oriented quantum algebras and invariants of knots and links abstract in our previous work oriented quantum algebras were motivated and introduced in a very natural categorical setting within the context of knots and links some examples were discussed and a rudimentary theory of oriented quantum algebras was sketched invariants of knots and links can be computed from oriented quantum algebras here we continue the study of oriented quantum algebras we view them from a more algebraic perspective and develop a more detailed theory for them and their associated invariants we study a class of examples associated with the homfly polynomial in depth

performance comparison of numerical inversion methods for laplace and hankel integral transforms in engineering problems abstract different methods for the numerical evaluations of the inverse laplace and inverse of joint laplace hankel integral transforms are applied to solve a wide range of initial boundary value problems often arising in engineering and applied mathematics the aim of the paper is to present a performance comparison among different numerical methods when they are applied to transformed functions related to actual engineering problems found in the literature most of our selected test functions have been found in the solution of boundary value problems of applied mechanics such as those related to transient responses of isotropic and transversely isotropic half space to concentrated impulse or those related to viscoelastic wave motion in layered media these classes of test functions are frequently encountered in similar problems such as those in boundary element or boundary integral equations theoretical seismology soil structure interaction in time domain and so on therefore their behavior with different numerical inversion algorithms could make a useful guide to a precise choice of more suitable inversion method to be used in similar problems some different methods are also investigated in detail and compared for the inversion of the joint hankel laplace transforms where more sophisticated integrand functions are encountered it is shown that durbin crump d amore fixed talbot gaver whyn rho gwr and direct integration methods have excellent performance and produce good results when applied to the same problems on the contrary gaver stehfest and piessens methods furnish results not very reliable for almost all classes of transformed functions and they seem good only for simple transformed functions particularly the performance of gwr algorithm is very good even for transformed functions with infinite number of singularities where the other methods fail in addition in case of double integral transforms only the fixed talbot durbin and weeks methods are recommended

numerical simulation for non linear thermal wave the present work applies the hybrid method of the laplace transform technique and a modified discretization scheme to analyze the non linear hyperbolic heat conduction problems in a semi infinite domain with either linearly or exponentially temperature dependent thermal conductivity the laplace transform method is used to remove the time dependent terms in the governing differential equation and the boundary conditions and then the transformed equations are discretized by a modified discretization scheme to show the rationality and reliability of the present results a comparison between the present numerical results and those in the literature is made results show the behavior of hyperbolic heat conduction is sensitive to the function form of thermal conductivity the speed of heat propagation changes for the variation of thermal conductivity

disturbance due to mechanical sources in micropolar elastic medium with voids the dynamic response of a homogeneous isotropic micropolar half space with voids subjected to a set of normal point sources is investigated the integral transforms have been inverted by using a numerical technique to obtain the normal force stress normal displacement tangential force stress tangential couple stress and volume fraction field in the physical domain for the two different sources the results of these quantities for a magnesium crystal like material are given and illustrated

periodically varying heat source response in a functionally graded microelongated medium abstract the present paper deals with the response due to periodically varying heat sources in the neighborhood of the origin of a functionally graded isotropic unbounded microelongated medium in the context of generalized thermoelastic theory the expressions for displacement microelongation and temperature fields have been obtained in laplace fourier transformed domain after computing the inverse fourier transforms by contour integration technique the inversion of laplace transforms has been obtained numerically the changes of displacement microelongation and normal strain have been shown graphically for different types of heat source

solving the two dimensional constant quantum yang baxter equation a detailed analysis of the constant quantum yang baxter equation rk1k2j1j2 rl1k3k1j3rl2l3k2k3 rk2k3j2j3 rk1l3j1k3rl1l2k1k2 in two dimensions is presented leading to an exhaustive list of its solutions the set of 64 equations for 16 unknowns was first reduced by hand to several subcases which were then solved by computer using the grobner basis methods each solution was then transformed into a canonical form based on the various trace matrices of r for final elimination of duplicates and subcases if we use homogeneous parametrization the solutions can be combined into 23 distinct cases modulo the well known c p and t reflections and rotations and scalings r q q r q q 1

study of non fickian diffusion problems with the potential field in the cylindrical co ordinate system the present study applies a hybrid numerical scheme of the laplace transform technique and the control volume method in conjunction with the hyperbolic shape functions to investigate the effect of a potential field on the one dimensional non fickian diffusion problems in the cylindrical co ordinate system the laplace transform method is used to remove the time dependent terms in the governing differential equation and the boundary conditions and then the resulting equations are discretized by the control volume scheme the primary difficulty in dealing with the present problem is the suppression of numerical oscillations in the vicinity of sharp discontinuities results show that the present numerical results do not exhibit numerical oscillations and the potential field plays an important role in the present problem the strength of the jump discontinuity can be reduced by increasing the value of the potential gradient the propagation speed of mass wave is independent of the potential gradient and the boundary condition copyright 2003 john wiley sons ltd

