three dimensional exact solution for the vibration of functionally graded rectangular plates abstract a three dimensional exact solution is presented for free and forced vibrations of simply supported functionally graded rectangular plates suitable displacement functions that identically satisfy boundary conditions are used to reduce equations governing steady state vibrations of a plate to a set of coupled ordinary differential equations which are then solved by employing the power series method the exact solution is valid for thick and thin plates and for arbitrary variation of material properties in the thickness direction results are presented for two constituent metal ceramic functionally graded rectangular plates that have a power law through the thickness variation of the volume fractions of the constituents the effective material properties at a point are estimated by either the mori tanaka or the self consistent schemes exact natural frequencies displacements and stresses are used to assess the accuracy of the classical plate theory the first order shear deformation theory and a third order shear deformation theory for functionally graded plates parametric studies are performed for varying ceramic volume fractions volume fraction profiles and length to thickness ratios results are also computed for a functionally graded plate that has a varying microstructure in the thickness direction using a combination of the mori tanaka and the self consistent methods forced vibrations of a plate with a sinusoidal spatial variation of the pressure applied on its top surface are scrutinized

analysis of four numerical schemes for a nonlinear klein gordon equation we compare the properties of four explicit finite difference schemes used to integrate the nonlinear klein gordon equation f t t f x x f f 0 it turns out that the energy conserving scheme is the most suitable to study the long time behavior of the solutions the same result is found for the special case of no spatial dependence

fractional langevin model of memory in financial markets the separation of the microscopic and macroscopic time scales is necessary for the validity of ordinary statistical physics and the dynamical description embodied in the langevin equation when the microscopic time scale diverges the differential equations on the macroscopic level are no longer valid and must be replaced with fractional differential equations of motion in particular we obtain a fractional differential stochastic equation of motion after decades of statistical analysis of financial time series certain stylized facts have emerged including the statistics of stock price fluctuations having fat tails and their linear correlations in time being exceedingly short lived on the other hand the magnitude of these fluctuations and other such measures of market volatility possess temporal correlations that decay as an inverse power law one explanation of this long term memory is that it is a consequence of the time scale separation between microscopic and macroscopic economic variables we propose a fractional langevin equation as a dynamical model of the observed memory in financial time series

interest rates in quantum finance the wilson expansion and hamiltonian interest rate instruments form a major component of the capital markets the libor market model lmm is the finance industry standard interest rate model for both libor and euribor which are the most important interest rates the quantum finance formulation of the libor market model is given in this paper and leads to a key generalization all the libors for different future times are imperfectly correlated a key difference between a forward interest rate model and the lmm lies in the fact that the lmm is calibrated directly from the observed market interest rates the short distance wilson expansion phys rev 179 1499 1969 of a gaussian quantum field is shown to provide the generalization of ito calculus in particular the wilson expansion of the gaussian quantum field a t x driving the libors yields a derivation of the libor drift term that incorporates imperfect correlations of the different libors the logarithm of libor phi t x is defined and provides an efficient and compact representation of the quantum field theory of the libor market model the lagrangian and feynman path integrals of the libor market model of interest rates are obtained as well as a derivation given by its hamiltonian the hamiltonian formulation of the martingale condition provides an exact solution for the nonlinear drift of the libor market model the quantum finance formulation of the lmm is shown to reduce to the industry standard bruce gatarek musiela jamshidian model when the forward interest rates are taken to be exactly correlated

an explicit form solution to the plane elasticity and thermoelasticity problems for anisotropic and inhomogeneous solids this paper presents an analytical approach to solve the plane elasticity and thermoelasticity problems for inhomogeneous orthotropic planes half planes and strips solution of the problems is reduced to the governing volterra integral equation formulated for the key function and accompanied by the corresponding integral conditions by making use of the resolvent kernel technique the governing equation is solved and the solution to the original problem is presented in explicit form

multifractal analysis of chinese stock volatilities based on the partition function approach abstract we have performed a detailed multifractal analysis on the 1 min volatility of two indexes and 1139 stocks in the chinese stock markets based on the partition function approach the partition function q s scales as a power law with respect to the box size s the scaling exponents q form a nonlinear function of q statistical tests based on bootstrapping show that the extracted multifractal nature is significant at the 1 significance level the individual securities can be well modeled by the p model in turbulence with p 0 40 0 02 based on the idea of ensemble averaging including quenched and annealed average we treat each stock exchange as a whole and confirm the existence of multifractal nature in the chinese stock markets

bonded dissimilar strips with a crack perpendicular to the functionally graded interface the mode i crack problem for two dissimilar infinite strips bonded through a functionally graded interfacial zone is investigated within the framework of plane elasticity the graded interfacial zone is treated as a nonhomogeneous continuum having the continuously varying elastic modulus between the dissimilar homogeneous strips a crack is assumed to be embedded in one of the strips perpendicular to the nominal interface with the aid of the stiffness matrix approach a set of homogeneous conditions relevant to the proposed crack problem is readily satisfied subsequent application of the mixed conditions on the cracked plane then leads to a singular integral equation of the first kind which is solved numerically in consequence the variations of stress intensity factors are provided as functions of geometric and material parameters of the bonded structure the effect of the material nonhomogeneity in the interfacial zone is further addressed by measuring the degree of correspondence with the results that are obtained based on the use of the homogenized interfacial elastic property

axsiymmetric crack problem in bonded materials with a graded interfacial region the problem of a penny shaped crack in homogeneous dissimilar materials bonded through an interfacial region with graded mechanical properties is considered the applied loads are assumed to be axisymmetric but otherwise arbitrary the shear modulus of the interfacial region is assumed to be 2 z 1exp z and that of the adherents 1 and 3 1 1exp h h being the thickness of the region a crack of radius is located at the z 0 plane the axisymmetric mode iii torsion problem is separated and treated elsewhere because of material nonhomogeneity the deformation modes i and ii considered in this study are always coupled the related mixed boundary value problem is reduced to a system of singular integral equations the asymptotic behavior of the stress state near the crack tip is examined and the influence of the thickness ratio ha and the material nonhomogeneity parameter on the stress intensity factors and the strain energy release rate is investigated the results show that the stress state near the crack tip would always have standard square root singularity provided h 0 or the material properties are continuous but not necessarily differentiable functions of z

