complex temperature singularities in potts models on the square lattice we report some results on the complex temperature ct singularities of q state potts models on the square lattice we concentrate on the problematic region mathrm re a l0 where a e k in which ct zeros of the partition function are sensitive to finite lattice artifacts from analyses of low temperature series expansions for 3l ql 8 we establish the existence in this region of complex conjugate ct singularities at which the magnetization and susceptibility diverge from calculations of zeros of the partition function we obtain evidence consistent with the inference that these singularities occur at endpoints a e a e of arcs protruding into the complex temperature extension of the ferromagnetic phase exponents for these singularities are determined e g for q 3 we find ensuremath beta e ensuremath 0 125 1 consistent with ensuremath beta e ensuremath frac 1 8 by duality these results also imply associated arcs extending into the ct extension of the symmetric paramagnetic phase analytic expressions are suggested for the positions of some of these singularities e g for q 5 our finding is consistent with the exact value a e a e 2 ensuremath 1 ensuremath mp i further discussions of complex temperature phase diagrams are given

low density series expansions for directed percolation on square and triangular lattices greatly extended series have been derived for moments of the pair connectedness for bond and site percolation on the directed square and triangular lattices the length of the various series has been at least doubled to more than 110 100 terms for the square lattice bond site problem and more than 55 terms for the bond and site problems on the triangular lattice analysis of the series leads to very accurate estimates for the critical parameters and generally seems to rule out simple rational values for the critical exponents the values of the critical exponents for the average cluster size parallel and perpendicular connectedness lengths are estimated by d 2 277 69 4 k d 1 733 825 25 and d 1 096 844 14 respectively an improved estimate for the percolation probability exponent is obtained from the scaling relation d k c 2 d 0 276 49 4 in all cases the leading correction to scaling term is analytic

universality of amplitude combinations in two dimensional percolation we generated extended low concentration series for the second moment of distances between cluster points a 2 in site and bond percolation on the square lattice and used them to calculate series for the correlation length we analysed these and other series for their critical amplitudes and compared them with results from monte carlo simulations of triangular site square site and square bond percolation the values obtained from the different models for the amplitude combination b 2 0 2 2 0 2 and b are the amplitudes of the second moment of the cluster size distribution m 2 and the strength of the infinite cluster p respectively are all within the range 2 23 0 10 confirming universality

precise critical exponents for the basic contact process we calculated some of the critical exponents of the directed percolation universality class through exact numerical diagonalizations of the master operator of the one dimensional basic contact process perusal of the power method together with finite size scaling allowed us to achieve a high degree of accuracy in our estimates with relatively little computational effort a simple reasoning leading to the appropriate choice of the microscopic time scale for time dependent simulations of markov chains within the so called quantum chain formulation is discussed our approach is applicable to any stochastic process with a finite number of absorbing states

adaptive mesh and algorithm refinement using direct simulation monte carlo adaptive mesh and algorithm refinement amar embeds a particle method within a continuum method at the finest level of an adaptive mesh refinement amr hierarchy the coupling between the particle region and the overlaying continuum grid is algorithmically equivalent to that between the fine and coarse levels of amr direct simulation monte carlo dsmc is used as the particle algorithm embedded within a godunov type compressible navier stokes solver several examples are presented and compared with purely continuum calculations

low density series expansions for directed percolation i a new efficient algorithm with applications to the square lattice a new algorithm for the derivation of low density series for percolation on directed lattices is introduced and applied to the square lattice bond and site problems numerical evidence shows that the computational complexity grows exponentially but with a growth factor which is much smaller than the growth factor of the previous best algorithm for bond site percolation on the directed square lattice the series has been extended to order 171 158 analysis of the series yields sharper estimates of the critical points and exponents

performance of vector perturbation multiuser mimo systems with limited feedback this paper considers the multiuser multiple input multiple output mimo rayleigh fading broadcast channel we consider the case where the multiple transmit antennas are used to deliver independent data streams to multiple users via a multiuser technique known as vector perturbation we propose lattice theoretic and rate distortion based approaches to analyze the performance of these systems taking into account the practical restrictions imposed by limited feedback and training we show that performance is primarily determined by the ratio between the number of users and the number of transmit antennas we then propose a new practical low complexity low rate feedback scheme and show that the performance approaches the ideal rate distortion based scheme

sum rate and fairness analysis for the mu mimo downlink under psk signalling interference suppression vs exploitation in this paper we analyze the sum rate performance of multi user multiple input multiple output mu mimo systems with a finite constellation phase shift keying psk input alphabet we analytically calculate and compare the achievable sum rate in three downlink transmission scenarios 1 without precoding 2 with zero forcing zf precoding and 3 with closed form constructive interference ci precoding technique in light of this new analytical expressions for the average sum rate are derived in the three cases and monte carlo simulations are provided throughout to validate the analysis furthermore based on the derived expressions a power allocation scheme that can ensure fairness among the users is also proposed the results in this work demonstrate that the ci strictly outperforms the other two schemes and the performance gap between the considered schemes increases with the increase in mimo size in addition the ci provides higher fairness and the power allocation algorithm proposed in this paper can achieve maximum fairness index

transfer matrix density matrix renormalization group for stochastic models the domany kinzel cellular automaton we apply the transfer matrix density matrix renormalization group tmrg to a stochastic model the domany kinzel cellular automaton which exhibits a non equilibrium phase transition in the directed percolation universality class estimates for the stochastic time evolution phase boundaries and critical exponents can be obtained with high precision this is possible using only modest numerical effort since the thermodynamic limit can be taken analytically in our approach we also point out further advantages of the tmrg over other numerical approaches such as classical dmrg or monte carlo simulations

