parametrization of the cumulant lattice boltzmann method for fourth order accurate diffusion part ii the optimized cumulant lattice boltzmann method with fourth order accurate diffusion is used to simulate the flow around a sphere up to reynolds number 106 the drag crisis is well captured by the method we demonstrate with our results that the drag crisis corresponds to an almost discrete jump in the flow conditions the intermediate values of drag in a small range of reynolds numbers around the drag crisis observed in averaged data sets are found to originate from the flow switching between the high and the low drag conditions around the critical reynolds number the time spent in the low drag condition increases with the reynolds number such that the average drag curve has a finite steepness we demonstrate that the cumulant lattice boltzmann model with optimized parameters captures the drag crisis for flows over a sphere no sub grid model and no wall function is required and the boundary layer is only marginally resolved it is observed that in the transition regime between the high and the low drag configuration the flow switches from one state to the other state

multiphase cascaded lattice boltzmann method to improve the stability of the lattice boltzmann method lbm at high reynolds number the cascaded lbm has recently been introduced as in the multiple relaxation time mrt method the cascaded lbm introduces additional relaxation times into the collision operator but does so in a co moving reference frame this has been shown to significantly increase stability at low viscosity in the single phase case here the cascaded lbm is further developed to include multiphase flow for this the force term is calculated by the interaction potential method and introduced into the collision operator via the exact difference method edm comparisons are made with the lattice bhatnagar gross krook lbgk method and an mrt implementation both the cascaded and mrt methods are shown to significantly reduce spurious velocities over the lbgk method for the particular case of the shan chen interparticle force term calculation with the edm the cascaded lbm is successfully combined with a multiphase method and shown to perform as well as the more established mrt method the cascaded lbm is found to be a considerably improved approach to the simulation of multiphase flow over the lbgk significantly increasing the stability range of both density ratio and reynolds number additionally the importance of including third order velocity terms in the equilibria of both the cascaded and mrt methods is discussed

proteus a coupled iterative force correction immersed boundary cascaded lattice boltzmann solver for moving and deformable boundary applications abstract many realistic fluid flow problems are characterised by high reynolds numbers and complex moving or deformable geometries in our previous study we presented a novel coupling between an iterative force correction immersed boundary and a multi domain cascaded lattice boltzmann method falagkaris et al and investigated flows around rigid bodies at reynolds numbers up to 1 0 5 here we extend its application to flows around moving and deformable bodies with prescribed motions emphasis is given on the influence of the internal mass on the computation of the aerodynamic forces including deforming boundary applications where the rigid body approximation is no longer valid both the rigid body and the internal lagrangian points approximations are examined the resulting solver has been applied to viscous flows around an in line oscillating cylinder a pitching foil a plunging sd7003 airfoil and a plunging and flapping naca 0014 airfoil good agreement with experimental results and other numerical schemes has been obtained it is shown that the internal lagrangian points approximation accurately captures the internal mass effects in linear and angular motions as well as in deforming motions at reynolds numbers up to 4 1 0 4 in all cases the aerodynamic loads are significantly affected by the internal fluid forces

diffusion in three dimensional random systems at their percolation thresholds extensive monte carlo simulations of theant in the labyrinth problem on randoml l l simple cubic lattices are performed forl up to 960 on a cray ymp supercomputer the exponentk for the rms displacementr witht inr t k is found to bek 0 190 0 003 as a second approach large percolation clusters with chemical shells up to 300 are generated on a simple cubic lattice at criticality the diffusion equation is then solved by using the exact enumeration technique the corresponding critical exponentd w is found to be 1 d w 0 250 0 003

multispeed models in off lattice boltzmann simulations the lattice boltzmann method is a highly promising approach to the simulation of complex flows here we realize recently proposed multispeed lattice boltzmann models s chikatamarla et al phys rev lett 97 190601 2006 by exploiting the flexibility offered by off lattice boltzmann methods the approach is based on the general characteristic based algorithm for off lattice boltzmann simulations that preserves all appealing properties of the standard lattice boltzmann method while extending the method to unstructured grids we show that the use of multispeed models indeed gives rise to major improvements in accuracy the suggested approach thus renders truly large scale off lattice boltzmann computations practical

