violation of the fluctuation dissipation theorem in glassy systems basic notions and the numerical evidence this review reports on the research done during past years on violations of the fluctuation dissipation theorem fdt in glassy systems it is focused on the existence of a quasi fluctuation dissipation theorem qfdt in glassy systems and the current supporting knowledge gained from numerical simulation studies it covers a broad range of non stationary aging and stationary driven systems such as structural glasses spin glasses coarsening systems ferromagnetic models at criticality trap models models with entropy barriers kinetically constrained models sheared systems and granular media the review is divided into four main parts 1 an introductory section explaining basic notions related to the existence of the fdt in equilibrium and its possible extension to the glassy regime qfdt 2 a description of the basic analytical tools and results derived in the framework of some exactly solvable models 3 a detailed report of the current evidence in favour of the qfdt and 4 a brief digression on the experimental evidence in its favour this review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the qfdt as well as for the more expert readers who may be interested in more specific results

geographic coarse graining analysis of the railway network of china abstract we investigate the detailed empirical analysis of the statistical properties of the railway network of china rnc in space l and space g constructed by geographic coarse graining process the rnc exhibits similar properties in the cumulative distributions of degree and strength in two spaces and it presents the hierarchical structure small world behavior and assortativity areciprocal connection both in space l and space g we also investigate the path length that every train runs the distribution of the railroad length per degree and the optimal distribution of stations

role of feedback and broadcasting in the naming game the naming game ng describes the agreement dynamics of a population of agents that interact locally in a pairwise fashion and in recent years statistical physics tools and techniques have greatly contributed to shed light on its rich phenomenology here we investigate in details the role played by the way in which the two agents update their states after an interaction we show that slightly modifying the ng rules in terms of which agent performs the update in given circumstances i e after a success can either alter dramatically the overall dynamics or leave it qualitatively unchanged we understand analytically the first case by casting the model in the broader framework of a generalized ng as for the second case on the other hand we note that the modified rule reproducing the main features of the usual ng corresponds in fact to a simplification of it consisting in the elimination of feedback between the agents this allows us to introduce and study a very natural broadcasting scheme on networks that can be potentially relevant for different applications such as the design and implementation of autonomous sensor networks as pointed out in the recent literature

nonexistence of the reversed flow solutions of the falkner skan equations abstract nonexistence of reversed flow solutions of the well known falkner skan equations arising in the boundary layer theory is considered analytically a new system of two singular integral equations are proposed and studied which plays a key role in the study of reversed flow solutions the properties of the velocity and the shear stress of the reversed flows are provided these properties describe the shapes and behaviors of the curves of the velocity and the shear stress functions a new lower bound of the skin friction which is useful in numerical analysis is given the results on the nonexistence of reversed flow solutions can be used to estimate the exact critical value which is of importance in aeronautics because separation occurs at this value

scaling in the aging dynamics of the site diluted ising model we study numerically the phase ordering kinetics of the two dimensional site diluted ising model the data can be interpreted in a framework motivated by renormalization group concepts apart from the usual fixed point of the nondiluted system there exist two disorder fixed points characterized by logarithmic and power law growth of the ordered domains this structure gives rise to a rich scaling behavior with an interesting crossover due to the competition between fixed points and violation of superuniversality

random geometric graphs we analyze graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present the critical connectivity is found numerically by examining the size of the largest cluster we derive an analytical expression for the cluster coefficient which shows that the graphs are distinctly different from standard random graphs even for infinite dimensionality insights relevant for graph bipartitioning are included

continuation theorems for periodic perturbations of autonomous systems it is first shown in this paper that whenever it exists the coincidence degree of the left hand member of an autonomous differential equation x g x 0 in the space of periodic functions with fixed period omega can be computed in terms of the brouwer degree of g this result provides efficient continuation theorems specially for omega periodic perturbations of autonomous systems extensions to differential equations in flow invariant enr s are also given

