a multi step method for partial quadratic pole assignment problem with time delay in this paper the partial quadratic pole assignment problem with time delay is considered we propose a multi step method for solving this problem in which the unwanted eigenvalues are moved to desired values and all other eigenpairs remain unchanged our method is easy to realize and need not use the receptance matrix or solve the sylvester equation numerical examples show that the proposed method is effective

partial eigenstructure assignment for the quadratic pencil abstract it is shown in this paper that by the appropriate choice of gain and input influence matrices certain eigenpairs of a vibrating system may be assigned while the other eigenpairs remain unchanged the system under consideration is modelled by a set of second order differential equations and the assignment is carried by multi input state feedback control the solution may be of particular interest in the stabilization and control of flexible structures using smart materials where only a small part of the eigenstructure is to be reassigned and the rest is required to remain unchanged the method presented is illustrated with a numerical example

quantitative phase field modeling of dendritic growth in two and three dimensions we report the results of quantitative phase field simulations of the dendritic crystallization of a pure melt in two and three dimensions these simulations exploit a recently developed thin interface limit of the phase field model a karma and w j rappel phys rev e 53 r3017 1996 which is given here a detailed exposition this limit makes it possible to perform efficient computations with a smaller ratio of capillary length to interface thickness and with an arbitrary interface kinetic coefficient simulations in one and two dimensions are first carried out to test the accuracy of phase field computations performed within this limit dendrite tip velocities and tip shapes are found to be in excellent quantitative agreement with exact numerical benchmarks of solvability theory obtained by a boundary integral method both with and without interface kinetics simulations in three dimensions exploit in addition to the asymptotics a methodology to calculate grid corrections due to the surface tension and kinetic anisotropies they are used to test basic aspects of dendritic growth theory that pertain to the selection of the operating state of the tip and to the three dimensional morphology of needle crystals without sidebranches for small crystalline anisotropy simulated values of ensuremath sigma are slightly larger than solvability theory predictions computed by the boundary integral method assuming an axisymmetric shape and agree relatively well with experiments for succinonitrile given the uncertainty in the measured anisotropy in contrast for large anisotropy simulated ensuremath sigma values are significantly larger than the predicted values this disagreement however does not signal a breakdown of solvability theory it is consistent with the finding that the amplitude of the mathrm cos 4 ensuremath varphi mode which measures the departure of the tip morphology from a shape of revolution increases with anisotropy this departure can therefore influence the tip selection in a way that is not accurately captured by the axisymmetric approximation for large anisotropy finally the tail shape at a distance behind the tip that is large compared to the diffusion length is described by a linear law r ensuremath sim z with a slope dr dz that is nearly equal to the ratio of the two dimensional and three dimensional steady state tip velocities furthermore the evolution of the cross section of a three dimensional needle crystal with increasing distance behind the tip is nearly identical to the evolution of a two dimensional growth shape in time in accord with the current theory of the three dimensional needle crystal shape

crystal growth and dendritic solidification we present a numerical method which computes the motion of complex solid liquid boundaries in crystal growth the model we solve includes physical effects such as crystalline anisotropy surface tension molecular kinetics and undercooling the method is based on two ideas first the equations of motion are recast as a single history dependent boundary integral equation on the solid liquid boundary a fast algorithm is used to solve the integral equation efficiently second the boundary is moved by solving a hamiltonjacobi type equation on a fixed domain formulated by osher and sethian for a function in which the boundary is a particular level set this equation is solved by finite difference schemes borrowed from the technology of hyperbolic conservation laws the two ideas are combined by constructing a smooth extension of the normal velocity off the moving boundary in a way suggested by the physics of the problem our numerical experiments show the evolution of complex crystalline shapes development of large spikes and corners dendrite formation and side branching and pieces of solid merging and breaking off freely

partial eigenstructure assignment for undamped vibration systems using acceleration and displacement feedback abstract a new method for partial eigenstructure assignment using acceleration and displacement feedback for undamped vibration systems is presented in this paper firstly a necessary and sufficient condition is proposed for the incremental mass and stiffness matrices that modify some eigenpairs while keeping other eigenpairs unchanged secondly based on this condition an algorithm for determining the required control gain matrices of acceleration and displacement feedback which assign the desired eigenstructure is developed this algorithm is easy to implement and works directly on the second order system model more importantly the algorithm allows the control matrix to be specified beforehand and also leads naturally to a small norm solution of the feedback gain matrices finally some numerical examples are given to demonstrate the effectiveness and accuracy of the proposed algorithm