sensitivity penalization based robust state estimation for uncertain linear systems this technical note deals with robust state estimation when parametric uncertainties nonlinearly affect a plant state space model based on a simultaneous minimization of nominal estimation errors and their sensitivities an analytic solution is derived for the optimal estimator which can be recursively realized this estimator has a form similar to the robust estimator of and its computational complexity is comparable to the kalman filter under certain conditions this robust estimator is proved to converge to a stable system its estimation errors have a bounded covariance matrix and the estimate is asymptotically unbiased numerical simulations show that the obtained estimator has nice estimation performances

technical communique robust state estimation for uncertain discrete time stochastic systems with missing measurements in this paper results of robust estimation of zhou 2010a are extended to state estimation with missing measurements a new procedure is derived which inherits the main properties of that of zhou 2010a in this extension a covariance matrix used in the recursions is replaced by its estimate which makes its asymptotic property investigation mathematically difficult though introducing a monotonic function and using the so called squeeze rule this new robust estimator is proved to converge to a stable system numerical simulation results indicate that the proposed estimator may have an estimation accuracy better than the estimator of wang yang daniel and liu 2005

correspondence comments on robust state estimation for uncertain discrete time stochastic systems with missing measurements automatica 47 2011 1520 1524 we show that some results presented in the aforementioned article are rather limited one of the major restrictions on applicability of the obtained results is the ergodic requirement on the received plant output measurements which is generally not satisfied by a time varying system another major restriction is that the comparisons are not appropriate for its numerical simulations that is using the state estimation results of an estimator that utilizing current and past observations to compare with those of a one step state predictor is not appropriate to evaluate the filter performances objectively we do a numerical simulation with the robust state estimator and the well known kalman filter that does not take either parametric errors or random measurement loss into account and the simulation results show that there is no significant difference in filtering performance between these two estimators

generalized local equilibrium in the cascaded lattice boltzmann method by realizing the insufficient degree of galilean invariance of the traditional multiple relaxation time collision operators geier et al phys rev e 73 066705 2006 proposed to relax differently the moments shifted by the macroscopic velocity leading to the so called cascaded lattice boltzmann method lbm this paper points out that a the cascaded lbm essentially consists in adopting a generalized local equilibrium in the frame at rest b this new equilibrium does not affect the consistency of lbm and finally c if the raw moments are relaxed in the frame at rest as usual and the number of relaxation frequencies is reduced the proposed derivation leads to the two relaxation time collisional operator with proper polynomial equilibrium

parametrization of the cumulant lattice boltzmann method for fourth order accurate diffusion part ii application to flow around a sphere at drag crisis the optimized cumulant lattice boltzmann method with fourth order accurate diffusion is used to simulate the flow around a sphere up to reynolds number 106 the drag crisis is well captured by the method we demonstrate with our results that the drag crisis corresponds to an almost discrete jump in the flow conditions the intermediate values of drag in a small range of reynolds numbers around the drag crisis observed in averaged data sets are found to originate from the flow switching between the high and the low drag conditions around the critical reynolds number the time spent in the low drag condition increases with the reynolds number such that the average drag curve has a finite steepness

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

on the three dimensional central moment lattice boltzmann method a three dimensional 3d lattice boltzmann method based on central moments is derived two main elements are the local attractors in the collision term and the source terms representing the effect of external and or self consistent internal forces for suitable choices of the orthogonal moment basis for the three dimensional twenty seven velocity d3q27 and its subset fifteen velocity d3q15 lattice models attractors are expressed in terms of factorization of lower order moments as suggested in an earlier work the corresponding source terms are specified to correctly influence lower order hydrodynamic fields while avoiding aliasing effects for higher order moments these are achieved by successively matching the corresponding continuous and discrete central moments at various orders with the final expressions written in terms of raw moments via a transformation based on the binomial theorem furthermore to alleviate the discrete effects with the source terms they are treated to be temporally semi implicit and second order with the implicitness subsequently removed by means of a transformation as a result the approach is frame invariant by construction and its emergent dynamics describing fully 3d fluid motion in the presence of force fields is galilean invariant numerical experiments for a set of benchmark problems demonstrate its accuracy

precise calculation of the dynamical exponent of two dimensional percolation we report numerical data obtained on the special purpose computer percola for the exponent tilde t of the electrical conductivity of 2d percolation the extrapolation yields tilde t 0 9745 pm 0 0015 and a correction to the scaling exponent 1 2 0 2

