on a class of inhomogeneous ising quantum chains the hamiltonian of an ising quantum chain with a square root increasing transverse magnetic field is exactly diagonalized and its spectrum determined by the zeros of charlier polynomials we compute also the magnetization at zero temperature as a function of the position in closed form

the relation between amplitudes and critical exponents in finite size scaling the relation between critical exponents and the amplitude of the correlation length divergence at the critical point of two dimensional systems as a function of finite size is investigated and generalised in two ways correlations more general than those of order order type are included a form appropriate for anisotropic systems is proposed the authors present a exact results for the ising and gaussian models and b numerical results for the symmetric eight vertex baxter continuous q state potts and continuous n component cubic models

the phase plane picture for a class of fourth order conservative differential equations we study the bounded solutions of a class of fourth order equations u u f u 0 0 we show that when is not too large then the paths in the u u plane of two bounded solutions do not cross moreover the conserved quantity associated with the equation puts an ordering on the bounded solutions in the phase plane and a continuation theorem shows that they fill up part of the phase plane we apply these results to the extended fisher kolmogorov efk equation a fourth order model equation for bi stable systems the uniqueness and ordering results imply that as long as the stable equilibrium points are real saddles the bounded solutions of the stationary efk equation correspond exactly to those of the classical second order fisher kolmogorov equation besides we establish the asymptotic stability of the heteroclinic solution of the efk equation

effective edwards wilkinson equation for single file diffusion in this work we present an effective discrete edwards wilkinson equation aimed to describe the single file diffusion process the key physical properties of the system are captured defining an effective elasticity which is proportional to the single particle diffusion coefficient and to the inverse squared mean separation between particles the effective equation gives a description of single file diffusion using the global roughness of the system of particles which presents three characteristic regimes namely normal diffusion subdiffusion and saturation separated by two crossover times we show how these regimes scale with the parameters of the original system additional repulsive interaction terms are also considered and we analyze how the crossover times depend on the intensity of the additional terms finally we show that the roughness distribution can be well characterized by the edwards wilkinson universal form for the different single file diffusion processes studied here

shift invariance and surface growth the invariance of equations for self affine surface growth to reparametrization under the abelian group of shift transformations h x t to h x t l is used to bound the form of nonlinear terms and related kinetic coefficients in relaxational surface growth equations for conserved growth small but relevant diffusive terms second order in the driving can always be expected it is also shown that the asymptotic growth distributions in d 2 can be expected to be skew and are not derivable from a hamiltonian description

effect of a columnar defect on the shape of slow combustion fronts we report experimental results for the behavior of slow combustion fronts in the presence of a columnar defect with enhanced or reduced driving and compare them with those of mean field theory we also compare them with simulation results for an analogous problem of driven flow of particles with hard core repulsion asep and a single defect bond with a different hopping probability the difference in the shape of the front profiles for enhanced vs reduced driving in the defect clearly demonstrates the existence of a kardar parisi zhang type nonlinear term in the effective evolution equation for the slow combustion fronts we also find that slow combustion fronts display a faceted form for large enough enhanced driving and that there is a corresponding increase then in the average front speed this increase in the average front speed disappears at a nonzero enhanced driving in agreement with the simulated behavior of the asep model

nonuniversal critical behaviour in planar ising models with extended radially symmetric defects using conformal mapping and finite size scaling the authors determine the local magnetic exponent near a defect characterized by couplings of the form j r j 1 a r in accordance with phenomenological considerations they find that it depends continuously on the amplitude a both for a defect in the interior and on the boundary

uniqueness of the stationary wave for the extended fisher kolmogorov equation abstract the extended fisher kolmogorov equation ut uxxxx uxx u u3 0 models a binary system near the lifshitz critical point and is known to exhibit a stationary heteroclinic solution joining the equilibria 1 for the classical case 0 the heteroclinic is u x tanh x 2 and is unique up to the obvious symmetries we prove the conjecture that the uniqueness persists all the way to 1 8 where the onset of spatial chaos associated with the loss of monotonicity of the stationary wave is known to occur our methods are non perturbative and employ a global cross section to the hamiltonian flow of the stationary fourth order equation on the energy level of 1 we also prove uniform a priori bounds on all bounded stationary solutions valid for any 0