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

an extinction survival type phase transition in the probabilistic cellular automaton p182 q200 we investigate the critical behaviour of a probabilistic mixture of cellular automata ca rules 182 and 200 in wolfram s enumeration scheme by mean field analysis and monte carlo simulations we found that as we switch off one ca and switch on the other by the variation of the single parameter of the model the probabilistic ca pca goes through an extinction survival type phase transition and the numerical data indicate that it belongs to the directed percolation universality class of critical behaviour the pca displays a characteristic stationary density profile and a slow diffusive dynamics close to the pure ca 200 point that we discuss briefly remarks on an interesting related stochastic lattice gas are addressed in the conclusions

directed compact percolation cluster size and hyperscaling exact recurrence relations are obtained for the length and size distributions of compact directed percolation clusters on the square lattice the corresponding relation for the moment generating function of the length distribution is obtained in closed form whereas in the case of the size distribution only the first three moments are obtained the work is carried out for clusters grown from a seed of arbitrary width on an anisotropic lattice a duality property is shown to exist which relates the moment generating functions on the two sides of the critical curve the moments of both distributions have critical exponents which satisfy a constant gap hypothesis with gap exponents nu 2 and delta 3 corresponding to the scaling length and scaling size respectively the usual hyperscaling relation for directed percolation is found to be invalid for compact clusters and is replaced by delta nu d nu perpendicular to where nu perpendicular to is the exponent corresponding to the cluster width and d is the number of transverse dimensions 1 for the square lattice

low density series expansions for directed percolation iv temporal disorder we introduce a model for temporally disordered directed percolation in which the probability of spreading from a vertex t x where t is the time and x is the spatial coordinate is independent of x but depends on t using a very efficient algorithm we calculate low density series for bond percolation on the directed square lattice analysis of the series yields estimates for the critical point pc and various critical exponents which are consistent with a continuous change of the critical parameters as the strength of the disorder is increased

density matrix formulation for quantum renormalization groups a generalization of the numerical renormalization group procedure used first by wilson for the kondo problem is presented it is shown that this formulation is optimal in a certain sense as a demonstration of the effectiveness of this approach results from numerical real space renormalization group calculations for heisenberg chains are presented

statistical properties of galaxy cluster distribution we analyze subsamples of abell and aco cluster catalogs in order to study the spatial properties of the large scale matter distribution the subsamples analyzed are estimated to be nearly complete and are the standard ones used in the correlation analysis by various authors the statistical analysis of cluster correlations is performed without any assumptions on the nature of the distribution itself the cluster samples show fractal correlations up to sample limits 70h 1 mpc with fractal dimension d 2 without any tendency towards homogenization our analysis shows that the standard correlation methods are incorrect since they give a finite correlation length for a distribution that does not possess one in particular the so called correlation length r0 is shown to be simply a fraction of the sample size moreover we conclude that galaxies and clusters are two different representations of the same self similar structure and that the correlations of clusters are the continuation of those of galaxies to larger scales

nonequilibrium critical behavior in unidirectionally coupled stochastic processes phase transitions from an active into an absorbing inactive state are generically described by the critical exponents of directed percolation dp with upper critical dimension d sub c 4 in the framework of single species reaction diffusion systems this universality class is realized by the combined processes a r arrow a a a a r arrow a and a r arrow 0 we study a hierarchy of such dp processes for particle species a b hor ellipsis ital unidirectionally coupled via the reactions a r arrow b hor ellipsis with rates mu sub ab hor ellipsis when the dp critical points at all levels coincide ital multicritical behavior emerges with density exponents beta sub i which are markedly reduced at each hierarchy level i ge 2 this scenario can be understood on the basis of the mean field rate equations which yield beta sub i 1 2 sup i minus 1 at the multicritical point using field theoretic renormalization group techniques in d 4 minus epsilon dimensions we identify a new crossover exponent phi and compute phi 1 o epsilon sup 2 in the multicritical regime for small mu sub ab of the second hierarchy level in the active phase we calculate the fluctuation correction to the density exponent on the second hierarchy level beta sub 2 1 2 minus epsilon 8 o epsilon sup 2 outside the multicritial region we discuss the crossover to ordinary dp behavior with the density exponent beta sub 1 1 minus epsilon 6 o epsilon sup 2 monte carlo simulations are then employed to confirm the crossovermore scenario and to determine the values for the new scaling exponents in dimensions d le 3 including the critical initial slip exponent our theory is connected to specific classes of growth processes and to certain cellular automata and the above ideas are also applied to unidirectionally coupled pair annihilation processes we also discuss some technical as well as conceptual problems of the loop expansion and suggest some possible interpretations of these difficulties copyright ital 1999 ital the american physical society less

generation of the chapman enskog distribution a pair of simple efficient and robust algorithms for generating random velocities sampled from the chapman enskog distribution is presented

series expansion of the percolation probability for the directed square lattice by extrapolation from finite lattices the authors extend the known series for the percolation probability on the directed square lattice from eight terms to 41 analysing the series they obtain the estimates qc 0 355 299 or 0 000 001 beta 0 2764 or 0 0001 for the critical probability and the critical exponent from this together with scaling relations and previous results on the moments of the pair connectedness function the authors conjecture that beta may be exactly 199 720

