a meshless method for one dimensional stefan problems the paper presents a new meshless numerical technique for solving one dimensional problems with moving boundaries including the stefan problems the technique presented is based on the use of the delta shaped functions and the method of approximate fundamental solutions mafs firstly suggested for solving elliptic problems and for heat equations in domains with fixed boundaries the numerical examples are presented and the results are compared with analytical solutions the comparison shows that the method presented provides a very high precision in determining the position of the moving boundary even for a region that initially has zero thickness

relations between 2 d and multichannel linear prediction a procedure for solving 2 d normal equations is derived by relating the 2 d linear prediction problem to a multichannel linear prediction problem and applying the multichannel levinson recursion

reconstructing an unknown time dependent function in the boundary conditions of a parabolic pde this work investigates the parabolic inverse problem of reconstructing an unknown time dependent function in the boundary conditions from additional terminal integral or point observations a numerical scheme is developed for obtaining an approximate solution for this problem the method consists of reducing the solution of the inverse problem to a system of integral equations the properties of sinc function are then utilized for replacing the resulting integral equations by a system of linear algebraic equations several numerical examples are presented to demonstrate the efficiency and accuracy of the numerical method

analysis of grazing bifurcations of quasiperiodic system attractors this paper presents the first application of the discontinuity mapping approach to the study of near grazing bifurcations of originally quasiperiodic co dimension two system attractors the paper establishes an exact formulation for the discontinuity mapping methodology under the assumption that a poincare section can be found that is everywhere transversal to the grazing attractor in particular it is shown that while a reduced formulation may be employed successfully in the case of co dimension one attractors it fails to capture dynamics in directions transversal to the original quasiperiodic attractor this shortcoming necessitates the full machinery presented here the generality of the proposed approach is illustrated through numerical analysis of two nonlinear dynamical systems of dimension three and four

asymptotic numerical and approximate techniques for a free boundary problem arising in the diffusion of glassy polymers this paper considers approximate solution methods for a one dimensional stefan problem describing solvent diffusion in glassy polymers similar to the classic stefan problem the region initially has zero thickness and so must be analysed carefully before performing a numerical computation a small time analysis gives the correct starting solution which is then incorporated into the second order accurate keller box finite difference scheme we also consider a detailed analysis of small and large time expansions as well as the large control parameter limit and show that our generalised approach enables us to obtain higher order terms than given in previous studies finally we apply the combined integral method cim to this problem which is a refinement of the popular heat balance integral method hbim and compare both the cim and asymptotic solutions to the numerical results

an efficient algorithm for two dimensional autoregressive spectrum estimation an algorithm similar to the burg algorithm is given for autoregressive estimation in one dimension coefficients of the filter used to decorrelate the signal are found recursively from lower order filters the coefficients needed to get the larger sized filters can be found at each stage of the recursion from the correlations of lower order filter outputs thus the resulting estimate does not assume knowledge of ensemble averages it offers a computational saving of 25 over the commonly used method in which an estimate of the correlation matrix is first computed and then inverted

a comparison of numerical models for one dimensional stefan problems in this paper we present a critical comparison of the suitability of several numerical methods level set moving grid and phase field model to address two well known stefan problems in phase transformation studies melting of a pure phase and diffusional solid state phase transformations in a binary system similarity solutions are applied to verify the numerical results the comparison shows that the type of phase transformation considered determines the convenience of the numerical techniques finally it is shown both numerically and analytically that the solid solid phase transformation is a limiting case of the solid liquid transformation

an integral equation method for spherical stefan problems abstract many applications in solidification or melting are described by a two phase stefan problem with spherical symmetry using green s representation theorem the heat equation is reformulated as a system of integral equations for the unknown fluxes on the interface the unknown radius of the solid liquid interface is determined from the stefan condition the integral equation is discretized with the nystrom method for which special singularity corrected quadrature rules are discussed numerical examples are presented that demonstrate the effectiveness of the method

dynamics and bifurcations of nonsmooth systems a survey abstract in this survey we discuss current directions of research in the dynamics of nonsmooth systems with emphasis on bifurcation theory an introduction to the state of the art also for non specialists is complemented by a presentation of the main open problems we illustrate the theory by means of elementary examples the main focus is on piecewise smooth systems which have recently attracted a lot of attention but we also briefly discuss other important classes of nonsmooth systems such as nowhere differentiable ones and differential variational inequalities this extended framework allows us to put the diverse range of papers and surveys in this special issue in a common context a dedicated section is devoted to concrete applications that stimulate the development of the field this survey is concluded by an extensive bibliography

a periodically forced piecewise linear oscillator a single degree of freedom non linear oscillator is considered the non linearity is in the restoring force and is piecewise linear with a single change in slope such oscillators provide models for mechanical systems in which components make intermittent contact a limiting case in which one slope approaches infinity an impact oscillator is also considered harmonic subharmonic and chaotic motions are found to exist and the bifurcations leading to them are analyzed

