a new rigorous expansion for the velocity potential of a circular piston source in the case of boundary value problems such as the sound scattering from a sphere placed in the nearfield of a plane piston source it is sometimes essential to express the velocity potentials in terms of the orthogonal expansion it is demonstrated in the present work that the rayleigh surface integral giving the velocity potential for a plane piston source surrounded by an infinite rigid flange reduces to a rigorous expansion of the simplest form for a circular piston as series of spherical surface harmonics the resulting equation is valid for any field points even on the piston surface sample calculations made with a microcomputer are presented with three dimensional and contour plots

near field characteristics of circular piston radiators with simple support a closed form expression for the pressure field produced by a circular piston radiator with simply supported boundary condition and continuous wave excitation is derived the method of hasegawa et al j acoust soc am 74 1044 1047 1983 developed for a uniformly vibrating piston is extended to include the nonuniform case the resulting expression is valid for all field points and for large ratio of source diameter to wavelength the average pressure on the surface of a circular receiver as a function of receiver size and distance from the transducer is also calculated

on the convergence rates of genetic algorithms this paper discusses the convergence rates of genetic algorithms by using the minorization condition in the markov chain theory we classify genetic algorithms into two kinds one with time invariant genetic operators another with time variant genetic operators for the former case we have obtained the bound on its convergence rate on the general state space for the later case we have bounded its convergence rate on the finite state space

randomized local search evolutionary algorithms and the minimum spanning tree problem randomized search heuristics among them randomized local search and evolutionary algorithms are applied to problems whose structure is not well understood as well as to problems in combinatorial optimization the analysis of these randomized search heuristics has been started for some well known problems and this approach is followed here for the minimum spanning tree problem after motivating this line of research it is shown that randomized search heuristics find minimum spanning trees in expected polynomial time without employing the global technique of greedy algorithms

finite element solution of the helmholtz equation with high wave number part i the h version of the fem abstract the paper addresses the properties of finite element solutions for the helmholtz equation the h version of the finite element method with piecewise linear approximation is applied to a one dimensional model problem new results are shown on stability and error estimation of the discrete model in all propositions assumptions are made on the magnitude of hk only where k is the wavelength and h is the stepwidth of the fe mesh previous analytical results had been shown with the assumption that k 2 h is small for medium and high wavenumber these results do not cover the meshsizes that are applied in practical applications the main estimate reveals that the error in h 1 norm of discrete solutions for the helmholtz equation is polluted when k 2 h is not small the error is then not quasioptimal i e the relation of the fe error to the error of best approximation generally depends on the wavenumber k it is noted that the pollution term in the relative error is of the same order as the phase lead of the numerical solution in the result of this analysis thorough and rigorous understanding of error behavior throughout the range of convergence is gained numerical results are presented that show sharpness of the error estimates and highlight some phenomena of the discrete solution behavior the h p version of the fem is studied in part ii

analysis of a multiobjective evolutionary algorithm on the 0 1 knapsack problem multiobjective evolutionary algorithms moeas are increasingly being used for effectively solving many real world problems and many empirical results are available however theoretical analysis is limited to a few simple toy functions in this work we select the well known knapsack problem for the analysis the multiobjective knapsack problem in its general form is np complete moreover the size of the set of pareto optimal solutions can grow exponentially with the number of items in the knapsack thus we formalize a 1 e approximate set of the knapsack problem and attempt to present a rigorous running time analysis of a moea to obtain the formalized set the algorithm used in the paper is based on a restricted mating pool with a separate archive to store the remaining population we call the algorithm a restricted evolutionary multiobjective optimizer remo we also analyze the running time of remo on a special bi objective linear function known as lotz leading ones trailing zeros whose pareto set is shown to be a subset of the knapsack an extension of the analysis to the simple evolutionary multiobjective optimizer semo is also presented a strategy based on partitioning of the decision space into fitness layers is used for the analysis

a numerical study of adding an artificial dissipation term for solving the nonlinear dispersive equations k n n a linearized implicit finite difference method is devised for k n n the stability and accuracy of the proposed methods are discussed a compacton wave solution of the equation k n n is used to examine the accuracy and efficiency of the proposed methods and study the effect of the added artificial dissipation term to solve the k n n equation using finite difference method the dynamics of waves having various initial wavepackets are discussed

on the analysis of the 1 1 evolutionary algorithm many experimental results are reported on all types of evolutionary algorithms but only few results have been proved a step towards a theory on evolutionary algorithms in particular the so called 1 1 evolutionary algorithm is performed linear functions are proved to be optimized in expected time o nlnn but only mutation rates of size 1 n can ensure this behavior for some polynomial of degree 2 the optimization needs exponential time the same is proved for a unimodal function both results were not expected by several other authors finally a hierarchy result is proved moreover methods are presented to analyze the behavior of the 1 1 evolutionary algorithm

an annular superposition integral for axisymmetric radiators a fast integral expression for computing the nearfield pressure is derived for axisymmetric radiators this method replaces the sum of contributions from concentric annuli with an exact double integral that converges much faster than methods that evaluate the rayleigh sommerfeld integral or the generalized king integral expressions are derived for plane circular pistons using both continuous wave and pulsed excitations several commonly used apodization schemes for the surface velocity distribution are considered including polynomial functions and a smooth piston function the effect of different apodization functions on the spectral content of the wave field is explored quantitative error and time comparisons between the new method the rayleigh sommerfeld integral and the generalized king integral are discussed at all error levels considered the annular superposition method achieves a speed up of at least a factor of 4 relative to the point source method and a factor of 3 relative to the generalized king integral without increasing the computational complexity

on axis and far field sound radiation from resilient flat and dome shaped radiators on axis and far field series expansions are developed for the sound pressure due to an arbitrary circular symmetric velocity distribution on a flat radiator in an infinite baffle these expansions are obtained by expanding the velocity distributions in terms of orthogonal polynomials r 2n 0 sigma a p n 2 sigma a 2 1 with p n the legendre polynomials the terms r 2n 0 give rise to a closed form expression for the pressure on axis as well as for the far field pressure furthermore for a large number of velocity profiles including those associated with the rigid piston the simply supported radiator and the clamped radiators as well as gaussian radiators there are closed form expressions for the required expansion coefficients in particular for the rigid simply supported and clamped radiators this results in explicit finite series expressions for both the on axis and far field pressures in the reverse direction a method of estimating velocity distributions from measured on axis pressures by matching in terms of expansion coefficients is proposed together with the forward far field computation scheme this yields a method for far field loudspeaker assessment from on axis data generalized keele scheme the forward computation scheme is extended to dome shaped radiators with arbitrary velocity distributions

