primal dual distance bounds of linear codes with application to cryptography let n d dperp denote the minimum length n of a linear code c with d and dperp where d is the minimum hamming distance of c and dperp is the minimum hamming distance of cperp in this correspondence we show lower bounds and an upper bound on n d dperp further for small values of d and dperp we determine n d dperp and give a generator matrix of the optimum linear code this problem is directly related to the design method of cryptographic boolean functions suggested by kurosawa et al

the critical behavior of dimer dimer surface reaction models monte carlo and finite size scaling investigation two models based upon the well known mechanism for the oxidation of hydrogen on transition metal surfaces which may also apply to generic dimerdimer surface reaction processes of the type 1 2 a2 b2 b2a are proposed and studied on the square lattice of sidel l 600 by means of monte carlo simulations and finite size analysis both models exhibit irreversible kinetic phase transitions ipt from a reactive state with sustained production of b2a molecules to off equilibrium surface poisoned states with the reactants i e without production the location of the critical points at which the ipts take place in thel limit is determined by means of a finite size scaling analysis also it is shown that at criticality some relevant quantities such as the rate of b2a production and the coverage with the reactants exhibit simple power law behavior which allow us to determine the corresponding critical exponents

frozen states of a disordered globular heteropolymer the disordered heteropolymer chain with a random sequence of links a simple model of globular protein is investigated using the replica approach in the mean field approximation it is shown that for low dimensions of space d 1 it follows that the set of equilibrium states is ultrametric with an anomalously large number of weakly overlapping states

a diagrammatic approach to hecke algebras of the reflection equation hecke algebra deformations of the wreath product cd sn arise in solutions to the yang baxter equations with boundary the reflection equation we use a simple diagrammatic approach to construct bases for these algebras we hence introduce quotient algebras suitable for constructing physical solutions to the reflection equation with a well defined thermodynamic large n limit for all d and n we determine the generic representation theory of these algebras developing a formalism suitable for the analysis of corresponding q spin chain hamiltonian and transfer matrix spectra

exact enumeration study of free energies of interacting polygons and walks in two dimensions we present analyses of substantially extended series for both interacting self avoiding walks isaw and polygons isap on the square lattice we argue that these provide good evidence that the free energies of both linear and ring polymers are equal above the temperature thus extending the application of a theorem of tesi et al to two dimensions below the temperature the conditions of this theorem break down in contradistinction to three dimensions but an analysis of the ratio of the partition functions for isap and isaw indicates that the free energies are in fact equal at all temperatures within at least any perceived difference can be interpreted as the difference in the size of corrections to scaling in both problems this may be used to explain the vastly different values of the crossover exponent previously estimated for isap to that predicted theoretically and numerically confirmed for isaw an analysis of newly extended neighbour avoiding self avoiding walk series is also given

the statistical mechanics of constructive algorithms the storage capacity of multilayer networks with overlapping receptive fields is studied for constructive algorithms using boolean perceptrons as their basic building block which have been investigated within a replica framework the assumption of weak coupling between subsequently constructed perceptrons is verified within a replica symmetric rs ansatz and shown to be negligible in most cases in comparison with correction due to replica symmetry breaking rsb in individual perceptrons the capacities of a tiling like and variants of the upstart algorithm are then calculated within rs and one step rsb with the quenched average taken over the individual units separately for networks with up to k 4000 and k 600 units respectively within this treatment the storage capacity seems to exhibit a power law behaviour in with an exponent n that may depend on the algorithm and the stability however due to finite size effects in k reliable estimates of n could not be extracted nevertheless the results strongly indicate that n should be strictly smaller than 1 within one step rsb whereas within rs the mitchison durbin bound is violated for finite k and n 1 may hold asymptotically

critical behaviour of a surface reaction model with infinitely many absorbing states in a recent letter yaldram et al 1993 studied the critical behaviour of a simple lattice gas model of the co no catalytic reaction the model exhibits a second order non equilibrium phase transition from an active state into one out of infinitely many absorbing states estimates for the critical exponent beta suggested that the model belongs to a new universality class the results reported in this article contradict this notion as estimates for various critical exponents show that the model belongs to the universality class of directed percolation

