scaling of reaction fronts under quenched disorder abstract the dynamics of fronts in diffusion limited reactions a b c with initially segregated reactants in strongly disordered media is studied the scaling of the front width w in the asymptotic limit w t is analyzed as a function of the disorder strength and spatial dimensionality d we show that exponent a in d dimensions is a monotonic decreasing function of disorder strength as measured from diffusive properties of reactants we also find that a has a mean field behavior for d 2 scaling anomalies are observed in related quantities such as nearest neighbor distance midpoint fluctuations and concentration profiles of reactants near the center of the front

internal diffusion limited aggregation parallel algorithms and complexity the computational complexity of internal diffusion limited aggregation dla is examined from both a theoretical and a practical point of view we show that for two or more dimensions the problem of predicting the cluster from a given set of paths is complete for the complexity class cc the subset of p characterized by circuits composed of comparator gates cc completeness is believed to imply that in the worst case growing a cluster of size n requires polynomial time in n even on a parallel computer a parallel relaxation algorithm is presented that uses the fact that clusters are nearly spherical to guess the cluster from a given set of paths and then corrects defects in the guessed cluster through a nonlocal annihilation process the parallel running time of the relaxation algorithm for two dimensional internal dla is studied by simulating it on a serial computer the numerical results are compatible with a running time that is either polylogarithmic in n or a small power of n thus the computational resources needed to grow large clusters are significantly less on average than the worst case analysis would suggest for a parallel machine with k processors we show that random clusters in d dimensions can be generated in mathcal o n k logk n 2 d steps this is a significant speedup over explicit sequential simulation which takes mathcal o n 1 2 d time on average finally we show that in one dimension internal dla can be predicted in mathcal o logn parallel time and so is in the complexity class nc

applications of field theoretic renormalization group methods to reaction diffusion problems we review the application of field theoretic renormalization group rg methods to the study of fluctuations in reaction diffusion problems we first investigate the physical origin of universality in these systems before comparing rg methods to other available analytic techniques including exact solutions and smoluchowski type approximations starting from the microscopic reaction diffusion master equation we then pedagogically detail the mapping to a field theory for the single species reaction ka a k we employ this particularly simple but non trivial system to introduce the field theoretic rg tools including the diagrammatic perturbation expansion renormalization and callan symanzik rg flow equation we demonstrate how these techniques permit the calculation of universal quantities such as density decay exponents and amplitudes via perturbative dc d expansions with respect to the upper critical dimension dc with these basics established we then provide an overview of more sophisticated applications to multiple species reactions disorder effects l evy flights persistence problems and the influence of spatial boundaries we also analyse field theoretic approaches to non equilibrium phase transitions separating active from absorbing states we focus particularly on the generic directed percolation universality class as well as on the most prominent exception to this class even offspring branching and annihilating random walks finally we summarize the state of the field and present our perspective on outstanding problems for the future

two species annihilation in three dimensions a numerical study two species diffusion limited annihilation in less than four dimensions is well known to have a concentration decaying as t d4 as opposed to the rate equation result of t 1 this result had not however been demonstrated numerically in three dimensions due to very strong transient effects a variant of the model is proposed here and is shown to reach the exactly known asymptotic behaviour in numerically accessible times this also allows one to investigate open questions in this system with some certainty that the results are indeed asymptotic in particular it is shown that the distance between two particles of the same species scales identically to the distance between particles of different species this is in contradistinction to recent numerical and scaling results in one and two dimensions some evidence is also presented that contrary to previous suggestions the domains formed in three dimensional two species annihilation are indeed regular objects with smooth interfaces

scaling of reaction zones in the a b 0 diffusion limited reaction we study reaction zones in three different versions of the a b 0 system for a steady state formed by opposing currents of a and b particles we derive scaling behavior via renormalization group analysis by use of a previously developed analogy these results are extended to the time dependent case of an initially segregated system we also consider an initially mixed system which forms reaction zones for dimension d 4 in this case an extension of the steady state analogy gives scaling results characterized by new exponents

classification of phase transitions in reaction diffusion models equilibrium phase transitions are associated with rearrangements of minima of a lagrangian potential treatment of nonequilibrium systems requires doubling of degrees of freedom which may be often interpreted as a transition from the coordinate to the phase space representation as a result one has to deal with the hamiltonian formulation of the field theory instead of the lagrangian one we suggest a classification scheme of phase transitions in reaction diffusion models based on the topology of the phase portraits of corresponding hamiltonians in models with an absorbing state such a topology is fully determined by intersecting curves of zero energy we identify four families of topologically distinct classes of phase portraits stable upon renormalization group transformations

some generalizations of the trapping problem abstract we consider two effects on kinetics that have not generally been taken into account in analyses of classical trapping models for the reactions a t t and a t 0 the effects due to correlations in the initial positions of the a s and those due to the state of mobility of each of the species our analysis is formulated in terms of three dimensional brownian motion we give a heuristic treatment of the short time regime based on statistical properties of the wiener sausage the effects of initially correlated positions are modelled in terms of a set of a multiplicity of a particles located at the origin

inhomogeneous two species annihilation in the steady state the authors investigate steady state geometrical properties of a reaction interface in the two species annihilation process a b to 0 when a flux j of a and b particles is injected at opposite extremities of a finite domain by balancing the input flux with the number of reactions they determine that the width w of the reaction zone scales as j 1 3 in the large flux limit and that the concentration in this zone is proportional to j2 3 this same behaviour is deduced from the solution to the reaction diffusion equation in the low flux limit the concentration is almost independent of position and is proportional to j in the latter case the local reaction rate reaches maximum at the edges of the system rather than at the midpoint when the two species approach at a finite velocity there exists a critical velocity above which the reactants essentially pass through each other results similar to those in one dimension are found in two and three dimensional radial geometries finally they apply the quasistatic approximation to their steady state solution to recover the known time dependence for the reaction zone width for the case of initially separated components with no external input

universal properties of the ma nb o diffusion limited reaction abstract the ma nb o diffusion limited reaction with homogeneous initial condition is studied analytically and numerically through renormalization group arguments it is shiown that the system exhibits the anomalous kinetic behavior below the critical dimension d c 4 m n 1 asymptotic behavior of the density below the critical dimension is universal and is predicted to be t d 4 in d dimensions irrespective of the reaction type m n these predictions are compared with the numerical simulations in one dimensions

