design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds

moving least squares particle hydrodynamics i consistency and stability the smooth particle hydrodynamics sph method is derived in a novel manner by means of a galerkin approximation applied to the lagrangian equations of continuum mechanics as in the finite element method this derivation is modified to replace the sph interpolant with the moving least squares mls interpolant of lancaster and saulkaskas and define a new particle volume which ensures thermodynamic compatibility a variable rank modification of the mls interpolants which retains their desirable summation properties is introduced to remove the singularities that occur when divergent flow reduces the number of neighbours of a particle to less than the minimum required a surprise benefit of the galerkin sph derivation is a theoretical justification of a common ad hoc technique for variable h sph the new mlsph method is conservative if an anti symmetric quadrature rule for the stiffness matrix elements can be supplied in this paper a simple one point collocation rule is used to retain similarity with sph leading to a non conservative method several examples document how mlsph renders dramatic improvements due to the linear consistency of its gradients on three canonical difficulties of the sph method spurious boundary effects erroneous rates of strain and rotation and tension instability two of these examples are non linear lagrangian patch tests with analytic solutions with which mlsph agrees almost exactly the examples also show that mlsph is not absolutely stable if the problems are run to very long times a linear stability analysis explains both why it is more stable than sph and not yet absolutely stable and an argument is made that for realistic dynamic problems mlsph is stable enough the notion of coherent particles for which the numerical stability is identical to the physical stability is introduced the new method is easily retrofitted into a generic sph code and some observations on performance are made copyright 1999 john wiley sons ltd

classical to critical crossovers from field theory we extend our previous determinations of nonasymptotic critical behavior of phys rev b 32 7209 1985 and 35 3585 1987 to accurate expressions of the complete classical to critical crossover in three dimensional field theory in terms of the temperaturelike scaling field i e along the critical isochore for 1 the correlation length the susceptibility and the specific heat in the homogeneous phase for the n vector model n 1 to 3 and 2 the spontaneous magnetization coexistence curve the susceptibility and the specific heat in the inhomogeneous phase for the ising model n 1 the present calculations include the seventh loop order of murray and nickel and closely account for the up to date estimates of universal asymptotic critical quantities exponents and amplitude combinations provided by guida and zinn justin j phys a 31 8103 1998

comparative study on accuracy and conservation properties of two particle regularization schemes and proposal of an optimized particle shifting scheme in isph context abstract the paper provides a comparative investigation on accuracy and conservation properties of two particle regularization schemes namely the dynamic stabilization ds 1 and generalized particle shifting ps 2 schemes in simulations of both internal and free surface flows in isph incompressible sph context the paper also presents an optimized ps ops scheme for accurate and consistent implementation of particle shifting for free surface flows in contrast to ps the ops does not contain any tuning parameters for free surface consistently resulting in perfect elimination of shifting normal to an interface and resolves the unphysical discontinuity beneath the interface seen in ps results

eliminating leading corrections to scaling in the three dimensional o n symmetric φ 4 model n 3 and 4 we study corrections to scaling in the o 3 and o 4 symmetric 4 model on the three dimensional simple cubic lattice with nearest neighbour interactions for this purpose we use monte carlo simulations in connection with a finite size scaling method we find that a finite value of the coupling exists for both values of n where leading corrections to scaling vanish as a first application we compute the critical exponents 0 710 2 and 0 0380 10 for n 3 and 0 749 2 and 0 0365 10 for n 4

smoothed particle hydrodynamics stability analysis abstract sph smoothed particle hydrodynamics is a gridless lagrangian technique which is appealing as a possible alternative to numerical techniques currently used to analyze large deformation events recent tests of the standard sph method using the cubic b spline kernel indicated the possibility of an instability in the tensile regime even though no such difficulties were observed in compression a von neumann stability analysis of the sph algorithm has been carried out which identifies the criterion for stability or instability in terms of the stress state and the second derivative of the kernel function the analysis explains the observation that the method is unstable in tension while apparently stable in compression but shows that it is possible to construct kernel functions which are stable in tension and unstable in compression the instability is shown to result from an effective stress with a negative modulus imaginary sound speed being produced by the interaction between the constitutive relation and the kernel function and is not caused by the numerical time integration algorithm that is changes in the effective stress act to amplify rather than reduce perturbations in the strain the analysis and the stability criterion provide insight into possible methods for removing the instability

