wave speed dispersion associated with an attenuation obeying a frequency power law an attenuation scaling as a power of frequency over an infinite bandwidth is neither analytic nor square integrable thus calling into question the application of the kramers kronig dispersion relations for determining the frequency dependence of the associated phase speed in this paper three different approaches are developed all of which return the dispersion formula for the wavenumber k the first analysis relies on the properties of generalized functions and the causality requirement that the impulse response k t the inverse fourier transform of ik must vanish for t 0 second a wave equation is introduced that yields the phase speed dispersion associated with a frequency power law attenuation finally it is shown that with minor modification the kramers kronig dispersion relations with no subtractions the plemelj formulas do in fact hold for an attenuation scaling as yielding the same dispersion formula as the other two derivations from this dispersion formula admissible values of the exponent are established physically the inadmissible values of which include all the integers correspond to attenuation dispersion pairs whose fourier components cannot combine in such a way as to make the impulse response k t vanish for t 0 there is no upper or lower limit on the value that may take

adjustments to zatsiorsky seluyanov s segment inertia parameters zatsiorsky et al in contemporary problems in biomechanics pp 272 291 crc press massachusetts 1990a obtained by means of a gamma ray scanning technique the relative body segment masses center of mass cm positions and radii of gyration for samples of college aged caucasian males and females although these data are the only available and comprehensive set of inertial parameters regarding young adult caucasians they have been rarely utilized for biomechanical analyses of subjects belonging to the same or a similar population the main reason is probably that zatsiorsky et al used bony landmarks as reference points for locating segment cms and defining segment lengths some of these landmarks were markedly distant from the joint centers currently used by most researchers as reference points the purpose of this study was to adjust the mean relative cm positions and radii of gyration reported by zatsiorsky et al in order to reference them to the joint centers or other commonly used landmarks rather than the original landmarks the adjustments were based on a number of carefully selected sources of anthropometric data

two classes of linearly implicit local energy preserving approach for general multi symplectic hamiltonian pdes abstract two classes of efficient and robust schemes are proposed for the general multi symplectic hamiltonian systems using the invariant energy quadratization ieq approach the schemes are linear second order accurate local energy preserving and preserve the global energy they are not restricted to specific forms of the nonlinear part of the state function and only require solving linear equations at each time step we applied the new schemes to various multi symplectic hamiltonian pdes to demonstrate their effectiveness computational efficiency and accuracy

lower extremity control during turns initiated with and without hip external rotation the pirouette turn is often initiated in neutral and externally rotated hip positions by dancers this provides an opportunity to investigate how dancers satisfy the same mechanical objectives at the whole body level when using different leg kinematics the purpose of this study was to compare lower extremity control strategies during the turn initiation phase of pirouettes performed with and without hip external rotation skilled dancers n 5 performed pirouette turns with and without hip external rotation joint kinetics during turn initiation were determined for both legs using ground reaction forces grfs and segment kinematics hip muscle activations were monitored using electromyography using probability based statistical methods variables were compared across turn conditions as a group and within dancer despite differences in grfs and impulse generation between turn conditions at least 90 of each grf was aligned with the respective leg plane a majority of the net joint moments at the ankle knee and hip acted about an axis perpendicular to the leg plane however differences in shank alignment relative to the leg plane affected the distribution of the knee net joint moment when represented with respect to the shank versus the thigh during the initiation of both turns most participants used ankle plantar flexor moments knee extensor moments flexor and abductor moments at the push leg s hip and extensor and abductor moments at the turn leg s hip representation of joint kinetics using multiple reference systems assisted in understanding control priorities

connecting the grain shearing mechanism of wave propagation in marine sediments to fractional order wave equations the characteristic time dependent viscosity of the intergranular pore fluid in buckingham s grain shearing gs model buckingham j acoust soc am 108 2796 2815 2000 is identified as the property of rheopecty the property corresponds to a rare type of a non newtonian fluid in rheology which has largely remained unexplored the material impulse response function from the gs model is found to be similar to the power law memory kernel which is inherent in the framework of fractional calculus the compressional wave equation and the shear wave equation derived from the gs model are shown to take the form of the kelvin voigt fractional derivative wave equation and the fractional diffusion wave equation respectively therefore an analogy is drawn between the dispersion relations obtained from the fractional framework and those from the gs model to establish the equivalence of the respective wave equations further a physical interpretation of the characteristic fractional order present in the wave e

hamiltonian conserving discrete canonical equations based on variational difference quotients abstract new discrete mechanics based on the assumption of the discrete time is proposed the discrete mechanics does not contain any continuous differentiation but contains only difference quotients resulting discrete hamiltonian s canonical equations are single time step difference equations and exactly conserve the hamiltonian the canonical equations give the numerical results more accurately than the heun scheme and the 4th order runge kutta scheme

