shape design sensitivity analysis for geometrically and materially nonlinear problems by the boundary element method abstract this paper is concerned with the determination of design sensitivity coefficients dscs for fully nonlinear problems i e problems with both material and geometric nonlincarities in solid mechanics the clastic strains arc assumed to be small but the nonclastic plastic or viscoplustic strains as well as rotations can be arbitrarily large dscs here refer to rates of change of response variables such as displacements or stresses in a deforming solid body with respect to parameters called design variables that define the initial undeformed shape of the body these dscs are history dependent the direct differentiation approach dda of the relevant derivative boundary element method dbem formulation is employed to obtain the dscs a general computer program is developed for the analysis of two dimensional plane strain and plane stress problems numerical results are obtained for illustrative problems and arc compared against direct solutions the results from the two methods agree almost perfectly for these problems this research has potential applications in the optimization of manufacturing processes such as extrusion rolling or forging

energy needed to send a bit earlier work demonstrated that quantum mechanical machinery can be used to transmit classical bits without a minimal unavoidable energy cost per bit it is shown that a very minor variation of the earlier proposal also works for qubits in addition some casual remarks about error control in quantum parallelism are provided

a quantum computing primer for operator theorists this is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory after a brief introduction we discuss quantum algorithms we outline basic properties of quantum channels or equivalently completely positive trace preserving maps the main theorems for quantum error detection and correction are presented and we conclude with a description of a particular passive method of quantum error correction

on the schrodinger equation for the gaussian potential a exp λr2 the energy eigenvalues of the attractive radial gaussian potential for various eigenstates are very accurately determined within the framework of the hypervirial pade scheme

on the schrodinger equation for the interaction x2 λx2 1 gx2 the method of obtaining the explicit expressions of all the even odd parity exact solutions of the schrodinger equation for the interaction x2 lambda x2 1 gx2 is discussed when the couplings lambda and g satisfy some specific relations in the general case a simple equation for approximating the energy eigenvalues has been developed

algebraic recurrence formulae for matrix elements between the solutions of the transformed jacobi eigenequation the algebraic recursive determination of matrix elements of some selected families of functions q1 x between the solutions psi jm x of factorisable equations is reinvestigated the possibilities of the procedure outlined in a previous paper are enlarged by using the connection between factorisation types i e the different possible factorisations of the same differential equation the computation of matrix elements between the jacobi eigenfunctions psi jm x approximately sin ax 2 alpha 1 2 cos ax 2 beta 12 pv alpha beta cos ax where a is a real or pure imaginary constant is studied in detail algebraic recurrence formulae satisfied by matrix elements of qt x cos ax 2 p sin ax 2 q tan ax 2 t qt x sin ax p tan ax q cos ax t qt x psi jt x and qt x psi tm x are given and for the particular cases qt x tan ax 2 t and qt x cos ax t closed form expressions are obtained as an illustrative application it is briefly shown how the expressions can serve to derive analytical approximations of the bound state energies for the potential v x a exp x2 l l 1 x2 some further applications are pointed out

perturbed factorization of the singular anharmonic oscillator eigenequation the perturbed ladder operator method is applied to the solution of the perturbed eigenequation d2 dx2 m m 1 x2 b2x2 v x ix 0 where v x b1 1 x 2 b2 1 x 4 is a singular perturbation this method which is the extension of the schrodinger infeld hull factorization method within the perturbation scheme provides closed form expressions of the perturbed eigenvalues and ladder functions by means of algebraic manipulations as an illustrative application an analytical solution of the spiked harmonic oscillator eigenequation d2 dx2 b2x2 x4 e x 0 is worked out up to the second order of the perturbation by considering specifically adapted m and dependent perturbing and unperturbed potentials in order to tentatively avoid the known difficulties of convergence of the perturbation series closed form expressions of the x4 anharmonic oscillator energies are obtained in terms of the coupling constant and the quantum number v results following from these expressions are compared wit

