classification of steady solutions of the full kinematic model abstract the geometric type of kinematic model governs any moving plane curve which propagates in the normal direction in the medium there have appeared some results in the literature via this model however these results are all based upon some simplification on the model or prior phenomenological assumptions on the solutions in this paper we use really full kinematic model to classify steady solutions i e curvature is independent of time with positive or negative curvature various type of solutions have been obtained such as rotating and translating waves especially for the rotating spiral waves spiral waves arise in many biological chemical and physiological systems the kinematical model can be used to describe the motion of the spiral arms approximated as curves in the plane in fact using our results theorem 3 8 we can answer the following questions is there any steadily rotating wave for a given weakly excitable medium if yes what kind of information we can know about these rotating waves e g the tip s curvature the tip s tangential velocity and the rotating frequency comparing our results with previous ones in the literature there are some differences between them the only evolving plane curves with positive or negative curvature must have monotonous curvatures via simplified model but full model admits solutions with any given oscillating number of the curvatures

optimal paths and growth processes interfaces in systems with strong quenched disorder are fractal and are thus in a dierent universality class than the self ane interfaces found in systems with weak quenched disorder the geometrical properties of strands arising in loopless invasion percolation clusters in loopless eden growth clusters and in the ballistic growth process are studied and their universality classes are identied c 1999 elsevier science b v all rights reserved

a geometrical theory for spiral waves in excitable media in this paper we develop a geometrical theory for waves in excitable reacting media using singular perturbation arguments and dispersion of traveling plane wave trains we derive an approximate theory of wave front propagation which has strong resemblance to the geometrical diffraction theory of high frequency waves in hyperbolic systems governed by the eikonal equation using this theory we study the effect of curvature on waves in excitable media specifically rotating spiral patterns in planar regions from this theory we are able to determine the frequency and wavelength for spiral patterns in excitable nonoscillatory media

functional renormalization group for anisotropic depinning and relation to branching processes in this article we review basic facts about disordered syst ems especially the existence of many metastable states and and the resulting failure of dimensional reduction besides techniques based on the gaussian variational method and replica symmetry breaking rsb the functional renormalization group frg is the only general method capable of attacking strongly disordered systems we explain the basic ideas of the latter method and why it is difficult to implement we finally review current progress fo r elastic manifolds in disorder

spiral selection as a free boundary problem abstract we present a new formulation of the spiral selection problem for the belousov zhabotinsky reaction in particular we focus on deriving an exact integro differential shape equation and discuss the possible behavior of solutions to this equation we also present some new results on the asymptotic far from core structure of spirals in the fife scaling regime

beyond the flow decomposition barrier we introduce a new approach to the maximum flow problem this approach is based on assigning arc lengths based on the residual flow value and the residual arc capacities our approach leads to an o min n 2 3 m 1 2 m log n 2 m log u time bound for a network with n vertices m arcs and integral arc capacities in the range 1 u this is a fundamental improvement over the previous time bounds we also improve bounds for the gomory hu tree problem the parametric flow problem and the approximate s t cut problem

distribution of sizes of erased loops for loop erased random walks the loop erased random walk lerw is a simpler variant of the well known self avoiding walk saw problem which retains the no self intersection property of saws but is closer to the ordinary random walk problem in this paper we study the distribution of sizes of erased loops for lerws on arbitrary graphs and relate it to the distribution of sizes of loops formed when a bond is added to a random spanning tree on the same graph in the themodynamic limit this distribution has a power law tail and we express the exponent in terms of the fractal dimension of the chemical paths on spanning trees we show also how this relation is modified for deterministic fractals in spite of the fact that the lerw model is somewhat more tractable analytically than the saw problem the number of papers devoted to this problem has remained rather small the model was defined by lawler 1 who called it the loop erased self avoiding walk lesaw this terminology is somewhat inappropriate and