existence and multiplicity results for heteroclinic orbits of second order hamiltonian systems abstract connecting orbits of nonlinear differential equations have long been studied in the dynamical systems literature generally in a setting involving perturbations and using a melnikov function in this article we consider a class of second order hamiltonian systems which possess infinitely many or finite number of equilibria using variational arguments and penalization methods we obtain the existence of multiple heteroclinic orbits joining pairs of equilibria

conserved noise restricted solid on solid model on fractal substrates a conserved noise restricted solid on solid model on both a sierpinski gasket substrate and a checkerboard fractal substrate is studied the interface width w grows as t at early time t and becomes saturated at l for t l z where l is the system size we obtain 0 0788 0 377 for a sierpinski gasket and 0 100 0 516 for a checkerboard fractal the dynamic exponent z 4 79 for a sierpinski gasket and z 5 16 for a checkerboard fractal are obtained by the relation z they satisfy the scaling relations 4 2 d f z and z 2 z rw where z rw is the random walk exponent of the fractal substrate a fractional langevin equation is introduced to describe the model

periodic solutions and their connecting orbits of hamiltonian systems abstract this article deals with second order periodic hamiltonian systems we apply variational methods to obtain non constant periodic solutions for the time reversible hamiltonian systems there exist connecting orbits joining pairs of periodic solutions our methods can also be used to treat heteroclinic orbits connecting an equilibrium to a periodic solution

dynamic scaling behaviors of linear fractal langevin type equation driven by nonconserved and conserved noise abstract in order to study the effects of the microscopic details of fractal substrates on the scaling behavior of the growth model a generalized linear fractal langevin type equation h t 1 m 1 m z r w h z r w is the dynamic exponent of random walk on substrates driven by nonconserved and conserved noise is proposed and investigated theoretically employing scaling analysis corresponding dynamic scaling exponents are obtained

shooting methods and topological transversality we show that shooting methods for homoclinic or heteroclinic orbits in dynamical systems may automatically guarantee the topological transversality of the stable and unstable manifolds the interest of such results is twofold first these orbits persist under perturbations which destroy the structure allowing the shooting method and second topological transversality is often sufficient when some kind of transversality is required to obtain chaotic dynamics we shall focus on heteroclinic solutions in the extended fisher kolmogorov equation

the crossover phenomena in surface growth models with height dependent noise abstract in this paper we consider several known growth processes with height dependent noise this type of noise is interesting from a theoretical standpoint for example it paves the way to the derivation of the exact height distribution of the kpz equation through the hopf cole transformation in addition it may have implications for experimental growth processes using numerical methods we observe that adding such a noise to different growth processes can change their universality class or ruin the scaling laws in the case of mullins herring equation a two fold cross over is observed

interface depinning in a disordered medium numerical results abstract we propose a lattice model to study the dynamics of a driven interface in a medium with random pinning forces the critical exponents characterizing the depinning transition are determined numerically in 1 1 and 2 1 dimensions our findings are compared with recent numerical and analytical results for a langevin equation with quenched noise which is expected to be in the same universality class

static fluctuations of a thick one dimensional interface in the 1 1 directed polymer formulation numerical study we study numerically the geometrical and free energy fluctuations of a static one dimensional 1d interface with a short range elasticity submitted to a quenched random bond gaussian disorder of finite correlation length ensuremath xi g0 and at finite temperature t using the exact mapping from the static 1d interface to the 1 1 directed polymer dp growing in a continuous space we focus our analysis on the disorder free energy of the dp end point a quantity which is strictly zero in the absence of disorder and whose sample to sample fluctuations at a fixed growing time t inherit the statistical translation invariance of the microscopic disorder explored by the dp constructing a new numerical scheme for the integration of the kardar parisi zhang evolution equation obeyed by the free energy we address numerically the time and temperature dependence of the disorder free energy fluctuations at fixed finite ensuremath xi we examine on one hand the amplitude stackrel ifmmode tilde else fi d t and effective correlation length stackrel ifmmode tilde else fi ensuremath xi t of the free energy fluctuations and on the other hand the imprint of the specific microscopic disorder correlator on the large time shape of the free energy two point correlator we observe numerically the crossover to a low temperature regime below a finite characteristic temperature t c ensuremath xi as previously predicted by gaussian variational method computations and scaling arguments and extensively investigated analytically in phys rev e 87 042406 2013 finally we address numerically the time and temperature dependence of the roughness b t which quantifies the dp end point transverse fluctuations and we show how the amplitude stackrel ifmmode tilde else fi d ensuremath infty t ensuremath xi controls the different regimes experienced by b t in agreement with the analytical predictions of a dp toy model approach

