multivariate radial basis interpolation for solving quantum fluid dynamical equations this paper proposes a new numerical technique for solving the quantum fluid dynamical equations within the lagrangian description an efficient and accurate numerical scheme is achieved by taking advantage of the smooth field variables obtained via the madelung transformation combined with the radial basis function interpolation applications to the 2d coherent state and a 2d model of no2 photodissociation dynamics show that the present method rivals the split operator method in both efficiency and accuracy the advantage of the new algorithm as a computational tool is expected to prevail for high dimensional systems

exponential power series expansion for the propagator of general diffusion processes abstract the propagator of a general diffusion process is determined by expanding its exponent in a power series of a time increment t the expansion coefficients can be analytically evaluated from recursive relations we are thus able to construct a covariant short time approximation for the propagator valid to any desired precision in t attention is given both to the mathematics and its physical interpretation this allows us to shed further light on the results already known in the literature on quantum mechanics and theory of continuous markov processes

two grid method for the two dimensional time dependent schrodinger equation by the finite element method abstract in this paper we construct a backward euler full discrete two grid finite element scheme for the two dimensional time dependent schrodinger equation with this method the solution of the original problem on the fine grid is reduced to the solution of same problem on a much coarser grid together with the solution of two poisson equations on the same fine grid we analyze the error estimate of the standard finite element solution and the two grid solution in the h 1 norm it is shown that the two grid algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy h o h k k 1 finally a numerical experiment indicates that our two grid algorithm is more efficient than the standard finite element method

conditional probabilities in multiplicative noise processes we address the calculation of transition probabilities in multiplicative noise stochastic differential equations using a path integral approach we show the equivalence between the conditional probability and the propagator of a quantum particle with variable mass introducing a time reparametrization we are able to transform the problem of multiplicative noise fluctuations into an equivalent additive one we illustrate the method by showing the explicit analytic computation of the conditional probability of a harmonic oscillator in a nonlinear multiplicative environment

invited paper survey of quantitative feedback theory qft abstract qft is an engineering design theory devoted to the practical design of feedback control systems the foundation of qft is that feedback is needed in control only when plant p parameter and or disturbance d uncertainties sets p p d d exceed the acceptable a system performance uncertainty set a a the principal properties of qft are as follows 1 the amount of feedback needed is tuned to the p d a sets if a exceeds p d feedback is not needed at all 2 the simplest modelling is used a command disturbance and sensor noise inputs and b the available sensing points and the defined outputs no special controllability test is needed in either linear or non linear plants it is inherent in the design procedure there is no observability problem because uncertainty is included the number of independent sensors determines the number of independent loop transmissions li the functions which provide the benefits of feedback 3 the simplest mathematical tools h

a penalty finite element approximation to a signorini two body contact problem in thermoelasticity in this work a numerical approximation by the finite element method of a quasi static frictionless unilateral contact problem between two thermoelastic bodies in two dimensions is considered the approximation scheme is based on a penalty formulation used to replace the signorini contact condition convergence results and error bounds are obtained and some numerical experiments presented

surmounting oscillating barriers path integral approach for weak noise we consider the thermally activated escape of an overdamped brownian particle over a potential barrier in the presence of periodic driving a time dependent path integral formalism is developed which allows us to derive asymptotically exact weak noise expressions for both the instantaneous and the time averaged escape rate our results comprise a conceptually different systematic treatment of the rate prefactor multiplying the exponentially leading arrhenius factor moreover an estimate for the deviations at finite noise strengths is provided and a supersymmetry type property of the time averaged escape rate is verified for piecewise parabolic potentials the rate expression can be evaluated in closed analytical form while in more general cases as exemplified by a cubic potential an action integral remains to be minimized numerically our comparison with very accurate numerical results demonstrates an excellent agreement with the theoretical predictions over a wide range of driving strengths and driving frequencies

a quasistatic contact problem for an elastoplastic rod abstract we consider a mathematical model which describes the quasistatic contact of an elastoplastic rod with an obstacle it is based on the prandtl reuss flow law and unilateral conditions imposed on the velocity two weak formulations are presented and existence and uniqueness results established the proofs are based on approximate problems with viscous regularization which have merit on their own and may be used as the basis for convergent numerical algorithms for the problem

lp parameter perturbation and design of robust controllers for linear systems in this paper linear systems with characteristic equations that are linearly dependent on some uncertain parameters are considered a new procedure is proposed for the calculation of d stability margins in the parameter space in general lp norms the procedure is simple and computationally efficient for several important regions of interest in the complex plane e g left hand plane sectors and circles centred at the origin it requires the solution of only one equation based on this result a new method is presented for the design of robust controllers robust placement of the closed loop poles inside the regions of interest is addressed the method provides a simple and computationally tractable solution to the robust controller design problem it can be used to synthesize robust controllers with general rational transfer functions for plants modelled as the ratio of two uncertain polynomials subjected to lp parameter perturbation