a numerical solution of the stefan problem with a neumann type boundary condition by enthalpy method in this paper the enthalpy method based on suitable finite difference approximations has been applied to the one dimensional moving boundary problem with a neumann type boundary condition known as the stefan problem the numerical results obtained by the hopscotch technique are compared with the exact solution of the problem it is shown that all results are found to be in very good agreement with each other and the numerical solution displays the expected convergence to the exact one as the mesh size is refined

nonlinear moving boundary problems and a keller box scheme a modification of the original kelley box scheme is used to approximate nonlinear parabolic partial differential equations with moving boundaries the proposed scheme solves two systems of linear algebraic equations at each time step to produce second order approximations to the solution its derivative the flux and the position of the moving boundary the scheme is applied to a physical problem which has a known similarity solution a comparison of numerical results with the similarity solution gives evidence of stability and convergence

an inverse problem for fractional diffusion equation in 2 dimensional case stability analysis and regularization abstract in this paper we investigate an inverse problem for a time fractional diffusion equation which is highly ill posed in the two dimensional setting based on an a priori assumption we give a conditional stability result some new regularization methods are constructed for solving the inverse problem and the corresponding error estimates are proved for numerical illustration several examples are constructed to demonstrate the feasibility and efficiency of the proposed methods

quasi trefftz spectral method for separable linear elliptic equations abstract a new numerical method qtsm which was earlier suggested for solving boundary value problems with elliptic operators with constant coefficients is applied to separable second order elliptic equations with varying coefficients the problems in irregular domains are considered the method combines the properties of the boundary methods with the spectral representation of the solution in the form of expansion over the eigenfunctions of some sturm liouville problem the method is tested on several one and two dimensional problems with exact analytic solution the possibilities of further developments of the method are discussed

quasi similarity solutions for one phase stefan problems with time dependent boundary conditions we consider the one dimensional one phase stefan problems with temperature or thermal flux boundary conditions exact and closed form solutions for these two free boundary problems are very limited and highly restricted to particular initial and boundary conditions and so are the similarity solutions in general only numerical methods allow one to completely solve such nonlinear problems in this paper the quasi similarity solutions are defined and for each problem an analytical approximation of the interfacial position is given as function of the time dependent boundary datum

approximation of multivariate functions and evaluation of particular solutions using chebyshev polynomial and trigonometric basis functions summary a two stage numerical procedure using chebyshev polynomials and trigonometric functions is proposed to approximate the source term of a given partial differential equation the purpose of such numerical schemes is crucial for the evaluation of particular solutions of a large class of partial differential equations our proposed scheme provides a highly efficient and accurate approximation of multivariate functions and particular solution of certain partial differential equations simultaneously numerical results on the approximation of eight two dimensional test functions and their derivatives are given to demonstrate that the scheme for the approximation of functions can be easily extended to evaluate the particular solution of certain partial differential equations we solve a modified helmholtz equation near machine precision can be achieved for all these test problems copyright 2006 john wiley sons ltd

local analysis of co dimension one and co dimension two grazing bifurcations in impact microactuators impact microactuators rely on repeated collisions to generate gross displacements of a microelectromechanical machine element without the need for large applied forces their design and control rely on an understanding of the critical transition between non impacting and impacting long term system dynamics and the associated changes in system behavior in this paper we present three co dimension one characteristically distinct transition scenarios associated with grazing conditions for a periodic response of an impact microactuator a discontinuous jump to an impacting periodic response associated with parameter hysteresis a continuous transition to an impacting chaotic attractor and a discontinuous jump to an impacting chaotic attractor using the concept of discontinuity mappings a theoretical analysis is presented that predicts the character of each transition from a set of quantities that are computable in terms of system properties at grazing specifically we show how this analysis can be applied to predict the bifurcation behavior on neighborhoods of two co dimension two bifurcation points that separate the co dimension one bifurcation scenarios the predictions are validated against results from numerical simulations of a model impact microactuator

an accurate finite difference method for ablation type stefan problems a recently derived numerical algorithm for one dimensional time dependent stefan problems is extended for the purpose of solving one phase ablation type moving boundary problems in tandem with the keller box finite difference scheme the so called boundary immobilization method is used an important component of the work is the use of variable transformations that must be built into the numerical algorithm in order to preserve second order accuracy in both time and space the analysis also determines that the ablation front initially moves as the time raised to the power 3 2 hence it evolves considerably more slowly than the phase change front in the classical stefan problem with isothermal cooling