three dimensional dendrite tip morphology at low undercooling we investigate the three dimensional morphology of the dendrite tip using the phase field method we find that for low undercoolings this morphology is ostensibly independent of anisotropy strength except for a localized shape distortion near the tip that only affects the value of the tip radius rho which is crudely approximated by rho approx equal 1 alpha rho sub iv where rho sub iv is the ivantsov tip radius of an isothermal paraboloid with the same tip velocity and alpha is the stiffness anisotropy the universal tip shape which excludes this distortion is well fitted by the form z r sup 2 2 a sub 4 r sup 4 cos 4 phi where z is the distance from the tip and all lengths are scaled by rho sub iv this fit yields a sub 4 in the range 0 004 0 005 in good quantitative agreement with the existing tip morphology measurements in succinonitrile lacombe et al phys rev e 52 2778 1995 which are reanalyzed here and found to be consistent with a single cos 4 phi mode nonaxisymmetric deviation from a paraboloid moreover the fin shape away from the tip is well fitted by the power law z a x sup 5 3 with a approx equal 0 68 finally the characterization of the operating state of the dendrite tip is revisited in the light of these results more c 2000 the american physical society less

growth and form of zero noise diffusion limited aggregation on the cubic lattice abstract the growth and form of zero noise dla clusters on a cubic lattice is investigated numerical simulations reveal a stable cluster consisting of six fourfold symmetric almost planar arms with a staircase structure along each arm empirical expressions are obtained for the shape of the arms in the vicinity of the tips the scaling of the arm lengths and the scaling of the tip growth rates the empirical expressions are used to derive results for the growth rates along the arms of the cluster and for the step lengths in a needle staircase these results are in good agreement with the numerical simulations

an optimization approach for minimum norm and robust partial quadratic eigenvalue assignment problems for vibrating structures the partial quadratic eigenvalue assignment problem pqevap concerns the reassignment of a small number of undesirable eigenvalues of a quadratic matrix pencil while leaving the remaining large number of eigenvalues and the corresponding eigenvectors unchanged the problem arises in controlling undesirable resonance in vibrating structures and in stabilizing control systems the solution of this problem requires computations of a pair of feedback matrices for practical effectiveness these feedback matrices must be computed in such a way that their norms and the condition number of the closed loop eigenvector matrix are as small as possible these considerations give rise to the minimum norm partial quadratic eigenvalue assignment problem mnpqevap and the robust partial quadratic eigenvalue assignment problem rpqevap respectively in this paper we propose new optimization based algorithms for solving these problems the problems are solved directly in a second order setting without resorting to a standard first order formulation so as to avoid the inversion of a possibly ill conditioned matrix and the loss of exploitable structures of the original model the algorithms require the knowledge of only the open loop eigenvalues to be replaced and their corresponding eigenvectors the remaining open loop eigenvalues and their corresponding eigenvectors are kept unchanged the invariance of the large number of eigenvalues and eigenvectors under feedback is guaranteed by a proven mathematical result furthermore the gradient formulas needed to solve the problems by using the quasi newton optimization technique employed are computed in terms of the known quantities only above all the proposed methods do not require the reduction of the model order or the order of the controller even when the underlying finite element model has a very large degree of freedom these attractive features coupled with minimal computational requirements such as solutions of small diagonal sylvester equations make the proposed algorithms ideally suited for application to large real life structures numerical results show significant improvement in feedback norms and in the condition number of the closed loop system also the closed loop eigenvalues have acceptable accuracy

minimum norm partial eigenvalue assignment of high order linear system with no spill over abstract in this paper we consider the partial eigenvalue assignment problem peap of high order linear system by state feedback to prevent spill over phenomenon we establish the new orthogonality relations for the eigenvectors of matrix polynomial such that the unwanted eigenvalues are moved to prescribed values and the wanted eigenvalues remain unchanged based on the orthogonality relations the solvability conditions for peap are presented and the parametric expression of feedback matrices is derived in terms of the known quantities only finally an optimization based algorithm is proposed to find the minimum norm solution two numerical examples are given to show the application of the proposed method

