higher order implicit strong numerical schemes for stochastic differential equations higher order implicit numerical methods which are suitable for stiff stochastic differential equations are proposed these are based on a stochastic taylor expansion and converge strongly to the corresponding solution of the stochastic differential equation as the time step size converges to zero the regions of absolute stability of these implicit and related explicit methods are also examined

fluctuations in the lattice gas for burgers equation the langevin equation for the biased random hopping of particles onto unoccupied sites of a lattice is obtained from the master equation for finite systems by invoking a limit theorem due to kurtz for a weakly asymmetric process with diffusive scaling the continuum limit of this equation yields a deterministic equation that is equivalent to burgers equation the stochastic equation for the leading lattice corrections is derived and the approach to the continuum limit is illustrated with simulations

solving langevin equation with the bicolour rooted tree method national basic research program of china 973 program 2007cb814800 national natural science foundation of china 10475067

universal property of the housekeeping entropy production the entropy production of a nonequilibrium system with broken detailed balance is a random variable whose mean value is nonnegative the housekeeping entropy production which is a part of total entropy production is associated with the heat dissipation in maintaining a nonequilibrium steady state we derive a langevin type stochastic differential equation for the housekeeping entropy production the equation allows us to define a housekeeping entropic time ensuremath tau remarkably it turns out that the probability distribution of the housekeeping entropy production at a fixed value of ensuremath tau is given by the gaussian distribution regardless of system details the gaussian distribution is universal for any systems whether in the steady state or in the transient state and whether they are driven by time independent or time dependent driving forces we demonstrate the universal distribution numerically for model systems

dynamical scaling of surface growth in simple lattice models we present extensive simulations of the atomistic edwards wilkinson ew and restricted edwards wilkinson rew models in 2 1 dimensions dynamic finite size scaling analyses of the interfacial width and structure factor provide the estimates for the dynamic exponent z 1 65 0 05 for the ew model and z 2 0 0 1 for the rew model the stochastic contribution to the interface velocity u due to the deposition and diffusion of particles is characterized for both the models using a blocking procedure for the ew model the time displaced temporal correlations in u show nonexponential decay while the temporal correlations decay exponentially for the rew model dynamical scaling of the temporal correlation function for the ew model yields a value of z which is consistent with the estimate obtained from finite size scaling of the interfacial width and structure factor

synchrony and variability induced by spatially correlated additive and multiplicative noise in the coupled langevin model the synchrony and variability of the coupled langevin model subjected to spatially correlated additive and multiplicative noise are discussed we have employed numerical simulations and the analytical augmented moment method which is the second order moment method for local and global variables h hasegawa phys rev e 67 041903 2003 it has been shown that the synchrony of an ensemble is increased decreased by a positive negative spatial correlation in both additive and multiplicative noise although the variability for local fluctuations is almost insensitive to spatial correlations that for global fluctuations is increased decreased by positive negative correlations when a pulse input is applied the synchrony is increased for the correlated multiplicative noise whereas it may be decreased for correlated additive noise coexisting with uncorrelated multiplicative noise an application of our study to neuron ensembles has demonstrated the possibility that information is conveyed by the variance and synchrony in input signals which accounts for some neuronal experiments

langevin equations and surface growth departamento de fi sica universidad nacional de san luis chacabuco 917 5700 san luis argentina received 9 january 1997 the three approaches usually used to study surface growth are i master equation ii stochastic langevinequation and iii microscopic models all of them give the same scaling exponents recently vvedenskyet al phys rev e 48 852 1993 derived a stochastic langevin equation from a master equation of the birthand death type for the epitaxial growth demonstrating the equivalence of both approaches in this paper astochastic langevin equation is derived from a discrete model the results are the same as those obtained byvvedensky et al demonstrating that the three approaches are equivalent as a nontrivial example our proce dure is used to derive the kardar parisi zhang kpz equation from the ballistic deposition process thismodel with vacancies and overhangs is very dif cult to handle due to the algebraic complications that arisewhen the master equation approach is used s1063 651x 97 11905 5 pacs number s 05 40 1ji introduction