radial basis function approximations as smoothing splines radial basis function methods for interpolation can be interpreted as roughness minimizing splines although this relationship has already been established for radial basis functions of the form g r r a and g r r alog r it is extended here to include a much larger class of functions this class includes the multiquadric g r r 2 c 2 1 2 and inverse multiquadric g r r 2 c 2 1 2 functions as well as the gaussian exp r 2 d the crucial condition is that the fourier transform of g x be positive except possibly at the origin the appropriate measure of roughness is defined in terms of this fourier transform to allow for possibility of noisy data the analysis is presented within the general framework of smoothing splines of which interpolation is a special case two diagnostic quantities the cross validation function and the sensitivity indicate the accuracy of the approximation

single boundary control of the two phase stefan system abstract this paper presents the control design of the two phase stefan problem the two phase stefan problem is a representative model of liquid solid phase transition by describing the time evolutions of the temperature profile which is divided by subdomains of liquid and solid phases as the liquid solid moving interface position the mathematical formulation is given by two diffusion partial differential equations pdes defined on a time varying spatial domain described by an ordinary differential equation ode driven by the neumann boundary values of both pde states resulting in a nonlinear coupled pde ode pde system we design a state feedback control law by means of energy shaping to stabilize the interface position to a desired setpoint by using single boundary heat input we prove that the closed loop system under the control law ensures some conditions for model validity and the global exponential stability estimate is shown in the spatial l 2 norm furthermore the robustness of the closed loop stability with respect to the uncertainties of the physical parameters is shown numerical simulation is provided to illustrate the desired performance of the proposed control law in comparison to the control design for the one phase stefan problem

discontinuity induced bifurcations in models of mechanical contact capillary adhesion and cell division a common framework abstract this paper collects four distinct instances of grazing contact of a periodic trajectory in a hybrid dynamical system under a common abstract framework and establishes selected general properties of the associated near grazing dynamics in particular it is shown that for critical choices of parameter values commonly used physical models of rigid or compliant mechanical contact capillary adhesion and cell division satisfy the conditions required by the general framework the paper relies on the well known discontinuity mapping formalism in contrast to previous treatments the proposed abstract framework more clearly establishes the origin of the large state space stretching in the initial and possibly only step of the construction of a discontinuity mapping it further highlights the nonuniqueness in the formulation of the discontinuity mapping and its connection to the choice of a locally smooth map with which the discontinuity mapping is composed to describe the near grazing dynamics the analysis is illustrated with examples from tapping mode atomic force microscopy in the presence of thin fluid layers on the sample and the probe tip and from the study of protein activity during a eukaryotic cell cycle

regularized method of fundamental solutions for boundary identification in two dimensional isotropic linear elasticity we investigate the stable numerical reconstruction of an unknown portion of the boundary of a two dimensional domain occupied by an isotropic linear elastic material from a prescribed boundary condition on this part of the boundary and additional displacement and traction measurements i e cauchy data on the remaining known portion of the boundary this inverse geometric problem is approached by combining the method of fundamental solutions mfs and the tikhonov regularization method whilst the optimal value of the regularization parameter is chosen according to the discrepancy principle various geometries are considered i e convex and non convex domains with a smooth or piecewise smooth boundary in order to show the numerical stability convergence consistency and computational efficiency of the proposed method

applying the combined integral method to two phase stefan problems with delayed onset of phase change in this paper the combined integral method cim is applied to non classical two phase stefan problems with delayed onset of phase change this can occur if the phase change is caused by a heat flux or robin boundary condition the method requires choosing an approximating function typically a polynomial but it is not clear what should be used as the exponent in the highest order term previous studies have determined exponents either from exact solutions or from expansions valid over short time scales neither approach is satisfactory and can be very inaccurate for larger times we combined the heat balance and refined integral methods to determine this exponent as part of the solution process allowing the exponent to be time dependent from comparing the approximate solutions with numerical and exact analytical solutions whenever possible we show that the cim greatly improves the accuracy on standard heat balance integral methods without detracting from its simplicity

finite difference methods with increased accuracy and correct initialization for one dimensional stefan problems although the numerical solution of one dimensional phase change or stefan problems is well documented a review of the most recent literature indicates that there are still unresolved issues regarding the start up of a computation for a region that initially has zero thickness as well as how to determine the location of the moving boundary thereafter this paper considers the so called boundary immobilization method for four benchmark melting problems in tandem with three finite difference discretization schemes we demonstrate a combined analytical and numerical approach that eliminates completely the ad hoc treatment of the starting solution that is often used and is numerically second order accurate in both time and space a point that has been consistently overlooked for this type of moving boundary problem

