information loss in coarse graining of stochastic particle dynamics recently a new class of approximating coarse grained stochastic processes and associated monte carlo algorithms were derived directly from microscopic stochastic lattice models for the adsorption desorption and diffusion of interacting particles 12 13 15 the resulting hierarchy of stochastic processes is ordered by the level of coarsening in the space time dimensions and describes mesoscopic scales while retaining a significant amount of microscopic detail on intermolecular forces and particle fluctuations here we rigorously compute in terms of specific relative entropy the information loss between non equilibrium exact and approximating coarse grained adsorption desorption lattice dynamics our result is an error estimate analogous to rigorous error estimates for finite element finite difference approximations of partial differential equations we prove this error to be small as long as the level of coarsening is small compared to the range of interaction of the microscopic model this result gives a first mathematical reasoning for the parameter regimes for which approximating coarse grained monte carlo algorithms are expected to give errors within a given tolerance

the nearness problems for symmetric matrix with a submatrix constraint in this paper we first give the representation of the general solution of the following least squares problem lsp given a matrix email protected r n x p and symmetric matrices email protected r p x p a email protected r r x r find an nxn symmetric matrix a such that x email protected min s t a 1 r a 0 where a 1 r is the rxr leading principal submatrix of the matrix a we then consider a best approximation problem given an nxn symmetric matrix email protected with email protected 1 r a 0 find email protected s e such that email protected email protected min a s email protected email protected email protected where s e is the solution set of lsp we show that the best approximation solution email protected is unique and derive an explicit formula for it

optimal prediction with memory abstract optimal prediction methods estimate the solution of nonlinear time dependent problems when that solution is too complex to be fully resolved or when data are missing the initial conditions for the unresolved components of the solution are drawn from a probability distribution and their effect on a small set of variables that are actually computed is evaluated via statistical projection the formalism resembles the projection methods of irreversible statistical mechanics supplemented by the systematic use of conditional expectations and new methods of solution for an auxiliary equation the orthogonal dynamics equation needed to evaluate a non markovian memory term the result of the computations is close to the best possible estimate that can be obtained given the partial data we present the constructions in detail together with several useful variants provide simple examples and point out the relation to the fluctuation dissipation formulas of statistical physics

optimal prediction and the rate of decay for solutions of the euler equations in two and three dimensions the t model for dimensional reduction is applied to the estimation of the rate of decay of solutions of the burgers equation and of the euler equations in two and three space dimensions the model was first derived in a statistical mechanics context but here we analyze it purely as a numerical tool and prove its convergence in the burgers case the model captures the rate of decay exactly as was previously shown for the euler equations in two space dimensions the model preserves energy as it should in three dimensions we find a power law decay in time and observe a temporal intermittency

non inner amenability of the thompson groups t and v abstract in this paper we prove that the thompson groups t and v are not inner amenable in particular their group von neumann algebras do not have property moreover we prove that if the reduced group c algebra of t is simple then the thompson group f is non amenable furthermore we give a few new equivalent characterizations of amenability of f

a multiscale coupling method for the modeling of dynamics of solids with application to brittle cracks we present a multiscale model for numerical simulations of dynamics of crystalline solids the method combines the continuum nonlinear elasto dynamics model which models the stress waves and physical loading conditions and molecular dynamics model which provides the nonlinear constitutive relation and resolves the atomic structures near local defects the coupling of the two models is achieved based on a general framework for multiscale modeling the heterogeneous multiscale method hmm we derive an explicit coupling condition at the atomistic continuum interface application to the dynamics of brittle cracks under various loading conditions is presented as test examples

an approximate orthogonal decomposition method for the solution of generalized liouville equations abstract an analytical numerical integration method for the generalized liouville equation t f q p t l f q p t is proposed and analyzed taking into account a cauchy condition f q p t t 0 f 0 q p for the phase space distribution function we constructed the problem solution as series expansion in time variable t using orthogonal polynomials and hermite function also we proved the corresponding convergence theorems under certain boundedness conditions upon a liouville operator

synthetic turbulence fractal interpolation and large eddy simulation fractal interpolation has been proposed in the literature as an efficient way to construct closure models for the numerical solution of coarse grained navier stokes equations it is based on synthetically generating a scale invariant subgrid scale field and analytically evaluating its effects on large resolved scales in this paper we propose an extension of previous work by developing a multiaffine fractal interpolation scheme and demonstrate that it preserves not only the fractal dimension but also the higher order structure functions and the non gaussian probability density function of the velocity increments extensive a priori analyses of atmospheric boundary layer measurements further reveal that this multiaffine closure model has the potential for satisfactory performance in large eddy simulations the pertinence of this newly proposed methodology in the case of passive scalars is also discussed

