moving least squares particle hydrodynamics i consistency and stability the smooth particle hydrodynamics sph method is derived in a novel manner by means of a galerkin approximation applied to the lagrangian equations of continuum mechanics as in the finite element method this derivation is modified to replace the sph interpolant with the moving least squares mls interpolant of lancaster and saulkaskas and define a new particle volume which ensures thermodynamic compatibility a variable rank modification of the mls interpolants which retains their desirable summation properties is introduced to remove the singularities that occur when divergent flow reduces the number of neighbours of a particle to less than the minimum required a surprise benefit of the galerkin sph derivation is a theoretical justification of a common ad hoc technique for variable h sph the new mlsph method is conservative if an anti symmetric quadrature rule for the stiffness matrix elements can be supplied in this paper a simple one point collocation rule is used to retain similarity with sph leading to a non conservative method several examples document how mlsph renders dramatic improvements due to the linear consistency of its gradients on three canonical difficulties of the sph method spurious boundary effects erroneous rates of strain and rotation and tension instability two of these examples are non linear lagrangian patch tests with analytic solutions with which mlsph agrees almost exactly the examples also show that mlsph is not absolutely stable if the problems are run to very long times a linear stability analysis explains both why it is more stable than sph and not yet absolutely stable and an argument is made that for realistic dynamic problems mlsph is stable enough the notion of coherent particles for which the numerical stability is identical to the physical stability is introduced the new method is easily retrofitted into a generic sph code and some observations on performance are made copyright 1999 john wiley sons ltd

exact energy and momentum conserving algorithms for general models in nonlinear elasticity implicit time integration schemes that inherit the conservation laws of total energy linear and angular momentum are considered for initial boundary value problems in finite deformation elastodynamics conserving schemes are constructed for general hyperelastic material models both compressible and incompressible and are formulated in a way that is independent of spatial discretization three numerical examples for ogden type material models implemented using a finite element discretization in space are given to illustrate the performance of the proposed schemes these examples show that relative to the standard implicit mid point rule the conserving schemes exhibit superior numerical stability properties without a compromise in accuracy

generic formalism and discrete variational derivative method for the two dimensional vorticity equation the vorticity equation for two dimensional incompressible viscous flows is formulated within the generic formalism for non equilibrium thermodynamics the laws of conservation of energy and increasing entropy derived from the generic formulation are properly inherited by the finite difference equations obtained by invoking the discrete variational derivative method the law of increasing entropy corresponds to the dissipation of enstrophy for the vorticity equation some numerical experiments have been done to examine the usefulness of the proposed method

parabolic manifolds in the scattering map and direct quantum processes we analyse the quantum effects of parabolic manifolds in jung s iterated scattering map for this purpose we consider the classical map proposed previously to be the exact classical analogue of rydberg molecules calculated with the approximations relevant to the multichannel quantum defect theory for energies above the ionization threshold the part corresponding to positive electron energies can be viewed as a jung scattering map without the trivial direct processes this map contains a parabolic manifold of fixed points which gives rise to a regular series of quantum states which behave very much like eigenchannels that miss the target

symplectic integration of constrained hamiltonian systems by composition methods recent work reported in the literature suggests that for the long term integration of hamiltonian dynamical systems one should use methods that preserve the symplectic structure of the flow in this paper the symplecticity of numerical integrators is investigated for constrained hamiltonian systems with holonomic constraints the following two results will be derived i it is shown that any first or second order symplectic integrator for unconstrained problems can be generalized to constrained systems such that the resulting scheme is symplectic and preserves the constraints based on this higher order methods can be derived by the same composition methods used for unconstrained problems ii leimkuhler and reich math comp 63 1994 pp 589 605 derived symplectic integrators based on dirac s reformulation of the constrained problem as an unconstrained hamiltonian system however although the unconstrained reformulation can be handled by direct application of any symplectic implicit runge kutta m