erratum renormalization group study of the a b φ diffusion limited reaction a recent argument of oerding shows that our calculation of the quantity which determines the amplitude of the asymptotic decay of the particle density in 2 d 4 was in error instead it is simply given by n0 the initial density for uncorrelated initial conditions

possibilities and limitations of gaussian closure approximations for phase ordering dynamics the nonlinear equations describing phase ordering dynamics can be closed by assuming the existence of an underlying gaussian stochastic field which is nonlinearly related to the observable order parameter field we discuss the relation between different implementations of the gaussian assumption and consider the limitations of this assumption for phase ordering dynamics the fact that the different approaches gives different results is a sign of the breakdown of the gaussian assumption we concentrate on the non conserved order parameter case but also touch on the conserved order parameter case we demonstrate that the gaussian assumption is fundamentally flawed in the latter case

existence characterizations of temporal safety supervisors this note shows that beyond the expected basic results on supervisor existence and synthesis the temporal logic systems analysis for the invariance control of an arbitrary past formula p yields new insights into supremal control of temporal safety these insights come in the form of equivalent temporal characterizations one characterization allows a natural language interpretation which provides a very good intuitive feel of the supremal controllability concept another provides a structurally elegant representation revealing that the past formula p must never be stronger than some fixed logic constant importantly from the control synthesis viewpoint these temporal characterizations provide the opportunity to use several industrial strength commercially available theorem provers to accomplish the synthesis task in a transparent fashion finally a controllable canonical form unifying the supremal exact and infimal existences of temporal safety control is exhibited and its theoretical significance is discussed

adiabatic liouvillean in the theory of diffusion limited recombination i a regular method of deriving the governing adiabatic liouvillean on a lattice for a many body system of locally and instantaneously recombining particles in reaction a b to 0 is described when the rate u of the recombination tends to infinity u to infinity the local reaction liouvillean is shown to be replaced with a non local operator involving renormalized matrix elements which are proportional to slow diffusive jump rates properties of the new liouvillean are described quantum field formalism is employed

spatial organization in two species annihilation the spatial structure of reactants in the two species annihilation reaction a b 0 is described in one dimension we investigate the distribution of domain sizes and the distributions of nearest neighbor distances between particles of the same and of opposite species the latter two quantities are characterized by a new length scale which is intermediate to the domain size t1 2 and the typical interparticle spacing t1 4 a scaling argument suggests that the typical distance between particles of opposite species or equivalently the gaps between domains grows ast with 3 8 and 1 3 respectively in spatial dimensiond 1 and 2 the average density profile of a single domain is spatially nonuniform with the density decaying to zero linearly as the domain edge is approached this behavior permits a determination of the distribution of nearest neighbor distances of same species reactants the corresponding moments of this distribution exhibit multiscaling which involves geometric averages of different powers of the domain size and the interparticle spacing

syntax based synthesis for temporal safety supervision this paper presents a supremal control generalization of a temporal version of supervisory control for temporal safety in discrete event systems the generalization is an outcome of the development of a temporal logic equations approach formulated using unary transformer concepts borrowed mainly from the predicate and predicate transform theory of dijkstra and scholten the proposed syntax based approach has not hitherto been formally augmented to the temporal logic framework and is shown to parallel and to generalize the boolean equations approach proposed in the existing predicate control theory of kumar garg and marcus a detailed example which cannot be handled by the existing predicate control theory demonstrates how the natural language basis of temporal logic for requirement specification and syntax based control synthesis can be unified in a common logic framework

asymptotic form of the approach to equilibrium in reversible recombination reactions the reversible reactions and are investigated from the exact langevin equations describing our model we set up a systematic approximation scheme to compute the approach of the density of c particles to its equilibrium value we show that for a sufficiently long time t this approach takes the form of a power law for any dimension d the amplitude a is also computed exactly but is expected to be model dependent for uncorrelated initial conditions the c density turns out to be a monotonic time function the cases of correlated initial conditions and unequal diffusion constants are investigated as well in the former correlations may break the monotonicity of the density or in some special cases they may change the long time behaviour for the latter the power law remains valid only the amplitude changes even in the extreme case of immobile c particles we also consider the case of segregated initial condition for which a reaction front is observed and confirm that its width is governed by mean field exponent in any dimension

on the evaluation of r chapman s evil determinant abstract we prove a conjecture of r chapman asserting that for any prime p 3 mod 4 the determinant of the p 1 2 p 1 2 matrix c c ij with c ji j i p is always 1

nearest neighbour distances of diffusing particles from a single trap we present a simple method for obtaining the typical smallest distance from an absorbing trap to the nearest particle in a system of brownian particles in terms of the overall density profile we also obtain the distribution function for the minimum distance by using a quasistatic approximation for the diffusion equation we derive new results for two dimensions the characteristic distance to the nearest particle increases asymptotically as m the technique is useful in diffusion reaction systems in the smoluchowski model for bimolecular reactions an ideal spherical trap centred at the origin is surrounded by a cloud of brownian particles which are captured upon contact with the trap the reaction rate in this formulation depends on the spatial distribution of particles about the trap recently interest has focused on finer details of this distribution such as the distance of the nearest surviving particle from the trap l 31 the density distribution function of that distance is the key to several exact results concerning some diffusion reaction systems in one dimension 4 while the spatial density of the particles surrounding the trap can be easily obtained by solving a diffusion equation with the appropriate boundary conditions the distance to the nearest particle from the trap seems to require a more sophisticated analysis 13 in this paper we suggest a simple derivation for the typical distance from the trap to the nearest particle and of the distribution of those distances based upon the more readily attainable spatial density of all particles and simple facts from the statistics of extremes 5 6 to demonstrate our method we rederive the known results for one and three dimensions the simplicity of our approach together with using a quasistatic approximation 7 for solving the diffusion equation allows us to solve the two dimensional case for the first time consider first the one dimensional problem a perfect trap is located at the origin and is initially surrounded by a homogeneous density co of brownian particles which diffuse with a diffusion constant d the density c x t of the surviving particles to the right of the trap is given by the diffusion equation

