discretization on non orthogonal quadrilateral grids for inhomogeneous anisotropic media two classes of discretization methods are proposed for control volume formulations on quadrilateral grids in two space dimensions curvilinear grids are considered as a special case the methods are applicable for any system of conservation laws where the flux is defined by a gradient law like darcy s law for porous media flow a strong feature of the methods is the ability to handle media inhomogeneities in combination with full tensor anisotropy and or non orthogonality of the grid further properties of the methods will be discussed and examples of their use will be presented

numerical treatment of grid interfaces to viscous flow abstract numerical treatment of grid interfaces is one of the most important considerations for algorithms that employ different grids within the computational domain the issue of numerical treatment of quadrilateral grid interfaces with a representative finite volume navier stokes integration scheme is addressed interfaces are created by local embedding of quadrilateral grids and are the borders between different grids grid embedding is one of the basic functions of adaptive algorithms that have been developed in order to increase both accuracy and efficiency of computations the present work both develops and investigates interface treatment schemes that have certain properties such as accuracy and conservation it is a novel study of interfaces for the case of viscous flow computations various treatments are proposed and evaluated with the emphasis being on a comparison between accurate and conservative treatments two methodologies have been followed in order to study interface treatments the first is analytical and yields orders of possible numerical errors while the second approach employs model test cases which are especially designed to evaluate certain aspects of the described interface treatments also a transonic airfoil flow case is included as an example of accuracy and robustness of a particular interface treatment scheme all numerical treatment schemes that are discussed have been coded and evaluated

source separation using a criterion based on second order statistics it is often assumed that blind separation of dynamically mixed sources cannot be done with second order statistics it is shown that separation of dynamically mixed sources indeed can be performed using second order statistics only a criterion based on second order statistics for the purpose of separating crosswise mixtures is stated the criterion is used in order to derive a gradient based separation algorithm as well as a newton type separation algorithm the uniqueness of the solution representing the separation is also investigated this reveals that 1 the channel system is parameter identifiable under weak conditions and 2 if the sources have the same color there exists at most two solutions the local convergence behavior of the proposed algorithm is studied and reveals a sufficient condition for local convergence furthermore the estimates of the channel system are shown to be consistent or to locally minimize the criterion

collective synchronization in spatially extended systems of coupled oscillators with random frequencies we study collective behavior of locally coupled limit cycle oscillators with random intrinsic frequencies spatially extended over d dimensional hypercubic lattices phase synchronization as well as frequency entrainment are explored analytically in the linear strong coupling regime and numerically in the nonlinear weak coupling regime our analysis shows that the oscillator phases are always desynchronized up to d 4 which implies the lower critical dimension d l p 4 for phase synchronization on the other hand the oscillators behave collectively in frequency phase velocity even in three dimensions d 3 indicating that the lower critical dimension for frequency entrainment is d l f 2 nonlinear effects due to the periodic nature of limit cycle oscillators are found to become significant in the weak coupling regime so called runaway oscillators destroy the synchronized ordered phase and there emerges a fully random disordered phase critical behavior near the synchronization transition into the fully random phase is unveiled via numerical investigation collective behavior of globally coupled oscillators is also examined and compared with that of locally coupled oscillators

a new blind method for separating m 1 sources from m mixtures in this paper we consider the problem of underdetermined blind source separation ubss i e there are more sources than mixtures by exploiting the time frequency tf sparsity of the source signals some tf ubss algorithms have recently been proposed in the literature these algorithms require that the number of active sources at any tf point should not exceed one or be strictly less than the number of mixtures in this paper we show that if the number of sources is greater than the number of mixtures by one the sparsity assumption can be further relaxed especially it is allowed to have as many sources as mixtures at any tf point in this case then we propose a new tf ubss method to recover the sources the relaxation on the maximum number of active sources at tf points ensures that the tf based methods can be used in a wider range of applications

