blending the eddy viscosity and reynolds stress models using uniform high order discretization accuracy robustness and efficiency are the three major goals of turbulence closure generally eddy viscosity models evms with the boussinesq approximation are numerically stable and efficient

a finite dimensional approximation of the effective diffusivity for a symmetric random walk in a random environment we consider a nearest neighbor symmetric random walk on a homogeneous ergodic random lattice z d the jump rates of the walk are independent identically bernoulli distributed random variables indexed by the bonds of the lattice a standard result from the homogenization theory see a de masi p a ferrari s goldstein w d wick an invariance principle for reversible markov processes applications to random walks in random environments j statist phys 55 3 4 1989 787 855 asserts that the scaled trajectory of the particle satisfies the functional central limit theorem the covariance matrix of the limiting normal distribution is called the effective diffusivity of the walk we use the duality structure corresponding to the product bernoulli measure to construct a numerical scheme that approximates this parameter when d 3 the estimates of the convergence rates are also provided

convergence analyses of galerkin least squares methods for symmetric advective diffusive forms of the stokes and incompressible navier stokes equations abstract symmetric advective diffusive forms of the stokes and incompressible navier stokes equations are presented the galerkin least squares method for advective diffusive equations is used for both systems and is related to other stabilized methods previously studied the presentation reveals that the convergence analysis for advective diffusive equations as applied before to a linearized form of the compressible navier stokes equations carries over in a straightforward manner to the stokes problem and to a linearized form of the incompressible navier stokes equations

normal approximation for a random elliptic equation we consider solutions of an elliptic partial differential equation in mathbb r d with a stationary random conductivity coefficient that is also periodic with period l boundary conditions on a square domain of width l are arranged so that the solution has a macroscopic unit gradient we then consider the average flux that results from this imposed boundary condition it is known that in the limit l rightarrow infty this quantity converges to a deterministic constant almost surely our main result is that the law of this random variable is very close to that of a normal random variable if the domain size l is large we quantify this approximation by an error estimate in total variation the error estimate relies on a second order poincare inequality developed recently by chatterjee

an invariance principle for non symmetric markov processes and reflecting diffusions in random domains we study an invariance principle for additive functionals of nonsymmetric markov processes with singular mean forward velocities we generalize results of kipnis and varadhan kv and de masi et al de in two directions markov processes are non symmetric and mean forward velocities are distributions we study continuous time markov processes we use our result to homogenize non symmetric reflecting diffusions in random domains

diffusion in turbulence we prove long time diffusive behavior homogenization for convection diffusion in a turbulent flow that it incompressible and has a stationary and square integrable stream matrix simple shear flow examples show that this result is sharp for flows that have stationary stream matrices

integer forcing linear receivers linear receivers are often used to reduce the implementation complexity of multiple antenna systems in a traditional linear receiver architecture the receive antennas are used to separate out the codewords sent by each transmit antenna which can then be decoded individually although easy to implement this approach can be highly suboptimal when the channel matrix is near singular this paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer valued entries rather than attempting to recover transmitted codewords directly the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix the codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords provided that the effective channel is full rank these integer combinations can then be digitally solved for the original codewords this paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter s which corresponds either to a multiuser uplink scenario or to single user v blast encoding in this setting the proposed integer forcing linear receiver significantly outperforms conventional linear architectures such as the zero forcing and linear minimum mean squared error receiver in the high signal to noise ratio regime the proposed receiver attains the optimal diversity multiplexing tradeoff for the standard multiple input multiple output mimo channel with no coding across transmit antennas it is further shown that in an extended mimo model with interference the integer forcing linear receiver achieves the optimal generalized degrees of freedom

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

adaptive finite element solution of compressible turbulent flows an adaptive e nite element method for solving compressible turbulent e ows up to transonic regime is presented pressure based methods previously developed for laminar compressible e ows and turbulent incompressible e ows are combined to solve compressible turbulent e ows turbulence is incorporated via the k model the algorithm uses the logarithms of k and as computational variables to preserve positivity solutionsare obtained in primitive variables using quadratic e nite elements on unstructured grids the error is estimated by a local projection method the solution algorithm and error estimation are validated on problems with known analytical solutions the method is then applied to compressible subsonic and transonic e ows and predictions are compared with experimental measurements