bracket formulations and energy and helicity preserving numerical methods for the three dimensional vorticity equation abstract the vorticity equation for three dimensional viscous incompressible fluid flows is formulated within different bracket formalisms using the poisson or nambu bracket together with a dissipative bracket the budgets of kinetic energy helicity and enstrophy derived from the bracket formulations are properly inherited by the finite difference equations obtained by invoking the discrete variational derivative method combined with the mimetic finite difference method in particular energy and helicity are conserved precisely in inviscid flow computations the energy and enstrophy dissipate properly owing to viscosity in viscous flow computations and the enstrophy is appropriately produced by the vortex stretching effect in both inviscid and viscous flow computations the relationships between the stream function velocity and vorticity as well as the solenoidal conditions on the velocity and vorticity fields are also inherited numerical experiments on a periodic array of rolls that permits analytical solutions have been done to examine the properties and usefulness of the proposed method

convergence dynamics of 2 dimensional isotropic and anisotropic bak sneppen models abstract the conventional hamming distance measurement captures only short time dynamics of the displacement between uncorrelated random configurations the minimum difference technique introduced by tirnakli and lyra u tirnakli m l lyra int j mod phys c 14 2003 805 is used to study short time and long time dynamics of the two distinct random configurations of isotropic and anisotropic bak sneppen models on a square lattice similar to a 1 dimensional case the time evolution of the displacement is intermittent the scaling behavior of the jump activity rate and waiting time distribution reveal the absence of typical spatial temporal scales in the mechanism of displacement jumps used to quantify convergence dynamics

asymmetric unimodal maps at the edge of chaos we numerically investigate the sensitivity to initial conditions of asymmetric unimodal maps x t 1 1 a x t z i i 1 2 correspond to x t 0 and x t 1 0 a or 2 t 0 1 2 at the edge of chaos we employ three distinct algorithms to characterize the power law sensitivity to initial conditions at the edge of chaos namely direct measure of the divergence of initially nearby trajectories the computation of the rate of increase of generalized non extensive entropies s q and multi fractal analysis the first two methods provide consistent estimates for the exponent governing the power law sensitivity in addition to this we verify that the multi fractal analysis does not provide precise estimates of the singularity spectrum f alpha especially near its extremal points such feature prevents to perform a fine check of the accuracy of the scaling relation between f alpha and the entropic index q thus restricting the applicability of the multi fractal analysis for studying the sensitivity to initial conditions in this class of asymmetric maps

on the phase space approach to complexity we elaborate in some detail on a new phase space approach to complexity due to y c zhang we show in particular that the connection between maximal complexity and power law noise or correlations can be derived from a simple variational principle for a 1d signal we find 1 f noise in accordance with zhang

geometrically non linear enhanced strain mixed methods and the method of incompatible modes a class of assumed strain mixed finite element methods for fully non linear problems in solid mechanics is presented which when restricted to geometrically linear problems encompasses the classical method of incompatible modes as a particular case the method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part formulated in the context of a three field variational formulation the resulting class of mixed methods provides a possible extension to the non linear regime of well known incompatible mode formulations in addition this class of methods includes non linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements the good performance of the proposed methodology is illustrated in a number of simulations including 2 d 3 d and axisymmetric finite deformation problems in elasticity and elastoplasticity remarkably these methods appear to be specially well suited for problems involving localization of the deformation as illustrated in several numerical examples

impact of localization on dyson s circular ensemble a wide variety of complex physical systems described by unitary matrices have been shown numerically to satisfy level statistics predicted by dyson s circular ensemble we argue that the impact of localization in such systems is to impose certain restrictions on the eigenvalues we consider a solvable model which takes into account such restrictions qualitatively and find that within the model a gap is created in the spectrum and there is a transition from the universal wigner distribution towards a poisson distribution with increasing localization

poincare map for scattering states for scattering states in classical mechanics a map is constructed which is an analogue to the poincare map for bound state trajectories iteration of this map indicates which parts of the phase space are filled by unstable trajectories that are sensitive to small changes in the initial conditions and which regions are filled by stable trajectories examples for this map are given by numerical calculations for scattering off a simple two dimensional model potential