construction of equilibrated singular basis functions without a priori knowledge of analytical singularity order in this paper a novel method is presented to construct singular basis functions for solving harmonic and bi harmonic problems with weak singularities such bases are found without any knowledge of the singularity order the singular bases are constructed by choosing a series as a tensor product of chebyshev polynomials and trigonometrical functions in radial and angular directions respectively and applying weak form of the governing equation with such features the singular bases are categorized as the equilibrated basis functions the constructed singular functions can be utilized as a complementary part to the smooth part of the approximation in the solution of problems with singularities to demonstrate the efficiency of employing such singular bases they are used in a boundary node method through the solution of some examples selected from the well known literature the capability of the method is shown it will be demonstrated that the main function and its derivatives are excellently approximated at very close neighborhood of the singular point the method may especially be found useful for those who research on the extended finite element method or similar ideas

comparing evolutionary algorithms to the 1 1 ea in this paper we study the conditions in which the random hill climbing algorithm 1 1 ea compares favorably to other evolutionary algorithms eas in terms of fitness function distribution at a given iteration and with respect to the average optimization time our approach is applicable when the reproduction operator of an evolutionary algorithm is dominated by the mutation operator of the 1 1 ea in this case one can extend the lower bounds obtained for the expected optimization time of the 1 1 ea to other eas based on the dominated reproduction operator this method is demonstrated on the sorting problem with ham landscape and the exchange mutation operator we consider several simple examples where the 1 1 ea is the best possible search strategy in the class of the eas

the low frequency axisymmetric modal sound radiation efficiency of an elastically supported annular plate abstract this paper deals with the sound radiation efficiency of a vibrating thin elastically supported annular plate embedded into a flat rigid baffle the free axisymmetric time harmonic vibrations have been considered for a single mode it has been assumed that the influence of the air column above the plate on the plate s vibrations is negligible first the sound radiation efficiency has been formulated as an integral further rigorous mathematical manipulations have been carried out based on the theory of summation of multiple expansion series containing the hypergeometric functions as a result the formulations have been expressed as some fast convergent expansion series containing only the bessel and struve functions of integer order and the spherical bessel functions the presented formulations of sound radiation efficiency of an elastically supported annular plate are useful for numerical calculations within the low frequency range what is important for practical reasons the formulations are valid for axisymmetric boundary conditions and they enable changing the values of boundary stiffness constants consequently the analysis of influence of the plate s edge attachment on the sound radiation efficiency has been performed the limiting transitions have also been performed from formulations valid for the elastically supported annular plates to the formulations valid for annular plates with classical boundary conditions clamped simply supported and free at one edge or at both edges

convergence analysis and improvements of quantum behaved particle swarm optimization motivated by concepts in quantum mechanics and particle swarm optimization pso quantum behaved particle swarm optimization qpso was proposed as a variant of pso with better global search ability although it has been shown to perform well in finding optimal solutions for many optimization problems there has so far been little theoretical analysis on its convergence and performance this paper presents a convergence analysis and performance evaluation of the qpso algorithm and it also proposes two variants of the qpso algorithm first we investigate in detail the convergence of the qpso algorithm on a probabilistic metric space and prove that the qpso algorithm is a form of contraction mapping and can converge to the global optimum this is the first time that the theory of probabilistic metric spaces has been employed to analyze a stochastic optimization algorithm we provided a new definition for the convergence rate of a stochastic algorithm as well as definitions for three types of convergence according to the correlations between the convergence rate and the objective function values with these definitions the effectiveness of the qpso is evaluated by computing and analyzing the time complexity and the convergence rate of the algorithm then the qpso with random mean best position qpso rm and the qpso with ranking operator qpso ro are proposed as two improvements of the qpso algorithm finally some empirical studies on popular benchmark functions are performed in order to make a full performance evaluation and comparison between qpso qpso rm qpso ro and other variants of pso

second harmonic generation of practical bessel beams a fast gaussian expansion approach is used to investigate fundamental and second harmonic generation in practical bessel beams of finite aperture the analysis is based on the integral solutions of the kzk equation under the quasilinear approximation the influence of the medium s attenuation on the beam profile is considered analysis results show that the absorption parameter has a significant effect on the far field beam profile of the second harmonic under certain circumstances the second harmonic of a practical bessel beam still has the main properties of an ideal bessel beam of infinite aperture when it propagates within its depth of field

how novel is the novel black hole optimization approach due to abundance of novel optimization algorithms in recent years the problem of large similarities among methods that are named differently is becoming troublesome and general the question arises if the novel source of inspiration is sufficient to breed an optimization algorithm with a novel name even if its search properties are almost the same as or are even a simplified variant of the search properties of an older and well known method in this paper it is rigidly shown that the recently proposed heuristic approach called the black hole optimization is in fact a simplified version of particle swarm optimization with inertia weight additionally because a large number of metaheuristics developed during the last decade is claimed to be nature inspired a short discussion on inspirations of optimization algorithms is presented

a coupled element free galerkin boundary element method for stress analysis of two dimensional solids element free galerkin efg method is a newly developed meshless method for solving partial differential equations using moving least squares interpolants it is however computationally expensive for many problems a coupled efg boundary element be method is proposed in this paper to improve the solution efficiency a procedure is developed for the coupled efg be method so that the continuity and compatibility are preserved on the interface of the two domains where the efg and be methods are applied the present coupled efg be method has been coded in fortran the validity and efficiency of the efg be method are demonstrated through a number of examples it is found that the present method can take the full advantages of both efg and be methods it is very easy to implement and very flexible for computing displacements and stresses of desired accuracy in solids with or without infinite domains

adiabatic perturbations for compactons under dissipation and numerically induced dissipation compacton propagation under dissipation shows amplitude damping and the generation of tails the numerical simulation of compactons by means of dissipative schemes also show the same behaviors the truncation error terms of a numerical method can be considered as a perturbation of the original partial differential equation and perturbation methods can be applied to its analysis for dissipative schemes or when artificial dissipation is added the adiabatic perturbation method yields evolution equations for the amplitude loss in the numerical solution and the amplitude of the numerically induced tails in this paper such methods are applied to the k 2 2 rosenau hyman equation showing a very good agreement between perturbative and numerical results

ultrasonic field modeling by distributed point source method for different transducer boundary conditions several investigators have modeled ultrasonic fields in front of transducers by huygens fresnel superposition principle that integrates the contributions of a number of point sources distributed on the transducer face this integral solution also known as the rayleigh integral or rayleigh sommerfeld integral solution assumes the strengths of the point sources distributed over the transducer face a newly developed technique called distributed point source method dpsm offers an alternative approach for modeling ultrasonic fields dpsm is capable of modeling the field for prescribed source strength distribution as well as for prescribed interface conditions with unknown source strengths it is investigated how the ultrasonic field in front of the transducer varies in different situations 1 when the point source strengths are known 2 when the point source strengths are unknown but obtained from the interface condition that only the normal component of the transducer velocity is continuous across th