superconvergence analysis of finite element method for the time dependent schrodinger equation in this paper we consider the two dimensional time dependent schrodinger equation firstly we use the rectangular lagrange type finite element of order p to get a semi discrete scheme of the equation and discuss the superconvergence error estimate in the h 1 norm secondly we use the crank nicolson method in time to get a fully discrete scheme of the equation and the superconvergence estimate in the h 1 norm can be obtained in this scheme finally a numerical example with the order p 1 is provided to verify our theoretical results

the real structured singular value is hardly approximable this paper investigates the problem of approximating the real structured singular value real spl mu a negative result is provided which shows that the problem of checking if spl mu 0 is np hard this result is much more negative than the known np hard result for the problem of checking if spl mu 0 even exponential functions of n unless np p a similar statement holds for the lower bound of spl mu our result strengthens a recent result by toker which demonstrates that obtaining a sublinear approximation for spl mu is np hard

practical stabilization of a quantum particle in a one dimensional infinite square potential well we consider a nonrelativistic charged particle in a one dimensional infinite square potential well this quantum system is subjected to a control which is a uniform in space time depending electric field it is represented by a complex probability amplitude solution of a schrodinger equation on a one dimensional bounded domain with dirichlet boundary conditions we prove the almost global practical stabilization of the eigenstates by explicit feedback laws

role of an intermediate state in homogeneous nucleation we explore the role of an intermediate state phase in homogeneous nucleation by examining the decay process through a double humped potential barrier we analyze the one dimensional fokker planck fp equations with the fourth and sixth order landau potentials in the low temperature case we apply the wkb method to the fp equation and obtain an analytic expression for the decay rate which is accurate for a wide range of depth and curvature of the middle well in the case of a deep middle well it reduces to an extended kramers formula in which the barrier height in the original formula is replaced by the arithmetic mean height of the higher outer and lower inner barriers and the curvature of the initial well in the original one is replaced by the geometric mean curvature of the initial and intermediate wells in the case of a shallow middle well the kramers escape rate is evaluated also within the standard framework of the mean first passage time problem whose result is consistent with our wkb analysis criteria for enhancement of the decay rate are revealed

gain in stochastic resonance precise numerics versus linear response theory beyond the two mode approximation in the context of the phenomenon of stochastic resonance sr we study the correlation function the signal to noise ratio snr and the ratio of output over input snr i e the gain which is associated to the nonlinear response of a bistable system driven by time periodic forces and white gaussian noise these quantifiers for sr are evaluated using the techniques of linear response theory lrt beyond the usually employed two mode approximation scheme we analytically demonstrate within such an extended lrt description that the gain can indeed not exceed unity we implement an efficient algorithm based on work by greenside and helfand detailed in the appendix to integrate the driven langevin equation over a wide range of parameter values the predictions of lrt are carefully tested against the results obtained from numerical solutions of the corresponding langevin equation over a wide range of parameter values we further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the snr and the gain as a main result we show for subthreshold driving that both the correlation function and the snr can deviate substantially from the predictions of lrt and yet the gain can be either larger or smaller than unity in particular we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle this latter result is in agreement with recent analog simulation results by gingl et al icnf 2001 edited by g bosman world scientific singapore 2002 pp 545 548 fluct noise lett 1 l181 2001

investigation of a class of stochastic processes using path integral techniques a study is made of the langevin equation x v chi g chi zeta t eta t where the noises eta t and zeta t are gaussian with zero mean and with eta t eta t 2r delta t t zeta t zeta t d tau exp mod t t mod tau path integral representations for conditional probability distributions are given for the two cases tau 0 and tau not 0 for r and d small but of the same order the appropriate path integrals are evaluated to leading order using the method of steepest descents in order to find the stationary probability distribution pst x and the mean relaxation time t for escape from a potential well analytical expressions are given for t when tau 0 and when tau is small for general tau the authors present numerical results for the stationary probability distribution using the particular forms v x 1 2ax2 1 4ax4 r 1n x and g x x which are appropriate to the dye laser

renormalized equations for a weakly nonlinear duffing oscillator abstract we derive fluctuation renormalized transport equations for the averages position and velocity of a weakly nonlinear duffing oscillator we take the nonlinearity as the expansion parameter and use a modification of the van kampen expasion method also we study the spectral density of the equilibrium time correlation function of position comparison with other theories and computer data is carried out

diffusion in a symmetric bistable potential a variational approach an approximation procedure for the solution of stochastic nonlinear equations which was derived from a variational principle in a previous paper is applied to the problem of a particle that diffuses in a symmetric bistable potential starting from the point of unstable equilibrium the second moment left langle widetilde x 2 t right rangle and variance left langle widetilde x 4 t right rangle left langle widetilde x 2 t right rangle 2 for the particle s position widetilde x t are calculated as functions of the timet good agreement is found with results recently obtained by baibuzet al from an approximate evaluation of a path integral expression for the probability density

on the accuracy of the spectral interpolation methods for sampled pseudoperiodic signals abstract the accuracy of a spectral interpolation method is studied on sampled pseudoperiodic signals an attempt is made to compute the accuracy of the characteristics of a particular component in terms of the remaining components contribution the weighting effect is shown to improve the characteristics computation by reducing the remaining components contribution to an order of 1 n 3 where n is the number of the samples the noise effect and the proximity effect are analyzed and the spectral interpolation is compared with a time domain method derived from a kumaresan tufts procedure