on the sphere decoding algorithm i expected complexity the problem of finding the least squares solution to a system of linear equations where the unknown vector is comprised of integers but the matrix coefficient and given vector are comprised of real numbers arises in many applications communications cryptography gps to name a few the problem is equivalent to finding the closest lattice point to a given point and is known to be np hard in communications applications however the given vector is not arbitrary but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known therefore in this paper rather than dwell on the worst case complexity of the integer least squares problem we study its expected complexity averaged over the noise and over the lattice for the sphere decoding algorithm of fincke and pohst we find a closed form expression for the expected complexity both for the infinite and finite lattice it is demonstrated in the second part of this paper that for a wide range of signal to noise ratios snrs and numbers of antennas the expected complexity is polynomial in fact often roughly cubic since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial this suggests that maximum likelihood decoding which was hitherto thought to be computationally intractable can in fact be implemented in real time a result with many practical implications

construction of a matrix product stationary state from solutions of a finite size system stationary states of stochastic models which have n states per site in matrix product form are considered first we give a necessary condition for the existence of a finite m dimensional matrix product stationary state for any n m second we give a method to construct the matrices from the stationary

yang lee zeros for a nonequilibrium phase transition equilibrium systems which exhibit a phase transition can be studied by investigating the complex zeros of the partition function this method pioneered by yang and lee has been widely used in equilibrium statistical physics we show that an analogous treatment is possible for a nonequilibrium phase transition into an absorbing state by investigating the complex zeros of the survival probability of directed percolation processes we demonstrate that the zeros provide information about universal properties moreover we identify certain nontrivial points where the survival probability for bond percolation can be computed exactly

low density series expansions for directed percolation iii some two dimensional lattices we use very efficient algorithms to calculate low density series for bond and site percolation on the directed triangular honeycomb kagome and 4 82 lattices analysis of the series yields accurate estimates of the critical point pc and various critical exponents the exponent estimates differ only in the 5th digit thus providing strong numerical evidence for the expected universality of the critical exponents for directed percolation problems in addition we also study the non physical singularities of the series

transverse size critical exponent of directed percolation from yang lee zeros of survival probability by using transfer matrix method we compute survival probabilities for the directed percolation problem on strips of a square lattice and get very precise estimates of their yang lee zeros lying closest to the real axis in the complex plane of occupation probability this allows us to get accurate values for transverse size critical exponent and percolation threshold

directed percolation near a wall series expansion methods are used to study directed bond percolation clusters on the square lattice whose lateral growth is restricted by a wall parallel to the growth direction the percolation threshold is found to be the same as that for the bulk however the values of the critical exponents for the percolation probability and mean cluster size are quite different from those for the bulk and are estimated by and respectively on the other hand the exponent characterizing the scale of the cluster size distribution is found to be unchanged by the presence of the wall the parallel connectedness length which is the scale for the cluster length distribution has an exponent which we estimate to be and is also unchanged the exponent of the mean cluster length is related to and by the scaling relation and using the above estimates yields to within the accuracy of our results we conjecture that this value of is exact and further support for the conjecture is provided by the direct series expansion estimate

universal scaling behaviour of directed percolation and the pair contact process in an external field we consider the scaling behaviour of directed percolation and of the pair contact process with a conjugated field in particular we determine numerically the equation of state and show that both models are characterized by the same universal scaling function furthermore we derive the equation of state for the pair contact process within a mean field approach which again agrees with the mean field equation of state of the directed percolation universality class

quasistationary distributions for the domany kinzel stochastic cellular automaton we construct the quasistationary qs probability distribution for the domany kinzel stochastic cellular automaton dkca a discrete time markov process with an absorbing state qs distributions are derived at both the one and two site levels we characterize the distributions by their mean and various moment ratios and analyze the lifetime of the qs state and the relaxation time to attain this state of particular interest are the scaling properties of the qs state along the critical line separating the active and absorbing phases these exhibit a high degree of similarity to the contact process and the malthus verhulst process the closest continuous time analogs of the dkca which extends to the scaling form of the qs distribution

an ol n 3 primal interior point algorithm for convex quadratic programming we present a primal interior point method for convex quadratic programming which is based upon a logarithmic barrier function approach this approach generates a sequence of problems each of which is approximately solved by taking a single newton step it is shown that the method requires o sqrt n l iterations and o n3 5l arithmetic operations by using modified newton steps the number of arithmetic operations required by the algorithm can be reduced to o n3l

universal scaling behavior of directed percolation around the upper critical dimension in this work we consider the steady state scaling behavior of directed percolation around the upper critical dimension in particular we determine numerically the order parameter its fluctuations as well as the susceptibility as a function of the control parameter and the conjugated field additionally to the universal scaling functions several universal amplitude combinations are considered we compare our results with those of a renormalization group approach

on the choice of the density matrix in the stochastic tmrg in applications of the density matrix renormalization group to nonhermitean problems the choice of the density matrix is not uniquely prescribed by the algorithm we demonstrate that for the recently introduced stochastic transfer matrix dmrg stochastic tmrg the necessity to use open boundary conditions makes asymmetrical reduced density matrices as used for renormalization in quantum tmrg an inappropriate choice an explicit construction of the largest left and right eigenvectors of the full transfer matrix allows us to show why symmetrical density matrices are the correct physical choice

modulo loss reduction for vector perturbation systems in this letter we present an improved precoding technique which reduces a modulo loss in vector perturbation with low complexity instead of searching perturbation vectors in the infinite lattice the proposed scheme restricts the search range by utilizing the distribution of the perturbation vector depending on transmitted data as a result we can achieve significant complexity savings at the transmitter while providing better performance compared to the original vector perturbation

