convection diffusion lattice boltzmann scheme for irregular lattices in this paper a lattice boltzmann lb scheme for convection diffusion on irregular lattices is presented which is free of any interpolation or coarse graining step the scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the maxwell boltzmann distribution the axioma holds for both bravais and irregular lattices implying a single framework for lb schemes for all lattice types by solving benchmark problems we have shown that the scheme is indeed consistent with convection diffusion furthermore we have compared the performance of the lb schemes with that of finite difference and finite element schemes the comparison shows that the lb scheme has a similar performance as the one step second order lax wendroff scheme it has little numerical diffusion but has a slight dispersion error by changing the relaxation parameter the dispersion error can be balanced by a small increase of the numerical diffusion

random copolymers and the morita approximation polymer adsorption and polymer localization we analyse directed walk models of random copolymer adsorption and localization ideally we would like t os olve thequenched problem but it appears to be intractable even for simple directed models the annealed approximation is solvable but is inadequate in the strong interaction regime fo rt he adsorption problem and gives a qualitatively incorrect phase diagram for the localization problem in this paper we treat these directed models using an approximation suggested by morita 1964 j math phys 5 1401 5 in which the proportion of each comonomer is fixed we find that the morita approximation leads to behaviour that is closer to that of the quenched average model and this is particularly interesting in the localization problem where the phase diagram is a tl east qualitatively very similar to that of the quenched average problem we also show that the phase boundaries in the morita approximation are bounds on the locations of the phase boundaries of the quenched model

hierarchical pinning models quadratic maps and quenched disorder we consider a hierarchical model of polymer pinning in presence of quenched disorder introduced by derrida et al j stat phys 66 1189 1213 1992 which can be re interpreted as an infinite dimensional dynamical system with random initial condition the disorder it is defined through a recurrence relation for the law of a random variable r n n 1 2 which in absence of disorder i e when the initial condition is degenerate reduces to a particular case of the well known logistic map the large n limit of the sequence of random variables 2 n log r n a non random quantity which is naturally interpreted as a free energy plays a central role in our analysis the model depends on a parameter 0 1 related to the geometry of the hierarchical lattice and has a phase transition in the sense that the free energy is positive if the expectation of r 0 is larger than a certain threshold value and it is zero otherwise it was conjectured in derrida et al j stat phys 66 1189 1213 1992 that disorder is relevant respectively irrelevant or marginally relevant if 1 2 1 2 we find the correct scaling form for weak disorder of the critical point shift

pinning and wetting transition for 1 1 dimensional fields with laplacian interaction we consider a random field 1 n as a model for a linear chain attracted to the defect line 0 that is the x axis the free law of the field is specified by the density exp iv i with respect to the lebesgue measure on n where is the discrete laplacian and we allow for a very large class of potentials v the interaction with the defect line is introduced by giving the field a reward 0 each time it touches the x axis we call this model the pinning model we consider a second model the wetting model in which in addition to the pinning reward the field is also constrained to stay nonnegative we show that both models undergo a phase transition as the intensity of the pinning reward varies both in the pinning a p and in the wetting a w case there exists a critical value ca such that when ca the field touches the defect line a positive fraction of times localization while this does not happen for ca delocalization the two critical values are nontrivial and distinct 0 cp cw and they are the only nonanalyticity points of the respective free energies for the pinning model the transition is of second order hence the field at cp is delocalized on the other hand the transition in the wetting model is of first order and for cw the field is localized the core of our approach is a markov renewal theory description of the field

study of the iterations of a mapping associated to a spin glass model we study the iterations of the mapping mathcal n f s frac f s 2 f 0 2 s f 0 2 with the constraintsf 1 1 f s ansn an 0 and find that except iff s s n f s approaches either 0 or 1 for s 1 ask

analysis of the lattice boltzmann treatment of hydrodynamics it is shown that the lattice boltzmann model can be made to obey the three dimensional thermal navier stokes equations by fixing 26 moments of the equilibrium distribution function this can be achieved on a cubic lattice with particle velocities connecting each lattice site to its first second and third nearest neighbors however this minimal model is not linearly stable in the limit of low transport coefficients additional particle velocities must be selected to achieve linear stability

one way hash function construction based on 2d coupled map lattices an algorithm for constructing one way hash function based on spatiotemporal chaos is proposed a two dimensional coupled map lattices 2d cml with parameters leading to the largest lyapunov exponent is employed the state of the 2d cml is dynamically determined by its previous state and the message bit at the corresponding positions the hash value is obtained by a linear transform on the final state of the 2d cml theoretical analysis and computer simulation indicate that our algorithm has good statistical properties strong collision resistance and high flexibility it is practical and reliable with high potential to be adopted as a strong hash function for providing data integrity

a method to discern complexity in two dimensional patterns generated by coupled map lattices complex patterns generated by the time evolution of a one dimensional digitalized coupled map lattice are quantitatively analyzed a method for discerning complexity among different patterns is implemented the quantitative results indicate two zones in parameter space where the dynamics show the most complex patterns these zones are located on the two edges of an absorbent region where the system displays spatio temporal intermittency

