observation of symmetry breaking state selection and sensitivity in a noisy electronic system abstract measurements of the time evolution of the statistical density as a control parameter is swept through a bifurcation point in the presence of additive noise are presented we have used these densities to study branch selectivity which results from a small additive interaction a universal time scale for all such processes is established the results are in good agreement with a recent theory

fluctuation slow down of the death of brownian particles in the case of movable traps the influence of trap diffusion on the fluctuation slow down of death of brownian particles discovered earlier in the case of stationary traps is analysed it is shown that fluctuation slow down also takes place with movable traps if the diffusion is slow enough

passage time statistics in a stochastic verhulst model using the stochastic paths perturbation approach analytic individual realizations of a stochastic verhulst model are introduced the escape of the unstable state is studied for any kind of noise from these individual realizations we infer from these paths the statistics of the first passage time distribution invoking the solution of an explicit equation with a random coefficient a stochastic population verhulst s dynamics with small perturbations of the wiener class is explicitly worked out the method can also be implemented for other type of stochastic perturbations like poisson noise shot white pulses etc

transitions and kinematics of reaction convection fronts in a cell population model abstract here we consider cell population dynamics in which there is a simultaneous proliferation and maturation the mathematical model of this process is formulated as a nonlinear first order partial differential equation for the cell density u t x in which there is retardation delay in the temporal t variable thus we consider a transient reaction convection equation in which the cell density is convected with maturation velocity r for localizedd initial perturbations the equation has positive and negative traveling front solutions positive fronts correspond to the invasion of the zero amplitude solution by a finite amplitude solution and negative fronts correspond to the reversed case three classes of fronts are found according to the strength of the convection velocity i for strong convection r 1 the fronts are simple translations of the initial data regardless of delay strength ii for weak convection r 1 two types of fronts exist a reaction convection fronts arise if the localized initial perturbation acts at a non zero maturation on the zero amplitude state and b convection fronts arise if the localized initial perturbation acts at zero maturation on a finite amplitude state for weak convection cases ii a and ii b a further classification arises according to whether the magnitude of the temporal delay is larger or smaller than a critical value b it is found that the critical delay b corresponds to the hopf bifircation of the reaction equation that is obtained in the absence of convection r 0 for delays larger than b the convective and reaction convection fronts are oscillatory in addition all the reaction convection fronts reverse their direction of motion undergo a positive to negative transition and display non uniform kinematics simulation results are validated and interpreted using solutions for the unretarded equations and by local stability analysis

blocks of cyclotomic hecke algebras abstract this paper classifies the blocks of the cyclotomic hecke algebras of type g r 1 n over an arbitrary field rather than working with the hecke algebras directly we work instead with the cyclotomic schur algebras the advantage of these algebras is that the cyclotomic jantzen sum formula gives an easy combinatorial characterization of the blocks of the cyclotomic schur algebras we obtain an explicit description of the blocks by analyzing the combinatorics of jantzen equivalence we remark that a proof of the classification of the blocks of the cyclotomic hecke algebras was announced in 1999 unfortunately cox has discovered that this previous proof is incomplete

fluctuations in reversible chemical reactions abstract the paper proposes a new approach to describe fluctuations of reversible chemical reactions in closed systems the deterministic rate laws are cast into the form of nonlinear onsager type closed laws by means of nonlinear transport theory a fokker planck equation describing the stochastic process of concentration fluctuations is obtained it is shown that the stochastic formulation reduces to the correct deterministic rate laws in the thermodynamic limit v with the concentrations kept fixed concrete examples of reactions in ideal mixtures are given and the results of the presented approach are compared with those of the usual approach by means of a birth and death type master equation it is shown that both approaches lead to the same stationary probability and exhibit the same natural boundaries reflecting the fact of a restricted state space the proposed fokker planck equation is different from the fokker planck equation obtained from the master equation by truncating its kramers moyal expansion however the two equations are shown to have identical fokker planck coefficients in the vicinity of the deterministic equilibrium state compared with the usual master equation approach the proposed stochastic modeling of chemical reactions has the advantage of allowing for a straightforward extension to reactions in non ideal mixtures

matrix units and generic degrees for the ariki koike algebras this paper uses the murphy basis of the ariki koike algebras to explicitly construct a complete set of primitive idempotents when these algebras are semisimple and q 1 as a consequence we obtain an explicit wedderburn basis for the ariki koike algebras finally we use these idempotents to compute the generic degrees of the ariki koike algebras