an efficient grid sectoring method for calculations of the near field pressure generated by a circular piston an analytical expression is derived for time harmonic calculations of the near field pressure produced by a circular piston the near field pressure is described by an efficient integral that eliminates redundant calculations and subtracts the singularity which in turn reduces the computation time and the peak numerical error the resulting single integral expression is then combined with an approach that divides the computational grid into sectors that are separated by straight lines the integral is computed with gauss quadrature in each sector and the number of gauss abscissas in each sector is determined by a linear mapping function that prevents large errors from occurring in the axial region by dividing the near field region into 10 sectors the raw computation time is reduced by nearly a factor of 2 for each expression evaluated in this grid the grid sectoring approach is most effective when the computation time is reduced without increasing the peak error and this is consistently accomplished with the efficient integral formulation of the four single integral expressions evaluated with grid sectoring the efficient formulation that eliminates redundant calculations and subtracts the singularity demonstrates the smallest computation time for a specified value of the maximum error

geometric convergence rates for stochastically ordered markov chains let n be a markov chain on the state space 0 that is stochastically ordered in its initial state that is a stochastically larger initial state produces a stochastically larger chain at all other times examples of such chains include random walks the number of customers in various queueing systems and a plethora of storage processes a large body of recent literature concentrates on establishing geometric ergodicity of n in total variation that is proving the existence of a limiting probability measure and a number r 1 such that lim n to infty r n sup a in cal b 0 infty vert p x phi n in a pia vert 0 for every deterministic initial state 0 x we seek to identity the largest r that satisfies this relationship a dependent sample path coupling and a foster lyapunov drift inequality are used to derive convergence rate bounds we then show that the bounds obtained are frequently the best possible application of the methods to queues and random walks are included

on the sound field of a circular membrane in free space and an infinite baffle an enhanced method for calculating the radiation characteristics of a tensioned circular membrane in free space is presented using an analytical solution to the infinite integral in the free space green s function in cylindrical coordinates this enables direct calculation of the surface pressure series coefficients by equating the coefficients of the resulting bessel series in a set of simultaneous equations eliminating both numerical integration and least squares minimization improves calculation speed and accuracy an infinite baffle is introduced to provide an indication of what the theoretical limit of the bass performance would be using a very large enclosure furthermore analytical solutions to the pressure field integrals are presented a force transmission coefficient is introduced which is the ratio of the total radiation impedance to the motional impedance the motional radiation and diaphragm impedances of the damped membrane are calculated together with the near and far field pressure responses and efficiency a comparison is made between the on axis response without damping calculated using this method and using a finite element model it is demonstrated that good correlation between the two calculation methods can be achieved provided the elements are small enough and a sufficiently large model is used at the frequency extremes

simplified expansions for radiation from a baffled circular piston computation of acoustic radiation from a baffled circular piston continues to be an active area of investigation both as a canonical problem and because of numerous practical applications for time harmonic radiation exact series expansions are an attractive approach because they do not require numerical integration or limiting approximations here series expansions due to hasegawa inoue and matsuzawa j acoust soc am 74 1044 1047 1983 75 1048 1051 1984 are shown to reduce to simpler expressions suitable for numerical computations for the region r a where a is the piston radius and r is the distance from the piston center an exact solution is given by a series of spherical hankel functions and legendre polynomials with explicit closed form position independent coefficients for the paraxial region w a where w is the distance from the piston axis a second exact series expansion is valid for all axial distances z and reduces to the known analytic solution for w 0 these two expansions allow the radiated field to be computed at any point with rapid convergence except for points near the circle bounding the piston example numerical results illustrate application of this method to ultrasonic sources

statistical dynamics of the royal road genetic algorithm abstract metastability is a common phenomenon many evolutionary processes both natural and artificial alternate between periods of stasis and brief periods of rapid change in their behavior in this paper an analytical model for the dynamics of a mutation only genetic algorithm ga is introduced that identifies a new and general mechanism causing metastability in evolutionary dynamics the ga s population dynamics is described in terms of flows in the space of fitness distributions the trajectories through fitness distribution space are derived in closed form in the limit of infinite populations we then show how finite populations induce metastability even in regions where fitness does not exhibit a local optimum in particular the model predicts the occurrence of fitness epochs periods of stasis in population fitness distributions at finite population size and identifies the locations of these fitness epochs with the flow s hyperbolic fixed points this enables exact predictions of the metastable fitness distributions during the fitness epochs as well as giving insight into the nature of the periods of stasis and the innovations between them all these results are obtained as closed form expressions in terms of the ga s parameters an analysis of the jacobian matrices in the neighborhood of an epoch s metastable fitness distribution allows for the calculation of its stable and unstable manifold dimensions and so reveals the state space s topological structure more general quantitative features of the dynamics fitness fluctuation amplitudes epoch stability and speed of the innovations are also determined from the jacobian eigenvalues the analysis shows how quantitative predictions for a range of dynamical behaviors that are specific to the finite population dynamics can be derived from the solution of the infinite population dynamics the theoretical predictions are shown to agree very well with statistics from ga simulations we also discuss the connections of our results with those from population genetics and molecular evolution theory

exponential basis functions in solution of incompressible fluid problems with moving free surfaces in this paper a new simple meshless method is presented for the solution of incompressible inviscid fluid flow problems with moving boundaries a lagrangian formulation established on pressure as a potential equation is employed in this method the approximate solution is expressed by a linear combination of exponential basis functions ebfs with complex valued exponents satisfying the governing equation constant coefficients of the solution series are evaluated through point collocation on the domain boundaries via a complex discrete transformation technique the numerical solution is performed in a time marching approach using an implicit algorithm in each time step the governing equation is solved at the beginning and the end of the step with the aid of an intermediate geometry the use of ebfs helps to find boundary velocities with high accuracy leading to a precise geometry updating the developed lagrangian meshless algorithm is applied to variety of linear and nonlinear benchmark problems non linear sloshing fluids in rigid rectangular two dimensional basins are particularly addressed

a gaussian finite element method for description of sound diffraction a new method for solving diffraction problems is presented it is based on the use of gaussian diffraction theory comparison of the gaussian beam expansion and fourier series expansion reveals that the gaussian expansion is a more general and more powerful technique the new method combines the gaussian beam superposition technique wen and breazeale j acoust soc am 83 1752 1756 1988 and the numerical finite element solution to the parabolic equation huang j acoust soc am 84 1405 1413 1988 the new method is capable of solving for the sound field even in an inhomogeneous medium or in the presence of reflection as shown by computer modeling the source may be a gaussian source or a distributed source calculated results are compared with experimental results in a laboratory water tank

fast multipole method for the biharmonic equation in three dimensions the evaluation of sums matrix vector products of the solutions of the three dimensional biharmonic equation can be accelerated using the fast multipole method while memory requirements can also be significantly reduced we develop a complete translation theory for these equations it is shown that translations of elementary solutions of the biharmonic equation can be achieved by considering the translation of a pair of elementary solutions of the laplace equations the extension of the theory to the case of polyharmonic equations in r 3 is also discussed an efficient way of performing the fmm for biharmonic equations using the solution of a complex valued fmm for the laplace equation is presented compared to previous methods presented for the biharmonic equation our method appears more efficient the theory is implemented and numerical tests presented that demonstrate the performance of the method for varying problem sizes and accuracy requirements in our implementation the fmm for the biharmonic equation is faster than direct matrix vector product for a matrix size of 550 for a relative l 2 accuracy e 2 10 4 and n 3550 for e 2 10 1 2

