an assessment of two classes of variational multiscale methods for the simulation of incompressible turbulent flows abstract a numerical assessment of two classes of variational multiscale vms methods for the simulation of incompressible flows is presented two types of residual based vms methods and two types of projection based vms methods are included in this assessment the numerical simulations are performed at turbulent channel flow problems with various friction reynolds numbers it turns out the residual based vms methods in particular when used with a pair of inf sup stable finite elements give usually the most accurate results for second order statistics for this pair of finite element spaces a flexible gmres method with a least squares commutator lsc preconditioner proved to be an efficient solver

computation theory of cellular automata self organizing behaviour in cellular automata is discussed as a computational process formal language theory is used to extend dynamical systems theory descriptions of cellular automata the sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages many examples are given the sizes of the minimal grammars for these languages provide measures of the complexities of the sets this complexity is usually found to be non decreasing with time the limit sets generated by some classes of cellular automata correspond to regular languages for other classes of cellular automata they appear to correspond to more complicated languages many properties of these sets are then formally non computable it is suggested that such undecidability is common in these and other dynamical systems

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

an algebraic variational multiscale multigrid method for large eddy simulation of turbulent flow an algebraic variational multiscale multigrid method for large eddy simulation of turbulent flow

z transform theory and the fdtd method in implementing the finite difference time domain fdtd method on materials which are dispersive or nonlinear the relationship between the flux density and the electric field can be the most complicated part of the problem because the fdtd method is a sampled time domain method this relationship can be can be looked upon as a digital filtering problem the z transform is typically used in digital filtering and signal processing problems the paper illustrates the use of the z transform in implementing the fdtd method where complicated dispersive or nonlinear materials are involved

effects of the computational time step on numerical solutions of turbulent flow effects of large computational time steps on the computed turbulence were investigated using a fully implicit method in turbulent channel flow computations the largest computational time step in wall units which led to accurate prediction of turbulence statistics was determined turbulence fluctuations could not be sustained if the computational time step was near or larger than the kolmogorov time scale

assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows in this work we study the performance of some variational multiscale models vms in the large eddy simulation les of turbulent flows we consider vms models obtained by different subgrid scale approximations which include either static or dynamic subscales linear or nonlinear multiscale splitting and different choices of the subscale space after a brief review of these models we discuss some implementation aspects particularly relevant to the simulation of turbulent flows namely the use of a skew symmetric form of the convective term and the computation of projections when orthogonal subscales are used we analyze the energy conservation and numerical dissipation of the alternative vms formulations which is numerically evaluated in the numerical study we have considered three well known problems the decay of homogeneous isotropic turbulence the taylor green vortex problem and the turbulent flow in a channel we compare the results obtained using different vms models paying special attention to the effect of using orthogonal subscale spaces the vms results are also compared against classical les scheme based on filtering and the dynamic smagorinsky closure altogether our results show the tremendous potential of vms for the numerical simulation of turbulence further we study the sensitivity of vms to the algorithmic constants and analyze the behavior in the small time step limit we have also carried out a computational cost comparison of the different formulations out of these experiments we can state that the numerical results obtained with the different vms formulations as far as they converge are quite similar however some choices are prone to instabilities and the results obtained in terms of computational cost are certainly different the dynamic orthogonal subscales model turns out to be best in terms of efficiency and robustness

absorbing boundary conditions for difference approximations to the multi dimensional wave equation construction des conditions aux limites absorbantes pour l equation des ondes multidimensionnelle a l aide d approximations aux differences formulation sous forme canonique des conditions aux limites absorbantes analytiques

