scaling of avalanche queues in directed dissipative sandpiles using numerical simulations and analytical methods we study a two dimensional directed sandpile automaton with nonconservative random defects concentration c and varying driving rate r the automaton is driven only at the top row and driving rate is measured by the number of added particles per time step of avalanche evolution the probability distribution of duration of elementary avalanches at zero driving rate is exactly given by p 1 t c t ensuremath 3 2 mathrm exp t mathrm ln 1 ensuremath c for driving rates in the interval 0lrl 1 the avalanches are queuing one after another increasing the periods of noninterrupted activity of the automaton recognizing the probability p 1 as a distribution of service time of jobs arriving at a server with frequency r the model represents an example of the class e 1 gi ensuremath infty 1 server queue in the queue theory we study scaling properties of the busy period and dissipated energy of sequences of noninterrupted activity in the limit stackrel ensuremath rightarrow c 0 and varying linear system size l ensuremath ll 1 c we find that at driving rates rl l ensuremath 1 2 the distributions of duration and energy of the avalanche queues are characterized by a multifractal scaling and we determine the corresponding spectral functions for l ensuremath gg 1 c increasing the driving rate somewhat compensates for the energy losses at defects above the line r ensuremath sim sqrt c the scaling exponents of the distributions in this region of phase diagram vary approximately linearly with the driving rate using properties of recurrent states and the probability theory we determine analytically the exact upper bound of the probability distribution of busy periods in the case of conservative dynamics c 0 the probability of a continuous flow increases as f ensuremath infty ensuremath sim r 2 for small driving rates

monotone iterative technique for first order impulsive difference equations with periodic boundary conditions this paper investigates the first order impulsive difference equations with periodic boundary conditions by establishing two comparison results and using the method of upper and lower solutions and the monotone iterative technique criteria on the existence of minimal and maximal solutions are obtained

analyticity and differentiability of semigroups associated with elastic systems with damping and gyroscopic forces abstract in this paper we consider a second order variational evolution equation in a hilbert space which can model an elastic system with damping and gyroscopic forces a new form of the corresponding first order evolution equation is introduced and its well posedness is proved by means of the semigroup theory we give sufficient conditions for analyticity and differentiablity of the associated semigroup the results are applied to several pdes with discontinuous coefficients and mechanical boundary conditions it is proved that russell s spacial hysteresis model of a vibrating beam 22 is associated with an exponentially stable analytic semigroup

directed abelian algebras and their application to stochastic models with each directed acyclic graph this includes some d dimensional lattices one can associate some abelian algebras that we call directed abelian algebras daas on each site of the graph one attaches a generator of the algebra these algebras depend on several parameters and are semisimple using any daa one can define a family of hamiltonians which give the continuous time evolution of a stochastic process the calculation of the spectra and ground state wave functions stationary state probability distributions is an easy algebraic exercise if one considers d dimensional lattices and chooses hamiltonians linear in the generators in finite size scaling the hamiltonian spectrum is gapless with a critical dynamic exponent z d one possible application of the daa is to sandpile models in the paper we present this application considering one and two dimensional lattices in the one dimensional case when the daa conserves the number of particles the avalanches belong to the random walker universality class critical exponent ensuremath sigma ensuremath tau 3 2 we study the local density of particles inside large avalanches showing a depletion of particles at the source of the avalanche and an enrichment at its end in two dimensions we did extensive monte carlo simulations and found ensuremath sigma ensuremath tau 1 780 ifmmode pm else textpm fi 0 005

on the mathematical model for linear elastic systems with analytic damping in the present paper we investigate linear elastic systems with damping ddot y b dot y ay 0 in hilbert spaces where a is a positive definite unbounded linear operator and b is a closed linear operator related in various ways to a alpha frac 1 2 leqq alpha leqq 1 we discuss the spectral property of these systems and obtain some fundamental results for the holomorphic property and the exponential stability of the semigroups associated with these systems

universality classes in directed sandpile models we perform large scale numerical simulations of a directed version of the two state stochastic sandpile model numerical results show that this stochastic model defines a new universality class with respect to the abelian directed sandpile the physical origin of the different critical behaviour has to be ascribed to the presence of multiple topplings in the stochastic model these results provide new insight into the long debated question of universality in abelian and stochastic sandpiles