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

synchronization in weighted uncorrelated complex networks in a noisy environment optimization and connections with transport efficiency motivated by synchronization problems in noisy environments we study the edwards wilkinson process on weighted uncorrelated scale free networks we consider a specific form of the weights where the strength and the associated cost of a link is proportional to kikj beta with ki and kj being the degrees of the nodes connected by the link subject to the constraint that the total edge cost is fixed we find that in the mean field approximation on uncorrelated scale free graphs synchronization is optimal at beta 1 numerical results based on exact numerical diagonalization of the corresponding network laplacian confirm the mean field results with small corrections to the optimal value of beta employing our recent connections between the edwards wilkinson process and resistor networks and some well known connections between random walks and resistor networks we also pursue a naturally related problem of optimizing performance in queue limited communication networks utilizing local weighted routing schemes

ballistic deposition on deterministic fractals observation of discrete scale invariance the growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations first we attempt the description of the evolving interface of the aggregates by applying the well established family vicsek dynamic scaling approach systematic deviations from that standard scaling law are observed suggesting that significant scaling corrections have to be introduced in order to achieve a more accurate understanding of the behavior of the interface subsequently we study the internal structure of the growing aggregates that can be rationalized in terms of the scaling behavior of frozen trees i e structures inhibited for further growth lying below the growing interface it is shown that the rms height h s and width w s of the trees of size s obey power laws of the form h s ensuremath propto s ensuremath nu ensuremath parallel and w s ensuremath propto s ensuremath nu ensuremath perp respectively also the tree size distribution n s behaves according to n s ensuremath sim s ensuremath ensuremath tau here ensuremath nu ensuremath parallel and ensuremath nu ensuremath perp are the correlation length exponents in the directions parallel and perpendicular to the interface respectively also ensuremath tau is a critical exponent however due to the interplay between the discrete scale invariance of the underlying fractal substrates and the dynamics of the growing process all these power laws are modulated by logarithmic periodic oscillations the fundamental scaling ratios characteristic of these oscillations can be linked to the spatial fundamental scaling ratio of the underlying fractal by means of relationships involving critical exponents we argue that the interplay between the spatial discrete scale invariance of the fractal substrate and the dynamics of the physical process occurring in those media is a quite general phenomenon that leads to the observation of logarithmic periodic modulations of physical observables

equilibrium restricted solid on solid growth model on fractal substrates the equilibrium restricted solid on solid growth model on fractal substrates is studied by introducing a fractional langevin equation the growth exponent beta and the roughness exponent alpha defined respectively by the surface width via w approximately t beta and the saturated width via w sat approximately l alpha l being the system size were obtained by a power counting analysis and the scaling relation 2alpha d f z rw was found to hold the numerical simulation data on sierpinski gasket checkerboard fractal and critical percolation cluster were found to agree well with the analytical predictions of the fractional langevin equation

cascades of reversible homoclinic orbits to a saddle focus equilibrium abstract in a reversible system we consider a homoclinic orbit being bi asymptotic to a saddle focus equilibrium as was proved by devaney 1977 there exists a one parameter family of periodic orbits accumulating onto this homoclinic orbit in the present paper we show that for any n 2 there exist infinitely many n homoclinic orbits in a neighborhood of the primary homoclinic orbit each of them is accompanied by one or more families of periodic orbits moreover we indicate how these families of periodic orbits correspond to branches of subharmonic periodic orbits