measured equation of invariance a new concept in field computations numerical computations of frequency domain field problems or elliptical partial differential equations may be based on differential equations or integral equations the new concept of field computation presented in this paper is based on the postulate of the existence of linear equations of the discretized nodal values of the fields different from the conventional equations but leading to the same solutions the postulated equations are local and invariant to excitation it is shown how the equations can be determined by a sequence of measures the measured equations are particularly useful at the mesh boundary where the finite difference methods fail the measured equations do not assume the physical condition of absorption so they are also applicable to concave boundaries using the measured equations one can terminate the finite difference mesh very close to the physical boundary and still obtain robust solutions it will definitely make a great impact on the way one applies finite difference and finite element methods in many problems computational results using the measured equations of invariance in two and three dimensions are presented

invertible cellular automata a review abstract in the light of recent developments in the theory of invertible cellular automata we attempt to give a unified presentation of the subject and discuss its relevance to computer science and mathematical physics

block transformations of one dimensional deterministic cellular automaton rules given a one dimensional cellular automaton rule f a block transform of f is a rule tbf such that there exists between the limit sets of both rules a bijection that replaces each site value x in a configuration belonging to the limit set of f with a string xb xx x of length b in the corresponding configuration belonging to the limit set of tbf if f is totalistic there exists a unique totalistic block transform and a large number of nontotalistic block transforms tbf if f is not totalistic there are no totalistic block transforms but there still exists a large number of non totalistic block transforms their number increases very rapidly with the block size b and the range of f the range of tbf may be any integer greater than or equal to rb many block transforms are studied the evolution according to rule tbf towards its limit set is discussed in terms of the annihilation of defects these defects are often simply related to the defects characterizing the evolution according to rule f

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

a general method for fdtd modeling of wave propagation in arbitrary frequency dispersive media a general formulation is presented for finite difference time domain fdtd modeling of wave propagation in arbitrary frequency dispersive media two algorithmic approaches are outlined for incorporating dispersion into the fdtd time stepping equations the first employs a frequency dependent complex permittivity denoted form 1 and the second employs a frequency dependent complex conductivity denoted form 2 a pade representation is used in z transform space to represent the frequency dependent permittivity form 1 or conductivity form 2 this is a generalization over several previous methods employing either debye lorentz or drude models the coefficients of the pade model may be obtained through an optimization process leading directly to a finite difference representation of the dispersion relation without introducing discretization error stability criteria for the dispersive fdtd algorithms are given we show that several previously developed dispersive fdtd algorithms can be cast as special cases of our more general framework simulation results are presented for a one dimensional 1 d air muscle example considered previously in the literature and a three dimensional 3 d radiation problem in dispersive lossy soil using measured soil data

piecewise linear recursive convolution for dispersive media using fdtd electromagnetic propagation through linear dispersive media can be analyzed using the finite difference time domain fdtd method by employing the recursive convolution rc approach to evaluate the discrete time convolution of the electric field and the dielectric susceptibility function the rc approach results in a fast and computationally efficient algorithm however the accuracy achieved is not generally as good as that obtained with other methods a new piecewise linear recursive convolution plrc method is described here that has greatly improved accuracy over the original rc approach but retains its speed and efficiency advantages

finite difference computation of head related transfer function for human hearing modeling the head related transfer function hrtf is a key to many applications in spatial audio to understand and predict the effects of head geometry and the surrounding environment on the hrtf a three dimensional finite difference time domain model 3d fdtd has been developed to simulate acoustic wave interaction with a human head a perfectly matched layer pml is used to absorb outgoing waves at the truncated boundary of an unbounded medium an external source is utilized to reduce the computational domain size through the scattered field total field formulation this numerical model has been validated by analytical solutions for a spherical head model the 3d fdtd code is then used as a computational tool to predict the hrtf for various scenarios in particular a simplified spherical head model is compared to a realistic head model up to about 7 khz the hrtf is also computed for a realistic head model in the presence of a wall it is demonstrated that this 3d fdtd model can be a useful tool for spatial audio applications