high order fdtd methods via derivative matching for maxwell s equations with material interfaces this paper introduces a series of novel hierarchical implicit derivative matching methods to restore the accuracy of high order finite difference time domain fdtd schemes of computational electromagnetics cem with material interfaces in one 1d and two spatial dimensions 2d by making use of fictitious points systematic approaches are proposed to locally enforce the physical jump conditions at material interfaces in a preprocessing stage to arbitrarily high orders of accuracy in principle while often limited by numerical instability orders up to 16 and 12 are achieved respectively in 1d and 2d detailed stability analyses are presented for the present approach to examine the upper limit in constructing embedded fdtd methods as natural generalizations of the high order fdtd schemes the proposed derivative matching methods automatically reduce to the standard fdtd schemes when the material interfaces are absent an interesting feature of the present approach is that it encompasses a variety of schemes of different orders in a single code another feature of the present approach is that it can be robustly implemented with other high accuracy time domain approaches such as the multiresolution time domain method and the local spectral time domain method to cope with material interfaces numerical experiments on both 1d and 2d problems are carried out to test the convergence examine the stability access the efficiency and explore the limitation of the proposed methods it is found that operating at their best capacity the proposed high order schemes could be over 2000 times more efficient than their fourth order versions in 2d in conclusion the present work indicates that the proposed hierarchical derivative matching methods might lead to practical high order schemes for numerical solution of time domain maxwell s equations with material interfaces

behavior of micropolar cubic crystal due to various sources the response of a micropolar cubic crystal due to various sources acting at the free surface has been studied the eigenvalue approach using integral transforms has been employed and the transforms have been inverted by using a numerical technique the displacement stress and microrotation components in the physical domain are obtained numerically the results of displacement and stresses have been compared for micropolar cubic crystal and micropolar isotropic solid the numerical results are illustrated graphically for a particular model

improvement of accuracy in numerical methods for inverting laplace transforms based on the post widder formula abstract the paper proposes a new computational version for numerical inversion of laplace transforms at a point and on an interval based on the post widder formula in this version the original sequence of post widder approximants is calculated using operations on series and the approximate value of the sought function is constructed as a limit of this sequence using polynomial and rational extrapolation to the limit some procedures are proposed for improvement of accuracy in the problem of inversion at equidistant points of an interval without computing additional approximants an extension of the method to the two dimensional case is discussed the one dimensional version is illustrated with some probabilistic examples involving both explicit and implicit functions the accuracy achieved in these examples with using the standard double precision arithmetic evaluated in terms of relative errors is about 10 10 10 14 even in case of out of scale parameters computational aspects are discussed in comparison with previously known realizations of the post widder method

magnetothermoelasticity with two relaxation times in conducting medium with variable electrical and thermal conductivity the equations of magneto thermoelasticity with two relaxation times and with variable electrical and thermal conductivity for one dimensional problems including heat sources are cast into matrix form using the state space and laplace transform techniques the resulting formulation is applied to a problem for the whole conducting space with a plane distribution of heat sources it also is applied to a semispace problem with a traction free surface and plane distribution of heat sources located inside the conducting medium the inversion of the laplace transforms is carried out using a numerical approach numerical results for the temperature displacement and stress distributions are given and illustrated graphically for both problems a comparison is made with the results obtained in the following cases a the electrical and thermal conductivities have constant values b the absence of magnetic field and c the coupled theory in magneto thermoelasticity

toward the construction of a fourth order difference scheme for transient em wave simulation staggered grid approach a compact central difference approximation in conjunction with the yee 1966 grid is used to compute the spatial derivatives in maxwell s equations to advance the semi discrete equations the four stage runge kutta rk integrator is invoked this combination of spatial and temporal differencing leads to a scheme that is fourth order accurate conditionally stable and highly efficient moreover the use of compact differencing allows one to apply the compact operator in the vicinity of a perfect conductor an attribute not found in other higher order methods results are provided that quantify the spectral properties of the method simulations are conducted on problem spaces that span one and three dimensions and whose domains are of the open and closed type results from these simulations are compared with exact closed form solutions the agreement between these results is consistent with numerical analysis

evaluation of inverse fourier transforms through romberg integration this study deals with evaluation of inverse integral transforms through numerical integration arguments are presented to explain that such a numerical evaluation is mathematically incorrect in recent years a sudden increase has been noticed in the number of research publications in which romberg integration is said to have used in evaluating the inverse fourier transforms in this regard even the references cited in these papers do not support such an evaluation but suggest contrary an immediate concern is to caution the researchers studying the source problems in the field of solid mechanics over the use and approval of an erroneous numerical technique

an explicit fourth order orthogonal curvilinear staggered grid fdtd method for maxwell s equations the explicit fourth order staggered finite difference time domain scheme previously proposed for a cartesian grid is extended to maxwell s equations in an orthogonal curvilinear coordinate system and applied to electromagnetic wave problems a simple technique is also presented for generating orthogonal curvilinear grids that conform to the material boundaries and interfaces of the problem numerical experiments are presented to illustrate the efficiency and accuracy of the method

interactions due to mechanical thermal sources in a micropolar thermoelastic medium possessing cubic symmetry abstract the present problem is the deformation of micropolar thermoelastic solids with cubic symmetry under the influence of various sources acting on the plane surface analytic expressions for displacement components microrotation force stress couple stress and temperature distribution are obtained in the physical domain for lord shulman l s and green lindsay g l theories of thermoelasticity by applying integral transforms a numerical inversion technique has been applied to obtain the solution in the physical domain the numerical results are presented graphically for a particular model