travelling fronts and entire solutions of the fisher kpp equation in ℝn this paper is devoted to time global solutions of the fisher kpp equation in n where f is a c 2 concave function on 0 1 such that f 0 f 1 0 and f 0 on 0 1 it is well known that this equation admits a finite dimensional manifold of planar travelling fronts solutions by considering the mixing of any density of travelling fronts we prove the existence of an infinite dimensional manifold of solutions in particular there are infinite dimensional manifolds of nonplanar travelling fronts and radial solutions furthermore up to an additional assumption a given solution u can be represented in terms of such a mixing of travelling fronts

symmetry based determination of space time functions in nonequilibrium growth processes we study the space time correlation and response functions in nonequilibrium growth processes described by linear stochastic langevin equations exploiting exclusively the existence of space and time dependent symmetries of the noiseless part of these equations we derive expressions for the universal scaling functions of two time quantities which are found to agree with the exact expressions obtained from the stochastic equations of motion the usefulness of the space time functions is illustrated through the investigation of two atomistic growth models the family model and the restricted family model which are shown to belong to a unique universality class in 1 1 and 2 1 space dimensions this corrects earlier studies which claimed that in 2 1 dimensions the two models belong to different universality classes

kinetic roughening global quantities and fluctuation dissipation relations abstract growth processes and interface fluctuations can be studied through the properties of global quantities we here discuss a global quantity that not only captures better the roughness of an interface than the widely studied surface width but that is also directly conjugate to an experimentally accessible parameter thereby allowing us to study in a consistent way the global response of the system to a global change of external conditions exploiting the full analyticity of the linear edwards wilkinson and mullins herring equations we study in detail various two time functions related to that quantity this quantity fulfills the fluctuation dissipation theorem when considering steady state equilibrium fluctuations

marginally inhomogeneous semiinfinite two dimensional ising models the scaling dimensions of the semiinfinite two dimensional ising model with smoothly inhomogeneous couplings are determined in general by the eigenvalues of a schrodinger type equation the author obtains exact results for a marginal two parameter inhomogeneity that corresponds to a supersymmetric quantum mechanical potential the results are compared with predictions of conformal invariance

oscillatory solutions of fourth order conservative systems via the conley index in this paper we investigate periodic solutions of second order lagrangian systems which oscillate around equilibrium points of center type the main ingredients are the discretization of second order lagrangian systems that satisfy the twist property and the theory of discrete braid invariants developed by ghrist et al 2003 5 the problem with applying this topological theory directly is that the braid types in our analysis are so called improper this implies that the braid invariants do not entirely depend on the topology the relevant braid classes are non isolating neighborhoods of the flow so that their conley index is not universal in first part of this paper we develop the theory of the braid invariant for improper braid classes and in the second part this theory is applied to second order lagrangian system and in particular to the swift hohenberg equation

global dynamics of stationary solutions of the extended fisher kolmogorov equation in this paper we study the fourth order differential equation d4udt4 qd2udt2 u3 u 0 which arises from the study of stationary solutions of the extended fisher kolmogorov equation denoting x u y dudt z d2udt2 v d3udt3 this equation becomes equivalent to the polynomial system x y y z z v v x qz x3 with x y z v r4 and q r as usual the dot denotes the derivative with respect to the time t since the system has a first integral we can reduce our analysis to a family of systems on r3 we provide the global phase portrait of these systems in the poincare ball i e in the compactification of r3 with the sphere s2 of the infinity

marginal extended perturbations in two dimensions and gap exponent relations the most general form of a marginal extended perturbation in a two dimensional system is deduced from scaling considerations it includes as particular cases extended perturbations decaying either from a surface a line or a point for which exact results have been previously obtained the first order corrections to the local exponents which are functions of the amplitude of the defect are deduced from a perturbation expansion of the two point correlation functions assuming covariance under conformal transformation the perturbed system is mapped onto a cylinder working in the hamiltonian limit the first order corrections to the lowest gaps are calculated for the ising model the results confirm the validity of the gap exponent relations for the perturbed system