propagation in linear dispersive media finite difference time domain methodologies finite difference time domain fdtd methodologies are presented for electromagnetic wave propagation in two different kinds of linear dispersive media an nth order lorentz and an mth order debye medium the temporal discretization is accomplished by invoking the central difference approximation for the temporal derivatives that appear in the first order differential equations from this the final equations are temporally advanced using the classical leapfrog method one dimensional scattering from a dielectric slab is chosen for a test case provided that the maximum operating frequency times the time step is small and that the wave is adequately resolved in space as shown in the error analysis the agreement between the computed and exact solutions will be excellent the attached data which are associated with the four pole lorentz dielectric and the five pole debye medium verify this assertion

a general framework for the finite difference time domain simulation of real metals we present an efficient framework for the finite difference time domain simulation of real metals the complex permittivity function of a metal is fitted to experimental data in the frequency domain using a non linear least squares algorithm a memory efficient finite difference time domain fdtd scheme is presented for the simulation of the dispersive behavior of a metal in the frequency domain the stability limit for the proposed scheme is determined and compared to the courant limit excellent agreement between our fdtd formulation and the analytical solution for reflections from a thin metal sheet is found

perfectly matched layer truncation for parabolic wave equation models solutions of the parabolic wave equation are extended to complex values of the height variable the fast decay of the solutions in certain directions of the complex plane is used to improve parabolic wave equation solvers the solution is marched on a suitably chosen contour in the complex plane rather than on the real line this interpretation of berenger s perfectly matched layer allows extremely efficient truncation of the computational domain with a split step fourier algorithm the theory is developed for both the wide angle and narrow angle parabolic wave equations and numerical results are presented

scale separating operators for variational multiscale large eddy simulation of turbulent flows a general class of scale separating operators based on combined multigrid operators is proposed and analyzed in this work the operators of this class are designed for variational multiscale large eddy simulation using a finite volume or finite element method two representatives are compared to discrete smooth filters which are widely used in the traditional large eddy simulation literature the comparison shows that they are not only theoretically different but also yield considerable differences in the respective numerical results dynamic as well as constant coefficient based subgrid scale modeling is used within the multiscale environment all of the scale separating operators are implemented in a second order accurate energy conserving finite volume method and tested for the case of a turbulent channel flow one operator shows particularly remarkable results in the framework of the variational multiscale large eddy simulation that is profiles are obtained for velocity and kinetic energy which are considerably closer to the respective profiles from a direct numerical simulation than are the profiles resulting from the application of the other operators considered in the present study furthermore this particular operator proves to be very efficient with regard to the important aspect of computational cost that is a reduction in computing time ranging from about 25 up to about 150 compared to the other operators the introduction of a substantial amount of subgrid viscosity to the small scales particularly in the buffer layer of the channel appears to be crucial for the good results achieved with this method

complementary operators a method to annihilate artificial reflections arising from the truncation of the computational domain in the solution of partial differential equations the ease and simplicity with which the finite difference time domain fdtd or the finite elements fe techniques can handle complex radiation or scattering problems have lead to a remarkable surge in the use of these methods while execution time is becoming less of an impediment when solving large problems the biggest constraint remains the memory needed to run the fdtd or the fe methods it is precisely this limitation that the article addresses a boundary operation is developed to minimize the artificial reflections that arise when truncating the computational domain of an open region scattering or radiation problem the method is based on the use of two boundary operators that are complementary in their action by solving the problem with each of the two operators and then averaging the two solutions the first order reflections that arise from the artificial boundary can be completely eliminated numerical results are presented to show that this new technique gives significant reduction in the error when compared to other widely used boundary conditions

