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

application of a quantum ensemble model to linguistic analysis abstract a new set of parameters to describe the behavior of word frequencies in texts is proposed an analogy between the word frequency distribution and the bose distribution is suggested and the notion of temperature is introduced for this case the calculations are made for english ukrainian and the guinean maninka languages a correlation between the language structure the level of analyticity and the defined parameters is shown to exist

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

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

statistical model with a standard γ distribution we study a statistical model consisting of n basic units which interact with each other by exchanging a physical entity according to a given microscopic random law depending on a parameter ensuremath lambda we focus on the equilibrium or stationary distribution of the entity exchanged and verify through numerical fitting of the simulation data that the final form of the equilibrium distribution is that of a standard gamma distribution the model can be interpreted as a simple closed economy in which economic agents trade money and a saving criterion is fixed by the saving propensity ensuremath lambda alternatively from the nature of the equilibrium distribution we show that the model can also be interpreted as a perfect gas at an effective temperature t ensuremath lambda where particles exchange energy in a space with an effective dimension d ensuremath lambda

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

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

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

gibbs versus non gibbs distributions in money dynamics abstract we review a simple model of closed economy where the economic agents make money transactions and a saving criterion is present we observe the gibbs distribution for zero saving propensity and non gibbs distributions otherwise while the exact solution in the case of zero saving propensity is already known to be given by the gibbs distribution here we provide the explicit analytical form of the equilibrium distribution for the general case of nonzero saving propensity we verify it through comparison with numerical data and show that it can be cast in the form of a gamma distribution

gaussian spectral rules for the three point second differences i a two point positive definite problem in a semi infinite domain we suggest an approach to grid optimization for a second order finite difference scheme for elliptic equations a model problem corresponding to the three point finite difference semidiscretization of the laplace equation on a semi infinite strip is considered we relate the approximate boundary neumann to dirichlet map to a rational function and calculate steps of our finite difference grid using the pade chebyshev approximation of the inverse square root it increases the convergence order of the neumann to dirichlet map from second to exponential without increasing the stencil of the finite difference scheme and losing stability

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

stretched exponentials from superstatistics abstract distributions exhibiting fat tails occur frequently in many different areas of science a dynamical reason for fat tails can be a so called superstatistics where one has a superposition of local gaussians whose variance fluctuates on a rather large spatio temporal scale after briefly reviewing this concept we explore in more detail a class of superstatistics that hasn t been subject of many investigations so far namely superstatistics for which a suitable power of the local inverse temperature is 2 distributed we show that 0 leads to power law distributions while 0 leads to stretched exponentials the special case 1 corresponds to tsallis statistics and the special case 1 to exponential statistics of the square root of energy possible applications for granular media and hydrodynamic turbulence are discussed

from microscopic taxation and redistribution models to macroscopic income distributions abstract we present here a general framework expressed by a system of nonlinear differential equations suitable for the modeling of taxation and redistribution in a closed society this framework allows one to describe the evolution of income distribution over the population and to explain the emergence of collective features based on knowledge of the individual interactions by making different choices of the framework parameters we construct different models whose long time behavior is then investigated asymptotic stationary distributions are found which enjoy similar properties as those observed in empirical distributions in particular they exhibit power law tails of pareto type and their lorenz curves and gini indices are consistent with some real world ones

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

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

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

anomalous hydrodynamical dispersion and the transport with multiple families of paths in porous media we investigate a family of probability distributions that shows anomalous hydrodynamic dispersion by solving a particular class of coupled generalized master equations the fourier laplace solution is obtained analytically in terms of the matrix green function method then the coats smith concentration profile is revisited in a particular case two models of disorder are worked out explicitly and the mean current is asymptotically calculated we present an approximation method to calculate the first passage time distribution for this stochastic transport process and as an example an exact markovian result is worked out scaling results are also shown we discuss the comparison with other different methods to work out complex diffusion phenomena in the presence of disordered multiple transport paths extensions when the models are nondiffusive can also be solved in the fourier laplace representation

multicanonical distribution statistical equilibrium of multiscale systems a multicanonical formalism is introduced to describe the statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales where the hierarchical structure is described as a set of nested internal heat reservoirs with fluctuating temperatures the probability distribution of states at small scales is written as an appropriate averaging of the large scale distribution the boltzmann gibbs distribution over these effective internal degrees of freedom for a large class of systems the multicanonical distribution is given explicitly in terms of generalized hypergeometric functions as a concrete example it is shown that generalized hypergeometric distributions describe remarkably well the statistics of acceleration measurements in lagrangian turbulence

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

a new κ deformed parametric model for the size distribution of wealth abstract it has been pointed out by patriarca et al 2005 that the power law tailed equilibrium distribution in heterogeneous kinetic exchange models with a distributed saving parameter can be resolved as a mixture of gamma distributions corresponding to particular subsets of agents here we propose a new four parameter statistical distribution which is a deformation of the generalized gamma distribution with a power law tail based on the deformed exponential and logarithm functions introduced by kaniadakis 2001 we found that this new distribution is also an extension to the generalized distribution proposed by clementi et al 2010 with an additional shape parameter and properly reproduces the whole range of the distribution of wealth in such heterogeneous kinetic exchange models we also provide various associated statistical measures and inequality measures