low concentration series in general dimension we discuss recent work on the development and analysis of low concentration series for many models the recent breakthrough in the extremely efficient no free end method of series generation facilitates the derivation of 15th order series for multiple moments in general dimension the 15th order series have been obtained for lattice animals percolation and the edwards anderson ising spin glass in the latter cases multiple moments have been found from complete graph tables through to 13th order general dimension 13th order series have been derived for the resistive susceptibility the moments of the logarithms of the distribution of currents in resistor networks and the average transmission coefficient in the quantum percolation problem 11th order series have been found for several other systems including the crossover from animals to percolation the full resistance distribution nonlinear resistive susceptibility and current distribution in dilute resistor networks diffusion on percolation clusters the dilute ising model dilute antiferromagnet in a field and random field ising model and self avoiding walks on percolation clusters series for the dilute spin 1 2 quantum heisenberg ferromagnet are in the process of development analysis of these series gives estimates for critical thresholds amplitude ratios and critical exponents for all dimensions where comparisons are possible our series results are in good agreement with bothe expansion results near the upper critical dimension and with exact results when available in low dimensions and are competitive with other numerical approaches in intermediate realistic dimensions

moderate deviations of a random riccati equation the paper characterizes the invariant filtering measures resulting from kalman filtering with intermittent observations in which the observation arrival is modeled as a bernoulli process with packet arrival probability our prior work showed that for 0 the sequence of random conditional error covariance matrices converges weakly to a unique invariant distribution this paper shows that as approaches one the family 0 satisfies a moderate deviations principle with good rate function i 1 as 1 the family converges weakly to the dirac measure p concentrated on the fixed point of the associated discrete time riccati operator 2 the probability of a rare event an event bounded away from p under decays to zero as a power law of 1 as 1 and 3 the best power law decay exponent is obtained by solving a deterministic variational problem involving the rate function i for specific scenarios the paper develops computationally tractable methods that lead to efficient estimates of rare event probabilities under

robust recursive state estimation with random measurement droppings a recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings this estimator has a similar form as that of kalman filter with intermittent observations but its parameters should be adjusted when a plant output measurement arrives a new recursive form is derived for the pseudo covariance matrix of estimation errors based on a riemannian metric for positive definite matrices some necessary and sufficient conditions have been obtained for the strict contractiveness of this recursion it has also been proved that under some controllability and observability conditions as well as some weak requirements on measurement arrival probability the update gain of this recursive robust state estimator and the mean of its squared estimation errors converge in probability one respectively to a corresponding stationary distribution numerical simulation results show that estimation accuracy of the suggested procedure is more robust against parametric modelling errors than kalman filter

lattice boltzmann equation linear stability analysis thermal and athermal models although several thermal lattice boltzmann models have been proposed this method has not yet been shown to be able to describe nonisothermal fully compressible flows in a satisfactory manner mostly due to the presence of important deviations from the advection diffusion macroscopic equations and also due to numerical instabilities in this context this paper presents a linear stability analysis for some lattice boltzmann models that were recently derived as discrete forms of the continuous boltzmann equation p c philippi l a hegele jr l o e dos santos and r surmas phys rev e 63 056702 2006 in order to investigate the sources of instability and to find for each model the upper and lower limits for the macroscopic variables between which it is possible to ensure a stable behavior the results for two dimensional 2d lattices with 9 17 25 and 37 velocities indicate that increasing the order of approximation of the lattice boltzmann equation enhances stability results are also presented for an athermal 2d nine velocity model the accuracy of which has been improved with respect to the standard d2q9 model by adding third order terms in the lattice boltzmann equation

series expansion evidence supporting the alexander orbach conjecture in two dimensions the authors extend the series expansion of fisch and harris 1978 for the resistive susceptibility chi r p by a further six terms on the square lattice this leads to a more precise estimate of the corresponding exponent gamma r 3 65 or 0 02 they also obtain the exact relation chi r p 2e tau mod f where tau is the sum of the relaxation times for charge diffusion on the cluster containing the origin and the expectation value is subject to the condition that the latter is finite a known scaling relation for the fracton dimension df in terms of gamma r and the static exponents is derived without the usual reference to the infinite cluster using the estimate of gamma r they find df 1 334 or 0 007 which is consistent with the ao conjecture df 4 3 they also note that gamma r is the same for directed and undirected percolation to within the accuracy of the calculations

the cumulant lattice boltzmann equation in three dimensions theory and validation we propose analyze and validate a lattice boltzmann model with a cumulant collision operator the new model is analytically and numerically shown to poses smaller errors than a moment based multiple relaxation time lattice boltzmann model we demonstrate the usability of the cumulant lattice boltzmann model by simulations of flow around a sphere for reynolds numbers from 200 to 105