surface growth on percolation networks by a conserved noise restricted solid on solid growth model surface growth by the conserved noise restricted solid on solid model is investigated on diluted lattices i e on percolation networks that are embedded in two spatial dimensions the growth exponent and the roughness exponent are defined respectively by the mean square surface width via w 2 t t 2 and the mean square saturated width via w sat 2 l l 2 where l is the system size these are measured on both an infinite network and a backbone network and the results are compared with power counting predictions obtained using the fractional langevin equation while the monte carlo results on deterministic fractal substrates show excellent agreement with the predictions d h kim and j m kim phys rev e 84 011105 2011 the results on critical percolation networks deviate by 8 12 from these predictions

heteroclinic solutions for the extended fisher kolmogorov equation abstract we study the extended fisher kolmogorov efk equation and its variants by variational approach we show that for every global minimum of the potential function v there is a pair of heteroclinic solutions one emanating from and the other terminating at we require neither superquadratic growth of v nor the presence of saddle focus equilibria moreover v is allowed to approach its minimal level near infinity

on the existence and non existence of bounded solutions for a fourth order ode abstract we prove that if f c 1 r is coercive and f 0 is discrete then the efk equation 1 u c 2 u f u 0 possesses l r solutions if and only if f changes sign at least twice as a corollary we prove that if u n solves u n c n 2 u n f u n 0 then u n if c n 0 provided f has a unique local minimum its only minimum is nondegenerate and int f 0 finally we give criteria ensuring existence and non existence of t periodic solutions to 1 when f has multiple wells

interface growth with competing surface currents the authors examine the dynamics of interface growth under the combined influence of a stabilizing and a destabilizing surface current in 1 1 dimensions it has been shown that the surface is weakly stabilized if a newly deposited particle can move locally to maximize the total number of nearest neighbour contacts with the surface curvature driven current the introduction of a weak destabilizing surface tension term results in an almost periodic grooved surface the width of the surface grows linearly in time and does not reach a steady state it appears that such a formation cannot be described by a continuous langevin equation

numerical study of a non equilibrium interface model we have carried out extensive computer simulations of one dimensional models related to the low noise solid on solid non equilibrium interface of a two dimensional anchored toom model with unbiased and biased noise for the unbiased case the computed fluctuations of the interface in this limit provide new numerical evidence for the logarithmic correction to the subnormal l frac 1 2 variance which was predicted by the dynamic renormalization group calculations on the modified edwards wilkinson equation in the biased case the simulations are in close quantitative agreement with the predictions of the collective variable approximation cva which gives the same l frac 2 3 behavior of the variance as the kpz equation

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

global branches of multi bump periodic solutions of the swift hohenberg equation in this paper we study the existence of single and multi bump periodic solutions of a class of fourth order ordinary differential equations arising in problems of pattern formation measuring the tendency to form patterns by a parameter q we view the problem as a nonlinear eigenvalue problem with the use of analytical as well as numerical methods branches of periodic solutions are investigated both locally and globally

instabilities induced by a weak breaking of a strong spatial resonance abstract through multiple scales and symmetry arguments we derive a model set of amplitude equations describing the interaction of two steady state pattern forming instabilities in the case that the wavelengths of the instabilities are nearly in the ratio 1 2 in the case of exact 1 2 resonance the amplitude equations are odes here they are pdes we discuss the stability of spatially periodic solutions to long wavelength disturbances by including these modulational effects we are able to explore the relevance of the exact 1 2 results to spatially extended physical systems for parameter values near to this codimension two bifurcation point these new instabilities can be described in terms of reduced normal form pdes near various secondary codimension two points the robust heteroclinic cycle in the odes is destabilised by long wavelength perturbations and a stable periodic orbit is generated that lies close to the cycle an analytic expression giving the approximate period of this orbit is derived

explicit estimates on the torus for the sup norm and the dissipative length scale of solutions of the swift hohenberg equation in one and two space dimensions abstract in this work we have obtained explicit and accurate estimates of the sup norm for solutions of the swift hohenberg equation she in one and two space dimensions by using the best so far available estimates of the embedding constants which appear in the classical functional interpolation inequalities used in the study of solutions of dissipative partial differential equations we have evaluated in an explicit manner the values of the sup norm of the solutions of the she in addition we have calculated the so called time averaged dissipative length scale associated to the above solutions