finite difference time domain dispersion reduction schemes the finite difference time domain fdtd although recognized as a flexible robust and simple to implement method for solving complex electromagnetic problems is subject to numerical dispersion errors in addition to the traditional ways for reducing dispersion i e increasing sampling rate and using higher order degrees of accuracy a number of schemes have been proposed recently in this work an unified methodology for deriving new difference schemes is presented it is based on certain modifications of the characteristic equation that accompanies any given discretized version of the wave equation the method is duly compared with existing schemes and verified numerically

a laplace transorm potential theoretic method for acoustic propagation in subsonic flows this paper introduces a competitive computational approach for determining time dependent far field sound generated by subsonic flows around lifting airfoils the procedure assumes the linearity of the sound field away from a bounded region surrounding the airfoil it is assumed that the sound pressure on the boundary of this enclosed region referred to as the kirchhoff surface is specified possibly by another procedure such as solving the full euler equations away from the kirchhoff surface the euler equations are linearized about a uniform mean flow it is well known that linearized euler equations can be uncoupled into a scalar convective wave equation however due to the anisotropy present in the convective wave equation it is difficult to compute solutions in this context direct numerical simulation of the convective wave equation requires proper numerical descriptions of far field boundary conditions which is a non trivial task moreover if accurate far field conditions can be formulated the computational cost of direct simulation can be prohibitive even in a modest computational domain in this paper we present an alternate solution procedure first the problem is transformed via the laplace transform with appropriate initial conditions into a reduced wave equation the convective term in the reduced wave equation is removed using a dependent variable transformation then we use gothert s rule to obtain a helmholtz like equation with complex wave number which is subsequently solved using double layer potential theory finally upon application of numerical inverse laplace transform techniques far field acoustic pressure is obtained as a function of space and time

reducing the phase error for finite difference methods without increasing the order the phase error in finite difference fd methods is related to the spatial resolution and thus limits the maximum grid size for a desired accuracy greater accuracy is typically achieved by defining finer resolutions or implementing higher order methods both these techniques require more memory and longer computation times in this paper new modified methods are presented which are optimized to problems of electromagnetics simple methods are presented that reduce numerical phase error without additional processing time or memory requirements furthermore these methods are applied to both the helmholtz equation in the frequency domain and the finite difference time domain fdtd method both analytical and numerical results are presented to demonstrate the accuracy of these new methods

dispersion relation preserving fdtd algorithms for large scale three dimensional problems we introduce dispersion relation preserving drp algorithms to minimize the numerical dispersion error in large scale three dimensional 3d finite difference time domain fdtd simulations the dispersion error is first expanded in spherical harmonics in terms of the propagation angle and the leading order terms of the series are made equal to zero frequency dependent fdtd coefficients are then obtained and subsequently expanded in a polynomial taylor series in the frequency variable an inverse fourier transformation is used to allow for the incorporation of the new coefficients into the fdtd updates butterworth or chebyshev filters are subsequently employed to fine tune the fdtd coefficients for a given narrowband or broadband range of frequencies of interest numerical results are used to compare the proposed 3d drp fdtd schemes against traditional high order fdtd schemes

prediction of evanescent coupling efficiency in two parallel silica nanowires abstract in this study the efficiency of evanescent wave coupling between two air clad silica nanowires in single mode operation is numerically predicted in time domain using the finite difference method to this end a three dimensional scheme developed for solving the maxwell s equations on staggered grids will be employed the electric and magnetic field solutions are sought subjected to the zero divergence condition or gauss s law in discrete level in addition we aim to conserve hamiltonians existing in ideal maxwell s equations at all times by adopting the explicit second order accurate symplectic partitioned runge kutta temporal scheme moreover all the spatial derivative terms in the faraday s and ampere s equations are approximated by the proposed scheme which can render not only fourth order spatial accuracy but also minimize the discrepancy between the exact and the derived numerical phase velocities

a method for the numerical inversion of laplace transforms abstract in this paper a numerical inversion method for laplace transforms based on a fourier series expansion developed by durbin 5 is presented the disadvantage of the inversion methods of that type the encountered dependence of discretization and truncation error on the free parameters is removed by the simultaneous application of a procedure for the reduction of the discretization error a method for accelerating the convergence of the fourier series and a procedure that computes approximately the best choice of the free parameters suitable for a given problem the inversion method allows the adequate application of these procedures therefore in a big range of applications a high accuracy can be achieved with only a few function evaluations of the laplace transform the inversion method is implemented as a fortran subroutine

natural frequencies of a functionally graded cracked beam using the differential quadrature method the present work is concerned with the free vibration analysis of an elastically supported cracked beam the beam is made of a functionally graded material and rested on a winkler pasternak foundation the line spring model is employed to formulate the problem the method of differential quadrature is applied to solve it the obtained results agreed with the previous similar ones further a parametric study is introduced to investigate the effects of the geometric and elastic characteristics of the problem on the values of natural frequencies and mode shape functions