adaptive quasi newton algorithm for source extraction via cca approach this paper addresses the problem of adaptive source extraction via the canonical correlation analysis cca approach based on liu s analysis of cca approach we propose a new criterion for source extraction which is proved to be equivalent to the cca criterion then a fast and efficient online algorithm using quasi newton iteration is developed the stability of the algorithm is also analyzed using lyapunov s method which shows that the proposed algorithm asymptotically converges to the global minimum of the criterion simulation results are presented to prove our theoretical analysis and demonstrate the merits of the proposed algorithm in terms of convergence speed and successful rate for source extraction

fourth order criteria for blind sources separation various criteria based on contrast functions as well as higher order statistics are used for solving the problem of blind separation of sources in the paper for the case of instantaneous mixtures of two sources it is proved that the minimization or the cancellation of a really simple criterion a fourth order cross cumulant leads to a set of solutions whose spurious ones can be simply cancelled by using a decorrelation

a generalized contrast function and stability analysis for overdetermined blind separation of instantaneous mixtures in this letter the problem of blind separation of n independent sources from their m linear instantaneous mixtures is considered first a generalized contrast function is defined as a valuable extension of the existing classical and nonsymmetrical contrast functions it is applicable to the overdetermined blind separation m n with an unknown number of sources because not only independent components but also redundant ones are allowed in the outputs of a separation system second a natural gradient learning algorithm developed primarily for the complete case m n is shown to work as well with an n m or m m separating matrix for each optimizes a certain mutual information contrast function finally we present stability analysis for a newly proposed generalized orthogonal natural gradient algorithm which can perform the overdetermined blind separation when n is unknown obtaining an expectable result that its local stability conditions are slightly stricter than those of the conventional natural gradient algorithm using an invertible mixing matrix m n

adaptive blind separation with an unknown number of sources the blind source separation bss problem with an unknown number of sources is an important practical issue that is usually skipped by assuming that the source number n is known and equal to the number m of sensors this letter studies the general bss problem satisfying m n first it is shown that the mutual information of outputs of the separation network is a cost function for bss provided that the mixing matrix is of full column rank and the m m separating matrix is nonsingular the mutual information reaches its local minima at the separation points where the m outputs consist of n desired source signals and m n redundant signals second it is proved that the natural gradient algorithm proposed primarily for complete bss m n can be generalized to deal with the overdetermined bss problem m n but it would diverge inevitably due to lack of a stationary point to overcome this shortcoming we present a modified algorithm which can perform bss steadily and provide the desired source signals at specified channels if some matrix is designed properly finally the validity of the proposed algorithm is confirmed by computer simulations on artificially synthesized data

super exponential methods for blind deconvolution a class of iterative methods for solving the blind deconvolution problem i e for recovering the input of an unknown possibly nonminimum phase linear system by observation of its output is presented these methods are universal do not require prior knowledge of the input distribution are computationally efficient and statistically stable and converge to the desired solution regardless of initialization at a very fast rate the effects of finite length of the data finite length of the equalizer and additive noise in the system on the attainable performance intersymbol interference are analyzed it is shown that in many cases of practical interest the performance of the proposed methods is far superior to linear prediction methods even for minimum phase systems recursive and sequential algorithms are also developed which allow real time implementation and adaptive equalization of time varying systems

adaptive online learning algorithms for blind separation maximum entropy and minimum mutual information there are two major approaches for blind separation maximum entropy me and minimum mutual information mmi both can be implemented by the stochastic gradient descent method for obtaining the demixing matrix the mi is the contrast function for blind separation the entropy is not to justify the me the relation between me and mmi is first elucidated by calculating the first derivative of the entropy and proving that the mean subtraction is necessary in applying the me and at the solution points determined by the mi the me will not update the demixing matrix in the directions of increasing the cross talking second the natural gradient instead of the ordinary gradient is introduced to obtain efficient algorithms because the parameter space is a riemannian space consisting of matrices the mutual information is calculated by applying the gram charlier expansion to approximate probability density functions of the outputs finally we propose an efficient learning algorithm that incorporates with an adaptive method of estimating the unknown cumulants it is shown by computer simulation that the convergence of the stochastic descent algorithms is improved by using the natural gradient and the adaptively estimated cumulants

