deterministic walks in random environments deterministic walks in random environments dwre occupy an intermediate position between purely random generated by random trials and purely deterministic generated by deterministic dynamical systems e g by maps models of diffusion these models combine deterministic and probabilistic features we review general properties of dwre and demonstrate that to a large extent their dynamics and their statistics can be analyzed consecutively and separately we also show that orbits of one dimensional walks in rigid environments with non constant rigidity almost surely visit each site infinitely many times

on the hull of two dimensional percolation clusters a recently proven equivalence between certain random walks with memory and the hull of percolation clusters in two dimensions is used to estimate the fractal dimension of the latter by means of monte carlo simulations the authors calculate the value dh 1 750 or 0 002 in agreement with a recent conjecture that dh 7 4 exactly

on the hulls of directed percolation clusters the properties of the hulls of directed percolation clusters are studied the scaling and finite size scaling of many quantities around the percolation threshold pc are derived and a novel monte carlo algorithm which is more than twice as fast as the standard algorithm at pc has been formulated to study these properties simulations have been conducted that enable an estimation of all the exponents involved in particular the central exponent x relating the average hull length of clusters to their mass has been estimated to be 0 773 4 at the percolation threshold this same exponent is estimated to be 0 905 5 for p p c thus this second value should hold for directed animals

scaling of particle trajectories on a lattice the scaling behavior of the closed trajectories of a moving particle generated by randomly placed rotators or mirrors on a square or triangular lattice is studied numerically on both lattices for most concentrations of the scatterers the trajectories close exponentially fast for special critical concentrations infinitely extended trajectories can occur which exhibit a scaling behavior similar to that of the perimeters of percolation clusters at criticality in addition to the two critical exponents 15 7 anddf 7 4 found before the critical exponent 3 7 appears this exponent determines structural scaling properties of closed trajectories of finite size when they approach infinity new scaling behavior was found for the square lattice partially occupied by rotators indicating a different universality class than that of percolation clusters near criticality in the critical region two scaling functions were determined numerically f x related to the trajectory length s distributionns andh x related to the trajectory sizers gyration radius distribution respectively the scaling functionf x is in most cases found to be a symmetric double gaussian with the same characteristic size exponent 0 43 3 7 as at criticality leading to a stretched exponential dependence ofns ons ns exp s6 7 however for the rotator model on the partially occupied square lattice an alternative scaling function is found leading to a new exponent 1 6 0 3 and a superexponential dependence ofns ons h x is essentially a constant which depends on the type of lattice and the concentration of the scatterers the appearance of the same exponent 3 7 at and near a critical point is discussed

lorentz gas cellular automata on graphs lorentz gas cellular automata lgca are models of parallel many tape turing machines generated by the motion of localized point objects particles signals wave trains etc on a graph in each vertex v of the graph we store a symbol a read write head of the turing machine is represented as an object that hops from one vertex of the graph to another according to a rule symbol stored in the vertex thus the symbols stored in the vertices represent scattering rules or simply scatterers of the lattice gas it is assumed that initially the scatterers are randomly distributed among the vertices of the graph the random environment formed by the scatterers may either be fixed or evolve due to collisions with the moving object the collisions simulate storing of a new symbol in the vertex of the graph we investigate these models with fixed environment in general types of graphs and the models with evolving environments on trees remarkably it occurred that all models with fixed environments and many models with evolving environment behave like a depth first search on the underlying graph observe that such behavior occurs for any initial random distribution of scatterers rather than for some specially prepared initial configurations of scatterers we also give estimates of periods of orbits on finite graphs

structure and perimeters of percolation clusters site percolation clusters are simulated at the percolation threshold on the square lattice an algorithm for walks around each cluster is used to obtain information on its fractal geometry the fractal dimensionality of the external perimeter is found to depend on the size of adsorbent particles used to measure it if the vacant perimeter sites have only nearest neighbour connectivity then the perimeter has dimension de 1 37 or 0 03 instead of that of the hull dh 1 75 the authors also measured the mass of internal dangling sites surrounded by the backbone s blobs singly and doubly connected sites the number of blobs and the average linear distance between entry into the exit from a blob

on the dynamical axisymmetric stress field in a finite pre stretched bilayered slab resting on a rigid foundation the dynamic axisymmetric stress field in an initially finite pre stretched bilayered slab resting on a rigid foundation is studied within the framework of the piecewise homogeneous body model the three dimensional linearized theory of elastic waves in initially stressed bodies is used it is assumed that a time harmonic point located normal force acts on the free face plane of the slab the considered problem is solved by employing the hankel integral transformation the materials of the layers are assumed to be incompressible and the elastic relations are given through the treloar potential the formulation and solution to the problem coincide with the corresponding ones of classical linear theory of elasticity for an incompressible body in the case where there is no initial stretching in the layers numerical results are presented and these results involve stresses acting on the interface planes in particular it is established that stresses on the interface planes decrease as the pre stretching is increased