numerical analysis and simulations of a quasistatic frictional contact problem with damage in viscoelasticity we consider a quasistatic problem which models the bilateral contact between a viscoelastic body and a foundation taking into account the damage and the friction the damage which results from tension or compression is then involved in the constitutive law and it is modelled using a nonlinear parabolic inclusion the variational problem is formulated as a coupled system of evolutionary equations for which we state the existence of a unique solution then we introduce a fully discrete scheme using the finite element method to approximate the spatial variable and the euler scheme to discretize the time derivatives error estimates are derived and under suitable regularity hypotheses the convergence of the numerical scheme obtained finally a numerical algorithm and results are presented for some two dimensional examples

a convex lower bound for the real bf l _2 parametric stability margin of linear control systems with restricted complexity controllers in this note the problem of restricted complexity stability margin maximization rcsmm for single input single output siso plants affected by rank one real perturbations is considered this problem amounts to maximizing the real l2 parametric stability margin over an assigned class of restricted complexity controllers which are described by rational transfer functions of fixed order with coefficients depending affinely on some free parameters it is shown that the rcsmm problem which is nonconvex in general can be approached by means of convex optimization methods specifically a lower bound of the stability margin whose maximization can be accomplished via linear matrix inequality lmi techniques is developed

a quasi static signorini contact problem for a thermoviscoelastic beam this paper is concerned with the existence uniqueness and numerical solution of a system of equations modelling the evolution of a quasi static thermoviscoelastic beam that may be in contact with two rigid obstacles a finite element approximation is proposed and analysed and some numerical results are given

a formula for computation of the real stability radius this paper presents a readily computable formula for the real stability radius with respect to an arbitrary stability region in the complex plane

mass preserving discontinuous galerkin methods for schrodinger equations we construct analyze and numerically validate a class of mass preserving direct discontinuous galerkin ddg schemes for schrodinger equations subject to both linear and nonlinear potentials up to round off error these schemes preserve the discrete version of the mass of the continuous solution for time discretization we use the crank nicolson for linear schrodinger equations and the strang splitting for nonlinear schrodinger equations so that numerical mass is still preserved at each time step the ddg method when applied to linear schrodinger equations is shown to have the optimal k 1 th order of accuracy for polynomial elements of degree k the numerical tests demonstrate both accuracy and capacity of these methods

a nonlocal parabolic system modelling axially symmetric thermoelastic contact of two discs abstract a system of parabolic integro differential equations modelling homogeneous and isotropic elastic thin discs subject to axially symmetric temperature fields and displacements is studied under some appropriate assumptions the questions of existence uniqueness and continuous dependence of the solutions upon the data are demonstrated the main feature of our method in this paper is that the difficulties associated with this physical problem can be seen clearly and overcome easily via the decoupling procedures and transformations

a set of stationary non maxwellian distributions abstract we propose a set of distribution functions stationary solutions of a fokker planck equation the frictional and diffusion coefficients having been expanded in a polynomial series with positive coefficients these distributions show tails depleted or increased with respect to the maxwellian distribution which can in any case be recovered if the coefficients of the expansion satisfy particular conditions the stationary non maxwellian distributions derived in this paper can be used in the calculations of rates in many different fields of physics where problems still have to be solved

eigenvalues and eigenfunctions of the kramers equation application to the brownian motion of a pendulum the brownian motion of s particle in a potential is described by a fokker planck equation with two variables position and velocity i e by the kramers equation eigenvalues and eigenfunctions can be obtained by a matrix continued fraction method this method is applied to the brownian motion of a pendulum where the force is proportional to sin x the real and complex eigenvalues with small real parts are plotted as a function of the damping constant in the low friction limit the real parts of the complex eigenvalues are proportional to the square of the friction constant whereas the real eigenvalues are proportional to the friction constant itself in the high friction limit the eigenvalues are real and the lowest ones are proportional to the inverse friction constant in the intermediate friction regime a complicated mixture of real and complex eigenvalues is found the same method is also applied to the boltzmann equation with the bgk collision operator

finite element approximation to a contact problem in linear thermoelasticity a finite element approximation to the solution of a one dimensional linear thermoelastic problem with unilateral contact of the signorini type and heat flux is proposed an error bound is derived and some numerical experiments are performed

numerical analysis of the smoluchowski equation using the split operator method abstract we apply the split operator method of feit fleck and steiger to the numerical solution of the smoluchowski equation we study the time evolution of the first few moments and of the equilibrium time correlation function for bistable potentials the time evolution of the probability density obtained by us is compared with the one predicted by the scaling theory of suzuki we also analyze the dependence of the total equilibrium relaxation time on the noise intensity d for small and large values of d the relaxation from an initial condition away from the unstable point is also discussed we find that the one well population is well described by a single exponential law with decay times which grow extremely large as the value of d is decreased