efficient thermal field computation in phase field models we solve the phase field equations in two dimensions to simulate crystal growth in the low undercooling regime the novelty is the use of a fast solver for the free space heat equation to compute the thermal field this solver is based on the efficient direct evaluation of the integral representation of the solution to the constant coefficient free space heat equation with a smooth source term the computational cost and memory requirements of the new solver are reasonable and no artificial boundary conditions are needed this allows one to solve for the thermal field in a computational domain whose size depends only on the size of the growing crystal and not on the extent of the thermal field which can result in significant computational savings in the low undercooling regime

sharp interface cartesian grid method iii solidification of pure materials and binary solutions a numerical technique is presented for computing dendritic growth of crystals from pure melts and binary solutions the governing equations are solved on a fixed cartesian mesh and the immersed phase boundary is treated as a sharp solid fluid interface the interface is tracked using a level set field a finite difference scheme is presented that incorporates the immersed phase boundary with only a small change to a standard cartesian grid poisson solver the scheme is simple to implement in three dimensions the results from our calculations show excellent agreement with two dimensional microscopic solvability theory for pure material solidification it is shown that the method predicts dendrite tip characteristics in excellent agreement with the theory the sharp interface treatment allows discontinuous material property variation at the solid liquid interface this facilitates sharp interface simulations of dendritic solidification of binary solutions

pattern formation in three dimensional dendritic growth abstract the entire solution for three dimensional 3d nonaxisymmetric dendrites is described analytically its construction involves the 3d selection theory for the tip of the dendrite plus matching of the tail to this tip both intermediate and final asymptotics of the tail shape are given this shape which deviates strongly from the ivantsov paraboloid is in qualitative agreement with experimental observations we consider the time dependent behavior of sidebranching deformations taking into account the actual nonaxisymmetric shape of the needle crystal it is found that the amplitude of the deformation grows faster than for the axisymmetric paraboloid shape of the needle we argue that this effect resolves the puzzle that experimentally observed side branches have much larger amplitudes that can be explained by thermal noise in the framework of the axisymmetric approach the coarsening behavior of sidebranches in the nonlinear regime is shortly discussed

phase field modelling of solidification microstructure formation using the discontinuous finite element method this paper presents a discontinuous galerkin finite element computational methodology for solving the coupled phase field and heat diffusion equations to predict the microstructure evolution during solidification the phase field modelling of microstructure formation is briefly discussed the discontinuous galerkin finite element formulation for the phase field model systems for solidification microstructure formation is described in detail numerical stability is performed using the neumann method the accuracy of the discontinuous model is verified by the analytic solution of a simple 1 d solidification problem numerical calculations using the discontinuous finite element phase field model have been performed for simulating the complex 2 d and 3 d dendrite structures formed in supercooled melts and the results are compared well with those in literature using the finite difference methods parallel computing algorithm is presented and results show that the minimization of the intercommunication between microprocessors is the key to increase the effectiveness in parallel computing with the discontinuous finite element phase field model for solidification microstructure formation copyright 2006 john wiley sons ltd

image and video encryption using scan patterns abstract this paper presents a new method for image and video encryption and a first stage lossy video compression based on frames difference before the encryption the encryption methods are based on the scan methodology which is a formal language based two dimensional spatial accessing methodology which can generate very large number of scanning paths or space filling curves the image encryption is performed by scan based permutation of pixels and a substitution rule which together form an iterated product cipher the video encryption is performed by first lossy compressing adjacent frame differences and then encrypting the compressed frame differences the main characteristics of the proposed methods are image encryption first stage compression based frames differences and encryption of video whose compression error can be bounded pixelwise by a user specified value very large number of encryption keys and ability to encrypt large blocks of any digital data results from the use of the methods proposed here are also provided