free energy of self interacting uniform stars we consider uniform star polymers on a variety of lattices with an additional contact interaction between pairs of vertices which are unit distance apart and are not joined by an edge of the star we present some rigorous results and other evidence which indicate that these systems have the same limiting free energy as self interacting self avoiding walks we discuss the extension of these results to other homeomorphism types and to systems with an additional surface interaction term

series expansions of the percolation probability for directed square and honeycomb lattices we have derived long series expansions of the percolation probability for site and bond percolation on directed square and honeycomb lattices for the square bond problem we have extended the series from 41 terms to 54 for the square site problem from 16 terms to 37 and for the honeycomb bond problem from 13 terms to 36 analysis of the series clearly shows that the critical exponent beta is the same for all the problems confirming expectations of universality for the critical probability and exponent we find in the square bond case qc 0 3552994 or 0 0000010 beta 0 27643 or 0 00010 in the square site case qc 0 294515 or 0 000005 beta 0 2763 or 0 0003 and in the honeycomb bond case qc 0 177143 or 0 000002 beta 0 2763 or 0 0002 in addition we have obtained accurate estimates for the critical amplitudes in all cases we find that the leading correction to scaling term is analytic i e the confluent exponent delta 1

results on binary linear codes with minimum distance 8 and 10 all linear binary codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified nonexistence of codes with parameters 33 18 8 and 33 14 10 is proved this leads to 8 new exact bounds for binary linear codes primarily two algorithms considering the dual codes are used namely extension of dual codes with a proper coordinate and a fast algorithm for finding a maximum clique in a graph which is modified to find a maximum set of vectors with the right dependency structure

extremal segments in random sequences we investigate the probability for the largest segment with total displacement q in an n step random walk to have length l using analytical exact enumeration and monte carlo methods we reveal the complex structure of the probability distribution in the large n limit in particular the size of the longest loop has a distribution with square root singularity at l identical to l n 1 an essential singularity at l 0 and a discontinuous derivative at l 1 2

some results for linear binary codes with minimum distance 5 and 6 we prove that a linear binary code with parameters 34 24 5 does not exist also we characterize some codes with minimum distance 5 and 6

impact of localization on dyson s circular ensemble a wide variety of complex physical systems described by unitary matrices have been shown numerically to satisfy level statistics predicted by dyson s circular ensemble we argue that the impact of localization in such systems is to impose certain restrictions on the eigenvalues we consider a solvable model which takes into account such restrictions qualitatively and find that within the model a gap is created in the spectrum and there is a transition from the universal wigner distribution towards a poisson distribution with increasing localization

energy level statistics of a critical random matrix ensemble we study energy level statistics of a critical random matrix ensemble of power law banded complex hermitian matrices we compute the level compressibility via the level number variance and compare it with the analytical formula for the exactly solvable model of moshe neuberger and shapiro

phase separation in a single step growth model with surface diffusion we consider a one dimensional solid on solid growth model in which the nearest neighbour height differences are restricted to take the values deposition occurs at local minima with probability f while diffusion moves of single adatoms within a layer occur with probability 1 f interlayer transport and detachment from step edges is suppressed for the stationary distribution of the model is known hence the growth induced surface current can be computed analytically for small diffusion rates in the opposite diffusion dominated limit a description in terms of step flow is possible for slopes larger than a critical slope for smaller slopes the surface phase separates into regions of slope the stationary domain size diverges for as where we suggest that the large scale behaviour in this limit can be described by the noisy kuramoto sivashinsky equation in its noise dominated regime

on the non existence of linear non reciprocal bi isotropic nrbi media we show that raab and sihvola s theses on the recognizable existence of linear nonreciprocal bi isotropic media are either incorrect or inconsequential to modern electromagnetic theory which has purely microscopic foundations

