mean field fluid behavior of the gaussian core model we show that the gaussian core model of particles interacting via a penetrable repulsive gaussian potential first considered by stillinger j chem phys 65 3968 1976 behaves as a weakly correlated mean field fluid over a surprisingly wide density and temperature range in the bulk the structure of the fluid phase is accurately described by the random phase approximation for the direct correlation function and by the more sophisticated hypernetted chain integral equation the resulting pressure deviates very little from a simple mean field like quadratic form in the density while the low density virial expansion turns out to have an extremely small radius of convergence density profiles near a hard wall are also very accurately described by the corresponding mean field free energy functional the binary version of the model exhibits a spinodal instability against demixing at high densities possible implications for semidilute polymer solutions are discussed

discontinuous galerkin methods for incompressible and nearly incompressible elasticity by nitsche s method we propose and analyze a discontinuous finite element method for nearly incompressible linear elasticity on triangular meshes we show optimal error estimates that are uniform with respect to poisson s ratio the method is thus locking free we also introduce an equivalent mixed formulation allowing for completely incompressible elasticity problems numerical results are presented

generalized geometric cluster algorithm for fluid simulation we present a detailed description of the generalized geometric cluster algorithm for the efficient simulation of continuum fluids the connection with well known cluster algorithms for lattice spin models is discussed and an explicit full cluster decomposition is derived for a particle configuration in a fluid we investigate a number of basic properties of the geometric cluster algorithm including the dependence of the cluster size distribution on density and temperature practical aspects of its implementation and possible extensions are discussed the capabilities and efficiency of our approach are illustrated by means of two example studies

localisation in a cosserat continuum under static and dynamic loading conditions abstract localisation studies have been carried out for an unconstrained elasto plastic strain softening cosserat continuum because of the presence of an internal length scale in this continuum model a perfect convergence is found upon mesh refinement a finite constant width of the localisation zone and a finite energy dissipation are computed under static as well as under transient loading conditions because of the existence of rotational degrees of freedom in a cosserat continuum additional wave types arise and wave propagation becomes dispersive this has been investigated analytically and numerically for an elastic cosserat continuum and an excellent agreement has been found between both solutions

hyperelliptic quasi periodic and soliton solutions of the nonlinear schrodinger equation on considere la construction de solutions par des methodes de geometrie algebriques et en particulier par les fonctions theta hyperelliptiques

a fast convergent rate preserving discontinuous galerkin framework for rate independent plasticity problems abstract in this paper a finite element framework based on the incomplete interior penalty galerkin formulation a non symmetric discontinuous galerkin method is consistently formulated for modeling plasticity problems with small deformation because of its pure displacement based framework this proposed discontinuous galerkin method is possibly able to completely preserve numerical integration algorithms efficiently developed in the traditional continuous galerkin framework besides stresses on element interior quadrature points stresses on element surface quadrature points are also required to return on yielding surfaces in this discontinuous galerkin framework which is able to provide more accurate material yielding profiles than the continuous galerkin framework the performance of the proposed discontinuous galerkin framework has been evaluated in detail for j 2 and pressure dependent plasticities using perfect plasticity plasticity with hardening and associative and non associative material models quadratic convergent rates compatible to the tradition continuous galerkin method for modeling plasticity problems have been achieved within a large penalty range in a nodal based discontinuous galerkin implementation

relations between enhanced strain methods and the hr method abstract the three field hu washizu functional is the starting point to develop a comparative analysis of approximate linear elastostatic problems in particular we will analyse the limitation phenomena concerning two mixed methods respectively denoted the strain gap method and the mixed enhanced strain method and the two field hellinger reissner hr finite element formulation accordingly two original limitation principles are contributed we provide the theoretical motivation of the numerical observations provided in computational literature on the coincidence of the displacement and stress solutions between the enhanced assumed strain method and the hr method if different choices of shape functions are made it is further shown that the hr method provides the exact stress solution and the exact nodal displacements with one element the related analytical motivation are thus given the theoretical analyses presented in the paper are supported by numerical examples on tipical benchmarks

hard sphere fluids in contact with curved substrates the properties of a hard sphere fluid in contact with hard spherical and cylindrical walls are studied rosenfeld s density functional theory dft is applied to determine the density profile and surface tension gamma for wide ranges of radii of the curved walls and densities of the hard sphere fluid particular attention is paid to investigate the curvature dependence and the possible existence of a contribution to gamma which is proportional to the logarithm of the radius of curvature moreover by treating the curved wall as a second component at infinite dilution we provide an analytical expression for the surface tension of a hard sphere fluid close to arbitrary hard convex walls the agreement between the analytical expression and dft is good our results show no signs for the existence of a logarithmic term in the curvature dependence of gamma