global space time multiquadric method for inverse heat conduction problem in this paper a radial basis collocation method rbcm based on the global space time multiquadric mq is proposed to solve the inverse heat conduction problem ihcp the global mq is simply constructed by incorporating time dimension into the mq function as a new variable in radial coordinate the method approximates the ihcp as an over determined linear system with the use of two sets of collocation points one is satisfied with the governing equation and another is for the given conditions the least square technique is introduced to find the solution of the over determined linear system the present work investigates two types of the ill posed heat conduction problems the ihcp to recover the surface temperature and heat flux history on a source point from the measurement data at interior locations and the backward heat conduction problem bhcp to retrieve the initial temperature distribution from the known temperature distribution at a given time numerical results of four benchmark examples show that the proposed method can provide accurate and stable numerical solutions for one dimensional and two dimensional ihcp problems the sensitivity of the method with respect to the measured data location of measurement time step shape parameter and scaling factor is also investigated

an isotherm migration formulation for one phase stefan problem with a time dependent neumann condition in this paper we present a numerical scheme based on an isotherm migration formulation for one dimensional one phase stefan problem with a time dependent neumann condition on the fixed boundary and a constant dirichlet condition on the moving boundary the numerical results obtained by the present method have been compared with exact one and also those obtained by earlier authors and are found to be in very good agreement with each other it is also shown that the numerical solution displays the expected convergence to the exact one as the mesh size is refined

on the numerical solution of a stefan problem with finite extinction time in many phase change problems of practical interest it is important to know when a phase is depleted a quantity referred to as the extinction time however there are no numerical schemes that are able to compute this with any degree of rigour or formal accuracy in this paper we develop such a scheme for the one dimensional time dependent problem of an evaporating spherical droplet the keller box finite difference scheme is used in tandem with the so called boundary immobilization method an important component of the work is the careful use of variable transformations that must be built into the numerical algorithm in order to preserve second order accuracy in both time and space in particular as regards resolving a square root singularity in the droplet radius as the extinction time is approached

two dimensional orthogonal lattice structures for autoregressive modeling of random fields two dimensional orthogonal lattice filters are developed as a natural extension of the 1 d lattice parameter theory the method offers a complete solution for the levinson type algorithm to compute the prediction error filter coefficients using lattice parameters from the given 2 d augmented normal equations the proposed theory can be used for the quarter plane and asymmetric half plane models depending on the indexing scheme in the prediction region it is shown that the final order backward prediction error may correspond to different quarter plane models in addition to developing the basic theory the article includes several properties of this lattice model conditions for lattice model stability and an efficient method for factoring the 2 d correlation matrix are given it is shown that the unended forward and backward prediction errors form orthogonal bases a simple procedure for reduced complexity 2 d orthogonal lattice filters is presented the proposed 2 d lattice method is compared with other alternative structures both in terms of conceptual background and complexity examples are considered for the given covariance case

new efficient 2 d lattice structures for general autoregressive modeling of random fields in this paper we present a new efficient general 2 d autoregressive ar lattice modeling technique of random fields our proposed approach is capable of simultaneously providing all possible types of 2 d causal quarter plane qp and asymmetric half plane ashp ar models for an arbitrary rectangular shape of the prediction support region psr it is shown that it is also possible to obtain various noncausal half plane ar models without any additional computational cost this new lattice structure introduces only one row or one column of new observation points into the existing rectangular psr when the order of the model increases in the horizontal or vertical direction at each of the recursive order incrementation stage respectively starting with a given random data field a set of auxiliary forward and backward prediction error fields pefs for the horizontal and vertical directions are generated after recursive order updates to the desired size of the rectangular psr all types of causal qp ashp and noncausal half plane 2 d lattice models are obtained by deriving the appropriate pef from the remaining ones in addition to developing the basic theory the presentation includes the derivation of the synthesis model transfer functions from the calculated lattice parameters it is shown that the proposed auxiliary horizontal and vertical backward prediction error filters inherently generates the mutually orthogonal realization vectors and thus are optimum for all stages the theory has been confirmed by computer simulations

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

analysis of box schemes for reactive flow problems key properties of the box scheme are shown to be advantageous for reactive flow problems unconditional stability and compact conservation are shown by a detailed modified equation analysis to enable the scheme to reflect exactly the reduced speed enhanced diffusion and dispersion which are typical of such hyperbolic conservation laws with relaxation a novel modified equation analysis is also used to show how the spurious checkerboard mode behaves and can be controlled numerical experiments for some nonlinear one dimensional problems and a two dimensional problem demonstrate that the behavior of the scheme deduced from a simple model problem has general validity

an inverse problem in thermal imaging this paper examines uniqueness and stability results for an inverse problem in thermal imaging the goal is to identify an unknown boundary of an object by applying a heat flux and measuring the induced temperature on the boundary of the sample the problem is studied both in the case in which one has data at every point on the boundary of the region and the case in which only finitely many measurements are available an inversion procedure is developed and used to study the stability of the inverse problem for various experimental configurations