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

modular feedback logic for discrete event systems we examine a modular approach to the synthesis of state feedback controls for the problem of maintaining a predicate on the state set of a discrete dynamic system invariant dynamical systems are modeled by automata together with a mechanism for enabling and disabling a subset of state transitions the basic problem of interest is to ensure by appropriate control action that a given predicate on the state set of the process remains invariantly true whenever it is initially satisfied assuming the predicate can be decomposed into the conjunction or disjunction of component predicates we determine conditions under which it is possible to synthesize the appropriate control in a modular fashion

diffusion controlled reaction a b c with initially separated reactants we review recent developments in the study of diffusion reaction systems of the type a b c in which the reactants are initially separated we consider two initial boundary conditions i the a and b particles are initially placed uniformly in euclidean space at x 0 and x 0 respectively and ii the a particles are diffusing and inserted at a given site and the b particles are static and distributed uniformly in space we present analytical and numerical results for both systems we consider d 1 2 3 dimensional systems as well as fractal lattices

predicates and predicate transformers for supervisory control of discrete event dynamical systems discrete event systems are studied treating the state space as the fundamental modeling concept the control of discrete event systems using predicates and predicate transformers is treated predicates have the advantage that they can concisely characterize an infinite state space the notion of controllability of a predicate is defined and the supervisory predicate control problem is solved a closed form expression for the weakest controllable predicate is obtained the problem of controlling discrete event systems under incomplete state observation is also considered and observability of predicates is defined techniques for finding extremal solutions of boolean equations are used to derive minimally restrictive supervisors

shear flows and segregation in the reaction a b we study theoretically and numerically the effects of the linear velocity field mathrm v v 0 y stackrel mathrm x on the irreversible reaction a b ensuremath rightarrow ensuremath emptyset assuming homogeneous initial conditions for the two species with equal initial densities we demonstrate the presence of a crossover time t c ensuremath sim v 0 ensuremath 1 for t ensuremath ll v 0 ensuremath 1 the kinetics are unaffected by the shear and we retain both the effect of species segregation for dl4 and the density decay rate a t ensuremath ensuremath alpha where ensuremath alpha min frac d 4 1 we calculate the amplitude a to leading order in a small density expansion for 2l dl4 and give bounds in d 4 however for t ensuremath gg v 0 ensuremath 1 the critical dimension for anomalous kinetics is reduced to d c 2 with the density decay rate b t ensuremath 1 holding for dg 2 bounds are calculated for the amplitude b in d 2 which depend on the velocity gradient v 0 and the equal diffusion constants d we also briefly consider the case of a nonlinear shear flow where we give a more general form for the crossover time t c finally we perform numerical simulations for a linear shear flow in d 2 with results in agreement with theoretical predictions

path integral evaluation of the one loop effective potential in field theory of diffusion limited reactions abstract the well established effective action and effective potential framework from the quantum field theory domain is adapted and successfully applied to classical field theories of the doi and peliti type for diffusion controlled reactions through a number of benchmark examples we show that the direct path integral calculation of the effective potential in fixed space dimension d 2 to one loop order reduces to a small set of simple elementary functions irrespective of the microscopic details of the specific model thus the technique which allows one to obtain with little additional effort the potentials for a wide variety of different models represents an alternative to the standard model dependent diagram based calculations the renormalized effective potential effective equations of motion and the associated renormalization group equations are computed in d 2 spatial dimensions for a number of single species field theories of increasing complexity

a renormalization group study of a class of reaction diffusion models with particles input we study a class of reaction diffusion models extrapolating continuously between the pure coagulation diffusion case and the pure annihilation diffusion one with particles input at a rate j for dimension the dynamics strongly depends on the fluctuations while for d 2 the behaviour is mean field like the models are mapped onto a field theory whose properties are studied in a renormalization group approach simple relations are found between the time dependent correlation functions of the different models of the class for the pure coagulation diffusion model the time dependent density is found to be of the form where d is the diffusion constant the critical exponent and are computed to all orders in where d is the dimension of the system while the scaling function is computed to second order in for the one dimensional case an exact analytical solution is provided whose predictions are compared with the results of the renormalization group approach for

fractal growth by local sensitive epidemic model lsem simulating the internal feeding systems ifs abstract the fractal systems may be classified into two families which are distinguishable by a different nutrient feeding during their growth process for the internal feeding systems ifs the source is directly connected to the growing interface while for the external feeding systems efs it is placed far away so that the released particles have to execute random walks before adhering to the aggregate a generalized model nicknamed local sensitive epidemic model lsem is developed to unify the main models simulating the growth of the ifsystems by combining all their growth parameters gp and growth rules gr this model considers in addition i a particle interaction extended to the kth neighbour which may be attractive or repulsive ii a continuous updating of the local characteristics of the surrounding medium and iii an aggregate relaxation which tends to optimize the total energy during or after the growth process the coupled effects of all these parameters allow one to simulate the main fractal phases observed experimentally and to discuss the conditions under which they may be obtained as well as their different morphological transitions

cellular automata approach to pattern formation in reaction diffusion systems abstract the dynamics of reaction diffusion systems in low dimensions is often driven by fluctuations and a simple minded description in terms of rate equations is not sufficient moreover the emergence of complex patterns in such systems can involve simultaneously several new mechanisms as for example aggregation and precipitation we shall show that the properties of these complex systems can be well understood in the framework of a mesoscopic description based on cellular automata models

supervisory control of discrete event systems with ctl temporal logic specifications the supervisory control problem of discrete event systems with temporal logic specifications is studied the full branching time logic of ctl is used for expressing specifications of discrete event systems the control problem of ctl is reduced to the decision problem of ctl a small model theorem for the control of ctl is obtained it is shown that the control problem of ctl resp ctl is complete for deterministic double resp single exponential time a sound and complete supervisor synthesis algorithm for the control of ctl is provided special cases of the control of computation tree logic ctl and linear time temporal logic are also studied

asymptotic upper bound of density for two particle annihilating exclusion we consider a stochastic process which presents an evolution of particles of two types on d with annihilations between particles of opposite types initially at each site of d independently of the other sites we put a particle with probability 2 1 and assign to it one of two types with equal chances each particle independently from the others waits an exponential time with mean 1 chooses one of its neighboring sites on the lattice d with equal probabilities and jumps to the site chosen if the site to which a particle attempts to move is occupied by another particle of the same type the jump is suppressed if it is occupied by a particle of the opposite type then both are annihilated and disappear from the system the considered process may serve as a model for the chemical reaction a b inert the paper concerns an upper bound of t the density of particles in the system at timet we prove that t t for all 0 in the dimensionsd 4 and asymptotically t ct 1 in the higher dimensions in our proofs we used the ideas and the technique developed by bramson and lebowitz and the tools which are customarily used to study a symmetric exclusion process