a symmetric nonlocal damage theory abstract the paper presents a thermodynamically consistent formulation for nonlocal damage models nonlocal models have been recognized as a theoretically clean and computationally efficient approach to overcome the shortcomings arising in continuum media with softening the main features of the presented formulation are i relations derived by the free energy potential fully complying with nonlocal thermodynamic principles ii nonlocal integral operator which is self adjoint at every point of the solid including zones near to the solid s boundary iii capacity of regularizing the softening ill posed continuum problem restoring a meaningful nonlocal boundary value problem in the present approach the nonlocal integral operator is applied consistently to the damage variable and to its thermodynamic conjugate force i e nonlocality is restricted to internal variables only the present model when associative nonlocal damage flow rules are assumed allows the derivation of the continuum tangent moduli tensor and the consistent tangent stiffness matrix which are symmetric the formulation has been compared with other available nonlocal damage theories finally the theory has been implemented in a finite element program and the numerical results obtained for 1 d and 2 d problems show its capability to reproduce in every circumstance a physical meaningful solution and fully mesh independent results

energy norm a posteriori error estimates for discontinuous galerkin approximations of the linear elasticity problem we present a residual based a posteriori error estimate in an energy norm of the error in a family of discontinuous galerkin approximations of linear elasticity problems the theory is developed in two and three spatial dimensions and general nonconvex polygonal domains are allowed we also present some illustrating numerical examples

penetrable square well fluids exact results in one dimension we introduce a model of attractive penetrable spheres by adding a short range attractive square well outside a penetrable core and we provide a detailed analysis of structural and thermodynamical properties in one dimension using the exact impenetrable counterpart as a starting point the model is expected to describe star polymers in regimes of good and moderate solvent under dilute conditions we derive the exact coefficients of a low density expansion up to second order for the radial distribution function and up to fourth order in the virial expansion these exact results are used as a benchmark to test the reliability of approximate theories percus yevick and hypernetted chain notwithstanding the lack of an exact solution for arbitrary densities our results are expected to be rather precise within a wide range of temperatures and densities a detailed analysis of some limiting cases is carried out in particular we provide a complete solution of the sticky penetrable sphere model in one dimension up to the same order in density the issue of ruelle s thermodynamics stability is analyzed and the region of a well defined thermodynamic limit is identified

a low order locking free hybrid discontinuous galerkin element formulation for large deformations abstract in this work a hybrid discontinuous galerkin dg quadrilateral element formulation is presented as usual in hybrid formulations the interior of the elements is treated separately from the skeleton which represents the element boundaries these are kinematically decoupled i e displacement jumps can occur between the skeleton and the interior of the elements the global degrees of freedom dofs are defined on the skeleton as the displacements at the corners which allows the implementation into existing finite element codes as usual in hybrid dg formulations the degrees of freedom in the interior are condensed out on the element level leading to the same number of global degrees of freedom as for continuous bilinear elements instead of using conventional shape functions in the interior the deformation gradient f is assumed constant within the element furthermore f is connected to the skeleton degrees of freedom via the weak form this leads to a very simple formulation and implementation the element is tested for several computational examples from the literature special choices of the penalty parameter are investigated which are partially derived analytically it is found that the element is free of volumetric and shear locking moreover the convergence is similar to that of other well known locking free finite element formulations

on an equivalence between a discontinuous galerkin method and reduced integration with hourglass stabilization for finite elasticity abstract discontinuous galerkin methods and methods of reduced integration with hourglass stabilization have different points of origin whereas the discontinuous galerkin idea was developed to investigate a wide range of applications among them problems of electrodynamics fluid and solid mechanics the reduced integration technology started out from the observation of the so called locking problem in linear elasticity today the two methodologies are still considered separately from each other although it has already been recognized that discontinuous galerkin methods can be also used to circumvent locking phenomena in elasticity the idea of the present contribution is to find a direct equivalence between a discontinuous galerkin method and a finite element technology based on reduced integration with hourglass stabilization the transfer between the two methods is carried out in the context of finite elasticity thus the derivation is valid for arbitrarily large deformations the main advantage of this analysis is that the choice of the free parameter in nitsche s method often also called stabilization parameter is no longer unclear but prescribed by the connection to the hourglass stabilization further important in this context is the replacement of the scalar parameter by a symmetric 2 2 matrix if two dimensional problems are considered which is here the case the result of the derivation is a discontinuous galerkin formulation which shows very good convergence behaviour not only in the limit of incompressibility but also for bending of thin structures