comparing experiments to the fault tolerance threshold achieving error rates that meet or exceed the fault tolerance threshold is a central goal for quantum computing experiments and measuring these error rates using randomized benchmarking is now routine however direct comparison between measured error rates and thresholds is complicated by the fact that benchmarking estimates average error rates while thresholds reflect worst case behavior when a gate is used as part of a large computation these two measures of error can differ by orders of magnitude in the regime of interest here we facilitate comparison between the experimentally accessible average error rates and the worst case quantities that arise in current threshold theorems by deriving relations between the two for a variety of physical noise sources our results indicate that it is coherent errors that lead to an enormous mismatch between average and worst case and we quantify how well these errors must be controlled to ensure fair comparison between average error probabilities and fault tolerance thresholds

adjoint sensitivity analysis for nonlinear dynamic thermoelastic systems an adjoint approach is presented to formulate explicit sensitivities for a general functional associated with a nonlinear dynamic thermoelastic system uncoupled thermoelastic response and small deformation behavior are assumed the formulation uses the lagrange multiplier method to define an adjoint system the convolution operator to incorporate transient effects and domain parameterization to describe shape variations variations of the functional are expressed in explicit form with respect to perturbations of the design fields structural shape material properties applied loads prescribed boundary conditions and initial conditions the functional is defined in terms of the design fields and the implicit response fields displacement temperature strain temperature gradient stress heat flux vector reaction force and reaction surface flux in an example problem the finite element method is used to evaluate the real and adjoint responses and the shape sensitivities for a tank design problem the tank is modeled as a nonlinear quasistatic uncoupled thermoelastic system

error scaling in fault tolerant quantum computation the threshold theorem states that quantum computations can scale robustly in the presence of certain types of noise processes e g markovian as long as the probability of error for each physical component remains below a critical threshold to satisfy this threshold a theoretical circuit requiring o s idealized noiseless gates can be implemented with o s polylog s gates to maintain an error rate that is constant with increasing s in this paper we argue that maintaining a fixed error rate is necessary but not sufficient to preserve complexity results obtained under an assumption of noiseless gates specifically we show that nontrivial quantum algorithms exhibit nonlinear sensitivity to any circuit error and that this sensitivity affects algorithmic complexity the joint effects of circuit error and quantum algorithmic iteration are examined for the case of quantum search and more complete complexity results are derived

exact solutions of the schrodinger equation d dx2 x2 λx2 1 gx2 ψ x eψ x the authors prove the existence of a class of exact eigenvalues and eigenfunctions of the schrodinger equation for the potential x2 x2 1 gx2 when certain algebraic relations between and g hold some of the properties of these solutions are discussed it is shown that in a certain sense they may be regarded as sturmians for the schrodinger equation with the potential x2 g g2x2

on the schrodinger equation for the interaction x2 λx2 1 gx2 by forming the 6 6 pade approximants to the energy perturbation series for the interaction x2 lambda x2 1 gx2 as obtained from the hypervirial relations the ground and the first three excited state energy levels are calculated for g or 2 the results of the present calculation are in good agreement with those of the variational calculations the authors also present another set of exact solutions to the schrodinger equation for the interaction x2 lambda x2 1 gx2

implicit bem formulations for usual and sensitivity problems in elasto plasticity using the consistent tangent operator concept this paper presents boundary element method bem formulations for usual and sensitivity problems in small strain elasto plasticity using the concept of the local consistent tangent operator cto usual problems here refer to analysis of nonlinear problems in structural and solid continua for which simo and taylor first proposed the use of the cto within the context of the finite element method fem a new implicit bem scheme for such problems using the cto is presented first a formulation for sensitivity analysis follows it is shown that the sensitivity of the strain increment associated with an infinitesimal variation of some design parameter solves a linear problem which is governed by the converged value of the same global cto as the one that appears in the usual problem numerical results for both usual and sensitivity problems are shown for a one dimensional example they demonstrate the effectiveness of the present approach in particular accurate sensitivities with respect to material parameters e g exponent of the power type hardening law are obtained even with few integration cells and for large load increments

eigenvalues from power series expansions an alternative approach an appropriate rational approximation to the eigenfunction of the schrodinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a sequence of roots of hankel determinants the convergence rate of this approach is greater than that for a well established method based on power series expansions weighted by a gaussian factor with an adjustable parameter the so called hill determinant method