some tractable supervisory control problems for discrete event systems modeled by buchi automata discrete event systems des are modeled by buchi automata together with a means of online control in this setting the concept of a controllable language is extended to infinite strings and conditions for the existence of a supervisor controller to implement a prescribed closed loop behavior are derived the focus is on a class of des called product systems these are des composed of a finite set of asynchronous components a control problem for such a system typically requires the synthesis of an online controller so as to achieve some prescribed coordinated behavior of the component subsystems one of the principal difficulties in this task is that the size of the state space increases exponentially with the number of components it is shown that despite this fact several interesting control synthesis problems for such systems are computationally feasible and algorithms are developed for solution

rare event statistics in reaction diffusion systems we present an efficient method to calculate probabilities of large deviations from the typical behavior rare events in reaction diffusion systems this method is based on a semiclassical treatment of an underlying quantum hamiltonian encoding the system s evolution to this end we formulate the corresponding canonical dynamical system and investigate its phase portrait this method is presented for a number of pedagogical examples

spatial structure in diffusion limited two particle reactions we analyze the limiting behavior of the densities a t and b t and the random spatial structure r a t b t for the diffusion controlled chemical reaction a b inert for equal initial densities b 0 b 0 there is a change in behavior fromd 4 where a t b t c td 4 tod 4 where a t b t c t ast the termc depends on the initial densities and changes withd there is a corresponding change in the spatial structure ind 4 both particle types are after large times present locally in concentrations not depending on type or location ind 4 both particle types are present locally but with random concentrations and the process tends to a limit

asymptotic behavior of the density for two particle annihilating exclusion we consider a stochastic process which presents an evolution of particles of two types a andb onzd with annihilations between particles of opposite types initially at each site ofzd independently of the other sites we put a particle with probability 2 1 and assign to it one of two types with equal chances each particle evolves onzd in the following manner independently from the others it waits an exponential time with mean 1 chooses one of its neighboring sites on the latticezd with equal probabilities and jumps to the site chosen if the site to which a particle attempts to move is occupied by another particle of the same type the jump is suppressed if it is occupied by a particle of the opposite type then both are annihilated and disappear from the system the considered process may serve as a model for the chemical reactiona b inert let t denote the density of particles in this process at timet we prove that there exist absolute finite constantsc d andc d such that for all sufficiently larget c d t d 4 t c d t d 4 in the dimensionsd 4 andc d t 1 t c d t 1 in all higher dimensions this completes and makes more precise the results obtained by us earlier and shows that asymptotically the density behaves like that in a similar process called two particle annihilating random walks which was studied by bramson and lebowitz our proofs are based on the approach developed in their and our works we use the basic properties of random walk and various tools which have been designed to study simple symmetric exclusion processes

controllability and control invariance in discrete event systems recently for discrete event systems modelled by automata ramadge and wonham 1987 a b have proposed two control techniques called supervisory control and state feedback logic if control specifications are given in terms of predicates on the set of states both techniques are applicable this paper discusses the relationship between these techniques it is shown that the language accepted by the discrete event system with maximally permissive feedback is equal to the supremal controllable language if the predicate is control invariant moreover it is shown that the predicate is control invariant if there exists a controllable language with a certain condition on the set of reachable states but the converse does not hold in general

gamow functionals on operator algebras we obtain the precise form of two gamow functionals representing the exponentially decaying part of a quantum resonance and its mirror image that grows exponentially as a linear positive and continuous functional on an algebra containing observables these functionals do not admit normalization and with an appropriate choice of the algebra are time reversal of each other

survival probability of a diffusing particle in the presence of poisson distributed mobile traps the problem of a diffusing particle moving among diffusing traps is analyzed in general space dimension d we consider the case where the traps are initially randomly distributed in space with uniform density ensuremath rho and derive upper and lower bounds for the probability q t averaged over all particle and trap trajectories that the particle survives up to time t we show that for 1l dl 2 the bounds converge asymptotically to give q t ensuremath sim mathrm exp ensuremath ensuremath lambda d t d 2 for 1l dl2 where ensuremath lambda d 2 ensuremath pi d mathrm sin ensuremath pi d 2 4 ensuremath pi d d 2 ensuremath rho and d is the diffusion constant of the traps and that q t ensuremath sim mathrm exp ensuremath 4 ensuremath pi ensuremath rho dt mathrm ln t for d 2 for dg2 bounds can still be derived but they no longer converge for large t for 1l dl 2 these asymptotic forms are independent of the diffusion constant of the particle the results are compared with simulation results obtained using a new algorithm v mehra and p grassberger phys rev e 65 050101 2002 which is described in detail deviations from the predicted asymptotic forms are found to be large even for very small values of q t indicating slowly decaying corrections whose form is consistent with the bounds we also present results in d 1 for the case where the trap densities on either side of the particle are different for this case we can still obtain exact bounds but they no longer converge

renormalization group study of thea b diffusion limited reaction thea b diffusion limited reaction with equal initial densitiesa 0 b 0 n0 is studied by means of a field theoretic renormalization group formulation of the problem for dimensiond 2 an effective theory is derived from which the density and correlation functions call be calculated we find the density decays in time as a b sim c sqrt delta dt d 4 ford 4 with n0 c n 0 d 2 wherec is a universal constant andc is nonuniversal the calculation is extended to the case of unequal diffusion constantsd a d b resulting in a new amplitude but the same exponent ford 2 a controlled calculation is not possible but a heuristic argument is presented that the results above give at least the leading term in an e 2 d expansion finally we address reaction zones formed in the steady state by opposing currents ofa andb particles and derive scaling properties

failure diagnosis of discrete event systems with linear time temporal logic specifications the paper studies failure diagnosis of discrete event systems dess with linear time temporal logic ltl specifications the ltl formulas are used for specifying failures in the system the ltl based specifications make the specification specifying process easier and more user friendly than the formal language automata based specifications and they can capture the failures representing the violation of both liveness and safety properties whereas the prior formal language automaton based specifications can capture the failures representing the violation of only the safety properties such as the occurrence of a faulty event or the arrival at a failed state prediagnosability and diagnosability of dess in the temporal logic setting are defined the problem of testing prediagnosability and diagnosability is reduced to the problem of model checking an algorithm for the test of prediagnosability and diagnosability and the synthesis of a diagnoser is obtained the complexity of the algorithm is exponential in the length of each specification ltl formula and polynomial in the number of system states and the number of specifications the requirement of nonexistence of unobservable cycles in the system which is needed for the diagnosis algorithms in prior methods to work is relaxed finally a simple example is given for illustration