topology induced coarsening in language games we investigate how very large populations are able to reach a global consensus out of local microscopic interaction rules in the framework of a recently introduced class of models of semiotic dynamics the so called naming game we compare in particular the convergence mechanism for interacting agents embedded in a low dimensional lattice with respect to the mean field case we highlight that in low dimensions consensus is reached through a coarsening process that requires less cognitive effort of the agents with respect to the mean field case but takes longer to complete in one dimension the dynamics of the boundaries is mapped onto a truncated markov process from which we analytically computed the diffusion coefficient more generally we show that the convergence process requires a memory per agent scaling as n and lasts a time n 1 2 d in dimension d 4 the upper critical dimension while in mean field both memory and time scale as n 3 2 for a population of n agents we present analytical and numerical evidence supporting this picture

kinetics of domain growth in systems with local barriers we study domain growth in spin 1 lattice models having nonconserved spin flip kinetics with local barriers our primary motivation is to model the relaxational behavior of physical systems in which molecular motion is impeded by local kinetic barriers the kinetic constraint is such that a spin from an up down state can flip to a down up state only via the zero state which has a higher energy we examine how the usual curvature driven domain growth is affected by these local barriers and whether the single spin barriers have a collective effect this paper presents comprehensive numerical results for phase ordering dynamics in this model using monte carlo simulations we demonstrate dynamical scaling for domain size distribution functions and spatial correlation functions we also present results for the time dependence of characteristic length scales and autocorrelation functions the length scale behavior is interpreted in terms of the random walk of steps on domain boundaries furthermore we present a simple stochastic model to derive an analytic expression for the autocorrelation function which exhibits a stretched exponential behavior over an extended regime in agreement with our numerical simulations

numerical solution of the falkner skan equation based on quasilinearization we present two iterative methods for solving the falkner skan equation based on the quasilinearization method we formulate the original problem as a new free boundary value problem the truncated boundary depending on a small parameter is an unknown free boundary and has to be determined as part of solution using a change of variables the free boundary value problem is transformed to a problem defined on 0 1 we apply the quasilinearization method to solve the resulting nonlinear problem then we propose two different iterative algorithms by means of a cubic spline solver numerical results for various instances are compared with those reported previously in the literature the comparisons show the accuracy robustness and efficiency of the presented methodology

a variational inequality theory in reflexive smooth banach spaces and applications to p laplacian elliptic inequalities abstract we develop a theory of variational inequality for demicontinuous s contractive maps in reflexive smooth banach spaces variational inequality theorems are proved and applied to study existence of nonzero positive weak solutions for p laplacian elliptic inequalities and a population model of one species arising in mathematical biology

coarsening in the q state potts model and the ising model with globally conserved magnetization we study the nonequilibrium dynamics of the q state potts model following a quench from the high temperature disordered phase to zero temperature the time dependent two point correlation functions of the order parameter field satisfy dynamic scaling with a length scale l t t 1 2 in particular the autocorrelation function decays as l t q we illustrate these properties by solving exactly the kinetic potts model in d 1 we then analyze a langevin equation of an appropriate field theory to compute these correlation functions for general q and d we establish a correspondence between the two point correlations of the q state potts model and those of a kinetic ising model evolving with a fixed magnetization 2 q 1 the dynamics of this ising model is solved exactly in the large q limit and in the limit of a large number of components n for the order parameter for general q and in any dimension we introduce a gaussian closure approximation and calculate within this approximation the scaling functions and the exponent q these are in good agreement with the direct numerical simulations of the potts model as well as the kinetic ising model with fixed magnetization we also discuss the existing and possible experimental realizations of these models

on similarity solutions of a boundary layer problem with an upstream moving wall this work deals with the problem of a boundary layer on a flat plate which has a constant velocity opposite in direction to that of the uniform mainstream it has previously been shown that the solution of this boundary value problem is crucially dependent on the parameter which is the ratio of the velocity of the plate to the velocity of the free stream in particular it was proved that a solution exists only if this parameter does not exceed a certain critical value and numerical evidence was adduced to show that this solution is nonunique using crocco formulation the present work proves this nonuniqueness also considered are the analyticity of solutions and the derivation of upper bounds on the critical value of wall velocity parameter