capacity and lattice strategies for canceling known interference we consider the generalized dirty paper channel y x s n e x sup 2 spl les p sub x where n is not necessarily gaussian and the interference s is known causally or noncausally to the transmitter we derive worst case capacity formulas and strategies for strong or arbitrarily varying interference in the causal side information si case we develop a capacity formula based on minimum noise entropy strategies we then show that strategies associated with entropy constrained quantizers provide lower and upper bounds on the capacity at high signal to noise ratio snr conditions i e if n is weak relative to the power constraint p sub x these bounds coincide the optimum strategies take the form of scalar lattice quantizers and the capacity loss due to not having s at the receiver is shown to be exactly the shaping gain 1 2log 2 spl pi e 12 spl ap 0 254 bit we extend the schemes to obtain achievable rates at any snr and to noncausal si by incorporating minimum mean squared error mmse scaling and by using k dimensional lattices for gaussian n the capacity loss of this scheme is upper bounded by 1 2log2 spl pi eg spl lambda where g spl lambda is the normalized second moment of the lattice with a proper choice of lattice the loss goes to zero as the dimension k goes to infinity in agreement with the results of costa these results provide an information theoretic framework for the study of common communication problems such as precoding for intersymbol interference isi channels and broadcast channels

directed random walks on directed percolation clusters 0 63 this probability distribution is independent of the cluster s length t up to d values comparable to the cluster s width t n the results are shown to be consistent with a tree description of the directed percolation clusters pacs number s 61 66 dk 64 60 cn 71 20 be the subject of random walks on percolation clusters known as the ant in the labyrinth problem 1 has drawn quite intensive attention in the physical literature 2 however in spite of the numerous efforts no simple connection was found between the static and dynamical exponents of percolation though the alexander orbach conjecture 3 comes close to this goal in this article it is shown that such a simple connection does exist in the special case of directed random walks on directed percolation clusters in the directed percolation model 4 there is a predefined direction in which the percolation clusters can grow in the directed random walk considered in the present study walks are also performed only in the same predefined direction balents and kardar 5 have already studied random walks on directed percolation clusters but while their main concern was the variability of distances between different clusters the main concern of the present article is the variability of distances within each cluster in order to study this issue numerical results were obtained for directed random walks performed along twodimensional directed percolation clusters grown at the critical probability pc these numerical results indicated that the distance d of the directed random walkers from their most probable end point is determined by a probability distribution p d d 2 11w n where w 0 50 and n 0 63 this probability distribution is independent of the cluster s length t up to d values comparable to the cluster s width t n the known values of these two exponents are shown to be consistent with a tree description of the directed percolation clusters the article starts with a description of the model and the way the numerical data were gathered the second part presents the numerical results which have similar characteristics to previous results 6 obtained for the directed polymer model 7 8 this similarity is investigated further in the final part of the article the connection between the directed percolation model and the directed polymer model was studied in a number of articles 9 13 and the present study points to some similarity between entropy in the directed percolation model and energy in the directed polymer model on an arbitrary lattice structure a directed percolation cluster can be defined as the set of lattice points sites which are connected to some origin while the connecting paths are oriented in a predefined direction thus all of them are of

percolation properties of a three dimensional random resistor diode network studies percolation in a random resistor diode network on the simple cubic lattice here the occupied bonds joining nearest neighbour sites may be either resistor like transmitting information or connectivity in either direction along a bond or diode like transmitting in only one direction they consider a model in which there exist both positive diodes which transmit in the x y or z directions and negative diodes which transmit oppositely they apply positive space renormalisation group methods to map out the phase diagram and calculate the exponents associated with the phase transitions of this system they find three novel types of transitions due to the presence of the diodes with only one species of diodes and vacancies unoccupied bonds present a directed threshold occurs at a critical concentration of diodes here an infinite cluster forms which transmits only in the direction of the average diode polarisation a reverse threshold occurs when resistors and only one species of diodes exist at this point the resistors mediate information flow in the infinite cluster opposite to the diode polarisation finally with all bond elements present a mixed threshold occurs

extension of the arrowsmith essam formula to the domany kinzel model arrowsmith and essam gave an expansion formula for point to point connectedness functions of the mixed site bond percolation model on oriented lattices in which each term is characterized by a graph we extend this formula to general k point correlation functions which are point to set with k points connectivities in the context of percolation of the two neighbor discrete time markov process stochastic cellular automata with two parameters in one dimension called the domany kinzel model which includes the mixed site bond oriented percolation model on a square lattice as a special case our proof of the formula is elementary and based on induction with respect to time step which is different from the original graph theoretical one given by arrowsmith and essam we introduce a system of m interacting random walkers called m friendly walkers m fw with two parameters following the argument of cardy and colaiori it is shown that our formula is useful to derive a theorem that the correlation functions of the domany kinzel model are obtained as an m 0 limit of the generating functions of the m fw

critical behavior of the two and three dimensional contact replication processes the two and three dimensional contact replication processes crp for monoclonal reproduction were analyzed through intensive monte carlo simulations in these models the occupation rates are equally divided among the empty nearest neighbor sites of an occupied site as the one dimensional case the two dimensional version of the model belongs to the directed percolation universality class and the critical rate defining the absorbing state transition is lambdac 1 083 20 7 however the critical exponents of the three dimensional crp are those of the four dimensional original contact process and consequently the data suggest that the crp model has a distinct upper critical dimension dc 3

contact process on a voronoi triangulation we study the continuous absorbing state phase transition in the contact process on the voronoi delaunay lattice the voronoi construction is a natural way to introduce quenched coordination disorder in lattice models we simulate the disordered system using the quasistationary simulation method and determine its critical exponents and moment ratios our results suggest that the critical behavior of the disordered system is unchanged with respect to that on a regular lattice i e that of directed percolation