eigenvector perturbations of complex networks abstract recently spectral perturbations involving eigenvalue and eigenvector perturbations which have attracted more attentions than conventional topological perturbations are used to analyze and promote the robustness of complex networks however to the best of our knowledge the study of eigenvector perturbation and the equivalence between it and topological perturbation has not been found yet in this paper we first deduce the mathematical relationship between eigenvalue perturbation and its corresponding eigenvector perturbation for network reconstructions afterwards two perturbed forms of eigenvector spectrum global perturbation and local perturbation are defined such that we can examine the impacts of eigenvector perturbations on network robustness and compare those to the impacts of topological perturbations on robustness meanwhile the theoretical ranges of the allowed values of two eigenvector perturbation factors are derived in terms of the accurate reconstruction condition of networks and validated by experimental simulations by comparison our finding is that the eigenvector perturbations we define seem equivalent to topological perturbations

solving shifted linear systems with restarted gmres augmented with error approximations abstract in this paper we investigate a variant of the restarted gmres method for solving a series of large sparse linear systems restarting is carried out by augmenting krylov subspaces with some recently generated error approximations from the seed system the method can preserve a nice property that allows solving the seed and the added linear systems at the cost of only one matrix vector multiplication per iteration compared with solving each added linear system separately the advantage of the new scheme is to lower down the overall cost of solving all added linear systems numerical experiments illustrate the efficiency of the acceleration strategy

trigonometric collocation methods based on lagrange basis polynomials for multi frequency oscillatory second order differential equations abstract in the present work a kind of trigonometric collocation methods based on lagrange basis polynomials is developed for effectively solving multi frequency oscillatory second order differential equations q t m q t f q t the properties of the obtained methods are investigated it is shown that the convergent condition of these methods is independent of m which is very crucial for solving oscillatory systems a fourth order scheme of the methods is presented numerical experiments are implemented to show the remarkable efficiency of the methods proposed in this paper

wave scattering by cracks in inhomogeneous continua using biem elastic wave scattering by cracks in inhomogeneous geological continua with depth dependent material parameters and under conditions of plane strain is studied in this work a restricted case of inhomogeneity is considered where poisson s ratio is fixed at one quarter while both shear modulus and density profile vary with depth but proportionally to each other furthermore time harmonic conditions are assumed to hold for this type of material the body wave speeds remain macroscopically constant and it becomes possible to recover exact green functions for the crack free inhomogeneous continuum by using an algebraic transformation method proposed in earlier work as a first step in a subsequent step the complete elastodynamic fundamental solution along with its spatial derivatives and an asymptotic expansion for small argument are all derived in closed form using the radon transform next a non hypersingular traction based boundary integral equation method biem formulation for solving boundary value problems with internal cracks is presented specifically the biem is used for computing stress intensity factors and scattered wave displacement amplitudes for an inclined line crack in an otherwise inhomogeneous continuum that is being swept by either pressure waves or vertically polarized shear waves at an arbitrary angle of incidence with respect to the horizontal direction the numerical results obtained herein reveal substantial differences between homogeneous and continuously inhomogeneous materials containing a crack in terms of their dynamic response where the latter case is assumed to give a more realistic representation of geological deposits compared to the former one finally these types of examples plus the benchmark case used for validation serve to illustrate the present approach and to show its potential for solving complex problems not just in geophysics but also in mechanics

generalized domain independent interaction integral for solving the stress intensity factors of nonhomogeneous materials abstract the generalized domain independent interaction integral dii integral is investigated due to its extremely promising application in solving the stress intensity factors sifs of nonhomogeneous materials with complex interfaces a recent study revealed that the dii integral which is domain independent for material interfaces can be established by defining an appropriate auxiliary field regrettably the kind of auxiliary field that can be used is not very clear this work first discusses the conditions that the auxiliary field must satisfy for establishing a dii integral and provides a framework for designing more applicable auxiliary fields in this framework a generalized auxiliary field and the corresponding generalized dii integral are derived the generalized auxiliary field contains two free constants and can be expressed as the linear combination of a widely used auxiliary field and a new auxiliary field which are referred to as the crack face traction free auxiliary field and the zero mean stress auxiliary field respectively the generalized auxiliary field is effective in establishing the dii integral for purely mechanical loading and the zero mean stress auxiliary field is also effective in the establishment of the dii integral for isotropic mismatch strain problems the generalized dii integral is the linear function of mode i and mode ii sifs and its expression does not involve the free constants in the generalized auxiliary field then a patched extended finite element method xfem is briefly introduced to remove the crack tip enrichment and instead employ a patched mesh in the modeling the patched xfem does not depend on the material constitutive relations and thus has a larger applicable scale than does the traditional xfem finally the dii integral combined with the patched xfem is employed to investigate four representative crack problems numerical examples show that the generalized dii integral exhibits good domain independence for homogeneous nonhomogeneous and discontinuous properties although the numerical values of the dii integral do not remain constant for different values of the free constants due to numerical errors good numerical precision can be achieved if the free constants do not deviate too much from those used in the crack face traction free auxiliary field in addition the dii integral using the zero mean stress auxiliary field is demonstrated to be reliable and convenient in solving the sifs of particulate composites under an initial thermal strain

fractionally integrated process with power law correlations in variables and magnitudes we propose a new stochastic process de ned by only two parameters 1 and 2 which generates power law correlations or anticorrelations in the variable increments and power law correlations in their magnitudes to account for empirical observations in a range of physical systems to demonstrate the utility of our process we consider the case with power law anticorrelations in the variable increments and power law correlations in their magnitudes to model scaling properties in heartbeat data the parameters 1 and 2 control separately the correlations in the increments and their magnitudes and we nd linear relations between each parameter and the corresponding correlation exponent