theoretical and numerical analysis on a thermo elastic system with discontinuities a second order accurate numerical scheme is proposed for a thermo elastic system which models a bar made of two distinct materials the physical parameters involved may be discontinuous across the joint of the two materials where there might be also singular heat and or force sources the solution components the temperature and the displacement may change rapidly across the joint by transforming the system into a different one time marching schemes can be used for the new system which is well posed the immersed interface method is employed to deal with the discontinuities of the coefficients and the singular sources the proposed numerical method can fit both explicit and implicit formulation for the implicit version a stable and fast prediction correction scheme is also developed convergence analysis shows that our method is second order accurate at all grid points in spite of the discontinuities across the interface numerical experiments are performed to support the theoretical analysis in this paper

numerical evaluation of coherent state path integrals in quantum dynamics the numerical evaluation of coherent state path integrals for quantum dynamical problems is discussed for one dimensional examples to propagate an initial state we use the normal and antinormal ordered coherent state path integrals combined with a split operator technique dividing the hamiltonian into harmonic and anharmonic parts for numerical purposes integrations must be approximated by quadrature formulae this leads to a matrix multiplication scheme which is systematically tested for the double well and morse potentials the method is accurate for propagation times much longer than the natural time scale of the system and it allows for short as well as long time steps without loss of stability

diffusion over barriers eigenanalysis of the smoluchowski equation for bistable potentials abstract a variational method is used to get the eigenvalues and eigenfunctions of the one dimensional smoluchowski equation for two types of symmetric bistable potential fields the effects of barrier height and width on the rate of escape of particles over the barrier first non zero eigenvalue are evaluated numerically and the results are compared with kramers theory in order to assess its range of application

dynamics of gompertzian tumour growth under environmental fluctuations abstract we investigate the effect of correlated additive and multiplicative gaussian white noise on the gompertzian growth of tumours our results are obtained by solving numerically the time dependent fokker planck equation fpe associated with the stochastic dynamics in our numerical approach we have adopted b spline functions as a truncated basis to expand the approximated eigenfunctions the eigenfunctions and eigenvalues obtained using this method are used to derive approximate solutions of the dynamics under study we perform simulations to analyze various aspects of the probability distribution of the tumour cell populations in the transient and steady state regimes more precisely we are concerned mainly with the behaviour of the relaxation time to the steady state distribution as a function of i of the correlation strength between the additive noise and the multiplicative noise and ii as a function of the multiplicative noise intensity d and additive noise intensity it is observed that both the correlation strength and the intensities of additive and multiplicative noise affect the relaxation time

robustness analysis for linear dynamical systems with linearly correlated parametric uncertainties the authors propose an approach for robust pole location analysis of linear dynamical systems with parametric uncertainties linear control systems with characteristic polynomials whose coefficients are affine in a vector of uncertain physical parameters are considered a design region in complex plane for system pole placement and a nominal parameter vector generating a characteristic polynomial with roots in that region are given the proposed method allows the computation of maximal domains bounded by linear inequalities and centered at the nominal point in system parameter space preserving system poles in the given region the solution of this problem is shown to also solve the problem of testing robot location of a given polytope of polynomials in parameter space it is proved that for stability problems for continuous time systems with independent perturbations on polynomial coefficients this method generates the four extreme kharitonov polynomials

a comparison of different propagation schemes for the time dependent schro dinger equation abstract a comparison of three widely used time propagation algorithms for the time dependent schrodinger equation is described a typical evolution problem is chosen to demonstrate the efficiency and accuracy of the various methods on a numerical grid using a pseudo spectral fft spatial representation for scattering and bound state evolution the methods used second order differencing split operator propagation chebyshev polynomial expansion are discussed in terms of their applicability to various classes of dynamic problems a new method is introduced which is based upon a low order lanczos technique this method appears to offer an accurate and flexible alternative to the existing techniques overall the chebyshev method is recommended for time independent potentials and the lanczos method for time dependent potentials

a variational approach to stochastic nonlinear problems a variational principle is formulated which enables the mean value and higher moments of the solution of a stochastic nonlinear differential equation to be expressed as stationary values of certain quantities approximations are generated by using suitable trial functions in this variational principle and some of these are investigated numerically for the case of a bernoulli oscillator driven by white noise comparison with exact data available for this system shows that the variational approach to such problems can be quite effective

numerical solution of a thermoviscoelastic contact problem by a penalty method we consider the numerical approximation of a one dimensional quasi static contact problem in linear thermoviscoelasticity a finite element approximation based on a penalized problem is proposed and analyzed we furnish an a priori estimate of the difference between the true and numerical solutions the results of some computations are also presented

application of a new functional expansion to the cubic anharmonic oscillator a new representation of causal functionals is introduced which makes use of noncommutative generating power series and iterated integrals this technique allows the solutions of nonlinear differential equations with forcing terms to be obtained in a simple and natural way it generalizes some properties of fourier and laplace transforms to nonlinear systems and leads to effective computations of various perturbative expansions illustrations by means of the cubic anharmonic oscillator are given in both the deterministic and the stochastic cases

