modeling microstructure evolution using gradient weighted moving finite elements microstructure evolution where grain boundaries evolve by mean curvature motion is modeled in three dimensions 3 d using gradient weighted moving finite elements gwmfe to do this we modify and extend an existing 2 d gwmfe code to create a new code grain3d which makes the 3 d microstructure modeling possible the right hand side term which drives the gwmfe motion can be viewed as surface tension forces that is as the negative gradient of the surface integral of a constant energy density mu on the triangular interfacial grid extensions to the method include equations for the motion of tetrahedra that are conformally attached to the moving piecewise linear triangular facets which represent the gwmfe discretization of the evolving grain boundaries we present some new regularization terms which control element quality as well as preventing element collapse in the simulation new capabilities for changing the mesh topology are used to keep the grid edge lengths below a maximum allowable length hmax and to mimic actual changes in the physical topology such as collapse and disappearance of individual grains validating runs are performed on some test cases that can be analytically solved including collapse of a spherical grain and the case of columnar microstructure in the spherical collapse case the gwmfe method appears to have an error in the surface area collapse rate da over dt which is cal o delta theta 2 where delta theta is a measure of the angular resolution of the mesh finally a run is presented where a true 3 d microstructure possessing triple lines and quadruple points in the interior and triple points on the exterior boundaries is evolved to a 2 d columnar microstructure and finally evolved down to a single grain

robust stabilization of a system with delays in control a robust stabilization problem is discussed for a system with delays in control the authors derive a robust stabilizing law against additive perturbations then motivated by the feature of predictive controllers they investigate the structure of robust stabilizing law and provide some interpretations on the relation between the value of time delay and the achievable margin of robust stabilizability

towards a statistical theory of texture evolution in polycrystals most technologically useful materials possess polycrystalline microstructures composed of a large number of small monocrystalline grains separated by grain boundaries the energetics and connectivity of the grain boundary network play a crucial role in determining the properties of a material across a wide range of scales a central problem in materials science is to develop technologies capable of producing an arrangement of grains a texture that provides for a desired set of material properties one of the most challenging aspects of this problem is to understand the role of topological reconfigurations during coarsening here we propose an upscaling procedure suitable for large complex systems the procedure is based on numerical experimentation combined with stochastic tools and consists of large scale numerical simulations of a system at a microscopic level statistical analysis of the microscopic data and formulation of the model based on stochastic characteristics predicted by the statistical analysis this approach promises to be valuable in establishing the effective model of microstructural evolution in realistic two and three dimensional systems to test ideas we use our upscaling procedure to study the mesoscopic behavior of a reduced one dimensional network of grain boundaries despite the simplicity of its formulation this model exhibits highly nontrivial behavior characterized by growth and disappearance of grain boundaries and develops probability distributions similar to those observed in higher dimensional simulations here we focus on the grain deletion events which are common to all coarsening systems

robust compensation of delay and diffusive actuator dynamics without distributed feedback this paper deals with robust observer based output feedback stabilization of systems whose actuator dynamics can be described in terms of partial differential equations pdes more specifically delay dynamics first order hyperbolic pde and diffusive dynamics parabolic pde are considered the proposed controllers have a pde observer based structure the main novelty is that stabilization for an arbitrarily large delay or diffusion domain length is achieved while distributed integral terms in the control law are avoided the exponential stability of the closed loop in both cases is proved using lyapunov functionals even in the presence of small uncertainties in the time delay or the diffusion coefficient the feasibility of this approach is illustrated in simulations using a second order plant with an exponentially unstable mode

a chain observer for nonlinear systems with multiple time varying measurement delays this paper presents a method for designing state observers with exponential error decay for nonlinear systems whose output measurements are affected by known time varying delays a modular approach is followed where subobservers are connected in cascade to achieve a desired exponential convergence rate chain observer when the delay is small a single step observer is sufficient to carry out the goal two or more subobservers are needed in the the presence of large delays the observer employs delay dependent time varying gains to achieve the desired exponential error decay the proposed approach allows to deal with vector output measurements where each output component can be affected by a different delay relationships among the error decay rate the bound on the measurement delays the observer gains and the lipschitz constants of the system are presented the method is illustrated on the synchronization problem of continuous time hyperchaotic systems with buffered measurements