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

compute and forward harnessing interference through structured codes interference is usually viewed as an obstacle to communication in wireless networks this paper proposes a new strategy compute and forward that exploits interference to obtain significantly higher rates between users in a network the key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise after decoding these linear equations the relays simply send them towards the destinations which given enough equations can recover their desired messages the underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field this scheme is applicable even if the transmitters lack channel state information

central limit theorem for additive functionals of reversible markov processes and applications to simple exclusions we prove a functional central limit theorem for additive functionals of stationary reversible ergodic markov chains under virtually no assumptions other than the necessary ones we use these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk

large deviations and concentration properties for ϕ interface models we consider the massless field with zero boundary conditions outside d n d d n n d a suitable subset of d i e the continuous spin gibbs measure n on d n with hamiltonian given by h x y x y 1 v x y and x 0 for x d n c the interaction v is taken to be strictly convex and with bounded second derivative this is a standard effective model for a d 1 dimensional interface represents the height of the interface over the base d n due to the choice of scaling of the base we scale the height with the same factor by setting n n we study various concentration and relaxation properties of the family of random surfaces n and of the induced family of gradient fields n n as the discretization step 1 n tends to zero n in particular we prove a large deviation principle for n and show that the corresponding rate function is given by d u x dx where is the surface tension of the model this is a multidimensional version of the sample path large deviation principle we use this result to study the concentration properties of n under the volume constraint i e the constraint that 1 n d x dn n x stays in a neighborhood of a fixed volume v 0 and the hard wall constraint i e n x 0 for all x this is therefore a model for a droplet of volume v lying above a hard wall we prove that under these constraints the field n of rescaled heights concentrates around the solution of a variational problem involving the surface tension as it would be predicted by the phenomenological theory of phase boundaries our principal result however asserts local relaxation properties of the gradient field n n to the corresponding extremal gibbs states thus our approach has little in common with traditional large deviation techniques and is closer in spirit to hydrodynamic limit type of arguments the proofs have both probabilistic and analytic aspects essential analytic tools are p estimates for elliptic equations and the theory of young measures on the side of probability tools a central role is played by the helffer sjostrand 31 pde representation for continuous spin systems which we rewrite in terms of random walk in random environment and by recent results of t funaki and h spohn 25 on the structure of gradient fields

the capacity region of the l user gaussian inverse compute and forward problem we consider an l user multiple access channel where transmitter m has access to the linear equation text u m bigoplus l 1 l f ml text w l of independent messages text w l in mathbb f p k l with f ml in mathbb f p and the destination wishes to recover all l messages this problem may be motivated as the last hop in a network where relay nodes employ the compute and forward strategy and decode linear equations of messages we seek to do the reverse and extract messages from sums over a multiple access channel in particular we exploit the particular form of dependencies between the equations at the different relays to improve the reliable communication rates beyond those achievable by simply forwarding all equations to the destination independently the presented achievable rate region for the discrete memoryless channel model is shown to be capacity for the additive white gaussian noise channel

equilibrium fluctuations for nabla_ varphi interface model we study the large scale space time fluctuations of an interface which is modeled by a massless scalar field with reversible langevin dynamics for a strictly convex interaction potential we prove that on a large space time scale these fluctuations are governed by an infinite dimensional ornstein uhlenbeck process its effective diffusion type covariance matrix is characterized through a variational formula

quantification of ergodicity in stochastic homogenization optimal bounds via spectral gap on glauber dynamics we study quantitatively the effective large scale behavior of discrete elliptic equations on the lattice mathbb z d with random coefficients the theory of stochastic homogenization relates the random stationary and ergodic field of coefficients with a deterministic matrix of effective coefficients this is done via the corrector problem which can be viewed as a highly degenerate elliptic equation on the infinite dimensional space of admissible coefficient fields in this contribution we develop new quantitative methods for the corrector problem based on the assumption that ergodicity holds in the quantitative form of a spectral gap estimate w r t a glauber dynamics on coefficient fields as it is the case for independent and identically distributed coefficients as a main result we prove an optimal decay in time of the semigroup associated with the corrector problem i e of the generator of the process called random environment as seen from the particle as a corollary we recover existence of stationary correctors in dimensions d 2 and prove new optimal estimates for regularized versions of the corrector in dimensions d ge 2 we also give a self contained proof of a new estimate on the gradient of the parabolic variable coefficient green s function which is a crucial analytic ingredient in our approach as an application of these results we prove the first and optimal estimates for the approximation of the homogenized coefficients by the popular periodization method in case of independent and identically distributed coefficients