elementary local configurations microscopic rules and langevin equations for two models of molecular beam epitaxy stochastic langevin equations for the wolf villain wv and das sarma tamborenea dt models are derived using the alternative method recently developed by costanza 1997 phys rev e 55 6501 which avoids the complications arising in the calculation of the first moment of the transition rate required in the master equation approach the calculations are compared with those recently published by zhi feng huang et al 1996 phys rev e 54 5935 obtaining the same results as is expected the microscopic rules are derived from the set of 243 elementary local configurations needed for the description of these two models and after using simple summation rules these were reduced to 16 for the dt model and to 25 for the wv model the number of microscopic rules needed for the description of the present models are considerably larger than the previously solved models

elliptic algebro geometric solutions of the kdv and akns hierarchies an analytic approach we provide an overview of elliptic algebro geometric solutions of the kdv and akns hierarchies with special emphasis on floquet theoretic and spectral theoretic methods our treatment includes an effective characterization of all stationary elliptic kdv and akns solutions based on a theory developed by hermite and picard

treibich verdier potentials and the stationary m kdv hierarchy here x x col co3 denotes the elliptic weierstrass function with fundamental periods f p 2a l 2co3 im co3 wl 5 0 see 1 ch 18 in the special case where col is real and co3 is purely imaginary the potential q is real valued and ince s striking result 31 in modern spectral theoretic terminology yields the fact that the self adjoint operator l associated with the differential expression d 2 q in l2 ir has a finite gap spectrum of the type

population rate codes carried by mean fluctuation and synchrony of neuronal firings abstract a population of firing neurons is expected to carry information not only by the mean firing rate but also by fluctuation and synchrony among neurons in order to examine this possibility we have studied responses of neuronal ensembles to three kinds of inputs mean fluctuation and synchrony driven inputs the generalized rate code model including additive and multiplicative noise h hasegawa phys rev e 75 2007 051904 has been studied by direct simulations dss and the augmented moment method amm in which equations of motion for mean firing rate fluctuation and synchrony are derived results calculated by the amm are in good agreement with those by dss the independent component analysis ica of our results has shown that mean firing rate fluctuation or variability and synchrony may carry independent information in the population rate code model the input output relation of mean firing rates is shown to have higher sensitivity for larger multiplicative noise as recently observed in prefrontal cortex a comparison is made between results obtained by the integrate and fire if model and our rate code model

commutation methods applied to the mkdv equation an explicit construction of solutions of the modified korteweg de vries equation given a solution of the ordinary korteweg de vries equation is provided our theory is based on commutation methods i e n 1 supersymmetry underlying miura s transformation that links solutions of the two evolution equations

particle smoothing in continuous time a fast approach via density estimation we consider the particle smoothing problem for state space models where the transition density is not available in closed form in particular for continuous time nonlinear models expressed via stochastic differential equations sdes conventional forward backward and two filter smoothers for the particle filter require a closed form transition density with the linear gaussian euler maruyama discretization usually applied to the sdes to achieve this we develop a pair of variants using kernel density approximations to relieve the dependence and in doing so enable use of faster and more accurate discretization schemes such as runge kutta in addition the new methods admit arbitrary proposal distributions providing an avenue to deal with degeneracy issues experimental results on a functional magnetic resonance imaging fmri deconvolution task demonstrate comparable accuracy and significantly improved runtime over conventional techniques

the anti self dual yang mills equation and the painleve iii equation the classical transcendental solutions to the painleve iii equation are derived from a family of solutions to the anti self dual yang mills equation it is also shown that the affine weyl group symmetry of piii is recovered from the symmetry of yang s equation

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

numerical integration of stochastic differential equations several numerical methods for treating stochastic differential equations are considered both the convergence in the mean square limit and the convergence of the moments is discussed and the generation of appropriate random numbers is treated the necessity of simulations at various time steps with an extrapolation to time step zero is emphasized and demonstrated by a simple example