a new approach to state observation of nonlinear systems with delayed output the article presents a new approach for the construction of a state observer for nonlinear systems when the output measurements are available for computations after a nonnegligible time delay the proposed observer consists of a chain of observation algorithms reconstructing the system state at different delayed time instants chain observer conditions are given for ensuring global exponential convergence to zero of the observation error for any given delay in the measurements the implementation of the observer is simple and computer simulations demonstrate its effectiveness

model for coarsening froths and foams the coarsening process of froths and foams is described statistically in two dimensions by a random neighbor model this nonlinear dynamical model contains no free parameters all rates are determined dynamically it describes normal growth agrees with experimental results throws light on old data and hopefully inspires new simulations and measurements lewis s law anat rec 38 341 1928 am j bot 30 74 1943 and some other properties can be derived analytically from the model

finite spectrum assignment of unstable time delay systems with a safe implementation the instability mechanisms related to the implementation of distributed delay controllers in the context of finite spectrum assignment were studied in detail in the past few years in this note we introduce a distributed delay control law that assigns a finite closed loop spectrum and whose implementation with a sum of point wise delays is safe this property is obtained by implicitly including a low pass filter in the control loop this leads to a closed loop characteristic quasipolynomial of retarded type and not one of neutral type which was shown to be a cause of instability in previous schemes

reduction model approach for linear time varying systems with delays we study stabilization problems for time varying linear systems with constant input delays our reduction method ensures input to state stability with respect to additive uncertainties under arbitrarily long delays it applies to rapidly time varying systems and gives a lower bound on the admissible rapidness parameters we also cover slowly time varying systems including upper bounds on the allowable slowness parameters we illustrate our work using a pendulum model

diffusion generated motion using signed distance functions we describe a new class of algorithms for generating a variety of geometric interfacial motions by alternating two steps construction of the signed distance function i e redistancing to the interface and convolution with a suitable kernel these algorithms can be seen as variants of merriman bence and osher s threshold dynamics 25 the new algorithms proposed here preserve the computational efficiency of the original threshold dynamics algorithm however unlike threshold dynamics the new algorithms also allow attaining high accuracy on uniform grids without adaptive refinement

diffusion generated motion for grain growth in two and three dimensions an efficient algorithm for accurately simulating curvature flow for large networks of curves in two dimensions and surfaces in three dimensions on uniform grids is proposed this motion arises in the technologically important problem of simulating grain boundary motion in polycrystalline materials in this formulation grain boundaries are zero level sets of signed distance functions curvature motion is achieved by first diffusing locally maintained signed distance functions followed by a reinitialization step a technique is devised to allow a single signed distance function to represent a large subset of spatially separated grains hundreds of thousands of grains can be simulated using a small number of signed distance functions in this work 32 in two dimensions and 64 in three dimensions are more than sufficient using modest computational hardware

a variational approach to modeling and simulation of grain growth most technologically useful materials arise as polycrystalline microstructures composed of a myriad of small crystallites called grains separated by their interfaces called grain boundaries the orientations and arrangements of the grains and their network of boundaries are implicated in many properties across wide scales for example functional properties like conductivity in microprocessors and lifetime properties like fracture toughness in structures simulation is becoming an important tool for understanding both materials properties and their processing requirements here we offer a consistent variational approach to the mesoscale simulation of these systems subject to the mullins equation of curvature driven growth in a two dimensional setting the main objective is to provide a calibration for future two dimensional and three dimensional efforts we discuss several novel features of our approach which we anticipate will render it a flexible scalable and robust tool to aid in microstructural prediction simulation results offer compelling evidence of the predictability and robustness of statistical properties of large systems such as grain size distribution and texture that are of immediate interest in materials science

a fast fixed point algorithm for independent component analysis we introduce a novel fast algorithm for independent component analysis which can be used for blind source separation and feature extraction we show how a neural network learning rule can be transformed into a fixedpoint iteration which provides an algorithm that is very simple does not depend on any user defined parameters and is fast to converge to the most accurate solution allowed by the data the algorithm finds one at a time all nongaussian independent components regardless of their probability distributions the computations can be performed in either batch mode or a semiadaptive manner the convergence of the algorithm is rigorously proved and the convergence speed is shown to be cubic some comparisons to gradient based algorithms are made showing that the new algorithm is usually 10 to 100 times faster sometimes giving the solution in just a few iterations

an extension of the prediction scheme to the case of systems with both input and state delay in this contribution we present an extension of the prediction scheme proposed in manitius and olbrot 1979 for the compensation of the input delay to the case of linear systems with both input delay and state delay for simplicity of the presentation we treat the case of systems with one state delay