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

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

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

multiplicative processes and power laws takayasu sato and takayasu phys rev lett 79 966 1997 revisited the question of stochastic processes with multiplicative noise which have been studied in several different contexts over the past decades we focus on the regime found for a generic set of control parameters in which stochastic processes with multiplicative noise produce intermittency of a special kind characterized by a power law probability density distribution we briefly explain the physical mechanism leading to a power law probability distribution function and provide a list of references for these results dating back from a quarter of century we explain how the formulation in terms of the characteristic function developed by takayasu sato and takayasu can be extended to exponents ensuremath mu g2 which explains the reason for the lucky coincidence the multidimensional generalization of the results of takayasu sato and takayasu and the present status of the problem are briefly summarized the discovery of stretched exponential tails in the presence of the cutoff introduced by takayasu sato and takayasu is explained theoretically we end by briefly listing applications

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

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

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

phase space geometry and slow dynamics we describe a non arrhenius mechanism for the slowing down of dynamics that is inherent to the high dimensionality of the phase space we show that such a mechanism is at work both in a family of mean field spin glass models without any domain structure and in the case of ferromagnetic domain growth the marginality of spin glass dynamics as well as the existence of a quasi equilibrium regime can be understood within this scenario we discuss the question of ergodicity in an out of equilibrium situation

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

an efficient finite difference scheme for electromagnetic logging in 3d anisotropic inhomogeneous media we consider a problem of computing the electromagnetic field in 3d anisotropic media for electromagnetic logging the proposed finite difference scheme for maxwell equations has the following new features based on some recent and not so recent developments in numerical analysis coercivity i e the complete discrete analogy of all continuous equations in every grid cell even for nondiagonal conductivity tensors a special conductivity averaging that does not require the grid to be small compared to layering or fractures and a spectrally optimal grid refinement minimizing the error at the receiver locations and optimizing the approximation of the boundary conditions at infinity all of these features significantly reduce the grid size and accelerate the computation of electromagnetic logs in 3d geometries without sacrificing accuracy

analytical solution of a stochastic content based network model we define and completely solve a content based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches for an alphabet with an arbitrary number of letters the analytic expression for the out degree distribution shows a crossover from a leading power law behaviour to a log periodic regime bounded by a different power law decay the leading exponents in the two regions have a weak dependence on the mean word length and an even weaker dependence on the alphabet size the in degree distribution on the other hand is much narrower and does not show any scaling behaviour

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

numerical methods for nonlinear second order hyperbolic partial differential equations i time linearized finite difference methods for 1 d problems abstract a three parameter family of finite difference methods for one dimensional hyperbolic equations with damping and nonlinearities based on the introduction of a new dependent variable and three implicitness parameters for the time discretization and the diffusion and reaction terms is presented and shown to result in two time level semi discrete equations second order accurate spatial discretizations and time linearization of the nonlinear source terms are shown to result in three time level linear finite difference equations which are second order accurate in time whenever the reaction and diffusion terms are allocated in the proportion 1 2 1 to the past current and future time levels second order accurate in time time linearized three point compact operator methods for the spatial derivatives which only involve three time levels and three grid points and are fourth order accurate in space are also presented and their linear stability analyzed an exhaustive comparison between analytical and numerical results indicates that the accuracy of time linearized methods increases as the time step and grid spacing are decreased and is nearly independent of the order of the spatial discretization when there is a sufficient number of grid points to resolve the wave structure and the best accuracy is achieved when the three implicitness parameters are equal to 1 2 it is also shown that the accuracy of time linearized methods is a strong function of the wave speed as the wave speed is increased and the wave equation tends to a parabolic one the methods are still three time level techniques which may not preserve the positivity of the solution whereas a crank nicolson discretization of the corresponding parabolic equation does preserve this property provided that there are no mathematical incompatibilities between the initial and the boundary conditions it is also shown that for one dimensional wave equations with monotonic kinetics and time dependent forcing there are very few differences between second and first order time accurate discretizations of the diffusion terms provided that the time step and grid size are sufficiently small and the discretization of the reaction terms plays a less important rule than that of the diffusion terms