feedback induced oscillations in one dimensional colloidal transport we investigate a driven one dimensional system of colloidal particles in a periodically corrugated narrow channel subject to a time delayed feedback control our goal is to identify conditions under which the control induces oscillatory time periodic states the investigations are based on the fokker planck equation involving the density distribution of the system first by using the numerical continuation technique we determine the linear stability of a stationary density second the nonlinear regimes are analyzed by studying numerically the temporal evolution of the first moment of the density distribution in this way we construct a bifurcation diagram revealing the nature of the instability apart from the case of a system with periodic boundary conditions we also consider a microchannel of finite length finally we study the influence of repulsive particle interactions based on dynamical density functional theory

an analysis of the discontinuous galerkin method for a scalar hyperbolic equation we prove lp stability and error estimates for the discontinuous galerkin method when applied to a scalar linear hyperbolic equation on a convex polygonal plane domain using finite element analysis techniques we obtain l2 estimates that are valid on an arbitrary locally regular triangulation of the domain and for an arbitrary degree of polynomials lp estimates for p 2 are restricted to either a uniform or piecewise uniform triangulation and to polynomials of not higher than first degree the latter estimates are proved by combining finite difference and finite element analysis techniques

numerical integration with taylor truncations for the quadrilateral and hexahedral finite elements for general quadrilateral or hexahedral meshes the finite element methods require evaluation of integrals of rational functions instead of traditional polynomials it remains as a challenge in mathematics to show the traditional gauss quadratures would ensure the correct order of approximation for the numerical integration in general however in the case of nested refinement the refined quadrilaterals and hexahedra converge to parallelograms and parallelepipeds respectively based on this observation the rational functions of inverse jacobians can be approximated by the taylor expansion with truncation then the gauss quadrature of exact order can be adopted for the resulting integrals of polynomials retaining the optimal order approximation of the finite element methods a theoretic justification and some numerical verification are provided in the paper

hourglass control in linear and nonlinear problems abstract mesh stabilization techniques for controlling the hourglass modes in under integrated hexahedral and quadrilateral elements are described it is shown that the orthogonal hourglass techniques previously developed can be obtained from simple requirements that insure the consistency of the finite element equations in the sense that the gradients of linear fields are evaluated correctly it is also shown that this leads to an hourglass control that satisfies the patch test the nature of the parameters which relate the generalized stresses and strains for controlling hourglass modes is examined by means of a mixed variational principle and some guidelines for their selection are discussed finally effective means of implementing these hourglass procedure in computer codes are described applications to both the laplace equation and the equations of solid mechanics in 2 and 3 dimensions are considered

a c0 discontinuous galerkin formulation for kirchhoff plates abstract a particular discontinuous galerkin finite element formulation for the simulation of kirchhoff plates is presented it is rotation free and utilises standard c 0 lagrange finite element basis functions with the required continuity imposed in a weak sense across element boundaries the implications of the scheme in terms of coercivity and convergence of the galerkin problem in various norms are studied with the formulation shown to be stable for any positive value of a penalty parameter a priori error estimates are supported by a range of numerical examples properties of the approach for the important eigenvalue problems of plate buckling and vibration are also examined through numerical examples based on the results of the analysis and numerical examples it is concluded that the formulation is robust accurate and relatively simple

three dimensional isogeometric solutions to general boundary value problems of toupin s gradient elasticity theory at finite strains abstract we present to the best of our knowledge the first complete three dimensional numerical solutions to a broad range of boundary value problems for a general theory of finite strain gradient elasticity we have chosen for our work toupin s theory toupin 1962 one of the more general formulations of strain gradient elasticity our framework has three crucial ingredients the first is isogeometric analysis hughes et al 2005 which we have adopted for its straightforward and robust representation of c 1 continuity the second is a weak treatment of the higher order dirichlet boundary conditions in the formulation which control the development of strain gradients in the solution the third ingredient is algorithmic automatic differentiation which eliminates the need for linearization by hand of the rather complicated geometric and material nonlinearities in gradient elasticity at finite strains we present a number of numerical solutions to demonstrate that the framework is applicable to arbitrary boundary value problems in three dimensions we discuss length scale effects the role of higher order boundary conditions and perhaps most importantly the relevance of the framework to problems with elastic free energy density functions that are non convex in strain space