control of vector discrete event systems i the base model a vector discrete event system vdes is a discrete event system model in which the system state is represented by a vector with integer components and state transitions by integer vector addition the authors investigate such structures from the viewpoint of control theory the objective is to specialize to vdes the general automation based control theory of p j ramadge and w m wonham 1987 and w m wonham and p j ramadge 1988 it is shown that within the vdes framework a useful class of control systems can be compactly modeled and some of the associated control problems of ramadge and wonham can be more efficiently solved

the dynamics of defect ensembles in one dimensional cellular automata we investigate the dynamics of ensembles of diffusive defects in one dimensional deterministic cellular automata the work builds on earlier results on individual random walks in cellular automata here we give a natural condition guaranteeing diffusive behavior also in the presence of other defects simple branching and birth mechanisms are introduced and prototype classes of cellular automata exhibiting weakly interacting walks capable of annihilation and coalescence are studied their equilibrium behavior is also characterized the design principles of cellular automata with desired diffusive interaction properties become transparent from this analysis

field theoretic treatment of an effective action for a model of catalyzed autoamplification reaction diffusion models can exhibit continuous phase transitions in behaviors and their dynamics at criticality often exhibit scalings with key parameters that can be characterized by exponents while models with only a single field that transitions between absorbing and nonabsorbing states are well characterized and typically fall in the directed percolation universality class the effects of coupling multiple fields remain poorly understood we recently introduced a model which has three fields one of which relaxes exponentially one of which displays critical behavior and one of which has purely diffusive dynamics but exerts an influence on the critical field tchernookov j chem phys 130 134906 2009 simulations suggested that this model is in a universality class distinct from other reaction diffusion systems studied previously although the three fields give rise to interesting physics they complicate analysis of the model with renormalization group methods here we show how to systematically simplify the action for this model such that analytical expressions for the exponents of this universality class can be obtained by standard means we expect the approach taken here to be of general applicability in reaction diffusion systems with coupled order parameters that display qualitatively different behaviors close to criticality

complex dynamics in initially separated reaction diffusion systems we review recent developments in the study of the diffusion reaction systems of the type a b c in which the reactants are initially separated we consider the case where the a and b particles are initially placed uniformly in euclidean space at x 0 and x 0 respectively we find that whereas for d 2 the mean field exponent characterizes the width of the reaction zone fluctuations are relevant in the one dimensional system we present analytical and numerical results for the reaction rate on fractals and percolation systems at criticality we also study the case where the particles are levy flights in d 1 finally we consider experimentally analytically and numerically the reaction a bstatic c where species a diffuses from a localized source

doi peliti path integral methods for stochastic systems with partial exclusion abstract doi peliti methods are developed for stochastic models with finite maximum occupation numbers per site we provide a generalized framework for the different fock spaces reported in the literature paragrassmannian techniques are then utilized to construct path integral formulations of factorial moments we show that for many models of interest a magnus expansion is required to construct a suitable action meaning actions containing a finite number of terms are not always feasible however for such systems perturbative techniques are still viable and for some examples including carrying capacity population dynamics and diffusion with partial exclusion the expansions are exactly summable

symmetry classes of alternating sign matrices under one roof in a previous article math co 9712207 we derived the alternating sign matrix asm theorem from the izergin korepin determinant for a partition function for square ice with domain wall boundary here we show that the same argument enumerates three other symmetry classes of alternating sign matrices vsasms vertically symmetric asms even htsasms half turn symmetric asms and even qtsasms quarter turn symmetric asms the vsasm enumeration was conjectured by mills the others by robbins math co 0008045 we introduce several new types of asms uasms asms with a u turn side uuasms two u turn sides osasms off diagonally symmetric asms oosasms off diagonally off antidiagonally symmetric and uosasms off diagonally symmetric with u turn sides uasms generalize vsasms while uuasms generalize vhsasms vertically and horizontally symmetric asms and another new class vhpasms vertically and horizontally perverse osasms oosasms and uosasms are related to the remaining symmetry classes of asms namely dsasms diagonally symmetric dasasms diagonally anti diagonally symmetric and tsasms totally symmetric asms we enumerate several of these new classes and we provide several 2 enumerations and 3 enumerations our main technical tool is a set of multi parameter determinant and pfaffian formulas generalizing the izergin korepin determinant for asms and the tsuchiya determinant for uasms solv int 9804010 we evaluate specializations of the determinants and pfaffians using the factor exhaustion method

field theory for a reaction diffusion model of quasispecies dynamics rna viruses are known to replicate with extremely high mutation rates these rates are actually close to the so called error threshold this threshold is in fact a critical point beyond which genetic information is lost through a second order phase transition which has been dubbed as the error catastrophe here we explore this phenomenon using a field theory approximation to the spatially extended swetina schuster quasispecies model j swetina and p schuster biophys chem 16 329 1982 a single sharp peak landscape in analogy with standard absorbing state phase transitions we develop a reaction diffusion model whose discrete rules mimic the swetina schuster model the field theory representation of the reaction diffusion system is constructed the proposed field theory belongs to the same universality class as a conserved reaction diffusion model previously proposed f van wijland et al physica a 251 179 1998 from the field theory we obtain the full set of exponents that characterize the critical behavior at the error threshold our results present the error catastrophe from a different point of view and suggest that spatial degrees of freedom can modify several mean field predictions previously considered leading to the definition of characteristic exponents that could be experimentally measurable

cluster mean field approximations with the coherent anomaly method analysis for the driven pair contact process with diffusion the cluster mean field approximations are performed up to 13 cluster sizes to study the critical behavior of the driven pair contact process with diffusion dpcpd and its precedent the pcpd in one dimension critical points are estimated by extrapolating our data to the infinite cluster size limit which are in good accordance with recent simulation results within the cluster mean field approximation scheme the pcpd and the dpcpd share the same mean field critical behavior the application of the coherent anomaly method however shows that the two models develop different coherent anomalies which lead to different true critical scaling the values of the critical exponents for the particle density the pair density the correlation length and the relaxation time are fairly well estimated for the dpcpd these results support and complement our recent simulation results for the dpcpd