a comparison of three error estimation techniques for finite volume solutions of compressible flows three techniques to obtain error estimates for finite volume solutions on unstructured grids are compared in this study the first estimation technique uses richardson extrapolation involving three flow solutions on different grids error estimates on these grids are computed simultaneously with the order of convergence the second technique is based on the difference between the computed solution and a higher order reconstruction obtained using the least squares method finally a third technique solves an error equation driven by source terms computed from the flux jump at cell interfaces the flows solved as test cases are governed by the two dimensional euler equations and the discretization employs roe s flux difference splitting scheme comparisons with exact errors allow the efficiency of each error estimation technique to be assessed for various types of flows

sequential blind extraction of instantaneously mixed sources this paper presents a general approach to sequential blind extraction of instantaneously mixed sources for several major ill conditioned cases as well as the regular case of full column rank mixing matrices four ill conditioned cases are considered the mixing matrix is square but singular the number of sensors is less than that of sources the number of sensors is larger than that of sources but the column rank of the mixing matrix is deficient and the number of sources is unknown and the column rank of the mixing matrix is deficient first a solvability analysis is presented for a general case a necessary and sufficient condition for extractability is derived a sequential blind extraction approach is then proposed to extract all theoretically separable sources next a principle and a cost function based on fourth order cumulants are presented for blind source extraction by minimizing the cost function under a nonsingularity constraint of the extraction matrix all theoretically separable sources can be extracted sequentially finally simulation results are presented to demonstrate the validity and performance of the blind source extraction approach

death of period doublings locating the homoclinic doubling cascade abstract this paper studies a natural mechanism called a homoclinic doubling cascade for the disappearance of period doubling cascades in vector fields simply put an entire period doubling cascade collides with a saddle type equilibrium homoclinic doubling cascades are known to have self similar structure in contrast to the well known feigenbaum constant the scaling constants for homoclinic doubling depend on the eigenvalues of the saddle equilibrium specifically we present here for the first time a detailed study of homoclinic doubling cascades in a smooth vector field namely a three dimensional polynomial model proposed by sandstede a numerical algorithm is presented for computing homoclinic doubling cascades in general vector fields which makes use of the program auto homcont this allows us to compute two types of homoclinic doubling cascades one where the primary homoclinic orbit undergoes an inclination flip bifurcation and one where it undergoes an orbit flip bifurcation our results bring out the scaling constants in good agreement with analytical estimates obtained from one dimensional maps

cumulant based blind identification of linear multi input multi output systems driven by colored inputs the blind identification problem of a linear multi input multi output mimo system is widely noticed by many researchers in diverse fields due to its relevance to blind signal separation however such a problem is ill posed and has no unique solution therefore we can only find a solution of the problem within an equivalence class we address the blind identification problem of the linear mimo system driven by unobservable colored inputs using higher order statistics hos particularly the fourth order cumulants of the outputs where the unobservable inputs are mutually independent but temporally colored linear processes we first define the set which is denoted by s of stable scalar transfer functions and then define the notion of a generalized permutation matrix which is abbreviated by a g matrix over s then it is shown that the transfer function matrix of an unknown system is identified only up to post multiplication by a g matrix this result is applied to identifying fir systems for blind signal separation

numerical method for coupled fluid flow heat transfer and stress analysis using unstructured moving meshes with cells of arbitrary topology abstract a numerical method is presented that can be used for both solid body stress analysis and fluid flow predictions independently as well as in a coupled manner the method uses an integral form of equations governing mass energy and momentum balance for an arbitrary control volume a detailed description is provided of a novel second order accurate spatial discretisation technique which can accommodate unstructured moving meshes with cells of arbitrary topology this is accompanied by a fully implicit temporal discretisation which makes the method stable for any time step size the resulting set of coupled non linear algebraic equations is solved by employing a segregated approach leading to a decoupled set of linear algebraic equations for each dependent variable with a sparse diagonally dominant coefficient matrix these equations are solved by an iterative conjugate gradient solver which retains the sparsity of the coefficient matrix thus achieving a very efficient use of computer resources the method has been tested on a number of fluid flow and stress analysis problems and numerical calculations show favourable agreement with analytical and or experimental results in order to demonstrate the full capabilities of the present method an example of numerically complex coupled fluid flow stress analysis and heat transfer calculations is presented