surface critical behaviour of the honeycomb o n loop model with mixed ordinary and special boundary conditions the o n loop model on the honeycomb lattice with mixed ordinary and special boundary conditions is solved exactly by means of the bethe ansatz the calculation of the dominant finite size corrections to the eigenspectrum yields the mixed boundary scaling index and the geometric scaling dimensions describing the universal surface critical behaviour exact results follow in the limit n 0 for the polymer adsorption transition with a mixed adsorbing and free boundary these include the new configurational exponent gamma l 85 64

zero temperature properties of randomly self interacting polymers we study the zero temperature behavior of several simple models for randomly self interacting polymers in one and 1 1 dimensions results are based on exact enumeration and closed form expressions

interacting self avoiding walks and polygons in three dimensions self interacting walks and polygons on the simple cubic lattice undergo a collapse transition at the point we consider self avoiding walks and polygons with an additional interaction between pairs of vertices which are unit distance apart but not joined by an edge of the walk or polygon we prove that these walks and polygons have the same limiting free energy if the interactions between nearest neighbour vertices are repulsive the attractive interaction regime is investigated using monte carlo methods and we find evidence that the limiting free energies are also equal here in particular this means that these models have the same point in the asymptotic limit the dimensions and shapes of walks and polygons are also examined as a function of the interaction strength

spatial scaling in persistence we discuss persistence in the context of non equilibrium processes such as coarsening in ising and potts models the persistence phenomenon shows strong spatial correlation with a correlation length which diverges with time in the correlated region r persistent sites form a fractal and the structure evolves in time obeying a dynamical scaling we discuss such fractal formation in the context of a reaction diffusion system in one dimension

effective plasma model for the level correlations at the mobility edge we consider the mapping of the energy level statistics for a d dimensional disordered electron system at the mobility edge between metallic and insulating phases onto the model of a classical one dimensional plasma of fictitious particles we deduce the effective pairwise interaction in the plasma that is consistent with the known universal two level correlation function at the mobility edge and show that for level separation epsilon delta it decreases as delta epsilon gamma where delta is the mean level spacing and gamma is the critical exponent related to the known critical exponent v of the correlation length as gamma 1 vd 1 we apply the plasma model to generalize wigner s semicircle law and to derive the large energy asymptotic form of the nearest level distribution in the limit gamma to 0 which corresponds to the original dyson mapping onto the plasma with logarithmic repulsion we recover the classical results of wigner dyson random matrix theory

shapes of tree representations of spin glass landscapes much of the information about the multi valley structure of disordered spin systems can be convened in a simple tree structure a barrier tree the leaves and internal nodes of which represent respectively the local minima and the lowest energy saddles connecting those minima here we apply several statistics used in the study of phylogenetic trees to barrier trees that result from the energy landscapes of p spin models these statistics give information about the shape of these barrier trees in particular about balance and symmetry we then ask if they can be used to classify different types of landscapes compare them with results obtained from random trees and investigate the structure of subtrees of the barrier trees we conclude that at least one of the used statistics is capable of distinguishing different types of landscapes that the barrier trees from p spin energy landscapes are quite different from random trees and that subtrees of barrier trees do not reflect the overall tree structure but their structure is correlated with their depth in the tree

reply to the comment by j w lee self attracting walk are the exponents universal problems concerning the value of the exponent in the relationship describing a self attracting walk are considered it is suggested that further study is needed to understand how the exponent depends on the coupling energy of the walk

sensitivity of the eigenfunctions and the level curvature distribution in quantum billiards in searching for the manifestations of the sensitivity of the eigenfunctions in quantum billiards with dirichlet boundary conditions with respect to the boundary data the normal derivative we have performed instead various numerical tests for the robnik billiard a quadratic conformal map of the unit disk for 600 shape parameter values where we have looked at the sensitivity of the energy levels with respect to the shape parameter we show the energy level flow diagrams for three stretches of fifty consecutive odd eigenstates each with index 1000 to 2000 in particular we have calculated the unfolded and normalized level curvature distribution and found that it continuously changes from a delta distribution for the integrable case circle to a broad distribution in the classically ergodic regime for some shape parameters the agreement with the goe von oppen formula is very good whereas we have also cases where the deviation from goe is significant and of physical origin in the intermediate case of mixed classical dynamics we have a semiclassical formula in the spirit of the berry robnik 1984 surmise here the agreement with theory is not good partially due to the localization phenomena which are expected to disappear in the semiclassical limit we stress that even for classically ergodic systems there is no global universality for the curvature distribution not even in the semiclassical limit

thermodynamics of a brownian bridge polymer model in a random environment we consider a directed random walk making either 0 or 1 moves and a brownian bridge independent of the walk conditioned to arrive at point b at time t the hamiltonian is defined as the sum of the square of the increments of the bridge between the moments of jump of the random walk and is interpreted as an energy function over the bridge configuration the random walk acts as the random environment this system provides a soluble model inspired by a closely related but distinct model of proteins the thermodynamic limit of the quenched specific free energy is shown to exist and to be self averaging i e it is equal to a trivial explicitly computed random variable an estimate of the asymptotic behaviour of the ground state energy is also obtained

directed random walks in random environments we use holding time methods to study the asymptotic behavior of pure birth processes with random transition rates both the normal and slow approaches to infinity are studied fluctuations are shown to obey the central limit theorem for almost all sample transition rates our results are stronger and our proofs simpler then those of recently published studies

geometric transfer and the homotopy type of the automorphism groups of a manifold introduction for m a compact manifold with or without boundary in one of the categories diff pl or top we denote by a m the semisimplicial ss group of automorphisms of m i e the group of diffeomorphisms pl homeomorphisms or homeomorphisms resp in this paper we describe in the stability range and localized away from two the homotopy structure of a m we do this in terms of a m the ss group of block automorphisms whose homotopy structure is a sophisticated formulation of surgery theory abk and some new homotopy functors 5 theorem c the functors 5 and 5 l here considered have already been studied in the pl category by hatcher h from a different point of view the present geometric description is appropriate to the description of the homotopy structure of a m and enables us to produce a natural map b sc x 5 x from the associative monoid of simple homotopy equivalence of x to 5 x which will be important for our study besides the geometric topology results blr two ideas partially developed in bli are basic the first is the transfer map and stability for concordances described in the pl context by hatcher and in the differentiable context in bli the second is the splitting of a z 1 weak commutative topological group with involution as a product up to homotopy of two pieces the symmetric respectively antisymmetric parts applied to our situation those parts manifest very different behavior the results of this paper have been sketched by the first author in the survey paper b there is an overlap between some but not all results of a and results of hatcher h2 published in the same volume as b the results of this paper are stated in the next section statement of results and the proofs are given in subsequent sections we continue this section with a description of the notations used

extinction survival and dynamical phase transition of branching annihilating random walk we analyze statistical properties of random walkers which disappear when they meet and make offsprings by a controllable rate numerical results for one two and three dimensions and for the sierpinski gasket are assessed in view of the mean field theory predictions universality classes are found to depend on the number of offsprings in space dimension less than 3

a new class of critical exponents in a dimer monomer catalytic surface reaction the critical behaviour of a dimer monomer bc a to 1 2c2 ab irreversible catalytic surface reaction is investigated by means of monte carlo simulation technique on a hexagonal lattice each site having six nearest neighbours the reaction exhibits a steady reactive state between two critical concentrations ya1 and ya2 of a the critical exponents associated with various order parameters i e coverages at the second order phase transition ya1 have been obtained these exponents do not fall in the universality class of reggeon field theory as is the case of 1 2b2 a to ab the usual dimer monomer reaction