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

numerical studies of critical percolation in three dimensions presents results of high statistics simulations of the spreading of 3d percolation close to the critical point the main results are i a more precise estimate of the spreading resp chemical distance dimension ii a novel heuristic scaling theory for percolation near surfaces and iii more precise values for critical surface and edge exponents in addition the author verifies the very precise results of ziff and stell 1988 for the percolation thresholds and studies in detail corrections to scaling the latter is made possible by simulating bond and site percolation in a number of different geometries in addition in most cases one could measure more than one observable during each simulation which provided quite severe internal consistency constraints in some cases the author found quite important deviations from scaling which are not easily described by a single power or logarithmic correction term

an interpretation and derivation of the lattice boltzmann method using strang splitting the lattice boltzmann space time discretisation as usually derived from integration along characteristics is shown to correspond to a strang splitting between decoupled streaming and collision steps strang splitting offers a second order accurate approximation to evolution under the combination of two non commuting operators here identified with the streaming and collision terms in the discrete boltzmann partial differential equation strang splitting achieves second order accuracy through a symmetric decomposition in which one operator is applied twice for half timesteps and the other operator is applied once for a full timestep we show that a natural definition of a half timestep of collisions leads to the same change of variables that was previously introduced using different reasoning to obtain a second order accurate and explicit scheme from an integration of the discrete boltzmann equation along characteristics this approach extends easily to include general matrix collision operators and also body forces finally we show that the validity of the lattice boltzmann discretisation for grid scale reynolds numbers larger than unity depends crucially on the use of a crank nicolson approximation to discretise the collision operator replacing this approximation with the readily available exact solution for collisions uncoupled from streaming leads to a scheme that becomes much too diffusive due to the splitting error unless the grid scale reynolds number remains well below unity

a transfer matrix approach to random resistor networks introduces a transfer matrix formulation to compute the conductance of random resistor networks the authors apply this method to strips of width up to 40 and use finite size scaling arguments to obtain an estimate for the conductivity critical exponent in two dimensions t 1 28 or 0 03

asymptotic analysis of the lattice boltzmann equation in this article we analyze the lattice boltzmann equation lbe by using the asymptotic expansion technique we first relate the lbe to the finite discrete velocity model fdvm of the boltzmann equation with the diffusive scaling the analysis of this model directly leads to the incompressible navier stokes equations as opposed to the compressible navier stokes equations obtained by the chapman enskog analysis with convective scaling we also apply the asymptotic analysis directly to the fully discrete lbe as opposed to the usual practice of analyzing a continuous equation obtained through the taylor expansion of the lbe this leads to a consistency analysis which provides order by order information about the numerical solution of the lbe the asymptotic technique enables us to analyze the structure of the leading order errors and the accuracy of numerically derived quantities such as vorticity it also justifies the use of richardson s extrapolation method as an example a two dimensional taylor vortex flow is used to validate our analysis the numerical results agree very well with our analytic predictions

a cascaded phase field lattice boltzmann model for the simulation of incompressible immiscible fluids with high density contrast abstract in this work a conservative phase field model for the simulation of immiscible multiphase flows is developed using an incompressible velocity based cascaded lattice boltzmann method clbm extensions are made to the lattice boltzmann lb equations for interface tracking and incompressible hydrodynamics proposed by fakhari et al 1 by performing relaxation operations in central moment space this was motivated by the work of fei et al 2 3 where promising results from such a transformation were observed the relaxation of central moments is defined in a reference frame moving with the fluid while the existing multiple relaxation time 4 5 scheme performs collision in a fixed frame of reference moreover the derivations make use of continuous maxwellian distribution functions as a result the clbm enhances the galilean invariance and stability of the method when high lattice mach numbers are evident the cascaded scheme has been previously used in the literature to simulate multiphase flows based on the pseudo potential model where it allowed for high density and viscosity contrasts to be captured 6 7 here the clbm is implemented within the phase field framework and is verified through the analysis of a layered poiseuille flow the performance of the clbm is then investigated in terms of spurious currents galilean invariance and computational efficiency finally the work of fakhari et al 1 is extended by validating the model s ability to capture the relation between surface tension and the rise velocity of a planar taylor bubble in both stagnant and flowing fluids new counter current results indicate that the rise velocity model of ha ngoc and fabre 8 also applies in this regime