equivalence of deterministic walks on regular lattices on the plane abstract we consider deterministic walks on square triangular and hexagonal two dimensional lattices in each case there is a scatterer at every lattice site that can be in one of two states that forces the walker to turn either to his her immediate right or left after the walker is scattered the scatterer changes state a lattice with an arrangement of scatterers is an environment we show that there are only two environments for which the scattering rules are injective mirrors or rotators on the three lattices on hexagonal lattices webb and cohen 2014 proved that if a walker with a given initial position and velocity moves through an environment of mirrors rotators then there is an environment of rotators mirrors through which the walker would move with the same trajectory we refer to these trajectories on mirror and rotator environments as equivalent walks we prove the equivalence of walks on square and triangular lattices and include a proof of the equivalence of walks on hexagonal lattices the proofs are based both on the geometry of the lattice and the structure of the scattering rule

optimal selective feedback policies for opportunistic beamforming this paper studies the structure of downlink sum rate maximizing selective decentralized feedback policies for opportunistic beamforming under finite feedback constraints on the average number of mobile users feeding back first it is shown that any sum rate maximizing selective decentralized feedback policy must be a threshold feedback policy this result holds for all fading channel models with continuous distribution functions second the resulting optimum threshold selection problem is analyzed in detail this is a nonconvex optimization problem over finite dimensional euclidean spaces by utilizing the theory of majorization an underlying schur concave structure in the sum rate function is identified and the sufficient conditions for the optimality of homogenous threshold feedback policies are obtained applications of these results are illustrated for well known fading channel models such as rayleigh nakagami and rician fading channels rather surprisingly it is shown that using the same threshold value at all mobile users is not always a rate wise optimal feedback strategy even for a network in which mobile users experience statistically the same channel conditions for the rayleigh fading channel model on the other hand homogenous threshold feedback policies are proven to be rate wise optimal if multiple orthonormal data carrying beams are used to communicate with multiple mobile users simultaneously

hamiltonian interpretation of the stroh formalism in anisotropic elasticity stroh s sextic formalism for static problems or steady motions in anisotropic elasticity is a formulation in which the equation of equilibrium motion is written as a system of first order differential equations for the displacement and traction in terms of one of the spatial variables the so called fundamental elasticity matrix n appearing in this formulation has the property that when partitioned as a 2 2 block matrix its 12 and 21 blocks are symmetric matrices and its 11 block is the transpose of its 22 block this property gives rise to a large number of orthogonality and closure relations and is fundamental to the success of the stroh formalism in solving a large variety of problems in general anisotropic elasticity first we show that the matrix n is guaranteed to have the above property by the fact that the stroh formulation is in fact a hamiltonian formulation with one of the spatial variables acting as the time like variable this interpretation provides a much desired guide in dealing with other problems for which the governing equations are different such as incompressible elasticity and problems associated with anisotropic elastic plates as described by the kirchhoff plate theory we show that for the last two problems the hamiltonian interpretation simplifies the derivations significantly leading to a stroh formulation in each case which is equivalent to but much simpler than what is available in the existing literature

percolation on two and three dimensional lattices in this work we apply a highly efficient monte carlo algorithm recently proposed by newman and ziff to treat percolation problems the site and bond percolations are studied on a number of lattices in two and three dimensions quite good results for the wrapping probabilities correlation length critical exponent and critical concentration are obtained for the square simple cubic hexagonal close packed and hexagonal lattices by using relatively small systems we also confirm the universal aspect of the wrapping probabilities regarding site and bond dilution

kinetics of gelation and universality the exact solution size distribution ck t and moments m t of smoluchowski s coagulation equation s model and of a modified equation f model with a coagulation rate k ij for i and j clusters is obtained for arbitrary ck 0 in the sol t phases where tc is the gel point the behaviour of ck t and m t is given for k co t co and t i the critical exponents critical amplitudes and scaling function that characterise the singularities near the non equilibrium phase transition are calculated for short range ck 0 i e all m a the f model belongs to the universality class of classical gelation theories and of bond percolation on cayley trees the s model does not

fast monte carlo algorithm for site or bond percolation we describe in detail an efficient algorithm for studying site or bond percolation on any lattice the algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time that scales linearly with the size of the system we demonstrate our algorithm by using it to investigate a number of issues in percolation theory including the position of the percolation transition for site percolation on the square lattice the stretched exponential behavior of spanning probabilities away from the critical point and the size of the giant component for site percolation on random graphs

analysis of the dispersion spectrum of fluid loaded anisotropic plates leaky wave branches the supersonic complex velocity versus real frequency dispersion spectrum of the leaky waves in fluid loaded anisotropic plates is discussed utilizing the sextic plate formalism provides approximate solutions for leaky wave velocity in a form that reveals their basic features such as the unique correspondence of the signs of its imaginary part and of the free plate group velocity the relation between the leakage and the rate of frequency dispersion and the principal trends at low high and near cutoff frequencies in arbitrary anisotropic plates a particular thrust of the study is the derivation of closed form asymptotics for the fundamental leaky wave velocity branch es at low frequency and for the continuum of leaky wave branches near the fluid coupled and fluid uncoupled thickness resonances conditions for the asymptotics accuracy are analysed and a comparison between an analytical approximation and exact numerical curves is presented for various cases