diffusion lattice boltzmann scheme on a orthorhombic lattice we present a diffusion lattice boltzmann dlb scheme which is derived from first principles as opposed to the traditional lattice bgk schemes the dlb is valid for orthorhombic lattices and it has two eigenvalues of the collision operator it is shown that the diffusion coefficient depends only on one eigenvalue of the collision operator hence the dlb scheme can be optimized with means of the additional eigenvalue of the collision operator and with different lattice spacing along the principal axes the properties of the dlb scheme concerning consistency stability and accuracy are studied with eigenmode analysis this analysis shows that the dlb scheme is consistent with diffusion for a wide range of diffusion coefficients it has unconditional stability and that it has third order accuracy furthermore it is shown that accuracy is improved by setting the additional eigenvalue to zero and by densifying the lattice spacing along the direction of the density gradient

finite difference lattice boltzmann method for compressible thermal fluids a splitting method to solve the modeled lattice boltzmann equation the splitting technique permits the boundary conditions for the lattice boltzmann equation to be set as conveniently as those required for the finite difference solution of the navier stokes equations it is shown that the compressible navier stokes equation can be recovered fully from this approach however the formulation requires the solution of a poisson equation governing a secondorder tensor thus constructed the method has no arbitrary constants the proposed method is used to simulate thermalcouette flow aeroacoustics andshockstructureswithanextendedthermodynamicsmodel thesimulations are carried out using a high order finite difference scheme with a two dimensional nine velocity lattice all simulations are performed using a single relaxation time and a set of constants deduced from the derivation it is found that the finite difference lattice boltzmann method is able to correctly replicate viscous effects in thermal couette flows aeroacoustics andshockstructures thesolutionsobtainedareidenticaleithertoanalyticalresults or obtained by solving the compressible navier stokes equations using a direct numerical simulation technique

the migdal kadanoff approximation optimisation generalisation ising model in external fields and the migdal kadanoff hierarchies the simplest migdal kadanoff approximation is optimised on hypercubic lattices generalisation is made to all regular lattices leading to recursion relations continuous in lattice coordination one variety of these relations shows universality whilst another variety shows duality on planar lattices the ising model in external fields both normal and staggered is investigated phase diagrams and exponents are found under a complete treatment of the ambiguity in the handling of external fields by bond moving finally the underlying exactly solved family of hierarchical lattices is considered it is shown that these lattices exhibit a complete breakdown in the concept of universality

oscillatory critical amplitudes in hierarchical models we study the oscillatory critical amplitudes of theq states potts model on a diamond hierarchical lattice we consider an example of the generic case finite critical index as well as the degenerate case essential singularity in both cases we compare the magnitude of the oscillations with geometrical characteristics of the julia set of zeroes of the partition function

spatiotemporal chaos in mixed linear nonlinear two dimensional coupled logistic map lattice abstract we investigate a new spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps for spatial coupling connections based on 2dcml here the coupling methods are including with linear neighborhood coupling and the nonlinear chaotic map coupling of lattices and the former 2dcml system is only a special case in the proposed system in this paper the criteria such kolmogorov sinai entropy density and universality bifurcation diagrams space amplitude and snapshot pattern diagrams are provided in order to investigate the chaotic behaviors of the proposed system furthermore we also investigate the parameter ranges of the proposed system which holds those features in comparisons with those of the 2dcml system and the mlncml system theoretical analysis and computer simulation indicate that the proposed system contains features such as the higher percentage of lattices in chaotic behaviors for most of parameters less periodic windows in bifurcation diagrams and the larger range of parameters for chaotic behaviors which is more suitable for cryptography

random coupling of chaotic maps leads to spatiotemporal synchronization we investigate the spatiotemporal dynamics of a network of coupled chaotic maps with varying degrees of randomness in coupling connections while strictly nearest neighbor coupling never allows spatiotemporal synchronization in our system randomly rewiring some of those connections stabilizes entire networks at x where x is the strongly unstable fixed point solution of the local chaotic map in fact the smallest degree of randomness in spatial connections opens up a window of stability for the synchronized fixed point in coupling parameter space further the coupling b i f r at which the onset of spatiotemporal synchronization occurs scales with the fraction of rewired sites p as a power law for 0 1 p 1 is we also show that the regularizing effect of random connections can be understood from stability analysis of the probabilistic evolution equation for the system and approximate analytical expressions for the range and b i f r are obtained

variational characterization of the critical curve for pinning of random polymers in this paper we look at the pinning of a directed polymer by a one dimensional linear interface carrying random charges there are two phases localized and delocalized depending on the inverse temperature and on the disorder bias using quenched and annealed large deviation principles for the empirical process of words drawn from a random letter sequence according to a random renewal process birkner greven and den hollander 6 we derive variational formulas for the quenched respectively annealed critical curve separating the two phases these variational formulas are used to obtain a necessary and sufficient criterion stated in terms of relative entropies for the two critical curves to be different at a given inverse temperature a property referred to as relevance of the disorder this criterion in turn is used to show that the regimes of relevant and irrelevant disorder are separated by a unique inverse critical temperature subsequently upper and lower bounds are derived for the inverse critical temperature from which sufficient conditions under which it is strictly positive respectively finite are obtained the former condition is believed to be necessary as well a problem that we will address in a forthcoming paper random pinning has been studied extensively in the literature the present paper opens up a window with a variational view our variational formulas for the quenched and the annealed critical curve are new and provide valuable insight into the nature of the phase transition our results on the inverse critical temperature drawn from these variational formulas are not new but they offer an alternative approach that is flexible enough to be extended to other models of random polymers with disorder