simulation of rotating objects in fluids with the cumulant lattice boltzmann model on sliding meshes abstract in this paper a rotating grid technique for the cumulant lattice boltzmann model is presented the rotating object is embedded in a rotating mesh that communicates with an enclosing stationary mesh via compact quadratic interpolation on the rotating mesh coriolis and centrifugal forces model the rotation with respect to the outer eulerian frame of reference a proper rotation of all moments is imposed in the interface between the moving and the static grid the fluid flow is simulated by the cumulant lattice boltzmann model profiles of pressure velocity and shear stress are compared with the analytical solution of taylor couette flow and we demonstrate that our scheme is second order accurate in space as a second numerical benchmark lift and drag coefficients for a rotating ellipsoidal cylinder in a laminar flow are simulated and successfully compared to a reference solution

central moment lattice boltzmann schemes with fixed and moving immersed boundaries lattice boltzmann lb schemes based on the relaxation of central moments have recently proved valuable in simulating flows with an improved stability with respect to the original single relaxation time bgk formulation while preserving the accuracy of the latter this has been assessed mainly for flows in simple geometries e g in periodic domains or with fixed rigid straight boundaries in the present study the properties of central moment lb schemes have been investigated against flow configurations involving arbitrarily shaped possibly moving boundaries within the framework of the so called immersed boundary ib method namely the presence of boundaries is accounted by an external force acting on the fluid that is encompassed in the central moment lb algorithm accuracy and stability issues are examined in comparison with existing results from the literature and lb simulations based on the original bgk scheme our results show that central moment lb schemes accompanied by the ib method provide an efficient tool for fluid structure interaction simulations

speculation on a scaling law for superconductor resistor mixture exponent s in a percolation system it is argued that looking for a relationship between the exponent s and the cluster exponents may be more promising than looking for one between the resistor insulator exponent t and the cluster exponents the author proposes s nu beta 2

corrections to scaling for diffusion exponents on three dimensional percolation systems at criticality recent results of monte carlo simulations of the ant in the labyrinth method in three dimensional percolation lattices are reanalyzed in the light of more accurate corrections to scaling ansatz motivated by inconsistent results that have appeared in the literature the results are observed to be sensitive to the form of the scaling correction terms using a single correction term we estimate the valuek 0 197 0 004 for the anomalous diffusion exponent at criticality when two correction terms are included k 0 200 0 002 is obtained these new estimates are consistent with known theoretical bounds with recent series expansion results and with numerical calculations of the conductance of random resistor networks above criticality

a framework for state space estimation with uncertain models develops a framework for state space estimation when the parameters of the underlying linear model are subject to uncertainties compared with existing robust filters the proposed filters perform regularization rather than deregularization it is shown that under certain stabilizability and detectability conditions the steady state filters are stable and that for quadratically stable models the filters guarantee a bounded error variance moreover the resulting filter structures are similar to various time and measurement update prediction and information forms of the kalman filter albeit ones that operate on corrected parameters rather than on the given nominal parameters simulation results and comparisons with spl hscr sub spl infin guaranteed cost and set valued state estimation filters are provided

on the relationship between the critical exponents of percolation conductivity and static exponents of percolation the author argues that the critical exponent t of random conductance networks near the percolation threshold is given by t d 1 nu for low dimensionalities and t 1 beta for high dimensionalities where nu is the correlation length exponent beta the backbone exponent and d is dimensionality the author argues that what separates the two regimes is a critical fractal dimensionality dl which equals 2 the author also argues that dl is also a critical fractal dimensionality for fractals such as lattice animals and diffusion limited aggregates the result for low dimensionalities has been also obtained by aharony and stauffer by a different argument