singular meshless method using double layer potentials for exterior acoustics time harmonic exterior acoustic problems are solved by using a singular meshless method in this paper it is well known that the source points cannot be located on the real boundary when the method of fundamental solutions mfs is used due to the singularity of the adopted kernel functions hence if the source points are right on the boundary the diagonal terms of the influence matrices cannot be derived herein we present an approach to obtain the diagonal terms of the influence matrices of the mfs for the numerical treatment of exterior acoustics by using the regularization technique to regularize the singularity and hypersingularity of the proposed kernel functions the source points can be located on the real boundary and therefore the diagonal terms of influence matrices are determined we also maintain the prominent features of the mfs that it is free from mesh singularity and numerical integration the normal derivative of the fundamental solution of the helmholtz equation is composed of a two point function which is one of the radial basis functions the solution of the problem is expressed in terms of a double layer potential representation on the physical boundary based on the potential theory the solutions of three selected examples are used to compare with the results of the exact solution conventional mfs boundary element method and dirichlet to neumann finite element method good numerical performance is demonstrated by close agreement with other solutions

finite difference solution to the parabolic wave equation in this article an implicit finite difference ifd scheme is introduced for solving underwater acoustic wave propagation problems this scheme is applied to the parabolic wave equation model for the acoustic problem with a free surface and arbitrary bottom and bottom boundary conditions the mathematical theory of the implicit finite difference method as applied to the parabolic equation is developed and a computer model to implement the ifd is introduced representative problems are presented to demonstrate the capability of the ifd model advantages and limitations of the ifd are discussed

a meshless method for unbounded acoustic problems in this paper an effective meshless method is proposed to solve time harmonic acoustic problems defined on unbounded domains to this end the near field is discretized by a set of nodes and the far field effect is taken into account by considering radiative boundary conditions the approximation within the near field is performed using a set of local residual free basis functions defined on a series of finite clouds for considering the far field effect a series of infinite clouds are defined on which another set of residual free bases satisfying the radiation conditions are considered for the approximation validation of the results is performed through solving some acoustic problems

a repository of equations with cosine sine compactons nonlinear evolution equations with cosine sine compacton solutions are reviewed including the rosenau hyman equation and generalizations of korteweg de vries camassa holm boussinesq benjamin bona mahony klein gordon and other equations each equation is generalized to three dimensions and the conditions for its cosine solitary waves to be either a compacton or a soliton are determined several equations claimed in the literature to be different among them are found to be equivalent

on the sound field of a resilient disk in an infinite baffle the rayleigh integral describing the near field pressure of an axisymmetric planar monopole source with an arbitrary velocity distribution is solved with a method similar to that used by mast and yu j acoust soc am 118 6 3457 3464 2005 for a rigid disk in an infinite baffle the closed form solution is in the form of a double expansion which is valid for distances from the observation point to the center of the source that are greater than its radius however for the remaining immediate near field the king integral is solved using a combination of gegenbauer s summation theorem and the lommel expansion resulting in a solution which is in the form of a triple expansion reducing to a double expansion along the source s axis of symmetry these relatively compact solutions in analytic form do not require numerical integration and therefore present no numerical difficulties except for a singularity at the rim as an example of a monopole source with an arbitrary velocity distribution equations

convergence of multi objective evolutionary algorithms to a uniformly distributed representation of the pareto front in evolutionary multi objective optimization emo the convergence to the pareto set of a multi objective optimization problem mop and the diversity of the final approximation of the pareto front are two important issues in the existing definitions and analyses of convergence in multi objective evolutionary algorithms moeas convergence with probability is easily obtained because diversity is not considered however diversity cannot be guaranteed by combining the convergence with diversity this paper presents a new definition for the finite representation of a pareto set the b pareto set and a convergence metric for moeas based on a new archive updating strategy the convergence of one such moea to the b pareto sets of mops is proved numerical results show that the obtained b pareto front is uniformly distributed along the pareto front when according to the new definition of convergence the algorithm is convergent

a radial propagator for axisymmetric pressure fields the concept of a propagator is central to the angular spectrum formulation of diffraction theory which expresses the pressure field diffracted by a two dimensional aperture as a superposition of a continuum of plane waves in the conventional form an exponential term known as a propagator is multiplied by the wavenumber spectrum obtained from a two dimensional spatial fourier transform of the aperture boundary condition to obtain the wavenumber spectrum in a plane parallel to the boundary offset by some distance specified in the propagator by repeated use of this propagator and fourier inversion it is possible to completely construct the homogeneous part of the pressure field in the positive half space beyond the planar boundary containing the aperture drawing upon preceding work relating the boundary condition to the axial pressure pees j acoust soc am 127 3 1381 1390 2010 it is shown in this article that when the aperture is axially symmetric an alternative type of propagator can b

choosing selection pressure for wide gap problems abstract to exploit an evolutionary algorithm s performance to the full extent the selection scheme should be chosen carefully empirically it is commonly acknowledged that low selection pressure can prevent an evolutionary algorithm from premature convergence and is thereby more suitable for wide gap problems however there are few theoretical time complexity studies that actually give the conditions under which a high or a low selection pressure is better in this paper we provide a rigorous time complexity analysis showing that low selection pressure is better for the wide gap problems with two optima

minorization conditions and convergence rates for markov chain monte carlo abstract general methods are provided for analyzing the convergence of discrete time general state space markov chains such as those used in stochastic simulation algorithms including the gibbs sampler the methods provide rigorous a priori bounds on how long these simulations should be run to give satisfactory results results are applied to two models of the gibbs sampler a bivariate normal model and a hierarchical poisson model with gamma conditionals the methods use the notion of minorization conditions for markov chains

exponential basis functions in solution of static and time harmonic elastic problems in a meshless style in this paper exponential basis functions ebfs are used in a boundary collocation style to solve engineering problems whose governing partial differential equations pdes are of constant coefficient type complex valued exponents are considered for the ebfs two dimensional elasto static and time harmonic elasto dynamic problems are chosen in this paper the solution procedure begins with first finding a set of appropriate ebfs and then considering the solution as a summation of such ebfs with unknown coefficients the unknown coefficients are determined by the satisfaction of the boundary conditions through a collocation method with the aid of a consistent and complex discrete transformation technique the basis and various forms of the transformation have been addressed and discussed we shall propose several strategies for selection of ebfs with the aid of the basis explained for the transformation while using the transformation the number of ebfs should not necessarily be equal to or less than the number of boundary information data a library of ebfs has also been presented for further use the effect of body forces is included in the solution via construction of particular solution by the use of the discrete transformation and another series of ebfs a number of sample problems are solved to demonstrate the capabilities of the method it has been shown that the time harmonic problems with high wave number can be solved without much effort the method categorized in meshless methods can be applied to many other problems in engineering mechanics and general physics since ebfs can easily be found for almost all problems with constant coefficient pdes