an accurate numerical solution for the transient heating of an evaporating spherical droplet a recently derived numerical algorithm for one dimensional time dependent stefan problems is extended for the purposes of solving a moving boundary problem for the transient heating of an evaporating spherical droplet the keller box finite difference scheme is used in tandem with the so called boundary immobilization method an important component of the work is the careful use of variable transformations that must be built into the numerical algorithm in order to preserve second order accuracy in both time and space an issue not previously discussed in relation to this widely used scheme in addition we demonstrate that our solution is in close agreement with the solution obtained using an alternative numerical scheme that employs an analytic solution of the heat conduction equation inside the droplet for which the droplet radius was assumed to be a piecewise linear function of time the advantages of the new method are discussed

continuous and discontinuous grazing bifurcations in impacting oscillators this paper seeks to formulate conditions for the persistence of a local attractor in the immediate vicinity of periodic and quasiperiodic grazing trajectories in an impacting mechanical system a local analysis based on the discontinuity mapping approach is employed to derive a normal form description of the dynamics near the grazing trajectory in agreement with previous studies of grazing periodic trajectories it is found that the catastrophic loss of a local attractor and strong instability characteristic of grazing bifurcations is directly associated with the repeated application of a square root term that appears to lowest order in the normal form expansion specifically it is found that the square root term is absent in the description of the dynamics normal to a quasiperiodic trajectory covering a co dimension one invariant torus resulting in a piecewise linear description of the normal dynamics and at most a weak instability in contrast for co dimension two or higher the square root term is generically present in the normal dynamics here however the quasiperiodicity of the grazing motion implies that there is no upper limit to the time between impacts on nearby trajectories suggesting the persistence of a local attractor for some interval about the parameter value corresponding to grazing the results of the analysis are illustrated through a series of model examples

a computational method for inverse free boundary determination problem based on the method of fundamental solutions and discrepancy principle for the choice of location for source points we extend in this paper the application of the computational method to determine an unknown free boundary of a cauchy problem of parabolic type equation from measured dirichlet and neumann data with noises the standard tikhonov regularization technique with the l curve method for an optimal regularized parameter is adopted for solving the resultant highly ill conditioned system of linear equations both one dimensional and two dimensional numerical examples are given to verify the efficiency and accuracy of the proposed computational method copyright 2007 john wiley sons ltd

an exponential heat balance integral method implementations of the heat balance integral method are discussed in which exponential functions are used in place of the familiar polynomial approximants the rationale is based upon that of least squares in that the use of appropriate basis functions can enhance solution accuracy whilst this is true in principle it is shown that considerable skill must be exercised when deviating from polynomial approximants the discussions are illustrated by application to a familiar single phase stefan problem that is typical of heat transfer problems exhibiting decay like spatial solution profiles

a galerkin method for stefan problems stefan problems are described by a parabolic partial differential equation along with two boundary conditions on a moving boundary which is to be determined as part of the solution the purpose of this paper is to develop a finite element method for the solution of a one dimensional stefan problem first a coordinate transformation is used to transform the changing physical domain into a fixed computational domain then the weak or galerkin formulation of the initial boundary value problem is used to reduce it to a system of initial value problems in ordinary differential equations several finite difference marching methods are used to solve the resulting initial value problems the method is developed and illustrated using the stefan problem concerning the heat transfer in an ice water medium the computational results are in very good agreement with the results produced earlier by several authors

impact oscillators with homoclinic orbit tangent to the wall abstract homoclinic bifurcation for a nonlinear inverted pendulum impacting between two rigid walls under external periodic excitation is analyzed under the hypothesis that the unperturbed system has a homoclinc orbit tangent to the wall consequently the impact surface cannot be chosen as the poincare section to measure the distance between the perturbed stable and unstable manifolds furthermore compared to the case that the unperturbed homoclinic orbit intersects the wall transversally more cases are involved as the parameters vary thus the analysis of the homoclinic orbit tangent to the wall is much more difficult in this paper by using a method of melnikov type we derive sufficient conditions under which the perturbed stable and unstable manifolds intersect transversally as an application an impact oscillator of duffing type is studied in detail

behavior of the solution of a stefan problem by changing thermal coefficients of the substance abstract we consider a one dimensional one phase stefan problem for a semi infinite substance we suppose that there is a transient heat flux at the fixed face and the thermal coefficients are constant the goal of this paper is to determine the behavior of the free boundary and the temperature by changing the thermal coefficients we use the maximum principle in order to obtain properties of monotony with respect to the latent heat of fusion the specific heat and the mass density we compute approximate solutions through the quasi stationary the goodman s heat balance integral and the biot s variational methods and a numerical solution through a finite difference scheme we show that the solution is not monotone with respect to the thermal conductivity the results obtained are important in technological applications