on higher order semi explicit symplectic partitioned runge kutta methods for constrained hamiltonian systems in this paper we generalize the class of explicit partitioned runge kutta prk methods for separable hamiltonian systems to systems with holonomic constraints for a convenient analysis of such schemes we first generalize the backward error analysis for systems in bbb r m to systems on manifolds embedded in bbb r m by applying this analysis to constrained prk methods we prove that such methods will in general suffer from order reduction as well known for higher index differential algebraic equations however this order reduction can be avoided by a proper modification of the standard prk methods this modification increases the number of projection steps onto the constraint manifold but leaves the number of force evaluations constant we also give a numerical comparison of several second fourth and sixth order methods

quantum signatures of an integrable system with a chaotic scattering map a rather simple completely integrable hamiltonian with a chaotic classical scattering map is analysed in quantum mechanics after the analytical computation of the s matrix we investigate numerically the distribution of scattering phases giving the nearest neighbour distribution the number variance and the fourier transform of the spectrum we find fair agreement with the random matrix prediction for the circular orthogonal ensemble coe as appropriate for the time reversal invariant system with a chaotic scattering map this example confirms that coe properties of the s matrix do not necessarily indicate topological chaos in the flow generated by the classical hamiltonian

a new class of particle methods particle methods are numerical methods designed to solve problems in fluid mechanics and related problems in continuum mechanics a general approach to the construction of such particle methods is presented in this article the particles are no mass points but possess a finite extension they can rotate in space and have a spin the conservation of mass is automatically guaranteed by the ansatz the forces of interaction between the particles are derived in a canonical way from the force laws of continuum mechanics and are directly based on a regularized stress tensor in the absence of external forces and of heat sources and sinks momentum angular momentum and energy are conserved as in the continuum case

surfaces generated by moving least squares methods an analysis of moving least squares m l s methods for smoothing and interpolating scattered data is presented in particular theorems are proved concerning the smoothness of interpolants and the description of m l s processes as projection methods some properties of compositions of the m l s projector with projectors associated with finiteelement schemes are also considered the analysis is accompanied by examples of univariate and bivariate problems

a new energy and momentum conserving algorithm for the non linear dynamics of shells a numerical time integration scheme for the dynamics of non linear elastic shells is presented that simultaneously and independent of the time step size inherits exactly the conservation laws of total linear total angular momentum as well as total energy the proposed technique generalizes to non linear shells recent work of the authors on non linear elastodynamics and is ideally suited for long term large scale simulations the algorithm is second order accurate and can be immediately extended with no modification to a fourth order accurate scheme the property of exact energy conservation induces a strong notion of non linear numerical stability which manifests itself in actual simulations

a unified stability analysis of meshless particle methods a uni ed stability analysis of meshless methods with eulerian and lagrangian kernels is presented three types of instabilities were identi ed in one dimension an instability due to rank de ciency a tensile instability and a material instability which is also found in continua the stability of particle methods with eulerian and lagrangian kernels is markedly di erent lagrangian kernels do not exhibit the tensile instability in both kernels the instability due to rank de ciency can be suppressed by stress points in two dimensions the stabilizing e ect of stress points is dependent on their locations it was found that the best approach to stable particle discretizations is to use lagrangian kernels with stress points the stability of the least squares stabilization was also studied copyright 2000 john wiley sons ltd

non linear dynamics of three dimensional rods exact energy and momentum conserving algorithms the long term dynamic response of non linear geometrically exact rods under going finite extension shear and bending accompanied by large overall motions is addressed in detail the central objective is the design of unconditionally stable time stepping algorithms which exactly preserve fundamental constants of the motion such as the total linear momentum the total angular momentum and for the hamiltonian case the total energy this objective is accomplished in two steps first a class of algorithms is introduced which conserves linear and angular momentum this result holds independently of the definition of the algorithmic stress resultants second an algorithmic counterpart of the elastic constitutive equations is developed such that the law of conservation of total energy is exactly preserved conventional schemes exhibiting no numerical dissipation symplectic algorithms in particular are shown to lead to unstable solutions when the high frequencies are not resolved compared to conventional schemes there is little if any additional computational cost involved in the proposed class of energy momentum methods the excellent performance of the new algorithm in comparison to other standard schemes is demonstrated in several numerical simulations