a wave function for stock market returns the instantaneous return on the financial times stock exchange ftse all share index is viewed as a frictionless particle moving in a one dimensional square well but where there is a non trivial probability of the particle tunneling into the well s retaining walls our analysis demonstrates how the complementarity principle from quantum mechanics applies to stock market prices and of how the wave function presented by it leads to a probability density which exhibits strong compatibility with returns earned on the ftse all share index in particular our analysis shows that the probability density for stock market returns is highly leptokurtic with slight though not significant negative skewness moreover the moments of the probability density determined under the complementarity principle employed here are all convergent in contrast to many of the probability density functions on which the received theory of finance is based

two dimensional thermoelastic contact problem of functionally graded materials involving frictional heating the two dimensional thermoelastic sliding frictional contact of functionally graded material fgm coated half plane under the plane strain deformation is investigated in this paper a rigid punch is sliding over the surface of the fgm coating with a constant velocity frictional heating with its value proportional to contact pressure friction coefficient and sliding velocity is generated at the interface between the punch and the fgm coating the material properties of the coating vary exponentially along the thickness direction in order to solve the heat conduction equation analytically the homogeneous multi layered model is adopted for treating the graded thermal diffusivity coefficient with other thermomechanical properties being kept as the given exponential forms the transfer matrix method and fourier integral transform technique are employed to convert the problem into a cauchy singular integral equation which is then solved numerically to obtain the unknown contact pressure and the in plane component of the surface stresses the effects of the gradient index peclet number and friction coefficient on the thermoelastic contact characteristics are discussed in detail numerical results show that the distribution of the contact stress can be altered and therefore the thermoelastic contact damage can be modified by adjusting the gradient index peclet number and friction coefficient

estimating the distribution of volatility of realized stock returns and exchange rate changes abstract realized stock return volatility is modelled with a distribution based on the laplace distribution the moment properties of suggested volatility distribution are derived the properties of distribution correspond to the empirical regularities found in the finance literature ml estimator for is also provided the advantage of laplace approach lies in estimating from returns distribution f x directly instead of volatility distribution based on bias sensitive standard deviation estimates the goodness to fit tests with 5 day standard deviations of daily hex closing price returns in period 3 1 1983 4 3 2003 daily s p500 closing stock index returns in period 1 3 1950 27 3 2003 and daily usd euro exchange rate changes in period 28 12 1978 28 2 2003 support the suggested volatility distribution model

path integral approach to quantum brownian motion abstract we apply the influence functional method of feynman and vernon to the study of brownian motion at arbitrary temperature by choosing a specific model for the dissipative interaction of the system of interest with its environment we are able to evaluate the influence functional in closed form and express it in terms of a few parameters such as the phenomenological viscosity coefficient we show that in the limit h 0 the results obtained from the influence functional formalism reduce to the classical fokker planck equation in the case of a simple harmonic oscillator with arbitrarily strong damping and at arbitrary temperature we obtain an explicit expression for the time evolution of the complete density matrix x x t when the system starts in a particular kind of pure state we compare our results with those of other approaches to the problem of dissipation in quantum mechanics

study of a market model with conservative exchanges on complex networks abstract many models of market dynamics make use of the idea of conservative wealth exchanges among economic agents a few years ago an exchange model using extremal dynamics was developed and a very interesting result was obtained a self generated minimum wealth or poverty line on the other hand the wealth distribution exhibited an exponential shape as a function of the square of the wealth these results have been obtained both considering exchanges between nearest neighbors or in a mean field scheme in the present paper we study the effect of distributing the agents on a complex network we have considered archetypical complex networks erdos renyi random networks and scale free networks the presence of a poverty line with finite wealth is preserved but spatial correlations are important particularly between the degree of the node and the wealth we present a detailed study of the correlations as well as the changes in the gini coefficient that measures the inequality as a function of the type and average degree of the considered networks

a filon type asymptotic approach to solving highly oscillatory second order initial value problems abstract in this paper we analyze and design filon type asymptotic methods for solving highly oscillatory second order initial value problems q t mq t f t q t q t where m is a non singular and diagonalizable matrix having large eigenvalues and m 1 we first derive filon type asymptotic methods for highly oscillatory linear systems and then extend the methods to highly oscillatory nonlinear systems the integrators are a blend of the existing filon type methods and asymptotic methods based on the variation of constants formula it is shown that the new integrators are convergent and the accuracy of the new integrators is improved as m grows large this point is significant and powerful for effectively dealing with highly oscillatory systems numerical experiments are carried out and the numerical results show the advantage and efficiency of our new integrators as compared with existing numerical methods for highly oscillatory problems from the scientific literature

modeling method for a crack problem of functionally graded materials with arbitrary properties piecewise exponential model abstract a new model piecewise exponential model pe model is developed to investigate the crack problem of the functionally graded materials fgms with arbitrary properties in the pe model the functionally graded material is divided into some nonhomogeneous layers along the gradient direction of the properties with each layer s properties varying exponentially by this way the real material properties can be approached by a series of exponential functions since the real material properties are used on both surfaces of each nonhomogeneous layer the nature of continuously varying properties of fgms can be approached accurately the influences of the local nonhomogeneity on the crack tip fields can be fully considered by using the new model the fracture problem of a functionally graded strip with arbitrary properties and a crack vertical to the free surfaces is studied the integral transform method the theory of residues and the theory of singular integral equation are applied some representative samples with different kinds of nonhomogeneous properties are analyzed and the corresponding stress intensity factors sifs are presented it is shown that the pe mode is effective for investigating the crack problems of the fgms with arbitrary properties