nonlinear aspects of the renormalization group flows of dyson s hierarchical model we review recent results concerning the renormalization group rg transformation of dyson s hierarchical model hm this model can be seen as an approximation of a scalar field theory on a lattice we introduce the hm and show that its large group of symmetry simplifies drastically the blockspinning procedure several equivalent forms of the recursion formula are presented with unified notations rigourous and numerical results concerning the recursion formula are summarized it is pointed out that the recursion formula of the hm is inequivalent to both wilson s approximate recursion formula and polchinski s equation in the local potential approximation despite the very small difference with the exponents of the latter we draw a comparison between the rg of the hm and functional rg equations in the local potential approximation the construction of the linear and nonlinear scaling variables is discussed in an operational way we describe the calculation of non universal critical amplitudes in terms of the scaling variables of two fixed points this question appears as a problem of interpolation between these fixed points universal amplitude ratios are calculated we discuss the large n limit and the complex singularities of the critical potential calculable in this limit the interpolation between the hm and more conventional lattice models is presented as a symmetry breaking problem we briefly introduce models with an approximate supersymmetry one important goal of this review is to present a configuration space counterpart suitable for lattice formulations of functional rg equations formulated in momentum space often called exact rg equations and abbreviated erge

master crossover functions for one component fluids by introducing three well defined dimensionless numbers we establish the link between the scale dilatation method able to estimate master i e unique singular behaviors of the one component fluid subclass and the universal crossover functions recently estimated garrabos and bervillier phys rev e 74 021113 2006 from the bounded results of the massive renormalization scheme applied to the ensuremath phi d 4 n model of scalar order parameter n 1 and three dimensions d 3 representative of the ising like universality class the master i e rescaled crossover functions are then able to fit the singular behaviors of any one component fluid without adjustable parameter using only one critical energy scale factor one critical length scale factor and two dimensionless asymptotic scale factors which characterize the fluid critical interaction cell at its liquid gas critical point an additional adjustable parameter accounts for quantum effects in light fluids at the critical temperature the effective extension of the thermal field range along the critical isochore where the master crossover functions seems to be valid corresponds to a correlation length greater than three times the effective range of the microscopic short range molecular interaction

efficient erasure correcting codes we introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete time random process as a result we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully with high probability by carefully designing these graphs we can construct for any given rate r and any given real number spl epsiv a family of linear codes of rate r which can be encoded in time proportional to ln 1 spl epsiv times their block length n furthermore a codeword can be recovered with high probability from a portion of its entries of length 1 spl epsiv rn or more the recovery algorithm also runs in time proportional to n ln 1 spl epsiv our algorithms have been implemented and work well in practice various implementation issues are discussed

on achievable rates and complexity of ldpc codes over parallel channels bounds and applications a variety of communication scenarios can be modeled by a set of parallel channels upper bounds on the achievable rates under maximum likelihood ml decoding and lower bounds on the decoding complexity per iteration of ensembles of low density parity check ldpc codes are presented the communication of these codes is assumed to take place over statistically independent parallel channels where the component channels are memoryless binary input and output symmetric the bounds are applied to ensembles of punctured ldpc codes where the puncturing patterns are either random or possess some structure our discussion is concluded by a diagram showing interconnections between the new theorems and some previously reported results

construction of quasi cyclic ldpc codes for awgn and binary erasure channels a finite field approach in the late 1950s and early 1960s finite fields were successfully used to construct linear block codes especially cyclic codes with large minimum distances for hard decision algebraic decoding such as bose chaudhuri hocquenghem bch and reed solomon rs codes this paper shows that finite fields can also be successfully used to construct algebraic low density parity check ldpc codes for iterative soft decision decoding methods of construction are presented ldpc codes constructed by these methods are quasi cyclic qc and they perform very well over the additive white gaussian noise awgn binary random and burst erasure channels with iterative decoding in terms of bit error probability block error probability error floor and rate of decoding convergence collectively particularly they have low error floors since the codes are qc they can be encoded using simple shift registers with linear complexity

incompressible smoothed particle hydrodynamics for free surface flows a generalised diffusion based algorithm for stability and validations for impulsive flows and propagating waves the incompressible smoothed particle hydrodynamics isph method with projection based pressure correction has been shown to be highly accurate and stable for internal flows and importantly for many problems the pressure field is virtually noise free in contrast to the weakly compressible sph approach xu et al 2009 31 however for almost inviscid fluids instabilities at the free surface occur due to errors associated with the truncated kernels a new algorithm is presented which remedies this issue giving stable and accurate solutions to both internal and free surface flows generalising the particle shifting approach of xu et al 2009 31 the algorithm is based upon fick s law of diffusion and shifts particles in a manner that prevents highly anisotropic distributions and the onset of numerical instability the algorithm is validated against analytical solutions for an internal flow at higher reynolds numbers than previously the flow due to an impulsively started plate and highly accurate solutions for wet bed dam break problems at zero and small times the method is then validated for progressive regular waves with paddle motion defined by linear theory the accurate predictions demonstrate the effectiveness of the algorithm in stabilising solutions and minimising the surface instabilities generated by the inevitable errors associated with truncated kernels the test cases are thought to provide a more thorough quantitative validation than previously undertaken