semi analytical elasticity solutions for bi directional functionally graded beams abstract elasticity solutions are presented for bending and thermal deformations of functionally graded beams with various end conditions using the state space based differential quadrature method the beams are assumed to be macroscopically isotropic with young s modulus varying exponentially along the thickness and longitudinal directions while poisson s ratio remaining constant the state space method is adopted to obtain analytically the thickness variation of the elastic field and when coupled with differential quadrature the longitudinal discretization can be analyzed in an approximate manner this approach is then validated by comparing the numerical results with the exact solutions for a special functionally graded beam and with finite element solutions the influences of material gradient indices on the response of bi directional functionally graded beams are finally investigated

hybrid laplace transform finite difference method for transient heat conduction problems the new method involving the combined use of the laplace transform and the finite difference method is applicable to the problem of time dependent heat flow systems the present method removes the time derivatives from the governing differential equation using the laplace transform and then solves the associated equation with the finite difference method the transformed temperature is inverted numerically by the method of honig and hirdes to obtain the result in the physical quantities the present results are compared in tables with exact solutions and those obtained from the combined use of the laplace transform and the finite element method it is found that the present method is reliable and efficient

exponential solution of a problem of two dimensional motion of micropolar fluid in a half plane in this paper we generalize the results of the homogenous equation in fluid mechanics in the half plane for the type of micropolar fluid when the shear stresses spin micro rotation and one component of the velocity are given on the boundary we use laplace fourier transforms and then we convert laplace transform to find the solution in laplace domain then the numerical solution is applied to obtain the real solution in the physical domain graphically

the spatial fourth order energy conserved s fdtd scheme for maxwell s equations abstract in this paper we develop a new spatial fourth order energy conserved splitting finite difference time domain method for maxwell s equations based on the staggered grids the splitting technique is applied to lead to a three stage energy conserved splitting scheme at each stage using the spatial fourth order difference operators on the strict interior nodes by a linear combination of two central differences one with a spatial step and the other with three spatial steps we first propose the spatial high order near boundary differences on the near boundary nodes which ensure the scheme to preserve energy conservations and to have fourth order accuracy in space step the proposed scheme has the important properties energy conserved unconditionally stable non dissipative high order accurate and computationally efficient we first prove that the scheme satisfies energy conversations and is in unconditional stability we then prove the optimal error estimates of fourth order in spatial step and second order in time step for the electric and magnetic fields and obtain the convergence and error estimate of divergence free as well numerical dispersion analysis and numerical experiments are presented to confirm our theoretical results

mechanical and thermal sources in a micropolar generalized thermoelastic medium abstract the disturbance due to mechanical and thermal sources in a homogeneous isotropic micropolar generalized thermoelastic half space is investigated by the use of laplace fourier transform technique the analytical expressions of displacement components normal force stress tangential force stress and temperature field so obtained have been inverted by using a numerical technique numerical results are presented graphically for a magnesium crystal like material

transient wave analysis of a cantilever timoshenko beam subjected to impact loading by laplace transform and normal mode methods abstract this study applies two analytical approaches laplace transform and normal mode methods to investigate the dynamic transient response of a cantilever timoshenko beam subjected to impact forces explicit solutions for the normal mode method and the laplace transform method are presented the durbin method is used to perform the laplace inverse transformation and numerical results based on these two approaches are compared the comparison indicates that the normal mode method is more efficient than the laplace transform method in the transient response analysis of a cantilever timoshenko beam whereas the laplace transform method is more appropriate than the normal mode method when analyzing the complicated multi span timoshenko beam furthermore a three dimensional finite element cantilever beam model is implemented the results are compared with the transient responses for displacement normal stress shear stress and the resonant frequencies of a timoshenko beam and bernoulli euler beam theories the transient displacement response for a cantilever beam can be appropriately evaluated using the timoshenko beam theory if the slender ratio is greater than 10 or using the bernoulli euler beam theory if the slender ratio is greater than 100 moreover the resonant frequency of a cantilever beam can be accurately determined by the timoshenko beam theory if the slender ratio is greater than 100 or by the bernoulli euler beam theory if the slender ratio is greater than 400

a numerical treatment to the solution of quasiparabolic partial differential equations this paper presents results obtained by the implementation of a hybrid laplace transform finite element method to the solution of quasiparabolic problem the present method removes the time derivatives from the quasiparabolic partial differential equation using the laplace transform and then solves the associated equation with the finite element method the numerical inverse of the laplace transform is realized by solving linear overdetermined systems and a polynomial equation of the kth order test examples are used to show that the numerical solution is comparable to the exact solution of the initial boundary value problem at the given grid points

optimized 2 4 stencil runge kutta ade adi fdtd with application to plasma this paper discusses the improvement of the numerical dispersion characteristics of alternating direction implicit adi finite difference time domain fdtd aimed at acquiring more accurate electromagnetic information of plasma through adding the optimization method which is based on the optimization of spatial derivative to the 2 4 stencil adi fdtd the optimized 2 4 stencil adi fdtd is proposed and its unconditional stability is proved theoretically the phase velocity error of the optimized 2 4 stencil adi fdtd versus propagation angle and grid density is investigated in addition the runge kutta auxiliary differential equation rkade scheme for tackling the constitutive relation equation of plasma is deduced which is without additional storage occupation and computational burden compared with ade scheme its numerical conductivity error is analyzed under different incident frequencies and electron collision frequencies through incorporating the rkade scheme into the optimized 2 4 stencil adi fdtd the optimized 2 4 stencil rkade adi fdtd is presented the accuracy and relatively wideband capability of the proposed method is validated by two numerical experiments