an exactly solvable model for depletion phenomena abstract the equilibrium properties of a one dimensional mixture of hard rods of two different lengths are obtained these are used to test the free volume approximation which has in the past been applied in the study of hard sphere mixtures in three dimensions three different versions of the free volume approximation are tested in the most primitive of these the smaller spheres or rods are assumed not to interact with each other in higher levels of the approximation the interactions between the smaller molecules are partly taken into account the results show the ranges of compositions and densities over which the approximations are accurate and they identify one form of the approximation as the most reliable

dispersion analysis and element free galerkin solutions of second and fourth order gradient enhanced damage models gradient dependent damage formulations incorporate higher order derivatives of state variables in the constitutive equations different formulations have been derived for this gradient enhancement comparison of which is difficult in a finite element context due to higher order continuity requirements for certain formulations on the other hand the higher order continuity requirements are met naturally by element free galerkin efg shape functions thus the efg method provides a suitable tool for the assessment of gradient enhanced continuum models dispersion analyses have been carried out to compare different gradient enhanced models with the non local damage model the formulation of the additional boundary conditions is addressed numerical examples show the objectivity with respect to the discretization and the differences between various gradient formulations with second and fourth order derivatives it is shown that with the same underlying internal length scale very different results can be obtained copyright 2000 john wiley sons ltd

demixing can occur in binary hard sphere mixtures with negative nonadditivity a binary fluid mixture of nonadditive hard spheres characterized by a size ratio gamma sigma 2 sigma 1 infinity a demixing transition with a critical consolute point at a packing fraction scaling as eta approximately d2 d is found even for slightly negative nonadditivity if delta 1 8 ln gamma 2 arguments concerning the stability of the demixing with respect to freezing are provided

depletion potentials in highly size asymmetric binary hard sphere mixtures comparison of simulation results with theory we report a detailed study using state of the art simulation and theoretical methods of the effective depletion potential between a pair of big hard spheres immersed in a reservoir of much smaller hard spheres the size disparity being measured by the ratio of diameters q ensuremath equiv ensuremath sigma s ensuremath sigma b small particles are treated grand canonically their influence being parameterized in terms of their packing fraction in the reservoir ensuremath eta s r two monte carlo simulation schemes the geometrical cluster algorithm and staged particle insertion are deployed to obtain accurate depletion potentials for a number of combinations of q ensuremath leqslant 0 1 and ensuremath eta s r after applying corrections for simulation finite size effects the depletion potentials are compared with the prediction of new density functional theory dft calculations based on the insertion trick using the rosenfeld functional and several subsequent modifications while agreement between the dft and simulation is generally good significant discrepancies are evident at the largest reservoir packing fraction accessible to our simulation methods namely ensuremath eta s r 0 35 these discrepancies are however small compared to those between simulation and the much poorer predictions of the derjaguin approximation at this ensuremath eta s r the recently proposed morphometric approximation performs better than derjaguin but is somewhat poorer than dft for the size ratios and small sphere packing fractions that we consider the effective potentials from simulation dft and the morphometric approximation were used to compute the second virial coefficient b 2 as a function of ensuremath eta s r comparison of the results enables an assessment of the extent to which dft can be expected to correctly predict the propensity toward fluid fluid phase separation in additive binary hard sphere mixtures with q ensuremath leqslant 0 1 in all the new simulation results provide a fully quantitative benchmark for assessing the relative accuracy of theoretical approaches for calculating depletion potentials in highly size asymmetric mixtures

stability and convergence of a class of enhanced strain methods a stability and convergence analysis is presented of a recently proposed variational formulation and finite element method for elasticity which incorporates an enhanced strain field the analysis is carried out for problems posed on polygonal domains in r n the finite element meshes of which are generated by affine maps from a master element the formulation incorporates as a special case the classical method of incompatible modes the problem initially has three variables viz displacement stress and enhanced strain but the stress is later eliminated by imposing a condition of orthogonality with respect to the enhanced strains two other conditions on the choice of finite element spaces ensure that the approximations are stable and convergent some features of nearly incompressible and incompressible problems are also investigated for these cases it is possible to argue that locking will not occur and that the only spurious pressures present are the so called checkerboard modes it is shown th