robust partial quadratic eigenvalue assignment with time delay using the receptance and the system matrices abstract in this paper we consider the robust partial quadratic eigenvalue assignment problem in vibration by active feedback control based on the receptance measurements and the system matrices we propose an optimization method for the robust and minimum norm partial quadratic eigenvalue assignment problem we provide a new cost function and the closed loop eigenvalue sensitivity and the feedback norms can be minimized simultaneously our method is also extended to the case of time delay between measurements of state and actuation of control numerical tests demonstrate the effectiveness of our method

multiscale finite difference diffusion monte carlo method for simulating dendritic solidification abstract we present a novel hybrid computational method to simulate accurately dendritic solidification in the low undercooling limit where the dendrite tip radius is one or more orders of magnitude smaller than the characteristic spatial scale of variation of the surrounding thermal or solutal diffusion field the first key feature of this method is an efficient multiscale diffusion monte carlo dmc algorithm which allows off lattice random walkers to take longer and concomitantly rarer steps with increasing distance away from the solid liquid interface as a result the computational cost of evolving the large scale diffusion field becomes insignificant when compared to that of calculating the interface evolution the second key feature is that random walks are only permitted outside of a thin liquid layer surrounding the interface inside this layer and in the solid the diffusion equation is solved using a standard finite difference algorithm that is interfaced with the dmc algorithm using the local conservation law for the diffusing quantity here we combine this algorithm with a previously developed phase field formulation of the interface dynamics and demonstrate that it can accurately simulate three dimensional dendritic growth in a previously unreachable range of low undercoolings that is of direct experimental relevance

orthogonality and partial pole assignment for the symmetric definite quadratic pencil abstract the eigenvectors of a symmetric matrix can be chosen to form an orthogonal set with respect to the identity and to the matrix itself similarly the eigenvectors of a symmetric definite linear pencil can be chosen to be orthogonal with respect to the pair this paper presents the three sets of matrix weights with respect to which the eigenvectors of the symmetric definite quadratic pencil are orthogonal one of these is used to derive an explicit solution of the partial pole assignment problem by state feedback control for a control system modeled by a system of second order differential equations the solution may be of particular interest in the stabilization and control of flexible large space structures where only a small part of the spectrum is to be reassigned and the rest of the spectrum is required to remain unchanged

structure formation and the morphology diagram of possible structures in two dimensional diffusional growth the morphology diagram of possible structures in two dimensional diffusional growth is given in the parameter space of undercooling ensuremath delta versus anisotropy of surface tension ensuremath epsilon the building block of the dendritic structure is a dendrite with parabolic tip and the basic element of the seaweed structure is a doublon the transition between these structures shows a jump in the growth velocity we also describe the structures and velocities of fractal dendrites and doublons destroyed by noise we introduce a renormalized capillary length and density of the solid phase and use scaling arguments to describe the fractal dendrites and doublons the resulting scaling exponents for the growth velocity and the different length scales are expressed in terms of the fractal dimensions for surface and bulk of these fractal structures all the considered structures are compact on length scales larger than the diffusion length and they show fractal behavior on intermediate length scales between the diffusion length and a small size cutoff which depends on the strength of noise textcopyright 1996 the american physical society

orthogonal basis selection method for robust partial eigenvalue assignment problem in second order control systems in this paper we study the robust partial eigenvalue assignment problem using state feedback control in second order control systems which means that the feedback control matrices not only assign specific eigenvalues to the second order closed loop system but also that the system is robust or insensitive to perturbations in the coefficient matrices some measures of robustness of the closed loop system are discussed and a numerical method is proposed such that it aims to minimize one measure of the conditioning of the closed loop system numerical examples show that the method is convergent and often leads to better conditioned closed loop system

numerical simulation of dendritic solidification with convection three dimensional flow a numerical method for the simulation of the effect of melt flow on the three dimensional growth of a dendrite is described the method is an extension of the technique for two dimensional flow described in al rawahi and tryggvason j comput phys 180 2002 471 and is based on the explicit tracking of connected marker points that describe the liquidsolid interface an explicit projection method is used to solve the energy and the navier stokes equations on a regular stationary grid and the solidified region is represented by setting the velocities in the solid phase to zero the latent heat released during solidification is calculated using the normal temperature gradient near the interface the method is validated by a comparison with an exact solution for a stefan problem and a grid refinement study the simulations show that the speed of a dendrite arm growing into the flow is increased due to an increase in the temperature gradient on the upstream side and the formation of side branches is promoted as in two dimensions the effect of the flow on the growth of dendrite arms growing in the downstream direction is smaller than in two dimensions due to a smaller wake