anomalous coalescence phenomena under stationary regime condition through thompson s method abstract in this work anomalous coalescence phenomena of type a a a 0 are considered in the case of stationary regime namely the case of an external homogeneous source h of single particles a in the limit of zero external field rate the main purpose here is to pick up new critical exponents in the stationary regime for the phenomenon of anomalous coalescence of bubbles found in one dimension by josserand and rica jr phys rev lett 78 1997 1215 the critical exponents of statical concentration relaxation time and the exponent for concentration decay are evaluated in the limit h 0 zero field rate we show that such critical exponents depend on the parameter physica a 334 2004 335 which characterizes the anomalous diffusion condition in order to explain the anomalous coalescence of jr s work as already made before by the present author physica a 334 2004 335 the parameter must display an explicit dependence on the dimensionality d 4 d for d 2 we use such a result d in order to pick up new critical exponents for the special case of anomalous coalescence found by jr we find 5 4 5 and 1 4 in 1 d we also verify that the known scaling relations among such critical indexes phys rev a 32 2 1985 1129 are obeyed so that in the special case of 2 brownian diffusion condition given to mean field regime we naturally recover those results previously obtained by racz phys rev a 32 2 1985 1129 we go further to give a better explanation for such new results taking into account another exponent physica a 334 2004 335 to explain the behavior of diffusion constant which depends on concentration d d 0 n that is to say we obtain analytically new critical indexes which controll the diffusion behavior d for long time regime in the presence of an external homogeneous source

wilson renormalization of a reaction diffusion process abstract healthy and sick individuals a and b particles diffuse independently with diffusion constants da and db sick individuals upon encounter infect healthy ones at rate k but may also spontaneously recover at rate 1 the propagation of the epidemic therefore couples to the fluctuations in the total population density global extinction occurs below a critical value c of the spatially averaged total density the epidemic evolves as the diffusion reaction decay process a b 2b b a for which we write down the field theory the stationary state properties of this theory when da db were obtained by kree et al the critical behavior for da db remains unsolved

on the birational geometry of spaces of complete forms ii skew forms abstract moduli spaces of complete skew forms are compactifications of spaces of skew symmetric linear maps of maximal rank on a fixed vector space where the added boundary divisor is simple normal crossing in this paper we compute their effective nef and movable cones the generators of their cox rings and for those spaces having picard rank two we give an explicit presentation of the cox ring furthermore we give a complete description of both the mori chamber and stable base locus decompositions of the effective cone of some spaces of complete skew forms having picard rank at most four

asymptotics of reaction diffusion fronts with one static and one diffusing reactant abstract the long time behavior of a reaction diffusion front between one static e g porous solid reactant a and one initially separated diffusing reactant b is analyzed for the mean field reaction rate density r a b k a m b n a uniformly valid asymptotic approximation is constructed from matched self similar solutions in a reaction front of width w t where r t enters the dominant balance and a diffusion layer of width w t 1 2 where r is negligible the limiting solution exists if and only if m n 1 in which case the scaling exponents are uniquely given by m 1 2 m 1 and m m 1 in the diffusion layer the common ad hoc approximation of neglecting reactions is given mathematical justification and the exact transient decay of the reaction rate is derived the physical effects of higher order kinetics m n 1 such as the broadening of the reaction front and the slowing of transients are also discussed

non equilibrium phase transitions activated random walks at criticality in this paper we present rigorous results on the critical behavior of the activated random walk model we conjecture that on a general class of graphs including mathbb z d and under general initial conditions the system at the critical point does not reach an absorbing state we prove this for the case where the sleep rate lambda is infinite moreover for the one dimensional asymmetric system we identify the scaling limit of the flow through the origin at criticality the case lambda infty remains largely open with the exception of the one dimensional totally asymmetric case for which it is known that there is no fixation at criticality

three species diffusion limited reaction with continuous density decay exponents we introduce a model of three species two particle diffusion limited reactions or b or c and or a with three persistence parameters survival probabilities in reaction of the hopping particle we consider isotropic and anisotropic diffusion hopping with a drift in one dimension we find that the particle density decays as a power law for certain choices of the persistence parameter values in the anisotropic case on one symmetric line in the parameter space the decay exponent is monotonically varying between the values close to 1 3 and 1 2 on another less symmetric line the exponent is constant for most parameter values the density does not follow a power law we also calculated various characteristic exponents for the distance of nearest particles and domain structure our results support the recently proposed possibility that one dimensional diffusion limited reactions with a drift do not fall within a limited number of distinct universality classes

fluctuation effects and multiscaling of the reaction diffusion front for a b to oe we consider the properties of the diffusion controlled reaction a b to oe in the steady state where fixed currents of a and b particles are maintained at opposite edges of the system using renormalization group methods we explicitly calculate the asymptotic forms of the reaction front and particle densities as expansions in jd 1 mod x mod d 1 1 where j are the equal applied currents and d the equal diffusion constants for the asymptotic densities of the minority species we find in addition to the expected exponential decay fluctuation induced power law tails which for d 2 we find similar power laws with mu d 3 but with non universal coefficients logarithmic corrections occur in d 2 these results imply that in the time dependent case with segregated initial conditions the moments integral mod x mod qr x t dx fail to satisfy simple scaling for q mu 1 finally it is shown that the fluctuation induced wandering of the position of the reaction front centre may be neglected for large enough systems

asymptotic behavior of densities for two particle annihilating random walks consider the system of particles on d where particles are of two types a andb and execute simple random walks in continuous time particles do not interact with their own type but when ana particle meets ab particle both disappear i e are annihilated this system serves as a model for the chemical reactiona b inert we analyze the limiting behavior of the densities a t and b t when the initial state is given by homogeneous poisson random fields we prove that for equal initial densities a 0 b 0 there is a change in behavior fromd 4 where a t b t c t d 4 tod 4 where a t b t c tast for unequal initial densities a 0 b 0 a t e c l ind 1 a t e ct logt ind 2 and a t e ct ind 3 the termc depends on the initial densities and changes withd techniques are from interacting particle systems the behavior for this two particle annihilation process has similarities to those for coalescing random walks a a a and annihilating random walks a a inert the analysis of the present process is made considerably more difficult by the lack of comparison with an attractive particle system

