quantum criticality analysis by finite size scaling and exponential basis sets we combine the finite size scaling method with the mesh free spectral method to calculate quantum critical parameters for a given hamiltonian the basic idea is to expand the exact wave function in a finite exponential basis set and extrapolate the information about system criticality from a finite basis to the infinite basis set limit the used exponential basis set though chosen intuitively allows handling a very wide range of exponential decay rates and calculating multiple eigenvalues simultaneously as a benchmark system to illustrate the combined approach we choose the hulthen potential the results show that the method is very accurate and converges faster when compared with other basis functions the approach is general and can be extended to examine near threshold phenomena for atomic and molecular systems based on even tempered exponential and gaussian basis functions

exponential control of a rotational motion of a rigid body using quaternions a new developed technique is used to study the problem of the exponential stabilization of the rotational motion of a rigid body about a fixed axis in the body with the help of rotors in this technique the exponential asymptotic stability of this motion is proved the control moments leading to the rotational motion are obtained the conditions that ensure the exponential asymptotic stabilization of this motion are used to obtain the stabilizing control law as non linear functions of the phase coordinates of the system finally many special cases and analyzing the results of the studied problem are investigated

numerical simulation of three dimensional nonlinear water waves we present an accurate and efficient numerical model for the simulation of fully nonlinear non breaking three dimensional surface water waves on infinite or finite depth as an extension of the work of craig and sulem 19 the numerical method is based on the reduction of the problem to a lower dimensional hamiltonian system involving surface quantities alone this is accomplished by introducing the dirichlet neumann operator which is described in terms of its taylor series expansion in homogeneous powers of the surface elevation each term in this taylor series can be computed efficiently using the fast fourier transform an important contribution of this paper is the development and implementation of a symplectic implicit scheme for the time integration of the hamiltonian equations of motion as well as detailed numerical tests on the convergence of the dirichlet neumann operator the performance of the model is illustrated by simulating the long time evolution of two dimensional steadily progressing waves as well as the development of three dimensional short crested nonlinear waves both in deep and shallow water

smooth orientation interpolation using parametric quintic polynomial based quaternion spline curve abstract in this paper a g 2 continuous quintic polynomial based unit quaternion interpolation spline curve with tension parameters is presented to interpolate a given sequence of solid orientations the curve in unit quaternion space s 3 is an extension of the quintic polynomial interpolation spline curve in euclidean space it preserves the interpolatory property and g 2 continuity meanwhile the unit quaternion interpolation spline curve possesses the local shape adjustability due to the presence of tension parameters the change of one tension parameter will only affect the adjacent two pieces of curves compared with the traditional b spline unit quaternion interpolation curve and v spline unit quaternion interpolation curve the proposed curve can automatically interpolate the given data points without solving the nonlinear system of equations over quaternions to obtain the control points which greatly improves the computational efficiency simulation results demonstrate the effectiveness of the proposed scheme

a high order spectral method for nonlinear water waves over moving bottom topography we present a numerical method for simulations of nonlinear surface water waves over variable bathymetry it is applicable to either two or three dimensional flows as well as to either static or moving bottom topography the method is based on the reduction of the problem to a lower dimensional hamiltonian system involving boundary quantities alone a key component of this formulation is the dirichlet neumann operator which in light of its joint analyticity properties with respect to surface and bottom deformations is computed using its taylor series representation we present new stabilized forms for the taylor terms each of which is efficiently computed by a pseudospectral method using the fast fourier transform physically relevant applications are displayed to illustrate the performance of the method comparisons with analytical solutions and laboratory experiments are provided

controllability observability and duality in singular systems the concepts of controllability and observability for systems of the form e dot x ax bu y cx e singular are considered a theory is presented which unifies the three main approaches to this topic already existing in the literature the development includes a generalization of the duality theorem from state space theory

h spl infin deconvolution filtering prediction and smoothing a krein space polynomial approach this correspondence is concerned with the infinite horizon h spl infin deconvolution for discrete time invariant systems described by polynomial equations a simple frequency domain approach in krein space is developed for the deconvolution problem with the help of an arma innovation model solutions to the problems of deconvolution filtering prediction and fixed lag smoothing are obtained the estimators are calculated by performing one j spectral factorization

a fast method for nonlinear three dimensional free surface waves an efficient numerical model for solving fully nonlinear potential flow equations with a free surface is presented like the code that was developed by grilli et al grilli et al 2001 int j numer methods fluids 35 829 867 it uses a high order three dimensional boundaryelement method combined with mixed eulerian lagrangian time updating based on second order explicit taylor expansions with adaptive time steps such methods are known to be accurate but expensive the efficiency of the code has been greatly improved by introducing the fast multipole algorithm by replacing every matrix vector product of the iterative solver and avoiding the building of the influence matrix this algorithm reduces the computing complexity from o n 2 to nearly o n where n is the number of nodes on the boundary the performance of the method is illustrated by the example of the overturning of a solitary wave over a three dimensional sloping bottom for this test case the accelerated method is indeed much faster than the former one even for quite coarse grids for instance a reduction of the complexity by a factor six is obtained for nz6022 for the same global accuracy the acceleration of the code allows the study of more complex physical problems and several examples are presented