minimum norm partial quadratic eigenvalue assignment with time delay in vibrating structures using the receptance and the system matrices abstract the partial quadratic eigenvalue assignment problem pqeap is to compute a pair of feedback matrices such that a small number of unwanted eigenvalues in a structure are reassigned to suitable locations while keeping the remaining large number of eigenvalues and the associated eigenvectors unchanged the problem arises in active vibration control of structures for real life applications it is not enough just to compute the feedback matrices they should be computed in such a way that both closed loop eigenvalue sensitivity and feedback norms are as small as possible also for practical effectiveness the time delay between the measurement of the state and implementation of the feedback controller should be considered while solving the pqeap these problems are usually solved using only system matrices and do not necessarily take advantage of the receptances which are available by measurements in this paper we propose hybrid methods combining the system matrices and measured receptances for solutions of the multi input pqeap and the minimum norm pqeap both for systems with and without time delay these hybrid methods are more efficient than the standard methods which only use the system matrices and not the receptances these hybrid methods also offer several other computational advantages over the standard methods our results generalize the recent work by ram et al partial pole placement with time delay in structures using the receptance and the system matrices linear algebra and its applications 434 2011 1689 1696 the results of numerical experiments demonstrate the effectiveness of the proposed methods

simulating hydrodynamics a pedestrian model a hele shaw cell contains two fluids seperated by an interface because the fluids are held in a narrow regions between two plates the cell can be described by a set of two dimensional hydrodynamic equations which determine the velocity fields in the fluids as well as the motion of the interface between them a discretized version of these equations can be implemented in terms of the motion of random walkers the walkers have the effect of carrying pieces of the fluid from one place to another they simulate a discrete version of the laplace equation and obey the appropriate boundary conditions for the fluid the walker hydrodynamic connection is explored in the limiting situation in which the viscosity of one of the fluids vanishes an algorithm is constructed and a few exemplary simulations are shown

numerical simulation of dendritic solidification with convection two dimensional geometry a front tracking method is presented for simulations of dendritic growth of pure substances in the presence of flow the liquid solid interface is explicitly tracked and the latent heat released during solidification is calculated using the normal temperature gradient near the interface a projection method is used to solve the navier stokes equations the no slip condition on the interface is enforced by setting the velocities in the solid phase to zero the method is validated through a comparison with an exact solution for a stefan problem a grid refinement test and a comparison with a solution obtained by a boundary integral method three sets of two dimensional simulations are presented a comparison with the simulations of beckermann et al j comput phys 154 468 1999 a study of the effect of different flow velocities and a study of the effect of the prandtl number on the growth of a group of dendrites growing together the simulations show that on the upstream side the dendrite tip velocity is increased due to the increase in the temperature gradient and the formation of side branches is promoted the flow has the opposite effect on the downstream side the results are in good qualitative agreement with published experimental results even though only the two dimensional aspects are examined here

personalized information encryption using ecg signals with chaotic functions the development of efficient data encryption to ensure high security of information transmission has long been a popular research subject because electrocardiogram ecg signals vary from person to person and can be used as a new tool for biometric recognition this study introduces an individual feature of ecg with chaotic henon and logistic maps for personalized cryptography this study also develops an encryption algorithm based on the chaos theory to generate initial keys for chaotic logistic and henon maps the proposed personalized encryption system uses a convenient handheld device to collect ecg signals from the user high quality randomness in ecg signals results in a widely expanded key space making it an ideal key generator for personalized data encryption the experiments reported in this study demonstrate the use of this approach in encrypting texts and images and applied of the proposed approach to secure communications