infinite conformal symmetry of critical fluctuations in two dimensions we study the massless quantum field theories describing the critical points in two dimensional statistical systems these theories are invariant with respect to the infinite dimensional group of conformal analytic transformations it is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the virasoro algebra exactly solvable theories associated with degenerate representations are analized in these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations

relaxation function and dynamic exponent for discrete growth models abstract we develop a new method of measuring the dynamic exponent z for discrete growth models starting from a sinusoidal initial surface of a selected wavelength l we consider a relaxation function r t l which is a quantity similar to the autocorrelation function of the surface height typically the relaxation function decays exponentially following e g t l where l is the relaxation time and it depends on the wavelength l the dynamic exponent z is measured by the relation l l z we find that g x scales as x 1 0 for the family model and as x 1 5 for the restricted solid on solid model the advantages of the method are also discussed

homoclinic solutions for swift hohenberg and suspension bridge type equations we establish the existence of homoclinic solutions for a class of fourth order equations which includes the swift hohenberg model and the suspension bridge equation in the first case the nonlinearity has three zeros corresponding to a double well potential while in the second case the nonlinearity is asymptotically constant on one side the swift hohenberg model is a higher order extension of the classical fisher kolmogorov model its more complicated dynamics give rise to further possibilities of pattern formation the suspension bridge equation as studied by chen and mckenna j differential equations 136 1997 325 355 we give a positive answer to an open question raised by the authors c 2002 elsevier science usa

generalized survival in equilibrium step fluctuations we investigate the dynamics of a generalized survival probability s t r defined with respect to an arbitrary reference level r rather than the average in equilibrium step fluctuations the exponential decay at large time scales of the generalized survival probability is numerically analyzed s t r is shown to exhibit simple scaling behavior as a function of system size l sampling time ensuremath delta t and the reference level r the generalized survival time scale ensuremath tau s r associated with s t r is shown to decay exponentially as a function of r

second order lagrangian twist systems simple closed characteristics we consider a special class of lagrangians that play a fundamental role in the theory of second order lagrangian systems twist systems this subclass of lagrangian systems is defined via a convenient monotonicity property that such systems share this monotonicity property twist property allows a finite dimensional reduction of the variational principle for finding closed characteristics in fixed energy levels this reduction has some similarities with the method of broken geodesics for the geodesic variational problem on riemannian manifolds on the other hand the monotonicity property can be related to the existence of local twist maps in the associated hamiltonian flow the finite dimensional reduction gives rise to a second order monotone recurrence relation we study these recurrence relations to find simple closed characteristics for the lagrangian system more complicated closed characteristics will be dealt with in future work furthermore we give conditions on the lagrangian that guarantee the twist property

a fully discrete c0 interior penalty galerkin approximation of the extended fisher kolmogorov equation a fully discrete c 0 interior penalty finite element method is proposed and analyzed for the extended fisher kolmogorov efk equation u email protected d email protected u 3 u 0 with appropriate initial and boundary conditions where c is a positive constant we derive a regularity estimate for the solution u of the efk equation that is explicit in c and as a consequence we derive a priori error estimates that are robust in c

extreme fluctuations in stochastic network coordination with time delays we study the effects of uniform time delays on the extreme fluctuations in stochastic synchronization and coordination problems with linear couplings in complex networks we obtain the average size of the fluctuations at the nodes from the behavior of the underlying modes of the network we then obtain the scaling behavior of the extreme fluctuations with system size as well as the distribution of the extremes on complex networks and compare them to those on regular one dimensional lattices for large complex networks when the delay is not too close to the critical one fluctuations at the nodes effectively decouple and the limit distributions converge to the fisher tippett gumbel density in contrast fluctuations in low dimensional spatial graphs are strongly correlated and the limit distribution of the extremes is the airy density finally we also explore the effects of nonlinear couplings on the stability and on the extremes of the synchronization landscapes