non negative matrix factorization with sparseness constraints non negative matrix factorization nmf is a recently developed technique for finding parts based linear representations of non negative data although it has successfully been applied in several applications it does not always result in parts based representations in this paper we show how explicitly incorporating the notion of sparseness improves the found decompositions additionally we provide complete matlab code both for standard nmf and for our extension our hope is that this will further the application of these methods to solving novel data analysis problems

probabilistic independent component analysis for functional magnetic resonance imaging we present an integrated approach to probabilistic independent component analysis ica for functional mri fmri data that allows for nonsquare mixing in the presence of gaussian noise in order to avoid overfitting we employ objective estimation of the amount of gaussian noise through bayesian analysis of the true dimensionality of the data i e the number of activation and non gaussian noise sources this enables us to carry out probabilistic modeling and achieves an asymptotically unique decomposition of the data it reduces problems of interpretation as each final independent component is now much more likely to be due to only one physical or physiological process we also describe other improvements to standard ica such as temporal prewhitening and variance normalization of timeseries the latter being particularly useful in the context of dimensionality reduction when weak activation is present we discuss the use of prior information about the spatiotemporal nature of the source processes and an alternative hypothesis testing approach for inference using gaussian mixture models the performance of our approach is illustrated and evaluated on real and artificial fmri data and compared to the spatio temporal accuracy of results obtained from classical ica and glm analyses

feedback stabilization of linear autonomous time lag systems a stabilization theory which employs well established finite dimensional control system tools is developed for the stabilization of linear autonomous time lag systems the main ideas include 1 a set whose elements are matrices each of which is a left zero of the system characteristic quasi polynomial matrix and 2 a linear transformation which reduces the delay system to a delay free system whose state matrix is a direct sum of n elements of the matrix set where n is some positive integer from the definition of this matrix set it is shown that each of its elements inherits its spectrum from that of the delay system so that by design the system unstable poles may be embedded in the spectrum of the delay free system under the assumption of spectral stabilizability it is then shown how to obtain a stabilizing feedback control law on the basis of the delay free system numerical examples are presented to confirm the theory

fast and robust fixed point algorithms for independent component analysis independent component analysis ica is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible we use a combination of two different approaches for linear ica comon s information theoretic approach and the projection pursuit approach using maximum entropy approximations of differential entropy we introduce a family of new contrast functions for ica these contrast functions enable both the estimation of the whole decomposition by minimizing mutual information and estimation of individual independent components as projection pursuit directions the statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model and it is shown how to choose contrast functions that are robust and or of minimum variance finally we introduce simple fixed point algorithms for practical optimization of the contrast functions

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

input delay compensation of linear systems with both state and input delays by nested prediction abstract in this paper we consider the input delay compensation of linear systems with both state and input delays under the condition that the open loop time delay systems in the absence of input delay can be stabilized by delayed state feedback a nested predictor based approach is established to predict the future states so that the delays in the input are compensated it is shown that the compensated closed loop system in the presence of input delay possesses the same characteristic equation as the closed loop system in the absence of input delay the proposed approach can be generalized to general linear systems having multiple state delays and or multiple input delays to implement the nested predictor based controllers by applying numerical integration approaches an augmented nested predictor based approach by adding input filters is proposed two numerical examples are worked out to show the effectiveness of the proposed approach

on distributed delay in linear control laws part i discrete delay implementations this note proposes two approaches to approximate distributed delay in linear control laws and furthermore to implement it in the z domain and in the s domain the h sup spl infin norm of the approximation error converges to 0 when the number n of approximation steps approaches spl infin hence the instability problem due to the approximation error which has been widely studied in recent years does not exist provided that n is large enough moreover the static gain is guaranteed so that no extra efforts are needed to retain the steady state performance as by products two new formulas for the forward and backward rectangular rules are obtained these formulas are more accurate than the conventional ones when the integrand has an exponential term

stabilization of linear systems with both input and state delays by observer predictors this paper studies the stabilization of linear systems with both state and input delays where the input delay can be arbitrarily large yet exactly known observer predictor based controllers are designed to predict the future states so that the input delay can be properly compensated necessary and sufficient conditions guaranteeing the stability of the closed loop system are provided in terms of the stability of some simple linear time delay systems refereed to as observer error systems by which the separation principle is discovered moreover approaches in terms of linear matrix inequalities are also provided to design both the state feedback gains and observer gains finally a numerical example illustrates that the proposed approaches are more effective and safe to implement than the existing methods