supplementary notes on the gaussian beam expansion the letter provides alternatively a simple way of computing the fresnel field integral a further extension to the gaussian beam expansion the zeroth order bessel function of the first kind is expanded into an approximate sum of gaussian functions the field integral is then expressible in terms of these simple functions the approach is useful in treatment of the field radiation problem for a large and important group of piston sources in acoustics as examples the calculation results for the uniform and the simply supported piston sources are presented in a good agreement with those evaluated by numerical integration

generation of the basis sets for multi gaussian ultrasonic beam models an overview by using a small number of gaussian basis functions one can synthesize the wave fields radiated from planar and focused piston transducers in the form of a superposition of gaussian beams since gaussian beams can be transmitted through complex geometries and media such multi gaussian beam models have become powerful simulation tools in previous studies the basis function expansion coefficients of multi gaussian beam models have been obtained by both spatial domain and k space domain methods here we will give an overview of these two methods and relate their expansion coefficients we will demonstrate that the expansion coefficients that have been optimized for circular piston transducers can also be used to generate improved field simulations for rectangular probes it will also be shown that because gaussian beams are only approximate paraxial solutions to the wave equation a multi gaussian beam model is ultimately limited in the accuracy it can obtain in the very near field

drift analysis and average time complexity of evolutionary algorithms the computational time complexity is an important topic in the theory of evolutionary algorithms eas this paper reports some new results on the average time complexity of eas based on drift analysis some useful drift conditions for deriving the time complexity of eas are studied including conditions under which an ea will take no more than polynomial time in problem size to solve a problem and conditions under which an ea will take at least exponential time in problem size to solve a problem the paper first presents the general results and then uses several problems as examples to illustrate how these general results can be applied to concrete problems in analyzing the average time complexity of eas while previous work only considered 1 1 eas without any crossover the eas considered in this paper are fairly general which use a finite population crossover mutation and selection 2001 elsevier science b v all rights reserved

reprint of on convergence analysis of particle swarm optimization algorithm abstract particle swarm optimization pso a population based stochastic optimization algorithm has been successfully used to solve many complicated optimization problems however analysis on algorithm convergence is still inadequate till now in this paper the martingale theory is applied to analyze the convergence of the standard pso spso firstly the swarm state sequence is defined and its markov properties are examined according to the theory of spso two closed sets the optimal particle state set and optimal swarm state set are then obtained afterwards a supermartingale is derived as the evolutionary sequence of particle swarm with the best fitness value finally the spso convergence analysis is carried out in terms of the supermartingale convergence theorem our results show that spso reaches the global optimum in probability moreover the analysis on spso proves that the quantum behaved particle swarm optimization qpso is also a global convergence algorithm the proof of the spso convergence in this work is new simple and more effective without specific implementation

population size versus runtime of a simple evolutionary algorithm evolutionary algorithms eas find numerous applications and practical knowledge on eas is immense in practice sophisticated population based eas employing selection mutation and crossover are applied in contrast theoretical analysis of eas often concentrates on very simple algorithms such as the 1 1 ea where the population size equals 1 in this paper the question is addressed whether the use of a population by itself can be advantageous a population based ea that neither makes use of crossover nor any diversity maintaining operator is investigated on an example function it is shown that an increase of the population size by a constant factor decreases the expected runtime from exponential to polynomial thereby the best gap known so far is improved from superpolynomial vs polynomial to exponential vs polynomial moreover it is proved that the exponential and polynomial runtime bounds occur with a probability exponentially close to one if the population size is a constant resp a small polynomial finally a second example function where only a small population leads to a polynomial runtime and a hierarchy result on the appropriate population size are presented the analyses show formally how the population size can lead to different attractors in the search space

a finite difference treatment of interface conditions for the parabolic wave equation the irregular interface a finite difference solution to the parabolic wave equation is extended to treat an irregular interface interface conditions are developed to preserve continuity of pressure and continuity of the normal component of particle velocity at the boundary between media having different sound speeds and densities a complete mathematical treatment for the case of an irregular interface is presented to demonstrate the method numerical results are obtained for sound propagation from deep to shallow water

rapid calculations of time harmonic nearfield pressures produced by rectangular pistons a rapid method for calculating the nearfield pressure distribution generated by a rectangular piston is derived for time harmonic excitations this rapid approach improves the numerical performance relative to the impulse response with an equivalent integral expression that removes the numerical singularities caused by inverse trigonometric functions the resulting errors are demonstrated in pressure field calculations using the time harmonic impulse response solution for a rectangular source 5 wavelengths wide by 7 5 wavelengths high simulations using this source geometry show that the rapid method eliminates the singularities introduced by the impulse response the results of pressure field computations are then evaluated in terms of relative errors and computational speeds the results show that when the same number of gauss abscissas are applied to both approaches for time harmonic pressure field calculations the rapid method is consistently faster than the impulse response and the rapid method consistently produces smaller maximum errors than the impulse response for specified maximum error values of 10 and 1 the rapid method is 2 6 times faster than the impulse response for pressure field calculations performed on a 61 by 101 point grid the rapid approach achieves even greater reductions in the computation time for smaller errors and larger grids

some extensions of the gaussian beam expansion radiation fields of the rectangular and the elliptical transducer a straightforward extension of gaussian beam expansion is presented for calculation of the fresnel field integral j j wen and m a breazeale j acoust soc am 83 1752 1756 1988 the source distribution function is expanded into the superposition of a series of two dimensional gaussian functions the corresponding radiation field is expressed as the superposition of these two dimensional gaussian beams and is then reduced to the computation of these simple functions this treatment overcomes the limit that the shape of source is of circular axial symmetry the numerical examples are presented for the field of the uniform elliptical and the rectangular piston transducers and agree well with the results given by complicated computation

an easily implementable fourth order method for the time integration of wave problems abstract we are concerned with the time integration of systems of ordinary differential equations arising from the space discretization of partial differential wave equations with smooth solutions a method is suggested that while being as easily implementable as the standard implicit mid point rule is fourth order accurate the new method is symplectic so that it is very well suited for long time integrations of problems with a hamiltonian structure numerical experiments are reported that refer to a fourth order galerkin space discretization of the korteweg de vries equation and to a pseudospectral space discretization of the same equation

method of lines study of nonlinear dispersive waves in this study we consider partial differential equation problems describing nonlinear wave phenomena e g a fully nonlinear third order korteweg de vries kdv equation the fourth order boussinesq equation the fifth order kaup kupershmidt equation and an extended kdv5 equation first we develop a method of lines solution strategy using an adaptive mesh refinement algorithm based on the equidistribution principle and spatial regularization techniques on the resulting highly nonuniform spatial grids the computation of high order derivative terms appears particularly delicate and we focus attention on the selection of appropriate approximation techniques finally we solve several illustrative problems and compare our computational approach to conventional solution techniques