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

a gautschi type method for oscillatory second order differential equations we study a numerical method for second order differential equations in which high frequency oscillations are generated by a linear part for example semilinear wave equations are of this type the numerical scheme is based on the requirement that it solves linear problems with constant inhomogeneity exactly we prove that the method admits second order error bounds which are independent of the product of the step size with the frequencies our analysis also provides new insight into the m ollified impulse method of garcia archilla sanz serna and skeel we include results of numerical experiments with the sine gordon equation

on the nonlinear axisymmetric dynamic buckling behavior of clamped functionally graded spherical caps abstract here the dynamic thermal buckling behavior of functionally graded spherical caps is studied considering geometric nonlinearity based on von karman s assumptions the formulation is based on first order shear deformation theory and it includes the in plane and rotary inertia effects the material properties are graded in the thickness direction according to the power law distribution in terms of volume fractions of the material constituents the effective material properties are evaluated using homogenization method the governing equations obtained using finite element approach are solved employing the newmark s integration technique coupled with a modified newton raphson iteration scheme the pressure load corresponding to a sudden jump in the maximum average displacement in the time history of the shell structure is taken as the dynamic buckling load the present model is validated against the available isotropic case a detailed numerical study is carried out to highlight the influences of shell geometries power law index of functional graded material and boundary conditions on the dynamic buckling load of shallow spherical shells

efficient energy preserving integrators for oscillatory hamiltonian systems in this paper we focus our attention on deriving and analyzing an efficient energy preserving formula for the system of nonlinear oscillatory or highly oscillatory second order differential equations q t mq t f q t where m is a symmetric positive semi definite matrix with m 1 and f q q u q is the negative gradient of a real valued function u q this system is a hamiltonian system with the hamiltonian h p q 1 2 p t p 1 2 q t mq u q the energy preserving formula exactly preserves the hamiltonian we analyze in detail the properties of the energy preserving formula and propose new efficient energy preserving integrators in the sense of numerical implementation the convergence analysis of the fixed point iteration is presented for the implicit integrators proposed in this paper it is shown that the convergence of implicit average vector field methods is dependent on m whereas the convergence of the new energy preserving integrators is independent of m the fermi pasta ulam problem and the sine gordon equation are carried out numerically to show the competence and efficiency of the novel integrators in comparison with the well known average vector field methods in the scientific literature

volume preserving exponential integrators and their applications abstract it is well known that various dynamical systems preserve volume in phase space such as all hamiltonian systems this qualitative geometrical property of the analytical solution should be respected in the sense of geometric integration this paper studies the volume preserving property of exponential integrators for different vector fields for exponential integrators we first derive a necessary and sufficient condition of volume preservation then based on this condition volume preserving exponential integrators are discussed in detail for four kinds of vector fields it is shown that symplectic exponential integrators can be volume preserving for a much larger class of vector fields than hamiltonian systems on the basis of the analysis some applications of volume preserving exponential integrators are discussed for solving highly oscillatory second order systems novel volume preserving exponential integrators are derived and for separable partitioned systems extended runge kutta nystrom erkn integrators of volume preservation are presented moreover the volume preservation of runge kutta nystrom rkn methods is also discussed five illustrative numerical experiments are carried out to demonstrate the notable superiority of volume preserving exponential integrators in comparison with volume preserving runge kutta methods

an operator like description of love affairs we adopt the so called occupation number representation originally used in quantum mechanics and recently considered in the description of stock markets in the analysis of the dynamics of love relations we start with a simple model involving two actors alice and bob in the linear case we obtain periodic dynamics whereas in the nonlinear regime either periodic or quasi periodic solutions are found then we extend the model to a love triangle involving alice bob and a third actress carla interesting features appear and in particular we find analytical conditions for the linear model of the love triangle to have periodic or quasi periodic solutions numerical solutions are exhibited in the nonlinear case

a quantum anharmonic oscillator model for the stock market abstract a financially interpretable quantum model is proposed to study the probability distributions of the stock price return the dynamics of a quantum particle is considered an analog of the motion of stock price then the probability distributions of price return can be computed from the wave functions that evolve according to schrodinger equation instead of a harmonic oscillator in previous studies a quantum anharmonic oscillator is applied to the stock in liquid market the leptokurtic distributions of price return can be reproduced by our quantum model with the introduction of mixed state and multi potential the trend following dominant market in which the price return follows a bimodal distribution is discussed as a specific case of the illiquid market

explicit exponential runge kutta methods for semilinear parabolic problems the aim of this paper is to analyze explicit exponential runge kutta methods for the time integration of semilinear parabolic problems the analysis is performed in an abstract banach space framework of sectorial operators and locally lipschitz continuous nonlinearities we commence by giving a new and short derivation of the classical nonstiff order conditions for exponential runge kutta methods but the main interest of our paper lies in the stiff case by expanding the errors of the numerical method in terms of the solution we derive new order conditions that form the basis of our error bounds for parabolic problems we show convergence for methods up to order four and we analyze methods that were recently presented in the literature these methods have classical order four but they do not satisfy some of the new conditions therefore an order reduction is expected we present numerical experiments which show that this order reduction in fact arises in practical examples based on our new conditions we finally construct methods that do not suffer from order reduction

axisymmetric problem on the indentation of a hot circular punch into an arbitrarily nonhomogeneous half space abstract this paper addresses an axisymmetric quasi static contact problem on both thermal and mechanical interactions of a circular punch and a nonhomogeneous elastic half space whose mechanical and thermophysical properties are assumed to be arbitrary functions of the depth coordinate to solve the formulated boundary value problem the technique of hankel s integral transformation is used using the bilateral asymptotic method an approximate analytical numerical solution is constructed for the heat flux boundary displacements of the half space and contact stress under the punch numerical implementation is performed for different dependences of the material properties on the depth of the half space

on semi convergence of parameterized shss method for a class of singular complex symmetric linear systems abstract in this paper we use the parameterized single step hss p shss iterative method to solve a broad class of singular complex symmetric linear systems the semi convergence properties of the p shss method are derived under suitable conditions moreover some properties of the preconditioned matrix and the optimal parameters are analyzed in detail numerical experiments are given to support our theoretical results and show the effectiveness of the p shss method either as a solver or as a preconditioner