the multisymplectic diamond scheme we introduce a class of general purpose linear multisymplectic integrators for hamiltonian wave equations based on a diamond shaped mesh on each diamond the pde is discretized by a symplectic runge kutta method the scheme advances in time by filling in each diamond locally leading to greater efficiency and parallelization and easier treatment of boundary conditions compared to methods based on rectangular meshes

numerical methods for hamiltonian pdes the paper provides an introduction and survey of conservative discretization methods for hamiltonian partial differential equations the emphasis is on variational symplectic and multi symplectic methods the derivation of methods as well as some of their fundamental geometric properties are discussed basic principles are illustrated by means of examples from wave and fluid dynamics

some new structure preserving algorithms for general multi symplectic formulations of hamiltonian pdes many partial differential equations pdes can be written as a multi symplectic hamiltonian system which has three local conservation laws namely multi symplectic conservation law local energy conservation law and local momentum conservation law in this paper we give several systematic methods for discretizing general multi symplectic formulations of hamiltonian pdes including a local energy preserving algorithm a class of global energy preserving methods and a local momentum preserving algorithm the methods are illustrated by the nonlinear schrodinger equation and the korteweg de vries equation numerical experiments are presented to demonstrate the conservative properties of the proposed numerical methods

restrictions on wave equations for passive media most derivations of acoustic wave equations involve ensuring that causality is satisfied here the consequences of also requiring that the medium should be passive are explored this is a stricter criterion than causality for a linear system and implies that there are restrictions on the relaxation modulus and its first few derivatives the viscous and relaxation models of acoustics satisfy passivity and have restrictions on not only a few but all derivatives of the relaxation modulus these models are described as a system of springs and dampers with positive parameters and belong to the important class of completely monotone systems it is shown here that the attenuation as a function of frequency for such media has to increase slower than a linear function likewise the phase velocity has to increase monotonically this gives criteria on which one may judge whether a proposed wave equation is passive or not as illustrated by comparing two different versions of the viscous wave equation

stochastic conformal schemes for damped stochastic klein gordon equation with additive noise abstract in this article stochastic conformal schemes of the damped stochastic klein gordon equation with additive noise are studied it is shown that this equation possesses the stochastic conformal multi symplectic conservation law under appropriate boundary conditions the global momentum evolution law and the global energy evolution law are proposed we chiefly develop the stochastic conformal preissman scheme the stochastic conformal discrete gradient scheme and the stochastic conformal euler box scheme to preserve the geometric structures of the original system specifically we make theoretical discussions on the three proposed schemes to obtain corresponding discrete conservation laws or discrete evolution laws then the damped stochastic linear klein gordon equation and the damped stochastic nonlinear klein gordon equation with cubic nonlinearity are taken as examples to demonstrate the validity of the proposed schemes through numerical experiments and comparisons the superiorities of the proposed schemes are fully shown which are consistent with our theoretical analysis moreover the mean square convergence orders of the three stochastic conformal schemes in time direction and space direction are tested numerically

high order compact splitting multisymplectic method for the coupled nonlinear schrodinger equations in this paper we develop a new kind of multisymplectic integrator for the coupled nonlinear schrodinger cnls equations the cnls equations are cast into multisymplectic formulation then it is split into a linear multisymplectic formulation and a nonlinear hamiltonian system the space of the linear subproblem is approximated by a high order compact hoc method which is new in multisymplectic context the nonlinear subproblem is integrated exactly for splitting and approximation we utilize an hoc sms integrator its stability and conservation laws are investigated in theory numerical results are presented to demonstrate the accuracy conservation laws and to simulate various solitons as well for the hoc sms integrator they are consistent with our theoretical analysis

predicting dynamic postural instability using center of mass time to contact information our purpose was to determine whether spatiotemporal measures of center of mass motion relative to the base of support boundary could predict stepping strategies after upper body postural perturbations in humans we expected that inclusion of center of mass acceleration in such time to contact ttc calculations would give better predictions and more advanced warning of perturbation severity ttc measures were compared with traditional postural variables which do not consider support boundaries and with an inverted pendulum model of dynamic stability developed by hof et al 2005 the condition for dynamic stability journal of biomechanics 38 1 8 a pendulum was used to deliver sequentially increasing perturbations to 10 young adults who were strapped to a wooden backboard that constrained motion to sagittal plane rotation about the ankle joint subjects were instructed to resist the perturbations stepping only if necessary to prevent a fall peak center of mass and center of pressure velocity and acceleration demonstrated linear increases with postural challenge in contrast boundary relevant minimum ttc values decreased nonlinearly with postural challenge enabling prediction of stepping responses using quadratic equations when ttc calculations incorporated center of mass acceleration the quadratic fits were better and gave more accurate predictions of the ttc values that would trigger stepping responses in addition ttc minima occurred earlier with acceleration inclusion giving more advanced warning of perturbation severity our results were in agreement with ttc predictions based on hof s model and suggest that ttc may function as a control parameter influencing the postural control system s decision to transition from a stationary base of support to a stepping strategy