technical communique robust state prediction for descriptor systems this paper deals with the problem of state prediction for descriptor systems subject to bounded uncertainties the problem is stated in terms of the optimization of an appropriate quadratic functional this functional is well suited to derive not only the robust predictor for descriptor systems but also that for usual state space systems numerical examples are included in order to demonstrate the performance of this new filter

kalman filtering and riccati equations for descriptor systems a general formulation of a discrete time filtering problem for descriptor systems is considered it is shown that the nature of descriptor systems leads directly to the need to examine singular estimation problems using a dual approach to estimation the authors derive a so called 3 block form for the optimal filter and a corresponding 3 block riccati equation for a general class of time varying descriptor models which need not represent a well posed system in that the dynamics may be either over or under constrained specializing in the time invariant case they examine the asymptotic properties of the 3 block filter and in particular analyze in detail the resulting 3 block algebraic riccati equation the noncausal nature of discrete time descriptor dynamics implies that future dynamics may provide some information about the present state a modified form for the descriptor kalman filter that takes this information into account is presented

optimal and self tuning white noise estimators with applications to deconvolution and filtering problems using the innovation analysis method in the time domain based on the autoregressive moving average arma innovation model this paper presents a unified white noise estimation theory that includes both input and measurement white noise estimators and presents a new steady state optimal state estimation theory non recursive optimal state estimators are given whose recursive version gives a steady state kalman filter where a new algorithm of the kalman filter gain is proposed two new algorithms of the kalman predictor gain are also derived local asymptotic stability of the kalman filter is proved the classical kalman filtering theory is extended and modified the method used covers unstable systems with correlation noises and singular transition matrix and also covers the self tuning white noise signal and state estimators when the noise statistics is unknown to illustrate three simulation examples are given

numerical techniques on improving computational efficiency of spectral boundary integral method numerical techniques are suggested in this paper in order to improve the computational efficiency of the spectral boundary integral method initiated by clamond grue d clamond and j grue a fast method for fully nonlinear water wave computations j fluid mech 2001 447 337 355 for simulating nonlinear water waves this method involves dealing with the high order convolutions by using fourier transform or inverse fourier transform and evaluating the integrals with weakly singular integrands a de singularity technique is proposed here to help in efficiently evaluating the integrals with weak singularity an anti aliasing technique is developed in this paper to overcome the aliasing problem associated with fourier transform or inverse fourier transform with a limited resolution this paper also presents a technique for determining a critical value of the free surface under which the integrals can be neglected numerical tests are carried out on the numerical techniques and on the improved method equipped with the techniques the tests will demonstrate that the improved method can significantly accelerate the computation in particular when waves are strongly nonlinear

on the accuracy and applicability of a new implicit taylor method and the high order spectral method on steady nonlinear waves this paper presents an investigation and discussion of the accuracy and applicability of an implicit taylor it method versus the classical higher order spectral hos method when used to simulate

paper efficient algorithm for matrix spectral factorization an algorithm is presented for the spectral factorization of polynomial or rational matrices arising in optimal control and filtering theory as well as in network theory there are two versions of the algorithm one applicable to continuous time problems the other to discrete time ones both versions are based on newton s method feature quadratic convergence and provide a significant improvement in efficiency over the existing methods

stability of high order perturbative methods for the computation of dirichlet neumann operators abstract in this paper we present results on the stability of perturbation methods for the evaluation of dirichlet neumann operators dno defined on domains that are viewed as complex deformations of a basic simple geometry in such cases geometric perturbation methods based on variations of the spatial domains of definition have long been recognized to constitute efficient and accurate means for the approximation of dno and in fact several numerical implementations have been previously proposed inspired by our recent analytical work here we demonstrate that the convergence of these algorithms is quite generally limited by numerical instability indeed we show that these standard perturbative methods for the calculation of dno suffer from significant ill conditioning which is manifest even for very smooth boundaries and whose severity increases with boundary roughness moreover and again motivated by our previous work we introduce an alternative perturbative approach that we show to be numerically stable this approach can be interpreted as a reformulation of classical perturbative algorithms in suitable independent variables and thus it allows for both direct comparison and the possibility of analytic continuation of the perturbation series it can also be related to classical preconditioned spectral approaches and as such it retains in finite arithmetic the spectral convergence properties of classical perturbative methods albeit at a higher computational cost as it does not take advantage of possible dimensional reductions still as we show an alternative approach such as the one we propose may be mandated in cases where substantial information is contained in high order harmonics and or perturbation coefficients of the solution

