violation of the fluctuation dissipation theorem in glassy systems basic notions and the numerical evidence this review reports on the research done during past years on violations of the fluctuation dissipation theorem fdt in glassy systems it is focused on the existence of a quasi fluctuation dissipation theorem qfdt in glassy systems and the current supporting knowledge gained from numerical simulation studies it covers a broad range of non stationary aging and stationary driven systems such as structural glasses spin glasses coarsening systems ferromagnetic models at criticality trap models models with entropy barriers kinetically constrained models sheared systems and granular media the review is divided into four main parts 1 an introductory section explaining basic notions related to the existence of the fdt in equilibrium and its possible extension to the glassy regime qfdt 2 a description of the basic analytical tools and results derived in the framework of some exactly solvable models 3 a detailed report of the current evidence in favour of the qfdt and 4 a brief digression on the experimental evidence in its favour this review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the qfdt as well as for the more expert readers who may be interested in more specific results

entropy barriers and slow relaxation in some random walk models we study the zero temperature limit of a simple model of slow relaxation without energy barriers proposed by ritort 1995 as well as two other closely related models with a much faster relaxation these models can be mapped onto random walk problems which allows for their analytic study we analyse in particular a specific aspect of the former model namely the existence of a bias leading to entropy barriers and to a very slow relaxation

a vertex based finite volume method applied to non linear material problems in computational solid mechanics a vertex based finite volume fv method is presented for the computational solution of quasi static solid mechanics problems involving material non linearity and infinitesimal strains the problems are analysed numerically with fully unstructured meshes that consist of a variety of two and threedimensional element types a detailed comparison between the vertex based fv and the standard galerkin fe methods is provided with regard to discretization solution accuracy and computational efficiency for some problem classes a direct equivalence of the two methods is demonstrated both theoretically and numerically however for other problems some interesting advantages and disadvantages of the fv formulation over the galerkin fe method are highlighted

a finite volume procedure to solve elastic solid mechanics problems in three dimensions on an unstructured mesh a finite volume fv procedure is described for solving the elastic solid mechanics equations in three dimensions on an unstructured mesh for bodies undergoing thermal or mechanical loads the fv procedure is developed in parallel with the conventional fe galerkin procedure so that the differences in each approach may be clearly distinguished the matrix form of the fv procedure is described and is implemented in parallel with the fe procedure both for two dimensional quadrilateral and three dimensional brick meshes the fv and fe procedures are then compared against a range of benchmark problems that test the basic capability of the fv technique it is shown to be approximately as accurate as the fe procedure on similar meshes though its system matrix set up time is twice as long for a node by node set up procedure

asymptotic iteration method solutions to the relativistic duffin kemmer petiau equation a simple exact analytical solution of the relativistic duffin kemmer petiau equation within the framework of the asymptotic iteration method is presented exact bound state energy eigenvalues and corresponding eigenfunctions are determined for the relativistic harmonic oscillator as well as the coulomb potentials as a nontrivial example the anharmonic oscillator is solved and the energy eigenvalues are obtained within the perturbation theory using the asymptotic iteration method

wave functions for a duffin kemmer petiau particle in a time dependent potential we present the solution of the duffin kemmer petiau equation of spin 0 in a time dependent linear scalar field the treatment is based on the use of the lewis jr riensfield invariant method

a finite volume method for analysing the bending deformation of thick and thin plates the formulation of a novel finite volume based procedure for determining deformations and moment distributions within transversely loaded plates is described in detail the formulation employs the mindlin theory of plate deformation transverse displacement and bending moment distributions are determined for a number of test problems the effect of mesh refinement upon the accuracy of the displacement and moment fields is investigated the finite volume procedure exhibits a number of interesting features it is conservative in the sense that equilibrium is satisfied locally within each cell and across cell boundaries it has the capacity to represent the behaviour of thick and thin plates and it is geometrically versatile because the cell shapes can take the form of multifaceted polygons