one sided local large deviation and renewal theorems in the case of infinite mean if s n n 0 is an integer valued random walk such that s n a n converges in distribution to a stable law of index 0 1 as n then gnedenko s local limit theorem provides a useful estimate for p s n r for values of r such that r a n is bounded the main point of this paper is to show that under certain circumstances there is another estimate which is valid when r a n in other words to establish a large deviation local limit theorem we also give an asymptotic bound for p s n r which is valid under weaker assumptions this last result is then used in establishing some local versions of generalized renewal theorems

analytic methods for obstruction to integrability in discrete dynamical systems a unique analytic continuation result is proven for solutions of a relatively general class of difference equations by using techniques of generalized borel summability this continuation allows for painleve property methods to be extended to difference equations it is shown that the painleve property pp induces under relatively general assumptions a dichotomy within first order difference equations all equations with pp can be solved in closed form on the contrary absence of pp implies under some further assumptions that the local conserved quantities are strictly local in the sense that they develop singularity barriers on the boundary of some compact set the technique produces analytic formulas to describe fractal sets originating in polynomial iterations 2004 wiley periodicals inc

on the irrelevant disorder regime of pinning models recent results have lead to substantial progress in understanding the role of disorder in the de localization transition of polymer pinning models notably there is an understanding of the crucial issue of disorder relevance and irrelevance that albeit still partial is now rigorous in this work we exploit interpolation and replica coupling methods to get sharper results on the irrelevant disorder regime of pinning models in particular we compute in this regime the first order term in the expansion of the free energy close to criticality and this term coincides with the first order of the formal ex pansion obtained by field theory methods we also show that the quenched and the quenched averaged correlation length exponents coincide while in general they are ex pected to be different interpolation and replica coupling methods in this class of models naturally lead to studying the behavior of the intersection of certain renewal sequences and one of the main tools in this work is precisely renewal theory and the study of these intersection renewals 2000 mathematics subject classification 60k35 60k05 82b41 82b44

marginal relevance of disorder for pinning models the effect of disorder on pinning and wetting models has attracted much attention in theoretical physics in particular it has been predicted on the basis of the harris criterion that disorder is relevant annealed and quenched model have different critical points and critical exponents if the return probability exponent alpha a positive number that characterizes the model is larger than 1 2 weak disorder has been predicted to be irrelevant i e coinciding critical points and exponents if alpha 1 2 recent mathematical work has put these predictions on firm grounds in renormalization group terms the case alpha 1 2 is a marginal case and there is no agreement in the literature as to whether one should expect disorder relevance or irrelevance at marginality the question is particularly intriguing also because the case alpha 1 2 includes the classical models of two dimensional wetting of a rough substrate of pinning of directed polymers on a defect line in dimension 3 1 or 1 1 and of pinning of an heteropolymer by a point potential in three dimensional space here we prove disorder relevance both for the general alpha 1 2 pinning model and for the hierarchical version of the model proposed by b derrida v hakim and j vannimenus jsp 1992 in the sense that we prove a shift of the quenched critical point with respect to the annealed one in both cases we work with gaussian disorder and we show that the shift is at least of order exp 1 beta 4 for beta small if beta is the standard deviation of the disorder

application of a ghost fluid approach for a thermal lattice boltzmann method in this paper a ghost fluid gf method is utilized to propose a numerical approach to enhance the capability of thermal lattice boltzmann method tlbm in dealing with complex geometries a ghost fluid approach is imposed on a double population thermal lattice boltzmann method a cartesian grid handles the flow and the boundaries are imposed by a ghost fluid approach the essence of this method is to decompose the unknown distribution functions into equilibrium and non equilibrium parts at each ghost points the major quantities are extrapolated from the image points to the corresponding ghost points to form the equilibrium parts the non equilibrium parts are then determined by using the bounce back scheme the method is relatively easy to apply and second order accurate there is no need to modify the original governing equations and both dirichlet and neumann boundary conditions can be handled the method is applied to couette flow between two concentric circular cylinders natural convection in a square cavity natural convection in an annulus and a forced convection in a lid driven semi circular cavity the results obtained are generally in good agreement with that predicted by other theoretical and numerical efforts

spatiotemporal evolution in a 2 1 dimensional chemotaxis model simulations are performed to investigate the nonlinear dynamics of a 2 1 dimensional chemotaxis model of keller segel ks type with a logistic growth term because of its ability to display a

the effect of disorder on polymer depinning transitions we consider a polymer with monomer locations modeled by the trajectory of a markov chain in the presence of a potential that interacts with the polymer when it visits a particular site 0 we assume that probability of an excursion of length n is given by n c varphi n for some 1 3 2 at high temperature the quenched and annealed curves differ significantly only in a very small neighborhood of the critical point the size of this neighborhood scales as beta 1 2c 3 where is the inverse temperature for c 0 for sufficiently high temperature the quenched and annealed curves are within a factor of 1 epsilon for all u near the critical point in particular the quenched and annealed critical points are equal for c 3 2 the regime depends on the slowly varying function varphi