size distributions of shocks and static avalanches from the functional renormalization group interfaces pinned by quenched disorder are often used to model jerky self organized critical motion we study static avalanches or shocks defined here as jumps between distinct global minima upon changing an external field we show how the full statistics of these jumps is encoded in the functional renormalizationgroup fixed point functions this allows us to obtain the size distribution p s of static avalanches in an expansion in the internal dimension d of the interface near and above d 4 this yields the mean field distribution p s s 3 2 e s 4sm where sm is a large scale cutoff in some cases calculable resumming all one loop contributions we find p s s exp c s sm 1 2 b 4 s sm where b c and are obtained to first order in 4 d our result is consistent to o with the relation a2 2 d where is the static roughness exponent often conjectured to hold at depinning our calculation applies to all static universality classes including random bond random field and random periodic disorders extended to long range elastic systems it yields a different size distribution for the case of contact line elasticity with an exponent compatible with 2 1 d to o 2 d we discuss consequences for avalanches at depinning and for sandpile models relations to burgers turbulence and the possibility that the relation be violated to higher loop order finally we show that the avalanche size distribution on a hyperplane of codimension one is in mean field valid close to and above d 4 given by p s k1 3 s s where k is the bessel k function thus hyper plane 4

conformal field theory correlations in the abelian sandpile model we calculate all multipoint correlation functions of all local bond modifications in the two dimensional abelian sandpile model both at the critical point and in the model with dissipation the set of local bond modifications includes as the most physically interesting case all weakly allowed cluster variables the correlation functions show that all local bond modifications have scaling dimension 2 and can be written as linear combinations of operators in the central charge ensuremath 2 logarithmic conformal field theory in agreement with a form conjectured earlier by mahieu and ruelle in phys rev e 64 066130 2001 we find closed form expressions for the coefficients of the operators and describe methods that allow their rapid calculation we determine the fields associated with adding or removing bonds both in the bulk and along open and closed boundaries some bond defects have scaling dimension 2 while others have scaling dimension 4 we also determine the corrections to bulk probabilities for local bond modifications near open and closed boundaries

width distribution of contact lines on a disordered substrate we have studied the roughness of a contact line on a disordered substrate by measuring its width distribution which characterizes the roughness completely the measured distribution is in excellent agreement with the distribution calculated in previous works extended here to the case of open boundary conditions this type of analysis which is performed here on experimental data provides a strong confirmation that the joanny de gennes model is not sufficient to describe the dynamics of the contact line at the depinning threshold

optimal cooperation and submodularity for computing potts partition functions with a large number of states the partition function of the q state potts model with random ferromagnetic couplings in the large q limit is generally dominated by the contribution of a single diagram of the high temperature expansion computing this dominant diagram amounts to minimizing a particular submodular function we provide a combinatorial optimization algorithm the optimal cooperation algorithm which works in polynomial time for any lattice the implementation of the method and its running time are also discussed

first principles derivation of static avalanche size distributions we study the energy minimization problem for an elastic interface in a random potential plus a quadratic well as the position of the well is varied the ground state undergoes jumps called shocks or static avalanches we introduce an efficient and systematic method to compute the statistics of avalanche sizes and manifold displacements the tree level calculation i e mean field limit is obtained by solving a saddle point equation graphically it can be interpreted as the sum of all tree graphs the 1 loop corrections are computed using results from the functional renormalization group at the upper critical dimension the shock statistics is described by the brownian force model bfm the static version of the so called alessandro beatrice bertotti montorsi abbm model in the nonequilibrium context of depinning this model can itself be treated exactly in any dimension and its shock statistics is that of a levy process contact is made with classical results in probability theory on the burgers equation with brownian initial conditions in particular we obtain a functional extension of an evolution equation introduced by carraro and duchon which recursively constructs the tree diagrams in the field theory

mean field behavior of the negative weight percolation model on random regular graphs we investigate both analytically and numerically the ensemble of minimum weight loops in the negative weight percolation model on random graphs with fixed connectivity and bimodal weight distribution this allows us to study the mean field behavior of this model the analytical study is based on a conjectured equivalence with the problem of self avoiding walks in a random medium the numerical study is based on a mapping to a standard minimum weight matching problem for which fast algorithms exist both approaches yield results that are in agreement on the location of the phase transition on the value of critical exponents and on the absence of any sizable indications of a glass phase by these results the previously conjectured upper critical dimension of d u 6 is confirmed