existence and nonuniqueness of solutions of a singular nonlinear boundary layer problem abstract sufficient conditions for existence and nonuniqueness of positive solutions of the singular boundary value problem g x g x h x 0 k x k 0 g k c g 1 0 are obtained also it is proved that the solutions with g k ck for c and g k k 2 2h k for c 0 are unique furthermore it is shown numerically that for h x x there are exactly two solutions for the problem

a class of expansive type krasnosel skii fixed point theorems abstract in this paper we establish some new fixed point theorems for the sum of two operators in particular one new theorem complements the well known krasnosel skii fixed point theorem in the sense that the mapping t is expansive rather than contractive some previous and related results are extended and developed as an application to one of our main results the existence of periodic solutions for some nonlinear integral equation is considered

on solutions of some singular non linear differential equations arising in boundary layer theory abstract solutions for a class of singular non linear second order differential equations arising in boundary layer theory with suction injection when crocco variables are employed are obtained existence uniqueness and analyticity results are established for boundary conditions corresponding to flow of a uniform stream past a semi infinite flat plate classical problem of blasius and for the flow behind weak expansion since the standardization technique in refs 8 9 11 does not work a new technique is developed and used in proving existence and uniqueness theorems furthermore the analytical solutions are compared with the numerical ones

naming games in two dimensional and small world connected random geometric networks we investigate a prototypical agent based model the naming game on two dimensional random geometric networks the naming game a baronchelli et al j stat mech theory exp 2006 p06014 is a minimal model employing local communications that captures the emergence of shared communication schemes languages in a population of autonomous semiotic agents implementing the naming games with local broadcasts on random geometric graphs serves as a model for agreement dynamics in large scale autonomously operating wireless sensor networks further it captures essential features of the scaling properties of the agreement process for spatiallyembedded autonomous agents among the relevant observables capturing the temporal properties of the agreement process we investigate the cluster size distribution and the distribution of the agreement times both exhibiting dynamic scaling we also present results for the case when a small density of long range communication links are added on top of the random geometric graph resulting in a small world like network and yielding a significantly reduced time to reach global agreement we construct a finite size scaling analysis for the agreement times in this case

a continuation approach to superlinear periodic boundary value problems this paper deals with the problem of the existence of t periodic solutions for the first order differential system x i t x 1 1 where f 0 t x r r is a caratheodory function in what follows we prove some results for the solvability of the periodic bvp in the case when the dimension of the space is even such a limitation is motivated by our interest in applications to the second order equation d g t u u o 1 2 which takes the form of 1 1 when it is written as the equivalent system u v 0 g t u v 1 3

crossover in growth law and violation of superuniversality in the random field ising model we study the nonconserved phase ordering dynamics of the d 2 3 random field ising model quenched to below the critical temperature motivated by the puzzling results of previous work in two and three dimensions reporting a crossover from power law to logarithmic growth together with superuniversal behavior of the correlation function we have undertaken a careful investigation of both the domain growth law and the autocorrelation function our main results are as follows we confirm the crossover to asymptotic logarithmic behavior in the growth law but at variance with previous findings we find the exponent in the preasymptotic power law to be disorder dependent rather than being that of the pure system furthermore we find that the autocorrelation function does not display superuniversal behavior this restores consistency with previous results for the d 1 system and fits nicely into the unifying scaling scheme we have recently proposed in the study of the random bond ising model

the role of droplet fluctuations in kinetic ising models the authors examine by monte carlo simulation and the damage algorithm the late time behaviour of fluctuations in the low temperature ordered phase of the two dimensional kinetic ising model it has been suggested that at late times correlations could be dominated by long lived droplet fluctuations of the other ordered phase giving rise to stretched exponential decays of the spin auto correlation function over the time regimes they have studied they see no evidence for anomalous long lived droplets and find that the probability distribution for droplet lifetimes decays by an ordinary exponential