effects of material gradients on transient dynamic mode iii stress intensity factors in a fgm abstract this paper presents a transient dynamic crack analysis for a functionally graded material fgm by using a hypersingular time domain boundary integral equation method the spatial variations of the material parameters of the fgm are described by an exponential law a numerical solution procedure is developed for solving the hypersingular time domain traction bie to avoid the use of time dependent green s functions which are not available for general fgm a convolution quadrature formula is adopted for approximating the temporal convolution while a galerkin method is applied for the spatial discretization of the hypersingular time domain traction bie numerical results for the transient dynamic stress intensity factors for a finite crack in an infinite and linear elastic fgm subjected to an impact anti plane crack face loading are presented and discussed the effects of the material gradients of the fgm on the transient dynamic stress intensity factors and their dynamic overshoot over the corresponding static stress intensity factors are analyzed

thermodynamics of inequalities from precariousness to economic stratification growing economic inequalities are observed in several countries throughout the world following pareto the power law structure of these inequalities has been the subject of much theoretical and empirical work but their nonequilibrium dynamics e g after a policy change remains incompletely understood here we introduce a thermodynamical theory of inequalities based on the analogy between economic stratification and statistical entropy within this framework we identify the combination of upward mobility with precariousness as a fundamental driver of inequality we formalize this statement by a second law inequality displaying upward mobility and precariousness as thermodynamic conjugate variables we estimate the time scale for the relaxation of the wealth distribution after a sudden change of the after tax return on capital our method can be generalized to gain insight into the dynamics of inequalities in any markovian model of socioeconomic interactions

dynamic stress intensity factors around a cylindrical crack in an infinite elastic medium subject to impact load this paper investigates transient stresses around a cylindrical crack in an infinite elastic medium subject to impact loads incoming stress waves resulting from the impact load impinge on the crack in a direction perpendicular to the crack axis in the laplace transform domain by means of the fourier transform technique the mixed boundary value equations with respect to stresses and displacements were reduced to two sets of dual integral equations to solve the equations the differences in the crack surface displacements were expanded in a series of functions that are zero outside the crack the boundary conditions for the crack were satisfied by means of the schmidt method stress intensity factors were defined in the laplace transform domain and were numerically inverted to physical space numerical calculations were carried out for the dynamic stress intensity factors corresponding to some typical shapes assumed for the cylindrical crack

the minimal length uncertainty and the quantum model for the stock market abstract we generalize the recently proposed quantum model for the stock market by zhang and huang to make it consistent with the discrete nature of the stock price in this formalism the price of the stock and its trend satisfy the generalized uncertainty relation and the corresponding generalized hamiltonian contains an additional term proportional to the fourth power of the trend we study a driven infinite quantum well where information as the external field periodically fluctuates and show that the presence of the minimal trading value of stocks results in a positive shift in the characteristic frequencies of the quantum system the connection between the information frequency and the transition probabilities is discussed finally

quantum diffusion of prices and profits abstract we discuss the time evolution of quotations of stocks and commodities and show that corrections to the orthodox bachelier model inspired by quantum mechanical time evolution of particles may be important our analysis shows that traders tactics can interfere as waves do and trader s strategies can be reproduced from the corresponding wigner functions the proposed interpretation of the chaotic movement of market prices imply that the bachelier behaviour follows from short time interference of tactics adopted paths followed by the rest of the world considered as a single trader and the ornstein uhlenbeck corrections to the bachelier model should qualitatively matter only for large time scales the famous smithonian invisible hand is interpreted as a short time tactics of whole the market considered as a single opponent we also propose a solution to the currency preference paradox

dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading abstract in this paper a formulation for the dynamic stability analysis of functionally graded shells under harmonic axial loading is presented a profile for the volume fraction is assumed and a normal mode expansion of the equations of motion yields a system of mathieu hill equations the stability of which is analyzed by the bolotin s method the present study examines the effects of the volume fraction of the material constituents and their distribution on the parametric response in particular the positions and sizes of the instability regions

multifractality in stock indexes fact or fiction abstract multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes including hsi szsc s p 500 and nasdaq to check whether the indexes instead of the returns possess multifractality we find that the mass exponent q is linear and the singularity q is close to 1 for all trading days and all indexes furthermore we find strong evidence showing that the scaling behaviors of the original data sets cannot be distinguished from those of shuffled time series hence the so called multifractality in the intraday stock market indexes is merely an illusion

long time energy conservation of numerical methods for oscillatory differential equations we consider second order differential systems where high frequency oscillations are generated by a linear part we present a frequency expansion of the solution and we discuss two invariants of the system that determine the coefficients of the frequency expansion these invariants are related to the total energy and the oscillatory harmonic energy of the original system for the numerical solution we study a class of symmetric methods that discretize the linear part without error we are interested in the case where the product of the step size with the highest frequency can be large in the sense of backward error analysis we represent the numerical solution by a frequency expansion where the coefficients are the solution of a modified system this allows us to prove the near conservation of the total and the oscillatory energy over very long time intervals

path integral for equities dynamic correlation and empirical analysis abstract this paper develops a model to describe the unequal time correlation between rate of returns of different stocks a non trivial fourth order derivative lagrangian is defined to provide an unequal time propagator which can be fitted to the market data a calibration algorithm is designed to find the empirical parameters for this model and different de noising methods are used to capture the signals concealed in the rate of return the detailed results of this gaussian model show that the different stocks can have strong correlation and the empirical unequal time correlator can be described by the model s propagator this preliminary study provides a novel model for the correlator of different instruments at different times