a staggered fourth order accurate explicit finite difference scheme for the time domain maxwell s equations abstract we consider a model explicit fourth order staggered finite difference method for the hyperbolic maxwell s equations appropriate fourth order accurate extrapolation and one sided difference operators are derived in order to complete the scheme near metal boundaries and dielectric interfaces an eigenvalue analysis of the overall scheme provides a necessary but not sufficient stability condition and indicates long time stability numerical results verify both the stability analysis and the scheme s fourth order convergence rate over complex domains that include dielectric interfaces and perfectly conducting surfaces for a fixed error level we find the fourth order scheme is computationally cheaper in comparison to the yee scheme by more than an order of magnitude some open problems encountered in the application of such high order schemes are also discussed

magnetohydrodynamic unsteady free convection flow of a couple stress fluid with one relaxation time through a porous medium the method of the matric exponential which constitutes the basis of the state space approach of modern control theory is applied to the non dimensional equations of a magnetohydrodynamic unsteady free convection flow of a couple stress fluid through a porous medium with one relaxation time the resulting formulation together with laplace transform technique is applied to a thermal shock problem also a problem with distribution of heat sources is considered numerical results for the velocity induced magnetic field angular velocity and temperature distributions are given and illustrated graphically for each problem

generalized thermoelastic functionally graded solid with a periodically varying heat source abstract this paper deals with the problem of thermoelastic interactions in a functionally graded isotropic unbounded medium due to the presence of periodically varying heat sources in the context of the linear theory of generalized thermoelasticity without energy dissipation tewoed the governing equations of generalized thermoelasticity without energy dissipation gn model type ii for a functionally graded materials fgm i e material with spatially varying material properties are established the governing equations are expressed in laplace fourier double transform domain and solved in that domain now the inversion of the fourier transform is carried out by using residual calculus where poles of the integrand is obtained numerically in complex domain by using laguerre s method and the inversion of laplace transform is done numerically using a method based on fourier series expansion technique the numerical estimates of the displacement temperature stress and strain are obtained for a hypothetical material the solution to the analogous problem for homogeneous isotropic material is obtained by taking nonhomogeneity parameter suitably finally the results obtained are presented graphically to show the effect of nonhomogeneity on displacement temperature stress and strain

a class of difference schemes with flexible local approximation solutions of many physical problems have salient local features that are qualitatively known a priori for example singularities at point sources edge and corners boundary layers derivative jumps at material interfaces strong dipole field components near polarized spherical particles cusps of electronic wavefunctions at the nuclei electrostatic double layers around colloidal particles etc the known methods capable of providing flexible local approximation of such features include the generalized finite element partition of unity method special variational difference schemes in broken sobolev spaces and a few other specialized techniques in the proposed new class of flexible local approximation methods flame a desirable set of local approximating functions such as cylindrical or spherical harmonics plane waves harmonic polynomials etc defines a finite difference scheme on a chosen grid stencil one motivation is to minimize the notorious staircase effect at curved and slanted interface boundaries however the new approach has much broader applications as illustrative examples the paper presents arbitrarily high order 3 point schemes for the 1d schrodinger equation and a 1d singular equation schemes for electrostatic interactions of colloidal particles electromagnetic wave propagation and scattering plasmon resonances moreover many classical finite difference schemes including the collatz mehrstellen schemes are direct particular cases of flame

mathematical solution for bending of short hybrid composite beams with variable fibers spacing in this study the static response is presented for a simply supported functionally graded hybrid beam subjected to a transverse uniform load material properties of the beam are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents by varying the fiber volume fraction within a symmetric laminated beam and combining two fiber types to create a hybrid functionally graded material fgm can offer desirable increases in axial and bending stiffness the equations governing the hybrid fgm beams are determined using the principle of virtual work pvw arising from the higher order shear deformation theories numerical results on the transverse deflection axial and shear stresses in a moderately thick hybrid fgm beam under uniform distributed load are discussed in depth the effect of power law exponent on the deflection and stresses are also commented

numerical solutions for the hyperbolic heat conduction problems in a layered solid cylinder with radiation surface the numerical scheme based on the hybrid application of the laplace transform method and a control volume formulation in conjunction with the hyperbolic shape functions is applied to investigate the hyperbolic heat conduction problems in an infinitely long layered solid cylinder with the nonlinear boundary conditions in order to perform the laplace transform method the nonlinear boundary conditions are linearized with taylor s series expansion results show that the present numerical scheme can overcome the mathematical difficulties induced by the nonlinear boundary conditions the geometry the composite interface and the singular point and has stability and reliability for such problems effects of the thermal properties of two dissimilar materials on heat transfer are also discussed