accuracy and stability in incompressible sph isph based on the projection method and a new approach the stability and accuracy of three methods which enforce either a divergence free velocity field density invariance or their combination are tested here through the standard taylor green and spin down vortex problems while various approaches to incompressible sph isph have been proposed in the past decade the present paper is restricted to the projection method for the pressure and velocity coupling it is shown that the divergence free isph method cannot maintain stability in certain situations although it is accurate before instability sets in the density invariant isph method is stable but inaccurate with random noise like disturbances the combined isph combining advantages in divergence free isph and density invariant isph can maintain accuracy and stability although at a higher computational cost redistribution of particles on a fixed uniform mesh is also shown to be effective but the attraction of a mesh free method is lost a new divergence free isph approach is proposed here which maintains accuracy and stability while remaining mesh free without increasing computational cost by slightly shifting particles away from streamlines although the necessary interpolation of hydrodynamic characteristics means the formulation ceases to be strictly conservative this avoids the highly anisotropic particle spacing which eventually triggers instability importantly pressure fields are free from spurious oscillations up to the highest reynolds numbers tested

parity check density versus performance of binary linear block codes new bounds and applications the moderate complexity of low density parity check ldpc codes under iterative decoding is attributed to the sparseness of their parity check matrices it is therefore of interest to consider how sparse parity check matrices of binary linear block codes can be a function of the gap between their achievable rates and the channel capacity this issue was addressed by sason and urbanke and it is revisited in this paper the remarkable performance of ldpc codes under practical and suboptimal decoding algorithms motivates the assessment of the inherent loss in performance which is attributed to the structure of the code or ensemble under maximum likelihood ml decoding and the additional loss which is imposed by the suboptimality of the decoder these issues are addressed by obtaining upper bounds on the achievable rates of binary linear block codes and lower bounds on the asymptotic density of their parity check matrices as a function of the gap between their achievable rates and the channel capacity these bounds are valid under ml decoding and hence they are valid for any suboptimal decoding algorithm the new bounds improve on previously reported results by burshtein and by sason and urbanke and they hold for the case where the transmission takes place over an arbitrary memoryless binary input output symmetric mbios channel the significance of these information theoretic bounds is in assessing the tradeoff between the asymptotic performance of ldpc codes and their decoding complexity per iteration under message passing decoding they are also helpful in studying the potential achievable rates of ensembles of ldpc codes under optimal decoding by comparing these thresholds with those calculated by the density evolution technique one obtains a measure for the asymptotic suboptimality of iterative decoding algorithms

renormalized meshfree schemes i consistency stability and hybrid methods for conservation laws this paper is devoted to the study of a new kind of meshfree scheme based on a new class of meshfree derivatives the renormalized meshfree derivatives which improve the consistency of the original weighted particle methods the weak renormalized meshfree scheme built from the weak formulation of general conservation laws turns out to be l 2 stable under some geometrical conditions on the distribution of particles and some regularity conditions of the transport field a time discretization is then performed by analogy with finite volume methods and the l 1 l infty and bv stabilities of the obtained time discretized scheme are studied from the same analogy with finite volume methods a hybrid particle scheme is built using the godunov method and is numerically compared to the weak renormalized scheme

an accurate low mach scheme for a compressible two fluid model applied to free surface flows classical approximate riemann solvers are known to be too much dissipative in the low mach number regime for this reason since the mach number in liquids is generally very small usual upwind schemes may provide inaccurate solutions when applied to the simulation of two phase flows in this paper to circumvent this difficulty while keeping a compressible model for the description of both gas and liquid an original accurate low mach scheme is introduced and theoretically studied extending some ideas already used for the gas dynamics system the proposed scheme is based on a centred formulation for the pressure gradient term in the momentum equation and on the introduction of a stabilising term proportional to the pressure difference between two neighbouring cells the scheme stability is ensured and theoretically proved under a convective cfl like condition by using a semi implicit time discretisation algorithm finally the correct asymptotic behaviour of the scheme in the limit of small mach numbers is assessed on several academic test cases

bounds on the decoding error probability of binary linear codes via their spectra bounds on the error probability of maximum likelihood decoding of a binary linear code are considered the bounds derived use the weight spectrum of the code and they are tighter than the conventional union bound in the case of large noise in the channel the bounds derived are applied to a code with an average spectrum and the result is compared to the random coding exponent the author shows that the bound considered for the binary symmetrical channel case coincides asymptotically with the random coding bound for the case of awgn channel the author shows that berlekamp s 1980 tangential bound can be improved but even this improved bound does not coincide with the random coding bound although it can be very close to it