iterative eigenvalue method using the bloch wave operator formalism with pade approximants and absorbing boundaries we present an iterative method for calculating eigenvalues and eigenvectors of large non hermitian matrices the method uses an iterative procedure to solve the basic bloch equation h ensuremath omega ensuremath omega h ensuremath omega of wave operator theory it involves nonlinear transformations such as the translation of diagonal matrix elements in the complex plane and the use of pad e approximants to treat the strongly coupled states which constitute an intermediate space around the model space in the particular case of floquet eigenstates the further step of adding time dependent absorbing boundaries significantly improves the convergence properties of the iterative calculations

quasilinear approximations for the propagator of the fokker planck equation abstract four novel classes of the approximate fokker planck propagators are developed by means of a decoupling operator treatment for a small time increment t these are correct at least through second order t the propagators have an ornstein uhlenbeck form thus leading to novel discrete path integrals with a linear reference system their ambiguities are characterized by an arbitrary function of the time increment and by a matrix and a vector field which may be both time and state dependent the efficiency of the treatment used is very sensitive to the choice of these functions several forms of which are proposed the power of the treatment is illustrated by a physically meaningful fokker planck equation relevant to laser physics being used as the global approximations the approximate propagators obtained are shown to provide a correct description of a bistable system in the entire time domain a scaling theory of suzuki including its unified version emerges from them in a very natural way another attractive feature of our general treatment when compared to the others known in the literature is that it allows for equations with singular diffusion matrices two of which a kramers equation and a colored noise problem are considered

brief paper identification and control joint input design and h state feedback with ellipsoidal parametric uncertainty via lmis one obstacle in connecting robust control with models generated from prediction error identification is that very few control design methods are able to directly cope with the ellipsoidal parametric uncertainty regions that are generated by such identification methods in this contribution we present a joint robust state feedback control input design procedure which guarantees stability and prescribed closed loop performance using models identified from experimental data this means that given h specifications on the closed loop transfer function are translated into sufficient requirements on the input signal spectrum used to identify the process the condition takes the form of a linear matrix inequality

stochastic evolution of systems of particles obeying an exclusion principle abstract we present numerical solutions of a nonlinear fokker planck equation to describe a fermi gas the model equation g kaniadakis p quarati phys rev e 49 1994 5103 includes a nonlinear term due to the pauli exclusion principle which has been disregarded up to now a new numerical method to study the time evolution of the distribution function is presented the method can be applied to any potential and allows us to describe accurately and efficiently a fermi gas in this work we focus on the differences between the results of the linear case in which the effects of the exclusion principle are not considered and the nonlinear case in which these effects are taken into account

suppression of thermally activated escape by heating the problem of thermally activated escape over a potential barrier is solved by means of path integrals for one dimensional reaction dynamics with very general time dependences for a suitably chosen but still quite simple static potential landscape the net escape rate may be substantially reduced by temporally increasing the temperature above its unperturbed constant level

structure of positive decompositions of exponential operators the solution of many physical evolution equations can be expressed as an exponential of two or more operators acting on initial data accurate solutions can be systematically derived by decomposing the exponential in a product form for time reversible equations such as the hamilton or the schr odinger equation it is immaterial whether or not the decomposition coefficients are positive in fact most symplectic algorithms for solving classical dynamics contain some negative coefficients for time irreversible systems such as the fokker planck equation or the quantum statistical propagator only positive coefficient decompositions which respect the time irreversibility of the diffusion kernel can yield practical algorithms these positive time steps only forward decompositions are a highly effective class of factorization algorithms this work presents a framework for understanding the structure of these algorithms by a suitable representation of the factorization coefficients we show that specific error terms and order conditions can be solved analytically using this framework we can go beyond the sheng suzuki theorem and derive a lower bound for the error coefficient e vtv by generalizing the framework perturbatively we can further prove that it is not possible to have a sixth order forward algorithm by including only the commutator vtv ensuremath equiv mathbf v t v mathbf the pattern of these higher order forward algorithms is that in going from the 2n mathrm th to the 2n 2 mathrm th order one must include a different commutator v t 2n ensuremath 1 v in the decomposition process

the contact problem in thermoviscoelastic materials abstract we stablish an existence result for the thermoviscoelastic degenerated contact problem the nonlinear stress strain relation we will consider here is given by m l 0 u x 2 dx u x u xt where m is a function satisfying m c 1 0 c 0 m s c s p moreover we show that the solution decays uniformly to zero that is denoting by e t the first order energy associated to the equation we show that there exist positive constants c satisfying e t c e 0 1 t p 2 p where p is a positive number which depends on nonlinear terms of the system

duality in har infty cone optimization positive real cones in the space har infty appear naturally in many optimization problems of control theory and signal processing although such problems can be solved by finite dimensional approximations e g ritz projection all such approximations are conservative providing one sided bounds for the optimal value in order to obtain both upper and lower bounds of the optimal value a dual problem approach is developed in this paper a finite dimensional approximation of the dual problem gives the opposite bound for the optimal value thus by combining the primal and dual problems a suboptimal solution to the original problem can be found with any required accuracy