a note on the schrodinger equation for the potential a exp x2 l l 1 x2 the bound states energies and eigenfunctions of the schrodinger equation with a radial gaussian potential are obtained using a perturbational and also a variational treatment on a conveniently chosen basis of transformed jacobi functions the accuracy of the results is fairly good

vectorial and parallel processing in stress analysis with the boundary element method the purpose of this short paper is to describe an experience at converting a scalar serial elastic axisymmetric bem code to a vector parallel environment on an ibm this is a single zone bem computer program

definite integrals as solutions for the x2 λx2 1 gx2 potential presents exact solutions and eigenvalues for the schrodinger equation with the x2 x2 1 gx2 interaction on the half axis x or 0 the solutions are given in the form of definite integrals and the eigenvalues by means of a well defined limiting procedure

a factorization method with application to perturbation theory a new implementation of perturbation theory is presented for separable problems which is a blend of two previously proposed factorization methods the resulting technique offers several advantages with respect to the parent methods and yields the perturbation corrections exactly in terms of the quantum numbers of the unperturbed problem through equations in which the unperturbed eigenfunction does not appear explicitly as an example a perturbed legendre equation is considered and the application of the approach to other problems of physical interest is discussed

almost any quantum logic gate is universal it is shown that if one can apply some hamiltonian repeatedly to a few variables at a time one can in general effect any desired unitary time evolution on an arbitrarily large number of variables as a result almost any quantum logic gate with two or more inputs is computationally universal in that copies of the gate can be wired together to effect any desired logic circuit and to perform any desired unitary transformation on a set of quantum variables

some solutions of a supersymmetric nonpolynomial oscillator a comparison between the swkb and wkb methods it is shown that the non polynomial oscillator represented by v x x2 lambda x2 1 gx2 can be given a supersymmetric form if the parameter lambda satisfies a certain constraint in this case one finds an exact analytic expression for the ground state excited states corresponding to this potential are computed for several values of g and lambda using the supersymmetric wkb method the ordinary wkb method and also numerical integration the results are compared

on the hill determinant method the conditions of applicability of the hill determinant method to the potentials v r v1r v2r2 and v x x2 lambda x2 1 gx2 are investigated it is shown that the procedure leads to the actual eigenvalues in the former case provided the ansatz is properly chosen but it completely fails to yield the right answer in the latter one

the jacobi eigenfunctions and the quantum mechanical hypervirial theorems method for bound state problems the jacobi eigenfunctions are suitably adjusted by means of the hypervirial theorems hvt scheme in order to obtain in many cases a very satisfactory analytic approximation of the s state eigenfunctions of the radial gaussian potential the results obtained show that the hvt scheme is a powerful method for obtaining analytically not only approximate eigenvalues but also the corresponding eigenfunctions

the energy levels of the schrodinger equation for various types of potentials using a renormalized method a perturbative method is used to compute energy levels for many different forms of potentials results of high accuracy are produced for various eigenstates

the perturbed ladder operator method perturbed eigenvalues and eigenfunctions from finite difference considerations the finite difference aspect of the perturbed ladder operator method is reinvestigated by the use of finite difference calculus resolution of the factorisability condition is achieved at any order of perturbation without assuming for the ladder and factorisation functions any particular dependence on the quantum number a novel procedure of obtaining perturbed eigenfunctions in terms of the unperturbed functions is described the method which holds for any type of factorisation types a to f is applied to resolution of the type a wave equation the perturbed type a problem which has not been previously treated contains as particular cases the perturbation of the spherical harmonics ylm or generalised yl gamma m functions of the symmetric top functions dmki and more generally of the hypergeometric functions f alpha beta gamma x

fixed point perturbation theory and the potential r2 λr2 1 gr2 i analysis of convergence the simplest illustration of the recently suggested asymptotic perturbative approach to the band matrix hamiltonians is found in the harmonic oscillator complemented by the non polynomial anharmonicity lambda r2 1 gr2 in the paper the detailed construction of the effective hamiltonian is given and the convergence of its fixed point expansion is shown