iterated scattering map for rearrangement scattering an iterated scattering map for three particle rearrangement scattering is constructed by forming sequences of scattering trajectories this map works in a similar way to the well known poincare map for bound trajectories it provides useful information for investigating the integrability properties of the system a numerical example is shown for the calogero moser system with hyperbolic potential functions

suppressing local particle oscillations in the hamiltonian particle method for elasticity the governing equation of elasticity is discretized into motion equations of the particles in a hamiltonian system a weighted least square method is adopted to evaluate the green lagrange strain using a symplectic scheme for the hamiltonian system we obtain the property of energy conservation in the discretized calculations however local particle oscillations occur and they excessively decrease low frequency motion in this study we propose the use of an artificial potential force to suppress the local oscillations the accuracy of the model with and without the inclusion of the artificial force is examined by analyzing a cantilever beam and wave propagation with the inclusion of the artificial force the local oscillations are reduced while energy conservation is maintained

connection between conserved quantities of the hamiltonian and of the s matrix a conserved quantity k of a hamiltonian h implies a conserved quantity j of the s matrix only if the forward and the backward asymptotic limits of k are equal a conserved quantity j of s implies a conserved quantity of h only if j is also a conserved quantity of the free hamiltonian h0 therefore the integrability or chaoticity of s does not necessarily decide the integrability of h

spectral fluctuation properties of hamiltonian systems the transition region between order and chaos the authors study numerically the classical dynamical behaviour and the spectral fluctuation properties of a class of hamiltonian systems with two degrees of freedom the quantum mechanical properties of these systems are monotonic but non universal functions of the fraction of classical phase space filled by chaotic trajectories it is found that the observed spectral fluctuation measures can be reproduced by a random matrix model which depends on one parameter only

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

an improved reproducing kernel particle method for nearly incompressible finite elasticity the previously developed reproducing kernel particle method rkpm employs a high order quadrature rule for desired domain integration accuracy this leads to an over constrained condition in the limit of incompressibility and volumetric locking and pressure oscillation were encountered the employment of a large support size in the reproducing kernel shape function increases the dependency in the discrete constraint equations at quadrature points and thereby relieves locking however this approach consumes high cpu and it cannot effectively resolve pressure oscillation difficulty in this paper a pressure projection method is introduced by locally projecting the pressure onto a lower order space to reduce the number of independent discrete constraint equations this approach relieves the over constrained condition and thus eliminates volumetric locking and pressure oscillation without the expense of employing large support size in rkpm the method is developed in a general framework of nearly incompressible finite elasticity and therefore linear problems are also applicable to further reduce the computational cost a stabilized reduced integration method based on an assumed strain approach on the gradient matrix associated with the deformation gradient is also introduced the resulting stiffness matrix and force vector of rkpm are obtained explicitly without numerical integration

a corrective smoothed particle method for boundary value problems in heat conduction combining the kernel estimate with the taylor series expansion is proposed to develop a corrective smoothed particle method cspm this algorithm resolves the general problem of particle deficiency at boundaries which is a shortcoming in standard smoothed particle hydrodynamics ssph in addition the method s ability to model derivatives of any order could make it applicable for any time dependent boundary value problems an example of the applications studied in this paper is unsteady heat conduction which is governed by second order derivatives numerical results demonstrate that besides the capability of directly imposing boundary conditions the present method enhances the solution accuracy not only near or on the boundary but also inside the domain published in 1999 by john wiley sons ltd this article is a u s government work and is in the public domain in the united states

residual bounds of approximate solutions of the algebraic riccati equation let tilde x geq 0 approximate the unique hermitian positive semi definite solution x to the algebraic riccati equation are where f g geq 0 a f is stabilizable and a g is detectable let be the residual of the are with respect to tilde x and define the linear operator vec l by by applying a new forward perturbation bound to the optimal backward perturbation corresponding to the approximate solution tilde x we obtained the following result if a f tilde x is stable and if 4 vec l 1 vec l 1 hat r f 1 for any unitarily invariant norm then