a finite dimensional quantum model for the stock market abstract we present a finite dimensional version of the quantum model for the stock market proposed in c zhang and l huang a quantum model for the stock market physica a 389 2010 5769 our approach is an attempt to make this model consistent with the discrete nature of the stock price and is based on the mathematical formalism used in the case of the quantum systems with finite dimensional hilbert space the rate of return is a discrete variable corresponding to the coordinate in the case of quantum systems and the operator of the conjugate variable describing the trend of the stock return is defined in terms of the finite fourier transform the stock return in equilibrium is described by a finite gaussian function and the time evolution of the stock price directly related to the rate of return is obtained by numerically solving a schrodinger type equation

price volume multifractal analysis and its application in chinese stock markets abstract an empirical research on chinese stock markets is conducted using statistical tools first the multifractality of stock price return series r i r i ln p t 1 ln p t and trading volume variation series v i v i ln v t 1 ln v t is confirmed using multifractal detrended fluctuation analysis furthermore a multifractal detrended cross correlation analysis between stock price return and trading volume variation in chinese stock markets is also conducted it is shown that the cross relationship between them is also found to be multifractal second the cross correlation between stock price p i and trading volume v i is empirically studied using cross correlation function and detrended cross correlation analysis it is found that both shanghai stock market and shenzhen stock market show pronounced long range cross correlations between stock price and trading volume third a composite index r based on price and trading volume is introduced compared with stock price return series r i and trading volume variation series v i r variation series not only remain the characteristics of original series but also demonstrate the relative correlation between stock price and trading volume finally we analyze the multifractal characteristics of r variation series before and after three financial events in china namely price limits reform of non tradable shares and financial crisis in 2008 in the whole period of sample to study the changes of stock market fluctuation and financial risk it is found that the empirical results verified the validity of r

cracks problem for non homogeneous composite material subjected to dynamic loading abstract in this paper we present a method to analyse the dynamic and steady response of non homogeneous composite materials differing from the existing works reported in literature the present method can be used for arbitrarily varying material properties through thickness direction and the crack number can be larger than one it is assumed that the composite material is orthotropic and all the material properties depend only on the coordinates y along the thickness direction the material non homogeneity is simulated by dividing the plate into a number of layers each layer is assigned slightly different material properties the method is based upon the fourier and laplace transforms to reduce the boundary value problem to a system of generalized singularity integral equations in the laplace transform domain the singular integral equations for the problem are derived and numerically solved by weighted residual value methods by utilized numerical laplace inversion the time dependent full field solutions are obtained as the numerical illustrates three different cracked specimens a functionally graded material a metal ceramic joint with functionally graded interlayer and a metal substrate functionally graded film structure are presented for various material non homogeneity parameters and or functionally graded layer thickness the results obtained demonstrate that the present model is an efficient tool in the fracture analysis of composite materials with properties varying in the thickness direction

exponential collocation methods for conservative or dissipative systems abstract in this paper we propose and analyse a novel class of exponential collocation methods for solving conservative or dissipative systems based on exponential integrators and collocation methods it is shown that these novel methods can be of arbitrarily high order and exactly or approximately preserve first integrals or lyapunov functions we also consider order estimates of the new methods furthermore we explore and discuss the application of our methods in important stiff gradient systems and it turns out that our methods are unconditionally energy diminishing and strongly damped even for very stiff gradient systems practical examples of the new methods are derived and the efficiency and superiority are confirmed and demonstrated by three numerical experiments including a nonlinear schrodinger equation as a byproduct of this paper arbitrary order trigonometric rkn collocation methods are also presented and analysed for second order highly oscillatory general systems the paper is accompanied by numerical results that demonstrate the great potential of this work

convolution quadrature and discretized operational calculus ii operational quadrature rules are applied to problems in numerical integration and the numerical solution of integral equations singular integrals power and logarithmic singularities finite part integrals multiple timescale convolution volterra integral equations wiener hopf integral equations frequency domain conditions which determine the stability of such equations can be carried over to the discretization

dynamic investigation of a functionally graded layered structure with a crack crossing the interface abstract the dynamic response of a functionally graded layered structure with a crack crossing the interface is analyzed the in plane impact loading condition is considered by using the laplace and fourier integral transforms singular integral equation method and residue theory the present problem is reduced to a singular integral equation in the laplace transform domain the influences of young s modulus ratio thickness ratio and crack length and location on the dynamic stress intensity factors dsifs are investigated particularly the dsifs corresponding to different crack locations are shown in the case when the crack center moves from one layer to another layer through the interface the peak and static values and overshoot characteristics of the dsifs are analyzed it is found that these values typically exhibit kinking behavior when the crack tips arrive at the interface this study is different from previous other investigations in the following respects 1 the dynamic response of a crack crossing the interface of a functionally graded structure is studied analytically which has hardly been done in the past and 2 the present model can be reduced to some important problems such as a functionally graded coating substrate structure with a crack in the graded coating or homogeneous substrate or one intersecting the interface

dynamic buckling of functionally graded spherical caps the dynamic behavior of functionally graded spherical caps under suddenly applied loads is studied by using a three noded axisymmetric curved shell element based on field consistency approach the formulation is based on first order shear deformation theory and it includes the in plane and rotary inertia effects geometric nonlin earity is introduced in the formulation using von karman s strain displacement relations the material properties are graded in the thickness direction according to the power law distribution in terms of volume fractions of the constituents of the material the effective material properties are evaluated using homogenization method the governing equations obtained are solved employing the newmark s integration technique coupled with a modified newton raphson iteration scheme the load corresponding to a sudden jump in the maximum average displace ment in the time history of the shell structure is taken as the dynamic buckling pressure the present model is validated against the available isotropic cases a detailed numerical study is carried out to bring out the effects of shell geometries power law index of functional graded material boundary conditions and finite pressure pulse with different duration on the axisymmetric dynamic buckling load of shallow spherical shells