the drazin inverse of an even order tensor and its application to singular tensor equations abstract the notion of the moore penrose inverses of matrices was recently extended from matrix space to even order tensor space with einstein product in the literature in this paper we further study the properties of even order tensors with einstein product we define the index and characterize the invertibility of an even order square tensor we also extend the notion of the drazin inverse of a square matrix to an even order square tensor an expression for the drazin inverse through the core nilpotent decomposition for a tensor of even order is obtained as an application the drazin inverse solution of the singular linear tensor equation a x b will also be included

a nonequilibrium statistical model of spectrally truncated burgers hopf dynamics exact spectral truncations of the unforced inviscid burgers hopf equation are hamiltonian systems with many degrees of freedom that exhibit intrinsic stochasticity and coherent scaling behavior for this reason recent studies have employed these systems as prototypes to test stochastic mode reduction strategies in the present paper the burgers hopf dynamics truncated to n fourier modes is treated by a new statistical model reduction technique and a closed system of evolution equations for the mean values of the m lowest modes is derived for m n in the reduced model the m mode macrostates are associated with trial probability densities on the phase space of the n mode microstates and a cost functional is introduced to quantify the lack of fit of paths of these densities to the liouville equation the best fit macrodynamics is obtained by minimizing the cost functional over paths and the equations governing the closure are then derived from hamilton jacobi theory the resulting reduced equations have a fractional diffusion and modified nonlinear interactions and the explicit form of both are determined up to a single closure parameter the accuracy and range of validity of this nonequilibrium closure is assessed by comparison against direct numerical simulations of statistical ensembles and the predicted behavior is found to be well represented by the reduced equations 2014 wiley periodicals inc

equation free modelling of evolving diseases coarse grained computations with individual based models we demonstrate how direct simulation of stochastic individualbased models can be combined with continuum numericalanalysis techniques to study the dynamics of evolving diseases sidestepping the necessity of obtaining explicit populationlevel models the approach analyses the unavailable in closed form coarse macroscopic equations estimating the necessary quantities through appropriately initialized short bursts of individualbased dynamic simulation we illustrate this approach by analysing a stochastic and discrete model for the evolution of disease agents caused by point mutations within individual hosts building up from classical susceptibleinfectedrecovered and susceptibleinfectedrecoveredsusceptible models our example uses a onedimensional lattice for variant space and assumes a finite number of individuals macroscopic computational tasks enabled through this approach include stationarystate computation coarse projective integration parametric continuation and stability analysis

fitting sde models to nonlinear kac zwanzig heat bath models we study a class of particle in a heat bath models which are a generalization of the well known kac zwanzig class of models but where the coupling between the distinguished particle and the n heat bath particles is through nonlinear springs the heat bath particles have random initial data drawn from an equilibrium gibbs density the primary objective is to approximate the forces exerted by the heat bath which we do not want to resolve by a stochastic process by means of the central limit theorem for gaussian processes and heuristics based on linear response theory we demonstrate conditions under which it is natural to expect that the trajectories of the distinguished particle can be weakly approximated as n by the solution of a markovian sde the quality of this approximation is verified by numerical calculations with parameters chosen according to the linear response theory alternatively the parameters of the effective equation can be chosen using time series analysis this is done and agreement with linear response theory is shown to be good

a restarted krylov subspace method for the evaluation of matrix functions we show how the arnoldi algorithm for approximating a function of a matrix times a vector can be restarted in a manner analogous to restarted krylov subspace methods for solving linear systems of equations the resulting restarted algorithm reduces to other known algorithms for the reciprocal and the exponential functions we further show that the restarted algorithm inherits the superlinear convergence property of its unrestarted counterpart for entire functions and present the results of numerical experiments

the generalized inverses of tensors and an application to linear models abstract in this paper we recall and extend some tensor operations then the generalized inverse of tensors is established by using tensor equations moreover we investigate the least squares solutions of tensor equations an algorithm to compute the moore penrose inverse of an arbitrary tensor is constructed finally we apply the obtained results to higher order gauss markov theorem