new approach to percolation lattice system results results of an integral equation approach to pair connectedness are given for lattice models with emphasis on site percolation the lowest order approximation is expressible in terms of the lattice green function and is isomorphic to a polya random walk it yields percolation exponents gamma 2 nu 1 for d 3 and gamma 1 nu 1 2 for d or 4 d dimension for simple hypercubic lattices it also yields usefully sharp estimates for the site percolation threshold probability pp a first correction is described

position space renormalisation group for isolated polymer chains we develop a cell position space renormalisation group psrg with which we study the scaling properties of isolated polymer chains we model a chain by a self avoiding walk constrained to a lattice for rescaling factors b s 6 we calculate recursion relations analytically on the square lattice with several different choices for the psrg weight function we also calculate implicit cell to cell transformations in which a cell of size b is rescaled to a cell of size b the results of these psrgs improve both as b increases and as b b 1 in addition we construct a true infinitesimal psrg transformation which appears to become exact as the dimensionality d approaches 1 we obtain the closed form expression for the correlation length exponent u d l d in d the flory formula deviates from this already at first order in d 1 we also develop a constant fugacity monte carlo method which enables us to simu late in an unbiased way within the grand canonical ensemble chains of up to lo3 bonds with this method we extend the psrg to larger cells b s 150 on the square lattice our numerical method provides high statistical accuracy for all cell sizes however in the range of b we study the asymptotic behaviour of our results appears to depend on the choice of weight function one weight function provides smooth behaviour as a function of b and with it we extrapolate to find u 0 756 0 004 further work is required to resolve the apparent anomalies in the results based on the other weight functions

a non intersecting random walk on the manhattan lattice and sle 6 we consider a random walk on the manhattan lattice the walker must follow the orientations of the bonds in this lattice and the walker is not allowed to visit a site more than once when both possible steps are allowed the walker chooses between them with equal probability the walks generated by this model are known to be related to interfaces for bond percolation on a square lattice so it is natural to conjecture that the scaling limit is hbox sle 6 we test this conjecture with monte carlo simulations of the random walk model and find strong support for the conjecture

the smart kinetic self avoiding walk and schramm loewner evolution the smart kinetic self avoiding walk sksaw is a random walk which never intersects itself and grows forever when run in the full plane at each time step the walk chooses the next step uniformly from among the allowable nearest neighbors of the current endpoint of the walk in the full plane a nearest neighbor is allowable if it has not been visited before and there is a path from the nearest neighbor to infinity through sites that have not been visited before it is well known that on the hexagonal lattice the sksaw in a bounded domain between two boundary points is equivalent to an interface in critical percolation and hence its scaling limit is the chordal schramm loewner evolution with kappa 6 sle 6 like sle there are variants of the sksaw depending on the domain and the initial and terminal points on the hexagonal lattice these variants have been shown to converge to the corresponding version of sle 6 it is believed that the scaling limit of all these variants on any regular lattice is the corresponding version of sle 6 we test this conjecture for the square lattice by simulating the sksaw in the full plane and find excellent agreement with the predictions of full plane sle 6

asymptotic analysis of reduced feedback strategies for mimo gaussian broadcast channels achieving the sum capacity of a multiple input multiple output mimo gaussian broadcast channel is known to require full channel state information csi at the base station which implies the need of a large amount of feedback information from the users different asymptotics of the sum capacity such as its scaling law with respect to the number of users n or the multiplexing gain are conventionally used to assess the performance of suboptimal schemes with reduced feedback or equivalently with partial channel state information at the transmitter in this correspondence the optimal scaling law of the sum rate with respect to n for fixed signal to noise ratio snr fixed number of transmit antennas m and any number of receiving antennas n i e m log log nn is proved to be achievable with a deterministic feedback of only one bit per user moreover the amount of feedback is shown to be further reduced with no asymptotic optimality loss by applying the selective feedback principle leading to an average feedback rate that scales as log n finally the asymptotic performance with respect to snr is studied by assessing how fast the number of users needs to increase with the snr in order to guarantee a noninterference limited behavior

duality achievable rates and sum rate capacity of gaussian mimo broadcast channels we consider a multiuser multiple input multiple output mimo gaussian broadcast channel bc where the transmitter and receivers have multiple antennas since the mimo bc is in general a nondegraded bc its capacity region remains an unsolved problem we establish a duality between what is termed the dirty paper achievable region the caire shamai see proc ieee int symp information theory washington dc june 2001 p 322 achievable region for the mimo bc and the capacity region of the mimo multiple access channel mac which is easy to compute using this duality we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the mimo bc we also show that the dirty paper achievable region achieves the sum rate capacity of the mimo bc by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the mimo bc

hull generating walks abstract a hull generating walk hgw is a type of kinetic random walk that generates the hull or perimeter of a percolation cluster and thus has a fractal dimension of 1 75 some examples of hgws for site and bond percolation on a square lattice are described

percolation and self avoiding random loops presents simulations supporting the conjecture that properly defined exterior perimeters of 2d critical percolation clusters have the same fractal dimension d 4 3 as self avoiding random walks in addition the authors discuss possible generalizations