an eulerian lagrangian incompressible sph formulation eli sph connected with a sharp interface abstract an eulerian lagrangian incompressible sph eli sph formulation is proposed that improves accuracy over a fully lagrangian formulation for many problems this develops the original formulation of lind and stansby 2016 by providing a sharp interface rather than a transition zone this is generally convenient and avoids any need for arbitrary lagrangian eulerian ale particle mass correction it also enables a simple accurate solid boundary condition in a lagrangian formulation by having the interface close to the solid boundary with an eulerian fluid domain typically three particles thick with mirror particles particle regularisation is necessary in a lagrangian domain and we apply a general form based on fick s shifting which is modified at the interface by ignoring eulerian particles and using mirror particles to give zero concentration gradient and hence zero shifting across the interface avoiding spurious migration continuity is enforced at the interface as part of the combined eulerian lagrangian domain the formulation is validated against the analytical solution for taylor green vortices vortex spin down in a box and propagating waves the use of mixed kernel order in the eulerian domain is also demonstrated

capacity achieving ldpc codes through puncturing the performance of punctured low definition parity check ldpc codes under maximum likelihood ml decoding is studied in this correspondence via deriving and analyzing their average weight distributions awds and the corresponding asymptotic growth rate of the awds in particular it is proved that capacity achieving codes of any rate and for any memoryless binary input output symmetric mbios channel under ml decoding can be constructed by puncturing some original ldpc code with small enough rate moreover it is shown that the gap to capacity of all the punctured codes can be the same as the original code with a small enough rate conditions under which puncturing results in no rate loss with asymptotically high probability are also given in the process these results show high potential for puncturing to be used in designing capacity achieving codes and in rate compatible coding under any mbios channel

critical crossover functions for simple fluids non analytical scaling determination of the ising like crossover parameter a non analytical scaling determination of the ising like crossover parameter is proposed considering the critical isochore of a simple fluid at finite distance from its critical temperature the mean crossover functions estimated from the bounded results of the massive renormalization scheme in field theory applied to the left phi 2 right d 2 left n right model in three dimensions d 3 and scalar order parameter n 1 are used to formulate the corresponding scaling equations valid in two well defined temperature ranges from the critical temperature the validity range and the ising like nature of the corresponding crossover description are discussed in terms of a single ising like scale factor characterizing the critical isochore the asymptotic value of this scale factor can be predicted within the ising like preasymptotic domain unfortunately the absence of precise experimental data in such a close vicinity of the critical point leads the direct testing impossible a contrario from our scaling equations and the use of precise measurements performed at finite distance from the critical point its local value can be estimated beyond the ising like preasymptotic domain this non analytical scaling determination only needs to make reference to the universal features estimated from the mean crossover functions and to introduce a single master dimensionless length common to all the simple fluids this latter parameter guaranties the uniqueness of the physical length unit used for the theoretical crossover functions and the fluid singular properties when the generalized critical coordinates of the vapor liquid critical point of each fluid are known xenon case along its critical isochore is considered as a typical example to demonstrate the singleness of the ising like crossover parameter with the measurements at finite temperature range of the effective singular behaviors of the isothermal compressibility in the homogeneous domain and the vapor liquid coexisting densities in the non homogeneous domain our scaling equations provide the local estimate of this crossover parameter as a function of the temperature distance from the critical temperature our results compare favorably with the single asymptotic value calculated only using four critical coordinates of xenon

raptor codes on binary memoryless symmetric channels in this paper we will investigate the performance of raptor codes on arbitrary binary input memoryless symmetric channels bimscs in doing so we generalize some of the results that were proved before for the erasure channel we will generalize the stability condition to the class of raptor codes this generalization gives a lower bound on the fraction of output nodes of degree 2 of a raptor code if the error probability of the belief propagation decoder converges to zero using information theoretic arguments we will show that if a sequence of output degree distributions is to achieve the capacity of the underlying channel then the fraction of nodes of degree 2 in these degree distributions has to converge to a certain quantity depending on the channel for the class of erasure channels this quantity is independent of the erasure probability of the channel but for many other classes of bimscs this fraction depends on the particular channel chosen this result has implications on the universality of raptor codes for classes other than the class of erasure channels in a sense that will be made more precise in the paper we will also investigate the performance of specific raptor codes which are optimized using a more exact version of the gaussian approximation technique

monte carlo investigations of phase transitions status and perspectives abstract using the concept of finite size scaling monte carlo calculations of various models have become a very useful tool for the study of critical phenomena with the system linear dimension as a variable as an example several recent studies of ising models are discussed as well as the extension to models of polymer mixtures and solutions it is shown that using appropriate cluster algorithms even the scaling functions describing the crossover from the ising universality class to the mean field behavior with increasing interaction range can be described additionally the issue of finite size scaling in ising models above the marginal dimension d 4 is discussed