multifractal subgrid scale modeling within a variational multiscale method for large eddy simulation of turbulent flow multifractal subgrid scale modeling within a variational multiscale method is proposed for large eddy simulation of turbulent flow in the multifractal subgrid scale modeling approach the subgrid scale velocity is evaluated from a multifractal description of the subgrid scale vorticity which is based on the multifractal scale similarity of gradient fields in turbulent flow the multifractal subgrid scale modeling approach is integrated into a variational multiscale formulation which constitutes a new application of the variational multiscale concept a focus of this study is on the application of the multifractal subgrid scale modeling approach to wall bounded turbulent flow therefore a near wall limit of the multifractal subgrid scale modeling approach is derived in this work the novel computational approach of multifractal subgrid scale modeling within a variational multiscale formulation is applied to turbulent channel flow at various reynolds numbers turbulent flow over a backward facing step and turbulent flow past a square section cylinder which are three of the most important and widely used benchmark examples for wall bounded turbulent flow all results presented in this study confirm a very good performance of the proposed method compared to a dynamic smagorinsky model and a residual based variational multiscale method improved results are obtained moreover it is demonstrated that the subgrid scale energy transfer incorporated by the proposed method very well approximates the expected energy transfer as obtained from appropriately filtered direct numerical simulation data the computational cost is notably reduced compared to a dynamic smagorinsky model and only marginally increased compared to a residual based variational multiscale method

a connection between subgrid scale eddy viscosity and mixed methods we consider a new mixed method related to the evss method in computational viscoelasticity for the convection dominated convection diffusion equation in which stabilization is added then removed through the extra mixed variables this consistent stabilization is equivalent to an artificial viscosity operator acting only on the fluctuations in u h by suitable choice of the mixed spaces a method of guermond is recovered exactly we show that for a different natural choice a new method results with global error estimates similar to both guermond s method and the streamline diffusion supg method

a nonreflecting boundary condition for discrete acoustic and elastic wave equations one of the nagging problems which arises in application of discrete solution methods for wave propagation calculations is the presence of reflections or wraparound from the boundaries of the numerical mesh these undesired events eventually override the actual seismic signals which propagate in the modeled region the solution to avoiding boundary effects used to be to enlarge the numerical mesh thus delaying the side reflections and wraparound longer than the range of times involved in the modeling obviously this solution considerably increases the expense of computation more recently nonreflecting boundary conditions were introduced for the finite difference method clayton and enquist 1977 reynolds 1978 these boundary conditions are based on replacing the wave equation in the boundary region by one way wave equations which do not permit energy to propagate from the boundaries into the numerical mesh this approach has been relatively successful except that its effectiveness degrades for event

padded continued fraction absorbing boundary conditions for dispersive waves continued fraction absorbing boundary conditions cfabcs are new arbitrarily high order local absorbing boundary conditions that are highly effective in simulating wave propagation in unbounded domains the current versions of cfabcs are developed for the non dispersive acoustic wave equation with convex polygonal computational domains in this paper the cfabcs are modified through augmentation of special padding elements and are effective for absorbing evanescent waves occurring in dispersive wave problems while retaining their absorption properties for propagating waves the padded cfabcs for dispersive wave equations result in fourth order evolution equations which are solved using an efficient combination of crank nicholson method newmark time stepping scheme and operator splitting ideas the effectiveness of the padded cfabcs and their implementation is illustrated through numerical examples with varying levels of dispersion

block preconditioners based on approximate commutators this paper introduces a strategy for automatically generating a block preconditioner for solving the incompressible navier stokes equations we consider the pressure convection diffusion preconditioners proposed by kay loghin and wathen siam j sci comput 24 2002 pp 237 256 and silvester elman kay and wathen j comput appl math 128 2001 pp 261 279 numerous theoretical and numerical studies have demonstrated mesh independent convergence on several problems and the overall efficacy of this methodology a drawback however is that it requires the construction of a convection diffusion operator denoted f p projected onto the discrete pressure space this means that integration of this idea into a code that models incompressible flow requires a sophisticated understanding of the discretization and other implementation issues something often held only by the developers of the model as an alternative we consider automatic ways of computing f p based on purely algebraic considerations the new methods are closely related to the bfbt preconditioner of elman siam j sci comput 20 1999 pp 1299 1316 we use the fact that the preconditioner is derived from considerations of commutativity between the gradient and convection diffusion operators together with methods for computing sparse approximate inverses to generate the required matrix f p automatically we demonstrate that with this strategy the favorable convergence properties of the preconditioning methodology are retained