the continuum disordered pinning model any renewal processes on mathbb n 0 with a polynomial tail with exponent alpha in 0 1 has a non trivial scaling limit known as the alpha stable regenerative set in this paper we consider gibbs transformations of such renewal processes in an i i d random environment called disordered pinning models we show that for alpha in left frac 1 2 1 right these models have a universal scaling limit which we call the continuum disordered pinning model cdpm this is a random closed subset of mathbb r in a white noise random environment with subtle features any fixed a s property of the alpha stable regenerative set e g its hausdorff dimension is also an a s property of the cdpm for almost every realization of the environment nonetheless the law of the cdpm is singular with respect to the law of the alpha stable regenerative set for almost every realization of the environment the existence of a disordered continuum model such as the cdpm is a manifestation of disorder relevance for pinning models with alpha in left frac 1 2 1 right

estimates on path delocalization for copolymers at selective interfaces starting from the simple symmetric random walk s n n we introduce a new process whose path measure is weighted by a factor exp open image in new window with h 0 w n n a typical realization of an iid process and n a positive integer we are looking for results in the large n limit this factor favors s n 0 if w n h 0 and s n 0 if w n h 0 the process can be interpreted as a model for a random heterogeneous polymer in the proximity of an interface separating two selective solvents it has been shown 6 that this model undergoes a de localization transition more precisely there exists a continuous increasing function h c such that if h h c then the model is localized while it is delocalized if h h c however localization and delocalization were not given in terms of path properties but in a free energy sense later on it has been shown that free energy localization does indeed correspond to a strong form of path localization 3 on the other hand only weak results on the delocalized regime have been known so far

non coincidence of quenched and annealed connective constants on the supercritical planar percolation cluster in this paper we study the abundance of self avoiding paths of a given length on a supercritical percolation cluster on mathbb z d more precisely we count z n the number of self avoiding paths of length n on the infinite cluster starting from the origin which we condition to be in the cluster we are interested in estimating the upper growth rate of z n limsup n rightarrow infty z n 1 n which we call the connective constant of the dilute lattice after proving that this connective constant is a s non random we focus on the two dimensional case and show that for every percolation parameter p in 1 2 1 almost surely z n grows exponentially slower than its expected value in other words we prove that limsup n rightarrow infty z n 1 n lim n rightarrow infty mathbb e z n 1 n where the expectation is taken with respect to the percolation process this result can be considered as a first mathematical attempt to understand the influence of disorder for self avoiding walks on a quenched dilute lattice our method which combines change of measure and coarse graining arguments does not rely on the specifics of percolation on mathbb z 2 so our result can be extended to a large family of two dimensional models including general self avoiding walks in a random environment

a numerical approach to copolymers at selective interfaces we consider a model of a random copolymer at a selective interface which undergoes a localization delocalization transition in spite of the several rigorous results available for this model the theoretical characterization of the phase transition has re mained elusive and there is still no agreement about several important issues for example the behavior of the polymer near the phase transition line from a rigorous viewpoint non coinciding upper and lower bounds on the critical line are known in this paper we combine numerical computations with rigorous arguments to get to a better understanding of the phase diagram our main results include various numerical observations that suggest that the critical line lies strictly in between the two bounds a rigorous statistical test based on concentration inequalities and super additivity for determining whether a given point of the phase diagram is in the localized phase this is applied in particular to show that with a very low level of error the lower bound does not coincide with the critical line an analysis of the precise asymptotic behavior of the partition function in the de localized phase with particular attention to the effect of rare atypical stretches in the disorder sequence and on whether or not in the delocalized regime the polymer path has a brownian scaling a new proof of the lower bound on the critical line this proof relies on a characteri zation of the localized regime which is more appealing for interpreting the numerical data

conversion of local transient chaos into global laminar states in coupled map lattices with long range interactions abstract spatially extended dynamical systems may exhibit intermittent behavior in both spatial and temporal scales characterized by repeated conversions from spatially localized transient chaos into global laminar patterns a simple model yet retaining some features of more complex systems consists of a lattice of a class of tent maps with an escaping region the coupling prescription we adopt in this work considers the interaction of a site with all its neighbors the corresponding strength decaying with the lattice distance as a power law this makes possible to pass continuously from a local nearest neighbor to a global kind of coupling we investigate statistical properties of both the chaotic transient bursts and the periodic laminar states with respect to the coupling parameters

enhancement of spatiotemporal regularity in an optimal window of random coupling we investigate the spatiotemporal dynamics of a lattice of coupled chaotic maps whose coupling connections are dynamically rewired to random sites with probability p namely at any instance of time with probability p a regular link is switched to a random one in a range of weak coupling where spatiotemporal chaos exists for regular lattices i e for p 0 we find that pg0 yields synchronized periodic orbits further we observe that this regularity occurs over a window of p values beyond which the basin of attraction of the synchronized cycle shrinks to zero thus we have evidence of an optimal range of randomness in coupling connections where spatiotemporal regularity is efficiently obtained this is in contrast to the commonly observed monotonic increase of synchronization with increasing p as seen for instance in the strong coupling regime of the very same system