on the origin and bifurcations of stick slip oscillations a recently proposed model of macroscopic friction is investigated using methods of dynamical systems analysis particular emphasis is put on the bifurcations associated with the appearance of stick

a boundary meshless method using chebyshev interpolation and trigonometric basis function for solving heat conduction problems a boundary meshless method has been developed to solve the heat conduction equations through the use of a newly established two stage approximation scheme and a trigonometric series expansion scheme to approximate the particular solution and fundamental solution respectively as a result no fundamental solution is required and the closed form of approximate particular solution is easy to obtain the effectiveness of the proposed computational scheme is demonstrated by several examples in 2d and 3d we also compare our proposed method with the finite difference method and the other meshless method showed in sarler and vertnik comput math appl 2006 51 1269 1282 excellent numerical results have been observed copyright 2007 john wiley sons ltd

an inverse problem for a fractional diffusion equation in this paper we consider an inverse problem for a fractional diffusion equation which is highly ill posed such a problem is obtained from the classical diffusion equation by replacing the first order time derivative by the caputo fractional derivative of order a 0 a 1 we show that the problem is severely ill posed and further apply an optimal regularization method to solve it based on the solution in the frequency domain we can prove the optimal convergence estimate which shows that the regularized solution depends continuously on the data and is a good approximation to the exact solution numerical examples show that the proposed method works well

two dimensional joint process lattice for adaptive restoration of images the two dimensional 2d joint process lattice tdjpl and its implementations for image restoration applications are examined a 2d adaptive lattice algorithm tdal is first developed convergence properties of the algorithm are covered for the 2d adaptive lattice least mean squares tdal lms case the complexity of the normalized algorithm is slightly more than that of the tdal lms but it is a faster converging algorithm implementations of the proposed tdjpl estimator as a 2d adaptive lattice noise canceler and as a 2d adaptive lattice line enhancer are then considered the performance of both schemes is evaluated using artificially degraded image data at different signal to noise ratios snrs the results show that substantial noise reduction has been achieved and the high improvement in the mean square error even at very low input snr is ensured the results obtained consistently demonstrate the efficacy of the proposed tdjpl implementations and illustrate the success in its use for adaptive restoration of images

extension of the schur cohn stability test for 2 d ar quarter plane model the schur cohn test plays an essential role in checking the stability of one dimensional 1d random processes such as autoregressive ar models via the so called reflection coefficients partial correlations or schur szego coefficients in the context of two dimensional 2d random field modeling one of the authors recently proposed a 2d ar quarter plane model representation using 2d reflection coefficients estimated by a fast recursive adaptive algorithm based on such 2d reflection coefficients we can therefore derive two necessary stability conditions for a 2d ar quarter plane model one of these conditions can be considered as an extension of the schur cohn stability criterion based on the 2d reflection coefficients

a direct algorithm for computing 2 d ar power spectrum estimates an algorithm for computing the parameters in a 2 d autoregressive spectral estimate without prior estimation of the correlation is described the algorithm utilizes the multichannel form of the burg algorithm and the relation between multichannel and 2 d ar modeling the procedure permits computation of the spectral matrix for several channels of 2 d data models with support in different quadrants are combined to form the spectral estimate

the numerical solution of one phase classical stefan problem in this paper variable space grid and boundary immobilisation techniques based on the explicit finite difference are applied to the one phase classical stefan problem it is shown that all the results obtained by the two methods are in good agreement with the exact solution and exhibit the expected convergence as the mesh size is refined

hybrids of the heat balance integral method abstract a framework for refining and hybridizing the heat balance integral method is proposed while showing the non uniqueness of a combined integral method in the sense of myers and mitchell t g myers s l mitchell application of the combined integral method to stefan problems applied mathematical modelling 35 9 2011 4281 4294 it is evinced through the hybrids advanced and benchmarks undertaken that for the class of finite puiseux series commonly employed there are no globally efficient exponents synthesis of local regions of high accuracy of these hybrids is realized through the introduction of an applicable splicing algorithm

heat balance integral methods applied to the one phase stefan problem with a convective boundary condition at the fixed face abstract in this paper we consider a one dimensional one phase stefan problem corresponding to the solidification process of a semi infinite material with a convective boundary condition at the fixed face the exact solution of this problem available recently in the literature enable us to test the accuracy of the approximate solutions obtained by applying the classical technique of the heat balance integral method and the refined integral method assuming a quadratic temperature profile in space we develop variations of these methods which turn out to be optimal in some cases throughout this paper a dimensionless analysis is carried out by using the parameters stefan number ste and the generalized biot number bi in addition it is studied the case when bi goes to infinity recovering the approximate solutions when a dirichlet condition is imposed at the fixed face some numerical simulations are provided in order to estimate the errors committed by each approach for the corresponding free boundary and temperature profiles