universal renormalization group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics we uncover the dynamics at the chaos threshold m of the logistic map and find that it consists of trajectories made of intertwined power laws that reproduce the entire period doubling cascade that occurs for m m we corroborate this structure analytically via the feigenbaum renormalization group rg transformation and find that the sensitivity to initial conditions has precisely the form of a q exponential of which we determine the q index and the q generalized lyapunov coefficientl q our results are an unequivocal validation of the applicability of the nonextensive generalization of boltzmann gibbs statistical mechanics to critical points of nonlinear maps critical points of nonlinear maps offer a suitable playground for testing the validity of the nonextensive generalization of the boltzmann gibbs bg statistical mechanics proposed by tsallis over a decade ago 1 2 here we describe universal properties related to the dynamics of iterates at the onset of chaos in unimodal maps 3 which provide a literal confirmation of the generalized nonextensive theory to this end we employ the celebrated one dimensional logistic map f m x 512muxu 2 21 x 1 and the properties of its renormalization group rg fixed point to present evidence of previously unexposed scaling properties at the onset of chaos m5m at this state the most prominent of the map critical points the trajectories of the iterates exhibit an intricate structure that we describe and show is governed by the feigenbaum rg transformation 3 the domain of validity of bg statistical mechanics has been implicitly challenged by the proposal of its nonextensive generalization subsequent studies have offered experimental and numerical evidence that point out both the inadequacy of the standard bg statistics and the plausible competence of the generalized theory in describing various types of phenomena and systems this theoretical development represents an exceptional event in the long and trustworthy history of bg statistical mechanics however it is still in the process of being converted into a rigorously corroborated and fully understood fact the suggested circumstances under which the generalized theory is believed to be applicable at least with regards to nonlinear dynamical systems are those associated to a phase space with power law sensitivity to initial conditions to the consequent vanishing of the largest lyapunov exponent and to a fractal or multifractal geometrical structure 2 here we show that our results for the dynamics at the onset of chaos in unimodal maps constitute an unequivocal proof of the universal validity of the nonextensive statistics at such critical points in fact at the chaos threshold as well as at other critical points of the map the lyapunov exponent l 1 vanishes and the sensitivity to initial conditions j t for large iteration time t ceases to obey exponential behavior exhibiting instead a power law behavior 4 in order to describe the dynamics at such critical points the q exponential expression

symplectic numerical integrators in constrained hamiltonian systems recent work reported in the literature suggests that for the long time integration of hamiltonian dynamical systems one should use methods that preserve the symplectic or canonical structure of the flow here we investigate the symplecticness of numerical integrators for constrained dynamics such as occur in molecular dynamics when bond lengths are made rigid in order to overcome stepsize limitations due to the highest frequencies this leads to a constrained hamiltonian system of smaller dimension previous work has shown that it is possible to have methods which are symplectic on the constraint manifold in phase space here it is shown that the very popular verlet method with shake type constraints is equivalent to the same method with rattle type constraints and that the latter is symplectic and time reversible this assumes that the iteration is carried to convergence we also demonstrate the global convergence of the verlet scheme in the presence of shake type and rattle type constraints we perform numerical experiments to compare these methods with the second order backward differentiation method commonly recommended for ordinary differential equations with constraints

hamiltonian moving particle semi implicit hmps method for incompressible fluid flows particle methods are meshless simulation techniques in which motion of continua is approximated by discrete dynamics of a finite number of particles and thus have a great degree of flexibility for instance in dealing with the complex motion of surfaces or boundaries in this paper a particle method is developed from a direct discretization of the lagrangian for inviscid incompressible fluid flows the discretized lagrangian is transformed into a hamiltonian with holonomic constraints that stem from the incompressibility condition the rattle algorithm that is a symplectic scheme for holonomically constrained hamiltonian systems is adopted so that the resulting particle method inherits structures possessed by the partial differential equations that govern inviscid incompressible flows the algorithm of the particle method is semi implicit so we call it the hamiltonian moving particle semi implicit hmps method some numerical tests indicate the excellence of the hmps method in conservation of mechanical energy as well as linear and angular momenta