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

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

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

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

hybrid laplace transform weighting function scheme for transient multidimensional conservation equations abstract a hybrid laplace transform weighting function scheme is developed for solving time dependent multidimensional conservation equations the new method removes the time derivatives from the governing differential equations using the laplace transform and solves the associated equation with the weighting function scheme the similarity transform method is used to treat the complex coefficient system of the equations which allows the simplest form of complex number functions to be obtained and then to use the partial fractions method or a numerical method to invert the laplace transform and transform the functions to the physical plane three different examples have been analyzed by the present method the present method solutions are compared in tables with the exact solutions and those obtained by the other numerical methods it is found that the present method is a reliable and efficient numerical tool

variational principle for the pareto power law a mechanism is proposed for the appearance of power law distributions in various complex systems it is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power law tail can appear in the equilibrium distribution of energy as a result of certain superpositions of the canonical equilibrium energy densities of the subsystems the derivation only uses a variational principle based on the boltzmann entropy without assumptions outside the framework of canonical equilibrium statistical mechanics two examples are discussed free diffusion on a complex network and a kinetic model of wealth exchange the mechanism is illustrated in the general case through an exactly solvable mechanical model of a dimensionally heterogeneous system

a 3d parametric inversion algorithm for triaxial induction data we develop a parametric inversion algorithm to determine simultaneously the horizontal and vertical resistivities of both the formation and invasion zones invasion radius bed boundary upper location and thickness and relative dip angle from electromagnetic triaxial induction logging data this is a full 3d inverse scattering problem in transversally isotropic media to acquire sufficient sensitivity to invert for all of these parameters we collect the data using a multicomponent multispacing induction array for each transmitter receiver spacing this multicomponent tool has sets of three orthogonal transmitter and receiver coils at each logging point single frequency data are collected at multiple spacings to obtain information at different depths of investigation this inversion problem is solved iteratively with a constrained regularized gauss newton minimization scheme as documented in the literature the main computational bottleneck when solving this full 3d inverse problem is the cpu time associated with constructing the jacobian matrix in this study to achieve the inversion results within a reasonable computational time we implement a dual grid approach wherein the jacobian matrix is computed using a very coarse optimal grid furthermore to regularize the inversion process we use the so called multiplicative regularization technique this technique automatically determines the regularization parameter synthetic data tests indicate the developed inversion algorithm is robust in extracting formation and invasion anisotropic resistivities invasion radii bed boundary locations relative dip and azimuth angle from multispacing multicomponent induction logging data

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

a two dimensional thermoelasticity problem for a half space subjected to heat sources the two dimensional problem for a half space whose surface is traction free and subjected to the effects of heat sources is considered within the context of the theory of thermoelasticity with two relaxation times laplace and fourier transform techniques are used the solution in the transformed domain is obtained by using a direct approach numerical inversion of both transforms is carried out to obtain the temperature stress and displacement distributions in the physical domain numerical results are represented graphically and discussed

content based network model with duplication and divergence abstract we construct a minimal content based realization of the duplication and divergence model of genomic networks introduced by wagner proc natl acad sci 91 1994 4387 and investigate the scaling properties of the directed degree distribution and clustering coefficient we find that the content based network exhibits crossover between two scaling regimes with log periodic oscillations for large degrees these features are not present in the original gene duplication model but inherent in the content based model of balcan and erzan the scaling form of the degree distribution of the content based model turns out to be robust under duplication and divergence with some re adjustment of the scaling exponents while the out clustering coefficient goes over from a weak power law dependence on the degree to an exponential decay under mutations which include splitting and merging of strings

a problem for an infinite elastic body with a spherical cavity in the theory of generalized thermoelastic diffusion in this work we study a one dimensional problem in a generalized thermoelastic diffusion in infinite medium with a spherical cavity subjected to a time dependent thermal shock of its internal boundary which is assumed to be traction free the chemical potential is also assumed to be a known function of time on the bounding cavity laplace transform techniques are used the solution of the problem in the transformed domain is obtained by using a direct approach without the customary use of potential functions by means of numerical laplace inversion the problem is solved in the physical domain numerical results predict finite speeds of propagation for thermoelastic and diffusive waves to investigate the diffusions effects a comparison is made with the results obtained in the thermoelastic problem

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

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

simple wealth distribution model causing inequality induced crisis without external shocks we address the issue of the dynamics of wealth accumulation and economic crisis triggered by extreme inequality attempting to stick to most possibly intrinsic assumptions our general framework is that of pure or modified multiplicative processes basically geometric brownian motions in contrast with the usual approach of injecting into such stochastic agent models either specific idiosyncratic internal nonlinear interaction patterns or macroscopic disruptive features we propose a dynamic inequality model where the attainment of a sizable fraction of the total wealth by very few agents induces a crisis regime with strong intermittency the explicit coupling between the richest and the rest being a mere normalization mechanism hence with minimal extrinsic assumptions the model thus harnesses the recognized lack of ergodicity of geometric brownian motions it also provides a statistical intuition to the consequences of thomas piketty s recent rgg return rate g growth rate paradigmatic analysis of very long term wealth trends we suggest that the water divide of wealth flow may define effective classes making an objective entry point to calibrate the model consistently we check that a tax mechanism associated to a few percent relative bias on elementary daily transactions is able to slow or stop the build up of large wealth when extreme fluctuations are tamed down to a stationary regime with sizable but steadier inequalities it should still offer opportunities to study the dynamics of crisis and the inner effective classes induced through external or internal factors

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

generalized statistical mechanics connection with thermodynamics the authors show the manner through which the recent generalization by tsallis 1988 of the boltzmann gibbs statistics becomes consistent with a generalized thermodynamics preserving the legendre transformation framework of standard thermodynamics in addition to that they generalize the shannon additivity