scalings in diffusion driven reaction a b c numerical simulations by lattice bgk models we are interested in applying lattice bgk models to the diffusion driven reactive systema b c which was investigated by galfi and racz with an asymptotic analysis and by chopard and droz with a cellular automaton model the lattice bgk model is free from noise and flexible for various applications we derive the general reaction diffusion equations for the lattice bgk models under the assumption of local diffusive equilibrium two fourth order terms are derived and verified by numerical simulations the motivation of this study is to compare the lattice bgk results with existing results before we apply the models to more complicated systems the scalings concern two exponents and appearing in the production rate ofc componentr x t t g xt we find the same values for 1 6 and 2 3 as galfi and racz found at the long time limit agaussian like function forg is numerically obtained which confirms a similar result of galfi and racz on the one hand when compared with the asymptotic analysis lattice bgk models are easy to apply to cases where no analytic or asymptotic results exist on the other hand when compared with cellular automaton models lattice bgk models are faster simpler and more accurate the discrepancy of the results between the cellular automaton model and the lattice bgk models for the exponents comes from the role of the intrinsic fluctuation once the time and space correlation of stochastic stirring is given we can incorporate a random fluctuating term in lattice bgk models the schlogl model is also tested showing the ability of lattice bgk models for generating turing patterns which may stimulate further interesting investigations

renormalisation of fluctuation effects in the a a to a reaction the field theoretical description of the a a to a reaction is exactly renormalised to all orders in perturbation theory it is confirmed that it belong to the same universality class as the a a to oe reaction and that the concentration decay like t d 2 for space dimensionality d smaller than two and like ln t t for d 2 are exact results

trapping reactions with randomly moving traps exact asymptotic results for compact exploration trapping a1b b and recombination a1b 0 reactions tr and rr involving randomly moving a and b particles which react when they meet at a certain distance b are ubiquitous in nature a few stray examples include quenching of delocalized excitations coagulation recombination of radicals charge carriers or defects or biological processes related to population survival 1 in recent years there has been much interest in the longtime behavior of these processes following a remarkable discovery 2 10 of many particle effects which induce essential departures from the conventionally expected behavior 1 a pronounced deviation from the text book predictions was found for the diffusion controlled rr in case when initially the particles of the a and b species are all distributed at random with strictly equal mean densities n0 it has been first shown 2 and subsequently proven 3 4 that as t the mean density n t follows n t a d n 0 dt 2d 4 where d is the space dimensionality a d is a constant and d5d a 1db is the sum of particles diffusion coefficients this law contradicts the decay law obtained within the smoluchowski approach sa n t 1 f bd t 1 where as t

reaction diffusion processes and non perturbative renormalization group this paper is devoted to investigating non equilibrium phase transitions to an absorbing state which are generically encountered in reaction diffusion processes it is a review based on canet delamotte deloubriere and wschebor 2004 phys rev lett 92 195703 canet chate and delamotte 2004 phys rev lett 92 255703 and canet et al 2005 phys rev lett 95 100601 of recent progress in this field that has been allowed by a non perturbative renormalization group approach we mainly focus on branching and annihilating random walks and show that their critical properties strongly rely on non perturbative features and that hence the use of a non perturbative method turns out to be crucial to get a correct picture of the physics of these models

adiabatic kinetics in the theory of diffusion limited recombination ii for pt i see ibid vol 25 p 5283 95 1992 deterministic evolution that corresponds to the adiabatic liouvillean for recombination a b to 0 derived in the preceding paper i is found it is expressed by a set of linear kinetics equations for occupation numbers nsigma i t sigma a b and describes flows of particles inside domains to time independent interfaces between a and b phases where the particles annihilate the interface locations are defined by a static potential averaging of nsigma i t has been carried out both over random distribution of locations of interfaces and a gaussian distribution of initial density profile for an arbitrary fraction of initial species and comparable diffusion coefficients the expectation value of density decays as t d 2 while standard variance delta csigma i 2 1 2 decreases more slowly at t to infinity i e a t d 4 for the d dimensional case pointing to the importance of initial fluctuations for the deterministic kinetics

advanced determinant calculus a complement abstract this is a complement to my previous article advanced determinant calculus c krattenthaler advanced determinant calculus seminaire lotharingien combin 42 1999 the andrews festschrift article b42q 67 pp in the present article i share with the reader my experience of applying the methods described in the previous article in order to solve a particular problem from number theory g almkvist c krattenthaler j petersson some new formulas for experiment math 12 2003 441 456 moreover i add a list of determinant evaluations which i consider as interesting which have been found since the appearance of the previous article or which i failed to mention there including several conjectures and open problems

les degres des varietes des matrices nilpotentes abstract nous calculons les degres des adherences des orbites de matrices nilpotentes et en particulier ceux des varietes a rang et indice donnes

recurrence and density decay for diffusion limited annihilating systems we study an infinite system of moving particles where each particle is of type a or b particles perform independent random walks at rates d a 0 and d b geqslant 0 and the interaction is given by mutual annihilation a b rightarrow emptyset the initial condition is i i d with finite first moment we show that this system is site recurrent that is each site is visited infinitely many times we also generalize a lower bound on the density decay of bramson and lebowitz by considering a construction that handles different jump rates

absorbing state phase transition for driven dissipative stochastic dynamics on ℤ we study the long time behavior of conservative interacting particle systems in the activated random walk model for reaction diffusion systems and the stochastic sandpile we prove that both systems undergo an absorbing state phase transition

general framework of the non perturbative renormalization group for non equilibrium steady states this paper is devoted to presenting in detail the non perturbative renormalization group nprg formalism to investigate out of equilibrium systems and critical dynamics in statistical physics the general nprg framework for studying non equilibrium steady states in stochastic models is expounded and fundamental technicalities are stressed mainly regarding the role of causality and of it s discretization we analyze the consequences of it s prescription in the nprg framework and eventually provide an adequate regularization to encode them automatically besides we show how to build a supersymmetric nprg formalism with emphasis on time reversal symmetric problems whose supersymmetric structure allows for a particularly simple implementation of nprg in which causality issues are transparent we illustrate the two approaches on the example of model a within the derivative expansion approximation at order 2 and check that they yield identical results we stress though that the framework presented here also applies to genuinely out of equilibrium problems