weak second order splitting schemes for lagrangian monte carlo particle methods for the composition pdf fdf transport equations we study a class of methods for the numerical solution of the system of stochastic differential equations sdes that arises in the modeling of turbulent combustion specifically in the monte carlo particle method for the solution of the model equations for the composition probability density function pdf and the filtered density function fdf this system consists of an sde for particle position and a random differential equation for particle composition the numerical methods considered advance the solution in time with weak second order accuracy with respect to the time step size the four primary contributions of the paper are i establishing that the coefficients in the particle equations can be frozen at the mid time while preserving second order accuracy ii examining the performance of three existing schemes for integrating the sdes iii developing and evaluating different splitting schemes which treat particle motion reaction and mixing on different sub steps and iv developing the method of manufactured solutions mms to assess the convergence of monte carlo particle methods tests using mms confirm the second order accuracy of the schemes in general the use of frozen coefficients reduces the numerical errors otherwise no significant differences are observed in the performance of the different sde schemes and splitting schemes

stochastic resonance in bistable systems with nonlinear dissipation and multiplicative noise a microscopic approach abstract we have studied the stochastic resonance sr of bistable systems coupled to a bath with a nonlinear system bath interaction by using the microscopic generalized caldeira leggett cl model the adopted cl model yields the non markovian langevin equation with nonlinear dissipation and state dependent multiplicative diffusion which preserve the fluctuation dissipation relation fdr results of our simulations are given as follows 1 the spectral power amplification spa exhibits sr not only for a and b but also for while the stationary probability distribution function is independent of them where a and b denote magnitudes of multiplicative and additive noises respectively and expresses the relaxation time of ornstein uhlenbeck ou colored noise 2 the spa for coexisting additive and multiplicative noises has a single peak but two peak structure as functions of a b and or results 1 and 2 are qualitatively different from previous ones obtained by phenomenological langevin models where the fdr is not held or indefinite these show an importance of the fdr in a study on sr of open bistable systems

population dynamics poisson approximation and its relation to the langevin process the description and analysis of interacting populations with a discrete number of individuals is a common subject in several branches of physics and other sciences 1 2 the members of the population can be molecules as in chemical reactions 3 7 photons as in lasers 8 10 or individual organisms as in population biology 11 we are particularly interested in stochastic systems which have a certain kind of deterministic limit namely for some size parameter v large enough the solutions of individual realizations follow closely the solutions of a system of ordinary differential equations 12 15 see 16 for a recent rediscovery of the inverse problem early results in the physics of brownian motion led physicists to simulate population dynamics in terms of a langevin process the approximation of the evolution equations for the probabilities of such systems can performed following van kampen s v expansion 1 the fokker planck equations 1 17 18 resulting from these approximations suggest that individual realizations of the stochastic dynamics follow a langevin equation with gaussian noise see 14 15 19 for rigorous results one of the conceptual difficulties with this presentation is that it cannot be used to simulate individual realizations of the stochastic process since the probability distributions for sufficiently small times cannot be considered smooth a requirement for the applicability of the approximation in contrast with early attempts recent developments have come to emphasize the importance of being discrete 20 21 i e that the replacement of populations that take discrete values by continuous variables can lead to large errors in what follows we introduce and discuss a finite difference poisson approximation of the stochastic process which respects the discreteness of the populations has the exact process as its infinitesimal in time limit and can be in turn approximated by a gaussian langevin process under conditions that are discussed we also emphasize the relation with previous work by kurtz to avoid making the present discussion unnecessarily

zeros of the wronskian and renormalized oscillation theory for general sturm liouville operators with separated boundary conditions we prove the following if e 1 2 r and if u 1 2 solve the differential equation hu j e ju j j 1 2 and respectively satisfy the boundary condition on the left right then the dimension of the spectral projection p e 1 e 2 h of h equals the number of zeros of the wronskian of u 1 and u 2

numerical procedures for sample structures on stochastic differential equations procedures are discussed for the numerical construction of sample processes on stochastic differential equations structures of a relevant class of gaussian white noise functionals are analyzed to some closed forms and new numerical algorithms for single noise problems are presented up to the accuracy of o h3 or within errors of o h7 2 in the sense of the mean square norm

numerical integration of multiplicative noise stochastic differential equations a two stage runge kutta algorithm for vector ito and by transform also stratonovich stochastic differential equations with multiplicative noise has been developed the method is second order accurate but for vanishing drift the algorithm yields a martingale independent of step size several examples are included to illustrate our method a discussion of errors shows that sample size can be as important as truncation