nature of crossover from classical to ising like critical behavior we present an accurate numerical determination of the crossover from classical to ising like critical behavior upon approach of the critical point in three dimensional systems the possibility of varying the ginzburg number in our simulations allows us to cover the entire crossover region we employ these results to scrutinize several semiphenomenological crossover scaling functions that are widely used for the analysis of experimental results in addition we present strong evidence that the exponent relations do not hold between effective exponents

master singular behavior for the sugden factor of one component fluids near their gas liquid critical point we present the master i e unique behavior of the squared capillary length the so called sugden factor as a function of the temperaturelike field along the critical isochore asymptotically close to the gas liquid critical point of about twenty one component fluids this master behavior is obtained using the scale dilatation of the relevant physical fields of the one component fluids the scale dilatation method introduces the fluid dependent scale factors in a manner analog to the linear relations between physical fields and scaling fields needed by the renormalization theory applied to any physical system belonging to the ising like universality class the master behavior for the sugden factor satisfies hyperscaling it can be asymptotically fitted by the leading terms of the theoretical crossover functions for the correlation length and the susceptibility in the homogeneous domain recently obtained from massive renormalization in field theory in the absence of corresponding estimation of the theoretical crossover functions for the interfacial tension we define the range of the temperaturelike field where the master leading power law can be practically used to predict the singular behavior of the sugden factor in conformity with the theoretical description provided by the massive renormalization scheme within the extended asymptotic domain of the one component fluid subclass

parity check density versus performance of binary linear block codes over memoryless symmetric channels we derive lower bounds on the density of parity check matrices of binary linear codes which are used over memoryless binary input output symmetric mbios channels the bounds are expressed in terms of the gap between the rate of these codes for which reliable communications is achievable and the channel capacity they are valid for every sequence of binary linear block codes if there exists a decoding algorithm under which the average bit error probability vanishes for every mbios channel we construct a sequence of ensembles of regular low density parity check ldpc codes so that an upper bound on the asymptotic density of their parity check matrices scales similarly to the lower bound the tightness of the lower bound is demonstrated for the binary erasure channel by analyzing a sequence of ensembles of right regular ldpc codes which was introduced by shokrollahi and which is known to achieve the capacity of this channel under iterative message passing decoding we show that this sequence of ensembles is asymptotically optimal in a sense to be defined in this paper strengthening a result of shokrollahi finally we derive lower bounds on the bit error probability and on the gap to capacity for binary linear block codes which are represented by bipartite graphs and study their performance limitations over mbios channels the latter bounds provide a quantitative measure for the number of cycles of bipartite graphs which represent good error correction codes

an explicit asymptotic preserving low froude scheme for the multilayer shallow water model with density stratification we present an explicit scheme for a two dimensional multilayer shallow water model with density stratification for general meshes and collocated variables the proposed strategy is based on a regularized model where the transport velocity in the advective fluxes is shifted proportionally to the pressure potential gradient using a similar strategy for the potential forces we show the stability of the method in the sense of a discrete dissipation of the mechanical energy in general multilayer and non linear frames these results are obtained at first order in space and time and extended using a simple second order muscl extension with the objective of minimizing the diffusive losses in realistic contexts sufficient conditions are exhibited on the regularizing terms to ensure the scheme s linear stability at first and second order in time and space the other main result stands in the consistency with respect to the asymptotics reached at small and large time scales in low froude regimes which governs large scale oceanic circulation additionally robustness and well balanced results for motionless steady states are also ensured these stability properties tend to provide a very robust and efficient approach easy to implement and particularly well suited for large scale simulations some numerical experiments are proposed to highlight the scheme efficiency an experiment of fast gravitational modes a smooth surface wave propagation an initial propagating surface water elevation jump considering a non trivial topography and a last experiment of slow rossby modes simulating the displacement of a baroclinic vortex subject to the coriolis force

on universal properties of capacity approaching ldpc code ensembles this paper is focused on the derivation of some universal properties of capacity approaching low density parity check ldpc code ensembles whose transmission takes place over memoryless binary input output symmetric mbios channels properties of the degree distributions graphical complexity and the number of fundamental cycles in the bipartite graphs are considered via the derivation of information theoretic bounds these bounds are expressed in terms of the target block bit error probability and the gap in rate to capacity most of the bounds are general for any decoding algorithm and some others are proved under belief propagation bp decoding proving these bounds under a certain decoding algorithm validates them automatically also under any suboptimal decoding algorithm a proper modification of these bounds makes them universal for the set of all mbios channels which exhibit a given capacity bounds on the degree distributions and graphical complexity apply to finite length ldpc codes and to the asymptotic case of an infinite block length the bounds are compared with capacity approaching ldpc code ensembles under bp decoding and they are shown to be informative and are easy to calculate finally some interesting open problems are considered