configurational statistics of a disordered polymer chain a problem of the configurational properties of a long flexible polymer chain with a quenched disorder is considered the chain is assumed to be randomly constructed from monomers of two different kinds with different constants for the two body interaction near the theta point i e when the average interaction of monomers is small the spatial correlation of the repulsive and attractive monomers of different kinds leads to an increase of effects of the disorder on large scales there is also the competing effect of the repulsive three body interaction which tends to screen the effects of disorder on large scales for both effects the upper critical dimension is dc 3 a solution of the renormalisation group equation indicates that there always exists a critical scale at which the relative dispersion of sizes of polymers with different random sequences of monomers becomes of the order of unity the magnitude of this critical scale depends strongly on the relation between the constant which characterises the dispersion of the two body interaction b0 and the constant of the repulsive three body interaction v0 if b0 3 32v0 at each physically attainable scale the effects of screening are prevalent and the dispersion of sizes of polymers with different sequences of monomers is small near the theta point if the reverse inequality holds the dispersion of sizes becomes of the order of unity near the theta point

a free energy bound for the hopfield model the author gives a simple upper and lower bound on the free energy density of the hopfield model of size n with p stored patterns in the limit where n and p tend to infinity with p n to alpha 1 the two bounds coincide for alpha 0

further remarks on the non existence of linear non reciprocal bi isotropic media this communication follows four manuscripts published in this journal in particular it is motivated by the most recent comments made by raab and sihvola here we show that these comments of raab and sihvola affirming the recognizable existence of linear non reciprocal bi isotropic nrbi media are based on i a factually incorrect statement and ii a confusion between static fields and fields with slow temporal variations

probabilistic analysis of the number partitioning problem given a sequence of n positive real numbers the number partitioning problem consists of partitioning them into two sets such that the absolute value of the difference of the sums of over the two sets is minimized in the case in which the s are statistically independent random variables uniformly distributed in the unit interval this np complete problem is equivalent to the problem of finding the ground state of an infinite range random antiferromagnetic ising model we employ the annealed approximation to derive analytical lower bounds to the average value of the difference for the best constrained and unconstrained partitions in the large n limit furthermore we calculate analytically the fraction of metastable states i e states that are stable against all single spin flips and found that it vanishes like

the dimer trimer model for heterogeneous catalysis a new universality class the authors study a new model for heterogeneous catalysis in which dimers a2 and trimers b3 are chemisorbed onto a triangular lattice nearest adsorbed a and b neighbours react and desorb leaving behind two empty sites they observe a phase diagram similar to that of the monomer dimer model of ziff gulari and barshad 1986 with a stationary reactive phase in between a dimer poisoned and a trimer poisoned phase there is a first order transition from the reactive phase to the dimer poisoned phase and a second order transition to the trimer poisoned phase however the second order transition is in a different universality class from reggeon field theory in contrast to all previously studied models for catalysis the difference stems from the infinite number of absorbing states in the trimer poisoned phase special to their model

a study of uniform stars using 1 d expansions and numerical methods we study a lattice model of an interacting uniform self avoiding star polymer with f branches a 1 d expansion for the limiting reduced free energy is derived through order 1 d for general f and for f 3 to order 1 d 2 the terms in the expansion are independent of f and agree term by term with the corresponding expansion for interacting self avoiding walks we also present a miscellany of numerical results obtained by more conventional series and monte carlo techniques all our results both past and present support the conjecture that the limiting reduced free energies of f stars walks and polygons are identical for all values of the interaction parameter

efficient computation of rna folding dynamics barrier trees consisting of local minima and their connecting saddle points imply a natural coarse graining for the description of the energy landscape of rna secondary structures here we show that based on this approach it is possible to predict the folding behaviour of rna molecules by numerical integration comparison with stochastic folding simulations shows reasonable agreement of the resulting folding dynamics and a drastic increase in computational efficiency that makes it possible to investigate the folding dynamics of rna of at least trna size our approach is readily applicable to bistable rna molecules and promises to facilitate studies on the dynamic behaviour of rna switches

low temperature properties of directed walks with random self interactions we consider a simple model for a chain with random self interactions each monomer on the chain carries a charge which is a random variable and the configurations of the chain are directed walks we show that at zero temperature the end to end distance r and the energy e of chains with total charge q approximately nx scale as r approximately nnu x and e approximately ntheta x the exponents thus depend on the total charge through the parameter x these exponents are measured numerically and compared to the predictions of some simple arguments at a finite temperature r is extensive and appears to be independent of x