exponent inequalities for the bulk conductivity of a hierarchical model the bulk conductivity p of the bond lattice in d is considered where the bonds have conductivity 1 with probabilityp or e 0 with probability 1 p various representations of the derivatives of p are developed these representations are used to analyze the behavior of p for e 0 near the percolation thresholdp c when the conducting backbone is assumed to have a hierarchical node link blob nlb structure this model has loops on arbitrarily many length scales and contains both singly and multiply connected bonds exact asymptotics of frac d 2 sigma dp 2 for the nlb model are proven under some technical assumptions the proof employs a novel technique whereby frac d 2 sigma dp 2 for the nlb model with e 0 andp nearp c is computed using perturbation theory for p for two and three component resistor lattices aroundp 1 with a sequence of e s converging to 1 as one goes deeper in the hierarchy these asymptotics establish convexity of p for the nlb model nearp c and that its critical exponentt obeys the inequalities 1 t 2 ford 2 3 while 2 t 3 ford 4 the upper boundt 2 ind 3 which is realizable in the nlb class virtually coincides with two very recent numerical estimates obtained from simulation and series expansion for the original model

relation between elastic and scalar transport exponent in percolation using simple variational considerations the author shows that the elastic critical exponent tau is related to the conductivity index t and to the correlation length exponent nu by tau or t 2 nu it is conjectured that this relation might be an equality

scaling behavior of permeability and conductivity anisotropy near the percolation threshold we use the finite size scaling method to estimate the critical exponent that characterizes the scaling behavior of conductivity and permeability anisotropy near the percolation thresholdpc here is defined by the scaling lawkl kt 1 p pc wherekt andkt are the conductivity or permeability of the system in the direction of the macroscopic potential gradient and perpendicular to this direction respectively the results are d 2 0 819 0 011 and d 3 0 518 0 001 we interpret these results in terms of the structure of percolation clusters and their chemical distance we also compare our results with the predictions of a scaling theory for due to straley and propose that d 2 t b wheret is the critical exponent of the conductivity or permeability of the system and b is the critical exponent of the backbone of percolation clusters

on correction to scaling for two and three dimensional scalar and vector percolation a reanalysis of the resistancer of two and three dimensional superconducting networks at the percolation thresholdp c together with the previous results for the elastic modulik of such networks shows that there is aunified description of finite size scaling for scalar and vector transport properties of percolation systems for a network of linear sizel atp c and forboth scalar and vector percolation inboth two and three dimensions k andr scale withl asl x a 1 a 2 lnl 1 a 3 l 1 wherex is the ratio of the associated critical exponent ofk orr and the correlation length exponentv of percolation although our estimates ofx for the resistance of percolation networks are consistent with the previous results they do indicate that inboth two and three dimensions and forboth scalar and vector percolation the leading nonanalytic correction to scaling exponent iszero from a reanalysis of data on diffusion on percolation clusters atp c we propose that such correction to scaling terms are a general property ofdynamics of percolation clusters we also suggest that for two dimensional percolation the conductivity exponentt and the superconductivity exponents are given by s t v 4 187 144 1 2986 and the elasticity exponentf is given byf t 2v 571 144 3 9652 where is the exponent of the strength of the infinite percolation cluster

cascaded digital lattice boltzmann automata for high reynolds number flow lattice boltzmann methods are of limited applicability for direct numerical simulation of turbulent flow due to instabilities in the zero viscosity limit we observe that this is caused by an insufficient degree of galilean invariance of the relaxation type lattice boltzmann collision operator the cascaded digital lattice boltzmann automata described here provides a method with which to achieve stable collision operators down to the limit of zero viscosity

proteus a coupled iterative force correction immersed boundary multi domain cascaded lattice boltzmann solver abstract most realistic fluid flow problems are characterized by high reynolds numbers and complex boundaries over the last ten years immersed boundary methods that are able to cope with realistic geometries have been applied to lattice boltzmann lb methods these methods however have normally been applied to low reynolds number problems here we present a novel coupling between an iterative force correction immersed boundary zhang et al 2016 and a multi domain cascaded lb method the iterative force correction immersed boundary method has been selected due to the improved accuracy of the computation while the cascaded lb formulation is used due to its superior stability at high reynolds numbers the coupling is shown to improve both the stability and numerical accuracy of the solution the resulting solver has been applied to viscous flow up to a reynolds number of 100000 passed a naca 0012 airfoil at a 10 degree angle of attack good agreement with results obtained using a body fitted navier stokes solver has been obtained the formulation provides a straight forward and efficient method for modeling realistic geometries and could easily be extended to problems with moving boundaries