equivariant adaptive source separation source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed this paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence easi the easi algorithms are based on the idea of serial updating this specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures most importantly the performance of an easi algorithm does not depend on the mixing matrix in particular convergence rates stability conditions and interference rejection levels depend only on the normalized distributions of the source signals closed form expressions of these quantities are given via an asymptotic performance analysis the theme of equivariance is stressed throughout the paper the source separation problem has an underlying multiplicative structure the parameter space forms a matrix multiplicative group we explore the favorable consequences of this fact on implementation performance and optimization of easi algorithms

discretisation procedures for multi physics phenomena procedures are described for solving the equations governing a multi physics process finite volume techniques are used to discretise using the same unstructured mesh the equations of fluid flow heat transfer with solidification and solid deformation these discretised equations are then solved in an integrated manner the computational mechanics environment physica which facilitates the building of multi physics models is described comparisons between model predictions and experimental data are presented for the casting of metal components

a novel blind deconvolution scheme for image restoration using recursive filtering we present a novel blind deconvolution technique for the restoration of linearly degraded images without explicit knowledge of either the original image or the point spread function the technique applies to situations in which the scene consists of a finite support object against a uniformly black grey or white background this occurs in certain types of astronomical imaging medical imaging and one dimensional 1 d gamma ray spectra processing among others the only information required are the nonnegativity of the true image and the support size of the original object the restoration procedure involves recursive filtering of the blurred image to minimize a convex cost function we prove convexity of the cost function establish sufficient conditions to guarantee a unique solution and examine the performance of the technique in the presence of noise the new approach is experimentally shown to be more reliable and to have faster convergence than existing nonparametric finite support blind deconvolution methods for situations in which the exact object support is unknown we propose a novel support finding algorithm

evam an eigenvector based algorithm for multichannel blind deconvolution of input colored signals a new algorithm is proposed for the deconvolution of an unknown possibly colored gaussian or nonstationary signal that is observed through two or more unknown channels described by rational system transfer functions more specifically not only the root pole and zero locations but also the orders of the channel transfer functions are unknown it is assumed that the channel orders may be overestimated the proposed algorithm estimates the orders and root locations of the channel transfer functions therefore it can also be used in multichannel system identification problems the input signal is allowed to be nonstationary and the channel transfer functions may be a nonminimum phase as well as noncausal hence the proposed algorithm is particularly suitable for applications such as dereverberation of speech signals recorded through multiple microphones several experimental results indicate improvement compared to the existing methods in the literature

on the use of surface interpolation techniques in generalised finite volume strategies for simulating transport in highly anisotropic porous media a control volume technique for solving a representative diffusion equation in an orthotropic medium is considered the approximation of the cross diffusion flux term is of utmost important for the accuracy of the solution a preliminary investigation that used exact function values from an available analytical solution to approximate this term during the numerical simulation provided excellent agreement with the exact solution this finding motivated the need for accurate surface interpolation techniques for estimating the cross diffusion term the use of radial basis functions is a well known interpolation technique for fitting scattered data which can be considered as a global interpolating method because function values in the whole solution domain contribute towards the interpolation a number of radial basis functions rbf was used to approximate the gradients in the cross diffusion flux term and it was found that the accuracy of the finite volume solution was generally poor it was concluded that the rbf estimated function does not reflect local variation of the solution particularly for the gradients another strategy for local function estimation concerns the weighted least squares method different variants of this method were analysed here for approximating the cross diffusion term and it was found that the numerical results well matched the exact solution the results highlight that the development of an accurate generalised finite volume strategy requires a highly accurate flux approximation to enable second order spatial accuracy to be achieved