discrete j spectral factorization abstract this paper deals with the j spectral factorization for general discrete rational matrices a simple approach based on the kalman filtering in krein space is proposed the main idea is to construct a stochastic state space filtering model in krein space such that the spectral matrix of the output is equal to the rational matrix to be factorized the spectral factor is then easily derived by using the generalized kalman filtering in krein space which is similar to the h 2 spectral factorization our approach unifies the treatment of the h 2 spectral factorization and the j spectral factorization the applications of the derived results in h and risk sensitive estimation for both nonsingular and singular systems are demonstrated

risk sensitive filtering and smoothing via reference probability methods we address the risk sensitive filtering problem which is minimizing the expectation of the exponential of the squared estimation error multiplied by a risk sensitive parameter such filtering can be more robust to plant and noise uncertainty than minimum error variance filtering although optimizing a differently formulated performance index to that of the so called h sub spl infin filtering risk sensitive filtering leads to a worst case deterministic noise estimation problem given from the differential game associated with h sub spl infin filtering we consider a class of discrete time stochastic nonlinear state space models we present linear recursions in the information state and the result for the filtered estimate that minimizes the risk sensitive cost index we also present fixed interval smoothing results for each of these signal models in addition a brief discussion is included on relations of the risk sensitive estimation problem to minimum variance estimation and a worst case estimation problem in a deterministic noise scenario related to minimax dynamic games the technique used in this paper is the so called reference probability method which defines a new probability measure where the observations are independent and translates the problem to the new measure the optimization problem is solved using simple estimation theory in the new measure and the results are interpreted as solutions in the original measure

absorbing boundary conditions for free surface waves in this paper the use of absorbing boundary conditions is investigated for the numerical simulation of gravity waves on an incompressible inviscid fluid in three dimensions a review of existing methods is given for linear and nonlinear waves after which first and second order partial differential equations are introduced as absorbing boundary conditions for the linearized model well posedness is investigated and it is shown that the reflection properties of the second order equation are superior to those of the first order equation

practical use of variational principles for modeling water waves this paper describes a method for deriving approximate equations for irrotational water waves the method is based on a relaxed variational principle i e on a lagrangian involving as many variables as possible this formulation is particularly suitable for the construction of approximate water wave models since it allows more freedom while preserving the variational structure the advantages of this relaxed formulation are illustrated with various examples in shallow and deep waters as well as arbitrary depths using subordinate constraints e g irrotationality or free surface impermeability in various combinations several model equations are derived some being well known other being new the models obtained are studied analytically and exact travelling wave solutions are constructed when possible

an efficient model for three dimensional surface wave simulations part ii generation and absorption water wave generation procedures and efficient numerical beaches are crucial components of a fully non linear numerical tank for water wave simulations linear formulae for pneumatic wave makers are optimized for efficient fully non linear wave generation in three dimensions analytical integration of the linear applied free surface pressure provides formulae valid for all times of the simulation the purely non linear part of the wave making procedure becomes integrated in the fully non linear formulation novel numerical beaches are introduced damping the scaled tangential velocity at the free surface more specifically an additional term is introduced in the bernoulli equation at the free surface namely 1 email protected email protected where c is a non zero smooth function in regions where damping is required and zero in the wave propagation domain email protected is the scaled tangential velocity at the free surface and 1 the inverse horizontal gradient operator the new term results in a modified dynamic free surface condition which is integrated in time in the fully non linear formulation extensive numerical tests show that the energy of the outgoing waves is completely absorbed by the new damper neither wave reflection nor emission are observed a steep solitary wave is completely absorbed at the numerical beach damping of waves due to advancing pressure distributions are efficient as well the implementation of the absorber in any existing numerical tank is rather trivial

a class of generalized b spline quaternion curves unit quaternion curves have gained considerable attention in the fields of robot control and computer animation kim et al proposed a general construction method of unit quaternion curves which can transform the closed form equation for kth order b spline basis functions in r3 into its unit quaternion analogue in so 3 while preserving the c k 2 continuity juhasz and roth generalized the classical b spline functions by means of monotone increasing continuously differentiable core functions based on the recurrence formula of b spline functions in order to extend the applications of the generalized b spline functions in computer animation the definition and construction scheme of generalized b spline quaternion curves in s3 are put forward in this paper the introduced nonlinear core functions are not only theoretically interesting but also offer a large variety of shapes some properties of this class of unit quaternion curves such as continuity and local controllability are also discussed experimental results show the effectiveness and usefulness of our construction methods of generalized b spline quaternion curves