a matrix free implicit unstructured multigrid finite volume method for simulating structural dynamics and fluid structure interaction a new three dimensional 3d matrix free implicit unstructured multigrid finite volume fv solver for structural dynamics is presented in this paper the solver is first validated using classical 2d and 3d cantilever problems it is shown that very accurate predictions of the fundamental natural frequencies of the problems can be obtained by the solver with fast convergence rates this method has been integrated into our existing fv compressible solver x lv y zhao et al an efficient parallel unstructured multigrid preconditioned implicit method for simulating 3d unsteady compressible flows with moving objects journal of computational physics 215 2 2006 661 690 based on the immersed membrane method imm x lv y zhao et al as mentioned above results for the interaction between the fluid and an immersed fixed free cantilever are also presented to demonstrate the potential of this integrated fluid structure interaction approach

a finite volume format for structural mechanics summary a general finite volume method fvm for the analysis of structural problems is presented it is shown that the fvm can be considered to be a particular case of finite elements with a non galerkin weighting for structural analysis this can readily be interpreted as equivalent to the unit displacement method which involves mainly surface integrals both displacement and mixed fv formulations are presented for static and dynamic problems the finite volume method fvm evolved in the early seventies via finite difference approxima tions on non orthogonal grids the popularity of the fvm has been extensive in the field of computational fluid dynamics cfd and heat transfer on the contrary in the field of computational solid mechanics csm the use of the fvm has never achieved such acceptance an early attempt to use fv concepts in csm is due to wilkins6 as an alternative approximation to derivatives in a cell in this he defines the average gradient of a function u in a volume l2 as using the well known divergence theorem such a definition of gradients can be written entirely in terms of function values at the boundary of a volume and has been used in the early hydrocodes of the lawrence livermore laboratory the reasons for the unpopularity of the fvm in structural mechanics is understandable as finite volumes are well known to be less accurate than galerkin based finite elements for self adjoint elliptic problems a comparison between fvm and fem has been recently pre sented by zienkiewicz and oiiate here the authors show that fvm and fem share concepts such as mesh discretization and interpolation giving precisely the same discretized systems of equations for some particular cases this coincidence also shows clearly for 2 d and 3 d structural problems as detailed in this work here however surface integrals are mostly involved and the number of computations can be shown to be proportional to the number of sides in the mesh this leads to an overall solution cost very similar to that of fe computations note that for a refined mesh of three node triangles the number of sides is 1 5 times that of elements this fact suggests that computational speed is not a prior one of the keys to the possible success of fvm in structural problems however the possibility of obtaining the element matrices and vectors in terms of computations along the element sides opens new possibilities for the solution of some structural problems which in the authors opinion may be worth exploring in detail indeed it

uncertainty relation in quantum mechanics with quantum group symmetry the commutation relations uncertainty relations and spectra of position and momentum operators were studied within the framework of quantum group symmetric heisenberg algebras and their bargmann fock representations as an effect of the underlying noncommutative geometry a length and a momentum scale appear leading to the existence of nonzero minimal uncertainties in the positions and momenta the usual quantum mechanical behavior is recovered as a limiting case for not too small and not too large distances and momenta

bounding spectral gaps of markov chains a novel exact multi decomposition technique we propose an exact technique to calculate lower bounds of spectral gaps of discrete time reversible markov chains on finite state sets spectral gaps are a common tool for evaluating convergence rates of markov chains as an illustration we successfully use this technique to evaluate the absorption time of the backgammon model a paradigmatic model for glassy dynamics we also discuss the application of this technique to the contingency table problem a notoriously difficult problem from probability theory the interest of this technique is that it connects spectral gaps which are quantities related to dynamics with static quantities calculated at equilibrium