simulating free surface flows with sph the sph smoothed particle hydrodynamics method is extended to deal with free surface incompressible flows the method is easy to use and examples will be given of its application to a breaking dam a bore the simulation of a wave maker and the propagation of waves towards a beach arbitrary moving boundaries can be included by modelling the boundaries by particles which repel the fluid particles the method is explicit and the time steps are therefore much shorter than required by other less flexible methods but it is robust and easy to program

mean crossover functions for uniaxial three dimensional ising like systems we give simple expressions for the mean of the max and min bounds of the critical to classical crossover functions previously calculated bagnuls and bervillier phys rev e 65 066132 2002 within the massive renormalization scheme of the phi d 4 n model in three dimensions d 3 and scalar order parameter n 1 of the ising like universality class the mean functions are determined relying on the properties of the theoretical functions in the two limiting three dimensional 3d ising like and mean field like descriptions close to the wilson fisher fixed point and to the gaussian fixed point respectively such descriptions correspond to the preasymptotic domains near each fixed point where a wegner expansion restricted to two terms leading and first confluent terms is valid the ising like preasymptotic domain description includes the correlations between parameters due to the error bar determination of the exponents and amplitude combinations very close to the wilson fisher fixed point adding the equivalent description of the mean field preasymptotic domain close to the gaussian fixed point leads to define each mean crossover function with three calculated parameters fixing a unique value of one parameter whatever the selected mean crossover function we use this parameter as a relative sensor to estimate the dominant nature either ising like critical or mean field like classical of the crossover behavior finally we obtain an explicit criterion to measure the extension of the ising like preasymptotic domain which can then permit to coherently account for measurements performed in systems where the asymptotical approach to the critical point remains finite using a well controlled number of system dependent parameters like in the subclass of one component fluids

bounds on the number of iterations for turbo like ensembles over the binary erasure channel this paper provides simple lower bounds on the number of iterations which is required for successful message passing decoding of some important families of graph based code ensembles including low density parity check ldpc codes and variations of repeat accumulate codes the transmission of the code ensembles is assumed to take place over a binary erasure channel and the bounds refer to the asymptotic case where we let the block length tend to infinity the simplicity of the bounds derived in this paper stems from the fact that they are easily evaluated and are expressed in terms of some basic parameters of the ensemble which include the fraction of degree 2 variable nodes the target bit erasure probability and the gap between the channel capacity and the design rate of the ensemble this paper demonstrates that the number of iterations which is required for successful message passing decoding scales at least like the inverse of the gap in rate to capacity provided that the fraction of degree 2 variable nodes of these turbo like ensembles does not vanish hence the number of iterations becomes unbounded as the gap to capacity vanishes

critical exponents of the n vector model recently the series for two renormalization group functions corresponding to the anomalous dimensions of the fields and of the three dimensional field theory have been extended to next order seven loops by murray and nickel we examine the influence of these additional terms on the estimates of critical exponents of the n vector model using some new ideas in the context of the borel summation techniques the estimates have slightly changed but remain within the errors of the previous evaluation exponents such as related to the field anomalous dimension which were poorly determined in the previous evaluation of le guillou zinn justin have seen their apparent errors significantly decrease more importantly perhaps summation errors are better determined the change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values finally because an error has been discovered in the last order of the published expansions order we have also re analysed the determination of exponents from the expansion the conclusion is that the general agreement between expansion and three dimensional series has improved with respect to le guillou zinn justin

sphere packing bounds revisited for moderate block lengths the main reference of this paper is the sphere packing bound of 1967 sp67 derived by shannon gallager and berlekamp it offers a lower bound on the decoding error probability over a very large variety of channels if it has failed so far to provide any usable material in practical implementation of telecommunication systems it is due to an original focus on asymptotic results making it inapplicable for moderate code lengths and to the difficulty of the involved methods which makes the derivation of sp67 quite hermetic and uninspiring for further research the purpose of this paper is two fold 1 to stir up some renewed interest in the topic on which shannon concluded his career in information theory thanks to a qualitative rather than technical review of the derivation of sp67 introduced by a review of the simpler sphere packing bound derived by shannon in 1959 2 to prove the practical interest of sp67 by extending its field of application to continuous output channels and particularly the additive white gaussian noise awgn channel used with any particular modulation scheme and by improving its lower bound for the moderate code length case so that it becomes the best lower bound for most iteratively decodable codes turbo codes low density parity check ldpc codes repeat accumulate ra codes etc of usual lengths