lattice lorentz gas kinetic theory standard approximation schemes in kinetic theory are compared with the effective medium approximation ema that was developed earlier for the stochastic lorentz gas on cubic lattices in models with reflecting collisions the low density results are in strong disagreement with molecular chaos and in excellent agreement with the simulation data the analysis identifies the diagrams that are taken into account in the different approximations the ema accounts in a self consistent way for all nested ring diagrams

on the user selection for mimo broadcast channels in this paper a downlink communication system in which a base station bs equipped with antennas communicates with users each equipped with receive antennas is considered an efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sum rate throughput of the system in a rayleigh fading environment for the asymptotic case when tends to infinity the necessary and sufficient conditions in order to achieve the maximum sum rate throughput such that the difference between the achievable sum rate and the maximum value approaches zero is derived the complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the bs as well as the number of searches required for selecting the users it is shown that the proposed method is capable of achieving a large portion of the sum rate capacity with a very low complexity

review paper characterization and stability of two phase piecewise homogeneous deformations many solid materials exhibit stress induced phase transformations such phenomena can be modelled with the aid of the nonlinear elasticity theory with appropriate choices of the strain energy function it is known that if a two phase deformation with gradient f in a finite elastic body is a local energy minimizer then given any point p of the surface of discontinuity the piecewise homogeneous deformation corresponding to the two values f p of f p is a global energy minimizer thus instability of the latter state would imply instability of the former state in this paper we investigate the stability properties of such piecewise homogeneous deformations more precisely we are concerned with two joined half spaces that correspond to two different phases of the same material we first show how such a two phase deformation can be constructed then the stability of the piecewise homogeneous deformation is investigated with the aid of two test criteria one is a kinetic stability criterion based on a quasi static approach and on the growth decay behaviour of the interface in the undeformed configuration when it is perturbed the other referred to as the energy criterion is used to determine whether the deformation is a minimizer of the total energy with respect to perturbations of the interface in both the current and undeformed configurations we clarify the differences between the two criteria and provide a compact formula which can be used to establish the stability instability of any two phase piecewise homogeneous deformations

fragmentation of percolation cluster perimeters we introduce a model for the fragmentation of porous random solids under the action of an external agent in our model the solid is represented by a bond percolation cluster on the square lattice and bonds are removed only at the external perimeter or hull of the cluster this model is shown to be related to the self avoiding walk on the manhattan lattice and to the disconnection events at a diffusion front these correspondences are used to predict the leading and the first correction to scaling exponents for several quantities defined for hull fragmentation our numerical results support these predictions in addition the algorithm used to construct the perimeters reveals itself to be a very efficient tool for detecting subtle correlations in the pseudo random number generator used we present a quantitative test of two generators which supports recent results reported in more systematic studies

on growth walks with self avoiding constraints the authors study a general class of growth walks in two dimensions with a self avoiding constraint which can be considered as dressed self avoiding walks a walker travels on a square lattice and chooses at each step one of the three forward directions with probability p1 p2 and p3 if the directions are allowed the self avoiding constraint is obtained by dressing the walk with black and white particles after each step such that the walk generates the external perimeter of arbitrary clusters consisting of black or white particles they discuss the critical values of p1 p2 and p3 which allow for infinite walks and study the end to end distance r t and the corresponding distribution function n r t furthermore they introduce a bias field in growth process and discuss how the time evolution of the walk is modified by the bias

manhattan lattice theta point exponents from kinetic growth walks and exact results from the nienhuis o n model kinetic growth walks kgw on the manhattan lattice have previously been shown to be equivalent to the static problem of interacting self avoiding walks on that lattice at the theta temperature here we illustrate how a complete set of exponents for the static problem including the crossover exponent phi and surface exponents at the ordinary and special transition points may be obtained from simulations of kinetic walks in the process we find that phi m 0 430 or 0 006 which encompasses the conjectured value 3 7 approximately 0 42857 for the theta point on an isotropic lattice our numerics confirm a predicted set of exponents for both the bulk and surface transitions in addition to results such as the exact internal energy at the bulk transition furthermore we point out that a recently examined variant of the nienhuis o n model can be mapped onto theta point walks on the manhattan lattice which allows identification of the scaling dimensions for that problem and thereby provides a method for proving all the numerical conjectures

motion in a random gyrotropic environment in d dimensions the authors construct a simple model of ballistic motion in a random environment in an arbitrary number of dimensions the motion is determined by a quenched set of random orthogonal matrices on a hypercubic lattice relating incoming and outgoing directions at a particular site they select study and classify a set of these matrices which agree with intuitive notions of isotropy a mean field theory is constructed of the transition between localised and extended trajectories and a qualitative discussion of various features of the phase diagram is made

precise determination of the bond percolation thresholds and finite size scaling corrections for the sc fcc and bcc lattices extensive monte carlo simulations were performed to study bond percolation on the simple cubic s c face centered cubic f c c and body centered cubic b c c lattices using an epidemic kind of approach these simulations provide very precise values of the critical thresholds for each of the lattices pc s c 0 2488126 0 0000005 pc f c c 0 1201635 0 0000010 and pc b c c 0 1802875 0 0000010 for p close to pc the results follow the expected finite size and scaling behavior with values for the fisher exponent 2 189 0 002 the finite size correction exponent 0 64 0 02 and the scaling function exponent 0 445 0 01 confirmed to be universal