linearly first and second order unconditionally energy stable schemes for the phase field crystal model in this paper we develop a series of linear unconditionally energy stable numerical schemes for solving the classical phase field crystal model the temporal discretizations are based on the first order euler method the second order backward differentiation formulas bdf2 and the second order crank nicolson method respectively the schemes lead to linear elliptic equations to be solved at each time step and the induced linear systems are symmetric positive definite we prove that all three schemes are unconditionally energy stable rigorously various classical numerical experiments in 2d and 3d are performed to validate the accuracy and efficiency of the proposed schemes

noise induced sidebranching in the three dimensional nonaxisymmetric dendritic growth we consider the time dependent behavior of sidebranching deformations taking into account the actual nonaxisymmetric shape of the needle crystal the green s function of the linearized problem is presented by a functional integral with the help of the mullins sekerka local spectrum for the short wavelength perturbations the functional integral can be calculated by the steepest descent method where the green s function behavior is determined by the extremal trajectories governed by hamilton equations the local spectrum plays the role of the hamilton s function as in the axisymmetric approach j s langer phys rev a 36 3350 1987 noise induced wave packets generated in the tip region grow in amplitude and spread and stretch as they move down the sides of the dendrite producing a train of sidebranches the amplitude grows exponentially as a function of ensuremath vert z mathrm ensuremath vert 2 5 mathrm ensuremath sigma 1 2 where ensuremath vert z ensuremath vert is the distance from the dendritic tip and ensuremath sigma is the stability parameter the important result is that the amplitude of the sidebranches for the anisotropic needle crystal grows faster than for the axisymmetric paraboloid shape in the latter case it grows exponentially but only as a function of ensuremath vert z mathrm ensuremath vert 1 4 mathrm ensuremath sigma 1 2 we argue that this effect can resolve the puzzle that experimentally observed sidebranches have much larger amplitudes than can be explained by thermal noise in the framework of the axisymmetric approach the coarsening behavior of sidebranches in the nonlinear regime is briefly discussed

an algorithm for pole assignment of time invariant linear systems an algorithm is suggested for the computation of a linear state feedback for a single input system such that the resultant closed loop system has specified eigenvalues the algorithm is more efficient than many comparable techniques and has some desirable numerical properties it is closely related to the qr algorithm for the eigenproblem and extends to descriptor systems

numerically robust pole assignment for second order systems we propose two new methods for solution of the eigenvalue assignment problem associated with the second order control system global hsize 30pc specifically the methods construct feedback matrices f 1 and f 2 such that the closed loop quadratic pencil has a desired set of eigenvalues and the associated eigenvectors are well conditioned method 1 is a modification of the singular value decomposition based method proposed by juang and maghami which is a second order adaptation of the well known robust eigenvalue assignment method by kautsky et al for first order systems method 2 is an extension of the recent non modal approach of datta and rincon for feedback stabilization of second order systems robustness to numerical round off errors is achieved by minimizing the condition numbers of the eigenvectors of the closed loop second order pencil control robustness to large plant uncertainty will not be explicitly considered in this paper numerical results for both the two methods are favourable a compara

energy and entropy preserving numerical approximations of thermodynamically consistent crystal growth models abstract we present a numerical scheme that preserves the total energy and the entropy production rate termed the energy and entropy production rate preserving scheme for a general class of thermodynamically consistent phase field models for dendritic crystal growth derived from the first and second law of thermodynamics the scheme is second order in time linear and energy and entropy production rate preserving for any time steps the scheme is first discretized in time aided by the energy quadratization eq method and then in space using compact finite difference methods the linear system resulting from the scheme is shown to be uniquely solvable at both the semi discrete and the fully discrete level mesh refinement tests are performed to show the second order time convergence rate in the scheme several numerical examples of dendritic crystal growth are provided to demonstrate the accuracy and efficiency of the scheme the effects of various model parameters on growth patterns of the crystal are further investigated in details with the numerical solver the approach to developing the energy and entropy production rate preserving numerical scheme proposed in this study is so general that it can be applied to a wide range of thermodynamically consistent models not limited to phase field models