some results on energy conserving lattice boltzmann models we consider the problem of energy conserving lattice boltzmann models a major difficulty observed in previous studies is the coupling between the viscous and thermal waves even at moderate wave numbers we propose a theoretical framework based on the knowledge of the partial equivalent equations of the lattice boltzmann scheme at several orders of precision with the help of linearized models inviscid and dissipative advective acoustics and classical acoustics we suggest natural sets of relations for the parameters of lattice boltzmann schemes the application is proposed for three two dimensional schemes numerical test cases for simple linear and nonlinear waves establish that the main difficulty in the previous contributions can now be overcome

pattern dynamics in spatiotemporal chaos pattern selection diffusion of defect and pattern competition intermettency abstract a class of coupled map lattices is investigated as a model for the spatiotemporal chaos as the parameters are changed phase transitions among the patterns are observed pattern selection through the chaotic motion of domain is observed chaos is suppressed by the selection selection of the zigzag pattern is studied where localized defects which separate the two anti phase domains are found they change chaotically in time and move randomly in space the diffusion of defect is related with its chaotic motion collapse of zigzag pattern and the defect turbulence are studied in connection with the crisis in high dimensional dynamical systems pattern selection with longer wavelengths is found in the stronger coupling regime transition from pattern selection phase to fully developed turbulence occurs via the intermittency selective flicker like noise and the pareto distribution of lifetime of pattern are observed at the intermittency regime for the quantitative characterization of each phase pattern distributions pattern transition matrix static and dynamical entropies lifetime distribution of pattern spatiotemporal power spectra and lyapunov spectra are calculated phase transition from the pattern selection to fully developed turbulence is investigated with the use of these quantifiers where some order parameters and critical indeces are introduced

fractal structure of zeros in hierarchical models we consider an ising and aq state potts model on a diamond hierarchical lattice we give pictures of the distribution of zeros of the partition function in the complex plane of temperatures for several choices ofq these zeros are just the julia set corresponding to the renormalization group transformation

an euler solver based on locally adaptive discrete velocities a new discrete velocity model is presented to solve the three dimensional euler equations the velocities in the model are of an adaptive nature both the origin of the discrete velocity space and the magnitudes of the discrete velocities are dependent on the local flow and are used in a finite volume context the numerical implementation of the model follows the near equilibrium flow method of nadiga and pullin and results in a scheme which is second order in space in the smooth regions and between first and second order at discontinuities and second order in time the three dimensional code is included for one choice of the scaling between the magnitude of the discrete velocities and the local internal energy of the flow the method reduces to a flux splitting scheme based on characteristics as a preliminary exercise the result of the sod shock tube simulation is compared to the exact solution

nonuniversal dependence of spatiotemporal regularity on randomness in coupling connections we investigate the spatiotemporal dynamics of a network of coupled nonlinear oscillators modeled by sine circle maps with varying degrees of randomness in coupling connections we show that the change in the basin of attraction of the spatiotemporal fixed point due to varying fraction of random links p is crucially related to the nature of the local dynamics even the qualitative dependence of spatiotemporal regularity on p changes drastically as the angular frequency of the oscillators change ranging from monotonic increase or monotonic decrease to non monotonic variation thus it is evident here that the influence of random coupling connections on spatiotemporal order is highly non universal and depends very strongly on the nodal dynamics

heat transfer in lattice bgk modeled fluid the thermal lattice bgk model is a recently suggested numerical tool aiming at solving problems of thermohydrodynamics the quality of the lattice bgk simulation is checked in this paper by calculating temperature profiles in the couette flow under different eckert and mach numbers a revised lower order model is proposed to improve the accuracy and the higher order model is proved to be advantageous in this respect especially in the flow regime with a higher mach number

a replica coupling approach to disordered pinning models we consider a renewal process 0 1 on the integers where the law of i i 1 has a power like tail p i i 1 n n 1 l n with 0 and l slowly varying we then assign a random n dependent reward penalty to the occurrence of the event that the site n belongs to in such generality this class of problems includes among others 1 d dimensional models of pinning of directed polymers on a one dimensional random defect 1 1 dimensional models of wetting of disordered substrates and the poland scheraga model of dna denaturation by varying the average of the reward the system undergoes a transition from a localized phase where occupies a finite fraction of mathbb n to a delocalized phase where the density of vanishes in absence of disorder i e if the reward is independent of n the transition is of first order for 1 and of higher order for 1 2 11 in physical terms disorder is relevant in this situation in agreement with the heuristic harris criterion on the other hand for 0 1 2 it has been proven recently by k alexander 2 that if disorder is sufficiently weak critical exponents are not modified by randomness disorder is irrelevant in this work generalizing techniques which in the framework of spin glasses are known as replica coupling and interpolation we give a new simpler proof of the main results of 2 moreover we partially justify a small disorder expansion worked out in 9 for 1 2 showing that it provides a free energy upper bound which improves the annealed one