dynamical localization of chaotic eigenstates in the mixed type systems spectral statistics in a billiard system after separation of regular and chaotic eigenstates we study the quantum mechanics of a billiard robnik 1983 j phys a math gen 16 3971 in the regime of mixed type classical phase space the shape parameter 0 15 at very high lying eigenstates starting at about 1 000 000th eigenstate and including the consecutive 587654 eigenstates by calculating the normalized poincare husimi functions of the eigenstates and comparing them with the classical phase space structure we introduce the overlap criterion which enables us to separate with great accuracy and reliability the regular and chaotic eigenstates and the corresponding energies the chaotic eigenstates appear all to be dynamically localized meaning that they do not uniformly occupy the entire available chaotic classical phase space component but are localized on a proper subset we find with unprecedented precision and statistical significance that the level spacing distributions of the regular levels obey the poisson statistics and the chaotic ones obey the brody statistics as anticipated in a recent paper by batistic and robnik 2010 j phys a math theor 43 215101 where the entire spectrum was found to obey the berry robnik brody statistics there are no effects of dynamical tunneling in this regime due to the high energies as they decay exponentially with the inverse effective planck constant which is proportional to the square root of the energy

a proof of the smale conjecture diff s3 0 4 the smale conjecture 9 is the assertion that the inclusion of the orthogonal group 0 4 into diff s3 the diffeomorphism group of the 3 sphere with the cw topology is a homotopy equivalence there are many equivalent forms of this conjecture some of which are listed in the appendix to this paper we shall prove

critical exponents for a dimer dimer irreversible surface reaction abstract a dimer dimer reaction model of the type a2 b2 2ab is investigated by means of computer simulations the desorption of b2 dimer with probability p is studied here we investigate the critical behaviour the critical exponents of our model do not fall into the reggeon field theory or directed percolation universality class the universality class of the reaction changes with changes in p

on spectral statistics of classically integrable systems this work is an extensive study of the spectral statistics of three representative classically integrable systems namely rectangle torus and circle billiards we analyse the statistics and focus on the related level spacing distribution p s and the delta statistics the agreement with the poissonian model is typically found to be perfect up to the outer unfolded energy scale beyond which the saturation is observed in agreement with berry s dynamical theory of the spectral rigidity where as the untypical systems are those where for example p s is not a smooth distribution but a sum of the delta functions due to the granularity of the energy scale for example in the rectangle with the rational squared sides ratio however even there we find reasonable trend towards poissonian statistics for large ranges l but we describe theoretically and numerically the broadening of the delta spikes when the rectangular billiard is slightly distorted away from a rational to an irrational shape and find excellent agreement also in irrational rectangle billiards we show and explain the existence of large fluctuations by one order of magnitude bigger than the statistical ones whose origin is in the closeness to some rational billiard shape these fluctuations and their amplitude are independent of the energy if the bin size shrinks inversely with energy finally we tested the mode distribution i e distribution of the reduced mode fluctuation number w and found that it was not poissonian in agreement with steiner s conjecture and in fact follows the prediction by bleher et al that its tail behaves as the general reason for non universal behaviour of p w is that at largest energy scales we are always in the saturation regime

critical behaviour of an interacting surface reaction model the authors investigate the kinetics of a generalized monomer monomer surface reaction model in which there is a variable excluded volume interaction between same species particles as and bs for no interaction this system reduces to the monomer monomer model for which there is a first order transition between a and b saturated phases as a function of the excluded volume interaction the first order transition line for weak interaction terminates at a tricritical point where two second order transitions meet these transitions which appear to be in the reggeon field theory universality class separate the a saturated reactive and b saturated phases series expansions and various time dependent monte carlo simulations are used to estimate the critical parameters and exponents associated with these transitions

learning by dilution in a neural network a perceptron with n random weights can store of the order of n patterns by removing a fraction of the weights without changing their strengths the critical storage capacity as a function of the concentration of the remaining bonds for random outputs and for outputs given by a teacher perceptron is calculated a simple hebb like dilution algorithm is presented which in the teacher case reaches the optimal generalization ability