further results on moore penrose inverses of tensors with application to tensor nearness problems abstract the notion of the moore penrose inverse of a matrix has been extended to tensor case with einstein product recently in this paper we continue this work and propose the full rank decomposition of tensors by introducing a new kind of tensor rank which gives a novel representation of the moore penrose inverse moreover we also obtain several formulae related to the moore penrose inverse of a tensor and its i j k inverses in addition we consider the tensor nearness problem associated with a tensor equation a generalization of matrix nearness problems that arise in many areas of applied matrix computations it is shown that the unique solution to the tensor nearness problem can be represented by using the moore penrose inverses of the given tensors

adaptive spacetime method using riemann jump conditions for coupled atomistic continuum dynamics abstract we combine the spacetime discontinuous galerkin sdg method for elastodynamics with the mathematically consistent atomistic discontinuous galerkin adg method in a new scheme that concurrently couples continuum and atomistic models of dynamic response in solids the formulation couples non overlapping continuum and atomistic models across sharp interfaces by weakly enforcing jump conditions for both momentum balance and kinematic compatibility using riemann values to preserve the characteristic structure of the underlying hyperbolic system momentum balances to within machine precision accuracy over every element on each atom and over the coupled system with small controllable energy dissipation in the continuum region that ensures numerical stability when implemented on suitable unstructured spacetime grids the continuum sdg model offers linear computational complexity in the number of elements and powerful adaptive analysis capabilities that readily bridge between atomic and continuum scales in both space and time a special trace operator for the atomic velocities and an associated atomistic traction field enter the jump conditions at the coupling interface the trace operator depends on parameters that specify at the scale of the atomic spacing the position of the coupling interface relative to the atoms in a key finding we demonstrate that optimizing these parameters suppresses spurious reflections at the coupling interface without the use of non physical damping or special boundary conditions we formulate the implicit sdg adg coupling scheme in up to three spatial dimensions and describe an efficient iterative solution scheme that outperforms common explicit schemes such as the velocity verlet integrator numerical examples in 1 d time and employing both linear and nonlinear potentials demonstrate the performance of the sdg adg method and show how adaptive spacetime meshing reconciles disparate time steps and resolves atomic scale signals in the continuum

fractal model for coarse grained nonlinear partial differential equations spatially coarse grained or effective versions of nonlinear partial differential equations must be closed with a model for the unresolved small scales for systems that are known to display fractal scaling we propose a model based on synthetically generating a scale invariant field at small scales using fractal interpolation and then analytically evaluating its effects on the large resolved scales the procedure is illustrated for the forced burgers equation solved numerically on a coarse grid detailed comparisons with direct simulation of the full burgers equation and with an effective viscosity model are presented s0031 9007 96 02215 6

synthetic turbulence constructed by spatially randomized fractal interpolation a spatially randomized fractal interpolation algorithm to construct synthetic fields with statistical properties close to real turbulence is proposed it improves the previous works on fractal interpolation so that the position mapping between large and small scales is chosen randomly and the stretching factors are drawn from any chosen random multiplier model in particular using different parameters of log poisson model synthetic fields with absolute scaling properties close to sl94 model for fully developed turbulence k41 model and mb2000 model for magnetohydrodynamic turbulence are obtained respectively to model real turbulence fields which do not obey absolute scaling laws but ess scaling laws a refined technique is added it is shown that both the velocity structure functions and the moments of subgrid scale stress can be precisely predicted when the scale invariance is broken

optimal prediction of underresolved dynamics abstract a method is presented for computing the average solution of problems that are too complicated for adequate resolution but where information about the statistics of the solution is available the method involves computing average derivatives by interpolation based on linear regression and an updating of a measure constrained by the available crude information examples are given

a comparative study of two stochastic mode reduction methods abstract we present a comparative study of two methods for the reduction of the dimensionality of a system of ordinary differential equations that exhibits time scale separation both methods lead to a reduced system of stochastic differential equations the novel feature of these methods is that they allow the use in the reduced system of higher order terms in the resolved variables the first method proposed by majda timofeyev and vanden eijnden is based on an asymptotic strategy developed by kurtz the second method is a short memory approximation of the mori zwanzig projection formalism of irreversible statistical mechanics as proposed by chorin hald and kupferman we present conditions under which the reduced models arising from the two methods should have similar predictive ability we apply the two methods to test cases that satisfy these conditions the form of the reduced models and the numerical simulations show that the two methods have similar predictive ability as expected