dynamic stress intensity factors for two parallel interface cracks between a nonhomogeneous bonding layer and two dissimilar elastic half planes subject to an impact load some composite materials are constructed of two dissimilar half planes bonded by a nonhomogeneous elastic layer in the present study a crack is situated at the interface between the upper half plane and the bonding layer of such a material and another crack is located at the interface between the lower half plane and the bonding layer the material properties of the bonding layer vary continuously from those of the lower half plane to those of the upper half plane incoming shock stress waves impinge upon the two interface cracks normal to their surfaces fourier transformations were used to reduce the boundary conditions for the cracks to two pairs of dual integral equations in the laplace domain to solve these equations the differences in the crack surface displacements were expanded in a series of functions that are zero valued outside the cracks the unknown coefficients in the series were solved using the schmidt method so as to satisfy the conditions inside the cracks the stress intensity factors were defined in the laplace domain and were inverted numerically to physical space dynamic stress intensity factors were calculated numerically for selected crack configurations

handbook of differential equations chapter headings definitions and concepts transformations exact analytical methods exact methods for odes exact methods for pdes approximate analytical methods numerical methods concepts numerical methods for odes numerical methods for pdes list of tables list of programs list of figures subject index

emergence of heavy tailed skew distributions from the heat equation abstract it is well known that the symmetric gaussian function called the fundamental solution serves as the green s function of the heat equation in reality on the other hand distribution functions obtained empirically often differ from the gaussian function this study presents a new solution of the heat equation satisfying localized initial conditions like the gaussian fundamental solution the new solution corresponds to a hetero mixture distribution which generalizes the gaussian distribution function to a skewed and heavy tailed distribution and thus provides a candidate for the empirical distribution functions

quantum finance hamiltonian for coupon bond european and barrier options coupon bond european and barrier options are financial derivatives that can be analyzed in the hamiltonian formulation of quantum finance forward interest rates are modeled as a two dimensional quantum field theory and its hamiltonian and state space is defined european and barrier options are realized as transition amplitudes of the time integrated hamiltonian operator the double barrier option for a financial instrument is knocked out terminated with zero value if the price of the underlying instrument exceeds or falls below preset limits the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates hamiltonian the price of the european coupon bond option and the zero coupon bond barrier option are calculated it is shown that is general the constraint function for a coupon bond barrier option can to a good approximation be linearized a calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function

quantum spatial periodic harmonic model for daily price limited stock markets abstract we investigate the behaviors of stocks in daily price limited stock markets by purposing a quantum spatial periodic harmonic model the stock price is considered to be oscillating and damping in a quantum spatial periodic harmonic oscillator potential well a complicated non linear relation including inter band positive correlation and intra band negative correlation between the volatility and trading volume of a stock is numerically derived with the energy band structure of the model concerned the effectiveness of price limit is re examined with some observed characteristics of price limited stock markets in china studied by applying our quantum model

a quantum model for the stock market abstract beginning with several basic hypotheses of quantum mechanics we give a new quantum model in econophysics in this model we define wave functions and operators of the stock market to establish the schrodinger equation for stock price based on this theoretical framework an example of a driven infinite quantum well is considered in which we use a cosine distribution to simulate the state of stock price in equilibrium after adding an external field into the hamiltonian to analytically calculate the wave function the distribution and the average value of the rate of return are shown

love dynamics the case of linear couples this paper proposes a minimal model composed of two ordinary differential equations to describe the dynamics of love between two individuals the equations take into account three mechanisms of love growth and decay the pleasure of being loved return the reaction to the partner s appeal instinct and the forgetting processes oblivion under suitable assumptions on the behavior of the individuals the model turns out to be a positive linear system enjoying as such a number of remarkable properties which are in agreement with common wisdom on the argument these properties are used to explore the consequences that individual behavior can have on the community structure the main result along this line is that individual appeal is the driving force that creates order in the community possible extensions of this theory of linear love dynamics are briefly discussed

a simple framework for the derivation and analysis of effective one step methods for odes in this paper we provide a simple framework to derive and analyse a class of one step methods that may be conceived as a generalization of the class of gauss methods the framework consists in coupling two simple tools firstly a local fourier expansion of the continuous problem is truncated after a finite number of terms and secondly the coefficients of the expansion are computed by a suitable quadrature formula different choices of the basis lead to different classes of methods even though we shall here consider only the case of an orthonormal polynomial basis from which a large subclass of runge kutta methods can be derived the obtained results are then applied to prove in a simplified way the order and stability properties of hamiltonian bvms hbvms a recently introduced class of energy preserving methods for canonical hamiltonian systems see 2 and references therein a few numerical tests are also included in order to confirm the effectiveness of the methods resulting from our analysis

long time step methods for oscillatory differential equations considered are numerical integration schemes for nondissipative dynamical systems in which multiple time scales are present it is assumed that one can do an explicit separation of the rhs forces into fast forces and slow forces such that i the fast forces contain the high frequency part of the solution ii the fast forces are conservative and iii the reduced problem consisting only of the fast forces can be integrated much more cheaply than the full problem the fast forces are allowed to have low frequency components particular applications for which the schemes are intended include n body problems for which most of the forces are slow and nonlinear wave phenomena for which the fast forces can be propagated by spectral methods the assumption of cheap integration of fast forces implies that the overall cost of integration is primarily determined by the step size used to sample the slow forces a long time step method is one in which this step size exceeds half the period of the fastest normal mode present in the full system an existing method that comes close to qualifying is the impulse method also known as verlet i and r respa it is shown that it might fail though for a couple of reasons first it suffers a serious loss of accuracy if the step size is near a multiple of the period of a normal mode and second it is unstable if the step size is near a multiple of half the period of a normal mode proposed in this paper is a mollified impulse method having an error bound that is independent of the frequency of the fast forces it is also shown to possess superior stability properties theoretical results are supplemented by numerical experiments the method is efficient and reasonably easy to implement