an accurate multi regime sph scheme for barotropic flows abstract this paper focuses on the use of a mesh less numerical method to solve barotropic fluid flows smooth particle hydrodynamics sph such methods suffer from a severe lack of accuracy when evaluating state variables as the pressure field sph ale methods based on riemann solvers significantly improve this evaluation but increase the scheme complexity and low mach issues are difficult to prevent we propose an alternative scheme called s p h a l e relying on the combination of the sph ale formalism and a finite volume stabilizing low mach scheme applied to monophasic barotropic euler equations its characteristics are detailed and evaluated through a nonlinear stability analysis highlighting cfl like conditions on the scheme parameters as far as we know it is the first time such nonlinear analysis is performed on a sph ale scheme finally its implementation on several academic test cases reveals that the proposed scheme actually increases both stability and accuracy in reduced computation time with respect to sph ale riemann solvers

critical crossover functions for simple fluids towards the crossover modelling uniqueness based on a single non universal temperature scaling factor present in a simple fluid case a detailed analysis of non universal parameters involved in different critical to classical crossover models is given for the infinite limit of the cutoff wave number a set of three scaling parameters is defined for each model such that it shows all the shapes of the theoretical crossover functions overlap on the mean crossover function shapes close to the non trivial fixed point the analysis of corresponding links between their fluid dependent parameters opens a route to define a parametric model of crossover equation of state closely satisfying the universal features calculated from the ising like limit in the massive renormalization scheme

static and dynamic critical behavior of thin magnetic ising films this work presents a study of the effect of film thickness on the static and dynamic critical behavior of thin magnetic ising films monte carlo simulations using the wolff algorithm were performed to determine the static and dynamic critical exponents of the films a dimensionality crossover from 2d to 3d due to the finiteness of the films in the static and dynamic critical behavior was observed as the film thickness increases in addition a slight increase in the effective dimension deff and a considerable increase in the critical temperature tc were found small values for the dynamic critical exponents were obtained indicating that the wolff algorithm is a very efficient method for these magnetic systems

fast free surface detection and level set function definition in sph solvers the present paper proposes a novel algorithm to detect the free surface in particle simulations both in two and three dimensions since the proposed algorithms are based on sph interpolations their implementation does not require complex geometrical procedures thus the free surface detection can be easily embedded in sph solvers without a significant increase of the cpu time throughout this procedure accurate normal vectors to the free surface are made available then it is possible to define a level set function algorithm which is presented in detail the latter allows in depth analyses of three dimensional free surface simulations by using standard visualization tools including internal features of the flow the algorithms proposed for detecting free surface particles and defining the level set function are validated on simple and complex two and three dimensional flow simulations the usefulness of the proposed procedures to post process and analyze complex flows are illustrated on realistic examples

a numerical reduced model for thin liquid films sheared by a gas flow the non linear dynamics of thin liquid films sheared by a laminar gas flow in a channel is investigated such a two layer flow is driven by pressure gradient and possibly by the gravity force we describe the liquid phase with a long wave integral model with the aim to save computational cost with respect to the full direct numerical simulation dns of the navier stokes equations we derive this long wave model by the integration of the navier stokes equations over the film thickness and by an asymptotic expansion up to the first order in terms of a long wave parameter these depth integrated or shallow water equations are discretized by means of an augmented system which holds an evolution equation for the surface tension in order to avoid numerical instabilities of classical upwind and centered schemes on the other side we study the gas phase with compressible navier stokes equations and we discretize them by means of a low mach scheme accounting also for moving meshes ale in order to analyze liquid gas interactions we introduce then a coupling methodology between depth integrated equations and navier stokes equations this approach represents a compromise between the two existing methods the full dns and the full long wave model applied to both phases in order to validate this approach we present comparisons with dns showing a good agreement of spatio temporal evolutions of the film thickness and the stress field furthermore interfacial shear stress and pressure gradient evolutions are shown to be in accordance with those provided by two layer second order low dimensional models

comparisons of weakly compressible and truly incompressible algorithms for the sph mesh free particle method in the smoothed particle hydrodynamics sph discretisation method for the navier stokes equations the most widespread method to solve for pressure and mass conservation is the weakly compressible assumption wcsph this includes hydraulics applications and leads to some drawbacks such as severe artificial pressure fluctuations and a limitation to very small time steps related to the wcsph mach number and explicit method this paper presents comparisons of a semi implicit and truly incompressible sph isph algorithm with the classical wcsph method showing how some of the problems encountered in wcsph have been resolved by using isph to simulate incompressible flows mathematical models are presented before describing sph formalism several standard boundary conditions are introduced and special attention is given to tracking the surface particles the lid driven cavity flow re 400 and 1000 is performed as a benchmarking test a bluff body test case a square cylinder in a closed channel re d 20 and 100 based on the cylinder diameter shows that pressure fields extracted from wcsph are very unreliable whereas isph predict pressures and forces in closer agreement with classical finite volume cfd methods dam breaking cases with dry or wet beds downstream are then presented to highlight free surface flow and rapid dynamics effects the wcsph and isph results are generally verified with reference data from experiment and or another numerical method all the comparisons show improvement with isph and good agreement in general