analysis of multiscale methods for stochastic differential equations we analyze a class of numerical schemes proposed in 26 for stochastic differential equations with multiple time scales both advective and diffusive time scales are considered weak as well as strong convergence theorems are proven most of our results are optimal they in turn allow us to provide a thorough discussion on the efficiency as well as optimal strategy for the method c 2005 wiley periodicals inc

coarse projective kmc integration forward reverse initial and boundary value problems in equation free multiscale computation a dynamic model is given at a fine microscopic level yet we believe that its coarse grained macroscopic dynamics can be described by closed equations involving only coarse variables these variables are typically various low order moments of the distributions evolved through the microscopic model we consider the problem of integrating these unavailable equations by acting directly on kinetic monte carlo microscopic simulators thus circumventing their derivation in closed form in particular we use projective multi step integration to solve the coarse initial value problem forward in time as well as backward in time under certain conditions macroscopic trajectories are thus traced back to unstable source type and even sometimes saddle like stationary points even though the microscopic simulator only evolves forward in time we also demonstrate the use of such projective integrators in a shooting boundary value problem formulation for the computation of coarse limit cycles of the macroscopic behavior and the approximation of their stability through estimates of the leading coarse floquet multipliers

modeling turbulent flow over fractal trees with renormalized numerical simulation high reynolds number flow over tree like fractals is considered with emphasis on the drag forces produced fractal objects display large scale disparity and complexity while being amenable to a simple and standardized description hence they offer an elegant idealization of the actual boundaries in practical applications where turbulence interacts with boundaries that are characterized by multiple length scales first using large eddy simulation of flow over prefractal shapes with increasing numbers of branch generations the dependence of the tree drag on the inner cutoff scale of the fractal is studied it is found that the convergence of the drag coefficient towards a value that is independent of inner cutoff scale is very slow in order to address this fundamental difficulty and avoid the need to resolve all the small scale branches of the fractal a new numerical modeling technique called renormalized numerical simulation rns is introduced rns models the drag of the unresolved branches using drag coefficients measured from both resolved branches and unresolved branches as modeled in previous iterations of the procedure the rns technique and its convergence properties are tested by means of a series of simulations using different levels of resolution then rns is used to investigate the influence of the tree fractal dimension on the drag coefficient the increase of the drag with fractal dimension is quantified for two types of tree geometry in two flow configurations results illustrate that rns enables numerical modeling of physical processes associated with fractal geometries using affordable computational resolution

tensor decompositions and applications this survey provides an overview of higher order tensor decompositions their applications and available software a tensor is a multidimensional or n way array decompositions of higher order tensors i e n way arrays with n geq 3 have applications in psycho metrics chemometrics signal processing numerical linear algebra computer vision numerical analysis data mining neuroscience graph analysis and elsewhere two particular tensor decompositions can be considered to be higher order extensions of the matrix singular value decomposition candecomp parafac cp decomposes a tensor as a sum of rank one tensors and the tucker decomposition is a higher order form of principal component analysis there are many other tensor decompositions including indscal parafac2 candelinc dedicom and paratuck2 as well as nonnegative variants of all of the above the n way toolbox tensor toolbox and multilinear engine are examples of software packages for working with tensors

computing a nearest symmetric positive semidefinite matrix the nearest symmetric positive semidefinite matrix in the frobenius norm to an arbitrary real matrix a is shown to be b h 2 where h is the symmetric polar factor of b a at 2 in the 2 norm a nearest symmetric positive semidefinite matrix and its distance 2 a from a are given by a computationally challenging formula due to halmos we show how the bisection method can be applied to this formula to compute upper and lower bounds for 2 a differing by no more than a given amount a key ingredient is a stable and efficient test for positive definiteness based on an attempted choleski decomposition for accurate computation of 2 a we formulate the problem as one of zero finding and apply a hybrid newton bisection algorithm some numerical difficulties are discussed and illustrated by example

homology and topological full groups of etale groupoids on totally disconnected spaces for almost finite groupoids we study how their homology groups reflect dynamical properties of their topological full groups it is shown that two clopen subsets of the unit space has the same class in h0 if and only if there exists an element in the topological full group which maps one to the other it is also shown that a natural homomorphism called the index map from the topological full group to h1 is surjective and any element of the kernel can be written as a product of four elements of finite order in particular the index map induces a homomorphism from h1 to k1 of the groupoid c algebra explicit computations of homology groups of af groupoids and etale groupoids arising from subshifts of finite type are also given