adaptive mesh refinement computation of solidification microstructures using dynamic data structures we study the evolution of solidification microstructures using a phase field model computed on an adaptive finite element grid we discuss the details of our algorithm and show that it greatly reduces the computational cost of solving the phase field model at low undercooling in particular we show that the computational complexity of solving any phase boundary problem scales with the interface arclength when using an adapting mesh moreover the use of dynamic data structures allows us to simulate system sizes corresponding to experimental conditions which would otherwise require lattices greater than 217 217elements we examine the convergence properties of our algorithm we also present two dimensional time dependent calculations of dendritic evolution with and without surface tension anisotropy we benchmark our results for dendritic growth with microscopic solvability theory finding them to be in good agreement with theory for high undercoolings at low undercooling however we obtain higher values of velocity than solvability theory at low undercooling where transients dominate in accord with a heuristic criterion which we derive

a multi step hybrid method for multi input partial quadratic eigenvalue assignment with time delay natural science foundation of fujian province of china for distinguished young scholars 2010j06002 ncet

compression unimpaired batch image encryption combining vector quantization and index compression as the network bandwidth has grown rapidly it has become common to share a large number of still images via the internet by means of batch transmission unfortunately most existing methods encrypt only a single image so there is room for improvement in our ability to send batches of images at one time a complete reconstruction of the methods is sometimes necessary especially when considering performance criteria this paper presents a novel batch image encryption algorithm that combines vector quantization vq and additional index compression process to benefit from their computational efficiency and low transmission bandwidth without affecting the original compression rate the experimental results show the performance of this new scheme in terms of compression rate and computational cost

computation of three dimensional dendrites with finite elements starting from an initial seed crystal inside an undercooled liquid the solid phase begins to grow rapidly and develops unstable growth patterns some growth directions are preferred because of anisotropic parameters in the physical model this results in the development of dendrites the physical model includes the heat equation for both the liquid and solid phases the gibbs thomson law couples velocity and curvature of the interface and the temperature we describe a numerical method that enables us to compute dendritic growth of crystals in two and three space dimensions the method consists of two coupled finite element algorithms the first one solves the heat equation the other operates on a discretization of the free boundary and computes the evolution of this moving interface the two methods work with totally independent grids by using timedependent locally refined and coarsened adaptive meshes in both methods we are able to reach a spatial resolution necessary to compute dendritic growth in two and three space dimensions

robust partial eigenvalue assignment problem for the second order system in this paper we study the partial eigenvalue assignment problem for the second order system where only a small part of eigenvalues of the open loop system is to be reassigned and the rest are required to remain unchanged it is desirable that the feedback controller not only assigns specific eigenvalues to the second order closed loop system but also that the system is robust or insensitive to perturbations we propose a numerical method such that the condition number of the matrix of the eigenvectors of the closed loop system is minimized in the method we only need the knowledge of the eigenvalues to be altered and the corresponding eigenvectors while we do not need the knowledge of the eigenstructures that are required to remain unchanged and are often unknown numerical examples show that the present method often leads to better conditioned closed loop system

symmetry preserving eigenvalue embedding in finite element model updating of vibrating structures the eigenvalue embedding problem addressed in this paper is the one of reassigning a few troublesome eigenvalues of a symmetric finite element model to some suitable chosen ones in such a way that the updated model remains symmetric and the remaining large number of eigenvalues and eigenvectors of the original model is to remain unchanged the problem naturally arises in stabilizing a large scale system or combating dangerous vibrations which can be responsible for undesired phenomena such as resonance in large vibrating structures a new computationally efficient and symmetry preserving method and associated theories are presented in this paper the model is updated using low rank symmetric updates and other computational requirements of the method include only simple operations such as matrix multiplications and solutions of low order algebraic linear systems these features make the method practical for large scale applications the results of numerical experiments on the simulated data obtained from the boeing company and on some benchmark examples are presented to show the accuracy of the method computable error bounds for the updated matrices are also given by means of rigorous mathematical analysis

pole assignment in vibratory systems by multi input control the problem of reassigning some poles of a vibratory system while keeping the other poles unchanged is considered the problem may be solved uniquely by single input state feedback control a family of solutions to the partial pole assignment problem may be obtained by applying multi input control forces an algorithm for determining a multi input control which is small in some sense is presented the non iterative algorithm proposed defines a closed form solution to the partial pole assignment problem in its natural second order form and no first order realization is used the reduction in the control effort achieved by the proposed method is demonstrated by numerical examples