exact solution of a stochastic directed sandpile model we introduce and analytically solve a directed sandpile model with stochastic toppling rules the model clearly belongs to a different universality class from its counterpart with deterministic toppling rules previously solved by dhar and ramaswamy the critical exponents are d 7 4 ensuremath tau 10 7 in two dimensions and d 3 2 ensuremath tau 4 3 in one dimension the upper critical dimension of the model is three at which the exponents apart from logarithmic corrections reach their mean field values d 2 ensuremath tau 3 2

steady state of stochastic sandpile models we study the steady state of the abelian sandpile models with stochastic toppling rules the particle addition operators commute with each other but in general these operators need not be diagonalizable we use their abelian algebra to determine their eigenvalues and the jordan block structure these are then used to determine the probability of different configurations in the steady state we illustrate this procedure by explicitly determining the numerically exact steady state for a one dimensional example for systems of size 12 and also study the density profile in the steady state

monotone iterative technique and positive solutions of lidstone boundary value problems the purpose of this paper is to investigate the existence and iteration of n symmetric positive solutions for lidstone boundary value problem 1 nw 2 n t f t w t 0

monotone iterative technique for the elastic systems with structural damping in banach spaces in this paper we use a monotone iterative technique in the presence of lower and upper solutions to discuss the existence of mild solutions to a second order evolution equation initial value problem in an ordered banach space which can model an elastic system with structural damping under monotone condition and the noncompactness measure condition on nonlinearity we obtain the existence of extremal mild solutions and positive mild solutions moreover some applications are given to illustrate our theoretical results

exact solution of the totally asymmetric oslo model recently it has been found pruessner g and jensen h j 2003 phys rev lett 91 244303 that a totally asymmetric variant of the oslo model christensen k et al 1996 phys rev lett 77 107 represents the entire universality class of the oslo model with anisotropy the totally asymmetric model can be solved without scaling assumptions by finding recursively the eigenvectors of the markov matrix which can be suitably modified to produce the moment generating function of the relevant observable this method should be applicable to many other stochastic processes

airy distribution function from the area under a brownian excursion to the maximal height of fluctuating interfaces the airy distribution function describes the probability distribution of the area under a brownian excursion over a unit interval surprisingly this function has appeared in a number of seemingly unrelated problems mostly in computer science and graph theory in this paper we show that this distribution function also appears in a rather well studied physical system namely the fluctuating interfaces we present an exact solution for the distribution p h m l of the maximal height h m measured with respect to the average spatial height in the steady state of a fluctuating interface in a one dimensional system of size l with both periodic and free boundary conditions for the periodic case we show that p h m l l 1 2f h m l 1 2 for all l 0 where the function f x is the airy distribution function this result is valid for both the edwards wilkinson ew and the kardar parisi zhang interfaces for the free boundary case the same scaling holds p h m l l 1 2f h m l 1 2 but the scaling function f x is different from that of the periodic case we compute this scaling function explicitly for the ew interface and call it the f airy distribution function numerical simulations are in excellent agreement with our analytical results our results provide a rather rare exactly solvable case for the distribution of extremum of a set of strongly correlated random variables some of these results were announced in a recent letter s n majumdar and a comtet phys rev lett 92 225501 2004

analyticity and exponential stability of semigroups for the elastic systems with structural damping in banach spaces abstract in this paper we consider a second order evolution equation in a banach space which can model an elastic system with structural damping new forms of the corresponding first order evolution equation are introduced and their well posed property is proved by means of the operator semigroup theory we give sufficient conditions for analyticity and exponential stability of the associated semigroups

scaling behavior of a directed sandpile automata with random defects in a recent paper b tadic u nowak k d usadel r ramaswamy and s padlewski phys rev a 45 8536 1992 the directed two dimensional sandpile is modified to include a concentration ital p of randomly placed holes for ital p gt 0 they observe a characteristic cutoff size for the duration and mass of avalanches this breaks the formal power law behavior that is a signature of self organized criticality the scaling of these characteristic sizes with the concentration of defects is observed empirically to follow a power law and the exponents are numerically determined in this brief report it is shown that a previously described mean field approximation can account for the observed exponents