a finite difference scheme for the k 2 2 compacton equation the k 2 2 equation introduced by rosenau and hyman is a wave equation that possesses solutions compactons that vanish outside a bounded interval of the spatial axis a finite difference scheme for this equation is suggested that can successfully cope with compacton interactions leading to negative waves we show rigorously that in those interactions a loss of smoothness of the solution necessarily takes place

on the approximation ability of evolutionary optimization with application to minimum set cover evolutionary algorithms eas are heuristic algorithms inspired by natural evolution they are often used to obtain satisficing solutions in practice in this paper we investigate a largely underexplored issue the approximation performance of eas in terms of how close the solution obtained is to an optimal solution we study an ea framework named simple ea with isolated population seip that can be implemented as a single or multi objective ea we analyze the approximation performance of seip using the partial ratio which characterizes the approximation ratio that can be guaranteed specifically we analyze seip using a set cover problem that is np hard we find that in a simple configuration seip efficiently achieves an h n approximation ratio the asymptotic lower bound for the unbounded set cover problem we also find that seip efficiently achieves an h k k 18k 9 approximation ratio the currently best achievable result for the k set cover problem moreover for an instance class of the k set cover problem we disclose how seip using either one bit or bit wise mutation can overcome the difficulty that limits the greedy algorithm

the normalized acoustic power of a thin clamped annular plate vibrating in a flat screen around a perpendicular semi infinite circular cylinder abstract the neumann boundary value problem is presented for the time harmonic excited steady state vibrations of a thin clamped annular plate embedded in a flat rigid baffle around a perpendicular circular cylindrical rigid semi infinite baffle the system of two coupled differential equations is solved for this purpose one of them being the wave equation of the fluid filling the space between the two baffles and the other being the equation of motion of the plate for its excited vibrations first the acoustic pressure is presented in its spectral form using the weber inverse transform then the time averaged acoustic power is presented using the plate s modal impedance coefficients and the coupling factors the modal coefficients are presented as the integrals together with the corresponding asymptotic formulations the influence of the cylindrical baffle on the acoustic power is analyzed numerically the fluid loading and the internal attenuation of the plate s vibrations are both included whereas the attenuation of the acoustic waves in fluid is neglected

on convergence analysis of particle swarm optimization algorithm abstract particle swarm optimization pso a population based stochastic optimization algorithm has been successfully used to solve many complicated optimization problems however analysis on algorithm convergence is still inadequate till now in this paper the martingale theory is applied to analyze the convergence of the standard pso spso firstly the swarm state sequence is defined and its markov properties are examined according to the theory of spso two closed sets the optimal particle state set and optimal swarm state set are then obtained afterwards a supermartingale is derived as the evolutionary sequence of particle swarm with the best fitness value finally the spso convergence analysis is carried out in terms of the supermartingale convergence theorem our results show that spso reaches the global optimum in probability moreover the analysis on spso proves that the quantum behaved particle swarm optimization qpso is also a global convergence algorithm the proof of the spso convergence in this work is new simple and more effective without specific implementation

rates of convergence of the hastings and metropolis algorithms we apply recent results in markov chain theory to hastings and metropolis algorithms with either independent or symmetric candidate distributions and provide necessary and sufficient conditions for the algorithms to converge at a geometric rate to a prescribed distribution pi in the independence case in mathbb r k these indicate that geometric convergence essentially occurs if and only if the candidate density is bounded below by a multiple of pi in the symmetric case in mathbb r only we show geometric convergence essentially occurs if and only if pi has geometric tails we also evaluate recently developed computable bounds on the rates of convergence in this context examples show that these theoretical bounds can be inherently extremely conservative although when the chain is stochastically monotone the bounds may well be effective

notes on the gaussian beam expansion a powerful gaussian beam expansion technique j j wen and m a breazeale j acoust soc am 83 1752 1756 1988 is widely used in calculating the fresnel field integral a basic ideal of this treatment is to expand the source distribution function into the superposition of a series of gaussian functions the evaluation of the radiation field is then greatly simplified as a supplement this paper presents a simple approach to determine the expansion coefficients for the sound source the results for the ultrasonic field radiated by piston transducers are typically given in a fairly good agreement with those calculated by numerical integration and breazeale s the limits of the present method are also discussed

a new simple fast and efficient algorithm for global optimization over continuous search space problems we propose a new stochastic global optimization method for continuous search space we chose ten benchmark functions to evaluate the ability of the proposed algorithm the results are compared with two other methods which are pso and de the proposed method obtains proper and fast solution and escapes from local optima being robust fast and needing less memory are the main features of the method optimization of non linear and non differentiable problems has been considered as an important issue for mathematicians and engineers a new stochastic global optimization method for non linear and non differentiable problems is proposed and extensively explained in this article it is a swarm based method which uses spherical boundaries in a vector search space to explore for the optimal solution having a few numbers of parameter to be adjusted being robust and fast needing small memory storage size and capability of escaping from local optima are the main features of this new algorithm to analyze and evaluate the capability of this novel method ten benchmark functions are chosen and the results are compared with two existing optimization algorithms which are differential evolution and particle swarm optimization comparisons are made based on the consistency in obtaining optimal solutions computation time and convergence profile results show the capability of the proposed method in finding a proper solution in a very short time and also escaping from local optima of the solution space

self similar radiation from numerical rosenau hyman compactons the numerical simulation of compactons solitary waves with compact support is characterized by the presence of spurious phenomena as numerically induced radiation which is illustrated here using four numerical methods applied to the rosenau hyman k p p equation both forward and backward radiations are emitted from the compacton presenting a self similar shape which has been illustrated graphically by the proper scaling a grid refinement study shows that the amplitude of the radiations decreases as the grid size does confirming its numerical origin the front velocity and the amplitude of both radiations have been studied as a function of both the compacton and the numerical parameters the amplitude of the radiations decreases exponentially in time being characterized by a nearly constant scaling exponent an ansatz for both the backward and forward radiations corresponding to a self similar function characterized by the scaling exponent is suggested by the present numerical results

finite element solution to the parabolic wave equation in seeking more ways to predict underwater sound fields the underwater acoustical parabolic wave equation is solved using the finite element fe method the mathematical theory for the finite element method in an n medium case is discussed when the conditions of continuity of pressure and continuity of the normal component of particle velocity are perfectly satisfied at each interface several propagation examples for horizontal and irregular interfaces are presented to demonstrate the capability of this effective fe method