unresolved computation and optimal predictions we present methods for predicting the solution of time dependent partial differential equations when that solution is so complex that it cannot be properly resolved numerically but when prior statistical information can be found the sparse numerical data are viewed as constraints on the solution and the gist of our proposal is a set of methods for advancing the constraints in time so that regression methods can be used to reconstruct the mean future for linear equations we offer general recipes for advancing the constraints the methods are generalized to certain classes of nonlinear problems and the conditions under which strongly nonlinear problems and partial statistical information can be handled are briefly discussed our methods are related to certain data acquisition schemes in oceanography and meteorology c 1999 john wiley sons inc

convergence of optimal prediction for nonlinear hamiltonian systems optimal prediction is a computational method for systems that cannot be properly resolved in which the unresolved variables are viewed as random this paper presents a first analysis of optimal prediction as a numerical method we prove the convergence of the scheme for a class of equations of schrodinger type and derive error bounds for the mean error between the optimal prediction solution and the set of exact solutions with random initial data it is shown that optimal prediction is the scheme that minimizes the mean truncation error

optimal prediction for hamiltonian partial differential equations optimal prediction methods compensate for a lack of resolution in the numerical solution of time dependent differential equations through the use of prior statistical information we present a new derivation of the basic methodology show that field theoretical perturbation theory provides a useful device for dealing with quasi linear problems and provide a nonlinear example that illuminates the difference between a pseudo spectral method and an optimal prediction method with fourier kernels along the way we explain the differences and similarities between optimal prediction the representer method in data assimilation and duality methods for finding weak solutions we also discuss the conditions under which a simple implementation of the optimal prediction method can be expected to perform well

the inverse rank and product of tensors abstract in this paper we give some basic properties for the left right inverse rank and product of tensors the existence of order 2 left right inverses of tensors is characterized we obtain some equalities and inequalities on the tensor rank we also show that the rank of a uniform hypergraph is independent of the ordering of its vertices and the laplacian tensor and the signless laplacian tensor have the same rank for odd bipartite even uniform hypergraphs

asymptotic and numerical analyses for mechanical models of heat baths a mechanical model of a particle immersed in a heat bath is studied in which a distinguished particle interacts via linear springs with a collection of n particles with variable masses and random initial conditions the jth particle oscillates with frequency jp where p is a parameter for p 1 2 the sequence of random processes that describe the trajectory of the distinguished particle tends almost surely as n to the solution of an integro differential equation with a random driving term the mean convergence rate is 1 np 1 2 we further investigate whether the motion of the distinguished particle can be well approximated by an integration scheme the symplectic euler scheme when the product of time step h and highest frequency np is of order 1 that is when high frequencies are underresolved for 1 2 p 1 the numerical solution is found to converge to the exact solution at a reduced rate of log h h2 1 p these results shed light on existing numerical data

fourth order cumulant based blind identification of underdetermined mixtures in this paper we study two fourth order cumulant based techniques for the estimation of the mixing matrix in underdetermined independent component analysis the first method is based on a simultaneous matrix diagonalization the second is based on a simultaneous off diagonalization the number of sources that can be allowed is roughly quadratic in the number of observations for both methods explicit expressions for the maximum number of sources are given simulations illustrate the performance of the techniques

a fractal model for large eddy simulation of turbulent flow abstract a new class of subgrid closures for large eddy simulation les of turbulence is developed based on the construction of synthetic fractal subgrid scale fields the relevant mathematical tool fractal interpolation allows to interpolate the resolved velocity with fields that have fluctuations down to much smaller scales and to compute the required stresses explicitly in one dimension the approach is used in the context of the coarse grained burgers equation then fractal interpolation is extended to three dimensions and is used to formulate a subgrid model for the filtered navier stokes equations the model is applied to les of both steady and freely decaying isotropic turbulence we find that the assumption of fractality per se is not enough to yield physically meaningful results and we explore several variants of the model in which the rules to generate the synthetic fields explicitly incorporate the condition that energy dissipation take place in one dimension this is accomplished by means of an additional transport equation that allows to dynamically determine the fractal dimension in three dimensions good results are obtained only once the fractal dimension is allowed to vary in different eigendirections of the resolved strain rate tensor so as to nearly maximize energy dissipation