on the escape rate from a metastable state in a nonpotential system abstract the escape rate from a metastable state is computed for a nonpotential system described by a general multivariate fokker planck equation the result is a generalization of the escape rate obtained by other authors in the case of potential systems a straightforward application is found in the derivation of the grote hynes result for chemical rates in solution another characteristic application is the theory of nucleation in nonlinear chemical systems far from equilibrium which has been developed in a previous paper of the authors without a proper derivation of the nucleation rate formula j stat phys 50 1988 935

the density profile for the klein kramers equation near an absorbing wall we derive asymptotic series for the expansion coefficients of a function in terms of the pagani functions which occur in the boundary layer solutions of the klein kramers equation the results enable us to determine the density profile in the stationary solution of this equation near an absorbing wall from the numerically determined velocity distribution at the wall with an accuracy of about 2 we also obtain information about the analytic behavior of the density profile this profile increases near the wall with the square root of the distance to the wall finally the asymptotic analysis leads to an understanding of the slow convergence of variational approximations to the solution of the absorbing wall problem and of the exponents that occur when one studies the variational approximations to various quantities of interest as functions of the number of terms in the variational ansatz this is used to obtain a better variational estimate for the density at the wall

analytical representations of the spread harmonic measure density we study the spread harmonic measure that characterizes the spatial distribution of reaction events on a partially reactive surface for euclidean domains in which brownian motion can be split into independent lateral and transverse displacements we derive analytical formulas for the spread harmonic measure density and analyze its asymptotic behavior this analysis is applicable to slab domains general cylindrical domains and a half space we investigate the spreading effect due to multiple reflections on the surface and the underlying role of finite reactivity we discuss further extensions and applications of analytical results to describe laplacian transfer phenomena such as permeation through semipermeable membranes secondary current distribution on partially blocking electrodes and surface relaxation in nuclear magnetic resonance

projective injective modules serre functors and symmetric algebras we describe serre functors for generalisations of the category o associated with a semisimple complex lie algebra in our approach projective injective modules that is modules which are both

random walks on lattices with randomly distributed traps i the average number of steps until trapping for a random walk on a lattice with a random distribution of traps we derive an asymptotic expansion valid for smallq for the average number of steps until trapping whereq is the probability that a lattice point is a trap we study the case of perfect traps where the walk comes to an end and the extension obtained by letting the traps be imperfect i e by giving the walker a finite probability to remain free when stepping on a trap several classes of random walks of varying dimensionality are considered and special care is taken to show that the expansion derived is exact up to and including the last term calculated the numerical accuracy of the expansion is discussed

first passage time problems for one dimensional random walks this note contains a development of the theory of first passage times for one dimensional lattice random walks with steps to nearest neighbor only the starting point is a recursion relation for the densities of first passage times from the set of lattice points when these densities are unrestricted the formalism allows us to discuss first passage times of continuous time random walks when they are negative exponential densities we show that the resulting equation is the adjoint of the master equation this is the lattice analog of a correspondence well known for systems describable by a fokker planck equation finally we discuss first passage problems for persistent random walks in which at each step the random walker continues in the same direction as the preceding step with probability a or reverses direction with probability 1

diffusion in a bistable potential abstract the problem of diffusion of a particle in a bistable potential is studied on the basis of the one dimensional smoluchowski equation for the space and time dependent probability distribution the potential is modeled as two parabolic wells separated by a parabolic barrier for the model potential the smoluchowski equation is solved exactly by a laplace transform with respect to time for the initial condition that at time zero the probability distribution is given by a thermal equilibrium distribution in one of the wells in the limit of a high barrier the rate of transition to the other well is given by an asymptotic result due to kramers for a potential barrier of moderate height there are significant corrections to the asymptotic result

proof of the modular branching rule for cyclotomic hecke algebras abstract we prove the modular branching rule of the cyclotomic hecke algebras which has remained open