kinematical theory of spiral waves in excitable media comparison with numerical simulations abstract the kinematical theory of spiral waves is compared with the data of numerical simulations using complete partial differential equations of a reaction diffusion model we find good agreement for temporal periods of spiral waves which rotate around minimal holes and in the free medium no adjustable parameters were used in the calculations

scaling laws for critical manifolds in polycrystalline materials we study the surfaces of lowest energy through model polycrystalline materials in two and three dimensions when the grain boundaries are sufficiently weak these critical manifolds cm s lie entirely on grain boundaries while when the grain boundaries are strong cleavage occurs a scaling theory for the intergranular to transgranular transition of cm s is developed the key parameters are the average grain size g the ratio of grain boundary to the grain interior energy epsilon and the sample size l the key result is that a critical length scale exists l c g epsilon so that on short length scales l l c the critical manifold is rough we develop a scaling theory for l c and find that in two dimensions l c approximately gx y 2 while in three dimensions l c approximately g exp bx y 3 where x epsilon 1 epsilon and b is a constant data from realistic polycrystalline grain structures are used to test the scaling theory the exact lowest energy surface through model grain structures is found using a mapping to the minimum cut maximum flow problem in computer science as a function of grain boundary energy we observe the crossover from grain boundary rupture to mixed mode failure a mixture of transgramular and intergranular modes and finally cleavage and that the two dimensional data are consistent with y 2 approximately 3 0 0 3 while the three dimensional data are more difficult to analyze but are consistent with y 3 approximately 3 5 1 0

spiral waves in the belousov zhabotinskii reaction abstract the beautiful spiral waves of oxidation in the belousov zhabotinskii reaction are the source of many interesting and important questions about periods structures in excitable media it has long been known that these spirals are similar to involutes of circles at least some distance from the center but until now no way has been known to determine the correct wavelength and frequency in this paper we show that the parameters of a spiral wave can be viwed s eigenvalues of a problem with unique solution the critical ingredients of the theory are the effects of curvature on the propagation of wavefronts in two dimensional media and the dispersion of plane waves our analytical results are shown to be in good agreement with experimental data for the belousov zhabotinskii reagent

polynomial combinatorial optimization methods for analysing the ground states of disordered systems we discuss the application of polynomial combinatorial optimization algorithms to extract the universal zero temperature properties of various disordered systems dijkstras algorithm is used for models of non directed elastic lines on general regular graphs with isotropically correlated random potentials the successive shortest path algorithm for minimum costflow problems is applied for the study of ground state properties and the entanglement of many elastic lines in a disordered environment and the disorder induced loop percolation transition in a vortex glass model the preflow push algorithm for minimum cut maximum flow problems is used for the investigation of a roughening transition occurring in a model for elastic manifolds in a periodic potential in the presence of point disorder

distribution of sizes of erased loops of loop erased random walks in two and three dimensions we show that in the loop erased random walk problem the exponent characterizing probability distribution of areas of erased loops is superuniversal in d dimensions the probability that the erased loop has an area a varies as a 2 for large a independent of d for 2 d 4 we estimate the exponents characterizing the distribution of perimeters and areas of erased loops in d 2 and 3 by large scale monte carlo simulations our estimate of the fractal dimension z in two dimensions is consistent with the known exact value 5 4 in three dimensions we get z 1 6183 0 0004 the exponent for the distribution of durations of avalanche in the three dimensional abelian sandpile model is determined from this by using scaling relations

two loop functional renormalization for elastic manifolds pinned by disorder in n dimensions we study elastic manifolds in an n dimensional random potential using a functional renormalization group we extend to n 1 our previous construction of a field theory renormalizable to two loops for isotropic disorder with o n symmetry we obtain the fixed point and roughness exponent to next order in epsilon 4 d where d is the internal dimension of the manifold extrapolation to the directed polymer limit d 1 allows some handle on the strong coupling phase of the equivalent n dimensional kardar parisi zhang growth equation and eventually suggests an upper critical dimension d u approximately 2 5