a generalized space time mathematical homogenization theory for bridging atomistic and continuum scales a generalized space time mathematical homogenization theory which constructs an equivalent continuum description directly from molecular dynamics md equations is developed the noteworthy theoretical findings of this work are i the coarse scale continuum equations pdes obtained from the homogenization of md equations are identical to those obtained from the classical homogenization of the fine scale continuum ii the lower order effective continuum properties such as the fourth order elasticity tensor have similar characteristics to those resulting from the homogenization of fine scale continuum iii the higher order effective properties such as polarization and dispersion tensors substantially differ from those of continuum due to the discreteness effect both the heterogeneous continuum and discrete media possess the size effect but only atomistic medium has the discreteness effect some demonstrative numerical examples are presented to verify the formulation copyright 2005 john wiley sons ltd

nonlinear manifold learning for model reduction in finite elastodynamics abstract model reduction in computational mechanics is generally addressed with linear dimensionality reduction methods such as principal components analysis pca hypothesizing that in many applications of interest the essential dynamics evolve on a nonlinear manifold we explore here reduced order modeling based on nonlinear dimensionality reduction methods such methods are gaining popularity in diverse fields of science and technology such as machine perception or molecular simulation we consider finite deformation elastodynamics as a model problem and identify the manifold where the dynamics essentially take place the slow manifold by nonlinear dimensionality reduction methods applied to a database of snapshots contrary to linear dimensionality reduction the smooth parametrization of the slow manifold needs special techniques and we use local maximum entropy approximants we then formulate the lagrangian mechanics on these data based generalized coordinates and develop variational time integrators our proof of concept example shows that a few nonlinear collective variables provide similar accuracy to tens of pca modes suggesting that the proposed method may be very attractive in control or optimization applications furthermore the reduced number of variables brings insight into the mechanics of the system under scrutiny our simulations also highlight the need of modeling the net effect of the disregarded degrees of freedom on the reduced dynamics at long times

three dimensional synthetic turbulence constructed by spatially randomized fractal interpolation a spatially randomized fractal interpolation algorithm to construct three dimensional synthetic turbulence from original coarse field is reported as in the one dimensional case by ding et al phys rev e 82 036311 2010 during the fractal interpolation positions mapping between large and small scale cubes are chosen randomly and the stretching factors are drawn from a log poisson random multiplicative process a linear combination function defined as the base part in fractal interpolation and a theoretical energy spectrum model for fully developed turbulence are introduced into the procedure statistical analysis shows that the synthetic field displays some properties very close to the direct numeric simulated field such as probability distributions of velocity velocity gradient velocity increment and the anomalous scaling behavior of the longitude velocity structure functions which follows the sl94 model precisely after a short time using direct numeric simulation with the synthetic field as initial data the typical local dynamical structures described by the teardrop shape of the q r plane for empirical turbulence can be reproduced

cantor systems piecewise translations and simple amenable groups we provide the rst examples of nitely generated simple groups that are amenable and innite to this end we prove that topological full groups of minimal systems are amenable this follows from a general existence result on invariant states for piecewise translations of the integers the states are obtained by constructing a suitable family of densities on the classical bernoulli space

regularization matrices determined by matrix nearness problems abstract this paper is concerned with the solution of large scale linear discrete ill posed problems with error contaminated data tikhonov regularization is a popular approach to determine meaningful approximate solutions of such problems the choice of regularization matrix in tikhonov regularization may significantly affect the quality of the computed approximate solution this matrix should be chosen to promote the recovery of known important features of the desired solution such as smoothness and monotonicity we describe a novel approach to determine regularization matrices with desired properties by solving a matrix nearness problem the constructed regularization matrix is the closest matrix in the frobenius norm with a prescribed null space to a given matrix numerical examples illustrate the performance of the regularization matrices so obtained

variational boundary conditions for molecular dynamics simulations treatment of the loading condition this paper aims to extend the variational boundary conditions for molecular dynamics simulation x li w e variational boundary conditions for molecular dynamics simulations of solids at low temperature commun comp phys 1 2006 136 176 x li w e boundary conditions for molecular dynamics simulations at finite temperature treatment of the heat bath phys rev b 76 2007 104107 to take into account external loading conditions two derivations of the exact boundary conditions are presented one with mori zwanzig projection procedure and the other using lattice green s functions approximate boundary conditions which are more efficient in practice are then discussed finally several numerical experiments are presented to demonstrate the effectiveness of these methods