optimum asymmetric half plane autoregressive lattice parameter modeling of 2 d fields in this paper we present a new optimum asymmetric half plane ashp autoregressive lattice parameter modeling of two dimensional 2 d random fields this structure introduces 4n points into the prediction support region when the order of the model increases from n 1 to n starting with a given data field a set of four auxiliary prediction errors are generated in order to obtain the growing number of 2 d ashp reflection coefficients at successive stages the theory has been applied to the high resolution radar imaging problem and has also been proven using the concepts of vector space orthogonal projection and subspace decomposition it is shown that the proposed ashp structure generates the orthogonal realization subspaces for different recurse directions in addition to developing the basic theory the presentation includes a comparison between the proposed theory and other alternative structures both in terms of conceptual background and complexity while the recently developed reduced complexity ashp lattice modeling structure requires o 4n sup 3 lattice sections with n equal to the order of the error filter the proposed configuration requires only o 2n sup 2 lattice sections

application of standard and refined heat balance integral methods to one dimensional stefan problems the work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems these include standard test problems both with one and two phase changes which have exact solutions that enable us to test the accuracy of the approximate solutions we also consider situations where no analytical solution is available and compare these to numerical solutions it is popular to use a quadratic profile as an approximation of the temperature but we show that a cubic profile seldom considered in the literature is far more accurate in most circumstances in addition the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases we assess which integral method is better for various problems showing that it is largely dependent on the specified boundary conditions

a meshless integration free and boundary only rbf technique based on the radial basis function rbf nonsingular general solution and dual reciprocity method drm this paper presents an inherently meshless integration free boundary only rbf collocation technique for numerical solution of various partial differential equation systems the basic ideas behind this methodology are very mathematically simple in this study the rbfs are employed to approximate the inhomogeneous terms via the drm while nonsingular general solution leads to a boundary only rbf formulation for homogenous solution the present scheme is named as the boundary knot method bkm to differentiate it from the other numerical techniques in particular due to the use of nonsingular general solutions rather than singular fundamental solutions the bkm is different from the method of fundamental solution in that the former does not require the artificial boundary and results in the symmetric system equations under certain conditions the efficiency and utility of this new technique are validated through a number of typical numerical examples completeness concern of the bkm due to the sole use of the nonsingular part of complete fundamental solution is also discussed

multichannel 2 d ar spectrum estimation spectral estimation for multiple 2 d signals by autoregressive modeling is discussed the procedure computes the entire spectral matrix of autospectra and cross spectra for the set of 2 d signals specific differences between ar models for this problem and those for lower dimensional problems are discussed experimental results are presented

lattice parameter autoregressive modeling of two dimensional fields part i the quarter plane case quarter plane autoregressive lattice parameter modeling of two dimensional fields is developed as a natural extension of one dimensional lattice parameter theory starting with a given data field four prediction error fields are generated their linear combination is used to define and calculate 2 d lattice parameter reflection factors for successive lattice parameter model stages in addition to developing the basic theory the presentation includes the relationships between the quarter plane two dimensional transfer function and the lattice parameters the lattice parameter synthesis model for generating a two dimensional field from a random field input and lattice parameter stability conditions the theory has been confirmed by computer simulations the extension of this lattice parameter theory for the asymmetric half plane case is to be presented in a subsequent paper

regularization for a fractional sideways heat equation we consider a sideways problem for a fractional heat equation which is highly ill posed this study gives a new dynamic method for choosing a regularization parameter by using the spectral methods some convergence rates on the temperature and heat flow are given for illustration several numerical examples are constructed to show the feasibility and efficiency of the proposed methods comparing with the traditional stationary methods for choosing regularization parameter the proposal methods are more accurate and effective

universal limit mapping in grazing bifurcations grazing bifurcations are nonsmooth bifurcations that occur in impacting mechanical oscillators a sign of the lack of smoothness is a square root expression that arises in mappings describing the dynamics certain types of grazing bifurcations involve chaotic bands or period adding cascades with or without chaotic bands there is also a characteristic scaling behavior present here this type of bifurcation is investigated and the self similarity under scaling is used to derive a renormalized limit mapping a study of the dynamics of the limit mapping identifying all attractors for all parameter values is also presented

control and state estimation of the one phase stefan problem via backstepping design this paper develops a control and estimation design for the one phase stefan problem the stefan problem represents a liquid solid phase transition as time evolution of a temperature profile in a liquid solid material and its moving interface this physical process is mathematically formulated as a diffusion partial differential equation pde evolving on a time varying spatial domain described by an ordinary differential equation ode the state dependency of the moving interface makes the coupled pde ode system a nonlinear and challenging problem we propose a full state feedback control law an observer design and the associated output feedback control law of both neumann and dirichlet boundary actuations via the backstepping method also the state feedback control law is provided when a robin boundary input is considered the designed observer allows the estimation of the temperature profile based on the available measurements of liquid phase length and the heat flux at the interface the associated output feedback controller ensures the global exponential stability of the estimation errors the mathcal h 1 norm of the distributed temperature and the moving interface at the desired setpoint under some explicitly given restrictions on the setpoint and observer gain