open perturbation and the riccati equation algebraic determination of the quartic anharmonic oscillator energies and eigenfunctions an algebraic procedure is proposed for the analytical solution of schrodinger equations that can be viewed as a factorizable equation with an additional potential v x once v x has been expanded in a series of suitable x basis functions u u x which are specific to each factorization type the solution of the riccati equation associated with the given equation is performed by means of an open perturbation technique i e at each order of the perturbation an additional balance u dependent term is introduced so that the resulting equation becomes solvable since the unperturbed potential involves the whole given potential and since the balance term is expected to be small improved results are expected at low orders of the perturbation even at the zeroth order the procedure well adapted to the use of computer algebra is applied to the solution of the gx4 anharmonic oscillator equation by means of very simple algebraic manipulations the trend of the exact values of the energies is rather well repr

nonlinear structural design sensivitity analysis for path dependent problems part 1 general theory abstract two procedures direct differentiation and adjoint structure for design sensitivity analysis of nonlinear structural systems with path dependent effects are described in this paper continuum formulation is used and both geometric and material nonlinearities are included in the derivations incremental nonlinear analysis based on the total lagrangian concept is adopted the reference volume concept is used to unify the shape and nonshape design problems to show the generality of the theory the derived expressions are reduced to some special cases that have been treated previously in the literature in part 2 of the paper a few analytical example problems will be solved to demonstrate the use of the design sensitivity analysis theory the theory has also beendiscretized elsewhere using finite element approximations for implementation into structural analysis programs these developments offer a firm foundation for design optimization of complex structural systems

axisymmetric viscoplastic deformation by the boundary element method abstract this paper presents a boundary element formulation and numerical implementation of the problem of small axisymmetric deformation of viscoplastic bodies while the extension from planar to axisymmetric problems can be carried out fairly simply for the finite element method fem this is far from true for the boundary element method bem the primary reason for this fact is that the axisymmetric kernels in the integral equations of the bem contain elliptic functions which cannot be integrated analytically even over boundary elements and internal cells of simple shape thus special methods have to be developed for the efficient and accurate numerical integration of these singular and sensitive kernels over discrete elements the accurate determination of stress rates by differentiation of the displacement rates presents another formidable challenge a successful numerical implementation of the boundary element method with elementwise called the mixed approach or pointwise called the pure bem or bem approach determination of stress rates has been carried out a computer program has been developed for the solution of general axisymmetric viscoplasticity problems comparisons of numerical results from the bem and fem for several illustrative problems are presented and discussed in the paper it is possible to get direct solutions for the simpler class of problems for cylinders of uniform cross section and these solutions are also compared with the bem and fem results for such cases

on the schrodinger equation with a gaussian potential eigenvalues and approximate eigenfunctions of the schrodinger equation with an attractive radial gaussian potential are obtained from a first order perturbation treatment based on a scale harmonic oscillator model the bound state energies are of comparable accuracy to those obtained using high order perturbation theory by numerical integration

design sensitivity analysis for parameters affecting geometry elastic viscoplastic material constant and boundary condition by consistent tangent operator based boundary element method abstract this paper presents a design sensitivity analysis method by the consistent tangent operator concept based boundary element implicit algorithm the design variables for sensitivity analysis include geometry parameters elastic viscoplastic material parameters and boundary condition parameters based on small strain theory perzyna s elastic viscoplastic material constitutive relation with a mixed hardening model and two flow functions is considered in the sensitivity analysis the related elastic viscoplastic radial return algorithm and the formula of elastic viscoplastic consistent tangent operator are derived and discussed based on the direct differentiation approach the incremental boundary integral equations and related algorithms for both geometric and elastic viscoplastic sensitivity analysis are developed a 2d boundary element program for geometry sensitivity elastic viscoplastic material constant sensitivity and boundary condition sensitivity has been developed comparison and discussion with the results of this paper analytical solution and finite element code ansys for four plane strain numerical examples are presented finally