an efficient model for three dimensional surface wave simulations an efficient numerical scheme for simulations of fully nonlinear non breaking surface water waves in 3d is presented the water depth is either shallow finite or infinite the method is based on a fast rapidly converging iterative algorithm to compute the dirichlet to neumann operator this is evaluated by expanding the operator as a sum of global convolution terms and local integrals with kernels that decay quickly in space the global terms are computed very quickly via fft the local terms are evaluated by numerical integration analytical integration of the linear part of the prognostic equations in fourier space is obtained to machine precision the remaining nonlinear components are integrated forward in time using an rk scheme combined with a special step size control technique this yields a very stable and accurate time marching procedure zeros padding in the spectral space represents the anti aliasing strategy the method requires no smoothing illustration through examples show that the total energy is well conserved during the numerical simulations the scheme is stable and accurate even for very long time simulations of very steep wave events the scheme is easily parallelizable it propagates for example a stokes wave of slope 0 2985 with a phase shift error of about 0 3 o after 1000 periods of propagation

kalman filtering for general discrete time linear systems recursive state estimation problems for explicit and implicit time invariant linear systems both for systems with and without unknown inputs can be formulated as a single problem usually referred to as descriptor kalman filtering solutions to this problem have been proposed in the literature however these solutions either neglect possible contributions of future dynamics to the current estimate or make unnecessary assumptions on the structure of the system in this paper the authors propose a solution to this problem which leads to a constructive method lifting these unnecessary assumptions this method uses a generalization of the shuffle algorithm

a unified approach to optimal state estimation for stochastic singular systems the steady state optimal state estimation problem for discrete time stochastic singular linear systems is considered via the innovation analysis method in the time domain the filter predictor and smoother are derived by using the projection formula and are calculated based on the arma innovation model the three cases of filter predictor and smoother are shown to have a unified form also the optimal white noise estimation method including both input and measurement noises is presented asymptotic stability of the estimators is proved the results of this paper can be applied to normal systems as a special case

brief risk sensitive filtering prediction and smoothing for discrete time singular systems this paper is concerned with steady state risk sensitive filtering prediction and smoothing problems for discrete time singular systems it is shown that a risk sensitive estimator can be obtained by ensuring the minimum of an indefinite quadratic form to be maximum minimum when the risk sensitivity parameter q is negative positive an auxiliary state space signal model and an innovation sequence in krein space are introduced to simplify the derivation of the estimator the estimator is calculated based on one j spectral factorization for risk seeking q 0 a numerical example is given to demonstrate the applicability of the result

linear estimation in krein spaces ii applications we have shown that several interesting problems in h sup spl infin filtering quadratic game theory and risk sensitive control and estimation follow as special cases of the krein space linear estimation theory developed in part i we show that all these problems can be cast into the problem of calculating the stationary point of certain second order forms and that by considering the appropriate state space models and error gramians we can use the krein space estimation theory to calculate the stationary points and study their properties the approach discussed here allows for interesting generalizations such as finite memory adaptive filtering with varying sliding patterns

filtering and lqg problems for discrete time stochastic singular systems discrete time stochastic singular systems are discussed filtering and linear quadratic gaussian lqg problems are considered the problems are first transformed into the normal form via state augmentation and then solved by utilizing standard results for nonsingular systems the linear unbiased least squares state estimation algorithm and the optimal control law for the lqg problem are given the order of the filtering algorithm obtained in this way is not much increased moreover this algorithm allows the presence of some kinds of control inputs

brief paper minimax state estimation for linear discrete time differential algebraic equations this paper presents a state estimation approach for an uncertain linear equation with a non invertible operator in hilbert space the approach addresses linear equations with uncertain deterministic input and noise in the measurements which belong to a given convex closed bounded set a new notion of a minimax observable subspace is introduced by means of the presented approach new equations describing the dynamics of a minimax recursive estimator for discrete time non causal differential algebraic equations daes are presented for the case of regular daes it is proved that the estimator s equation coincides with the equation describing the seminal kalman filter the properties of the estimator are illustrated by a numerical example

numerical simulation of gravity waves abstract we present a new spectral method to simulate numerically the waterwave problem in a channel for a fluid of finite or infinite depth it is formulated in terms of the free surface elevation and the velocity potential the numerical method is based on the reduction of this problem to a lower dimensional computation involving surface variables alone to accomplish this we describe the taylor expansion of the dirichlet neumann operator in homogeneous powers of the surface elevation each term is a concatenation of fourier multipliers with powers of and its derivatives and is valid uniformly in wavenumber these are easily calculated using the fast fourier transform the method is illustrated by computing the long time evolution of modulated wave packets and of approximations to the stokes steady wave train by imposing a surface pressure we observe surface steepening in large amplitude evolution and wake and bow wave development for flows with a close to critical froude number finally we give an example of nonlinear evolution of the distribution of energy among normal modes