adsorption of a random heteropolymer at a potential well revisited location of transition point and design of sequences the adsorption of an ideal heteropolymer loop at a potential point well is investigated within the framework of standard random matrix theory on the basis of a semi analytical semi numerical approach a histogram of transition points for the ensemble of quenched heteropolymer structures with bimodal symmetric distribution of types of chain links is constructed it is shown that the sequences having transition points in the tail of the histogram display correlations between nearest neighbour monomers

log periodic critical amplitudes a perturbative approach log periodic amplitudes appear in the critical behavior of a large class of systems in particular when a discrete scale invariance is present here we show how to compute these critical amplitudes perturbatively when they originate from a renormalization map which is close to a monomial in this case the log periodic amplitudes of the subdominant corrections to the leading critical behavior can also be calculated

self organized memories in coupled map lattices abstract spatially extended dynamical systems subjected to a periodic external input are able to store short term memories as a result of self organization this phenomenon has been used to interpret sliding charge density wave experiments and has been found in lattices of coupled maps and oscillators in this paper we aim to describe the influence of a stochastic perturbation in the self organized memories in a lattice of coupled linear and weakly nonlinear maps we consider the case in which the coupling between maps depends on the lattice distance as a power law

influence of spatial correlation for directed polymers in this paper we study a model of a brownian polymer in x d introduced by rovira and tindel j funct anal 222 2005 178 201 our investigation focuses mainly on the effect of strong spatial correlation in the environment in that model in terms of free energy fluctuation exponent and volume exponent in particular we prove that under some assumptions very strong disorder and superdiffusivity hold at all temperatures when d 3 and provide a novel approach to petermann s superdiffusivity result in dimension one superdiffusivity of directed polymers in random environment 2000 ph d thesis we also derive results for a brownian model of pinning in a nonrandom potential with power law decay at infinity

on the localization transition of random copolymers near selective interfaces in this note we consider the de localization transition for random directed 1 1 dimensional copolymers in the proximity of an interface separating selective solvents we derive a rigorous lower bound on the free energy this yields a substantial improvement on the bounds from below on the critical line that were known so far our result implies that the critical curve does not lie below the critical curve set forth by monthus eur phys j b 13 111 130 2000 on the base of a renormalization group analysis we discuss this result in the light of the rigorous and non rigorous approaches present in the literature and by making an analogy with a particular asymptotics of a disordered wetting model we propose a simplified framework in which the question of identifying the critical curve as well as understanding the nature of the transition may be approached

high temperature scaling limit for directed polymers on a hierarchical lattice with bond disorder diamond lattices are sequences of recursively defined graphs that provide a network of directed pathways between two fixed root nodes a and b the construction recipe for diamond graphs depends on a branching number b in mathbb n and a segmenting number s in mathbb n for which a larger value of the ratio s b intuitively corresponds to more opportunities for intersections between two randomly chosen paths by attaching i i d random variables to the bonds of the graphs we construct a random gibbs measure on the set of directed paths by assigning each path an energy through summing the random variables along the path for the case b s we propose a scaling regime in which the temperature grows along with the number of hierarchical layers of the graphs and the partition function the normalization factor of the gibbs measure appears to converge in law we prove that all of the positive integer moments of the partition function converge in this limiting regime the motivation of this work is to prove a functional limit theorem that is analogous to a previous result obtained in the b s case

critical points of quadratic renormalizations of random variables and phase transitions of disordered polymer models on diamond lattices we study the wetting transition and the directed polymer delocalization transition on diamond hierarchical lattices these two phase transitions with frozen disorder correspond to the critical points of quadratic renormalizations of the partition function these exact renormalizations on diamond lattices can also be considered as approximate migdal kadanoff renormalizations for hypercubic lattices in terms of the rescaled partition function z z z typ we find that the critical point corresponds to a fixed point distribution with a power law tail p c z phi ln z z 1 mu as z infinity up to some subleading logarithmic correction phi ln z so that all moments z n with n mu diverge for the wetting transition the first moment diverges z infinity case 0 mu 1 and the critical temperature is strictly below the annealed temperature t c t ann for the directed polymer case the second moment diverges z 2 infinity case 1 mu 2 and the critical temperature is strictly below the exactly known transition temperature t2 of the second moment we then consider the correlation length exponent nu the linearized renormalization around the fixed point distribution coincides with the transfer matrix describing a directed polymer on the cayley tree but the random weights determined by the fixed point distribution p c z are broadly distributed this induces some changes in the traveling wave solutions with respect to the usual case of more narrow distributions

copolymers at selective interfaces new bounds on the phase diagram we investigate the phase diagram of disordered copolymers at the interface between two selective solvents and in particular its weak coupling behavior encoded in the slope mc of the critical line at the origin we focus on the directed walk case which has turned out to be in spite of the apparent simplicity extremely challenging in mathematical terms the partition function of such a model does not depend on all the details of the markov chain that models the polymer but only on the time elapsed between successive returns to zero and on whether the walk is in the upper or lower half plane between such returns this observation leads to a natural generalization of the model in terms of arbitrary laws of return times the most interesting case being the one of return times with power law tails with exponent 1 1 2 in the case of the symmetric random walk the main results we present here are