zeros of the partition function for higher spin 2d ising models we present calculations of the complex temperature zeros of the partition functions for 2d ising models on the square lattice with spin s 1 3 2 and 2 these give an insight into complex temperature phase diagrams of these models in the thermodynamic limit support is adduced for a conjecture that all divergences of the magnetization occur at endpoints of arcs of zeros protruding into the fm phase we conjecture that there are 4 s2 2 such arcs for s or 1 where x denotes the integral part of x

a comparative study for the pair creation contact process using series expansions a comparative study between two distinct perturbative series expansions for the pair creation contact process is presented in contrast to the ordinary contact process whose supercritical series expansions provide accurate estimates for its critical behaviour the supercritical approach does not work properly when applied to the pair creation process to circumvent this problem a procedure is introduced in which one site creation is added to the pair creation an alternative method is the generation of subcritical series expansions which works even for the case of the pure pair creation process in contrast to the supercritical case the subcritical series yields estimates that are compatible with numerical simulations

complex temperature partition function zeros of the potts model on the honeycomb and kagome lattices we calculate complex temperature ct zeros of the partition function for the q state potts model on the honeycomb and kagom e lattices for several values of q these give information on the ct phase diagrams a comparison of results obtained for different boundary conditions and a discussion of some ct singularities are given among other results our findings show that the potts antiferromagnet with q 4 and q 5 on the kagom e lattice has no phase transition at either finite or zero temperature

non universality of the absorbing state phase transition in a linear chain with power law diluted long range connections abstract in this work we study the critical behavior of the absorbing state phase transition exhibited by the contact process in a linear chain with power law diluted long range connections each pair of sites is connected with a probability p r that decays with the distance between the sites r as 1 r the model allows for a continuous tuning between a standard one dimensional chain with only nearest neighbor couplings to a fully connected network 0 we develop a finite size scaling analysis to obtain the critical point and a set of dynamical and stationary critical exponents for distinct values of the decay exponent 2 corresponding to finite average bond lengths and low average site connectivity data for the order parameter collapse over a universal curve when plotted after a proper rescaling of parameters we show further that the critical exponents depend on in the regime of diverging bond length fluctuations 3

a transfer matrix study of directed lattice animals and directed percolation on a square lattice we studied the large scale properties of directed lattice animals and directed percolation on a square lattice using a transfer matrix approach on strips of finite widths we generated relatively long sequences of estimates for effective values of critical fugacity percolation threshold and correlation length critical exponents we applied two different extrapolation methods to obtain estimates for infinite systems the precision of our final estimates is comparable to or better than the precision of the best currently available results

approximation for directed percolation in d 1 1 we introduce an approximation specific to a continuous variable formulation of directed percolation which is strictly equivalent to 1 1 dimensional directed bond percolation we find that the critical exponent associated with the order parameter percolation probability is beta 1 1 square root 5 2 0 276 393 202 em leader in remarkable agreement with the best current numerical estimate beta 0 276 486 8

finite lattice extrapolation algorithms two algorithms for sequence extrapolation due to van den broeck and schwartz 1979 and bulirsch and stoer 1964 are reviewed and critically compared applications to three state and six state quantum chains and to the 2 1 d ising model show that the algorithm of bulirsch and stoer is superior in particular if only very few finite lattice data are available

a vector perturbation technique for near capacity multiantenna multiuser communication part ii perturbation recent theoretical results describing the sum capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity we introduce a simple encoding algorithm that achieves near capacity at sum rates of tens of bits channel use the algorithm is a variation on channel inversion that regularizes the inverse and uses a sphere encoder to perturb the data to reduce the energy of the transmitted signal the paper is comprised of two parts in this second part we show that after the regularization of the channel inverse introduced in the first part a certain perturbation of the data using a sphere encoder can be chosen to further reduce the energy of the transmitted signal the performance difference with and without this perturbation is shown to be dramatic with the perturbation we achieve excellent performance at all signal to noise ratios the results of both uncoded and turbo coded simulations are presented

quasi stationary distributions for stochastic processes with an absorbing state we study the long time behaviour of stochastic models with an absorbing state conditioned on survival for a large class of processes in which saturation prevents unlimited growth statistical properties of the surviving sample attain time independent limiting values we may then define a quasi stationary probability distribution as one in which the ratios pn t pm t for any pair of non absorbing states n and m are time independent this is not a true stationary distribution since the overall normalization decays as probability flows irreversibly to the absorbing state we construct quasi stationary solutions for the contact process on a complete graph the malthus verhulst process

closest point search in lattices in this semitutorial paper a comprehensive survey of closest point search methods for lattices without a regular structure is presented the existing search strategies are described in a unified framework and differences between them are elucidated an efficient closest point search algorithm based on the schnorr euchner 1995 variation of the pohst 1981 method is implemented given an arbitrary point x spl isin spl ropf sup m and a generator matrix for a lattice spl lambda the algorithm computes the point of spl lambda that is closest to x the algorithm is shown to be substantially faster than other known methods by means of a theoretical comparison with the kannan 1983 1987 algorithm and an experimental comparison with the pohst 1981 algorithm and its variants such as the viterbo boutros see ibid vol 45 p 1639 42 1999 decoder modifications of the algorithm are developed to solve a number of related search problems for lattices such as finding a shortest vector determining the kissing number computing the voronoi 1908 relevant vectors and finding a korkine zolotareff 1873 reduced basis

directed percolation and generalized friendly random walkers the problem of directed percolation dp rst intro duced by broadbent and hammersley 1 continues to at tract interest even though it has so far de ed all attempts atan exact solution even in two dimensions although theproblem was originally formulated statically on a latticewith a preferred direction when the latter is interpreted astime the universal behavior close to the percolation thresh old is also believed to describe the transition from a noise less absorbing state to a noisy active one which occurs ina wide class of stochastic processes 2 it also maps ontoreggeon eld theory which describes high energy diffrac tion scattering in particle physics 3 some time ago arrowsmith mason and essam 4 argued that the pair connectedness probability