q tensor space and q weyl modules we obtain the irreducible representations of the q schur algebra motivated by the fact that these representations give all the irreducible representations of gln q in the nondescribing characteristic the irreducible polynomial representations of the general linear groups in the describing characteristic are a special case of this construction the theory of polynomial representations of general linear groups is equivalent to the representation theory of schur algebras see green s book 5 and the bibliography therein in 4 we defined q analogues of schur algebras when q 1 these are the usual schur algebras and when q is a prime power representations of q schur algebras give a substantial part of the representation theory of finite general linear groups in the nondescribing characteristic case including all irreducible representations of these groups and important information about decomposition numbers it is natural to ask what features of the classical schur algebras have qanalogues in this paper we define q analogues of tensor space of weyl modules and of weight spaces thereby generalizing the main reslllts which appear in green s book 5 for example we classify the irreducible modules for qschur algebras we determine bases for q weyl modules compatible with weight spaces and we give results on composition multiplicities of the irreducible modules in q weyl modules the proofs are largely self contained so by specializing q to 1 we recover the corresponding results in 5 this paper therefore is relevant to the representation theory of symmetric groups and to the representation theory of general linear groups in the describing and in the nondescribing characteristics 1 the q schur algebra let r be a natural number let r be an integral domain and let q be a unit in r we denote the symmetric group on r letters by er the hecke algebra z is the r free r algebra with basis twlw e er where the multiplication is determined by the following rule if a i i 1 is a basic transposition in received by the editors august 15 1989 1980 mathematics subject classification 198 5 revision primary 1 6a64 1 6a6 5 secondary 20c30 this research was supported in part by nsf grant no dms 8802290 the authors gratefully acknowledge support received from nato grant no 0222 87 r 1991 american mathematical society 0002 9947 91 1 00 25 per page

escape by diffusion from a square well across a square barrier abstract the problem of escape of a particle by diffusion from a square potential well across a square barrier is studied on the basis of the one dimensional smoluchowski equation for the space and time dependent probability distribution for the model potential the smoluchowski equation is solved exactly by a laplace transform with respect to time in the limit of a high barrier the rate of escape is given by an asymptotic result similar to that derived by kramers for a curved well and a curved barrier an approximate analytic formula is derived for the outward time dependent probability current in terms of the width and depth of the well and the width and height of the barrier a similar expression holds for the complete probability distribution

the kinetic boundary layer for the klein kramers equation a new numerical approach we explore a numerical technique for determining the structure of the kinetic boundary layer of the klein kramers equation for noninteracting brownian particles in a fluid near a wall that absorbs the brownian particles the equation is of interest in the theory of diffusion controlled reactions and of the coagulation of colloidal suspensions by numerical simulation of the langevin equation equivalent to the klein kramers equation we amass statistics of the velocities at the first return to the wall and of the return times for particles injected into the fluid at the wall with given velocities the data can be used to construct the solutions of the standard problems at an absorbing wall the milne and the albedo problem we confirm and extend earlier results by burschka and titulaer obtained by a variational method vexed by the slow convergence of the underlying eigenfunction expansion we briefly discuss some further boundary layer problems that can be attacked by exploiting the results reported here

on fluctuations and relaxation in systems described by a one dimensional fokker planck equation with a time dependent potential abstract we study the effect of a time variation of a bistable potential on kramers relaxation and on suzuki s fluctuation enhancement for a system described by a one variable fokker planck equation in the limit of a small constant diffusion coefficient we show that the two processes must be described with two different approximations 1 i kramers relaxation can be treated in a quasi adiabatic scheme we then show that for a large range of potential modulation rates the local populations in each well obey adiabatic balance equations the solution of which we discuss in various limits 2 ii suzuki s description of the fluctuation enhancement can be extended to the dynamical case we reformulate the technique set up by ahlers et al to describe the crossing of the bifurcation from a mono to a bistable potential we show that the extended suzuki approximation is valid provided that the crossing velocity is larger than a limit which we estimate

symmetric cyclotomic hecke algebras abstract in this paper we prove that the generic cyclotomic hecke algebras for imprimitive complex reflection groups are symmetric over any ring containing inverses of the parameters for this we show that the determinant of the gram matrix of a certain canonical symmetrizing form introduced by k bremke and g malle indag math 8 1997 453 469 is a unit in any such ring on the way we show that the ariki koike bases of these algebras are also quasi symmetric

half range completeness for the fokker planck equation half range completeness theorems are proved for eigenfunctions associated to the one dimensional fokker planck equation in a semi infinite medium existence and uniqueness results for perfectly absorbing partially absorbing and purely specularly reflecting boundary conditions are deduced for the stationary and time dependent problems similar results are obtained for a slab geometry

the kinetic boundary layer for the fokker planck equation with absorbing boundary the fokker planck equation for the distribution of position and velocity of a brownian particle is a particularly simple linear transport equation its normal solutions and an apparently complete set of stationary boundary layer solutions can be determined explicitly by a numerical algorithm we select linear combinations of them that approximately fulfill the boundary condition for a completely absorbing plane wall and that approach a linearly increasing position space density far from the wall various aspects of these approximate solutions are discussed in particular we find that the extrapolated asymptotic density reaches zero at a distance xm beyond the wall we find xm 1 46 in units of the velocity persistence length of the brownian particle this study was motivated by certain problems in the theory of diffusion controlled reactions and the results might be used to test approximate theories employed in that field