threshold induced phase transitions in perceptrons error rates of a boolean perceptron with threshold and either spherical or ising constraint on the weight vector are calculated for storing patterns from biased input and output distributions derived within a one step replica symmetry breaking rsb treatment for unbiased output distribution and non zero stability of the patterns we find a critical load p above which two solutions to the saddlepoint equations appear one with higher free energy and zero threshold and a dominant solution with non zero threshold we examine this second order phase transition and the dependence of p on the required pattern stability for both one step rsb and replica symmetry rs in the spherical case and for one step rsb in the ising case

on spin systems related to the temperley lieb algebra the spectrum of the transfer matrices constructed from the spectral parameter dependent temperley lieb r matrix is found using functional relations identical to those of the spin 1 2 xxz magnet

the smallest length of eight dimensional binary linear codes with prescribed minimum distance let n 8 d be the smallest integer n for which a binary linear code of length n dimension 8 and minimum distance d exists we prove that n 8 18 42 n 8 26 58 n 8 28 61 n 8 30 65 n 8 34 74 n 8 36 77 n 8 38 81 n 8 42 89 and n 8 60 124 after these results all values of n 8 d are known

directed percolation in 2 1 dimensions the author presents results of monte carlo simulations for directed percolation in 2 1 dimensions very close to the percolation threshold his values for pc for bond and site percolation on the bcc and simple cubic lattices are more precise than previous estimates by one to two orders of magnitude the improvement on the critical exponents describing the behaviour at pc is less impressive but they are also substantially more precise than previous ones

dynamical exponents for one dimensional random random directed walks the dynamical exponents of the coordinate and of the mean square displacement are explicitly calculated in the case of a directed random walk on a one dimensional random lattice moreover it is shown that in the dynamical phase where the coordinate increases slower thant the latter is not a self averaging quantity

conservation laws and universality in branching annihilating random walks takayasu and tretyakov 1992 studied branching annihilating random walks with n 1 5 offspring these models exhibit a continuous phase transition to an absorbing state for odd n the models belong to the universality class of directed percolation for even n the particle number is conserved modulo two and the critical behaviour is not compatible with directed percolation branching annihilating random walks with n 4 additional process spontaneous annihilation which breaks the conservation law are studied the inclusion of spontaneous annihilation even at very small rates leads to directed percolation critical behaviour

the statistical mechanics of random copolymers random copolymers are polymers with two or more types of monomer where the monomer sequence is determined by some random process once determined the sequence is fixed so random copolymers are an example of a system with quenched randomness we review the statistical mechanics of random copolymers focusing on self avoiding walk models where there are two types of monomers a and b which are randomly distributed along the polymer chain theoretical approximate and numerical results are reviewed for models of the random copolymer adsorption localization and collapse phase transitions we concentrate on what is known about the existence of phase transitions the morita approximation and results about self averaging we also discuss in less detail the replica trick and numerical methods including monte carlo methods exact enumeration and transfer matrix methods important open problems are identified throughout and highlighted in the conclusions

pseudo isotopies of irreducible 3 manifolds it is shown that a certain subspace of the space of all pseudo isotopies of any irreducible 3 manifold is connected this subspace consists of those pseudo isotopies corresponding to 1 parameter families of functions which have nondegenerate critical points of index 1 and 2 only and which contain no slides among the 2 handles some of the techniques developed are used to prove a weak four dimensional h cobordism theorem