general approach to blind source separation this paper identifies and studies two major issues in the blind source separation problem separability and separation principles we show that separability is an intrinsic property of the measured signals and can be described by the concept of m row decomposability introduced in this paper we also show that separation principles can be developed by using the structure characterization theory of random variables in particular we show that these principles can be derived concisely and intuitively by applying the darmois skitovich theorem which is well known in statistical inference theory and psychology some new insights are gained for designing blind source separation filters

three dimensional numerical simulations of viscoelastic flows predictability and accuracy in this paper fully three dimensional 3 d numerical simulations of viscoelastic flows using an implicit finite volume method are discussed with the focus on the predictability and accuracy of the method the viscoelastic flow problems involving the stress singularity including plane stick slip flow the flow past a junction in a channel and the 3 d edge flow are used to test the ability of the method to predict the singularity features with accuracy the accuracy of the numerical predictions is judged by comparing with the known asymptotic behaviour for newtonian fluids and some viscoelastic fluids and the investigations are extended to the viscoelastic cases with unknown singular behaviour the phan thien tanner ptt model and in some cases the upper convected maxwell ucm model are used to describe viscoelastic fluids the numerical results with mesh refinement show that the accuracy is quite satisfactory especially for newtonian flows for viscoelastic flows the asymptotic results for the flow around a re entrant corner for the ucm as well as the ptt fluid are reproduced numerically in the stick slip flow a newtonian like asymptotic behaviour is predicted for the ucm fluid in edge flow it is verified numerically that the kinematics are newtonian for viscoelastic fluids described by models with a constant viscosity and a zero second normal stress difference for viscoelastic fluids described by the models with a shear thinning viscosity and zero second normal stress difference the fluid behaves like a power law fluid and the difference from its newtonian kinematics is localized in the region near the singularity and to capture the asymptotic behaviour a parameter dependent mesh has to be used with the 3 d simulations it is confirmed that in edge flow the flow around the edge could not be rectilinear and some secondary flows on the plane normal to the primary flow direction are expected for viscoelastic fluids described by the models with a shear dependent second normal stress difference such as the full ptt model the strength of the secondary flows will depend on the level of the departure of the second normal stress difference from a fixed constant multiple of viscosity of the fluid

stability of a chain of phase oscillators we study a chain of n 1 phase oscillators with asymmetric but uniform coupling this type of chain possesses 2 n ways to synchronize in so called traveling wave states i e states where the phases of the single oscillators are in relative equilibrium we show that the number of unstable dimensions of a traveling wave equals the number of oscillators with relative phase close to ensuremath pi this implies that only the relative equilibrium corresponding to approximate in phase synchronization is locally stable despite the presence of a lyapunov type functional periodic or chaotic phase slipping occurs for chains of lengths 3 and 4 we locate the region in parameter space where rotations corresponding to phase slipping are present

collective synchronisation in lattices of nonlinear oscillators with randomness the authors study mutual synchronisation in a model of interacting limit cycle oscillators with random intrinsic frequencies it is shown rigorously that the model exhibits no long range order in one dimension and that in higher dimensional lattices large clusters of synchronised oscillators necessarily have a sponge like structure surprisingly the phase locking behaviour of the mean field model is completely different from that of any finite dimensional lattice indicating that d infinity is the upper critical dimension for phase locking

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

a 3d finite volume scheme for the euler equations on adaptive tetrahedral grids the paper describes the development and application of a new euler solver for adaptive tetrahedral grids spatial discretization uses a finite volume node based scheme that is of central differencing type a second order taylor series expansion is employed to march the solution in time according to the lax wendroff approach special upwind like smoothing operators for unstructured grids are developed for shock capturing as well as for suppression of solution oscillations the scheme is formulated so that all operations are edge based which reduces the computational effort significantly an adaptive grid algorithm is employed in order to resolve local flow features this is achieved by dividing the tetrahedral cells locally guided by a flow feature detection algorithm application cases include transonic flow around the onera m6 wing and transonic flow past a transport aircraft configuration comparisons with experimental data evaluate accuracy of the developed adaptive solver