q analogues of clifford and weyl algebras spinor and oscillator representations of quantum enveloping algebras we introduceq analogues of clifford and weyl algebras using these we construct spinor and oscillator representations of quantum enveloping algebras of typean 1 bn cn dn andan 1 1 also we discuss the irreducibility and the unitarity of these representations

global stability of a partial differential equation with distributed delay due to cellular replication in this paper we investigate a nonlinear partial differential equation arising from a model of cellular proliferation this model describes the production of blood cells in the bone marrow it is represented by a partial differential equation with a retardation of the maturation variable and a distributed temporal delay our aim is to prove that the behaviour of primitive cells influences the global behaviour of the population

asymptotic behavior for a cellular replication and maturation model abstract we consider a nonlocal first order partial differential equation with time delay that models simultaneous cell replication and maturation processes we establish a comparison principle and construct monotone sequences to show the existence and uniqueness of the solution to the equation we then analyze the asymptotic behavior of the solution via upper lower solution technique

koszul duality patterns in representation theory the aim of this paper is to work out a concrete example as well as to provide the general pattern of applications of koszul duality to repre sentation theory the paper consists of three parts relatively independent of each other the first part gives a reasonably selfcontained introduction to koszul rings and koszul duality koszul rings are certain z graded rings with particularly nice homological properties which involve a kind of duality thus to a koszul ring one associates naturally the dual koszul ring the second part is devoted to an application to representation theory of semisimple lie algebras we show license or copyright restrictions may apply to redistribution see http www ams org journal terms of use koszul duality patterns 527 that the block of the bernstein gelfand gelfand category o that corresponds to any fixed central character is governed by the koszul ring moreover the dual of that ring governs a certain subcategory of the category o again this generalizes the selfduality theorem conjectured by beilinson and ginsburg in 1986 and proved by soergel in 1990 in the third part we study certain cate gories of mixed perverse sheaves on a variety stratified by affine linear spaces we provide a general criterion for such a category to be governed by a koszul ring in the flag variety case this reduces to the setup of part two in the more general case of affine flag manifolds and affine grassmannians the criterion should yield interesting results about representations of quantum groups and affine lie algebras department of mathematics massachusetts institute of technology cambridge massachusetts 02139 e mail address sasha math mit edu department of mathematics the university of chicago chicago illinois 60637 e mail address ginzburg math uchicago edu max planck institut fur mathematik gottfried claren strase 26 d 53 bonn 3 germany current address mathematisches institut universitat freiburg albertstrase 23b d 79104 freiburg germany e mail address soergel sun1 mathematik uni freiburg de license or copyright restrictions may apply to redistribution see http www ams org journal terms of use

modified kramers formulas for the decay rate in agreement with dynamical modeling abstract accuracy of the kramers approximate formulas for the thermal decay rate of the metastable state is studied for the anharmonic shapes of the potential pocket and the barrier this is done by the comparison with the quasistationary rate resulting from the dynamical modeling disagreement between the kramers rate and the dynamical one is shown to reach 15 in the cases when much better agreement is expected corrections to the kramers formulas accounting for the higher derivatives of the potential are obtained the small parameters are the ratios of the thermal energy to the stiffnesses at the extremes of the potential the distance between the potential barrier and the absorptive border is accounted for as well this corrected kramers rate is demonstrated to agree with the dynamical rate typically within 2 probably the most interesting result is that despite the corrections are derived in the case of the overdamped brownian motion the above 2 agreement holds even in the case of medium friction

transient survival probability of a particle diffusing in a disordered system of perfectly absorbing spherical sinks abstract the transient survival probability of a particle diffusing in a disordered system of perfectly absorbing non overlapping spherical sinks is studied by use of a self consistent cluster expansion for its laplace transform the self consistent cluster expansion which in principle is exact is formulated in two alternative versions corresponding to different ways of handling the instantaneous absorption of particles created initially inside a sink in each version of the theory the cluster expansion is truncated at either the singlet or the pair level so that four different approximations to the exact result are obtained an approximation on the pair level constitutes an improvement to the corresponding singlet approximation it is shown that at moderate volume fraction of the sink system the two pair approximations yield almost identical results for the survival probability all four approximations lead to a band gap in the spectrum of relaxation rates followed by a continuum extending to infinity