new universal aspects of diffusion in strongly chaotic systems we study some new universal aspects of diffusion in chaotic systems especially those having very large lyapunov coefficients on the chaotic indecomposable topologically transitive component we do this by discretizing the chaotic component on the surface of section sos in a large number n of simplectically equally big cells in the sense of equal relative invariant ergodic measure normalized so that the total measure of the chaotic component is unity by iterating the transition of the chaotic orbit through the sos where j counts the number of iterations discrete time and assuming complete lack of correlation even between consecutive crossings which can be justified due to the very large lyapunov exponents we show the universal approach of the relative measure of the occupied cells denoted by to the asymptotic value of unity in the following way so that in the limit of big n we have for j n fixed the exponential law this analytic result is verified numerically in a variety of specific systems for a plane billiard robnik 1983 for a 3d billiard prosen 1997 for an ergodic logistic map tent map for a standard map k 400 and for the hydrogen atom in a strong magnetic field the agreement is almost perfect except in the latter two systems for some long time deviations on very small scales however for henon heiles system and for the standard map k 3 the deviations are noticeable though not very big only about 1 we have tested the random number generators press et al 1986 and confirmed that some are almost perfect ran0 and ran3 whilst two of them ran1 and ran2 exhibit big deviations

intermediate statistics in the regime of mixed classical dynamics we explain the arguments in support of the berry robnik 1984 17 2413 picture of the energy level statistics in the asymptotic strict far semiclassical limit of sufficiently small where the entire energy spectrum can be represented as a statistically independent superposition of regular and irregular level sequences the regular ones obeying the poissonian statistics and the irregular ones the rmt statistics goe or gue we generalize the results to describe not only the level spacing distribution the number variance and the delta statistics but also arbitrary statistics the probability to find k levels inside an interval of length l after unfolding very useful and effective approximations for are described we demonstrate very clearly that this regime is excellently described by this picture for k as high as the outer energy scale even when taking into account the regular component and only one the dominant chaotic component this we show numerically for the compactified standard map and for the quartic 2d billiard

a model of continuous polymers with random charges we study a model of polymers with random charges the possible shapes of the polymer are represented by the sample paths of a brownian motion and the cumulative charge distribution along a polymer is modeled by a realization of a brownian bridge charges interact through a general positive definite two body potential we study the infinite volume free energy density for a fixed realization of the brownian motion this is not self averaging but shows on the contrary a sample dependence through the local time of the brownian motion we obtain an explicit series representation for the free energy density this has a finite radius of convergence but the free energy is nevertheless analytic in the inverse temperature in the physical domain

evidence for the validity of the berry robnik surmise in a periodically pulsed spin system we study the statistical properties of the spectrum of a quantum dynamical system whose classical counterpart has mixed phase space structure consisting of two regular regions separated by a chaotic one we make use of a simple symmetry of the system to separate the eigenstates of the time evolution operator into two classes in agreement with the percival classification scheme we then use a method firstly developed by bohigas et al 1990 to evaluate the fractional measure of states belonging to the regular class and finally present the level spacing statistics for each class the level spacing distribution of states belonging to the irregular part of the spectra as well as that of the complete set of levels corroborate the berry robnik surmise we further present a statistical study of the regular levels the presence of intermediate states states which belong to neither class as long as r is finite phase spatially mixed among the set of regular ones together with the small fractional measure of regular states strongly affects the corresponding level spacing statistics resulting in a non negligible deviation from the expected poisson distribution we see however the remarkable agreement of the irregular level spacing statistics as a direct confirmation of the berry robnik surmise

on the existence of linear non reciprocal bi isotropic nrbi media a recent letter in this journal and a number of related publications have purported to prove that maxwell s equations forbid the existence of linear non reciprocal bi isotropic nrbi media the basis of such proofs is shown to be unfounded with the constraint on matter being due not to electromagnetism but to symmetry it is also shown that linear nrbi media may exist in some situations in the form of certain magnetic cubic crystals in addition in their response to an electromagnetic wave there are also magnetic cubics in which propagation although not perfectly isotropic deviates in practice to an extent which is probably undetectable finally the existence of a tellegen medium as an example of a nrbi substance is shown to be possible in principle in contrast to the findings of recent papers

exact results and self averaging properties for random random walks on a one dimensional infinite lattice we present new exact results for a one dimensional asymmetric disordered hopping model the lattice is taken infinite from the start and we do not resort to the periodization scheme used by derrida an explicit resummation allows for the calculation of the velocityv and the diffusion constantd which are found to coincide with those given by derrida and for demonstrating thatv is indeed a self averaging quantity the same property is established ford in the limiting case of a directed walk