robust control under parametric uncertainty via primal dual convex analysis a numerical method is proposed for optimal robust control synthesis the method applies to the case when the coefficients of the characteristic polynomial depend linearly on the uncertain parameters a primal dual pair of infinite dimensional convex problems is solved by successive finite dimensional approximations the primal dual pair has no duality gap and both upper and lower bounds produced by the approximations converge monotonically to the optimal value

solution of the schrodinger equation by a spectral method abstract a new computational method for determining the eigenvalues and eigenfunctions of the schrodinger equation is described conventional methods for solving this problem rely on diagonalization of a hamiltonian matrix or iterative numerical solutions of a time independent wave equation the new method in contrast is based on the spectral properties of solutions to the time dependent schrodinger equation the method requires the computation of a correlation function r 0 r t from a numerical solution r t fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system analysis of the location of these peaks reveals the eigenvalues with high accuracy additional fourier transforms of r t with respect to time generate the eigenfunctions the effectiveness of the method is demonstrated for a one dimensional asymmetric double well potential and for the two dimensional henon heiles potential

robust parametric classical control design this paper extends well known graphical design tools such as the nyquist plot bode plot and nichols charts to the domain of control systems containing parameter uncertainty we have specifically considered linear interval control systems namely those where the uncertain parameters appear linearly in the characteristic polynomial and vary in intervals because in these cases exact construction of frequency envelopes is possible using these developments we calculate various extremal stability margins for such systems and these are used with standard classical control design techniques to deal with robustness with respect to parametric uncertainty in addition we give an effective technique to iteratively select values of the design parameters within given ranges so that the closed loop system produces improved gain or phase margin

numerical solution of a two dimensional hyperbolic transmission problem an initial boundary value problem for a two dimensional hyperbolic equation in two disjoint rectangles is investigated the existence and uniqueness and a priori estimates for weak solutions in appropriate sobolev like spaces are proved few finite difference schemes approximating this problem are proposed and analyzed

an improved acoustical wave propagator method and its application to a duct structure the pseudospectral time domain method has long been used to describe the acoustical wave propagation however due to the limitation and difficulties of the fast fourier transform fft in dealing with nonperiodic problems the dispersion error is inevitable and the numerical accuracy greatly decreases after the waves arrive at the boundary to resolve this problem the lagrange chebyshev interpolation polynomials were used to replace the previous fft which however brings in an additional restriction on the time step in this paper a mapped chebyshev method is introduced providing the dual benefit of preserving the spectral accuracy and overcoming the time step restriction at the same time three main issues are addressed to assess the proposed technique a spatial derivatives in the system operator and the boundary treatment b parameter selections and c the maximum time step in the temporal operator furthermore a numerical example involving the time domain evolution of wave propagation in

diffusion in a bistable potential the functional integral approach we study with the help of the onsager machlup functional integral approach the distributionp of a single stochastic variable the evolution of which is described by a fokker planck equation with a first moment deriving from a bistable potential we set up the approximation scheme appropriate in this approach to the limit of constant and small diffusion coefficient two regimes are to be distinguished very long times kramers regime are treated within the frame of a free instanton molecule gas approximation and at intermediate times suzuki regime a standard semiclassical calculation is legitimate we thus rederive exactly the results obtained from the mode expansion and wkb method

diffusion in a potential field path integral approach abstract within the framework of the path integral formalism we develop a simple method to solve the fokker planck diffusion problems in a potential field including the decay of an unstable state unlike previous approaches it yields a unified treatment of all time regimes and is legitimate for any value of the diffusion coefficient an attractive feature of our method is that it provides numerical results in regions where there are no analytical solutions in particular being valid for an arbitrary shape of the potential it is very useful for studying a diffusion problem near and in the critical point where the standard treatments break down moreover our method after a simple transformation permits to obtain also the first passage times of the process

efficient computation of a guaranteed lower bound on the robust stability margin for a class of uncertain systems sufficient conditions for the robust stability of a class of uncertain systems with several different assumptions on the structure and nature of the uncertainties can be derived in a unified manner in the framework of integral quadratic constraints these sufficient conditions in turn can be used to derive lower bounds on the robust stability margin for such systems the lower bound is typically computed with a bisection scheme with each iteration requiring the solution of a linear matrix inequality feasibility problem we show how this bisection can be avoided altogether by reformulating the lower bound computation problem as a single generalized eigenvalue minimization problem which can be solved very efficiently using standard algorithms we illustrate this with several important commonly encountered special cases diagonal nonlinear uncertainties diagonal memoryless time invariant sector bounded popov uncertainties structured dynamic uncertainties and structured parametric uncertainties we also present a numerical example that demonstrates the computational savings that can be obtained with our approach

global existence and exponential stability for a contact problem between two thermoelastic beams in this paper we analyze a dynamic unilateral contact problem between two thermoelastic beams we establish the existence of a weak global in time solution by a penalization method moreover we study the asymptotic behavior of such a solution proving that the energy associated to the system decays exponentially to zero as time goes to infinity