improving the low mach number steady state convergence of the cascaded lattice boltzmann method by preconditioning abstract cascaded lattice boltzmann method lbm involves the use of central moments in a multiple relaxation time formulation in prescribing the collision step when the goal is to simulate low mach number stationary flows the greater the disparity between the magnitude of fluid speed and the sound speed the higher is the numerical stiffness which results in relatively large number of time steps for convergence of the lbm one way to improve the steady state convergence of the scheme is to precondition the cascaded lbm which reduces the disparities between the characteristic speeds or equivalently those between the eigenvalues of the system in this paper we present a new preconditioned two dimensional cascaded lbm where a preconditioning parameter is introduced into the equilibrium moments as well as the forcing terms particular focus is given to preconditioning differently the moments due to forcing at first and second orders so as to avoid any spurious effects in the emergent macroscopic equations a chapman enskog analysis performed on this approach shows consistency to the preconditioned navier stokes equations this modified central moment based scheme is then validated for accuracy by comparison against prior analytical or numerical results for certain benchmark problems including those involving spatially variable body forces finally significant steady state convergence acceleration of the preconditioned cascaded lbm is demonstrated for a set of characteristic parameters

on the range of validity of the 6 e expansion for percolation in 6 epsilon dimensions the critical properties of percolation can be computed starting from a phi 3 theory having the same symmetry of the one state potts model the authors argue that this fixed point must be unstable with respect to a phi 4 interaction in two dimensions therefore a phi 4 perturbation is relevant this suggestion is confirmed by an explicit two loops computation

a central moments based lattice boltzmann scheme for shallow water equations abstract in this paper we explore the possibility to derive an original lattice boltzmann scheme for solving shallow water equations specifically it is proposed to decompose the collision operator by means of a non orthogonal basis of central moments which relax independently to a discrete equilibrium our method is strictly consistent with the bgk operator as the latter is recovered exactly if all the moments relax with a common frequency the methodology is validated against five well consolidated established benchmark problems showing very good agreement moreover it possesses very high properties in terms of stability

on the convergence and stability of a robust state estimator convergence and stability of the robust state estimator obtained in is reinvestigated in this technical note some new relations have been established for matrix updates in the recursive state estimation it is proved that under certain stabilizability and detectability conditions this robust estimator converges to a stable time invariant system provided that plant nominal parameters are time invariant and the filter design parameter is fixed these results are consistent with existent ones but different from them at the point that there are no orthogonality constraints on uncertainty related system matrices and therefore widen theoretical guarantees for the effectiveness of the estimation procedure

generic rigidity percolation in two dimensions we study rigidity percolation for random central force networks on the bondand site diluted generic triangular lattice here each site location is randomly displaced from the perfect lattice removing any special symmetries using the pebble game algorithm the total number of floppy modes are counted exactly and exhibit a cusp singularity in the second derivative at the transition from a rigid to a floppy structure the critical thresholds for bond and site dilution are found to be 0 66020 ifmmode pm else textpm fi 0 0003 and 0 69755 ifmmode pm else textpm fi 0 0003 respectively the network is decomposed into unique rigid clusters and we apply the usual percolation scaling theory from finite size scaling we find that the generic rigidity percolation transition is second order but in a different universality class from connectivity percolation with the exponents ensuremath alpha 0 48 ifmmode pm else textpm fi 0 05 ensuremath beta 0 175 ifmmode pm else textpm fi 0 02 and ensuremath nu 1 21 ifmmode pm else textpm fi 0 06 the fractal dimension of the spanning rigid clusters and the spanning stressed regions at the critical threshold are found to be mathit d mathit f 1 86 ifmmode pm else textpm fi 0 02 and mathit d mathit bb 1 80 ifmmode pm else textpm fi 0 03 respectively textcopyright 1996 the american physical society

spreading and backbone dimensions of 2d percolation the author presents results of high statistics simulations of the spreading of 2d percolation and of backbones of 2d percolation clusters while the algorithm employed for the spreading is more or less standard for identifying backbones the author uses a new and very efficient recursive algorithm the author uses new critical exponents to test previous conjectures