the use of tail inequalities on the probable computational time of randomized search heuristics for the purpose of analyzing the time cost of evolutionary algorithms eas or other types of randomized search heuristics rshs with certain requirements on the probability of obtaining a target solution this paper proposes a new index called the probable computational time pct which complements expected running time analysis using simple tail inequalities such as markov s inequality and chebyshev s inequality we also provide basic properties of pct explicitly exhibiting the general relationships between the expected running time and the pct to present deeper estimations of the pct for specific rshs and problems we demonstrate a new inequality that is based on the general form of the chernoff inequality and previous methods such as fitness based partitions and potential functions which have been used to analyze the expected running time of rshs the precondition of the new inequality is that the total running time can be described as the sum of a linear combination of some independent geometrically distributed variables and a constant term the new inequality always provides meaningful upper bounds for the pct under such circumstances some applications of the new inequality for simple eas ant colony optimization aco and particle swarm optimization pso algorithms on simple pseudo boolean functions are illustrated in this paper

a 2d fast near field method for calculating near field pressures generated by apodized rectangular pistons analytical two dimensional 2d integral expressions are derived for fast calculations of time harmonic and transient near field pressures generated by apodized rectangular pistons these 2d expressions represent an extension of the fast near field method fnm for uniformly excited pistons after subdividing the rectangular piston into smaller rectangles the pressure produced by each of the smaller rectangles is calculated using the uniformly excited fnm expression for a rectangular piston and the total pressure generated by an apodized rectangular piston is the superposition of the pressures produced by all of the subdivided rectangles by exchanging summation variables and performing integration by parts a 2d apodized fnm expression is obtained and the resulting expression eliminates the numerical singularities that are otherwise present in numerical models of pressure fields generated by apodized rectangular pistons a simplified time space decomposition method is also described and this method further reduces the computation time for transient pressure fields the results are compared with the rayleigh sommerfeld integral and the field ii program for a rectangular source with each side equal to four wavelengths for time harmonic calculations with a 0 1 normalized root mean square error nrmse the apodized fnm is 4 14 times faster than the rayleigh sommerfeld integral and 59 43 times faster than the field ii program and for a 0 01 nrmse the apodized fnm is 12 50 times faster than the rayleigh sommerfeld integral and 155 06 times faster than the field ii program for transient calculations with a 0 1 nrmse the apodized fnm is 2 31 times faster than the rayleigh sommerfeld integral and 4 66 times faster than the field ii program and for a 0 01 nrmse the apodized fnm is 11 90 times faster than the rayleigh sommerfeld integral and 24 04 times faster than the field ii program thus the 2d apodized fnm is ideal for fast pressure calculations and for accurate reference calculations in the near field region

boundary infinite elements for the helmholtz equation in exterior domains a novel approach to the development of infinite element formulations for exterior problems of time harmonic acoustics is presented this approach is based on a functional which provides a general framework for domain based computation of exterior problems special cases include non reflecting boundary conditions such as the dtn method a prominent feature of this formulation is the lack of integration over the unbounded domain simplifying the task of discretization the original formulation is generalized to account for derivative discontinuities across infinite element boundaries typical of standard infinite element approximations continuity between finite elements and infinite elements is enforced weakly precluding compatibility requirements various infinite element approximations for two dimensional configurations with circular interfaces are presented implementation requirements are relatively simple numerical results demonstrate the good performance of this scheme 1998 john wiley sons ltd

on the convergence of the markov chain simulation method the markov chain simulation method has been successfully used in many problems including some that arise in bayesian statistics we give a self contained proof of the convergence of this method in general state spaces under conditions that are easy to verify

numerical radiation boundary conditions for unsteady transonic flow a family of numerical boundary conditions for far field computational boundaries in calculations involving unsteady transonic flow is devised these boundary conditions are developed in a systematic fashion from general principles both numerical and analytic comparisons with other currently used methods are given

local discontinuous galerkin methods for nonlinear dispersive equations we develop local discontinuous galerkin dg methods for solving nonlinear dispersive partial differential equations that have compactly supported traveling waves solutions the so called compactons the schemes we present extend the previous works of yan and shu on approximating solutions for linear dispersive equations and for certain kdv type equations we present two classes of dg methods for approximating solutions of such pdes first we generate nonlinearly stable numerical schemes with a stability condition that is induced from a conservation law of the pde an alternative approach is based on constructing linearly stable schemes i e schemes that are linearly stable to small perturbations the numerical simulations we present verify the desired properties of the methods including their expected order of accuracy in particular we demonstrate the potential advantages of using dg methods over pseudospectral methods in situations where discontinuous fronts and rapid oscillations co exist in a solution

transient field of a baffled planar piston having an arbitrary vibration amplitude distribution a theoretical model is presented for evaluating the transient velocity potential and pressure fields radiated by a pulsed planar piston set in an infinite rigid baffle and having an arbitrary spatial velocity distribution the method is based on the development of a generalized spatial impulse response function which describes the velocity potential either at a point or averaged over a finite receiving surface resulting from the velocity impulse excitation of a uniformly or nonuniformly vibrating piston source for the specific case of a circular source and receiver this function is plotted using several source distributions and receiver sizes then corresponding plots are presented for two piston velocity waveforms a gaussian pulse and a gaussian modulated sinusoidal burst these plots are compared and the effects of a nonuniformly vibrating source and finite receiver are discussed lastly a previous solution by schoch in which the field of a rigid piston is separated into geometrical and boundary d

on the method of modified equations i asymptotic analysis of the euler forward difference method the method of modified equations is studied as a technique for the analysis of finite difference equations the non uniqueness of the modified equation of a difference method is stressed and three kinds of modified equations are introduced the first modified or equivalent equation is the natural pseudo differential operator associated to the original numerical method linear and nonlinear combinations of the equivalent equation and their derivatives yield the second modified or second equivalent equation and the third modified or simply modified equation respectively for linear problems with constant coefficients the three kinds of modified equations are equivalent among them and to the original difference scheme for nonlinear problems the three kinds of modified equations are asymptotically equivalent in the sense that an asymptotic analysis of these equations with the time step as small parameter yields exactly the same results in this paper both regular and multiple scales asymptotic techniques are used for the analysis of the euler forward difference method and the resulting asymptotic expansions are verified for several nonlinear autonomous ordinary differential equations it is shown that when the resulting asymptotic expansion is uniformly valid the asymptotic method yields very accurate results if the solution of the leading order equation is smooth and does not blow up even for large step sizes

a broadband fast multipole accelerated boundary element method for the three dimensional helmholtz equation the development of a fast multipole method fmm accelerated iterative solution of the boundary element method bem for the helmholtz equations in three dimensions is described the fmm for the helmholtz equation is significantly different for problems with low and high kd where k is the wavenumber and d the domain size and for large problems the method must be switched between levels of the hierarchy the bem requires several approximate computations numerical quadrature approximations of the boundary shapes using elements and these errors must be balanced against approximations introduced by the fmm and the convergence criterion for iterative solution these different errors must all be chosen in a way that on the one hand excess work is not done and on the other that the error achieved by the overall computation is acceptable details of translation operators for low and high kd choice of representations and bem quadrature schemes all consistent with these approximations are described