a singular perturbation approach to kramers diffusion problem we consider kramers diffusion problem which seeks to calculate the rate of escape of a particle from one potential well over a barrier to another presumably deeper and therefore more stable well though kramers introduced the problem as a model for chemical reactions it applies to numerous rate processes including atomic migration and ionic conductivity in crystals and transitions due to noise between stable states of dynamical systems with multi stable states to name but a few we propose a new approach not based on a fokker planck equation but rather on the solution of a singularly perturbed boundary value problem specifically we relate the rate of escape to the first passage time from the domain of attraction of the stable point corresponding to the first well the first passage time is then characterized via the ito calculus as a solution of an elliptic partial differential equation of singular perturbation type finally this equation is solved asymptotically by methods previously develop

functional integral approach for diffusion in a random media the authors present a local functional integral representation for the random diffusion equation studied by kardar parisi and zhang 1986

diffusion effusion and chaotic scattering an exactly solvable liouvillian dynamics we study diffusion and chaotic scattering in a chain of baker maps coupled together which forms an area preserving mapping of an infinitely extended strip onto itself this exactly solvable mapping sustains chaotic behaviors and diffusion processes the relationship between the diffusion coefficient the lyapunov exponent and the entropy per unit time is derived the long lived classical resonances of the liouville evolution operator are proved to converge toward the eigenvalues of the phenomenological diffusion equation in this sense there is a quasi isomorphism between the resonance spectrum of the liouville evolution and the eigenvalue spectrum of the phenomenological diffusion equation furthermore we show that a fractal repeller is associated to each non equilibrium state in the isolated and finite multibaker chain the nonequilibrium states are all unstable with respect to the equilibrium validating a weak form of the second principle of thermodynamics for the present dynamical system consequences of nonequilibrium fractals on classical measurements are discussed we then describe the open multibaker chain as a scattering system fractal properties of chaotic scattering are here shown to be related to diffusion in the chain

tilting modules for cyclotomic schur algebras this paper investigates the tilting modules of the cycloto mic q schur alge bras the young modules of the ariki koike algebras and the interconnections between them the main tools used to understand the tilting modules are contragredient duality and the specht filtrations and dual specht filtrations of cert ain permutation modules sur prisingly weyl filtrations which are in general more power ful than specht filtrations play only a secondary role

a phase transition in the dynamics of an exact model for hopping transport the authors analyse an exact model for hopping transport of a random walker in the presence of randomly distributed deep trapping sites for an exponential distribution of the depth of traps they find a phase transition in the diffusive behaviour as a function of temperature they show that above a critical temperature transport is purely diffusive while below it one finds anomalous diffusion characterised by a diffusion exponent that increases with decreasing temperature the analysis combines theory with accurate simulation in one and two dimensions the analytical and numerical results indicate that the upper critical dimension is dc 2 i e for d or dc 2 the mean field theory can be applied

symmetric structure for the endomorphism algebra of projective injective module in parabolic category abstract we show that for any singular dominant integral weight of a complex semisimple lie algebra g the endomorphism algebra b of any projective injective module of the parabolic bgg category o p is a symmetric algebra as conjectured by khovanov extending the results of mazorchuk and stroppel for the regular dominant integral weight moreover the endomorphism algebra b is equipped with a homogeneous non degenerate symmetrizing form in the appendix there is a short proof due to k coulembier and v mazorchuk showing that the endomorphism algebra b p of the basic projective injective module of o p is a symmetric algebra

weights of multipartitions and representations of ariki koike algebras abstract we consider representations of the ariki koike algebra a q deformation of the group algebra of the complex reflection group c r s n the representations of this algebra are naturally indexed by multipartitions of n and for each multipartition we define a non negative integer called the weight of we prove some basic properties of this weight function and examine blocks of small weight

flux to a trap the flux of particles to a single trap is investigated for two systems 1 particles in 3d space which jump a fixed step lengthl the rayleigh flight and are adsorbed by a spherical surface and 2 particles on a lattice jumping to nearest neighbor sites with a single adsorbing site initially the particles are uniformly distributed outside the traps when the jump length goes to zero both processes go over to regular diffusion and the first case yields the diffusive flux to a sphere as solved by smoluchowski for nonzero step length the flux for large times is given by a modified form of smoluchowski s result with the effective radius replaced byr cl wherec 0 29795219 andcl is the milne extrapolation length for this problem for the second problem a similar expression for the flux is found with the effective trap radius a function of the lattice sc bcc fcc being considered