numerical analysis for the hyperbolic heat conduction problem under a pulsed surface disturbance a hybrid application of the laplace transform method and a control volume formulation in conjunction with the hyperbolic shape functions is applied to investigate the hyperbolic diffusion problems with the pulsed boundary conditions in various coordinate systems the laplace transform method is used to remove the time dependent terms in the governing differential equations and the boundary conditions and then the transformed equations are discretized by the control volume scheme the primary difficulty in dealing with the present problem is the suppression of numerical oscillations in the vicinity of sharp discontinuities the results show that the numerical results agree well with the analytic solution and do not exhibit numerical oscillations in the vicinity of the jump discontinuity the present method also can solve the problems with the singular point

state space approach of two temperature generalized thermoelasticity of one dimensional problem abstract in this paper we will consider a half space filled with an elastic material which has constant elastic parameters the governing equations are taken in the context of the two temperature generalized thermoelasticity theory youssef h 2005a the dependence of the modulus of elasticity and the thermal conductivity on the reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity j appl math mech 26 4 4827 youssef h 2005b theory of two temperature generalized thermoelasticity ima j appl math 1 8 the medium is assumed initially quiescent laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions the general solution obtained is applied to a specific problem of a half space subjected to thermal shock and traction free the inverse laplace transforms are computed numerically using a method based on fourier expansion techniques some comparisons have been shown in figures to estimate the effect of the two temperature parameter

vibration analysis of functionally graded thin walled rotating blades under high temperature supersonic flow using the differential quadrature method in this study differential quadrature dq vibration analysis of a rotating thin walled blade made of functionally graded materials fgms operating under high temperature supersonic gas flow is investigated the governing equations are based on the first order shear deformation theory of beams which include the effects of the rotary inertias and the blade presetting angle quasi steady aerodynamic pressure loadings and steady wall temperature assumptions are made the explicit dq discretized form of the equations of motion and the related boundary conditions are presented the convergence of the method is examined and to verify its accuracy the results are compared with those of the galerkin method where excellent agreements are observed the effects of the mach number rotating speed geometric parameters and blade material properties on the natural frequencies are examined

elastodynamics of an axisymmetric problem in an anisotropic liquid saturated porous medium the laplace and hankel transforms have been employed to find the general solution to the field equations in an anisotropic liquid saturated porous medium for plain axisymmetric problem in the transformed form an application of an infinite space with impulsive force at the origin has been considered to show the utility of the solution obtained the results of the corresponding problem in isotropic liquid saturated porous medium can be derived as a special case to get the solutions in the physical form a numerical inversion technique has been applied the results in the form of displacement and stress components have been obtained numerically and discussed graphically for a particular model

passage times of asymmetric anomalous walks with multiple paths we investigate the transient and the long time behaviour of asymmetric anomalous walks in heterogeneous media two types of disorder are worked out explicitly weak and strong disorder in addition the occurrence of disordered multiple paths is considered we calculate the first passage time distribution of the associated stochastic transport process we discuss the occurrence of the crossover from a power law to an exponential decay for the long time behaviour of the distribution of the first passage times of disordered biased walks

on a numerical technique regarding inversion of the laplace transform abstract we have discussed a method to convert the laplace transform into an integral equation of the first kind of convolution type which is an ill posed problem and used a regularization method to solve it we investigated the behavior of the optimal regularization parameter the optimal choice of parameter in the regularization of ill posed inverse problems depends on several features of a given problem we have compared our results with varah s 1979 1983 results and they are shown in respective diagrams for comparison purposes

development of a 3d staggered fdtd scheme for solving maxwell s equations in drude medium an explicit finite difference scheme is developed to solve the three dimensional maxwell s equations in drude medium our aim of developing this scheme in time domain is to compute solutions in staggered grids from the faraday s and ampere s equations the electric and magnetic field solutions are sought subject to the discrete zero divergence condition gauss s law the local conservation laws in ideal maxwell s equations are also numerically preserved all the time using the explicit second order accurate symplectic partitioned runge kutta temporal scheme the spatial derivative terms in the faraday s and ampere s equations are discretized to obtain fourth order accuracy using the developed scheme underlying the concept of minimizing the discrepancy between the exact and the derived numerical phase velocities dispersion and anisotropy errors have been much reduced through the procedure of minimizing phase velocity error in addition to performing the fundamental analysis on the proposed scheme the computational efficiency and long term accurate properties embedded in the proposed symplectic dispersion error reduction centered scheme are numerically demonstrated through several test problems investigated in ideal and drude media

an application of the ltdrm to transient diffusion problems with nonlinear material properties and nonlinear boundary conditions in this paper we shall present an application of the laplace transform dual reciprocity method ltdrm to the solution of transient diffusion problems with nonlinear material properties and nonlinear boundary conditions two methods with and without utilizing the kirchhoff transformation will be discussed the nonlinear terms in both governing equation and boundary conditions are linearized first followed by the removal of the time variable from the linearized differential system with the laplace transformation and then the problem is solved by the dual reciprocity method as a result a solution at any specific time can be obtained without step by step calculations in time domain and computations of domain integrals to show the efficiency and accuracy of the present method several problems are analyzed and their solutions are compared with those obtained either analytically or numerically