surface dynamics of the wolf villain model for epitaxial growth in 1 1 dimensions we investigated the spatiotemporal behavior of growing surfaces of the wolf villain model in 1 1 dimensions we measured the four physical quantities 1 the height height correlation function 2 the surface fluctuation width 3 the tilt tilt correlation function and 4 the height step fluctuation width by performing exclusive monte carlo simulations the crossover behavior from the 4h driven surface growth to the 2h driven surface growth has been observed in our numerical data of the four quantities moreover we found an evidence that the model belongs to the edwards wilkinson universality class in the limit of long time and large system size

stochastic equations for simple discrete models of epitaxial growth we derive continuous stochastic equations governing the asymptotic behavior of growth from a master equation for discrete growth models with local relaxation we consider several simple models of epitaxial growth the family the wolf villain and the das sarma tamborenea models and their modifications i n 1 11 dimensions we derive for each model the corresponding langevin equation and identify leading terms that determine the universality class our results for models with local relaxation are in agreement with recent computer simulations the applicability of the method in 211 dimensions is demonstrated in the case of the family model problems of the procedure in particular regularization in the continuous limit are discussed s1063 651x 96 00710 6

renormalization of stochastic lattice models basic formulation we describe a general method for the multiscale analysis of stochastic lattice models beginning with a lattice langevin formulation of site fluctuations we derive stochastic partial differential equations by regularizing the transition rules of the model subsequent coarse graining is accomplished by calculating renormalization group rg trajectories from initial conditions determined by the regularized atomistic models the rg trajectories correspond to hierarchies of continuum equations describing lattice models over expanding length and time scales these continuum equations retain a quantitative connection over different scales as well as to the underlying atomistic dynamics this provides a systematic method for the derivation of continuum equations from the transition rules of lattice models for any length and time scales as an illustration we consider the one dimensional 1d wolf villain wv model europhys lett 13 389 1990 the rg analysis of this model which we develop in detail is generic and can be applied to a wide range of conservative lattice models the rg trajectory of the 1d wv model shows a complex crossover sequence of linear and nonlinear stochastic differential equations which is in excellent agreement with kinetic monte carlo simulations of this model we conclude by discussing possible applications of the multiscale method described here to other nonequilibrium systems

perturbations of orthogonal polynomials with periodic recursion coefficients the results of denisov rakhmanov szeg shohat nevai and killip simon are extended from asymptotically constant orthogonal polynomials on the real line oprl and unit circle opuc to asymptotically periodic oprl and opuc the key tool is a characterization of the isospectral torus that is well adapted to the study of perturbations

minimum memory for generating rare events we classify the rare events of structured memoryful stochastic processes and use this to analyze sequential and parallel generators for these events given a stochastic process we introduce a method to construct a process whose typical realizations are a given process rare events this leads to an expression for the minimum memory required to generate rare events we then show that the recently discovered classical quantum ambiguity of simplicity also occurs when comparing the structure of process fluctuations

the anti self dual yang mills equation and classical transcendental solutions to the painleve ii and iv equations we present a determinant expression for a family of solutions to the sl 2 c anti self dual yang mills equation that corresponds to the classical transcendental solutions of the painleve ii and painleve iv equations

stochastic calculus application to dynamic bifurcations and threshold crossings for the dynamic pitchfork bifurcation in the presence of white noise the statistics of the last time at zero are calculated as a function of the noise level and the rate of change of the parameter the threshold crossing problem used for example to model the firing of a single cortical neuron is considered concentrating on quantities that may be experimentally measurable but have so far received little attention expressions for the statistics of pre threshold excursions occupation density and last crossing time of zero are compared with results from numerical generation of paths

studies on the painlev equations iii second and fourth painlev equations p ii andp iv etude des transformations birationnelles canoniques du systeme de painleve associe a chacune des equations

accurate monte carlo tests of the stochastic ginzburg landau model with multiplicative colored noise an accurate and fast monte carlo algorithm is proposed for solving the ginzburg landau equation with multiplicative colored noise the stable cases of solution for choosing time steps and trajectory numbers are discussed