limits of recovery against slip induced falls while walking abstract slip induced falls in gait often have devastating consequences the purposes of this study were 1 to select the determinants that can best discriminate the outcomes recoveries or falls of an unannounced slip induced in gait and to find their corresponding threshold i e the limits of recovery which can clearly separate these two outcomes and 2 to verify these results in a subset of repeated slip trials based on the data collected from 69 young subjects during a slip induced in gait nine different ways of combining the center of mass com stability the hip height and its vertical velocity were investigated with the aid of logistic regression the results revealed that the com stability s and limb support represented by the quotient of hip vertical velocity to hip height s hip recorded at the instant immediately prior to the recovery step touchdown were sufficiently sensitive to account for all 100 variance in falls and specific enough to account for nearly all 98 3 variability in recoveries this boundary s hip 0 22 s 0 25 which quantifies the risk of falls in the stability limb support quotient s s hip domain was fully verified using second slip and third slip trials n 76 with classification of falls at 100 and recoveries at 98 6 the severity of an actual fall is likely to be greater further below the boundary while the likelihood of a fall diminishes above it finally the slope of the boundary also indicates the tradeoff between the stability and limb support whereby high stability can compensate for the insufficiency in limb support or vice versa

analysis of a galerkin approach applied to a system of coupled schrodinger equations abstract we study error and convergence rate of a fully discrete fourier galerkin scheme to approximate the solutions of a system consisting of two coupled cubic schrodinger equations with cross modulation which is a model for the propagation of a nonlinear pulse in a linearly birefringent kerr optical fiber we also establish a result on existence and uniqueness of a solution of the corresponding initial value problem

decoupled local global energy preserving schemes for the n coupled nonlinear schrodinger equations abstract we develop two local energy preserving integrators and a global energy preserving integrator for the general multisymplectic hamiltonian system when applied to the 1d and multi dimensional n coupled nonlinear schrodinger equations the given schemes have the exact preservation of the local global conservation law and are decoupled in the components n n 1 2 n i e each of the components can be solved independently the decoupled feature is significant and helpful for overcoming the computational difficulty of the n coupled n 3 nonlinear schrodinger equations especially of the multi dimensional case the composition method is employed to improve the accuracy of the schemes in time and the discrete fast fourier transform is used to reduce the computational complexity several numerical experiments are carried out to exhibit the behaviors of the wave solutions numerical results confirm the theoretical results

general local energy preserving integrators for solving multi symplectic hamiltonian pdes in this paper we propose and investigate a general approach to constructing local energy preserving algorithms which can be of arbitrarily high order in time for solving hamiltonian pdes this approach is based on the temporal discretization using continuous runge kutta type methods and the spatial discretization using pseudospectral methods or gauss legendre collocation methods the local energy conservation law of our new schemes is analyzed in detail the effectiveness of the novel local energy preserving integrators is demonstrated by coupled nonlinear schrodinger equations and 2d nonlinear schrodinger equations with external fields our new schemes are compared with some classical multi symplectic and symplectic schemes in numerical experiments the numerical results show the remarkable long term behaviour of our new schemes

a causal and fractional all frequency wave equation for lossy media this work presents a lossy partial differential acoustic wave equation including fractional derivative terms it is derived from first principles of physics mass and momentum conservation and an equation of state given by the fractional zener stress strain constitutive relation for a derivative order in the fractional zener relation the resulting absorption k obeys frequency power laws as k 1 in a low frequency regime k 1 2 in an intermediate frequency regime and k 1 in a high frequency regime the value 1 corresponds to the case of a single relaxation process the wave equation is causal for all frequencies in addition the sound speed does not diverge as the frequency approaches infinity this is an improvement over a previously published wave equation building on the fractional kelvin voigt constitutive relation

deriving fractional acoustic wave equations from mechanical and thermal constitutive equations it is argued that fractional acoustic wave equations come in two kinds the first kind is constructed ad hoc to have loss operators that fit power law measurements the second kind is more fundamental as they in addition are based on underlying physical equations here that means constitutive equations these equations are the fractional kelvin voigt and the more general fractional zener stress strain relationships as well as a fractional version of the fourier heat law the properties of the wave equations are given in terms of attenuation and phase group velocities for low intermediate and high frequency regions in the most general case the attenuation exhibits power law behavior in all frequency ranges while the phase and group velocities increase sharply in the intermediate frequency range and converge to a constant finite value for high frequencies it is also shown that the fractional zener wave equation is equivalent to the multiple relaxation model for attenuation

a new class of energy preserving numerical integration methods the first ever energy preserving b series numerical integration method for ordinary differential equations is presented and applied to several hamiltonian systems related novel lie algebraic results are also discussed

efficient energy preserving wavelet collocation schemes for the coupled nonlinear schrodinger boussinesq system abstract second and fourth order energy preserving wavelet collocation schemes are proposed for the coupled nonlinear schrodinger boussinesq system based on the hamiltonian structure and composition technique a fast solver improves the computational efficiency of the schemes some numerical experiments are conducted to show the efficiency and accuracy of the present schemes