a half space problem in the theory of generalized thermoelastic diffusion abstract in this work we consider the problem of a thermoelastic half space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time the bounding surface of the half space is taken to be traction free and subjected to a time dependent thermal shock the chemical potential is also assumed to be a known function of time on the bounding plane laplace transform techniques are used the solution is obtained in the laplace transform domain by using a direct approach the solution of the problem in the physical domain is obtained numerically using a numerical method for the inversion of the laplace transform based on fourier expansion techniques the temperature displacement stress and concentration as well as the chemical potential are obtained numerical computations are carried out and represented graphically

the extended durbin method and its application for piezoelectric wave propagation problems abstract based on the well known durbin method an efficient numerical method was developed for the inversion of the two sided laplace transform the accuracy of the method was verified using examples as an application of the method transient elastic waves propagating in a two layered piezoelectric medium subjected to anti plane concentrated loading and in plane electric displacement loading were investigated one sided and two sided laplace transforms were applied to determine the shear stresses and electric displacements in the double laplace transform domain subsequently the durbin method for one sided laplace transform inversion and the extended durbin method for two sided laplace transform inversion were used to implement the numerical inversions additionally the numerical results of the transient stresses and electric displacements were evaluated and discussed it showed that the arrival time of transient waves satisfies physical phenomena and the transient solution oscillates near the static solution and rapidly approximates the static solution

effect of body forces on a 2d generalized thermoelastic long cylinder in this work we consider a two dimensional problem for an infinitely long solid cylinder the lateral surface of the cylinder is taken to be traction free and is subjected to a known temperature distribution under the action of solenoidal body forces laplace transform techniques are used the solution in the transformed domain is obtained by using a direct approach in the form of an infinite series the inverse laplace transforms are obtained by using a numerical method based on fourier expansion techniques numerical results are computed for the temperature displacement and stress distributions and shown graphically

optimized three dimensional fdtd discretizations of maxwell s equations on cartesian grids in this paper novel finite difference time domain fdtd schemes are introduced for the numerical solution of maxwell s equations on dual staggered cartesian three dimensional lattices the proposed techniques are designed to accomplish optimized performance according to certain features and requirements dictated by the investigated problems thus making efficient use of the available computational resources starting from only few initial assumptions a construction process based on the minimization of specific error formulae is developed which is later exploited to derive the final form of the finite difference operators previously an elaborate analysis of the proposed indicators is provided targeting at global error control over all propagation angles our methodology guarantees upgraded flexibility as accuracy can be maximized within either narrow or wider frequency bands without practically inducing significant computational overhead attractive qualities such as high convergence rates are now the natural consequence of the effective design process rather than the minimization of the truncation errors of the difference expressions in fact the proposed fdtd approaches verify the possibility to attain improved levels of accuracy without resorting to the traditional taylor based forms of the individual operators a theoretical analysis of the inherent dispersion artifacts reveals the full potential of the new algorithms while numerical tests and comparisons unveil their unquestionable merits in practical applications

numerical inversion of the laplace transform from the real axis a numerical method for inversion of the laplace transform f p given for p 0 only is proposed recommendations for the choice of the abscissa of convergence and parameters of numerical integration are given the results of the numerical tests are discussed

high order split step unconditionally stable fdtd methods and numerical analysis high order split step unconditionally stable finite difference time domain fdtd methods in three dimensional 3 d domains are presented symmetric operator and uniform splitting are adopted simultaneously to split the matrix derived from the classical maxwell s equations into four sub matrices accordingly the time step is divided into four sub steps in addition high order central finite difference operators based on the taylor central finite difference method are used to approximate the spatial differential operators first and then the uniform formulation of the proposed high order schemes is generalized subsequently the analysis shows that all the proposed high order methods are unconditionally stable the generalized form of the dispersion relations of the proposed high order methods is carried out moreover the effects of the mesh size the time step and the order of schemes on the dispersion are illustrated through numerical results specifically the normalized numerical phase velocity error nnpve and the maximum nnpve of the proposed second order scheme are lower than that of the alternating direction implicit adi fdtd method furthermore the analysis of the accuracy of the proposed methods is presented in order to demonstrate the efficiency of the proposed methods numerical experiments are presented

state space approach to generalized thermoelastic problem with thermomechanical shock in this work the state space formulation for one dimensional problem of generalized thermoelasticity with one relaxation time is introduced the resulting formulation together with the laplace transform technique is applied to a thermomechanical shock half space problem the solution in the transformed domain is obtained the inverse laplace transforms is evaluated numerically the results are obtained and represented graphically

thermal stresses in functionally graded beams thermoelastic equilibrium equations for a functionally graded beam are solved in closed form to obtain the axial stress distribution the thermoelastic constants of the beam and the temperature were assumed to vary exponentially through the thickness the poisson ratio was held constant the exponential variation of the elastic constants and the temperature allow exact solution for the plane thermoelasticity equations a simple euler bernoulli type beam theory is also developed based on the assumption that plane sections remain plane and normal to the beam axis the stresses were calculated for cases for which the elastic constants vary in the same manner as the temperature and vice versa the residual thermal stresses are greatly reduced when the variation of thermoelastic constants are opposite to that of the temperature distribution when both elastic constants and temperature increasethrough the thickness in the samedirection they causea signie cant raise in thermal stresses for the case of nearly uniform temperature along the length of the beam beam theory is adequate in predicting thermal residual stresses