multidimensional contact problems in thermoelasticity we consider dynamical and quasi static thermoelastic contact problems in hbox bbb r n modeling the evolution of temperature and displacement in an elastic body that may come into contact with a rigid foundation the existence of solutions to these dynamical and quasi static nonlinear problems and the exponential stability are investigated using a penalty method interior smoothing effects in the quasi static case are also discussed

estimating the conservatism of popov s criterion for real parametric uncertainties abstract we consider the problems of robust stability and performance analysis of linear systems subject to parametric uncertainties the popov criterion provides lower bounds of stability margins and upper bounds on robust performance in this paper we propose a method for obtaining upper bounds on stability margin or lower bounds on robust h2 performance based on the outcome of the lower bound computation for the stability problem or the upper bound computation for the h2 performance problem we make several numerical tests

the application of statistical linearization to the problem of decay from an unstable state abstract it is shown that the method of statistical linearization for the approximate treatment of stochastic nonlinear systems driven by gaussian white noise may be applied successfully to systems which evolve from a state of unstable equilibrium thereby developing non gaussian statistics the essential idea is the replacement of the full ensemble of realizations by subensembles according to the values taken by a small number of linear functionals of the noise the method is illustrated by applying it to two problems i strongly damped linear motion of a particle in a symmetric bistable potential ii the single mode laser in both cases it is found that low order moments can be calculated quite easily to an accuracy of a few per cent and that corrections with error estimates can be found by using the approximation to provide a control variate for numerical simulation

a unified approach for the stability robustness of polynomials in a convex set abstract consider a polynomial p s k which is affine in the parameter k assume that the vector k is uncertain but belongs to a bounded closed convex set which contains the origin as an interior point and call a polynomial stable if all of its roots are contained in a pre specified stability region in the complex plane then the stability robustness of p s k can be measured by the maximal nonnegative number with the property that if the gauge or the minkowski functional of k with respect to the convex set is less than the polynomial p s k is always stable this paper develops a unified approach to compute the robustness measure using the framework of convex analysis the approach is very general because of two reasons i the stability region in the complex plane can be an arbitrary open set which includes the open left half plane and the open unit disc as special cases ii the convex set in which k is contained can be assumed to have an arbitrary shape which includes polytopes and ellipsoids as special cases the computational procedure to compute which results from this approach is easy to implement an example is included to illustrate the type of results which may be obtained the approach developed in this paper when specialized leads to some of the available results in the literature moreover it generates many new and interesting results another important feature of this approach is that it provides a rich mathematical insight to the stability robustness problem of polynomials

global existence and decay for the semilinear thermoelastic contact problem in this paper a class of semilinear thermoelastic contact problems is considered and the existence and exponential decay of the weak solutions are obtained

numerical estimation of the path integral and the diffusion in an anharmonic oscillator abstract the solution of the fokker planck equation given in the form of the path integral is estimated by the contribution from paths around the most probable path a numerical procedure for this estimation is given and applied to the regression of an anharmonic oscillator under a random force from unstable positions to a stable position

solution of fokker planck equation using trotter s formula solution of fokker planck equation using trotter s formula is discussed the method is illustrated on the linear fokker planck equation and the ornstein uhlenbeck solution is obtained for the case of a general nonlinear fokker planck equation the method yields an integral representation amenable to approximations in the lowest order approximation suzuki s scaling result emerges physical interpretation and limitations of the approximations are also discussed

symbolic calculation in development of algorithms split step methods for the gross pitaevskii equation we employ symbolic calculation to perform a systematic study of the accuracy of split step fourier transform methods for the time dependent gross pitaevskii equation gpe provided the most recent approximation for the wave function is always used in the nonlinear atom atom interaction energy every split step algorithm we have tried has the same order time stepping error for the nonlinear gpe and for the linear schroedinger equation

the thermoelastic and viscoelastic contact of two rods we consider the thermoelastic and viscoelastic contact problem of two rods and prove the existence of a weak solution using a penalization method and compensated compactness moreover for the thermoelastic contact we show that the weak solution converges to zero exponentially as time goes to infinity and for the viscoelastic contact we prove that the weak solution decays to zero with the same rates as the relaxation functions do

the robust root locus abstract in this paper a simple technique is described for generating the root loci of a feedback system which includes perturbations q rl entering affine linearly into the coefficients of the plant denoting the perturbed plant by p s q and the compensator by c s we address the following problem given a bounding set q rl for q find the locus of points z in the complex plane such that 1 kp z q c z 0 for some k 0 and some q q such points z are said to lie on the robust root locus one of the strengths of the technique presented in this paper is that it avoids the combinatoric explosion synonymous with gridding the l dimensional set q and plotting a large number of ordinary root loci associated with gridding the points instead the technique given here exploits only a 2 dimensional gridding of a bounded subset of the complex plane for the more general case when perturbations enter multilinearly into the coefficients a certain convex hull robust root locus is constructed finally the robust root locus technique is illustrated using a model of a supersonic transport plane

existence and decay to contact problems for thermoviscoelastic plates we consider the dynamic contact problem for thermoviscoelastic plates we show the existence of weak solutions as well as exponential decay of the solution

quaternionic madelung transformation and non abelian fluid dynamics abstract we find the quaternionic generalization of the madelung transformation of the schroedinger equation the non abelian nature of the full su 2 gauge group of the quaternionic schroedinger equation leads to a more complex set of equations for the fluid variables we identify the hydrodynamic variables for the quaternionic madelung transformation in order to find equations of motion for these quantities we cast the madelung transformation in the form of a non canonical transformation of the classical hamiltonian field theory for the quaternionic schroedinger equation we first define the canonical bracket and hamiltonian for the quaternionic schroedinger equation and then obtain the non canonical brackets yielding the equations of motion for the quaternionic madelung variables these equations are a particularly natural set of equations for a non abelian fluid and differ from those obtained by bistrovic et al only by a global gauge transformation hep th 0210143 2002 obtaining these equations by a transformation of the quaternionic schroedinger equation makes their simulation by a variety of methods particularly simple

numerical analysis of a unilateral problem in planar thermoelasticity we consider in this paper the numerical approximation of a quasi static contact problem in linear thermoelasticity that models the evolution of the temperature and displacement of an elastic homogeneous and isotropic body that may come in contact with an elastic obstacle we propose a finite element method to numerically approximate the continuous solution convergence without any regularity assumptions is proved and error estimates are obtained if the continuous solution is sufficiently regular

how to calculate the wigner function from phase space we present a method for the direct computation of the wigner function by solving a coupled system of linear partial differential equations in phase space our modified spectral method relies on chebyshev polynomials since this approach allows us to include arbitrary high orders of partial derivatives our procedure is applicable to arbitrary binding potentials we apply our scheme to wigner functions of the harmonic oscillator the morse oscillator and an asymmetric double well potential

a convex parameterization of robustly stabilizing controllers this paper treats synthesis of robust controllers for linear time invariant systems uncertain real parameters are assumed to appear linearly in the closed loop characteristic polynomial the main contribution is to give a convex parameterization of all controllers that simultaneously stabilize the system for all possible parameter combinations with the new parameterization certain robust performance problems can be stated in terms of quasi convex optimization

a contact problem in generalized thermoelasticity abstract in this work we study a one dimensional contact problem in generalized thermoelasticity under the green lindsay theory unilateral contact with an elastic obstacle is assumed we consider the quasi static and the fully dynamic situations we prove existence and uniqueness results and propose finite element approximations in space with backward euler discretization in time stability results are given and some numerical experiments reported the second sound effect of heat conduction is observed in the simulations

a numerical method for a nonlinear system of integro differential equations arising in thermoviscoelasticity this paper deals with the numerical solution of nonlinear integro differential equations modelling a one dimensional quasi static contact problem in thermoviscoelasticity a finite element approximation is proposed and analysed and some numerical results are given

error analysis for a finite element approximation of a thermoviscoelastic contact problem in this article a finite element approximation based on a variational inequality to the solution of a one dimensional quasi static signorini contact problem in linear thermoviscoelasticity is proposed stability and error estimates are obtained

chebyshev spectral methods for radiative transfer we study the performance of chebyshev spectral methods for time dependent radiative transfer equations starting with a method for one dimensional problems in homogeneous media we show that the modifications needed to consider more general problems such as inhomogeneous media polarization and higher dimensions are straightforward in this method we approximate the spatial dependence of the intensity by an expansion of chebyshev polynomials this yields a coupled system of integro differential equations for the expansion coefficients that depend on angle and time next we approximate the integral operation on the angle variables using a gaussian quadrature rule resulting in a coupled system of differential equations with respect to time using a second order finite difference approximation we discretize the time variable we solve the resultant system of equations with an efficient algorithm that makes chebyshev spectral methods competitive with other methods for radiative transfer equations

numerical solutions to one dimensional problems of thermoelastic contact abstract a numerical method based on the crank nicolson discretisation is applied to one dimensional thermoelastic contact problems such problems can be reduced using an appropriate transformation to the heat equation with a nonlinear and nonlocal source term it is proved that the method converges a number of numerical experiments are presented to illustrate the method and the behavior of the solutions to the problem

decay to the nonequilibrium steady state of the thermal diffusion in a tilted periodic potential abstract we investigate the phenomenon of asymptotic decay towards the nonequilibrium steady state of the thermal diffusion in the presence of a tilted periodic potential the parameter dependence of the decay rate is revealed by investigating the fokker planck fp equation in the low temperature case under the spatially periodic boundary condition pbc we apply the wkb method to the associated schrodinger equation while eigenvalues of the non hermitian fp operator are complex in general in a small tilting case the imaginary parts of the eigenvalues are almost vanishing then the schrodinger equation is solved with pbc the decay rate is analyzed in the context of quantum tunneling through a triple well effective periodic potential in a large tilting case the imaginary parts of the eigenvalues of the fp operator are crucial we apply the complex valued wkb method to the schrodinger equation with the absorbing boundary condition finding that the decay rate saturates and depends only on the temperature the potential periodicity and the viscous constant the intermediate tilting case is also explored the analytic results agree well with the numerical data for a wide range of tilting