langevin equations for fluctuating surfaces exact langevin equations are derived for the height fluctuations of surfaces driven by the deposition of material from a molecular beam we consider two types of model deposition models where growth proceeds by the deposition and instantaneous local relaxation of particles with no subsequent movement and models with concurrent random deposition and surface diffusion starting from a chapman kolmogorov equation the deposition relaxation and hopping rules of these models are first expressed as transition rates within a master equation for the joint height probability density function the kramers moyal van kampen expansion of the master equation in terms of an appropriate largeness parameter yields according to a limit theorem due to kurtz stoch proc appl 6 223 1978 a fokker planck equation that embodies the statistical properties of the original lattice model the statistical equivalence of this fokker planck equation solved in terms of its associated langevin equation and solutions of the chapman kolmogorov equation as determined by kinetic monte carlo kmc simulations of the lattice transition rules is demonstrated explicitly by comparing the surface roughness and the lateral height correlations obtained from the two formulations for the edwards wilkinson proc roy soc london ser a 381 17 1982 and wolfvillain europhys lett 13 389 1990 deposition models and for a model with random deposition and surface diffusion in each case as the largeness parameter is increased the langevin equation converges to the surface roughness and lateral height correlations produced by kmc simulations for all times including the crossover between different scaling regimes we conclude by examining some of the wider implications of these results including applications to heteroepitaxial systems and the passage to the continuum limit

exponential timestepping with boundary test for stochastic differential equations we present new numerical methods for scalar stochastic differential equations successive time increments are independent random variables with an exponential distribution we perform numerical experiments using a double well potential exponential timestepping algorithms are efficient for escape time problems because a simple boundary test can be performed at the end of each step

periodic solutions of the kdv equation in this paper we construct a large family of special solutions of the kdv equation which are periodic in x and almost periodic in t these solutions lie on n dimensional tori very likely they are dense among all solutions the special solutions are characterized variationally they minimize fn u subject to the constraints fj u aj j 1 n 1 here fj denote the remarkable sequence of conserved functionals discovered by kruskal and zabusky the above minimum problem was originally suggested by them in exploring the manifold of solutions of this minimum problem we make essential use of gardner s discovery that these functionals are in involution with respect to a suitable poisson bracket gardner greene kruskal and miura have shown that the eigenvalues of the schrodinger operator are conserved functionals if the potential is a function of t and satisfies the kdv equation in section 6 a new set of conserved quantities is constructed which serve as a link between the eigenvalues of the schrodinger operator and the fj another result in section 6 is a slight sharpening of an earlier result of the author and j moser for the special solutions constructed above all but 2n 1 eigenvalues of the schrodinger operator are double the simplest class of special solutions n 1 are cnoidal waves in an appendix m hyman describes the results of computing numerically the next simplest case n 2 these calculations show that the shape of these solutions recurs exactly after a finite time in a shifted position the theory verifies this fact

width distributions and the upper critical dimension of kardar parisi zhang interfaces simulations of restricted solid on solid growth models are used to build the width distributions of d 2 5 dimensional kardar parisi zhang kpz interfaces we find that the universal scaling function associated with the steady state width distribution changes smoothly as d is increased thus strongly suggesting that d 4 is not an upper critical dimension for the kpz equation the dimensional trends observed in the scaling functions indicate that the upper critical dimension is at infinity

multivariate hypergeometric cascades isomonodromy problems and ward ansatze the ward ansatze in twistor theory generate solutions of the anti self dual yang mills equations from solutions of the wave equation in spacetime the theory has a straightforward generalization in which the spacetime is an open set in the grassmannian gr 2 n the linear wave equation in this case has special solutions called the generalized confluent hypergeometric functions which are equivariant under the natural action of jordan groups on spacetime using the generalized penrose ward transform ward ansatze of increasing weight arising from such hypergeometric functions give a cascade of solutions to isomonodromy problems for systems of ordinary differential equations generally with irregular singularities the extended construction is explored in detail and two examples are given in the first solutions of the schlesinger equations are constructed from the lauricella fd functions in the second solutions of the isomonodromy problem for systems with two double poles and any number of simple poles are obtained from the generalized bessel functions