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

monte carlo investigation of the critical behavior of stavskaya s probabilistic cellular automaton stavskaya s model is a one dimensional probabilistic cellular automaton pca introduced in the end of the 1960s as an example of a model displaying a nonequilibrium phase transition although its absorbing state phase transition is well understood nowadays the model never received a full numerical treatment to investigate its critical behavior in this brief report we characterize the critical behavior of stavskaya s pca by means of monte carlo simulations and finite size scaling analysis the critical exponents of the model are calculated and indicate that its phase transition belongs to the directed percolation universality class of critical behavior as would be expected on the basis of the directed percolation conjecture we also explicitly establish the relationship of the model with the domany kinzel pca on its directed site percolation line a connection that seems to have gone unnoticed in the literature so far

vector perturbation based on symbol scaling for limited feedback miso downlinks we propose a low complexity vector precoding vp scheme for the downlink of multi user multiple input single output mu miso systems with limited feedback conventional vp requires the use of modulo operation and knowledge of the scaling factor used at the transmitter in order to remove the perturbation quantity at the receiver the latter may be problematic in certain limited feedback scenarios where only quantized versions of the scaling factor can be made available at the receiver to circumvent this shortcoming we propose a modified vp technique where the search of perturbing vectors is limited to the area in the symbol constellation which is constrictive to the information symbols i e the area where the distances from the decision thresholds are increased with respect to a distance threshold by doing this the perturbation quantities can only enhance detection and need not be removed at the receiver successful detection can therefore be done without the use of the modulo operation and the scaling factor which makes the proposed vp scheme applicable to limited feedback scenarios analytical and simulation results show that the performance of the proposed scheme is free of the error floor typically encountered with conventional vp in the presence of limited feedback

directed percolation mean field theory and series expansions for some two dimensional lattices the shape of percolation clusters in the directed percolation problem is studied within mean field theory low density series expansions are obtained for bond and site problems on the square and triangular lattices these are used to test a scaling formula for the pair connectedness which involves two lengths xi sub rho and xi perpendicular to rho determination of the exponents nu sub and nu perpendicular to for these lengths shows that all four problems are in the same universality class and the values support the hyperscaling relation beta 1 2 d nu perpendicular to nu sub gamma an independent argument is given for this relation

on vector perturbation precoding for the mimo gaussian broadcast channel precoding schemes in the framework of vector perturbation vp for the multiple input multiple output mimo gaussian broadcast channel gbc are investigated the vp scheme originally a one shot technique is generalized to encompass processing over multiple time instances using lattice based extended alphabets perturbations and considering the infinite time span extension limit a lower bound on the achievable sum rate using the generalized vp scheme is analytically obtained the lower bound is shown to asymptotically achieve the optimum sum rate in the high signal to noise ratio snr regime both in terms of degrees of freedom and power offset for any number of users and transmit antennas for the two user cases it is shown that the lower bound coincides with the sum capacity for low snr the above lower bound is constructively obtained by means of an efficient practically oriented suboptimal transmit energy minimization algorithm which exhibits a polynomial complexity in the number of users the proposed precoding scheme demonstrates that the shaping gain is achievable for vp schemes when employing good multidimensional lattices it is also shown that the suboptimum algorithm has its merits even when processing over multiple time instances is not employed for the 2 times 2 mimo gbc the vp scheme is generalized further and an inner bound for the entire achievable rate region is obtained by which an interesting correspondence is identified with the ultimate capacity region as obtained by dirty paper coding

on two dimensional directed percolation extended series expansions for the mean size and the first and second moments of the pair connectedness for both bond and site percolation on the directed square and triangular lattices have been obtained analysis based on differential approximants allows the critical percolation probabilities and exponents to be estimated and as a result the critical exponents are conjectured to be gamma 41 18 nu perpendicular to 79 72 and nu sub 26 15 scaling then gives beta 199 720 alpha 299 360 and delta 1839 199

low density series expansions for directed percolation ii the square lattice with a wall a new algorithm for the derivation of low density expansions has been used to greatly extend the series for moments of the pair connectedness on the directed square lattice near an impenetrable wall analysis of the series yields very accurate estimates for the critical point and exponents in particular the estimate for the exponent characterizing the average cluster length near the wall 1 1 00014 2 appears to exclude the conjecture 1 1 the critical point and the exponents and have the same values as for the bulk problem

re entrant behaviour in the domany kinzel cellular automaton we present numerical and analytical results for a special kind of one dimensional probabilistic cellular automaton the so called domany kinzel automaton it is shown that the phase boundary separating the active and the recently found chaotic phase exhibits re entrant behaviour furthermore exact results for the p2 0 line are discussed

critical behavior and griffiths effects in the disordered contact process we study the nonequilibrium phase transition in the one dimensional contact process with quenched spatial disorder by means of large scale monte carlo simulations for times up to 10 9 and system sizes up to 10 7 sites in agreement with recent predictions of an infinite randomness fixed point our simulations demonstrate activated exponential dynamical scaling at the critical point the critical behavior turns out to be universal even for weak disorder however the approach to this asymptotic behavior is extremely slow with crossover times of the order of 10 4 or larger in the griffiths region between the clean and the dirty critical points we find power law dynamical behavior with continuously varying exponents we discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder

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

generating function for particle number probability distribution in directed percolation we derive a generic expression for the generating function gf of the particle number probability distribution pnpd for a simple reaction diffusion model that belongs to the directed percolation universality class starting with a single particle on a lattice we show that the gf of the pnpd can be written as an infinite series of cumulants taken at zero momentum this series can be summed up into a complete form at the level of a mean field approximation using the renormalization group techniques we determine logarithmic corrections for the gf at the upper critical dimension we also find the critical scaling form for the pnpd and check its universality numerically in one dimension the critical scaling function is found to be universal up to two non universal metric factors

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

reaction diffusion processes and non perturbative renormalization group this paper is devoted to investigating non equilibrium phase transitions to an absorbing state which are generically encountered in reaction diffusion processes it is a review based on canet delamotte deloubriere and wschebor 2004 phys rev lett 92 195703 canet chate and delamotte 2004 phys rev lett 92 255703 and canet et al 2005 phys rev lett 95 100601 of recent progress in this field that has been allowed by a non perturbative renormalization group approach we mainly focus on branching and annihilating random walks and show that their critical properties strongly rely on non perturbative features and that hence the use of a non perturbative method turns out to be crucial to get a correct picture of the physics of these models

extension of the kasteleyn fortuin formulas to directed percolation it is shown that the pair connectedness for percolation on an arbitrary directed graph may be obtained by setting 1 in the transmissivity function for a state chiral potts model the odd flow model and that the pair connectedness of the dual percolation model is expressible in terms of the correlation function of a second chiral potts model the odd potential difference model there is an important distinction between odd and even and only those models with odd exhibit chirality the duality relation between the transmissivity and correlation functions leads to a duality relation for pair connectedness of directed percolation theory which extends the result of dhar barna and phani for percolation probabilities

change in order of phase transitions on fractal lattices abstract we re examine a population model which exhibits a continuous absorbing phase transition belonging to directed percolation in 1d and a first order transition in 2d and above studying the model on sierpinski carpets of varying fractal dimensions we examine at what fractal dimension 1 d f 2 the change in order occurs as well as commenting on the order of the transitions we produce estimates for the critical points and for continuous transitions some critical exponents

relationship between directed percolation and the synchronization transition in spatially extended systems we study the nature of the synchronization transition in spatially extended systems by discussing a simple stochastic model an analytic argument is put forward showing that in the limit of discontinuous processes the transition belongs to the directed percolation dp universality class the analysis is complemented by a detailed investigation of the dependence of the first passage time for the amplitude of the difference field on the adopted threshold we find the existence of a critical threshold separating the regime controlled by linear mechanisms from that controlled by collective phenomena as a result of this analysis we conclude that the synchronization transition belongs to the dp class also in continuous models the conclusions are supported by numerical checks on coupled map lattices too

stochastic light cone ctmrg a new dmrg approach to stochastic models we develop a new variant of the recently introduced stochastic transfer matrix dmrg which we call stochastic light cone corner transfer matrix dmrg lctmrg it is a numerical method to compute dynamic properties of one dimensional stochastic processes as suggested by its name the lctmrg is a modification of the corner transfer matrix dmrg adjusted by an additional causality argument as an example two reaction diffusion models the diffusion annihilation process and the branch fusion process are studied and compared with exact data and monte carlo simulations to estimate the capability and accuracy of the new method the number of possible trotter steps of more than 105 shows a considerable improvement on the old stochastic tmrg algorithm

mixed order phase transition of the contact process near multiple junctions we have studied the phase transition of the contact process near a multiple junction of m semi infinite chains by monte carlo simulations as opposed to the continuous transitions of the translationally invariant m 2 and semi infinite m 1 system the local order parameter is found to be discontinuous for m 2 furthermore the temporal correlation length diverges algebraically as the critical point is approached but with different exponents on the two sides of the transition in the active phase the estimate is compatible with the bulk value while in the inactive phase it exceeds the bulk value and increases with m the unusual local critical behavior is explained by a scaling theory with an irrelevant variable which becomes dangerous in the inactive phase quenched spatial disorder is found to make the transition continuous in agreement with earlier renormalization group results

computationally efficient vector perturbation precoding using thresholded optimization we propose a low complexity vector perturbation vp precoding scheme for the downlink of multi user multiple input multiple output mu mimo systems while conventional vp performs a computationally intensive sphere search through multiple candidate perturbation vectors to minimize the norm of the precoded signal the proposed precoder applies a threshold to the desired norm to reduce the number of search nodes visited by the sphere encoder this threshold is determined by the performance requirements of the mobile users once the threshold is met the search for the perturbation vectors finishes thus saving significant computational burden at the transmitter to evaluate the advantages of the proposed technique compared to vp we further derive the computational complexity in terms of the volume of the associated search space and the resulting numerical operations in addition we use a new performance complexity metric to study the relevant tradeoff and look at the power efficiency of the system both of which metrics can be used to optimize the user determined threshold accordingly color black the presented analysis and results show that the proposed thresholded vp tvp offers a favorable tradeoff between performance and complexity where significant complexity reduction is attained while the user threshold performance is guaranteed