perturbed harmonic oscillator ladder operators eigenenergies and eigenfunctions for the x2 λx2 1 gx2 interaction the perturbed ladder operators method is applied to the resolution of the perturbed harmonic oscillator wave equation for the case where the perturbation is expandable in a convergent series of hermite polynomials hk when v x b2x2 sigma kckhk b12 x it is found that the use of a hermite polynomials basis together with the use of binomial coefficient functions in the quantum number greatly simplifies the determination of the perturbed ladder and factorisation functions thus one obtains analytical expressions of the eigenenergies and eigenfunctions up to any order of the perturbation without increasing intricacy thorough calculation has been given for a perturbing potential v x function even in x as an illustrative application of the procedure the resolution of the schrodinger equation with a potential function v x x2 lambda x2 1 gx2 g 0 is reinvestigated

hypersingular residuals a new approach for error estimation in the boundary element method summary this paper presents a new approach for a posteriori pointwise error estimation in the boundary element method the estimator relies upon evaluation of the residual of hypersingular integral equations and is therefore intrinsic to the boundary integral equation approach a methodology is developed for approximating the error on the boundary as well as in the interior of the domain extensive computational experiments have been performed for the two dimensional laplace equation and the numerical results indicate that the error estimates successfully track the form of the exact error curve moreover a reasonable estimate of the magnitude of the actual error is also predicted

sizing design sensitivity analysis of non linear structural systems part ii numerical method a numerical method is presented to carry out sizing design sensitivity calculations outside established finite element analysis codes using postprocessing data only geometric as well as material non linearities are treated to demonstrate the accuracy of the proposed method numerical results are presented for structural systems with linear elastic material large displacements large rotations and small strains a distributed parameter approach to structural design sensitivity analysis is used to retain the continuum elasticity formulation throughout the derivation of design sensitivity results using this approach and an adjoint variable method design sensitivity computations are carried out for structural performance functionals stress and displacement are considered it is shown that computations can be performed with the same computational effort as for sizing design sensitivity analysis of linear structural systems accurate design sensitivity results are obtained for both linear and non linear structural systems without the uncertainty of numerical accuracy and high cost associated with the selection of finite difference perturbations also the method does not require differentiation of element stiffness and mass matrices in conventional finite element models

design sensitivity coefficients for elasto viscoplastic problems by boundary element methods this paper is concerned with accurate and efficient determination of design sensitivity coefficients dscs for solid mechanics problems with small strains and rotations but with material non linearities present elasto plastic or elasto viscoplastic problems this approach is based on direct differentiation dda of the relevant derivative boundary element method dbem formulation of the problem analytical differentiation of the dbem equations leads to singular integral equations for the dscs with weakly logarithmically for 2 d singular kernels which are easy to deal with also stress components and their sensitivities are obtained on the boundary of a body with great accuracy these quantities are typically difficult to obtain accurately from finite element methods fem a computer program for general two dimensional plane strain and plane stress problems has been developed based on the above formulation numerical results are presented for some sample problems and these are compared against direct solutions the agreement between the dbem and direct solutions is excellent for these examples

bem first order regularisation method in linear elasticity for boundary identification in this paper we study the identification of an unknown portion of the boundary of a two dimensional domain occupied by an isotropic linear elastic material from additional cauchy data on the remaining known portion of the boundary this inverse problem is approached using the boundary element method bem in conjunction with the tikhonov first order regularisation procedure the choice of the regularisation parameter is based on the l curve criterion the numerical results obtained show that the proposed method produces a convergent and stable solution

graph concatenation for quantum codes graphs are closely related to quantum error correcting codes every stabilizer code is locally equivalent to a graph code and every codeword stabilized code can be described by a graph and a classical code for the construction of good quantum codes of relatively large block length concatenated quantum codes and their generalizations play an important role we develop a systematic method for constructing concatenated quantum codes based on graph concatenation where graphs representing the inner and outer codes are concatenated via a simple graph operation called generalized local complementation our method applies to both binary and nonbinary concatenated quantum codes as well as their generalizations