a theorem on the absence of phase transitions in one dimensional growth models with on site periodic potentials we rigorously prove that a wide class of one dimensional growth models with on site periodic potential such as the discrete sine gordon model have no phase transition at any temperature t 0 the proof relies on the spectral analysis of the transfer operator associated with the models we show that this operator is hilbert schmidt and that its maximum eigenvalue is an analytical function of temperature

on the spatial formulation of discontinuous galerkin methods for finite elastoplasticity abstract in this paper we present a consistent spatial formulation for discontinuous galerkin dg methods applied to solid mechanics problems with finite deformation this spatial formulation provides a general accurate and efficient dg finite element computational framework for modeling nonlinear solid mechanics problems to obtain a consistent formulation we employ the incomplete interior penalty galerkin iipg method another requirement for achieving a fast convergence rate for newton s iterations is the consistent formulation of material integrators we show that material integrators that are well developed and tested in continuous galerkin cg methods can be fully exploited for dg methods by additionally performing stress returning on element interfaces finally for problems with pressure or follower loading stiffness contributed from loaded surfaces must also be consistently incorporated in this work we propose the truesdell objective stress rate for both hypoelastoplastic and hyperelastoplastic problems two formulations based on the co rotational and multiplicative decomposition based frameworks are implemented for hypoelastoplasticity and hyperelastoplasticity respectively two new terminologies the so called standard surface geometry stiffness and the penalty surface geometry stiffness are introduced and derived through consistently linearizing the virtual work contributed from interior surface integrals the performance of our dg formulation has been demonstrated through solving a cantilever beam problem undergoing large rotations as well as a bipolar void coalescence problem where the voids grow up to several hundred times of their original volumes fast convergence rates for newton s iterations have been achieved in our iipg implementation

a stable affine approximate finite element method the notion of the affine figure closest to a given quadrilateral can be given a precise mathematical definition the resulting figure is referred to as the equivalent parallelogram associated with a quadrilateral equipped with such a concept it is then feasible to consider finite element approximations in which the original quadrilateral elements are replaced by their equivalent parallelograms the idea is appealing not least because of the resulting economy arising from computations performed on an element generated by an affine map furthermore numerical experiments reported recently indicate that highly efficient and accurate schemes result when such a concept is combined with the enhanced strain method or the method of incompatible modes the purpose of this work is to analyze finite element schemes resulting from approximation of quadrilaterals by their equivalent parallelograms the focus is on low order bilinear elements and the analysis is carried out in the context of linear elasticity for standard approximations as well as for those which use enhanced strains the affine approximation applies only to the element map and the primary unknown the displacement vector in the context of elasticity is approximated by conventional piecewise bilinear functions the analysis confirms convergence at the optimal rate provided that the deviations of the quadrilaterals from their equivalent parallelograms are at most o h

a discontinuous galerkin formulation of non linear kirchhoff love shells discontinuous galerkin dg methods provide a means of weakly enforcing the continuity of the unknown field derivatives and have particular appeal in problems involving high order derivatives this feature has previously been successfully exploited comput methods appl mech eng 2008 197 2901 2929 to develop a formulation of linear kirchhoff love shells considering only the membrane and bending responses in this proposed one field method the displacements are the only unknowns while the displacement field is continuous the continuity in the displacement derivative between two elements is weakly enforced by recourse to a dg formulation it is the purpose of the present paper to extend this formulation to finite deformations and non linear elastic behaviors while the initial linear formulation was relying on the direct linear computation of the effective membrane stress and effective bending couple stress from the displacement field at the mid surface of the shell the non linear formulation considered implies the evaluation of the general stress tensor across the shell thickness leading to a reformulation of the internal forces of the shell nevertheless since the interface terms resulting from the discontinuous galerkin method involve only the resultant couple stress at the edges of the shells the extension to non linear deformations is straightforward copyright 2008 john wiley sons ltd

on whitham theory for perturbed integrable equations abstract whitham theory of modulations is developed for periodic waves described by nonlinear wave equations integrable by the inverse scattering transform method associated with 2 2 matrix or second order scalar spectral problems the theory is illustrated by derivation of the whitham equations for perturbed korteweg de vries equation and nonlinear schrodinger equation with linear damping

discrete coupled derivative nonlinear schrodinger equations and their quasi periodic solutions a hierarchy of nonlinear differential difference equations associated with a discrete isospectral problem is proposed in which a typical differential difference equation is a discrete coupled derivative nonlinear schrodinger equation with the help of the nonlinearization of the lax pairs the hierarchy of nonlinear differential difference equations is decomposed into a new integrable symplectic map and a class of finite dimensional integrable hamiltonian systems based on the theory of algebraic curve the abel jacobi coordinates are introduced to straighten out the corresponding flows from which quasi periodic solutions for these differential difference equations are obtained resorting to the riemann theta functions moreover a 2 1 dimensional discrete coupled derivative nonlinear schrodinger equation is proposed and its quasi periodic solutions are derived