statistical mechanics of kinks for quasi exactly solvable potentials we study the thermodynamics of kinks in the presence of quasi exactly solvable qes potentials using a langevin code implemented on a massively parallel computer specifically we study the potential v 2 1 2 for which certain exact solutions of the schrodinger equation are known provided the parameters and satisfy certain constraints for 1 this potential has two degenerate minima otherwise it has only one minimum thus a system with this potential is capable of describing a second order phase transition a la the 4 model however no exact solutions of the schrodinger equation for this potential exist we have obtained an exact solution for the kink in this model in addition we have calculated in a 1d model such quantities as the probability density function pdf field configuration and field field correlation functions both above and below the transition temperature tc for several temperatures these quantities help us understand the contribution to the specific heat from coherent structures such as domain walls kinks as opposed to the contribution from lattice vibrations we have calibrated our results against known exact solutions for limiting cases with very high accuracy

theoretical analysis for critical fluctuations of relaxation trajectory near a saddle node bifurcation a langevin equation whose deterministic part undergoes a saddle node bifurcation is investigated theoretically it is found that statistical properties of relaxation trajectories in this system exhibit divergent behaviors near a saddle node bifurcation point in the weak noise limit while the final value of the deterministic solution changes discontinuously at the point a systematic formulation for analyzing a path probability measure is constructed on the basis of a singular perturbation method in this formulation the critical nature turns out to originate from the neutrality of exiting time from a saddle point the theoretical calculation explains results of numerical simulations

derivation of continuum stochastic equations for discrete growth models we present a formalism to derive the stochastic differential equations sdes for several solid on solid growth models our formalism begins with a mapping of the microscopic dynamics of growth models onto the particle systems with reactions and diffusion we then write the master equations for these corresponding particle systems and find the sdes for the particle densities finally by connecting the particle densities with the growth heights we derive the sdes for the height variables applying this formalism to discrete growth models we find the edwards wilkinson equation for the symmetric body centered solid on solid bcsos model the kardar parisi zhang equation for the asymmetric bcsos model and the generalized restricted solid on solid rsos model and the villain lai das sarma equation for the conserved rsos model in addition to the consistent forms of equations for growth models we also obtain the coefficients associated with the sdes

numerical treatment of stochastic differential equations we define general runge kutta approximations for the solution of stochastic differential equations sde these approximations are proved to converge in quadratic mean to the solution of an sde with a corrected drift the explicit form of the correction term is given concerning the order of convergence we show that in general it is impossible for the quadratic mean of the one step error to be of an order greater than o h 3 this order is attained e g by the stochastic analogue of heun s method in the n dimensional case the highest order of convergence is in general only o h 2 attained by euler s method the order o h 3 can only be reached if nabla x sigma r sigma s nabla x sigma s sigma r for the diffusion matrix

statistical mechanics of double sinh gordon kinks abstract we study the classical thermodynamics of the double sinh gordon dshg theory in 1 1 dimensions this model theory has a double well potential v cosh2 n 2 when n thus allowing for the existence of kinks and antikinks though it is non integrable the dshg model is remarkably amenable to analysis below we obtain exact single kink and kink lattice solutions as well as the asymptotic kink antikink interaction in the continuum limit finding the classical partition function is equivalent to solving for the ground state of a schrodinger like equation obtained via the transfer integral method for the dshg model this equation turns out to be quasi exactly solvable we exploit this property to obtain exact energy eigenvalues and wavefunctions for several temperatures both above and below the symmetry breaking transition temperature provided n 1 2 6 the availability of exact results provides an excellent testing ground for large scale langevin simulations the probability distribution function pdf calculated from langevin dynamics is found to be in striking agreement with the exact pdf obtained from the ground state wavefunction this validation points to the utility of a pdf based computation of thermodynamics utilizing langevin methods in addition to the pdf field field and field fluctuation correlation functions were computed and also found to be in excellent agreement with the exact results

crossover and universality in the wolf villain model the transition rules of the wolf villain model for the deposition and instantaneous relaxation of particles on a lattice are expressed as a langevin equation for the height fluctuations at each site a coarse graining transformation of this equation shows directly that this model belongs to the edwards wilkinson universality class in agreement with kinetic monte carlo simulations the crossover from the mullins herring equation is explained by the transformation under coarse graining of the coefficients in the equation of motion