a variable time step galerkin method for a one dimensional stefan problem a variable time step vts method is presented for the solution of a one dimensional stefan problem describing the evaporation of droplets the method uses a simple coordinate transformation and transforms the moving boundary problem into a problem on a fixed domain the weak or galerkin formulation of the resulting initial boundary value problem is then used to derive a system of initial value problems in ordinary differential equations the solution is advanced in time by an implicit marching technique coupled with an iterative computation of the time step for a given advancement of the moving boundary an integral relationship is used to correct the time step in each iteration the numerical results obtained by the present method exhibit very good agreement with those obtained by previous methods

on the accurate numerical solution of a two phase stefan problem with phase formation and depletion in this paper the keller box finite difference scheme is employed in tandem with the so called boundary immobilization method for the purposes of solving a two phase stefan problem that has both phase formation and phase depletion an important component of the work is the use of variable transformations that must be built into the numerical algorithm in order to resolve the boundary condition discontinuities that are associated with the onset of phase formation and depletion in particular this allows the depletion time to be determined and the solution to be computed after depletion the method gives second order accuracy in both time and space for all variables throughout the entire computation

numerical schemes for one dimensional stefan like problems with a forcing term variable space grid and boundary immobilisation schemes based on the explicit finite difference method are applied to the one phase stefan like problems with a forcing term in order to evaluate the temperature distribution and the interface movement location and speed the numerical results obtained by the two schemes have been compared with the exact values and are found to be in good agreement with each other it is shown that the numerical solutions exhibit the expected convergence to the exact one as the mesh size is reduced a von neumann stability analysis of each scheme is also investigated

on the numerical solution of two phase stefan problems with heat flux boundary conditions a recently derived numerical algorithm for one dimensional one phase stefan problems is extended for the purpose of two phase moving boundary problems in which the second phase first appears only after a finite delay time this can occur if the phase change is caused by a heat flux boundary condition in tandem with the keller box finite difference scheme the so called boundary immobilization method is used an important component of the work is the use of variable transformations that must be built into the numerical algorithm to resolve the boundary condition discontinuity that is associated with the onset of phase change this allows the delay time until solidification begins to be determined and gives second order accuracy in both time and space

an improved moving least squares ritz method for two dimensional elasticity problems we propose an improved moving least squares ritz imls ritz method with its element free framework developed for studying two dimensional elasticity problems using the imls approximation for the field variables the discretized governing equations of the problem are derived via the ritz procedure in the imls an orthogonal function system with a weight function is employed as the basis for construction of its displacement field by using the element free imls ritz method solutions of the two dimensional elasticity problems are obtained the applicability of the element free imls ritz method is illustrated through three selected example problems the convergence characteristics of the method are examined by varying the number of nodes and geometric parameters of these examples the accuracy of the method is validated by comparing the computed results with the efg and exact solutions

a fixed grid local method for 1 d stefan problems abstract this note is concerned with a fixed grid local method for the solution of 1 d free boundary problems the method uses a coordinate transformation after the coordinate transformation it is then possible to obtain exact solutions for the resulting equations in terms of the local variables these exact solutions are in terms of constants of integration that are unknown by imposing the given boundary conditions and some smoothness requirements it is possible to furnish a set of linearly independent conditions that can be used to solve for the constants of integration a number of examples are used to study the applicability of the method

control of near grazing dynamics in impact oscillators a method is presented for controlling the persistence of a local attractor near a grazing periodic trajectory in a piecewise smooth dynamical system in the presence of discontinuous jumps in the state associated with intersections with system discontinuities in particular it is shown that a discrete linear feedback strategy may be employed to retain the existence of an attractor near the grazing trajectory such that the deviation of the attractor from the grazing trajectory goes to zero as the system parameters approach those corresponding to grazing contact the implementation relies on a local analysis of the near grazing dynamics using the concept of discontinuity mappings numerical results are presented for a linear and a nonlinear oscillator

the method of approximate fundamental solutions mafs for stefan problems for the sphere the paper presents a new meshless in space numerical method the method of approximate fundamental solutions mafs for solving problems with moving boundaries of the stefan type this technique first suggested for solving the stefan problems in plane geometry is now extended onto the cases of inward and outward spherical problems computed results for the inward and outward spherical problems are numerically evaluated for comparison with the results obtained by other authors the comparison shows that the method presented provides a very high precision in determining the position of the moving boundary and the results are in a good agreement with the previous studies