exponential basis functions in solution of problems with fully incompressible materials in this paper exponential basis functions ebfs satisfying the governing equations of elastic problems with incompressible materials are introduced due to similarity between elasticity problems and steady state fluid problems the bases found for the former problems are used for latter problems we discuss on using single field form known as displacement velocity based formulation and also on using a two field form known as u p formulation in the first formulation we find the pressure bases through performing a limit analysis using a fictitious bulk modulus while in the second formulation the bases are found directly by considering the pressure as a separate variable in the second formulation we directly apply the condition of incompressibility it is shown that both formulations yield identical bases meaning that the first one may be used in a standard approach however it is also shown that when the incompressibility condition is applied by a laplacian of pressure in the second formulation some additional spurious ebfs may be obtained having defined appropriate bases we follow the solution strategy recently introduced by the authors for other engineering problems some well known benchmark problems are solved to show the capabilities of the method

a new approach to estimating the expected first hitting time of evolutionary algorithms evolutionary algorithms ea have been shown to be very effective in solving practical problems yet many important theoretical issues of them are not clear the expected first hitting time is one of the most important theoretical issues of evolutionary algorithms since it implies the average computational time complexity in this paper we establish a bridge between the expected first hitting time and another important theoretical issue i e convergence rate through this bridge we propose a new general approach to estimating the expected first hitting time using this approach we analyze eas with different configurations including three mutation operators with without population a recombination operator and a time variant mutation operator on a hard problem the results show that the proposed approach is helpful for analyzing a broad range of evolutionary algorithms moreover we give an explanation of what makes a problem hard to eas and based on the recognition we prove the hardness of a general problem

time stepping in petrov galerkin methods based on cubic b splines for compactons abstract four numerical methods with first to fourth order of accuracy have been developed for the time integration of the rosenau hyman k 2 2 equation the error in the solution and the invariants for the propagation of one compacton and the stability in collisions among compactons have been studied using these methods numerically induced radiation has also been characterized by means of wavefront velocity and wavefront amplitude showing that the self similarity of the radiation wavepackets observed in the numerical results is a consequence of the time stepping method among the four methods studied in this paper the best results in terms of accuracy computational cost and stability have been obtained by means of using the second order time integration method

how to analyse evolutionary algorithms many variants of evolutionary algorithms have been designed and applied the experimental knowledge is immense the rigorous analysis of evolutionary algorithms is difficult but such a theory can help to understand design and teach evolutionary algorithms in this survey first the history of attempts to analyse evolutionary algorithms is described and then new methods for continuous as well as discrete search spaces are presented and discussed

stability and dynamical properties of rosenau hyman compactons using pade approximants we present a systematic approach for calculating higher order derivatives of smooth functions on a uniform grid using pade approximants we illustrate our findings by deriving higher order approximations using traditional second order finite difference formulas as our starting point we employ these schemes to study the stability and dynamical properties of k 2 2 rosenau hyman compactons including the collision of two compactons and resultant shock formation our approach uses a differencing scheme involving only nearest and next to nearest neighbors on a uniform spatial grid the partial differential equation for the compactons involves first second and third partial derivatives in the spatial coordinate and we concentrate on four different fourth order methods which differ in the possibility of increasing the degree of accuracy or not of one of the spatial derivatives to sixth order a method designed to reduce round off errors was found to be the most accurate approximation in stability studies of single solitary waves even though all derivates are accurate only to fourth order simulating compacton scattering requires the addition of fourth derivatives related to artificial viscosity for those problems the different choices lead to different amounts of spurious radiation and we compare the virtues of the different choices

element free galerkin solutions for helmholtz problems fomulation and numerical assessment of the pollution effect abstract the element free galerkin method efgm a particular case of the meshless methods is examined in its application to acoustic wave propagation addressed by the helmholtz equation dispersion and pollution effects two problems encountered by the classical numerical methods are reviewed numerical tests on two dimensional problems focus on the parameters governing the formulation of the efgm they also demonstrate that the efgm is affected by dispersion and pollution effects as well as fem but these effects are rather low showing that the efgm is a promising method

numerical methods based on modified equations for nonlinear evolution equations with compactons abstract compactons are traveling wave solutions with compact support resulting from the balance of both nonlinearity and nonlinear dispersion numerical methods with second fourth sixth and eighth order approximations to the spatial derivatives obtained by means of the method of modified equations applied to the ismail taha finite difference scheme for the rosenau hyman equation are developed the whole set of methods is compared among them in accuracy invariant conservation and in compacton collisions the best method among those studied in terms of the tradeoff between accuracy and computational cost is determined

comparison of spheroidal and eigenfunction expansion trial functions for a membrane in an infinite baffle the on axis far field pressure response of a circular membrane in an infinite baffle when driven by a uniformly distributed electrostatic force is calculated using two different trial functions for the surface velocity distribution the first is an expansion based upon a solution to the free space wave equation in oblate spheroidal coordinates which has already been derived in a previous paper j acoust soc am 120 5 2460 2477 2006 and the second is a membrane eigenfunction expansion or bessel series which is rigorously derived in this letter although the latter can be used as a basis for calculating a number of different radiation characteristics such as the radiation impedance or directivity etc only the on axis far field sound pressure is considered here the results are compared and discussed

exponential basis functions in space and time a meshless method for 2d time dependent problems in this paper we present a method based on using exponential basis functions ebfs to solve well known two dimensional time dependent engineering problems such as elasto dynamic ones the formulation has much in common with those in three dimensional problems while time is taken as the third axis the solution is first approximated by a summation of ebfs and then completed by satisfying the time dependent boundary conditions as well as the initial conditions through a collocation method this is performed by considering a series of spatial and time dependent boundary points to satisfy the boundary conditions through a mixed collocation method the solution method is presented in a time marching form which is capable of solving variety of problems such as transient heat conduction and wave propagation in solids several problems are solved to demonstrate the capabilities of the method

towards an analytic framework for analysing the computation time of evolutionary algorithms in spite of many applications of evolutionary algorithms in optimisation theoretical results on the computation time and time complexity of evolutionary algorithms on different optimisation problems are relatively few it is still unclear when an evolutionary algorithm is expected to solve an optimisation problem efficiently or otherwise this paper gives a general analytic framework for analysing first hitting times of evolutionary algorithms the framework is built on the absorbing markov chain model of evolutionary algorithms the first step towards a systematic comparative study among different eas and their first hitting times has been made in the paper

convergence analysis of canonical genetic algorithms this paper analyzes the convergence properties of the canonical genetic algorithm cga with mutation crossover and proportional reproduction applied to static optimization problems it is proved by means of homogeneous finite markov chain analysis that a cga will never converge to the global optimum regardless of the initialization crossover operator and objective function but variants of cga s that always maintain the best solution in the population either before or after selection are shown to converge to the global optimum due to the irreducibility property of the underlying original nonconvergent cga these results are discussed with respect to the schema theorem