absorbing boundary conditions for acoustic media by decomposing the acoustic wave equation into incoming and outgoing components an absorbing boundary condition can be derived to eliminate reflections from plane waves according to their direction of propagation this boundary condition is characterized by a first order differential operator the differential operator or absorbing boundary operator is the basic element from which more complicated boundary conditions can be constructed the absorbing boundary operator can be designed to absorb perfectly plane waves traveling in any two directions by combining two or more absorption operators boundary conditions can be created which absorb plane waves propagating in any number of directions absorbing boundary operators simplify the task of designing boundary conditions to reduce the detrimental effects of outgoing waves in many wave propagation problems

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

an fdtd algorithm with perfectly matched layers for general dispersive media a three dimensional 3 d finite difference time domain fdtd algorithm with perfectly matched layer pml absorbing boundary condition abc is presented for general inhomogeneous dispersive conductive media the modified time domain maxwell s equations for dispersive media are expressed in terms of coordinate stretching variables we extend the recursive convolution rc and piecewise linear recursive convolution plrc approaches to arbitrary dispersive media in a more general form the algorithm is tested for homogeneous and inhomogeneous media with three typical kinds of dispersive media i e lorentz medium unmagnetized plasma and debye medium excellent agreement between the fdtd results and analytical solutions is obtained for all testing cases with both rc and plrc approaches we demonstrate the applications of the algorithm with several examples in subsurface radar detection of mine like objects cylinders and spheres buried in a dispersive half space and the mapping of a curved interface because of their generality the algorithm and computer program can be used to model biological materials artificial dielectrics optical materials and other dispersive media

finite volumes and finite elements two good friends in this paper a comparison between the finite element and the finite volume methods is presented in the context of elliptic convective diffusion and fluid flow problems the paper shows that both procedures share a number of features like mesh discretization and approximation moreover it is shown that in many cases both techniques are completely equivalent

frequency domain acoustic wave modeling with hybrid absorbing boundary conditions abstractacoustic waves are modeled using a 2d frequency domain finite difference scheme with three different artificial damping boundaries the absorbing boundary condition abc perfectly matched layer pml and a hybrid strategy combining pml and abc we evaluated the features of each simulation for a given artificial boundary condition for homogeneous and heterogeneous media for shorter pml layers the hybrid absorbing scheme gave better results when compared with the traditional pml technique with a significant reduction of the spurious reflections and a shorter computational run time

a variational multiscale method for turbulent flow simulation with adaptive large scale space in turbulent flows it is only feasible to simulate large flow structures variational multiscale vms methods define these flow structures by projections onto appropriate function spaces this paper presents a finite element vms method which chooses the large scale projection space adaptively the adaption controls the influence of an eddy viscosity model and it is based on the size of the so called resolved small scales the adaptive procedure is described in detail numerical studies at a turbulent channel flow and a turbulent flow around a cylinder are presented it is shown that the method selects the large scale space in a reasonable way and that appropriately chosen parameters improve the results compared to the basic method which uses the same local large scale space in the whole domain and for all times

least squares preconditioners for stabilized discretizations of the navier stokes equations this paper introduces two stabilization schemes for the least squares commutator lsc preconditioner developed by elman howle shadid shuttleworth and tuminaro siam j sci comput 27 2006 pp 1651 1668 for the incompressible navier stokes equations this preconditioning methodology is one of several choices that are effective for navier stokes equations and it has the advantage of being defined from strictly algebraic considerations it has previously been limited in its applicability to div stable discretizations of the navier stokes equations this paper shows how to extend the same methodology to stabilized low order mixed finite element approximation methods

upper bound on the products of particle interactions in cellular automata abstract particle like objects are observed to propagate and interact in many spatially extended dynamical systems for one of the simplest classes of such systems one dimensional cellular automata we establish a rigorous upper bound on the number of distinct products that these interactions can generate the upper bound is controlled by the structural complexity of the interacting particles a quantity which is defined here and which measures the amount of spatio temporal information that a particle stores along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata thereby elucidating why that approach is of general utility the upper bound is tested against several relatively complex domain particle cellular automata and found to be tight