on the incompressible constraint of the 4 node quadrilateral element the standard plane 4 node element is written as the summation of a constant gradient matrix usually obtained from underintegration and a stabilization matrix the split is based on a taylor series expansion of element basis functions in the incompressible limit the locking effect of the quadrilateral is traced back to the stabilization matrix which reflects the incomplete higher order term in the taylor series the incompressibility condition is formulated in a weak sense so that the element displacement field is divergence free when integrated over the element volume the resulting algebraic constraint is shown to coincide with a particular eigenvector of the constant gradient matrix which is obtained from the first order terms of the taylor series the corresponding eigenvalue enforces incompressibility implicitly by means of a penalty constraint analytical expressions for that constant dilatation eigenpair are derived for arbitrary element geometries it is shown how the incompressible constraint carries over to the element stiffness matrix if the element stabilization is performed in a particular manner for several classical and recent elements the eigensystems are analysed numerically it is shown that most of the formulations reflect the incompressible constraint identically in the incompressible limit the numerical accuracies of the elements are compared

correlation and response in the backgammon model the ehrenfest legacy we pursue our investigation of the non equilibrium dynamics of the backgammon model a dynamical urn model which exhibits aging and glassy behaviour at low temperature we present an analytical study of the scaling behaviour of the local correlation and response functions of the density fluctuations of the model and of the associated fluctuation dissipation ratios throughout the regime of low temperature and long times this analysis includes the aging regime the convergence to equilibrium and the crossover behaviour between them

absorption time in certain urn models we show that the average absorption time in a certain m urn model recently introduced by ritort in the context of glassy dynamics has a lower bound where n is the number of balls a monte carlo scheme which accurately estimates the absorption time even when indicates that for large n we have

stress computations for nearly incompressible materials by the p version of the finite element method in the case of nearly incompressible elastic materials the strain energy the shear stress and the difference of normal stresses can be computed accurately by direct methods when the p version of the finite element method is used computation of the sum of the normal stresses requires special procedures in this paper such procedures are described and examples are presented

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 finite volume method for large strain analysis of incompressible hyperelastic materials this paper describes development of a displacement pressure based finite volume formulation for modelling of large strain problems involving incompressible hyperelastic materials the method is based on the solution of the integral conservation equations governing momentum balance in total lagrangian description the incompressibility constraint is enforced by employing the integral form of the mass conservation equation in deformed configurations of the body a mooney rivlin incompressible material model is used for material description a collocated variable arrangement is used and the spatial domain is discretized using finite volumes of an arbitrary polyhedral shape a segregated approach is employed to solve resulting set of coupled non linear algebraic equations utilizing a simple based algorithm for displacement pressure coupling comparisons of numerical and analytical results show a very good agreement for the limited range of cell topologies tested the developed method appears to be locking free copyright 2005 john wiley sons ltd

numerical method for coupled fluid flow heat transfer and stress analysis using unstructured moving meshes with cells of arbitrary topology abstract a numerical method is presented that can be used for both solid body stress analysis and fluid flow predictions independently as well as in a coupled manner the method uses an integral form of equations governing mass energy and momentum balance for an arbitrary control volume a detailed description is provided of a novel second order accurate spatial discretisation technique which can accommodate unstructured moving meshes with cells of arbitrary topology this is accompanied by a fully implicit temporal discretisation which makes the method stable for any time step size the resulting set of coupled non linear algebraic equations is solved by employing a segregated approach leading to a decoupled set of linear algebraic equations for each dependent variable with a sparse diagonally dominant coefficient matrix these equations are solved by an iterative conjugate gradient solver which retains the sparsity of the coefficient matrix thus achieving a very efficient use of computer resources the method has been tested on a number of fluid flow and stress analysis problems and numerical calculations show favourable agreement with analytical and or experimental results in order to demonstrate the full capabilities of the present method an example of numerically complex coupled fluid flow stress analysis and heat transfer calculations is presented

dynamics of the condensate in zero range processes for stochastic processes leading to condensation the condensate once it is formed performs an ergodic stationary state motion over the system we analyse this motion and especially its characteristic time for zero range processes the characteristic time is found to grow with the system size much faster than the diffusive time scale but not exponentially fast this holds both in the mean field geometry and on finite dimensional lattices in the generic situation where the critical mass distribution follows a power law the characteristic time grows as a power of the system size