two dimensional maps at the edge of chaos numerical results for the henon map the mixing properties or sensitivity to initial conditions of the two dimensional henon map have been explored numerically at the edge of chaos three independent methods which have been developed and used so far for one dimensional maps have been used to accomplish this task these methods are i the measure of the divergence of initially nearby orbits ii analysis of the multifractal spectrum and iii computation of nonextensive entropy increase rates the results obtained closely agree with those of the one dimensional cases and constitute a verification of this scenario in two dimensional maps this obviously makes the idea of weak chaos even more robust

short time dynamics of isotropic and anisotropic bak sneppen model extensive simulation results abstract in this work the short time dynamics of the isotropic and anisotropic versions of the bak sneppen bs model has been investigated using the standard damage spreading technique since the system sizes attained in our simulations are larger than the ones employed in previous studies our results for the dynamic scaling exponents are expected to be more accurate than the results of the existing literature the obtained scaling exponents of both versions of the bs model are found to be greater than the ones given in previous works these findings are in agreement with the recent claim of cafiero et al eur phys j b7 1999 505 moreover it is found that the short time dynamics of the anisotropic model is only slightly affected by finite size effects and the reported estimate of 0 53 can be considered as a good estimate of the true exponent in the thermodynamic limit

semiclassical theory of spectral rigidity the spectral rigidity l of a set of quantal energy levels is the mean square deviation of the spectral staircase from the straight line that best fits it over a range of l mean level spacings in the semiclassical limit 0 formulae are obtained giving l as a sum over classical periodic orbits when l l max where l max n 1 for a system of n freedoms l is shown to display the following universal behaviour as a result of properties of very long classical orbits if the system is classically integrable all periodic orbits filling tori l 1 5 l as in an uncorrelated poisson eigenvalue sequence if the system is classically chaotic all periodic orbits isolated and unstable and has no symmetry l in l 2 2 d if 1 l l max as in the gaussian unitary ensemble of random matrix theory if the system is chaotic and has time reversal symmetry l in l 2 e if 1 l l max as in the gaussian orthogonal ensemble when l l max l saturates non universally at a value determined by short classical orbits of order n 1 for integrable systems and in 1 for chaotic systems these results are obtained by using the periodic orbit expansion for the spectral density together with classical sum rules for the intensities of long orbits and a semiclassical sum rule restricting the manner in which their contributions interfere for two examples l is studied in detail the rectangular billiard integrable and the riemann zeta function assuming its zeros to be the eigenvalues of an unknown quantum system whose unknown classical limit is chaotic

moving least square reproducing kernel methods i methodology and convergence this paper formulates the moving least square interpolation scheme in a framework of the so called moving least square reproducing kernel mlsrk representation in this study the procedure of constructing moving least square interpolation function is facilitated by using the notion of reproducing kernel formulation which as a generalization of the early discrete approach establishes a continuous basis for a partition of unity this new formulation possesses the quality of simplicity and it is easy to implement moreover the reproducing kernel formula proposed is not only able to reproduce any mth order polynomial exactly on an irregular particle distribution but also serves as a projection operator that can approximate any smooth function globally with an optimal accuracy in this contribution a generic m consistency relation has been found which is the essential property of the mlsrk approximation an interpolation error estimate is given to assess the convergence rate of the approximation it is shown that for sufficiently smooth function the interpolant expansion in terms of sampled values will converge to the original function in the sobolev norms as a meshless method the convergence rate is measured by a new control variable dilation parameter of the window function instead of the mesh size h as usually done in the finite element analysis to illustrate the procedure convergence has been shown for the numerical solution of the second order elliptic differential equations in a galerkin procedure invoked with this interpolant in the numerical example a two point boundary problem is solved by using the method and an optimal convergence rate is observed with respect to various norms