statistical properties of the distance between a trapping center and a uniform density of diffusing particles in two dimensions several analyses of self segregation properties of reaction diffusion systems in low dimensions have been based on a simplified model in which an initially uniform concentration of point particles is depleted by reaction with an immobilized trap a measure of selfsegregation in this system is the distance of the trap from the nearest untrapped particle in one dimension the average of this distance has been shown to increase at a rate proportional to t 4 we show that this rate in a two dimensional system is asymptotically proportional to in t 2 and that the concentration profile in the neighborhood of the trap is proportional to in r ln t

divergent series and memory of the initial condition in the long time solution of some anomalous diffusion problems we consider various anomalous d dimensional diffusion problems in the presence of an absorbing boundary with radial symmetry the motion of particles is described by a fractional diffusion equation their mean square displacement is given by r 2 t 0 1 resulting in normal diffusive motion if 1 and subdiffusive motion otherwise for the subdiffusive case in sufficiently high dimensions divergent series appear when the concentration or survival probabilities are evaluated via the method of separation of variables while the solution for normal diffusion problems is at most divergent as t 0 the emergence of such series in the long time domain is a specific feature of subdiffusion problems we present a method to regularize such series and in some cases validate the procedure by using alternative techniques laplace transform method and numerical simulations in the normal diffusion case we find that the signature of the initial condition on the approach to the steady state rapidly fades away and the solution approaches a single the main decay mode in the long time regime in remarkable contrast long time memory of the initial condition is present in the subdiffusive case as the spatial part 1 r describing the long time decay of the solution to the steady state is determined by a weighted superposition of all spatial modes characteristic of the normal diffusion problem the weight being dependent on the initial condition interestingly 1 r turns out to be independent of the anomalous diffusion exponent

non trivial exponents in the zero temperature dynamics of the 1d ising and potts models we consider the glauber dynamics of the q state potts model in one dimension at zero temperature starting with a random initial configuration we measure the density r t of spins which have never flipped from the beginning of the simulation until time t we find that for large t the density r t has a power law decay left r t sim t theta right where the exponent theta varies with q our simulations lead to theta simeq 37 for q 2 theta simeq 53 for q 3 and theta longrightarrow 1 as q longrightarrow infty

field theory of branching and annihilating random walks we develop a systematic analytic approach to the problem of branching and annihilating random walks equivalent to the diffusion limited reaction processes 2a and a m 1 a where m 1 starting from the master equation a field theoretic representation of the problem is derived and fluctuation effects are taken into account via diagrammatic and renormalization group methods for d 2 the mean field rate equation which predicts an active phase as soon as the branching process is switched on applies qualitatively for both even and odd m but the behavior in lower dimensions is shown to be quite different for these two cases for even m and d near 2 the active phase still appears immediately but with nontrivial crossover exponents which we compute in an expansion in 2 d and with logarithmic corrections in d 2 however there exists a second critical dimension d c 4 3 below which a nontrivial inactive phase emerges with asymptotic behavior characteristic of the pure annihilation process this is confirmed by an exact calculation in d 1 the subsequent transition to the active phase which represents a new nontrivial dynamic universality class is then investigated within a truncated loop expansion which appears to give a correct qualitative picture the model with m 2 is also generalized to n species of particles which provides yet another universality class and which is exactly solvable in the limit n for odd m we show that the fluctuations of the annihilation process are strong enough to create a nontrivial inactive phase for all d 2 in this case the transition to the active phase is in the directed percolation universality class finally we study the modification when the annihilation reaction is 3a when m 0 mod 3 the system is always in its active phase but with logarithmic crossover corrections for d 1 while the other cases should exhibit a directed percolation transition out of a fluctuation driven inactive phase

optimal information transfer in enzymatic networks a field theoretic formulation signaling in enzymatic networks is typically triggered by environmental fluctuations resulting in a series of stochastic chemical reactions leading to corruption of the signal by noise for example information flow is initiated by binding of extracellular ligands to receptors which is transmitted through a cascade involving kinase phosphatase stochastic chemical reactions for a class of such networks we develop a general field theoretic approach to calculate the error in signal transmission as a function of an appropriate control variable application of the theory to a simple push pull network a module in the kinase phosphatase cascade recovers the exact results for error in signal transmission previously obtained using umbral calculus hinczewski and thirumalai phys rev x 4 041017 2014 2160 330810 1103 physrevx 4 041017 we illustrate the generality of the theory by studying the minimal errors in noise reduction in a reaction cascade with two connected push pull modules such a cascade behaves as an effective three species network with a pseudointermediate in this case optimal information transfer resulting in the smallest square of the error between the input and output occurs with a time delay which is given by the inverse of the decay rate of the pseudointermediate surprisingly in these examples the minimum error computed using simulations that take nonlinearities and discrete nature of molecules into account coincides with the predictions of a linear theory in contrast there are substantial deviations between simulations and predictions of the linear theory in error in signal propagation in an enzymatic push pull network for a certain range of parameters inclusion of second order perturbative corrections shows that differences between simulations and theoretical predictions are minimized our study establishes that a field theoretic formulation of stochastic biological signaling offers a systematic way to understand error propagation in networks of arbitrary complexity

a temporal logic approach to discrete event control for the safety canonical class this paper presents a temporal logic formulation of discrete event control which forms a new theoretical basis for control analysis and synthesis of a class of discrete event systems des based on the formulation a basic supervisory control theory is developed for a control objective specified by an invariance formula belonging to the safety canonical class of manna and pneuli using the safety canonical class as a basis the refinement and generalization of the existing basic predicate framework are demonstrated a simple example illustrates the formal axiomatic means to perform control theoretic analysis and synthesis under the new formulation

a field theoretic approach to the wiener sausage the wiener sausage the volume traced out by a sphere attached to a brownian particle is a classical problem in statistics and mathematical physics initially motivated by a range of field theoretic technical questions we present a single loop renormalised perturbation theory of a stochastic process closely related to the wiener sausage which however proves to be exact for the exponents and some amplitudes the field theoretic approach is particularly elegant and very enjoyable to see at work on such a classic problem while we recover a number of known classical results the field theoretic techniques deployed provide a particularly versatile framework which allows easy calculation with different boundary conditions even of higher momenta and more complicated correlation functions at the same time we provide a highly instructive non trivial example for some of the technical particularities of the field theoretic description of stochastic processes such as excluded volume lack of translational invariance and immobile particles the aim of the present work is not to improve upon the well established results for the wiener sausage but to provide a field theoretic approach to it in order to gain a better understanding of the field theoretic obstacles to overcome