brief paper optimal linear estimation for systems with multiple packet dropouts this paper is concerned with the optimal linear estimation problem for linear discrete time stochastic systems with multiple packet dropouts based on a packet dropout model the optimal linear estimators including filter predictor and smoother are developed via an innovation analysis approach the estimators are computed recursively in terms of the solution of a riccati difference equation of dimension equal to the order of the system state plus that of the measurement output the steady state estimators are also investigated a sufficient condition for the convergence of the optimal linear estimators is given simulation results show the effectiveness of the proposed optimal linear estimators

diffusion on random systems above below and at their percolation threshold in two and three dimensions a detailed monte carlo study is presented for classical diffusion random walks on random l l triangular and l l l simple cubic lattices with l up to 4096 and 256 respectively the speed of a cyber 205 vector computer is found to be about one order of magnitude larger than that of a usual cdc cyber 76 computer to reach the asymptotic scaling regime walks with up to 10 million steps were simulated with about 10 jl steps in total for l 256 at the percolation threshold we review and extend the dynamical scaling description for the distance traveled as function of time the diffusivity above the threshold and the cluster radius below earlier discrepancies between scaling theory and computer experiment are shown to be due to insufficient monte carlo data the conductivity exponent is found to be 2 0 0 2 in three and 1 28 0 02 in two dimensions our data in three dimensions follow well the finite size scaling theory below the threshold the approach of the distance traveled to its asymptotic value is consistent with theoretical speculations and an exponent 2 5 independent of dimensionality the correction to scaling exponent at pc seems to be larger in two than in three dimensions

molecular trajectory algorithm for random walks on percolation systems at criticality in two and three dimensions abstract random walk simulations based on a molecular trajectory algorithm are performed on critical percolation clusters the analysis of corrections to scaling is carried out it has been found that the fractal dimension of the random walk on the incipient infinite cluster is d w 2 873 0 008 in two dimensions and 3 78 0 02 in three dimensions if instead the diffusion is averaged over all clusters at the threshold not subject to the infinite restriction the corresponding critical exponent k is found to be k 0 3307 0 0014 for two dimensional space and 0 199 0 002 for three dimensional space moreover in our simulations the asymptotic behaviors of local critical exponents are reached much earlier than in other numerical methods

from the continuous to the lattice boltzmann equation the discretization problem and thermal models the velocity discretization is a critical step in deriving the lattice boltzmann lbe from the continuous boltzmann equation this problem is considered in the present paper following an alternative approach and giving the minimal discrete velocity sets in accordance with the order of approximation that is required for the lbe with respect to the continuous boltzmann equation and with the lattice structure considering n to be the order of the polynomial approximation to the maxwell boltzmann equilibrium distribution it is shown that solving the discretization problem is equivalent to finding the inner product in the discrete space induced by the inner product in the continuous space that preserves the norm and the orthogonality of the hermite polynomial tensors in the hilbert space generated by the functions that map the velocity space onto the real numbers space as a consequence it is shown that for each order n of approximation the even parity velocity tensors are isotropic up to rank 2n in the discrete space the norm and the orthogonality restrictions lead to space filling lattices with increased dimensionality when compared with presently known lattices this problem is discussed in relation with a discretization approach based on a finite set of orthogonal functions in the discrete space two dimensional square lattices intended to be used in thermal problems and their respective equilibrium distributions are presented and discussed

field theoretic approaches to biconnectedness in percolating systems two field theoretic formulations for the percolation problem are presented from which the critical exponents describing the backbone of the infinite cluster at the percolation threshold are obtained at high spatial dimension d the order parameter exponent for the backbone beta 2 is given by beta 2 2 beta psi 2 nu where beta is the critical exponent for the density of the infinite cluster and psi 2 is a new crossover exponent in mean field theory psi 2 0 and for d 6 epsilon psi 2 2 epsilon 2 49 o epsilon 3 presumably psi 2 d is a smooth function of d for d d where numerical and theoretical work indicates that d is about 3 the result indicates that the fractal dimensionality of the backbone is given in terms of the percolation exponents as gamma nu psi 2

the transport exponent in percolation models with additional loops abstract several percolation models with additional loops were studied the transport exponents for these models were estimated numerically by means of a transfer matrix approach it was found that the transport exponent has a drastically changed value for some of the models this result supports some previous numerical studies on the vibrational properties of similar models with additional loops