numerical results for the ground state interface in a random medium the problem of determining the ground state of a d dimensional interface embedded in a d 1 dimensional random medium is treated numerically using a minimum cut algorithm the exact ground states can be found for a number of problems for which other numerical methods are inexact and slow in particular results are presented for the roughness exponents and ground state energy fluctuations in a random bond ising model it is found that the roughness exponent ensuremath zeta 0 41 ifmmode pm else textpm fi 0 01 0 22 ifmmode pm else textpm fi 0 01 with the related energy exponent being ensuremath theta 0 84 ifmmode pm else textpm fi 0 03 1 45 ifmmode pm else textpm fi 0 04 in d 2 3 respectively these results are compared with previous analytical and numerical estimates

anisotropic percolation and the d dimensional surface roughening problem we review recent numerical simulations of several models of interface growth in ddimensional media with quenched disorder these models belong to the universality class of anisotropic diode resistor percolation networks the values of the roughness exponent y 0 63 0 01 d 1 1 and y 0 48 2 0 02 d 2 1 are in good agreement with our recent experiments the values of y in higher dimensions a 0 38 5 0 03 in d 4 and y 0 27 0 05 in d 5 do not support a recent theoretical conjecture

survival and residence times in disordered chains with bias we present a unified framework for first passage time and residence time of random walks in finite one dimensional disordered biased systems the derivation is based on the exact expansion of the backward master equation in cumulants the dependence on the initial condition system size and bias strength is explicitly studied for models with weak and strong disorders application to thermally activated processes is also developed

higher correlations universal distributions and finite size scaling in the field theory of depinning recently we constructed a renormalizable field theory up to two loops for the quasi static depinning of elastic manifolds in a disordered environment here we explore further properties of the theory we show how higher correlation functions of the displacement field can be computed drastic simplifications occur unveiling much simpler diagrammatic rules than anticipated this is applied to the universal scaled width distribution the expansion in d 4 epsilon predicts that the scaled distribution coincides to the lowest orders with the one for a gaussian theory with propagator g q 1 q d 2 zeta zeta being the roughness exponent the deviations from this gaussian result are small and involve higher correlation functions which are computed here for different boundary conditions other universal quantities are defined and evaluated we perform a general analysis of the stability of the fixed point we find that the correction to scaling exponent is omega epsilon and not epsilon 3 as used in the analysis of some simulations a more detailed study of the upper critical dimension is given where the roughness of interfaces grows as a power of a logarithm instead of a pure power

mean first passage and residence times of random walks on asymmetric disordered chains an algebraic derivation is presented which yields the exact solution of the mean first passage and mean residence times of a one dimensional asymmetric random walk for quenched disorder two models of disorder are analytically treated both absorbing absorbing and reflecting absorbing boundaries are considered particularly the interplay between asymmetry and disorder is studied

perturbation theory for fractional brownian motion in presence of absorbing boundaries fractional brownian motion is a gaussian process x t with zero mean and two time correlations x t 1 x t 2 d t 1 2h t 2 2h t 1 t 2 2h where h with 0 h 1 is called the hurst exponent for h 1 2 x t is a brownian motion while for h 1 2 x t is a non markovian process here we study x t in presence of an absorbing boundary at the origin and focus on the probability density p x t for the process to arrive at x at time t starting near the origin at time 0 given that it has never crossed the origin it has a scaling form p x t t h r x t h our objective is to compute the scaling function r y which up to now was only known for the markov case h 1 2 we develop a systematic perturbation theory around this limit setting h 1 2 e to calculate the scaling function r y to first order in e we find that r y behaves as r y y as y 0 near the absorbing boundary while r y y exp y 2 2 as y with 1 4e o e 2 and 1 2e o e 2 our e expansion result confirms the scaling relation 1 h h proposed in zoia rosso and majumdar phys rev lett 102 120602 2009 we verify our findings via numerical simulations for h 2 3 the tools developed here are versatile powerful and adaptable to different situations

passage times of asymmetric anomalous walks with multiple paths we investigate the transient and the long time behaviour of asymmetric anomalous walks in heterogeneous media two types of disorder are worked out explicitly weak and strong disorder in addition the occurrence of disordered multiple paths is considered we calculate the first passage time distribution of the associated stochastic transport process we discuss the occurrence of the crossover from a power law to an exponential decay for the long time behaviour of the distribution of the first passage times of disordered biased walks

