicholson blowflies equation is obtained by employing the monotone iteration technique as well as the upper and lower solution method

percolation of clusters with a residence time in the bond definition integral equation theory we consider the clustering and percolation of continuum systems whose particles interact via the lennard jones pair potential a cluster definition is used according to which two particles are considered directly connected bonded at time t if they remain within a distance d the connectivity distance during at least a time of duration tau the residence time an integral equation for the corresponding pair connectedness function recently proposed by two of the authors phys rev e 61 r6067 2000 is solved using the orthogonal polynomial approach developed by another of the authors phys rev e 55 426 1997 we compare our results with those obtained by molecular dynamics simulations

spatial structures and periodic travelling waves in an integro differential reaction diffusion population model an integro differential reaction diffusion equation is proposed as a model for populations where local aggregation is advantageous but intraspecific competition increases as global populations increase it is claimed that this is inherently more realistic than the usual kind of reaction diffusion model for mobile populations three kinds of bifurcation from the uniform steady state solution are considered i to steady spatially periodic structures ii to periodic standing wave solutions and iii to periodic travelling wave solutions these correspond to aggregation and motion of populations

asymptotic stability of traveling wave fronts in nonlocal reaction diffusion equations with delay abstract this paper is concerned with the asymptotic stability of traveling wave fronts of a class of nonlocal reaction diffusion equations with delay under monostable assumption we prove that the traveling wave front is exponentially stable by means of the technical weighted energy method when the initial perturbation around the wave is suitable small in a weighted norm the exponential convergent rate is also obtained finally we apply our results to some population models and obtain some new results which recover complement and or improve a number of existing ones

traveling wavefronts in diffusive and cooperative lotka volterra system with delays existence of traveling wave front solutions is established for diffusive and cooperative lotka volterra system with delays the result is an extension of an existing result for delayed logistic scaler equation to systems and is somewhat parallel to the existing result for diffusive and competitive lotka volterra systems without delay the approach used in this paper is the upper lower solution technique and the monotone iteration recently developed by wu and zou j dynam differential equations 13 2001 651 687 for delayed reaction diffusion systems without the so called quasimonotonicity 2002 elsevier science usa all rights reserved

traveling wave fronts for generalized fisher equations with spatio temporal delays we study the existence of traveling wave fronts for a reaction diffusion equation with spatio temporal delays and small parameters the equation reduces to a generalized fisher equation if small parameters are zero we present two results in the first one we deal with the equation with very general kernels and show the persistence of fisher wave fronts for all sufficiently small parameters in the second one we deal with some particular kernels with which the nonlocal equation can be reduced to a system of singularly perturbed odes and we are then able to apply the geometric singular perturbation theory and phase plane arguments to this system to show the existence of the minimal wave speed the existence of a continuum of wave fronts and the global uniqueness of the physical wave front with each wave speed

integral equation theory of polydisperse colloidal suspensions using orthogonal polynomial expansions a procedure is described for the calculation of the generalized pair distribution function g r s s8 where s is a molecular random variable with distribution f s using generalized integral equations familiar from simple liquid theory the method is based on expansions of all s dependent functions in the orthogonal polynomials p j s associated with the weight f s and is computationally efficient to illustrate the procedure calculations are made for a charge stabilized polydisperse colloidal suspension with schulz distribution of diameters s the method can be immediately generalized to fluids with internal degrees of freedom for which f s must itself be self consistently determined s1063 651x 96 12610 6

monostable waves in a class of non local convolution differential equation abstract the current paper is devoted to the study of wave propagation dynamics for a class of convolution equation with monostable structure it is shown that this equation admits traveling wave solution connecting the zero steady state even when the nonlinear term of this equation is without monotonicity a sufficient condition for the traveling wave solution that converges to the positive steady state is also established

traveling waves for the diffusive nicholson s blowflies equation we consider traveling wave front solutions for the diffusive nicholson s blowflies equation on the real line the existence of such solutions is proved using the technique developed by j wu and x zou j dyn differ equations 13 3 2001 some numerical simulation using the iteration formula of wu and zou 7 is also provided

entire solutions in monostable reaction diffusion equations with delayed nonlinearity abstract entire solutions for monostable reaction diffusion equations with nonlocal delay in one dimensional spatial domain are considered a comparison argument is employed to prove the existence of entire solutions which behave as two traveling wave solutions coming from both directions some new entire solutions are also constructed by mixing traveling wave solutions with heteroclinic orbits of the spatially averaged ordinary differential equations and the existence of such a heteroclinic orbit is established using the monotone dynamical systems theory key techniques include the characterization of the asymptotic behaviors of solutions as t in term of appropriate subsolutions and supersolutions two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are given to illustrate main results

bistable wavefronts in a diffusive and competitive lotka volterra type system with nonlocal delays abstract a diffusive lotka volterra type model with nonlocal delays for two competitive species is considered the existence of a traveling wavefront analogous to a bistable wavefront for a single species is proved by transforming the system with nonlocal delays to a four dimensional system without delay furthermore in order to prove the asymptotic stability up to translation of bistable wavefronts of the system the existence regularity and comparison theorem of solutions of the corresponding cauchy problem are first established for the systems on r by appealing to the theory of abstract functional differential equations the asymptotic stability up to translation of bistable wavefronts are then proved by spectral methods in particular we also prove that the spreading speed is unique by upper and lower solutions technique from the point of view of ecology our results indicate that the nonlocal delays appeared in the interaction terms are not sensitive to the invasion of species of spatial isolation