advanced boundary element analysis of two and three dimensional problems of elasto plasticity an advanced formulation of the boundary element method has been developed for inelastic analysis based on an initial stress approach the iterative solution algorithm makes use of an accelerated initial stress approach in which the past history of initial stresses are used to obtain an initial estimate for the current increment in the present analysis the geometry and functions are represented by higher order quadratic shape functions to model complex geometries and rapid functional variations accurately the methods of numerical integration of the kernels particularly the singular type are substantially improved by devising suitable automatic sub segmentation routines that incorporate the recent developments in mapping procedures the formulations have been implemented for two dimensional plane stress plane strain and three dimensional elasto plasticity problems

randomized benchmarking of multiqubit gates we describe an extension of single qubit gate randomized benchmarking that measures the error of multiqubit gates in a quantum information processor this platform independent protocol evaluates the performance of clifford unitaries which form a basis of fault tolerant quantum computing we implemented the benchmarking protocol with trapped ions and found an error per random two qubit clifford unitary of 0 162 ifmmode pm else textpm fi 0 008 thus setting the first benchmark for such unitaries by implementing a second set of sequences with an extra two qubit phase gate inserted after each step we extracted an error per phase gate of 0 069 ifmmode pm else textpm fi 0 017 we conducted these experiments with transported sympathetically cooled ions in a multizone paul trap a system that can in principle be scaled to larger numbers of ions

boundary element analysis of inelastic axisymmetric problems with large strains and rotations abstract the subject of this paper is a boundary element method bem formulation and numerical implementation for inelastic axisymmetric problems in the presence of small elastic strains but large inelastic strains and rotations a rate formulation with an elastic viscoplastic material model together with an updated lagrangian description of the problem is used in this paper careful attention is paid here to the analytical and numerical treatment of the complicated and sensitive kernels that arise in these integral equations for axisymmetric problems a bem computer program has been developed for the solution of general large strain large rotation inelastic axisymmetric boundary initial value problems numerical results for some sample problems are obtained from the bem computer program and these results are compared against direct solutions

double exponential sinc collocation method for solving the energy eigenvalues of harmonic oscillators perturbed by a rational function we show that the double exponential sinc collocation method provides an efficient uniformly accurate solution to the one dimensional time independent schrodinger equation for a general class of rational potentials of the form v x p x q x the derived algorithm is based on the discretization of the hamiltonian of the schrodinger equation using sinc expansions this discretization results in a generalized eigenvalue problem the eigenvalues of which correspond to approximations of the energy values of the starting hamiltonian a systematic numerical study is conducted beginning with test potentials with known eigenvalues and moving to rational potentials of increasing degree

two sided bounds on minimum error quantum measurement on the reversibility of quantum dynamics and on maximum overlap using directional iterates in a unified framework we estimate the following quantities of interest in quantum information theory 1 the minimum error distinguishability of arbitrary ensembles of mixed quantum states 2 the approximate reversibility of quantum dynamics in terms of entanglement fidelity this is referred to as channel adapted quantum error recovery when applied to the composition of an encoding operation and a noise channel 3 the maximum overlap between a bipartite pure quantum state and a bipartite mixed state that may be achieved by applying a local quantum operation to one part of the mixed state and 4 the conditional min entropy of bipartite quantum states a refined version of the author s techniques j tyson j math phys 50 032016 2009 for bounding the first quantity is employed to give two sided estimates of the remaining three quantities we obtain a closed form approximate reversal channel using a state dependent kraus decomposition our reversal may be interpreted as a quadratically

universal collective rotation channels and quantum error correction we present and investigate a new class of quantum channels what we call universal collective rotation channels that includes the class of collective rotation channels as a special case the fixed point set and noise commutant coincide for a channel in this class computing the precise structure of this c algebra is a core problem in a particular noiseless subsystem method of quantum error correction we prove that there is an abundance of noiseless subsystems for every channel in this class and that the young tableaux combinatorial machine may be used to explicitly compute these subsystems

bound state energy eigenvalues for a general class of one dimensional problems on the whole axis via the prufer transformation an extension of the prufer phase function method for the bound state energy calculation is presented it is applicable to one dimensional problems described by the schrodingere quation on the whole axis with a general class of potentials theorems are given which are a generalization of the analogous ones concerning the half axis 0 problems that have been presented in previous papers the method is suitable especially for numerical calculations of the bound state energy eignevalues