functional renormalization group and the field theory of disordered elastic systems we study elastic systems such as interfaces or lattices pinned by quenched disorder to escape triviality as a result of dimensional reduction we use the functional renormalization group difficulties arise in the calculation of the renormalization group functions beyond one loop order even worse observables such as the two point correlation function exhibit the same problem already at one loop order these difficulties are due to the nonanalyticity of the renormalized disorder correlator at zero temperature which is inherent to the physics beyond the larkin length characterized by many metastable states as a result two loop diagrams which involve derivatives of the disorder correlator at the nonanalytic point are naively ambiguous we examine several routes out of this dilemma which lead to a unique renormalizable field theory at two loop order it is also the only theory consistent with the potentiality of the problem the beta function differs from previous work and the one at depinning by novel anomalous terms for interfaces and random bond disorder we find a roughness exponent zeta 0 208 298 04epsilon 0 006 858epsilon 2 epsilon 4 d for random field disorder we find zeta epsilon 3 and compute universal amplitudes to order o epsilon 2 for periodic systems we evaluate the universal amplitude of the two point function we also clarify the dependence of universal amplitudes on the boundary conditions at large scale all predictions are in good agreement with numerical and exact results and are an improvement over one loop finally we calculate higher correlation functions which turn out to be equivalent to those at depinning to leading order in epsilon

equivalence between the abelian sandpile model and the q 0 limit of the potts model abstract we establish an equivalence between the undirected abelian sandpile model and the q 0 limit of the q state potts model the equivalence is valid for arbitrary finite graphs two dimensional abelian sandpile models thus correspond to a conformal field theory with central charge c 2 the equivalence also gives a monte carlo algorithm to generate random spanning trees we study the growth process of the spread of fire under the burning algorithm in the background of a random recurrent configuration of the abelian sandpile model the average number of sites burnt upto time t varies at ta in two dimensions our numerically determined value of a agrees with the theoretical prediction a 8 5 we relate this exponent to the conventional exponents characterizing the distributions of avalanche sizes

overhangs in interface growth and ground state paths we report on numerical investigations concerning the statistics of the ground state path in a disordered medium for a distribution of energies having a positive support these paths are almost directed even though some overhangs are present computing both the directed minimum energy path and the unconstrained ground state paths allows us to understand whether the two problems belong to the same universality class we present numerical results in dimensions up to d 6 5 1 which suggests that both problems are in the same universality class

universal interface width distributions at the depinning threshold the scaling properties of driven elastic interfaces in random media play an important role in a wide variety of physical situations ranging from stochastic surface growth to domain walls in disordered magnetic materials the spreading of fluids on rough substrates and the dynamics of cracks 1 2 these problems share many features with critical phenomena and provide a challenge for theoretical approaches to disordered systems and nonequilibrium phenomena 3 8 here we study interfaces described by a scalar height function h x where x is the d dimensional internal coordinate we measure the deviation from the mean position as u x 5h x 2 h where iii stands for the spatial average over all x of a given interface cf fig 1 the mean square width of a single interface w 2 n u x o5 u 2 can be used to characterize its roughness and explore universal properties after averaging over the ensemble of interfaces w 2 grows with the lateral extension l of the system as w 2

critical properties of loop percolation models with optimization constraints we study loop percolation models in two and in three space dimensions in which configurations of occupied bonds are forced to form a closed loop we show that the uncorrelated occupation of elementary plaquettes of the square and the simple cubic lattice by elementary loops leads to a percolation transition that is in the same universality class as the conventional percolation in contrast to this an optimization constraint for the loop configurations which then have to minimize a particular generic energy function leads to a percolation transition that constitutes a universality class for which we report the critical exponents implication for the physics of solid on solid and vortex glass models are discussed

optimal path in two and three dimensions we apply the dijkstra algorithm to generate optimal paths between two given sites on a lattice representing a disordered energy landscape we study the geometrical and energetic scaling properties of the optimal path where the energies are taken from a uniform distribution our numerical results for both two and three dimensions suggest that the optimal path for random uniformly distributed energies is in the same universality class as the directed polymers we present physical realizations of polymers in a disordered energy landscape for which this result is relevant s1063 651x9808212 9