asymptotic behavior and convergence of solutions of a semilinear transport equation with delay this paper analyses the behavior and convergence of the solutions for a generalized singular transport equation which arises as a model of the blood production system by using the characteristic theory of first order partial differential equations and iterative methods

trapping of random walks on the line several features of the trapping of random walks on a one dimensional lattice are analyzed the results of this investigation are as follows 1 the correction term to the known asymptotic form for the survival probability ton steps is o 2n 1 3 where ln 1 c andc is the trap concentration 2 the short time form for the survival probability is found to be exp a c n1 2 wherea c is given in eq 21 3 the mean square displacement of a surviving random walker is found to go liken2 3for largen 4 when the distribution of trap free regions is changed so that very large regions are much rarer than for ideally random trap placement the asymptotic survival probability changes its dependence onn one such model is studied

overview of theoretical models for reaction rates there is enormous recent interest in the development of models for rate processes because rates are an almost universal characterization in the physical and biological sciences in this paper we provide an introduction to several of the problems to be discussed in greater depth by other speakers at a symposium held at the national institutes of health on may 6 8 1985 this review will focus on 1 the smoluchowski model for reaction rates together with its extension by onsager 2 first passage time formalism for discrete and continuous master equations and fokker planck equations 3 the kramers model and its extensions 4 diffusion in the presence of trapping centers

first passage time problems for a class of master equations with separable kernels abstract we discuss first passage time problems for a class of one dimensional master equations with separable kernels for this class of master equations the integral equation for first passage time moments can be transformed exactly into ordinary differential equations when the separable kernel has only a single term the equation for the mean first passage time obtained is exactly that for simple diffusion the boundary conditions however differ from those appropriate to simple diffusion the equations for higher moments differ slightly from those for simple diffusion analysis is presented of a generalization of a model of a random walk with long range jumps first investigated by lindenberg and shuler since the equations can be solved exactly one can study the behavior of boundary conditions in the continuum limit the generalization to a larger number of terms in the separable kernel leads to higher order equations for the first passage time moments in each case boundary conditions can be found directly from the original master equation

subdiffusion in a bounded domain with a partially absorbing reflecting boundary the exit time of a subdiffusive process from a bounded domain with a partially absorbing reflecting boundary is considered the short time and long time behaviors of the exit time probability density are investigated by using a spectral decomposition on the basis of the laplace operator eigenfunctions rotation invariant domains are analyzed in depth in order to illustrate the use of theoretical formulas and to compare them to numerical simulations the asymptotic results obtained are relevant for describing subdiffusion inside a living cell with a semipermeable membrane in a chemical reactor filled with catalytic grains of finite reactivity or in mineral or biological samples which are probed by nuclear magnetic resonance measurements subject to surface relaxation

propagation of population pulses and fronts in a cell replication problem non locality and dependence on the initial function abstract here we study the solution types in a simplified equation arising from a cell population dynamics model formulated as a non linear first order partial differential equation for the cell density u t x in the presence of non local maturational x interactions this can be considered as a reaction convection equation in which the cell density is convected with maturation velocity r the non local action affects only the reaction birth rate an initial function representing a pulse of small amplitude on an almost extinguished population may be dissipated may produce multiple pulses or may remain intact as it travels driven by reaction and convection depending on the magnitude of the non local action alternately for localized initial perturbations the equation also has positive traveling front solutions positive fronts correspond to the invasion of the zero amplitude solution by a finite amplitude solution for weak convection r 1 which is the only case treated here reaction driven fronts arise if the localized initial perturbation acts at a non zero maturation on the zero amplitude state a classification arises according to whether the magnitude of the maturation delay is larger or smaller than a critical value and scaling arguments are used to determine the critical delay for delays larger than critical the reaction driven fronts are oscillatory and correspond to the case for which the correlation length for non local action is of the same order as the characteristic length of maturation population gradients that yield oscillatory birth rates simulation results are validated and interpreted using scaling arguments and solutions for the local equations

localized partial traps in diffusion processes and random walks reaction diffusion equations in which the reaction is described by a sink term consisting of a sum of delta functions are studied it is shown that the laplace transform of the reactive green s function can be analytically expressed in terms of the green s function for diffusion in the absence of reaction moreover a simple relation between the green s functions satisfying the radiation boundary condition and the reflecting boundary condition is obtained several applications are presented and the formalism is used to establish the relationship between the time dependent geminate recombination yield and the bimolecular reaction rate for diffusion influenced reactions finally an analogous development for lattice random walks is presented