thermal lattice boltzmann method based on a theoretically simple derivation of the taylor expansion we propose an approach to derive the thermal lattice boltzmann method that is based on the taylor expansion in variables of temperature as well as velocity and a direct calculation upon the gaussian quadrature based hypothesis this enables us to overcome the isothermal limitation and the low order accuracy simultaneously a systematic framework is explained for constructing numerically stable lattice boltzmann models the stability of this one dimensional lattice boltzmann model is demonstrated with a shock tube simulation

collective behavior in coupled chaotic map lattices with random perturbations abstract numerical simulations of coupled map lattices with non local interactions i e the coupling of a given map occurs with all lattice sites often involve a large computer time if the lattice size is too large in order to study dynamical effects which depend on the lattice size we considered the use of small truncated lattices with random inputs at their boundaries chosen from a uniform probability distribution this emulates a thermal bath where deterministic degrees of freedom exhibiting chaotic behavior are replaced by random perturbations of finite amplitude we demonstrate the usefulness of this idea to investigate the occurrence of completely synchronized chaotic states as the coupling parameters are varied we considered one dimensional lattices of chaotic logistic maps at outer crisis x 4 x 1 x

critical lattice size limit for synchronized chaotic state in one and two dimensional diffusively coupled map lattices we consider diffusively coupled map lattices with p neighbors where p is arbitrary and study the stability of the synchronized state we show that there exists a critical lattice size beyond which the synchronized state is unstable this generalizes earlier results for nearest neighbor coupling we confirm the analytical results by performing numerical simulations on coupled map lattices with logistic map at each node the above analysis is also extended to two dimensional p neighbor diffusively coupled map lattices

dynamics of the generalized kp mew burgers equation with external periodic perturbation the generalized kadomtsevpetviashvili modified equal width burgers kp mew burgers equation is introduced for the first time the qualitative change of the traveling wave solutions of the kp mew burgers equation is studied using numerical simulations considering an external periodic perturbation the periodic and chaotic motions of the perturbed kp mew burgers equation are investigated by using the phase projection analysis time series analysis poincare section and bifurcation diagram the parameter a nonlinear coefficient plays a crucial role in the periodic motions and chaotic motions through period doubling route to chaos of the perturbed kp mew burgers equation

hierarchical lattices some examples with a comparison of intrinsic dimension and connectivity and ising model exponents the recently recognised class of hierarchical lattices is examined through a number of examples definitions of length intrinsic dimension and connectivity are made and used to discuss variations of exponents calculated on the ising model generalisations of regular lattice results are found for exponents at discontinuity fixed points and in 1 epsilon dimensions

an exactly solvable continuous time derrida retaux model to study the depinning transition in the limit of strong disorder derrida and retaux j stat phys 156 2 26 290 2014 introduced a discrete time max type recursive model it is believed that for a large class of recursive models including derrida and retaux model there is a highly non trivial phase transition in this article we present a continuous time version of derrida and retaux model built on a yule tree which yields an exactly solvable model belonging to this universality class the integrability of this model allows us to study in details the phase transition near criticality and can be used to confirm the infinite order phase transition predicted by physicists we also study the scaling limit of this model at criticality which we believe to be universal

preliminary results in the use of energy dependent octagonal lattices for thermal lattice boltzmann simulations thermal lattice boltzmann simulations are prone to severe numerical instabilities while octagonal velocity lattices increase the range of temperatures that can be successfully simulated the ranges are insufficient for many applications second order interpolation is required to correlate diagonal streaming to the square spatial grid here the role of energy dependent octagonal lattices is examined an idea spawned from gauss hermite quadratures a nontrivial allocation scheme is now required to ensure moment conservation in connecting to the spatial grid for the energy dependent lattices it is shown that there are no lower bounds to the temperature thus allowing for higher reynolds number simulations simulations are presented and compared to theory viscosity and sound speed dependence on temperature showing excellent agreement

diffusion on the scaling limit of the critical percolation cluster in the diamond hierarchical lattice we construct critical percolation clusters on the diamond hierarchical lattice and show that the scaling limit is a graph directed random recursive fractal a dirichlet form can be constructed on the limit set and we consider the properties of the associated laplace operator and diffusion process in particular we contrast and compare the behaviour of the high frequency asymptotics of the spectrum and the short time behaviour of the on diagonal heat kernel for the percolation clusters and for the underlying lattice in this setting a number of features of the lattice are inherited by the critical cluster

ks entropy and mean lyapunov exponent for coupled map lattices abstract the statistics of kolmogorov sinai ks entropy for a coupled map lattice model are analyzed from the viewpoint of the thermodynamic formalism it is shown that the fluctuation of ks entropy for a coupled map lattice model satisfies the large deviation statistics also the probability density of lyapunov exponents pdle is studied and it is shown that the pdle gives the measure of the irregularity for the spatio temporal patterns mean lyapunov exponent is introduced and compared with ks entropy