superabsorption a method to improve absorbing boundary conditions electromagnetic waves the authors propose a technique which they call superabsorption for improving absorbing boundary conditions in finite difference time domain methods this method can be applied to every known absorbing boundary condition and greatly reduces the numerical error caused by the boundary reflection the principle and analysis of the superabsorption method are presented numerical tests indicating the improvements obtained on many absorbing boundary conditions are reported

a stabilized finite element method for computing turbulence abstract for many flows reynold averaged navier stokes simulation ranss techniques do not give an acceptable description of the flow in these cases a more detailed simulation of the turbulence is required one such detailed simulation technique large eddy simulation les has matured to the point of application to complex flows historically these simulations have been carried out with structured grids which suffer from two major difficulties the extension to higher reynolds numbers leads to an impractical number of grid points and most real world flows are rather difficult to represent geometrically with structured grids unstructured grid methods offer a release from both of these constraints herein we describe the development and validation of a massively parallel stabilized finite element method for les

a finite element variational multiscale method for the navier stokes equations this paper presents a variational multiscale method vms for the incompressible navier stokes equations which is defined by a large scale space lh for the velocity deformation tensor and a turbulent viscosity nu t the connection of this method to the standard formulation of a vms is explained the conditions on lh under which the vms can be implemented easily and efficiently into an existing finite element code for solving the navier stokes equations are studied numerical tests with the smagorinsky large eddy simulation model for nu t are presented

fdtd for nth order dispersive media previously a method for applying the finite difference time domain fdtd method to dispersive media with complex permittivity described by a function with a single first order pole was presented this method involved the recursive evaluation of a discrete convolution and was therefore relatively efficient in this work the recursive convolution approach is extended to media with dispersions described by multiple second order poles the significant change from the first order implementation is that the single backstore variable for each second order pole is complex the approach is demonstrated for a pulsed plane wave incident on a medium with a complex permittivity described by two second order poles and excellent agreement is obtained with the exact solution

frequency dependent fdtd methods using z transforms the frequency dependent finite difference time domain method fd sup 2 td method has been shown to be capable of correctly calculating electromagnetic propagation through media whose dielectric properties are frequency dependent however as researchers search for more elaborate applications the formulation of the fd sup 2 td methods becomes more complex in this work the mathematics of the fd sup 2 td method is developed using z transform theory this has the advantages of presenting a clearer formulation and allowing researchers to draw on the literature of systems analysis and signal processing disciplines

a novel piecewise linear recursive convolution approach for dispersive media using the finite difference time domain method two novel methods for implementing recursively the convolution between the electric field and a time dependent electric susceptibility function in the finite difference time domain fdtd method are presented both resulting algorithms are straightforward to implement and employ an inclusive susceptibility function which holds as special cases the lorentz debye and drude media relaxations the accuracy of the new proposed algorithms is found to be systematically improved when compared to existing standard piecewise linear recursive convolution plrc approaches it is conjectured that the reason for this improvement is that the new proposed algorithms do not make any assumptions about the time variation of the polarization density in each time interval no finite difference or semi implicit schemes are used for the calculation of the polarization density the only assumption that these two new methods make is that the first time derivative of the electric field is constant within each fdtd time interval

variational multiscale residual based turbulence modeling for large eddy simulation of incompressible flows we present an les type variational multiscale theory of turbulence our approach derives completely from the incompressible navier stokes equations and does not employ any ad hoc devices such as eddy viscosities we tested the formulation on forced homogeneous isotropic turbulence and turbulent channel flows in the calculations we employed linear quadratic and cubic nurbs a dispersion analysis of simple model problems revealed nurbs elements to be superior to classical finite elements in approximating advective and diffusive processes which play a significant role in turbulence computations the numerical results are very good and confirm the viability of the theoretical framework