non algebraic domain growth in binary alloys with quenched disorder the authors present detailed numerical results from a computationally efficient cell dynamical system model of domain growth in binary alloys with quenched disorder their numerical results suggest that the domain growth law for the disordered case is compatible with r t approximately 1nt x where x has a weak dependence on the disorder amplitude however it is possible that their simulations do not access the true asymptotic regime they also find that the scaled structure factor for the disordered case is independent of the amplitude of disorder and is the same as that for the pure system

comparison of voter and glauber ordering dynamics on networks we study numerically the ordering process of two very simple dynamical models for a two state variable on several topologies with increasing levels of heterogeneity in the degree distribution we find that the zero temperature glauber dynamics for the ising model may get trapped in sets of partially ordered metastable states even for finite system size and this becomes more probable as the size increases voter dynamics instead always converges to full order on finite networks even if this does not occur via coherent growth of domains the time needed for order to be reached diverges with the system size in both cases the ordering process is rather insensitive to the variation of the degreee distribution from sharply peaked to scale free

new results of falkner skan equation arising in boundary layer theory abstract this paper presents a new nonexistence result and upper and lower bounds of the shear stress f 0 to the well known falkner skan equation arising from the boundary layer problems f f f 1 f 2 0 0 subject to the boundary condition f 0 f 0 0 f 1 and the side condition 0 f 1 for 0

erratum small world networks evidence for a crossover picture phys rev lett 82 3180 1999 we have performed new calculations using the breadth first search algorithm 1 2 we are now able to study systems with sizes up to n 5500 as shown in fig 1 we now find t o 1 in agreement with the simple argument given in our letter but different from the originally reported numerical result st 0 67 6 0 10d the reason for the incorrect numerical result reported initially is the small system sizes we studied which did not allow us to reach the asymptotic regime we thank a barrat 3 and m e j newman and d j watts 4 for alerting us to the possibility of an error on our estimate of t we also thank m argollo de menezes for directing us to the breadth first search algorithm

numerical solution of the falkner skan equation using piecewise linear functions we present a finite element method for the solution of the falkner skan equation the method uses a coordinate transformation to map the semi infinite domain of the problem to the unit interval 0 1 by means of a suitable change of variables the transformed third order boundary value problem is further rewritten as a system of differential equations consisting of a second order equation and a first order equation the second order equation is approximated using a galerkin formulation with piecewise linear elements and the first order equation is approximated using a centered difference approximation in the process of the initial transformation a finite computational boundary is introduced this boundary is obtained as part of the computational solution by imposing an additional asymptotic boundary condition the solutions obtained thus are in excellent agreement with those obtained by previous authors

on the solution of falkner skan equations abstract new existence and uniqueness proofs are given for the solutions of the equations governing the self similar compressible boundary layer falkner skan equations the properties of the solutions are studied and some bounds on important quantities are concluded the paper is restricted to favourable pressure gradients and to wall cooling

existence of solutions of laminar boundary layer equations with decelerating external flows abstract new results on the existence and nonexistence of solutions of laminar boundary layer equations with decelerating external flows are obtained some previous results treated these equations with accelerating or constant external flows our approach is to establish a system of two integral equations with singularities which will be proved to be equivalent to the laminar boundary layer equations and prove that the system has solutions by using the leray schauder fixed point theorem and the helly selection principle

boundary layer flow of a second grade fluid with variable heat flux at the wall we study the boundary layer stagnation flow of a second grade fluid with a prescribed variable heat flux at the wall the flow is assumed to be steady and laminar the governing equations are solved using an iterative central difference approximation method in a non uniform grid domain the effects of the non newtonian nature of the fluid and the heat flux parameter on the thermal boundary layer are also presented

autocorrelation functions for phase separation in ternary mixtures we present numerical and analytical results for the autocorrelation functions which characterize domain growth in ternary mixtures the numerical results are obtained from monte carlo simulations of the spin 1 blume emery griffiths model with spin exchange kinetics further we model the autocorrelation functions using an approach based on the continuous time random walk formalism the aging property of these functions is related to the time dependence of the domain size distribution our analytical results are found to be in good agreement with the numerical data