diffusion laws for random walks on various heterogeneous lattices diffusion laws and diffusion coefficients are given for random walks on lattices whose scattering probabilities differ from site to site models are considered in which the direction of the particle after scattering depends on its direction before scattering

scaling behaviour of cluster hulls in spiral site percolation the scaling behaviour of the percolation hull rotationally constrained site percolation on the square and triangular lattices is studied the single cluster growth method has been used to determine the values of some critical exponents evidence is obtained for a scaling form of the hull size distribution function

quasiconvexity at the boundary positivity of the second variation and elastic stability for one dimensional problems of the calculus of variations there is a well developed theory relating the positivity of the second variation at a critical point i e linearized stability to strong relative minima these results largely due to weierstrass are usually proved by the method of fields of extremals as is described in bolza 1904 and morrey 1966 or by an argument involving a careful use of taylor series as in hestenes 1966 chapter 3 14

the efficient determination of the percolation threshold by a frontier generating walk in a gradient the frontier in gradient percolation is generated directly by a type of self avoiding random walk the existence of the gradient permits one to generate an infinite walk on a computer of finite memory from this walk the percolation threshold pc for a two dimensional lattice can be determined with apparently maximum efficiency for a naive monte carlo calculation or n 12 for a square lattice the value pc 0 592745 or 0 000002 is found for a simulation of n 2 6 1011 total steps occupied and blocked perimeter sites the power of the method is verified on the kagome site percolation case

site percolation on the penrose rhomb lattice abstract an epidemic analysis of cluster growth on the rhomb form of the penrose lattice yields the site percolation threshold p c 0 58391 0 00001 the corrections to scaling exponent 0 7 is consistent with the value 0 77 0 02 found here for the square lattice and triangular lattices

a direct electrifying algorithm for backbone identification this paper proposes a new algorithm for identifying backbones in the application of percolation theory this algorithm is based on the current carrying definition of backbone and is carried out on the predetermined spanning cluster it is fairly easy to implement and further parallelize the efficiency is enhanced by the fact that the conductivity of a percolating system can be obtained in the same processing of backbone identification the critical exponents of backbone mass red bonds sites and conductivity obtained by this algorithm are in very good agreement with the existing results

asymptotic analysis of the amount of csi feedback in mimo broadcast channels in this paper we consider a downlink communication system in which a base station bs equipped with m antennas and power constraint p communicates with n users each equipped with k receive antennas it is assumed that the users have perfect channel state information csi of their own channels while the bs only knows the partial csi provided by the receivers via a feedback channel we study the fundamental limits on the amount of feedback required at the bs to achieve the sum rate capacity of the system when bs has perfect csi for all users in the asymptotic case of n considering various signal to noise ratio snr regimes the main results of this paper can be expressed as follows 1 in the fixed snr regime where the snr does not scale with n and low snr regime where the snr is much smaller than 1 in n to achieve the 1 e portion of the sum rate capacity the total amount of feedback should scale at least with e 1 in the fixed snr regime to reduce the gap between the achievable sum rate and the sum rate capacity of the system which is defined as the sum rate gap to zero the amount of feedback should scale at least logarithmically with the sum rate capacity which is achievable by using the random beam forming rbf scheme proposed by sharif and hassibi in the low snr regime we propose an opportunistic beam forming obf scheme which is shown to be asymptotically feedback optimal 2 in the high snr regime where the snr grows to infinity as n the total amount of feedback depends on the number of receive antennas in particular to reduce the sum rate gap to zero in the case of k 1 m 1 should scale at least logarithmically with the snr in the case of k m the amount of feedback does not need to scale with the snr moreover we show that rbf is asymptotically feedback optimal in the high snr regime

scaling properties of antipercolation hulls on the triangular lattice the critical properties of the perimeters or hulls of antipercolation clusters are studied in two dimensions by monte carlo simulations on the triangular lattice two different types of hulls are constructed with the help of two kinetic walk algorithms for the standard hull the authors very accurately determine the size distribution exponent tau 2 14250 0003 as well as the fractal dimension dfs 1 7500 001 the corresponding exponents for regular percolation hulls 15 7 and 7 4 respectively are within the error bars of their results for antipercolation for the reduced hull they obtain the estimate dfr 1 3340 004 for the fractal dimension a result which is again close to that found for regular percolation

structure of backbone perimeters of percolation clusters the author studies perimeters of backbones of percolation clusters at the percolation threshold in two dimensions these perimeters are self avoiding for all lattices they simulate these perimeters by three independent processes measure the average size of them and study their variation with length they find the exponent characterising this variation to be 0 744 or 0 012 it seems likely that these perimeters are in the self avoiding walk universality class

percolation and motion in a simple random environment the authors present a particularly simple model of deterministic classical motion in a two dimensional random environment as the parameters of the model are varied a transition occurs from all trajectories being localised to some being extended they construct a mean field theory for this transition and relate the model exactly to percolation models in particular parameter ranges they point out that it is a member of a new class of site percolation analogues of direct bond percolation