radial fredholm perturbation in the two dimensional ising model and gap exponent relation we consider concentric circular defects in the two dimensional ising model which are distributed according to a generalized fredholm sequence i e at exponentially increasing radii this type of aperiodicity does not change the bulk critical behaviour but introduces a marginal extended perturbation the critical exponent of the local magnetization is obtained through finite size scaling using a corner transfer matrix approach in the extreme anisotropic limit it varies continuously with the amplitude of the modulation and is closely related to the magnetic exponent of the radial hilhorst van leeuwen model through a conformal mapping of the system onto a strip the gap exponent relation is shown to remain valid for such an aperiodic defect

joint distributions of partial and global maxima of a brownian bridge we analyze the joint distributions and temporal correlations between the partial maximum m and the global maximum m achieved by a brownian bridge on the subinterval and on the entire interval respectively we determine three probability distribution functions the joint distribution of both maxima the distribution p m of the partial maximum and the distribution of the gap between the maxima we present exact results for the moments of these distributions and quantify the temporal correlations between m and m by calculating the pearson correlation coefficient

minimal heteroclinics for a class of fourth order o d e systems abstract we prove the existence of minimal heteroclinic orbits for a class of fourth order o d e systems with variational structure in our general set up the set of equilibria of these systems is a union of manifolds and the heteroclinic orbits connect two disjoint components of this set

stable patterns for fourth order parabolic equations we consider fourth order parabolic equations of gradient type for the sake of simplicity the analysis is carried out for the specific equation u

roughening of the interfaces in 1 1 dimensional two component surface growth with an admixture of random deposition we simulate competitive two component growth on a one dimensional substrate of l sites one component is a poisson type deposition that generates kardar parisi zhang kpz correlations the other is random deposition rd we derive the universal scaling function of the interface width for this model and show that the rd admixture acts as a dilatation mechanism to the fundamental time and height scales but leaves the kpz correlations intact this observation is generalized to other growth models it is shown that the flat substrate initial condition is responsible for the existence of an early nonscaling phase in the interface evolution the length of this initial phase is a nonuniversal parameter but its presence is universal we introduce a method to measure the length of this initial nonscaling phase in application to parallel and distributed computations the important consequence of the derived scaling is the existence of the upper bound for the desynchronization in a conservative update algorithm for parallel discrete event simulations it is shown that such algorithms are generally scalable in a ring communication topology

positivity and the attractor dimension in a fourth order reaction diffusion equation in this paper we investigate the semilinear partial differential equation ut fuxxxx uxx u 1 u2 with a view particularly to obtaining some insight into how one might establish positivity preservation results for equations containing fourth order spatial derivatives the maximum principle cannot be applied to such equations however progress can be made by employing some very recent best possible interpolation inequalities due to the third named author in which the interpolation constants are both explicitly known and sharp these are used to estimate the lx distance between u and 1 during the evolution a positivity preservation result can be obtained under certain restrictions on the initial datum we also establish an explicit two sided estimate for the fractal dimension of the attractor which is sharp in terms of the physical parameters

homotopy classes for stable connections between hamiltonian saddle focus equilibria for a class of hamiltonian systems in 4 the set of homoclinic and heteroclinic orbits which connect saddle focus equilibria is studied using a variational approach the oscillatory properties of a saddle focus equilibrium and the variational nature of the problem give rise to connections in many homotopy classes of the configuration plane punctured at the saddle foci this variational approach does not require any assumptions on the intersections of stable and unstable manifolds such as transversality moreover these connections are shown to be local minimizers of an associated action functional this result has applications to spatial pattern formation in a class of fourth order bistable evolution equations

entire solutions of the kpp equation this paper deals with the solutions defined for all time of the kpp equation ut uxx f u 0 0 f 0 1 0i n 0 1 and f 0 s f 0 0 in 0 1 this equation admits infinitely many traveling wave type solutions increasing or decreasing in x i t also admits solutions that depend only on t in this paper we build four other manifolds of solutions one is 5 dimensional one is 4 dimensional and two are 3 dimensional some of these new solutions are obtained by considering two traveling waves that come from both sides of the real axis and mix furthermore the traveling wave solutions are on the boundary of these four manifolds c 1999 john wiley sons inc