transformations of one dimensional cellular automation rules by translation invariant local surjective mappings abstract if m is a noninvertible translation invariant local surjective mapping it is shown that some local one dimensional deterministic cellular automaton rules f have a transform by m defined by m m f when it exists is local and its wolfram s class is the same as f the evolution of a cellular automaton according to rule is simply related to the evolution according to rule f in the case of class 3 rules the evolution to the attractor may often be viewed as particle like structures evolving in a regular background if the structure of these particles and their interactions for a rule f are known then the structure and interactions of the transformed particles for rule are also known if m is a nontrivial invertible translation invariant local surjective mapping always exists but it is in general site and time dependent

a staggered upwind embedded boundary sueb method to eliminate the fdtd staircasing error in spite of its flexibility and second order accuracy in a homogeneous medium yee s finite difference time domain fdtd method suffers from serious degradation when treating material interfaces greatly reducing its accuracy in the presence of inhomogeneous media and perfect conductors indeed such so called staircasing approximation may lead to local zeroth order and global first order errors in this work an embedded fdtd scheme the staggered upwind embedded boundary sueb method is developed for the solution of oneand two dimensional maxwell s equations this simple embedded technique uses upwind conditions in the fdtd method to correctly represent the location and physical conditions of material and metallic boundaries hence eliminating problems caused by the staircasing approximation accuracy analysis has been made to show that the sueb method maintains a second order accuracy globally since the entire problem has been embedded into the simple staggered grid similar to that employed by the yee s scheme extra effort is only needed when treating the grid points close to the interfaces therefore little additional computational cost is needed over yee s scheme the sueb method has been validated by analytical solutions for plane wave normally incident to a planar boundary and for the tm wave propagation in the presence of a dielectric cylinder and a perfectly electrically conducting cylinder

numerical studies of finite element variational multiscale methods for turbulent flow simulations different realizations of variational multiscale vms methods within the framework of finite element methods are studied in turbulent channel flow simulations one class of vms methods uses bubble functions to model resolved small scales whereas the other class contains the definition of the resolved small scales by an explicit projection in its set of equations all methods are employed with eddy viscosity models of smagorinsky type the simulations are performed on grids for which a direct numerical simulation blows up in finite time

time dependent subgrid scales in residual based large eddy simulation of turbulent channel flow the present study investigates the effect of taking into account the time dependency of the fine subgrid scales in a residual based variational multiscale approach for large eddy simulation the residual based variational multiscale method with time dependent dynamic subgrid scales is presented and the impact of the time dependency is studied for the well known test case of turbulent channel flow results are presented from computations for various values of the reynolds number namely ret 180 ret 395 and ret 590 and several time step sizes a generalized a time integration scheme is employed results from our numerical experiments with dynamic subgrid scales are compared to results obtained with an approximation not explicitly taking the time dependency of the subgrid scales into account for all re t values and time step sizes under consideration results for resolved quantities computed by both approaches are very similar this statement applies to both mean streamwise velocity and root mean square velocity fluctuations however it provides a model for the subgrid scales not depend ing on the time step size and enabling a more robust representation of unresolved scales thus we conclude that the time dependent subgrid scale approximation is not capable of producing more accurate results for this type of flow if the time step size is chosen within an optimal range however we expect it to be more advantageous for more complex problems since our results indicate that it provides a more reliable representation of unresolved scales

chaotic like behaviour in chains of stable nonlinear oscillators abstract irregular evolution is observed in a chain of forced duffing oscillators even when the maximum lyapunov exponent is strictly negative this phenomenon generalizes similar results previously obtained in the context of coupled map lattices the relationship with chaotic cellular automata is investigated by introducing a suitable encoding while in some parameter region the evolution of the chain of oscillators turns out to be described exactly by a deterministic cellular automaton with a finite interaction range in other regions even automata with an infinite range are unable to reproduce the observed patterms we discuss the possible connection with an information downgrade occurring during the observation process