a simple and efficient algorithm to compute tail probabilities from transforms we present an algorithm to approximately compute the tail probability that a random variable exceeds a specified number given only an expression for its transform we also show that the problem is p hard more difficult than np hard suggesting that no efficient procedure can solve it exactly our method consists essentially of summing a power series and thus is easy to perform and requires little memory furthermore its computational effort is nearly linear in the reciprocal of a prespecified worst case error bound

a problem of numerical inversion of implicitly defined laplace transforms abstract a procedure is proposed for numerical inversion of laplace transforms x s implicitly defined from the functional equation x s g a s cx s where a and g are known functions c is a known constant this equation is encountered in queueing inventory and insurance problems the procedure constructs coefficients of the laguerre series for the original in the laguerre series inversion method and a sequence of approximants in the post widder inversion method scalar and matrix cases are treated in the same fashion the numerical results are compared with those attainable with the fourier series method

exact solution for thermoelastic deformations of functionally graded thick rectangular plates an exact solution is obtained for three dimensional deformations of a simply supported functionally graded rectangular plate subjected to mechanical and thermal loads on its top and or bottom surfaces suitable temperature and displacement functions that identically satisfy boundary conditions at the edges are used to reduce the partial differential equations governing the thermomechanical deformations to a set of coupled ordinary differential equations in the thickness coordinate which are then solved by employing the power series method the exact solution is applicable to both thick and thin plates results are presented for two constituent metal ceramic functionally graded rectangular plates that have a power law through the thickness variation of the volume fractions of the constituents the effective material properties at a point are estimated by either the mori tanaka or the self consistentschemes exact displacementsand stressesatseveral locations for mechanical and thermal loads are used toassess theaccuracyof the classical plate theory thee rst ordershear deformation theory and athird order shear deformation theory for functionally graded plates results are alsocomputed for a functionally graded plate with material properties derived by the mori tanaka method the self consistent scheme and a combination of these two methods

high order accurate modeling of electromagnetic wave propagation across media grid conforming bodies the maxwell equations contain a dielectric permittivity e that describes the particular media for homogeneous materials at low temperatures this coefficient is constant within a material however it jumps at the interface between different media this discontinuity can significantly reduce the order of accuracy of the numerical scheme we solve the maxwell equations with an interface between two media using a fourth order accurate algorithm we regularize the discontinuous dielectric permittivity by a continuous function either locally near the interface or globally in the entire domain we study the effect of this regularization on the order of accuracy for a one dimensional time dependent problem we then implement this for the three dimensional maxwell equations in spherical coordinates with appropriate physical and artificial absorbing boundary conditions we use fourier filtering of the high frequency modes near the poles to increase the time step

a modified fdtd 2 4 scheme for modeling electrically large structures with high phase accuracy a new fourth order finite difference time domain fdtd scheme has been developed that exhibits extremely low phase errors at low grid resolutions compared to the conventional fdtd scheme moreover this new scheme is capable of combining with the standard yee 1966 scheme to produce a stable hybrid algorithm the problem of wave propagation through a building is simulated using this new hybrid algorithm to demonstrate the large savings in computing resources it could afford with this new development the fdtd method can now be used to successfully model structures that are thousands of wavelengths large using the present day computer technology

solutions to the quantum yang baxter equation arising from pointed bialgebras let r m m m m be a solution to the quantum yang baxter equation where m is a finite dimensional vector space over a field k we introduce a quotient ana r of the bialgebra a r constructed by fadeev reshetihkin and takhtajan whose characteristics seem to more faith fully reflect properties r possesses as a linear operator we characterize all r such that ared r is a pointed bialgebra and we determine all solutions r to the quantum yang baxter equation when ared r is pointed and dim m 2 with a few technical exceptions when k has characteristic 2 extensions of such solutions to the quantum plane are studied in this paper we study the quantum yang baxter equation from the point of view of the faddeev reshetikhin and takhtajan construction 2 to refine techniques for constructing solutions using bialgebra methods applying our methods in the two dimensional case we generate with relative ease six extensive classes of solutions in particular we find all solutions r m m m m where m is a two dimensional vector space over a field k of characteristic not 2 which are represented by an invertible upper triangular matrix with respect to a basis of the form m m n m m n n n included among these is the familiar quantum yang baxter operator

on a parameterized family of twist quantum coalgebras and the bracket polynomial quantum coalgebras over a field k are structures that produce regular isotopy invariants of 1 1 tangles and twist quantum coalgebras over k are structures that produce regular isotopy invariants of knots these structures are introduced and studied in 9 in 6 and 8 certain families of quantum coalgebras and their resulting invariants of 1 1 tangles are examined in detail in this paper we use the simple coalgebra c k the dual of the algebra mn k of n x n matrices over k as a starting point for constructing twist quantum coalgebras among the twist quantum coalgebras we construct is a parameterized family related to the jones polynomial in an interesting way the jones polynomial can be computed by the normalized bracket polynomial 5 theorem 5 2 the bracket polynomial for knots in turn can be calculated from a quantum algebra structure on m2 c which is described in 5 p 580 the dual of this quantum algebra is a certain twist quantum coalgebra structure on c2 c which is discussed in 9 sect 8 thus the jones polynomial for knots can be computed from a twist quantum coalgebra structure on c2 c