edwards wilkinson equation from lattice transition rules continuum equations of motion for the height fluctuations of lattice growth models are derived from their transition rules by regularizing and coarse graining the associated discrete langevin equations for models with random deposition followed by instantaneous relaxation to a neighboring site based on identifying the local height minimum our methodology yields the edwards wilkinson equation the application of this procedure to other growth models is discussed

the edwards wilkinson model revisited large scale simulations of dynamic scaling in 2 1 dimensions abstract using extensive simulations of surface growth in the 2 1 dimensional atomistic model of edwards and wilkinson ew we have calculated both interfacial width and the structure factor to extract the dynamic exponent z in contrast to theoretical expectations finite size scaling of the data for both surface properties is achieved using z 1 63 instead of the predicted value of 2 0 a restricted variant of the ew model gives z 2 0 clarifying these non trivial differences in dynamical correlations now represents an intriguing theoretical challenge

stationary solutions of linear stochastic delay differential equations applications to biological systems recently k uchler and mensch stochastics stochastics rep 40 23 1992 derived exact stationary probability densities for linear stochastic delay differential equations this paper presents an alternative derivation of these solutions by means of the fokker planck approach introduced by guillouzic phys rev e 59 3970 1999 61 4906 2000 applications of this approach which is argued to have greater generality are discussed in the context of stochastic models for population growth and tracking movements

the inverse periodic problem for hill s equation with a finite gap potential let h q d d q x be the hill s operator with a periodic potential q of period one consider the following inverse problem find all potentials q x with the same periodic spectrum as a given potential p x two explicit solutions are known for finite gap potentials its and matveev 6 give an explicit formula in terms of theta functions their solution was generalized by mckean and trubowitz lo to infinite gap potentials finkel et al 5 give a second formula which expresses q in terms of the base potential p the dirichlet eigenfunctions of p and the floquet solutions of p the formula involves no algebraic geometry in this paper we represent finite gap potentials q as rational functions of the base potential p and the derivatives ofp the representation makes use of the finkel isaacson trubowitz fit formula

molecular modeling of proteins and mathematical prediction of protein structure this paper discusses the mathematical formulation of and solution attempts for the so called protein folding problem the static aspect is concerned with how to predict the folded native tertiary structure of a protein given its sequence of amino acids the dynamic aspect asks about the possible pathways to folding and unfolding including the stability of the folded protein from a mathematical point of view there are several main sides to the static problem the selection of an appropriate potential energy function the parameter identification by fitting to experimental data and the global optimization of the potential the dynamic problem entails in addition the solution of because of multiple time scales very stiff ordinary or stochastic differential equations molecular dynamics simulation or in case of constrained molecular dynamics of differential algebraic equations a theme connecting the static and dynamic aspect is the determination and formation of secondary structure motifs the present paper gives a self contained introduction to the necessary background from physics and chemistry and surveys some of the literature it also discusses the various mathematical problems arising some deficiencies of the current models and algorithms and possible past and future attacks to arrive at solutions to the protein folding problem

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

numerical solution of the kardar parisi zhang equation in one two and three dimensions abstract on a course grained level a family of microscopic growth processes may be described by a stochastic differential equation which is solved numerically for surface dimensions d 1 2 and 3 dimensional analysis shows that the spatial discretization parameter has the meaning of an effective coupling constant the numerical stability of the euler integration scheme is discussed for the strong coupling exponents defined by surface width time the following effective values were obtained d 1 0 330 0 004 and d 2 0 24 0 005 considering the width and its ensemble fluctuations at constant dimensionless time the transition between strong and weak coupling phases is located in d 3 for the largest coupling for which reliable data are available we obtain an effective exponent close to the best estimates on discrete models d 3 0 17

fokker planck equation for lattice deposition models an asymptotically exact fokker planck equation for the height fluctuations of lattice deposition models is derived from a van kampen expansion of the master equation using an edwards wilkinson type model as an example the solution of the equivalent langevin equation reproduces the surface roughness and lateral height correlations obtained with kinetic monte carlo kmc simulations our discrete equations of motion thereby provide an exact analytic and computational alternative to kmc simulations of these models