the exit distribution for smart kinetic walk with symmetric and asymmetric transition probability it has been proved that the distribution of the point where the smart kinetic walk skw exits a domain converges in distribution to harmonic measure on the hexagonal lattice for other lattices it is believed that this result still holds and there is good numerical evidence to support this conjecture here we examine the effect of the symmetry and asymmetry of the transition probability on each step of the skw on the square lattice and test if the exit distribution converges in distribution to harmonic measure as well from our simulations the limiting exit distribution of the skw with a non uniform but symmetric transition probability as the lattice spacing goes to zero is the harmonic measure this result does not hold for asymmetric transition probability we are also interested in the difference between the skw with symmetric transition probability exit distribution and harmonic measure our simulations provide strong support for a explicit conjecture about this first order difference the explicit formula for the conjecture will be given below

deterministic lattice lorentz gas i chiral model the author studies diffusion by using a specific type of cellular automaton where particles move in an environment of scatterers the deterministic collision rules used in the model give rise to certain difficulties related to nonergodicity the class of models introduced by gunn and ortuno 1985 also contains the model studied by gates 1972 previously developed theory including the boltzmann approximation the ring and repeated ring approximations and the effective medium approximation ema is generalized for this model the validity is further investigated using computer simulations in the presence of reflecting scatterers ema yields low density results that show the breakdown of the boltzmann equation while they agree quantitatively with the low density simulations ema also agrees with a phase transition that occurs for some parameter choices

a new identity for the surface impedance matrix and its application to the determination of surface wave speeds it is well known in surface wave theory that the secular equation for the surface wave speed can be written as det m 0 in terms of the surface impedance matrix m it is shown in this paper that m satisfies the simple identity m i r t 1 m i r t q 2 i 0 in the usual notation in the stroh formalism this identity provides an efficient method for calculating the wave speed of surface waves in unstressed or pre stressed elastic half spaces the method is explained and illustrated by examples it is also shown that the buckling wrinkling pre stress for a pre stressed elastic half space can be calculated using the same procedure but with pre stress playing the role of

recurrence properties of lorentz lattice gas cellular automata recurrence properties of a point particle moving on a regular lattice randomly occupied with scatterers are studied for strictly deterministic nondeterministic and purely random scattering rules

some general relations between dressed self avoiding walks and percolation perimeters on lattices the author shows for some simple examples the relations between some recently proposed dressed self avoiding walks and site percolation connection between matching pairs and dressed walk generators is specified and some features of the corresponding bond percolation problem are given the case of surface generators for dressed self avoiding surfaces is briefly examined

universality of the excess number of clusters and the crossing probability function in three dimensional percolation extensive monte carlo simulations were performed to evaluate the excess number of clusters and the crossing probability function for three dimensional percolation on the simple cubic s c face centred cubic f c c and body centred cubic b c c lattices systems l l l0 with l0 l were studied for both bond s c f c c b c c and site f c c percolation the excess number of clusters q b per unit length was confirmed to be a universal quantity with a value q b 0 412 likewise the critical crossing probability in the l0 direction with periodic boundary conditions in thell plane was found to follow a universal exponential decay as a function of r d l 0 l for large r simulations were also carried out to find new precise values of the critical thresholds for site percolation on the f c c and b c c lattices yielding pc f c c d 0 199 2365 0 000 0010 pc b c c d 0 245 9615 0 000 0010 we also report the value pc s c d 0 311 6080 0 000 0004 for site percolation

probability density of the 2d percolation cluster perimeter the authors study the form of the probability density p r t of the end to end distance r of a segment of length t of the perimeter of the 2d percolation cluster at criticality they find that p r t behaves as p r t varies as t 2dh exp r t1dh delta where delta 1 1 1 dh the exponent dh 7 4 is the fractal dimension of the hull the external perimeter of a percolation cluster this result fits very well with recent numerical data

the coastline and lake shores on a fractal island we compute the fractal dimensions of the hulls or external boundary and the boundaries of the internal cavities in several deterministic as well as random fractal structures our conclusion is that the two fractal dimensions are in fact identical the deterministic fractals we study are sierpinski carpets sc in a two dimensional space and the random fractals are percolation clusters at criticality as an intermediate case we present results on some randomized sc in the random structures statistics of the area and perimeters of all internal cavities or holes are taken and the fractal dimension of the hull borderline is computed two different definitions of the borderline are used considering nearest neighbours as well as nearest and second nearest neighbours as connected the conclusion is valid for both cases

sum capacity of gaussian vector broadcast channels this paper characterizes the sum capacity of a class of potentially nondegraded gaussian vector broadcast channels where a single transmitter with multiple transmit terminals sends independent information to multiple receivers coordination is allowed among the transmit terminals but not among the receive terminals the sum capacity is shown to be a saddle point of a gaussian mutual information game where a signal player chooses a transmit covariance matrix to maximize the mutual information and a fictitious noise player chooses a noise correlation to minimize the mutual information the sum capacity is achieved using a precoding strategy for gaussian channels with additive side information noncausally known at the transmitter the optimal precoding structure is shown to correspond to a decision feedback equalizer that decomposes the broadcast channel into a series of single user channels with interference pre subtracted at the transmitter