optimization and plasticity in disordered media we study the plastic yielding of disordered media using the perfectly plastic random fuse model the yield surfaces are shown to be different from those obtained minimizing the sum of the local yield thresholds i e the so called minimum energy surfaces as a result the global yield stress is lower than expected from naive optimization and the difference persists as the sample size increases at variance with minimum energy surfaces height height fluctuations of yield surfaces exhibit multiscaling we provide a theoretical argument that explains how this behavior arises from the very different nature of the optimization problem in both cases

theory of the spiral core in excitable media abstract a rigorous asymptotic spiral solution to an excitable reaction diffusion system is found by separating space into two scaling regions an outer region having the same spatial scaling as the overall spiral structure which exhibits a singularity at the spiral tip and a core region around the spiral tip where space is scaled so as to resolve the tip singularity the stability of the spiral structure is investigated for both the outer region which is found to possess no intrinsic instability and the core region which is found to be unstable both the zero and small diffusion systems are found to exhibit qualitatively similar behaviour the implication of these results for both experiment and simulation in particular within the context of the observed meandering instability are addressed

the abelian sandpile and related models abstract the abelian sandpile model is the simplest analytically tractable model of self organized criticality this paper presents a brief review of known results about the model the abelian group structure of the algebra of operators allows an exact calculation of many of its properties in particular when there is a preferred direction one can calculate all the critical exponents characterizing the distribution of avalanche sizes in all dimensions for the undirected case the model is related to q 0 state potts model this enables exact calculation of some exponents in two dimensions and there are some conjectures about others we also discuss a generalization of the model to a network of communicating reactive processors this includes sandpile models with stochastic toppling rules as a special case we also consider a nondashabelian stochastic variant which lies in a different universality class related to directed percolation

abelian sandpile model on the bethe lattice the authors study bak tang and wiesenfeld s abelian sandpile model 1987 of self organised criticality on the bethe lattice exact expressions for various distribution functions including the height distribution at a site and the joint distribution of heights at two sites separated by an arbitrary distance are obtained they also determine the probability distribution of the number of distinct sites that topple at least once the number of toplings at the origin and the total number of toplings in an avalanche the probability that an avalanche consists of more than n toplings varies as n 1 2 for large n the probability that its duration exceeds t decreases as 1 t for large t these exponents are the same as for the critical percolation clusters in mean field theory

winding angle distributions for random walks and flux lines we study analytically and numerically the winding of a flux line around a columnar defect reflecting and absorbing boundary conditions apply to marginal or repulsive defects respectively in both cases the winding angle distribution decays exponentially for large angles with a decay constant depending only on the boundary condition but not on microscopic features nonuniversal distributions are encountered for chiral defects that preferentially twist the flux line in one direction the resulting asymmetric distributions have decay constants that depend on the degree of chirality in particular strong chirality encourages entanglements and leads to broad distributions we also examine the windings of flux lines in the presence of point impurities random bonds our results suggest that pinning to impurities reduces entanglements leading to a narrow gaussian distribution textcopyright 1996 the american physical society

bifurcation and stability analysis of rotating chemical spirals in circular domains boundary induced meandering and stabilization recent experimental and model studies have revealed that the domain size may strongly influence the dynamics of rotating spirals in two dimensional pattern forming chemical reactions hartmann et al phys rev lett 76 1384 1996 report a frequency increase of spirals in circular domains with diameters substantially smaller than the spiral wavelength in a large domain for the catalytic no co reaction on a microstructured platinum surface accompanying simulations with a simple reaction diffusion system reproduced the behavior here we supplement these studies by a numerical bifurcation and stability analysis of rotating spirals in a simple activator inhibitor model the problem is solved in a corotating frame of reference no flux conditions are imposed at the boundary of the circular domain at large domain sizes eigenvalues and eigenvectors very close to those corresponding to infinite medium translational invariance are observed upon decrease of domain size we observe a simultaneous change in the rotation frequency and a deviation of these eigenvalues from being neutrally stable zero real part the latter phenomenon indicates that the translation symmetry of the spiral solution is appreciably broken due to the interaction with the now nearby wall various dynamical regimes are found first the spiral simply tries to avoid the boundary and its tip moves towards the center of the circular domain corresponding to a negative real part of the translational eigenvalues this effect is noticeable at a domain radius of r r c r 1 the spiral subsequently exhibits an oscillatory instability the tip trajectory displays a meandering motion which may be characterized as boundary induced spiral meandering a systematic study of the spiral rotation as a function of a control parameter and the domain size reveals that the meandering instability in large domains becomes suppressed and the spiral rotation becomes rigid at a critical radius r c r 0 boundary induced meandering arises below a second critical radius r c r 2 r c r 0