discrete growth models on deterministic fractal substrate abstract the growth of the modified family model and the etching model on the sierpinski carpet is studied by means of numerical simulations the evolving interface of the aggregates is described by the well established family vicsek dynamic scaling approach the results of the modified family model prove the universality of the fractional langevin equation introduced by lee and kim s b lee j m kim phys rev e 80 2009 021101 the etching model also shows good scaling behavior we conjecture that the systematic deviations of the data found in the ballistic deposition c m horowitz f roma e v albano phys rev e 78 2008 061118 may be due to the finite size effects of the ballistic deposition model

schramm loewner evolution theory of the asymptotic behaviors of 2 1 dimensional wolf villain model abstract although extensive analytical and numerical work has focus on investigating the 2 1 dimensional wolf villain wv model some problems concerning its asymptotical behaviors such as the universality class to which it belongs remain controversial the schramm loewner evolution sle theory is an attractive approach to describe the fluctuation phenomena and random processes and has also been applied to the analysis of the stochastic growth of surfaces in this work we applied sle theory to the analysis of the saturated surface to conduct in depth research with a new perspective on the asymptotical behaviors of the 2 1 dimensional wv model on the basis of the analysis of the saturated surface contour lines we determine that the diffusion coefficient calculated for 2 1 dimensional wv model is 2 91 0 01 and that for family model is 2 88 0 01 accordingly we can conclude from the view of sle theory that the 2 1 dimensional wv model similar to the family model also belongs to the edwards wilkinson universality class

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

mapping spatial persistent large deviations of nonequilibrium surface growth processes onto the temporal persistent large deviations of stochastic random walk processes spatial persistent large deviations probability of surface growth processes governed by the edwards wilkinson dynamics px x s with 1 or s or 1 is mapped isomorphically onto the temporal persistent large deviations probability pt t s associated with the stochastic markovian random walk problem we show using numerical simulations that the infinite family of spatial persistent large deviations exponents thetax s characterizing the power law decay of px x s agrees as predicted on theoretical grounds by phys rev lett 86 3700 2001 with the numerical measurements of thetat s the continuous family of exponents characterizing the long time power law behavior of pt t s we also discuss the simulations of the spatial persistence probability corresponding to a discrete model in the mullins herring universality class where our discrete simulations do not agree well with the theoretical predictions perhaps because of the severe finite size corrections which are known to strongly inhibit the manifestation of the asymptotic continuum behavior in discrete models involving large values of the dynamical exponent and the associated extremely slow convergence to the asymptotic regime

on the distribution of surface extrema in several one and two dimensional random landscapes we study here a standard next nearest neighbor nnn model of ballistic growth on one and two dimensional substrates focusing our analysis on the probability distribution function p m l of the number m of maximal points i e local peaks of growing surfaces our analysis is based on two central results i the proof presented here of the fact that uniform one dimensional ballistic growth process in the steady state can be mapped onto rise and descent sequences in the ensemble of random permutation matrices and ii the fact established in ref g oshanin and r voituriez j phys a math gen 37 6221 2004 that different characteristics of rise and descent patterns in random permutations can be interpreted in terms of a certain continuous space hammersley type process for one dimensional system we compute p m l exactly and also present explicit results for the correlation function characterizing the enveloping surface for surfaces grown on 2d substrates we pursue similar approach considering the ensemble of permutation matrices with long ranged correlations determining exactly the first three cumulants of the corresponding distribution function we define it in the scaling limit using an expansion in the edgeworth series and show that it converges to a gaussian function as l

existence and stability of traveling fronts in the extended fisher kolmogorov equation abstract we study traveling wave solutions to a general fourth order differential equation that is a singular perturbation of the fisher kolmogorov equation we apply the geometric method for singularly perturbed systems to show that for every positive wavespeed there exists a traveling wave also we find that there exists a critical wavespeed c which divides these solutions into monotonic c c and oscillatory c c solutions we show that the monotonic fronts are locally stable under perturbations in appropriate weighted sobolev spaces by using various energy functionals