a finite volume method for incompressible linear elasticity abstract this paper describes development of a finite volume based method for modelling of incompressible linear elastic body problems the method is based on the solution of the integral form of conservation equations governing momentum balance and the introduction of pressure as an additional variable the incompressibility is enforced by employing the volumetric constraint equation a collocated variable arrangement is used and the spatial domain is discretised using finite volumes of arbitrary polyhedral shapes a segregated approach is employed to solve resulting set of coupled linear algebraic equations embedding a simple based algorithm for displacement pressure coupling numerical experiments showed that the developed method appears to be locking free

a unified formulation for continuum mechanics applied to fluid structure interaction in flexible tubes this paper outlines the development of a new procedure for analysing continuum mechanics problems with a particular focus on fluid structure interaction in flexible tubes a review of current methods of fluid structure coupling highlights common limitations of high computational cost and solution instability it is proposed that these limitations can be overcome by an alternative approach in which both fluid and solid components are solved within a single discretized continuum domain a single system of momentum and continuity equations is therefore derived that governs both fluids and solids and which are solved with a single mesh using finite volume discretization schemes the method is validated first by simulating dynamic oscillation of a clamped elastic beam it is then applied to study the case of interest wave propagation in highly flexible tubes in which a predicted wave speed of 8 58m s falls within 2 of an approximate analytical solution the method shows further good agreement with analytical solutions for tubes of increasing rigidity covering a range of wave speeds from those found in arteries to that in the undisturbed fluid

finite volume method for thermo elasto plastic stress analysis abstract in this paper a new numerical method for prediction of stresses and displacements in thermo elasto plastic material is presented the method is based on the direct solution of the governing equations for thermal energy and momentum balance expressed in terms of temperature and displacements as dependent variables via corresponding constitutive relations and discretized by the finite volume technique as a result the unsteady fields of temperature displacements and stresses as well as residual stresses in a solid body subjected to a non uniform temperature and or external loads are obtained the method has been applied to a number of test cases and the results are compared with the analytical solution calculations obtained by another numerical method or experimental data results show that the method is accurate stable and efficient and that it can be used as a useful tool for predicting thermo mechanical deformation processes in a solid body

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

a novel pressure velocity formulation and solution method for fluid structure interaction problems in the standard approach for simulating fluid structure interaction problems the solution of the set of equations for solids provides the three displacement components while the solution of equations for fluids provides the three velocity components and pressure in the present paper a novel reformulation of the elastodynamic equations for hookean solids is proposed so that they contain the same unknowns as the navier stokes equations namely velocities and pressure a separate equation for pressure correction is derived from the constitutive equation of the solid material the system of equations for both media is discretised using the same method finite volume on collocated grids and the same iterative technique simple algorithm is employed for the pressure velocity coupling with this approach the continuity of the velocity field at the interface is automatically satisfied a special pressure correction procedure that enforces the compatibility of stresses at the interface is also developed the new method is employed for the prediction of pressure wave propagation in an elastic tube computations were carried out with different meshes and time steps and compared with available analytic solutions as well as with numerical results obtained using the flugge equations that describe the deformation of thin shells for all cases examined the method showed very good performance

duffin kemmer petiau oscillator with snyder de sitter algebra we present an exact solution of the one dimensional bosonic oscillator for spin 1 and spin 0 particles with the snyder de sitter model where the energy eigenvalues and eigenfunctions are determined for both cases the wave functions can be given in terms of gegenbauer polynomials we also comment on the thermodynamic properties of the system

relaxation at late stages in an entropy barrier model for glassy systems the ground state dynamics of an entropy barrier model proposed recently for describing relaxation of glassy systems is considered at late stages of evolution the dynamics can be described by a simple variant of the ehrenfest urn model analytical expressions for the relaxation times from arbitrary initial states to the ground state are derived upper and lower bounds for the relaxation times as a function of system size are obtained