design sensitivity analysis and optimization of nonlinear structuralresponse using incremental procedure this paper describes procedures for design sensitivity analysis of nonlinear structural response using the incremental solution scheme the total and updated lagrangian approaches are discussed sensitivity analyses for the stress strain and displacement constraints are developed in the optimization process the buckling load constraint is also imposed numerical aspects of design sensitivity analysis are discussed three numerical examples are solved to illustrate the design sensitivity analysis and optimization process the numerical procedures are stable and work well they can be applied to more complex structures to optimize them

resilient quantum computation error models and thresholds recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms these problems include factoring integers and certain physics simulations practical quantum computation requires overcoming the problems of environmental noise and operational errors problems which appear to be much more severe than in classical computation due to the inherent fragility of quantum superpositions involving many degrees of freedom here we show that arbitrarily accurate quantum computations are possible provided that the error per operation is below a threshold value the result is obtained by combining quantum error correction fault tolerant state recovery fault tolerant encoding of operations and concatenation it holds under physically realistic assumptions on the errors

design sensitivity coefficients for linear elastic bodies with zones and corners by the derivative boundary element method abstract the subject of this paper is the efficient and accurate determination of design sensitivity coefficients dscs in an elastic solid with zones and corners direct differentiation of the relevant derivative boundary element method dbem formulation of the problem is carried out here corners and zones in a body are treated carefully with conforming elements a numerical implementation of the method is carried out with isoparametric quadratic boundary elements the power of this approach is demonstrated through several numerical examples it is shown that the dscs of the various mechanical quantities of interest are obtained accurately and efficiently in one example even the dsc of the stress at a corner with respect to the corner angle is obtained very accurately by this method

shape optimization in elasticity and elasto viscoplasticity by the boundary element method abstract this paper is concerned with the optimal shape design of solids undergoing small strain small rotation elasto viscoplastic deformation shape sensitivities for this class of problems are determined by using a direct differentiation approach dda to the governing boundary element method bem equations of the problem the standard bem and the sensitivity equations are discretized and solved numerically shape optimization is carried out by coupling the standard and sensitivity analyses with an optimizer the optimization algorithm chosen here uses sequential quadratic programming to obtain the desired optimal shape of a body in an iterative manner numerical solutions for optimal shapes of cutouts in plates two dimensional plane stress are presented the difference between optimal shapes of solids undergoing purely elastic and elasto viscoplastic deformation is shown clearly in these examples

study of a class of non polynomial oscillator potentials we develop a variational method to obtain accurate bounds for the eigenenergies of h v in arbitrary dimensions n 1 where v r is the nonpolynomial oscillator potential the variational bounds are compared with results previously obtained in the literature an infinite set of exact solutions is also obtained and used as a source of comparison eigenvalues

nonlinear structural design sensitivity analysis for path dependent problems part 2 analytical examples abstract in part 1 of this paper a general theory of design sensitivity analysis for nonlinear structures with history dependent effects is given the theory is also reduced to several special cases to show its generality in the present paper three examples are used to analytically verify the theory both the adjoint structure method asm and the direct differentiation method ddm are demonstrated the examples are 1 reaction force sensitivity for an indeterminate beam 2 displacement sensitivity for several cases of an axial force element and 3 stress and displacement sensitivities for a visco elastic problem these examples provide insights for numerical implementation of the theory for more complex design problems

1 n expansion for gaussian potential the method of large n expansion has been applied to an attractive radial gaussian potential to obtain its bound state energy levels it has been shown that the shifted 1 n expansion technique provides a better approximation than the method of unshifted 1 n expansion and yields energy values which are in good agreement with the accurate numerical and analytic results

on the x2 λx2 1 gx2 interaction presents an infinite set of exact solutions of odd parity for the one dimensional schrodinger equation with the interaction x2 lambda x2 1 gx2 these complement the exact solutions of even parity that have been obtained recently by flessas phys lett a vol 84 p 121 1981

interaction λx2 1 gx2 revisited abstract it is shown that the refined non perturbative hill s method solves in a very neat way the schrodinger equation e x 2 x 2 1 gx 2 0 the refinement of the standard hill s method consists in finding a renormalized frequency to optimize the calculation this method appears to be preferable to the variational one recently used by a k mitra in the same context