directed polymers with random interaction an exactly solvable case we propose a model for two d 1 dimensional directed polymers subjected to a mutual function interaction with a random coupling constant and present an exact renormalization group study for this system the exact function evaluated through an e 1 d expansion for second and third moments of the partition function exhibits the marginal relevance of the disorder at d 1 and the presence of a phase transition from a weak to strong disorder regime for d 1 the length scale exponent for the critical point is 2 e 1 we give details of the renormalization we show that higher moments do not require any new interaction and hence the function remains the same for all moments the method is extended to multicritical systems involving an m chain interaction the corresponding disorder induced phase transition for d d m 1 m 1 has the critical exponent v m 2d m 1 2 1 for both the cases an essential singularity appears for the length scale right at the upper critical dimension d m we also discuss the strainge behavior of an annealed system with more than two chains with pairwise random interactions among each other

finite difference lattice boltzmann method with arbitrary specific heat ratio applicable to supersonic flow simulations abstract the current finite difference lattice boltzmann method fdlbm gives a fixed specific heat ratio because internal energy is limited to the translational freedom of the space yan et al and kataoka et al clarified the conditions for deriving models with arbitrary specific heat ratio and proposed euler models however these model applications to numerical simulations showed the weakness in the numerical stability in this paper a two dimensional fdlbm navier stokes model and a three dimensional fdlbm euler model which allow arbitrary values to be set for the specific heat ratio were proposed these models stably performed numerical simulations from subsonic to supersonic ranges

lattice boltzmann computational fluid dynamics in three dimensions the recent development of the lattice gas method and its extension to the lattice boltzmann method have provided new computational schemes for fluid dynamics both methods are fully paralleled and can easily model many different physical problems including flows with complicated boundary conditions in this paper basic principles of a lattice boltzmann computational method are described and applied to several three dimensional benchmark problems in most previous lattice gas and lattice boltzmann methods a face centered hyper cubic lattice in four dimensional space was used to obtain an isotropic stress tensor to conserve computer memory we develop a model which requires 14 moving directions instead of the usual 24 directions lattice boltzmann models describing two phase fluid flows and magnetohydrodynamics can be developed based on this simpler 14 directional lattice comparisons between three dimensional spectral code results and results using our method are given for simple periodic geometries an important property of the lattice boltzmann method is that simulations for flow in simple and complex geometries have the same speed and efficiency while all other methods including the spectral method are unable to model complicated geometries efficiently

oscillatory critical amplitudes in hierarchical models and the harris function of branching processes oscillatory critical amplitudes have been repeatedly observed in hierarchical models and in the cases that have been taken into consideration these oscillations are so small to be hardly detectable hierarchical models are tightly related to iteration of maps and in fact very similar phenomena have been repeatedly reported in many fields of mathematics like combinatorial evaluations and discrete branching processes it is precisely in the context of branching processes with bounded off spring that t harris in 1948 first set forth the possibility that the logarithm of the moment generating function of the rescaled population size in the super critical regime does not grow near infinity as a power but it has an oscillatory prefactor the harris function these oscillations have been observed numerically only much later and while the origin is clearly tied to the discrete character of the iteration the amplitude size is not so well understood the purpose of this note is to reconsider the issue for hierarchical models and in what is arguably the most elementary setting the pinning model that actually just boils down to iteration of polynomial maps and notably quadratic maps in this note we show that the oscillatory critical amplitude for pinning models and the harris function coincide moreover we make explicit the link between these oscillatory functions and the geometry of the julia set of the map making thus rigorous and quantitative some ideas set forth in derrida et al commun math phys 94 115 132 1984

hierarchical pinning model with site disorder disorder is marginally relevant we study a hierarchical disordered pinning model with site disorder for which like in the bond disordered case derrida et al in j stat phys 66 1189 1213 1992 and giacomin et al in probab theor rel fields 2009 arxiv 0711 4649 math pr there exists a value of a parameter b which enters in the definition of the hierarchical lattice that separates an irrelevant disorder regime and a relevant disorder regime we show that for such a value of b the critical point of the disordered system is different from the critical point of the annealed version of the model the proof goes beyond the technique used in giacomin et al probab theor rel fields 2009 arxiv 0711 4649 math pr and it takes explicitly advantage of the inhomogeneous character of the green function of the model

renormalisation group study of a disordered model we study the potts model on a diamond hierarchical lattice with random interactions using weak disorder expansions we calculate analytically the position and the exponents of the random fixed point which appears when the specific heat exponent ap of the pure system becomes positive at ap 0 we find how the logarithmic singularity is modified by the disorder lastly we suggest that this model should present griffiths like singularities

rapidly switched random links enhance spatiotemporal regularity we investigate the spatiotemporal properties of a lattice of chaotic maps whose coupling connections are rewired to random sites with probability p keeping p constant we change the random links at different frequencies in order to discern the effect if any of the time dependence of the links we observe two different regimes in this network i when the network is rewired slowly namely when the random connections are quite static the dynamics of the network is spatiotemporally chaotic and ii when these random links are switched around fast namely the network is rewired frequently one obtains a spatiotemporal fixed point over a large range of coupling strengths we provide evidence of a sharp transition from a globally attracting spatiotemporal fixed point to spatiotemporal chaos as the rewiring frequency is decreased thus in addition to geometrical properties such as the fraction of random links in the network dynamical information on the time dependence of these links is crucial in determining the spatiotemporal properties of complex dynamical networks