cluster hull algorithms for large systems with small memory requirement improved hull walking algorithms for two dimensional percolation are proposed in these algorithms a walker explores the external perimeter of percolation clusters with our modifications very large systems sizel can be studied with finite and small memory requirement and in computation time l7 4 applications in determining spanning probabilities continuum percolation and percolation with nonuniform occupation probability are pointed out

deterministic lattice lorentz gas ii mirror model for pt i see ibid vol 24 p 787 806 1991 as a model for diffusion a lattice version of the lorentz gas is studied using specular collision rules a previously developed theory containing the molecular chaos approximation several ring approximations and the effective medium approximation ema is applied and compared with simulations the correction to the boltzmann equation result resulting from effective medium approximation ema is opposite to the simulation results this indicates that other diagrams than ring diagrams should be considered which is peculiar if one considers the successes of the ema for other models this is investigated by using variants of the model the diffusion tensor is in general nonisotropic the corresponding features are qualitatively described by theory

hull percolation and standard percolation the author shows that the hull percolation problem considered recently by roux et al 1988 is in one to one correspondence with standard bond percolation their random tiling of the plane by squares with circles is identical with the baxter kelland wu polygon decomposition associated with clusters of the q state potts model which in the q to 1 limit gives percolation

langton s flies langton s ant is an automaton defined over a two dimensional grid its movement is governed by the environment in a very simple way it turns to the left over white vertices and to the right over black vertices this definition only applies on a two dimensional space we look for generalizations of this automaton to n dimensional lattices remembering the different ways through which the ant was originally defined we consider two approaches the first comes from physics lattice gas and the second from artificial life virtual ants two generalizations are proposed defining two families of dynamical systems from the physics point of view the ant is seen as a particle and hence it has no internal state other than its velocity from the artificial life point of view the ant is viewed as an insect and it has an orientation in space which we represent by an orthogonal basis this constitutes the ant s internal state this formulation allows us to define the ant s behaviour without drawing upon any information relative to the global system of external coordinates each model yields different sets of rules with distinctive behaviours we characterize all the possible rules satisfying some basic restrictions we found that many rules produce trajectories which are restricted to a diagonal plane and are equivalent to a version of langton s ant over a two dimensional grid squared or hexagonal in the particle model only two of them use the whole space and it is shown that such rules do not admit periodical trajectories this result reinforces a previous one reported by leonid bunimovich who states that the skeleton of any bounded trajectory cannot contain any three dimensional polyhedron

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

accessible external perimeters of percolation clusters the authors introduce a new definition of a cluster s accessible external perimeter which is different from the usual definition of the hull this external perimeter can be measured by probing adsorbent particles coming from the cluster s exterior the size of these particles determines which perimeter sites are accessible from the outside and hence one can define different external or accessible perimeters according to this size using a monte carlo simulation they measured the fractal dimensions of these accessible perimeters de for percolation clusters at the threshold on the square and the triangular lattices the fractal dimension of the accessible perimeter is found to depend on the size of the probing particles for several sizes which are larger than some lattice dependent threshold they find de approximately 4 3 which is significantly smaller than the hull dimension dh 7 4 found with smaller probing particles

generation of percolation cluster perimeters by a random walk a type of self avoiding random walk whish generates the perimeter of two dimensional lattice percolation clusters is given the algorithm has been simulated on a computer yielding the mean perimeter length as a function of occupation probability

kinetic growth walks and trails on oriented square lattices hull percolation and percolation hulls the authors have studied kinetic growth walks on the manhattan lattice and kinetic growth trails on the l lattice they find that the directional properties of these lattices prevent the kinetic growth walks from being trapped except at the origin as a consequence kgws are found to be in the skw universality class for these lattices extensive numerical calculations support this fact moreover it has been shown that the recently introduced hull percolation is equivalent to the kinetic growth walks on the manhattan lattice and the bond percolation hull on the square lattice at the percolation threshold is equivalent to the kinetic growth trails on the l lattice their numerical estimates agree nicely with the original estimates and thus support the equivalence

the stroh formalism for elastic surface waves of general profile the stroh formalism is widely used in the study of surface waves on anisotropic elastic half spaces to analyse existence and for calculating the resultant wave speed normally the formalism treats complex exponential solutions however since waves are non dispersive a generalization to waves having general waveform exists and is here found by various techniques fourier superposition yields a description in which displacements are expressed in terms of three copies of a single pair of conjugate harmonic functions an equivalent representation involving just one analytic function also is deduced both these show that at the traction free boundary just one component typically the normal component of displacement may be specified arbitrarily the others then being specific combinations of it and its hilbert transform the algebra is closely related to that used for complex exponential waves although the surface impedance matrix is replaced by a transfer matrix which better embodies the scale invariance properties of the waves using the scale invariance property of the boundary value problem a further derivation is presented in terms of real quantities

new universality classes in percolative dynamics we study a site analogue of directed percolation random trajectories are generated and their critical behavior is studied the critical behavior corresponds to that of simple percolation in some of the parameter space but elsewhere the exponents reveal new universality classes as a byproduct we use the model to make an improved estimate of the percolation hull exponents and to calculate the site percolation probability for the square lattice