on the convergence of galerkin approximation schemes for second order hyperbolic equations in energy and negative norms given certain semidiscrete and single step fully discrete galerkin approximations to the solution of an initial boundary value problem for a second order hyperbolic equation h and l2 error estimates are obtained these estimates are valid simultaneously when the approximation to the initial data is taken to be the projection onto the approximating space with respect to the inner product which induces the energy norm that is naturally associated with the problem the l2 estimate is obtained as a by product of the analysis of convergence in certain negative norms estimates are also obtained for the convergence of higher order time derivatives in the presence of sufficiently smooth data

high order contrasts for independent component analysis this article considers high order measures of independence for the independent component analysis problem and discusses the class of jacobi algorithms for their optimization several implementations are discussed we compare the proposed approaches with gradient based techniques from the algorithmic point of view and also on a set of biomedical data

error analysis of coarse graining for stochastic lattice dynamics the coarse grained monte carlo cgmc algorithm was originally proposed in the series of works m a katsoulakis a j majda and d g vlachos j comput phys 186 2003 pp 250 278 m a katsoulakis a j majda and d g vlachos proc natl acad sci usa 100 2003 pp 782 787 m a katsoulakis and d g vlachos j chem phys 119 2003 pp 9412 9427 in this paper we further investigate the approximation properties of the coarse graining procedure and provide both analytical and numerical evidence that the hierarchy of the coarse models is built in a systematic way that allows for error control in both transient and long time simulations we demonstrate that the numerical accuracy of the cgmc algorithm as an approximation of stochastic lattice spin flip dynamics is of order two in terms of the coarse graining ratio and that the natural small parameter is the coarse graining ratio over the range of particle particle interactions the error estimate is shown to hold in the weak convergence sense we employ the derived analytical results to guide cgmc algorithms and demonstrate a cpu speed up in demanding computational regimes that involve nucleation phase transitions and metastability

third order tensors as linear operators on a space of matrices abstract a recently proposed tensor tensor multiplication m e kilmer c d martin l perrone a third order generalization of the matrix svd as a product of third order tensors tech rep tr 2008 4 tufts university october 2008 opens up new avenues to understanding the action of n n n tensors on a space of n n matrices in particular it emphasizes the need to understand the space of objects upon which tensors act this paper defines a free module and shows that every linear transformation on that module can be represented by tensor multiplication in addition it presents a generalization of ideas of eigenvalue and eigenvector to the space of n n n tensors

wavelets and quantum algebras wavelets known to be useful in nonlinear multiscale processes and in multiresolution analysis are shown to have a q deformed algebraic structure the translation and dilation operators associate to any scaling equation a nonlinear two parameter algebra this structure can be mapped onto the quantum group slq 2 in one limit and approaches a fourier series generating algebra in another limit a duality between any scaling function and its corresponding nonlinear algebra is obtained examples for the haar and b wavelets are worked out in detail

c simplicity and representations of topological full groups of groupoids abstract given an ample groupoid g with compact unit space we study the canonical representation of the topological full group g in the full groupoid c algebra c g in particular we show that the image of this representation generates c g if and only if c g admits no tracial state the techniques that we use include the notion of groups covering groupoids as an application we provide sufficient conditions for c simplicity of certain topological full groups including those associated with topologically free and minimal actions of non amenable and countable groups on the cantor set

topological full groups of one sided shifts of finite type we explore the topological full group g of an essentially principal etale groupoid g on a cantor set when g is minimal we show that g and its certain normal subgroup is a complete invariant for the isomorphism class of the etale groupoid g furthermore when g is either almost finite or purely infinite the commutator subgroup d g is shown to be simple the etale groupoid g arising from a onesided irreducible shift of finite type is a typical example of a purely infinite minimal groupoid for such g g is thought of as a generalization of the higman thompson group we prove that g is of type f and so in particular it is finitely presented this gives us a new infinite family of finitely presented infinite simple groups also the abelianization of g is calculated and described in terms of the homology groups of g

coarse graining molecular dynamics models using an extended galerkin projection method summary we present a new framework for coarse graining molecular dynamics models for crystalline solids the reduction method is based on a galerkin projection to a subspace whose dimension is much smaller than that of the full atomistic model to effectively reduce artificial reflections of phonons at the interface we construct extended subspaces with increasing accuracy by adding more coarse grained variables near the interface between lattice defects and the surrounding region this approach is equivalent to the generalized langevin model but it eliminates the need to precompute the memory function a well known practical difficulty further the variational formulation preserves the stability of the molecular models copyright 2014 john wiley sons ltd