non algebraic domain growth in random magnets a cell dynamical approach the authors develop a novel numerical approach based on a computationally efficient cell dynamical system cds model for studying the kinetics of ordering in systems described by a non conserved order parameter with quenched disorder evolving from unstable initial states they use this model to study the kinetics of domain growth in a coarse grained version of the random exchange ising model their numerical data strongly indicate quantitative agreement with the theoretically predicted asymptotic growth law over a limited range of disorder amplitudes they also compare their observations with those in laboratory experiments and make important predictions regarding dynamical scaling in these systems

non equilibrium dynamics of the ising model for t less than equal totc the growth of order in ising models with nonconserved order parameter is considered for quenches to final temperatures tf 0 and tf tc the results of numerical simulations in spatial dimension d 2 are presented in all cases a scaling regime is entered for sufficiently long times where the characteristic length scale is the domain size l t approximately t12 for tf 0 and the nonequilibrium correlation length xi t approximately t1z for tf tc the equal time correlation function has the expected scaling forms f r l t and r d 2 eta fc r xi t for tf 0 and tc respectively the scaling function fc x has interesting short distance behaviour which is elucidated using scaling arguments and by in and 1 n expansions the t 0 scaling function f x depends on whether the spin correlations present in the initial conditions are of long or short range as does the exponent which describes the decay of the autocorrelation function a t si t si o approximately l t results for a quench from the equilibrium critical state to tf 0 are consistent with theoretical predictions

universality class for domain growth in random magnets a 2d ising model with random ferromagnetic bonds is studied by monte carlo simulation following a quench from t infinity to t tc the domain size grows as l t approximately in t to x at late times the data are consistent with the theoretical prediction chi 4 the exponent defined by si 0 si t approximately l t and the scaling functions for the spatial correlations are very close to those of the pure system suggesting that pure and random systems belong to the same universality class

correction to scaling in the response function of the two dimensional kinetic ising model the aging part r ag t s of the impulsive response function of the two dimensional ferromagnetic ising model quenched below the critical point is studied numerically employing an algorithm without the imposition of the external field we find that the simple scaling form r ag t s s ensuremath 1 a f t s which is usually believed to hold in the aging regime is not obeyed we analyze the data assuming the existence of a correction to scaling we find a 0 273 ifmmode pm else textpm fi 0 006 in agreement with previous numerical results obtained from the zero field cooled magnetization we investigate in detail also the scaling function f t s and we compare the results with the predictions of analytical theories we make an ansatz for the correction to scaling deriving an analytical expression for r ag t s this gives a satisfactory qualitative agreement with the numerical data for r ag t s and for the integrated response functions with the analytical model we explore the overall behavior extrapolating beyond the time regime accessible with the simulations we explain why the data for the zero field cooled susceptibility are not too sensitive to the existence of the correction to scaling in r ag t s making this quantity the most convenient for the study of the asymptotic scaling properties

a variational inequality index for condensing maps in hilbert spaces and applications to semilinear elliptic inequalities a variational inequality index for condensing maps is established in hilbert spaces new results on existence of nonzero positive solutions of variational inequalities for such maps are proved by using the theory of variational inequality index applications of such a theory are given to existence of nonzero positive weak solutions for semilinear second order elliptic inequalities where previous results of variational inequalities for s contractive maps cannot be applied

fixed sign solutions for a system of singular focal boundary value problems we consider a system of focal boundary value problems where the nonlinearities may be singular in the independent variable and may also be singular in the dependent arguments using schauder fixed point theorem we establish criteria such that the system of boundary value problems has at least one fixed sign solution

dynamics of social balance on networks we study the evolution of social networks that contain both friendly and unfriendly pairwise links between individual nodes the network is endowed with dynamics in which the sense of a link in an imbalanced triad a triangular loop with one or three unfriendly links is reversed to make the triad balanced with this dynamics an infinite network undergoes a dynamic phase transition from a steady state to paradise all links are friendly as the propensity p for friendly links in an update event passes through 1 2 a finite network always falls into a socially balanced absorbing state where no imbalanced triads remain if the additional constraint that the number of imbalanced triads in the network not increase in an update is imposed then the network quickly reaches a balanced final state i introduction in this work we investigate the role of friends and enemies on the evolution of social networks we represent individuals as nodes in a graph and a relationship between individuals as a link that joins the corresponding nodes to quantify a relationship we assign the binary variable sij 1 to link ij with sij 1 if nodes i and j are friends and sij 1 ifi and j are enemies fig 1 a basic characterization of relationships between mutual acquaintances is the notion of social balance 1 2 the triad ijk is defined as balanced if the sign of the product of the links in the triad sijsjkski equals 1 while the triad is imbalanced otherwise we define a triad to be of type k if it contains k negative links thus 0 and 2 are balanced while 1 and 3 are imbalanced a balanced triad therefore fulfills the adage that i a friend of my friend is my friend ii an enemy of my friend

multiple solutions of the falkner skan equation for flow past a stretching boundary similarity solutions for pressure gradient driven flow over a stretching boundary may be obtained when the external velocity and the boundary velocity are each proportional to the same power law of the downstream coordinate the problem is governed by a two parameter falkner skan equation with beta measuring the stretch rate of the moving boundary and lambda equal to the ratio of free stream velocity to boundary velocity numerical calculations for beta leqq 1 over a range of positive and negative lambda display rich solution behavior for 1 leqq beta leqq 0 dual solutions no solution are found below above a critical value lambda m beta when lambda 0 one observes triple solutions for 0 beta lesssim 0 14 unique solutions for 0 14 lesssim beta leqq 0 5 and dual solutions for 0 5 beta leqq 1 an exact solution is given for beta 1 and asymptotic analysis is employed to elucidate the solution behavior for beta 0 as lambda to 0 and for

singular nonlinear boundary value problems arising in boundary layer theory abstract the singular nonlinear boundary value problem equation arises in the boundary layer theory we prove in this paper that the problem has a unique positive solution for each fixed 0 and there is no positive solution for 1 2

coincidence theory for multimaps abstract several continuation principles in a variety of settings are presented which guarantee the existence of coincidence points for a general class of multimaps

domain growth in the three dimensional random field ising model domain growth in the three dimensional random field ising model is investigated by monte carlo simulation the time dependence of the average domain size is monitored following a quench to a low temperature the logarithmic growth predicted by the theories of villain 1984 and of grinstein and fernandez 1984 is observed the dynamical scaling of the structure factor is also studied and found to be well satisfied the field strength dependence of the scaling function is found to be weak

scaling of the linear response function from zero field cooled and thermoremanent magnetization in phase ordering kinetics in this paper we investigate the relation between the scaling properties of the linear response function r t s of the thermoremanent magnetization trm and of the zero field cooled zfc magnetization in the context of phase ordering kinetics we explain why the retrieval of the scaling properties of r t s from those of trm and zfc magnetization is not trivial preasymptotic contributions generate a long crossover in trm while zfc magnetization is affected by a dangerous irrelevant variable lack of understanding of both these points has generated some confusion in the literature the full picture relating the exponents of all the quantities involved is explicitly illustrated in the framework of the large n model following this scheme an assessment of the present status of numerical simulations for the ising model can be made we reach the conclusion that on the basis of the data available up to now statements on the scaling properties of r t s can be made from zfc magnetization but not from trm from zfc data for the ising model with d 2 3 4 we confirm the previously found linear dependence on dimensionality of the exponent a entering r t s ensuremath sim s ensuremath 1 a f t s we also find evidence that a recently derived form of the scaling function f x using local scale invariance arguments m henkel m pleimling c godr eche and j m luck phys rev lett 87 265701 2001 does not hold for the ising model

a variational inequality theory for demicontinuous s contractive maps with applications to semilinear elliptic inequalities abstract a variational inequality theory for demicontinuous s contractive maps in hilbert spaces is established by employing the ideas of granas topological transversality such a variational inequality theory has many properties similar to those of fixed point theory for demicontinuous weakly inward s contractive maps and to those of fixed point index for condensing maps the variational inequality theory will be applied to study the existence of positive weak solutions and eigenvalue problems for semilinear second order elliptic inequalities with nonlinearities which satisfy suitable lower bound conditions involving the critical sobolev exponent there has been little discussion for such elliptic inequalities involving the critical sobolev exponent in the literature

domain statistics in coarsening systems we study the domain number and size distributions in the one dimensional ising and q state potts models subject to zero temperature glauber dynamics the survival probability of a domain s t t 2c and an unreacted domain q1 t t 2d are characterized by two independent nontrivial exponents for the ising case we find c50 126 and d51 27 using numerical simulations we develop an independent interval approximation that predicts the qualitative behavior of the domain distribution and provides good estimates for the exponents exact results for the domain distribution are also obtained in several solvable cases s1063 651x 97 00110 4

domain growth in weakly disordered magnets we present results from extensive numerical simulations of phase ordering dynamics in a mean field dynamical model of weakly disordered random magnets we apply a stringent test of dynamical scaling to confirm that the domain growth is superuniversal i e the scaling function for the disordered case is the same as for the pure case at least for the disorder amplitudes we consider however we are not able to ascertain a universal functional form for the domain growth law

series solution to the falkner skan equation with stretching boundary abstract a new analytical method namely homotopy analysis method ham is applied to solve the nonlinear falkner skan equation with stretching boundary and a series solution is given in this paper the comparisons are also made among the results of the present work riley and weidman s and numerical method by fourth order runge kutta method combined with newton raphson technique it shows that the analytical approximate solution agrees well with numerical method for falkner skan wedge flow 0 when 0 and also satisfy the conclusion of riley and weidman that there is unique solution in this case which shows the validity of the present work in this condition for the case of the analytical approximate solution gives upper solution branch of the multiple solutions of the falkner skan equation with stretching boundary by numerical methods of both riley and weidman s and the author s and the possible reasons are further analyzed

consensus formation on adaptive networks the structure of a network can significantly influence the properties of the dynamical processes that take place on them while many studies have been paid to this influence much less attention has been devoted to the interplay and feedback mechanisms between dynamical processes and network topology on adaptive networks adaptive rewiring of links can happen in real life systems such as acquaintance networks where people are more likely to maintain a social connection if their views and values are similar in our study we consider different variants of a model for consensus formation our investigations reveal that the adaptation of the network topology fosters cluster formation by enhancing communication between agents of similar opinion although it also promotes the division of these clusters the temporal behavior is also strongly affected by adaptivity while on static networks it is influenced by percolation properties on adaptive networks both the early and late time evolutions of the system are determined by the rewiring process the investigation of a variant of the model reveals that the scenarios of transitions between consensus and polarized states are more robust on adaptive networks

hidden invariances in problems of two dimensional and three dimensional wall jets for newtonian and non newtonian fluids this work is devoted to the investigation of self similar solutions for steady wall jets the problem is considered in the context of two and three dimensional prandtl boundary layer equations and three dimensional parabolized navier stokes equations for newtonian and non newtonian fluids in contrast to dimensional analysis which does not allow the determination of self similar solutions in this case a generating functions approach elaborated by vinogradov soviet math dokl 19 1978 pp 144 148 enables one to derive conservation laws for the above mentioned problems and as a consequence to find new self similarities of the navier stokes equations

dynamics of majority rule in two state interacting spin systems we introduce a two state opinion dynamics model where agents evolve by majority rule in each update a group of agents is specified whose members then all adopt the local majority state in the mean field limit where a group consists of randomly selected agents consensus is reached in a time that scales ln n where n is the number of agents on finite dimensional lattices where a group is a contiguous cluster the consensus time fluctuates strongly between realizations and grows as a dimension dependent power of n the upper critical dimension appears to be larger than 4 the final opinion always equals that of the initial majority except in one dimension

universal scaling function for domain growth in the glauber ising chain the equal time correlation function is calculated at t 0 for the one dimensional ising model with glauber dynamics random initial conditions appropriate to a sudden quench from non zero temperature are imposed averaging over initial conditions yields the scaling form c r t f r2 t the scaling function is given by f x integral 01 dy pi y 1 y 1 2 exp x 4y and is universal i e independent of the probability distribution for the initial conditions

nontrivial solution of third order nonlinear eigenvalue problems ii abstract in this paper we firstly make some corrections for typos errors on our paper nontrivial solution of third order nonlinear eigenvalue problems appl math comput 176 2006 714 721 and then we supplement some cases which have not been studied in the above paper

distribution of domain sizes in the zero temperature glauber dynamics of the one dimensional potts model for the zero temperature glauber dynamics of the q state potts model we calculate the exact distribution of domain sizes by mapping the problem on an exactly soluble one species coagulation model a1a a in the long time limit this distribution is universal and from its complicated exact expression we extract its behavior in various regimes our results are tested in a simulation and compared to the predictions of a simple approximation proposed recently considering the dynamics of domain walls as a reaction diffusion model a1a a with probability q22 q21 and a1a f with probability 1 q21 we calculate the pair correlation function in the long time regime s1063 651x 96 12809 9

the velocity and shear stress functions of the falkner skan equation arising in boundary layer theory abstract new compactness results on the velocity functions and shear stress functions of the well known falkner skan equation are obtained the methodology is to utilize the equivalence between the falkner skan equation and a singular integral equation established recently by lan and yang

coarsening and persistence in the voter model the voter model is a simple model for coarsening with a nonconserved scalar order parameter we investigate coarsening and persistence in the voter model by introducing the quantity pn t defined as the fraction of voters who changed their opinion n times up to time t we show that pn t exhibits scaling behavior that strongly depends on the dimension as well as on the initial opinion concentrations exact results are obtained for the average number of opinion changes n and the autocorrelation function a t 21 n pn t 2d 2 in arbitrary dimension d these exact results are complemented by a mean field theory heuristic arguments and numerical simulations for dimensions d 2 the system does not coarsen and the opinion changes follow a nearly poissonian distribution in agreement with mean field theory for dimensions d 2 the distribution is given by a different scaling form which is characterized by nontrivial scaling exponents for unequal opinion concentrations an unusual situation occurs where different scaling functions correspond to the majority and the minority as well as for even and odd n

off equilibrium response function in the one dimensional random field ising model a thorough numerical investigation of the slow dynamics in the d 1 random field ising model in the limit of an infinite ferromagnetic coupling is presented in this paper crossovers from the preasymptotic pure regime tothe asymptotic sinai regime are investigated for the average domain size the autocorrelation function and staggered magnetization by switching on an additional small random field at the time t w the linear off equilibrium response function is obtained which displays as well the crossover from the nontrivial behavior of the d 1 pure ising model to the asymptotic behavior where it vanishes identically

non algebraic domain growth for phase ordering dynamics in a random field discusses the three stage numerical exposition of the effects of quenched disorder on phase ordering dynamics the authors study the effects of random fields on domain growth the numerical results indicate that the domain growth law is logarithmic for both the cases with non conserve and conserved order parameter this is compatible with theoretical expectations they also study the dynamical scaling of the structure factor for both the non conserved and conserved cases

evolution of cooperation on spatially embedded networks in this work we study the behavior of classical two person two strategies evolutionary games on networks embedded in a euclidean two dimensional space with different kinds of degree distributions and topologies going from regular to random and to scale free ones using several imitative microscopic dynamics we study the evolution of global cooperation on the above network classes and find that specific topologies having a hierarchical structure and an inhomogeneous degree distribution such as apollonian and grid based networks are very conducive to cooperation spatial scale free networks are still good for cooperation but to a lesser degree both classes of networks enhance average cooperation in all games with respect to standard random geometric graphs and regular grids by shifting the boundaries between cooperative and defective regions these findings might be useful in the design of interaction structures that maintain cooperation when the agents are constrained to live in physical two dimensional space