implementation of regularized isogeometric boundary element methods for gradient based shape optimization in two dimensional linear elasticity the present work addresses shape sensitivity analysis and optimization in two dimensional elasticity with a regularized isogeometric boundary element method igabem non uniform rational b splines are used both for the geometry and the basis functions to discretize the regularized boundary integral equations with the advantage of tight integration of design and analysis the application of igabem in shape optimization reduces the mesh generation regeneration burden greatly the work is distinct from the previous literatures in igabem shape optimization mainly in two aspects 1 the structural and sensitivity analysis takes advantage of the regularized form of the boundary integral equations eliminating completely the need of evaluating strongly singular integrals and jump terms and their shape derivatives which were the main implementation difficulty in igabem and 2 although based on the same computer aided design cad model the mesh for structural and shape sensitivity analysis is separated from the geometrical design mesh thus achieving a balance between less design variables for efficiency and refined mesh for accuracy this technique was initially used in isogeometric finite element method and was incorporated into the present igabem implementation

the exponential cosine screened potential the concept of forward nested multiplication is used to develop a unified power series hill determinant method for the calculation of schrodinger equation energy levels a numerical application is made to the exponential cosine screened potential

variational method for design sensitivity analysis in nonlinear structural mechanics this paper describes a unified variational theory of design sensitivity analysis of linear and nonlinear structures for shape nonshape and material selection problems the concepts of reference volume and adjoint structure are used to develop the unified viewpoint a general formula for design sensitivity analysis is derived several analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use such analytical examples give insight into the application of the general formula to more complex problems that must be treated numerically adjoint state fields are also interpreted as sensitivities for the functional related to the primary structure

the hvt technique and the uncertainty relation for central potentials the quantum mechanical hypervirial theorems hvt technique is used to treat the so called uncertainty relation for quite a general class of central potential wells including the reduced poeschl teller and the gaussian one it is shown that this technique is quite suitable in deriving an approximate analytic expression in the form of a truncated power series expansion for

fast eigenvalue algorithm for central potentials an algorithm is described that seeks out schrodinger eigenvalues enl for a given central potential v r the algorithm has in principle arbitrary precision a particular implementation has absolute error mod e enl mod decreasing as t 3 where t is machine computing time the method is tested on the central gaussian potential v r a exp lambda r2 of recent interest

on exact solutions of the schrodinger equation a new approach has been used to show what kind of potentials can be used to obtain a series of exact solutions in closed forms of the schrodinger equation for bound states in particular the well known coulombic and oscillator solutions and others are reproduced as special cases

quantum theory the church turing principle and the universal quantum computer it is argued that underlying the church turing hypothesis there is an implicit physical assertion here this assertion is presented explicitly as a physical principle every finitely realizable physical system can be perfectly simulated by a universal model computing machine operating by finite means classical physics and the universal turing machine because the former is continuous and the latter discrete do not obey the principle at least in the strong form above a class of model computing machines that is the quantum generalization of the class of turing machines is described and it is shown that quantum theory and the universal quantum computer are compatible with the principle computing machines resembling the universal quantum computer could in principle be built and would have many remarkable properties not reproducible by any turing machine these do not include the computation of non recursive functions but they do include quantum parallelism a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it the intuitive explanation of these properties places an intolerable strain on all interpretations of quantum theory other than everett s some of the numerous connections between the quantum theory of computation and the rest of physics are explored quantum complexity theory allows a physically more reasonable definition of the complexity or knowledge in a physical system than does classical complexity theory

algebraic recursive determination of matrix elements from ladder operator considerations a manufacturing process is proposed for calculating matrix elements of families of basic functions qt x between the eigenfunctions psi mj x of factorisable equations this procedure well adapted for computer algebra relies on the well known property that solutions of factorisable equations are also solutions of a couple of first order difference differential equations as a particular case it is applied to the determination of closed form expressions of the curved hydrogenic pseudoradial integrals which are needed when studying space curvature effects in atomic structure calculations several other applications are pointed out