predictor based control of linear systems with large and variable measurement delays this paper concerns the problem of the control of linear systems by means of feedback from delayed output where the delay is known and time varying the main advantage of the approach is that it can be applied to systems with any delay bound i e not only small delays the predictor is based on a combination of finite dimensional elementary predictors whose number can be suitably chosen to compensate any delay the single predictor element is an original proposal and the class of delays to which the schema can be applied includes but it is not limited to continuous delay functions

input delay compensation of linear systems with both state and input delays by adding integrators abstract this paper studies stabilization of linear systems with both state and input delays a dynamic input delay compensator obtained by adding integrators is established to compensate the input delays that can be arbitrarily large with the input delay compensator the original stabilization problem reduces to the problem of stabilizing an augmented linear time delay system without input delay three methods are also proposed to design stabilizing controllers for the augmented linear time delay system the first method is based on linear matrix inequalities lmis and the second method is based on model reduction the third method is based on pole placement and is built for the particular case that the original time delay system has only a pure delayed state vector on its right hand side for this method the optimal gain such that the decay rate of the closed loop system is maximized is also proposed the effectiveness of the proposed approaches is illustrated by three linear time delay systems that are open loop unstable

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

threshold dynamics for networks with arbitrary surface tensions we present and study a new algorithm for simulating the n phase mean curvature motion for an arbitrary set of isotropic surface tensions the departure point is the threshold dynamics algorithm of merriman bence and osher for the two phase case a new energetic interpretation of this algorithm allows us to extend it in a natural way to the case of n phases for arbitrary surface tensions and arbitrary isotropic mobilities for a large class of surface tensions the algorithm is shown to be consistent in the sense that at every time step it decreases an energy functional that is an approximation in the sense of gamma convergence of the interfacial energy a broad range of numerical tests shows good convergence properties an important application is the motion of grain boundaries in polycrystalline materials it is also established that the above mentioned large class of surface tensions contains the read shockley surface tensions both in the two dimensional and three dimensional settings 2015 wiley periodicals inc

brief paper exponential stability of nonlinear time delay systems with delayed impulse effects the problem of exponential stability for nonlinear time delay systems with delayed impulses is addressed in this paper lyapunov based sufficient conditions for exponential stability are derived respectively for two kinds of delayed impulses i e destabilizing delayed impulses and stabilizing delayed impulses it is shown that if a nonlinear impulsive time delay system without impulse input delays is exponentially stable then under some conditions its stability is robust with respect to small impulse input delays moreover it is also shown that for a stable nonlinear impulsive time delay system if the magnitude of the delayed impulses is sufficiently small then under some conditions the delayed impulses do not destroy the stability irrespective of the sizes of the impulse input delays the efficiency of the proposed results is illustrated by three numerical examples

output feedback control of linear systems with input state and output delays by chains of predictors abstract in this paper we consider the control problem of linear systems with state time delays when the control signal is affected by a possibly time varying delay the problem is solved by a chain of predictors under the assumption that a stabilizing control exists for the case of no input delay this solution is then extended to the case of partial information when only delayed output is available both the input and the output delays may have arbitrary bounds with respect to previous approaches to the same problem appeared recently in the literature the method proposed here has a simpler structure and in particular it does not need the computation of distributed terms as a by product we show that it is possible to derive an observer for a system with state and output delays from an observer for the same system without output delays

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

defect detection of uneven brightness in low contrast images using basis image representation in this paper we propose a machine vision approach for detecting local irregular brightness in low contrast surface images and especially focus on mura brightness non uniformity defects in liquid crystal display lcd panels a mura defect embedded in a low contrast surface image shows no distinct intensity from its surrounding region and even worse the sensed image may also present uneven illumination on the surface all these make the mura defect detection in low contrast surface images extremely difficult a set of basis images derived from defect free surface images are used to represent the general appearance of a clear surface an image to be inspected is then constructed as a linear combination of the basis images and the coefficients of the combination form the feature vector for discriminating mura defects from clear surfaces in order to find minimum number of basis images for efficient and effective representation the basis images are designed such that they are both statistically independent and spatially exclusive an independent component analysis based model that finds both the maximum negentropy for statistical independency and minimum spatial correlation for spatial redundancy is proposed to extract the representative basis images experimental results have shown that the proposed method can effectively detect various mura defects in low contrast lcd panel images