the fractal dimension of cluster perimeters generated by a kinetic walk the fractal dimension dg of cluster perimeters generated by a recently proposed butterfly growth walk is considered in the long range limit of the walk on a percolation cluster dg appears to be equal to the fractal dimension of the singly connected bonds dg 1 nu the new relation for chemical dimension dl is proposed dl df df dg in the short range limit the butterfly walk on a euclidean lattice appears to be in the same universality class as a random walk the dynamic aspect of the growth walk is discussed and the continuously tunable spectral dimension is obtained both short and long range limits of this diffusion process are different from a random diffusion on percolation

similarity of percolation thresholds on the hcp and fcc lattices extensive monte carlo simulations were performed in order to determine the precise values of the critical thresholds for site phcpc s 0 199 255 5 0 000 001 0 and bond phcpc b 0 120 164 0 0 000 001 0 percolation on the hcp lattice to compare with previous precise measurements on the fcc lattice also exact enumeration of the hcp and fcc lattices was performed and yielded generating functions and series for the zeroth first and second moments of both lattices when these series and the values of pc are compared to those for the fcc lattice it is apparent that the site percolation thresholds are different however the bond percolation thresholds are equal within error bars and the series only differ slightly in the higher order terms suggesting the actual values are very close to each other if not identical

topological dynamics of flipping lorentz lattice gas models we study the topological dynamics of the flipping mirror model of ruijgrok and cohen with one or an infinite number of particles in particular we prove the topological transitivity and topological mixing up to a natural first integral for the one particle model

critical properties of island perimeters in the flooding transition of stochastic and rotational sandpile models critical properties of external perimeters of islands that appear at the flooding transition in the toppling surfaces defined by the toppling number si of each sand column of stochastic and rotational sandpile models are studied a set of new critical exponents are estimated by extensive numerical simulation and finite size scaling analysis the values of the critical exponents are found different for these sandpile models several scaling relations among the critical exponents and the hurst exponent describing the self affinity of the toppling surfaces are established and verified the critical exponents obtained here are also found connected to the exponents describing the avalanche size distribution

efficient measurement of the percolation threshold for fully penetrable discs we study the percolation threshold for fully penetrable discs by measuring the average location of the frontier for a statistically inhomogeneous distribution of fully penetrable discs we use two different algorithms to efficiently simulate the frontier including the continuum analogue of an algorithm previously used for gradient percolation on a square lattice we find that c 0 676 339 0 000 004 thus providing an extra significant digit of accuracy to this constant some figures in this article appear in colour in the electronic version see www iop org

determination of the bond percolation threshold for the kagome lattice the hull gradient method is used to determine the critical threshold for bond percolation on the two dimensional kagome lattice and its dual the dice lattice for this system the hull walk is represented as a self avoiding trail or mirror model trajectory on the 3 4 6 4 archimedean tiling lattice the result one standard deviation of error is not consistent with previously conjectured values

on beamforming with finite rate feedback in multiple antenna systems we study a multiple antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations assuming that the transmitter uses the quantized information for beamforming we derive a universal lower bound on the outage probability for any finite set of beamformers the universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel using the bound it is shown that finite information systems approach the perfect information case as t 1 2 sup b t 1 where b is the number of feedback bits and t is the number of transmit antennas the geometrical bounding technique used in the proof of the lower bound also leads to a design criterion for good beamformers whose outage performance approaches the lower bound the design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook and is equivalent to the problem of designing unitary space time codes under certain conditions finally we show that good beamformers are good packings of two dimensional subspaces in a 2t dimensional real grassmannian manifold with chordal distance as the metric

site percolation threshold for honeycomb and square lattices a new method of estimating the critical percolation threshold is proposed based on stauffer s cluster number scaling hypothesis and the universality with respect to lattice structure of the corresponding stauffer scaling function this method is illustrated by obtaining estimates of the site percolation threshold for the honeycomb lattice pc 0 6962 or 0 0006 and for the square lattice pc 0 5923 or 0 0007 the error bars or confidence limits of our estimates are substantially smaller than previous series estimates and for the honeycomb lattice would have to be multiplied by the factor 18 to include the value pc 2 12 recently proposed by kondor 1980 to be exact an additional result is r 4 95 or 0 15 where r lims to infinity rs and rs is the ratio of the cluster number scaling function at its maximum to its value at pc for clusters of size s

dispersion relations of axisymmetric wave propagation in initially twisted bi material compounded cylinders abstract this paper investigates the dispersion relations of axisymmetric wave propagation in initially twisted bi material compound cylinders within the scope of the piecewise homogeneous body model utilizing 3d linearized wave propagation theory in an initially stressed body it is assumed that the constituents of the compound cylinder are isotropic and homogeneous the corresponding eigen value problem is formulated and the solution method for this problem as well as the algorithm for obtaining the numerical results is developed the numerical results illustrate the influence of the initial twisting of the compound cylinder on the dispersion of the axisymmetric wave propagation as presented and discussed in the present paper in particular it is established that as a result of the existence of the initial twisting at least in one constituent of the considered compound cylinder the axisymmetric longitudinal and torsional waves cannot propagate separately i e the new type axisymmetric waves which differ from the axisymmetric torsional and longitudinal waves must appear