interface view of directed sandpile dynamics we present a directed unloading sand box type avalanche model driven by slowly lowering the retaining wall at the bottom of the slope the avalanche propagation in the two dimensional surface is related to the space time configurations in one dimensional kardar parisi zhang kpz interface growth we relate the scaling exponents of the avalanche cluster distribution to those for the growing surface the numerical results are close but deviate significantly from the exact kpz values this might reflect stronger than usual corrections to scaling or be more fundamental due to correlations between subsequent space time interface configurations

extremal solutions of nonlinear impulsive integrodifferential equations in banach spaces abstract in this paper we combine the monotone iterative technique with fixed point theory to investigate the extremal solutions of nonlinear impulsive integrodifferential equations in banach spaces existence criteria are obtained and several examples are worked out

genetic algorithm based identification of nonlinear systems by sparse volterra filters a parsimonious parameterization scheme is proposed to model the sparse volterra filter so that the number of volterra kernels to be estimated is greatly reduced representing the volterra filter using a linear vector equation the genetic algorithm is applied to search the significant terms among all possible candidate vectors as the significant terms are detected the associated volterra kernels are estimated using the least square error method the problem to be solved is in essence the application of the genetic algorithm to combinatorial optimization an operator called forced mutation is proposed along with the genetic algorithm to overcome the difficulties usually encountered when applying the genetic algorithm to combinatorial optimization

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

monotone iterative technique for differential equations in a banach space iffis continuous steps i and iii are standard and straightforward it is step ii that deserves attention this in turn leads to three possibilities namely to show that the sequence of approximate solutions is a a cauchy sequence b relatively compact so that one can appeal to ascoli s theorem and c a monotone sequence in a cone the first two possibilities are well known and are discussed in 2 31 this paper is devoted to the investigation of c which leads to the development of a monotone iterative technique in an arbitrary cone

one dimensional directed sandpile models and the area under a brownian curve we derive the steady state properties of a general directed sandpile model in one dimension using a central limit theorem for dependent random variables we find the precise conditions for the model to belong to the universality class of the totally asymmetric oslo model thereby identifying a large universality class of directed sandpiles we map the avalanche size to the area under a brownian curve with an absorbing boundary at the origin motivating us to solve this brownian curve problem thus we are able to determine the moment generating function for the avalanche size probability in this universality class explicitly calculating amplitudes of the leading order terms

some results and a conjecture for manna s stochastic sandpile model we present some analytical results for the stochastic sandpile model studied earlier by manna in this model the operators corresponding to particle addition at different sites commute the eigenvalues of operators satisfy a system of coupled polynomial equations for an l l square we construct a nontrivial toppling invariant and hence a ladder operator which acting on eigenvectors of the evolution operator gives new eigenvectors with different eigenvalues for periodic boundary conditions in one direction one more toppling invariant can be constructed we show that there are many forbidden subconfigurations and only an exponentially small fraction of all stable configurations are recurrent we obtain rigorous lower and upper bounds for the minimum number of particles in a recurrent configuration and conjecture a formula for its exact value for finite size rectangles

mixed monotone iterative technique for a class of semilinear impulsive evolution equations in banach spaces abstract this paper deals with the existence of mild l quasi solutions to the initial value problem for a class of semilinear impulsive evolution equations in an ordered banach space e under a new concept of upper and lower solutions a new monotone iterative technique on the initial value problem of impulsive evolution equations has been established the results improve and extend some relevant results in ordinary differential equations and partial differential equations an example is also given

exactly solved model of self organized critical phenomena we define a variant of the model of bak tang and wiesenfeld of self organized critial behavior by introducing a preferred direction we characterize the critical state and by establishing equivalence to a voter model determine the critical exponents exactly in arbitrary dimension d the upper critical dimension for this model is three in two dimensions the model is equivalent to an earlier solved special case of directed percolation

monotone iterative technique for addressing impulsive integro differential equations in banach spaces abstract in this paper we use a monotone iterative technique in the presence of lower and upper solutions to discuss the existence of solutions for the initial value problem of the impulsive integro differential equation of volterra type in a banach space e u t f t u t t u t t j t t k u t t k i k u t k k 1 2 m u 0 x 0 where f c j e e e j 0 a 0 t 1 t 2 t m a and i k c e e k 1 2 m under wide monotone conditions and the noncompactness measure condition of nonlinearity f we obtain the existence of extremal solutions and a unique solution between lower and upper solutions our result improves and extends some relevant results in abstract differential equations