a combined continuum dsmc technique for multiscale analysis of microfluidic filters a multiscale method that combines continuum fluid models with the direct simulation monte carlo dsmc method is presented the continuum regions are treated by stokes equations and a scattered point based finite cloud method is employed to solve the stokes equations the continuum and dsmc regions are combined by an overlapped schwarz alternating method with dirichlet dirichlet type boundary conditions a scattered point interpolation scheme is developed to interpolate the solution between subdomains the convergence characteristics of the multiscale approach are investigated in detail specifically the dependence of convergence on the overlap size the dsmc noise and the number of time steps employed in the dsmc algorithm are studied while the convergence depends weakly on the dsmc noise and the overlap size the number of dsmc time steps simulated in each coupling iteration should be selected so that the total time steps simulated until convergence of the coupled process is close to the time constant of the dsmc subsystem steady state analysis of microfluidic filters is studied in detail using the multiscale approach the multiscale approach is also applied for the simulation of a membrane with an array of microfluidic filters and a dual stage microfluidic device with an array of microfluidic filters for particle trapping and sorting

ageing phenomena without detailed balance the contact process the long time dynamics of the 1d contact process suddenly brought out of an uncorrelated initial state is studied through a light cone transfer matrix renormalization group approach at criticality the system undergoes ageing which is characterized through the dynamical scaling of the two times autocorrelation and autoresponse functions the observed non equality of the ageing exponents a and b excludes the possibility of a finite fluctuation dissipation ratio in the ageing regime the scaling form of the critical autoresponse function is in agreement with the prediction of local scale invariance

the resistive susceptibility of random diode insulator networks the authors consider regular crystal lattices in which the bonds are either diodes probability p or insulators the mean number of backbone bonds lbb p when averaged over lattice points is found to be related to the mean size of clusters s p by lbb p zps p where z is the number of bonds directed away from any lattice site thus lbb diverges at pc with the mean size exponent gamma the resistive susceptibility chi r p of harris and fisch 1977 1978 is expanded graphically as a power series in p and it is found that term by term chi r p psi r p s p 2 where psi r p is obtained from chi r p by ignoring contributions from nodal graphs the above results are valid for bond and site dilution in any dimension for bond dilution on the square lattice the authors have determined psi r p to p17 and pade analysis of the resulting series for chi r p shows that it diverges with exponent gamma r 3 654 or 0 017 using a scaling relation the exponent t for the conductivity of the infinite cluster is estimated to be t 0 75 or 0 02

generation of the maxwellian inflow distribution this paper presents several efficient exact acceptance rejection methods for generating the maxwellian inflow distribution the velocity distribution of gas molecules crossing a plane the new methods are demonstrated to be computationally faster and more accurate than the schemes commonly used for open boundary conditions in particle simulations

per antenna constant envelope precoding for large multi user mimo systems we consider the multi user mimo broadcast channel with m single antenna users and n transmit antennas under the constraint that each antenna emits signals having constant envelope ce the motivation for this is that ce signals facilitate the use of power efficient rf power amplifiers analytical and numerical results show that under certain mild conditions on the channel gains for a fixed m an array gain is achievable even under the stringent per antenna ce constraint essentially for a fixed m at sufficiently large n the total transmitted power can be reduced with increasing n while maintaining a fixed information rate to each user simulations for the i i d rayleigh fading channel show that the total transmit power can be reduced linearly with increasing n i e an o n array gain we also propose a precoding scheme which finds near optimal ce signals to be transmitted and has o mn complexity also in terms of the total transmit power required to achieve a fixed desired information sum rate despite the stringent per antenna ce constraint the proposed ce precoding scheme performs close to the sum capacity achieving scheme for an average only total transmit power constrained channel

mean field theory of percolation with application to surface effects a probabilistic formulation of mean field theory for percolation in a general medium is given the theory covers the whole density range and above the critical density provides the necessary generalisation of the random walk approximation application to surface percolation enables the calculation of scaling functions and critical exponents for the ordinary surface special and extraordinary transitions considered by previous authors to the context of ferromagnetism

phase transitions in a lattice population model we introduce a model for a population on a lattice with diffusion and birth death according to and for a particle a we find that the model displays a phase transition from an active to an absorbing state which is continuous in 1 1 dimensions and of first order in higher dimensions in agreement with the mean field equation for the 1 1 dimensional case we examine the critical exponents and a scaling function for the survival probability and show that it belongs to the universality class of directed percolation in higher dimensions we look at the first order phase transition by plotting a histogram of the population density and use the presence of phase coexistence to find an accurate value for the critical point in 2 1 dimensions

crossover from isotropic to directed percolation we generalize the directed percolation dp model by relaxing the strict directionality of dp such that propagation can occur in either direction but with anisotropic probabilities we denote the probabilities as p p pd and p p 1 pd with p representing the average occupation probability and pd controlling the anisotropy the leath alexandrowicz method is used to grow a cluster from an active seed site we call this model with two main growth directions biased directed percolation bdp standard isotropic percolation ip and dp are the two limiting cases of the bdp model corresponding to pd 1 2 and pd 0 1 respectively in this work besides ip and dp we also consider the 1 2 pd 1 region extensive monte carlo simulations are carried out on the square and the simple cubic lattices and the numerical data are analyzed by finite size scaling we locate the percolation thresholds of the bdp model for pd 0 6 and 0 8 and determine various critical exponents these exponents are found to be consistent with those for standard dp we also determine the renormalization exponent associated with the asymmetric perturbation due to pd 1 2 6 0 near ip and confirm that such an asymmetric scaling field is relevant at ip

critical exponents for the restricted sandpile i report large scale monte carlo studies of a one dimensional height restricted stochastic sandpile using the quasistationary simulation method results for systems of up to 50 000 sites yield estimates for critical exponents that differ significantly from those obtained using smaller systems but are consistent with recent predictions derived from a langevin equation for stochastic sandpiles ramasco phys rev e 69 045105 r 2004 this suggests that apparent violations of universality in one dimensional sandpiles are due to strong corrections to scaling and finite size effects