criticality and phase transition in stock price fluctuations we analyze the behavior of the u s s p 500 index from 1984 to 1995 and characterize the non gaussian probability density functions pdf of the log returns the temporal dependence of fat tails in the pdf of a ten minute log return shows a gradual systematic increase in the probability of the appearance of large increments on approaching black monday in october 1987 reminiscent of parameter tuning towards criticality on the occurrence of the black monday crash this culminates in an abrupt transition of the scale dependence of the non gaussian pdf towards scale invariance characteristic of critical behavior these facts suggest the need for revisiting the turbulent cascade paradigm recently proposed for modeling the underlying dynamics of the financial index to account for time varying phase transitionlike and scale invariant critical like behavior

simulation of nonlinear interest rates in quantum finance libor market model abstract the simulation of the libor market model lmm is extensively studied in the framework of quantum finance the imperfectly correlated libor rates are simulated based on a gaussian quantum field and a recursion equation of nontrivial stochastic drift the libor options are studied using both the simulation method and the analytical formula the caplet price of simulation is compared with black s caplet formula which can be exactly derived from the lmm the invariance of caplet price for different forward bond numeraire is verified by using the simulation the simulation results for coupon bond options and swaptions are compared with the approximate price which are limited for the reason that the approximate price is derived using the small volatility expansion the simulation method is shown to have great potential in the application of pricing interest rate instruments

exponential rosenbrock type methods we introduce a new class of exponential integrators for the numerical integration of large scale systems of stiff differential equations these so called rosenbrock type methods linearize the flow in each time step and make use of the matrix exponential and related functions of the jacobian in contrast to standard integrators the methods are fully explicit and do not require the numerical solution of linear systems we analyze the convergence properties of these integrators in a semigroup framework of semilinear evolution equations in banach spaces in particular we derive an abstract stability and convergence result for variable step sizes this analysis further provides the required order conditions and thus allows us to construct pairs of embedded methods we present a third order method with two stages and a fourth order method with three stages respectively the application of the required matrix functions to vectors are computed by krylov subspace approximations we briefly discuss these implementation issues and we give numerical examples that demonstrate the efficiency of the new integrators

the nonlinear dynamic buckling response of functionally graded truncated conical shells abstract in this study the nonlinear dynamic buckling of functionally graded fg truncated conical shells subjected to axial compressive load varying as a linear function of time is investigated the material properties of the fg truncated shell are assumed to vary continuously through the thickness of the shell the nonlinear pre buckling deformations of the fg truncated conical shell are taken into account the fundamental relations and modified donnell type nonlinear dynamic stability and compatibility equations of the fg truncated conical shell are derived and solved by using the superposition principle galerkin and runge kutta methods the values of the dimensionless nonlinear critical time parameter have been found numerically finally carrying out some computations the effects of the compositional profiles the variation of the truncated conical shell geometric parameters and the axial loading speed on the dimensionless linear and nonlinear critical time parameters have been studied comparing the results of this study with those in the literature validates the present analysis

an accelerated symmetric sor like method for augmented systems abstract recently njeru and guo presented an accelerated sor like asor method for solving the large and sparse augmented systems in this paper we establish an accelerated symmetric sor like assor method which is an extension of the asor method furthermore the convergence properties of the assor method for augmented systems are studied under suitable restrictions and the functional equation between the iteration parameters and the eigenvalues of the relevant iteration matrix is established in detail finally numerical examples show that the assor is an efficient iteration method

reconstruction of inhomogeneous properties of orthotropic viscoelastic layer abstract the consecutive scheme of reconstructing the functions characterizing the instantaneous and long termed modules for inhomogeneous orthotropic viscoelastic layer whose properties continuously vary through a thickness is proposed the identification problem is solved on the basis of the additional information on the integral characteristics of displacement fields measured on top border of a layer iterative process of reconstruction of six unknown functions is formulated to reconstruct the rest six functions systems of fredholm s integral equations of the first kind with smooth kernels are received computational experiment on a reconstruction of various laws of inhomogeneity is conducted a comparative analysis of the results obtained is carried out

quantum brownian motion model for the stock market abstract it is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality using the physical concepts and mathematical structures of quantum mechanics we construct an econophysical framework for the stock market based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system a quantum brownian particle in particular the irrationality of stock transactions is quantitatively considered as the planck constant within heisenberg s uncertainty relationship of quantum mechanics in an analogous manner we analyze real stock data of shanghai stock exchange of china and investigate fat tail phenomena and non markovian behaviors of the stock index with the assistance of the quantum brownian motion model thereby interpreting and studying the limitations of the classical brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics

a quantum statistical approach to simplified stock markets we use standard perturbation techniques originally formulated in quantum statistical mechanics in the analysis of a toy model of a stock market which is given in terms of bosonic operators in particular we discuss the probability of transition from a given value of the portfolio of a certain trader to a different one this computation can also be carried out using some kind of feynman graphs adapted to the present context

dynamic behavior of a cylindrical crack in a functionally graded interlayer under torsional loading in this paper the problem of a cylindrical crack located in a functionally graded material fgm interlayer between two coaxial elastic dissimilar homogeneous cylinders and subjected to a torsional impact loading is considered the shear modulus and the mass density of the fgm interlayer are assumed to vary continuously between those of the two coaxial cylinders this mixed boundary value problem is first reduced to a singular integral equation with a cauchy type kernel in the laplace domain by applying laplace and fourier integral transforms the singular integral equation is then solved numerically and the dynamic stress intensity factor dsif is also obtained by a numerical laplace inversion technique the dsif is found to rise rapidly to a peak and then reduce and tend to the static value almost without oscillation the influences of the crack location the fgm interlayer thickness and the relative magnitudes of the adjoining material properties are examined it is found among others that by increasing the fgm gradient the dsif can be greatly reduced

stock markets and quantum dynamics a second quantized description abstract in this paper we continue our description of stock markets in terms of some non abelian operators which are used to describe the portfolio of the various traders and other observable quantities after a first prototype model with only two traders we discuss a more realistic model of market involving an arbitrary number of traders for both models we find approximated solutions for the time evolution of the portfolio of each trader in particular for the more realistic model we use the stochastic limit approach and a fixed point like approximation