convergence to the critical attractor of dissipative maps log periodic oscillations fractality and nonextensivity for a family of logisticlike maps we investigate the rate of convergence to the critical attractor when an ensemble of initial conditions is uniformly spread over the entire phase space we found that the phase space volume occupied by the ensemble w t depicts a power law decay with log periodic oscillations reflecting the multifractal character of the critical attractor we explore the parametric dependence of the power law exponent and the amplitude of the log periodic oscillations with the attractor s fractal dimension governed by the inflection of the map near its extremal point further we investigate the temporal evolution of w t for the circle map whose critical attractor is dense in this case we found w t to exhibit a rich pattern with a slow logarithmic decay of the lower bounds these results are discussed in the context of nonextensive tsallis entropies

on the transition to chaotic scattering a classical scattering system is chaotic if it possesses a fractal set of trapped unstable orbits resulting in singular deflection functions a scattering system is regular if it supports only a countable set of trapped unstable orbits its deflection functions are piecewise smooth with at most a countable number of scattering singularities caused by the trapped orbits despite the simple structure of the deflection functions the poincare scattering mapping psm may be regular hyperbolic or display mixed dynamics thus the degree of chaoticity of the psm serves as a finer scale for the discussion of the transition to chaotic scattering in the classical domain in the quantum domain the authors show that the properties of the psm determine the statistics of the eigenphases of the s matrix and that if the psm is hyperbolic the eigenphases follow the statistics predicted by random matrix theory

asynchronous variational integrators we describe a class of asynchronous variational integrators avi for nonlinear elastodynamics the avis are characterized by the following distinguishing attributes i the algorithms permit the selection of independent time steps in each element and the local time steps need not bear an integral relation to each other ii the algorithms derive from a spacetime form of a discrete version of hamilton s principle as a consequence of this variational structure the algorithms conserve local energy and momenta exactly subject to solvability of the local time steps numerical tests reveal that even when local energy balance is not enforced exactly the global and local energy behavior of the avis is quite remarkable a property which can probably be traced to the symplectic nature of the algorithm

the finite mass method the finite mass method a new lagrangian method for the numerical simulation of gas flows is presented and analyzed in contrast to the finite volume and the finite element method the finite mass method is founded on a discretization of mass not of space mass is subdivided into small mass packets of finite extension each of which is equipped with finitely many internal degrees of freedom these mass packets move under the influence of internal and external forces and the laws of thermodynamics and can undergo arbitrary linear deformations the method is based on an approach recently developed by yserentant and can attain a very high accuracy

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

a hamiltonian particle method for non linear elastodynamics particle methods are meshless simulation techniques in which motion of continua is approximated by discrete dynamics of a finite number of particles they have a great degree of flexibility for instance in dealing with complex large deformations or the fragmentation of solids in this paper a particle method for non linear elastodynamics of compressible and incompressible materials is developed based on a discretization of the lagrangian from which the governing equations of elastodynamics are derived using the principle of least action the discretized lagrangian leads to a finite dimensional hamiltonian system via the legendre transformation if the material is incompressible the hamiltonian system is accompanied by holonomic constraints depending on whether the material is compressible or incompressible the symplectic scheme adopted for numerical time integration is either the stormer verlet scheme or the rattle method respectively the resulting particle method inherits the symplectic structure possessed by the governing equations of elastodynamics in the case of incompressible materials incompressibility is strictly enforced at each time step some numerical tests indicate the excellence of the method for conservation of mechanical energy besides that of linear and angular momenta

convergence dynamics of the bak sneppen model activity rate and waiting time distribution abstract in this work we study the convergence dynamics of two independent random configurations of the bak sneppen model of self organized criticality evolving under the same external noise a recently proposed measure of the hamming distance which considers the minimum difference between displaced configurations is used the displacement evolves in time intermittently we compute the jump activity rate and waiting time distribution and report on their asymptotic power law scaling which characterizes the slow relaxation and the absence of typical length and time scales typical of critical dynamical systems