positivity preservation and adaptive solution for the k model of turbulence a simple change of dependent variables that guarantees positivity of turbulence variables in numerical simulation codes is presented the approach consists of solving for the natural logarithm of the turbulence variables which are known to be strictly positive the approach is valid for any numerical scheme be it finite difference a finite volume or a finite element method the work focuses on the advantages of the proposed change of dependent variables within the framework of an adaptive finite element method the turbulence equations in logarithmic variables are presented for the standard e model error estimation and mesh adaptation procedures are described the formulation is validated on a shear layer case for which an analytical solution is available this provides a framework for rigorous comparison of the proposed approach with the standard solution technique which makes use of k and e as dependent variables the approach is then applied to solve turbulent flow over a naca0012 airfoil for which experimental measurements are available the proposed procedure results in a robust adaptive algorithm improved predictions of turbulence variables are obtained using the proposed formulation

stochastic homogenization of the keller segel chemotaxis system abstract in this paper we focus on the keller segel chemotaxis system in a random heterogeneous domain we assume that the corresponding diffusion and chemotaxis coefficients are given by stationary ergodic random fields and apply stochastic two scale convergence methods to derive the homogenized macroscopic equations in establishing our results we also derive a priori estimates for the keller segel system that rely only on the boundedness of the coefficients in particular no differentiability assumption on the diffusion and chemotaxis coefficients for the chemotactic species is required finally we prove the convergence of a periodization procedure for approximating the homogenized macroscopic coefficients

long time behaviour of heat flow global estimates and exact asymptotics we obtain global upper and lower bounds on the heat kernel of an elliptic second order differential operator which become sharp in certain long time and large space asymptotics we prove a generalization of aronson s gaussian bounds which identifies correctly an effective drift for heat flow in the case of periodic coefficients we give variational characterizations of the effective conductivity which is then made to appear in heat kernel bounds these results are for heat kernels with measurable coefficients for differentiable coefficients we prove tighter estimates in which the rate of homogenization is known to be optimal

adaptive remeshing for the k epsilon model of turbulence an adaptive nite element method for solving incompressible turbulentows using the k model of turbulence is presented solutions are obtained in primitive variables using a highly accurate quadratic nite element on unstructured grids turbulence is modeled using the k model of turbulence two error estimators are presented that take into account in a rigorous way the relative importance of the errors in velocity pressure turbulence variables and eddy viscosity the ef ciency and convergence rate of the methodology are evaluated by solving problemswith known analytical solutions themethod isthen applied to turbulent free shearowsand predictions are compared to measurements nomenclature cl c1 c2 k model constants e error f body force h element size k element in the mesh k turbulent kinetic energy n outward unit vector p u production of turbulence p pressure u velocity vector

mott law as upper bound for a random walk in a random environment we consider a random walk on the support of an ergodic simple point process on mathbb r d d 2 furnished with independent energy marks the jump rates of the random walk decay exponentially in the jump length and depend on the energy marks via a boltzmann type factor this is an effective model for the phonon induced hopping of electrons in disordered solids in the regime of strong anderson localization under some technical assumption on the point process we prove an upper bound for the diffusion matrix of the random walk in agreement with mott law a lower bound for d 2 in agreement with mott law was proved in 8

the superconvergent patch recovery and a posteriori error estimates part 2 error estimates and adaptivity in this second part of the paper the issue of a posteriori error estimation is discussed in particular we derive a theorem showing the dependence of the effectivity index for the zienkiewicz zhu error estimator on the convergence rate of the recovered solution this shows that with superconvergent recovery the effectivity index tends asymptotically to unity the superconvergent recovery technique developed in the first part of the paper1 is the used in the computation of the zienkiewicz zhu error estimator to demonstrate accurate estimation of the exact error attainable numerical tests are shown for various element types illustrating the excellent effectivity of the error estimator in the energy norm and pointwise gradient stress error estimation several examples of the performance of the error estimator in adaptive mesh refinement are also presented

approximation of the effective conductivity of ergodic media by periodization this paper is concerned with the approximation of the effective conductivity a associated to an elliptic operator xa x x where for x d d 1 a x is a bounded elliptic random symmetric d d matrix and takes value in an ergodic probability space x writing an x the periodization of a x on the torus tdn of dimension d and side n we prove that for almost all we extend this result to non symmetric operators x a e x x corresponding to diffusions in ergodic divergence free flows a is d d elliptic symmetric matrix and e x an ergodic skew symmetric matrix and to discrete operators corresponding to random walks on d with ergodic jump rates

symmetric simple exclusion process regularity of the self diffusion coefficient we prove that the self diffusion coefficient of a tagged particle in the symmetric exclusion process in zd which is in equilibrium at density is of class c as a function of in the closed interval 0 1 the proof provides also a recursive method to compute the taylor expansion at the boundaries

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner