hydraulic conductivity estimation in partially saturated soils using the adjoint method abstract an iterative algorithm based on the adjoint method for the estimation of the saturated hydraulic conductivity k in a partially saturated soil q is proposed groundwater flow in q is assumed to be described by richards equation the optimization problem minimizes the l2 error between the pressure head values p k x t calculated as the solution of a direct problem and the measured values of the pressure head at discrete points inside the domain q the exact gradient of the cost functional is obtained by solving an appropriate adjoint problem which is derived from the equations of the g teaux derivatives of the pressure head with respect to the parameter k a finite element procedure is used to obtain approximate solutions of the direct and adjoint problems and the g teaux derivatives a discrete form of the expression of the gradient of the cost functional at the continuous level is used inside a nonlinear conjugate gradient iteration to solve the optimization problem a numerical example showing the implementation of the algorithm to estimate the saturated hydraulic conductivity k x during an hypothetical infiltration experiment in a heterogeneous soil is also presented

estimation of nonlinearities in parabolic models for growth predation and dispersal of populations a convergence theory is given for approximation techniques to treat inverse problems involving systems of nonlinear parabolic partial differential equations these techniques can be used to estimate density dependent dispersal coefficients in population models as well as nonlinear growth and predation terms numerical experiences with the resulting algorithms on both conventional scalar and vector computers are reported along with an indication of performance of the methods with field data from prey predator experiments

free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule the generalized differential quadrature rule proposed recently by these authors is applied here to the free vibration analyses of solid circular plates with radially varying thickness and elastic restraints the thickness can vary radially in any given continuous form and it varies exponentially and linearly in this work two regularity conditions corresponding to the plate center are expressed in explicit formulae since they have been inexactly or even wrongly expressed in the literature such errors are pointed out in the application of the differential quadrature techniques and in the expression of the regularity conditions at the plate center numerical results are presented for a number of plates illustrating the versatility and accuracy of the approach

on the solution of an inverse scattering problem in seismic while drilling technology abstract this paper concerns the solution of an inverse scattering problem arising in seismic exploration the problem to be analyzed is the prediction of the acoustic wave speeds ahead of a drill bit device located at the center of a well bore and regarded as a seismic source from measurements of the displacements at recording positions located near the surface of the exploration well the forward model is stated in terms of displacements assuming cylindrical symmetry with the symmetry axis located at the center of the borehole absorbing boundary conditions are employed at the artificial boundaries the inverse problem is formulated as the minimization of a quadratic cost functional which is solved using a nonlinear iterative procedure known as quasilinearization that uses the frechet derivatives of the displacements with respect to the wave speed parameters to update the parameter values during the iteration approximations to the solution of the differential equations associated with the forward problem and the frechet derivatives which are needed to discretize the optimization procedure were obtained using an explicit finite element procedure results on the existence uniqueness and regularity of the differential problem and the frechet derivatives are derived as well as on their continuity with respect to the parameter convergence results for the iterative estimation procedure are also given numerical examples illustrating the application of the algorithm to estimate the wave speeds in model problems within the context of the seismic while drilling technique are presented

simultaneous estimation and prediction using the expected coverage measure criterion on utilise des methodes d invariance pour construire des procedures minimax dans les modeles lineaires multivariables

estimation of variable coefficients in parabolic distributed systems we present techniques based on cubic spline approximations for estimating coefficients e g diffusion convector velocity etc depending on time and the spatial variable in parabolic distributed systems such as those that arise in transport models convergence results and a summary of numerical performance of the resulting algorithms are given

transverse vibrations of circular plates and membranes with intermediate supports the present paper deals with an approximate solution of the title problem in the case of a a concentric circular support and b a secant support fundamental frequency coefficients are determined by means of the rayleigh minimization procedure the modal shapes been approximated by simple polynomial co ordinate functions in the case of a circular plate with a secant support an independent solution is obtained by means of a finite element code and very good agreement is shown to exist

asymptotic efficiency in parametric structural models with parameter dependent support in certain auction search and related models the boundary of the support of the observed data depends on some of the parameters of interest for such nonregular models standard asymptotic distribution theory does not apply previous work has focused on characterizing the nonstandard limiting distributions of particular estimators in these models in contrast we study the problem of constructing efficient point estimators we show that the maximum likelihood estimator is generally inefficient but that the bayes estimator is efficient according to the local asymptotic minmax criterion for conventional loss functions we provide intuition for this result using le cam s limits of experiments framework

vibration analysis of circular mindlin plates using the differential quadrature method abstract axisymmetric free vibrations of moderately thick circular plates described by the linear shear deformation mindlin theory are analyzed by the differential quadrature dq method the first fifteen natural frequencies of vibration are calculated for uniform circular plates with free simply supported and clamped edges through these computations the capability and simplicity of the differential quadrature method for moderately thick plate eigenvalue analysis is demonstrated and convergence and accuracy are thoughtfully examined the case of rigid point support at the plate centre is also considered in the present paper for which special attention is paid to the capability and convergence of the current method

axisymmetric vibrations of polar orthotropic mindlin annular plates of variable thickness abstract analysis and numerical results are presented for the axisymmetric vibrations of polar orthotropic annular plates with linear variation in thickness according to mindlin s shear theory of plates a chebyshev collocation technique has been employed to obtain the frequency equations for the transverse motion of such plates for three different boundary conditions frequencies mode shapes and moments for the first three modes of vibration have been computed for different plate parameters a comparison of frequencies with the corresponding values obtained by classical plate theory leads to some interesting conclusions

estimation of parameters in two dimensional transport equations a general approximation framework based on bicubic splines is developed for estimating temporally and spatially varying parameters in two dimensional transport equations the parameter estimation problem is first cast as an abstract infinite dimensional minimization problem then a sequence of approximate finite dimensional minimization problems is defined which yields a sequence of parameter estimates since convergence results relating the approximate problems to the full infinite dimensional problem are presented in 6 and 17 this paper will focus only on the computer implementation of our technique and the results of numerical tests using analytically generated data the technique is also applied to the analysis of actual biological data from an insect dispersal experiment in which the movement of cabbage root flies in the presence of a cabbage crop was studied

vibrations of circular plates with clamped v notches or rigidly constrained radial cracks abstract this study offers the first known free vibration data for thin circular plates with clamped v notches the classical ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements these sets include 1 mathematically complete algebraic trigonometric polynomials which guarantee convergence to exact frequencies as sufficient terms are retained and 2 corner functions which account for the bending moment singularities at the sharp corner of the v notch extensive convergence studies summarized herein confirm that the corner functions substantially enhance the convergence and accuracy of non dimensional frequencies for circular plates with clamped notches numerical results are obtained for plates having their circular edges completely free accurate five significant figure frequencies are presented for a wide spectrum of notch angles 0 5 10 30 60 and 90 and depths for very small notch angles a rigidly constrained radial crack ensues some general findings are that for the spectrum of notch angles examined the first six frequencies increase as the notch depth increases more so in the higher modes than the lower ones the frequency increase with increasing notch depth is quite substantial for the semi circular plates and for segmented plates with sector angles less than 180 for a constant notch depth it is found that there is a substantial reduction in the first six frequencies as notch angle decreases normalized contours of the transverse vibratory displacement are shown for plates having 90 and 5 notches of various depths ranging from deep to very shallow the first known frequencies and mode shapes for sectorial semi circular and segmented plates with clamped radial edges are also presented as special cases of the title problem

three dimensional elasticity solutions for free vibrations of circular plates a polynomials ritz analysis this paper presents accurate three dimensional elasticity solutions for free vibration of circular plates the derivation of a linear frequency equation based on an exact three dimensional small strain linearly elastic principle is detailed the solution to this problem is made possible by using the ritz method with a set of orthogonal polynomial series to approximate the spatial displacements of the circular plate in cylindrical polar coordinates the perturbation of frequency responses due to the variations of boundary conditions and thickness is investigated first known frequency parameters and three dimensional deformed mode shapes are presented in vivid graphical forms the accuracy of these results are verified by appropriate convergence studies and when possible are checked with existing solutions

frequency domain sample maximum likelihood estimation for spatially dependent parameter estimation in pdes the identification of the spatially dependent parameters in partial differential equations pdes is important in both physics and control problems a methodology is presented to identify spatially dependent parameters from spatio temporal measurements local non rational transfer functions are derived based on three local measurements allowing for a local estimate of the parameters a sample maximum likelihood estimator smle in the frequency domain is used because it takes noise properties into account and allows for high accuracy consistent parameter estimation confidence bounds on the parameters are estimated based on the noise properties of the measurements this method is successfully applied to the simulations of a finite difference model of a parabolic pde with piecewise constant parameters

quantum hypothesis testing for gaussian states quantum analogues of χ 2 t and f tests we consider quantum counterparts of testing problems for which the optimal tests are the 2 t and f tests these quantum counterparts are formulated as quantum hypothesis testing problems concerning gaussian state families and they contain nuisance parameters which have group symmetry the quantum hunt stein theorem removes some of these nuisance parameters but other difficulties remain in order to remove them we combine the quantum hunt stein theorem and other reduction methods to establish a general reduction theorem that reduces a complicated quantum hypothesis testing problem to a fundamental quantum hypothesis testing problem using these methods we derive quantum counterparts of the 2 t and f tests as optimal tests in the respective settings

free vibration of continuous polar orthotropic annular and circular plates abstract the free vibration of a polar orthotropic annular plate supported on concentric circles is analyzed by the ritz method with use of lagrange multipliers a trial function for the deflection of the plate is expressed in terms of simple power series and a frequency equation for the plate is derived by the condition for minimizing the total potential energy with the constraint equations included in the numerical examples it is also shown that the method can directly yield quite accurate frequency values for a solid circular plate natural frequencies of annular and circular plates are calculated for wide ranges of the support location and orthotropic parameters

exact vibration solutions for circular mindlin plates with multiple concentric ring supports this paper presents an analytical approach to investigate the vibration behaviour of circular mindlin plates with multiple concentric ring supports a circular plate is first divided into multiple annular segments and a circular segment at the locations of the ring supports the governing differential equations and the solutions of these equations for the annular and circular segments based on the mindlin plate theory are presented a homogenous equation system governing the vibration of circular mindlin plates with ring supports is derived by imposing the essential and natural boundary and segment interface conditions the first known exact vibration frequencies for circular mindlin plates with multiple concentric ring supports are obtained and the modal shapes of displacement fields and stress resultants for several selected cases are presented the influence of the ring support locations plate boundary conditions and plate thickness ratios on the vibration behaviour of circular plates is discussed

cubic spline approximation techniques for parameter estimation in distributed systems approximation schemes employing cubic splines in the context of a linear semigroup framework are developed for both parabolic and and hyperbolic second order partial differential equation parameter estimation problems convergence results are established for problems with linear and nonlinear systems and a summary of numerical experiments with the techniques proposed is given

free vibration analysis of stepped circular mindlin plates this paper presents the first known investigation on exact vibration of circular mindlin plates with multiple step wise thickness variations a stepped circular plate is divided into multiple annular and one circular segments along the locations of the step variations the governing differential equations for harmonic vibration of annual and circular segments are derived and an analytical method based on the domain decomposition technique is developed to solve the plate vibration problem exact vibration solutions are presented for circular mindlin plates of different edge support conditions and various combinations of step wise thickness variations the influence of plate boundary conditions plate thickness ratios step location ratios and step thickness ratios on the vibration behaviour of stepped circular mindlin plates are examined the exact vibration results can serve as benchmark values for researchers to validate their numerical methods for such circular plate problems

estimation of discontinuous coefficients in parabolic systems applications to reservoir simulation we present spline based techniques for estimating spatially varying parameters that appear in parabolic distributed systems typical of those found in reservoir simulation problems in particular we discuss the problem of determining discontinuous coefficients estimating both the functional shape and points of discontinuity for such parameters in addition our ideas may also be applied to problems with unknown initial conditions and unknown parameters appearing in terms representing external forces convergence results and a summary of numerical performance of the resulting algorithms are given

elasticity solutions for free vibrations of annular plates from three dimensional analysis abstract this article examines the vibrational characteristics of annular plates by using the three dimensional elasticity theory it aims to raise the quality of the investigation beyond that provided by the two dimensional plate theories by resorting to a full three dimensional analysis a polynomials ritz model based on sets of orthogonally generated polynomial functions to approximate the spatial displacements of the plates in cylindrical polar coordinates is presented the model is then used to extract the full vibration spectrum of natural frequencies and mode shapes the vibration responses due to the variations of boundary conditions and thickness are investigated frequency parameters and three dimensional deformed mode shapes are presented in vivid graphical forms the accuracy of the method is validated through appropriate convergence and comparison studies

optimal design of internal ring supports for vibrating circular plates this paper presents the optimality conditions for optimum locations of internal ring supports in circular plates for maximum frequency of axisymmetric vibration of a specified order the optimality conditions require both the reaction forces and moments at the internal supports to vanish for optimal solutions this means that the internal ring supports should be placed at the nodal rings of the appropriate higher order vibration mode of a corresponding unsupported circular plate for maximum effectiveness in raising the vibration frequency of the plate some design examples are given to verify the derived optimality conditions

a diffusion problem on a semi infinite interval approximate solutions and parameter estimations on considere le probleme de diffusion canonique pour x 0 t 0 u t x t k 2 q u xx x t f q x t u u x o f x q u o t 0 u x t dans l 2 0 q estun vecteur fixe et peut representer des parametres inconnus

on the lateral vibration of thin annular and circular composite plates subject to certain complicating effects abstract series comprising orthogonally generated polynomial functions are used in the rayleigh ritz method to obtain an eigenvalue equation for the flexural vibration of thin flat annular and circular plates the plates may be of isotropic or polar orthotropic material of uniform or radially varying thickness and may pass over intermediate concentric ring supports numerical results are presented for a number of plates illustrating the versatility and accuracy of the approach

vibration analysis of annular plates with concentric supports using a variant of rayleigh ritz method a variant of the rayleigh ritz method is presented for solving the free vibration problem of annular plates with internal axisymmetric supports the method is simple accurate and may be readily programmed and run on a microcomputer a comprehensive tabulation of the fundamental frequencies is presented for isotropic annular plates with an internal concentric support results for full circular plates with concentric supports are also obtained by making the inner radial edge free and permitting the inner radius to become very small

an approximation theory for nonlinear partial differential equations with applications to identification and control approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations these ideas are used to establish theoretical convergence results for parameter identification using modal eigenfunction approximation techniques results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given

fitting numerical solutions of differential equations to experimental data a case study and some general remarks summary a simple and efficient algorithm for least squares estimation of the parameters of a numerically solved diffusion model is presented the algorithm has been specially developed for the analysis of data obtained by vitreous fluorophotometry a method in clinical eye research but it has several straightforward generalizations which are also outlined in the paper it happens that these equations are difficult or impossible to solve explicitly and that numerical methods are employed often it is desired to estimate the parameters of such models from experimental data using the method of least squares or one of its relatives the main body of differential equation models in biometry consists of initial value problems for systems of ordinary differential equations such as occur in compartment models but also partial differential equations appear banks and kareiva 1983 discuss the transport of glucose in the cat brain as well as deterministic population dynamic models for insect dispersal the current study deals with the transport of a fluorescent dye in the vitreous body of the human eye and in general questions of diffusion or heat transfer involve similar equations further applications might include fluid flow problems or equations of elasticity in biomechanics since numerical methods for the solution of partial differential equations are computationally demanding it is important to choose an efficient algorithm for the estimation of model parameters particularly in situations where the algorithm is to be applied many times for instance when several curves are to be fitted for each examination of each patient as part of an interactive routine for coordination of data from different sources the current study deals with vitreous fluorophotometry a method in clinical eye research where the model involves the diffusion equation and the parameters are the diffusion coefficient in the vitreous body of the eye and the permeability of the blood retinal barrier the data are concentration measurements in the vitreous body we have found that for this

an iterative procedure for estimation of variable coefficients in a hyperbolic system a parameter estimation problem for the acoustic wave equation in a multidimensional bounded domain with absorbing boundary conditions depending on the parameter is solved by using quasilinearization techniques results on the frechet differentiability of the solution with respect to the parameter are derived by applying the energy method an iterative procedure employing quasilinearization at each iteration step is given to solve the estimation problem results on the convergence of the method are presented numerical examples illustrate the application of our algorithm

amenability a survey for statistical applications of hunt stein and related conditions on groups a number of conditions on groups have appeared in the literature of invariant statistical models in connection with minimaxity approximation of invariant bayes priors by proper priors the relationship between bayesian and classical inference ergodic theorems and other matters in the last decade rapid development has occurred in the field and many of these conditions are now known to be equivalent we survey the subject make the equivalences explicit and list some groups of statistical interest which do and also some which do not have these properties in particular it is shown that the existence of the asymptotically invariant sequence of probabilities in the hypothesis of the hunt stein theorem is equivalent to amenability a condition that has been much studied by functional analysts

flexural vibration of shear deformable circular and annular plates on ring supports this paper presents an analysis of free flexural vibration of circular and annular mindlin plates lying on multiple internal concentric ring supports the rayleigh ritz method with an admissible displacement function expressed in terms of a set of simple polynomials is used to obtain the governing eigenvalue equation the natural frequencies of circular and annular mindlin plates with one or two ring supports having inner and outer peripheries with different combinations of free simply supported and clamped conditions are determined a comprehensive set of vibration results is presented and where possible these have been verified with existing solutions published in the open literature no previous theoretical results for thick annular plates supported with internal rings are known to exist thus the study should be useful and valuable to engineers and researchers

free vibration analysis of mindlin plates with linearly varying thickness abstract a method based on the variational principles in conjunction with the finite difference technique is applied to examine the free vibration characteristics of isotropic rectangular plates of linearly varying thickness by including the effects of transverse shear deformation and rotary inertia the validity of the present approach is demonstrated by comparing the results with other solutions proposed for plates with uniform and linearly varying thickness natural frequencies and mode shapes of mindlin plates with simply supported and clamped edges are determined for various values of relative thickness ratio and the taper thickness constant

buckling and vibration of annular mindlin plates with internal concentric ring supports subject to in plane radial pressure abstract this paper is concerned with the buckling and vibration of annular mindlin plates with internal concentric ring supports subjected to external and internal isotropic in plane radial pressure the governing eigenvalue equation is obtained by using the rayleigh ritz approach with the transverse displacement and rotations being approximated by the product of a complete one dimensional polynomial function and a basic function the basic function is the product of the boundary equations and ensures the automatic satisfaction of the kinematic boundary conditions comprehensive sets of buckling factors and vibration frequencies for the aforementioned mindlin plate problems are tabulated for the first time to the author s knowledge additionally useful design charts are presented for a large number of annular mindlin plates on multiple concentric ring supports with the outer and inner edges subjected to isotropic in plane radial pressure computations based on the model reveal the significant effect of internal rings on the buckling factors and vibration frequencies of the plates

estimation of variable coefficients in the fokker planck equations using moving node finite elements inverse problems are considered for the estimation of temporally and spatially varying coefficients in the fokker planck or forward kolmogorov equation that often arise in size age structured population models these are difficult problems even for simulation studies since they share certain numerical difficulties with transport dominated diffusion convection problems of fluid dynamics these difficulties stem from the fact that when the convection is large compared to the diffusion both traditional finite difference or finite element methods produce erroneous oscillatory solutions in this paper computational techniques are presented that combine a variation of the moving finite element method with spline approximations for the parameter estimation problems computational details of our numerical algorithm along with theoretical convergence results are presented several numerical examples illustrating the effectiveness of the method are also given

special capacities the hunt stein theorem and transformation groups the problem of maximin testing between families of probability measures generated by special capacities and transformation groups is solved by showing that the hunt stein theorem is applicable to such generally nondominated families of probability measures and that the problem reduces to maximin testing between neighbourhoods of distributions of maximal invariant defined by special capacities closely related to the initial ones an application to testing approximate binormality is also sketched

reduction of distributed system identification complexity using intelligent sensors abstract the identification problems of distributed parameter systems dps is dealt with a special method of data collection by using moving sensors is proposed the sensors are intelligent in the sense that they are able to track the positions of the exiremum values of a system state at each time instant it is shown how to reduce the identification problem for dps to that of identifying a certain system described by ordinary differential equations ode the proposed approach is applicable to the dps described by quasi linear partial differential equations of the hyperbolic type attention is focused on the problem of reduction while the identification of the resulting ode is not considered in detail since it is an easier task