normalized smoothing functions for sph impact computations this paper presents a normalized smoothing function nsf algorithm that can improve the accuracy of smooth particle hydrodynamics sph impact computations it is presented specifically for axisymmetric geometry but the principles also apply to plane strain and three dimensional geometry the approach consists of adjusting the standard smoothing functions for every node and every cycle such that the normal strain rates are computed exactly for conditions of constant strain rates linear velocity distributions this in turn generally improves accuracy for non uniform strain rates this can significantly improve the accuracy for free boundaries for non uniform arrangements of sph nodes and for small smoothing distances a new smoothing function is also introduced the nsf algorithm is shown to provide improved accuracy for a series of cylinder impact examples that includes two different smoothing functions and two different smoothing distances

crossover scaling from classical to non classical critical behaviour interacting physical systems in the neighborhood of criticality and massive continuum field theories can often be characterized by just two physical scales a macroscopic correlation length and a microscopic interaction range related to the coupling and measured by the ginzburg number g a critical crossover limit can be defined when both scales become large while their ratio stays finite the corresponding scaling functions are universal and they are related to the standard field theory renormalization group functions the critical crossover describes the unique flow from the gaussian to the nonclassical fixed point

two parameter scaling of correlation functions near continuous phase transitions we discuss the order parameter correlation function in the vicinity of continuous phase transitions using a two parameter scaling form g k k 2 c g k k k c where k is the wave vector and is the correlation length and the interaction dependent nonuniversal momentum scale k c remains finite at the critical fixed point the correlation function describes the entire critical regime and captures the classical to critical crossover one parameter scaling is recovered only in the limit k k c 0 we present an approximate calculation of g x y for the ising universality class using the functional renormalization group

does the performance of ldpc codes depend on the channel in this letter we discuss the performance of low density parity check ldpc codes on memoryless channels using a recently proposed analysis technique based on extrinsic information transfer exit charts we present an interpretation of the known fact that the bit error rate ber performance of an ensemble of ldpc codes shows little dependence on the specific memoryless channel this result has been partially observed in the literature for symmetric channels and is here extended to asymmetric channels we conjecture and demonstrate that the performance of an ensemble of ldpc codes depends primarily and solely on the mutual information mi between the input and the output of the channel as a validation of this conjecture we compare the performance of a few ldpc codes with various rates for five representative memoryless both symmetric and asymmetric channels obtaining results in excellent agreement with the exit chart based prediction

on the corrections to scaling in three dimensional ising models the leading correction to scaling amplitudes for the spin 1 2 nearest neighbor sc bcc and fee ising models are considered with the particular aim of determining their signs on the basis of previous two variable series analyses by chen fisher and nickel and renormalization group 4 d expansions it is concluded that the correction amplitudes for the susceptibility correlation length specific heat and spontaneous magnetization arenegative for all three lattices thus for example the effective exponent eff t asymptotically approaches the true susceptibility exponent fromabove other earlier and more recent high temperature series and field theoretic analyses are seen to be consistent with this result however the usual nonasymptotic perturbative field theoretic approaches are essentially committed to positive correction amplitudes the question of the signs therefore relates directly to the applicability of these non asymptotic field theoretic calculations to three dimensional ising models as well as to different experimental systems

crossover scaling in two dimensions we determine the scaling functions describing the crossover from ising like critical behavior to classical critical behavior in two dimensional systems with a variable interaction range since this crossover spans several decades in the reduced temperature as well as in the finite size crossover variable it has up to now largely evaded a satisfactory numerical determination using a dedicated monte carlo method we could obtain accurate results for sufficiently large interaction ranges our data cover the full crossover region both above and below the critical temperature and support the hypothesis that the crossover functions are universal also the so called effective exponents are discussed and we show that these can vary nonmonotonically in the crossover region

sign of corrections to scaling amplitudes field theoretic considerations and results for self repelling walks i discuss the application of renormalized field theory to such critical systems where the renormalized coupling approaches the fixed point from the wrong strong coupling side in contrast to a belief sometimes expressed in the literature i find that also this situation can be described within the standard formalism only the interpretation of the strong coupling branch relies on the existence of a finite cutoff i illustrate these considerations with an analysis of monte carlo data for self avoiding walks finding that the data support the theory in all respects however it is stressed that the nonuniversal parameters of the renormalized theory in general have no simple relation to the parameters of the underlying bare model