on the perturbation expansion of the kpz equation we present a simple argument to show that the function of the d dimensional kpz equation d 2 is to all orders in perturbation theory given by beta g r d 2 g r 2 8 pi d 2 text gamma 2 d 2 g r 2 neither the dynamical exponent z nor the roughness exponent have any correction in any order of perturbation theory this shows that standard perturbation theory cannot attain the strong coupling regime and in addition breaks down at d 4 we also calculate a class of correlation functions exactly

introduction to the sandpile model abstract this article is based on a talk given by one of us evi at the conference statphys taipei 1997 it overviews the exact results in the theory of the sandpile model and discusses briefly the yet unsolved problem of calculation of avalanche distribution exponents the key ingredients include the analogy with the critical reaction diffusion system the spanning tree representation of height configurations and the decomposition of the avalanche process into waves of topplings

statics and dynamics of elastic manifolds in media with long range correlated disorder we study the statics and dynamics of an elastic manifold in a disordered medium with quenched defects correlated as approximately r a for large separation r we derive the functional renormalization group equations to one loop order which allow us to describe the universal properties of the system in equilibrium and at the depinning transition using a double epsilon 4 d and delta 4 a expansion we compute the fixed points characterizing different universality classes and analyze their regions of stability the long range disorder correlator remains analytic but generates short range disorder whose correlator exhibits the usual cusp the critical exponents and universal amplitudes are computed to first order in epsilon and delta at the fixed points at depinning a velocity versus force exponent beta larger than unity can occur we discuss possible realizations using extended defects

bak tang wiesenfeld sandpile model around the upper critical dimension we consider the bak tang wiesenfeld sandpile model phys rev lett 59 381 1987 phys rev a 38 364 1988 on square lattices in different dimensions dl 6 a finite size scaling analysis of the avalanche probability distributions yields the values of the distribution exponents the dynamical exponent and the dimension of the avalanches above the upper critical dimension d u 4 the exponents equal the known mean field values an analysis of the area probability distributions indicates that the avalanches are fractal above the critical dimension

dispersion of traveling waves in the belousov zhabotinskii reaction abstract we use perturbation and numerical methods to calculate the dispersion relation for periodic wave train solutions of diffusion reaction equations modeling the belousov zhabotinskii reaction these results are compared with experimental data for the belousov zhabotinskii reagent and shown to be in good agreement

singular perturbation theory of traveling waves in excitable media a review abstract waves of chemical or electrical activity traveling through space have been observed in several contexts chemical reaction mixtures in non convecting liquid phase cell suspensions nerve axons and neuromuscular tissues typically wave supporting preparations are excitable that is they respond and sensitivity to perturbations are rapidly damped out but suprathreshold disturbances trigger an abrupt and substantial response the abruptness of the response can be exploited by the methods of singular perturbation theory to obtain a mathematical description of wave propagation in spatially distributed excitable media singular perturbation analysis of propagating waves in one spatial dimension is straightforward and uncontentious but the analysis of propagating waves in one spatial dimension is straightforward and several fundamentally different ways we compare and contrast the approaches taken by greenberg zykov fife krinskii and his collaborators and ourselves with particular emphasis on the case of rotating spiral waves our intention is to bring some order to the important but difficult theory of propagating waves in two dimensional excitable media in conclusion we discuss briefly some possible extensions of the singular perturbation approach to propagating wave surfaces in three dimensional space