low temperature and high temperature approximations for penetrable sphere fluids comparison with monte carlo simulations and integral equation theories the two body interaction in dilute solutions of polymer chains in good solvents can be modeled by means of effective bounded potentials the simplest of which being that of penetrable spheres pss in this paper we construct two simple analytical theories for the structural properties of ps fluids a low temperature lt approximation that can be seen as an extension to pss of the well known solution of the percus yevick py equation for hard spheres and a high temperature ht approximation based on the exact asymptotic behavior in the limit of infinite temperature monte carlo simulations for a wide range of temperatures and densities are performed to assess the validity of both theories it is found that despite their simplicity the ht and lt approximations exhibit a fair agreement with the simulation data within their respective domains of applicability so that they complement each other a comparison with numerical solutions of the py and the hypernetted chain approximations is also carried out the latter showing a very good performance except inside the core at low temperatures

improved versions of assumed enhanced strain tri linear elements for 3d finite deformation problems abstract improved three dimensional tri linear elements for finite deformation problems are developed based on an assumed enhanced strain methodology which in the linear regime incorporates the classical method of incompatible modes as a particular case three crucial modifications of a recently proposed element which reduces to wilson s brick in the linear regime are introduced to prevent locking response in distorted configurations and to maintain proper rank while preserving excellent performance in bending dominated and localization problems i a modified quadrature rule ii an additional enhancement of the divergence term and iii a modification of the isoparametric shape function derivatives for the three dimensional problem moreover these modified shape function derivatives are shown to improve the performance of the standard tri linear brick in distorted configurations in addition a strategy is described to circumvent the memory storage requirements in the static condensation procedure of the enhanced strain parameters the excellent performance of the improved methodology is illustrated in representative numerical simulations

influence of polydispersity on the critical parameters of an effective potential model for asymmetric hard sphere mixtures we report a monte carlo simulation study of the properties of highly asymmetric binary hard sphere mixtures this system is treated within an effective fluid approximation in which the large particles interact through a depletion potential r roth et al phys rev e 62 5360 2000 designed to capture the effects of a virtual sea of small particles we generalize this depletion potential to include the effects of explicit size dispersity in the large particles and consider the case in which the particle diameters are distributed according to a schulz form having a degree of polydispersity 14 the resulting alteration with respect to the monodisperse limit of the metastable fluid fluid critical point parameters is determined for two values of the ratio of the diameters of the small and large particles qs b 0 1 and q 0 05 we find that the inclusion of polydispersity moves the critical point to lower reservoir volume fractions of the small particles and high volume fractions of the large ones the estimated critical point parameters are found to be in good agreement with those predicted by a generalized corresponding states argument which provides a link to the known critical adhesion parameter of the adhesive hard sphere model finite size scaling estimates of the cluster percolation line in the one phase fluid region indicate that inclusion of polydispersity moves the critical point deeper into the percolating regime this suggests that phase separation is more likely to be preempted by dynamical arrest in polydisperse systems

a general discontinuous galerkin method for finite hyperelasticity formulation and numerical applications a discontinuous galerkin formulation of the boundary value problem of finite deformation elasticity is presented the primary purpose is to establish a discontinuous galerkin framework for large deformations of solids in the context of statics and simple material behaviour with a view toward further developments involving behaviour or models where the dg concept can show its superiority compared to the continuous formulation the method is based on a general hu washizu de veubeke functional allowing for displacement and stress discontinuities in the domain interior it is shown that this approach naturally leads to the formulation of average stress fluxes at interelement boundaries in a finite element implementation the consistency and linearized stability of the method in the non linear range as well as its convergence rate are proven an implementation in three dimensions is developed showing that the proposed method can be integrated into conventional finite element codes in a straightforward manner in order to demonstrate the versatility accuracy and robustness of the method examples of application and convergence studies in three dimensions are provided copyright 2006 john wiley sons ltd

further results for enhanced strain methods with isoparametric elements abstract in this contribution the enhanced strain finite element method is investigated further with particular attention given to the analysis of the method for isoparametric elements it is shown that the results established earlier b d reddy and j c simo stability and convergence of a class of enhanced strain methods siam j numer anal 32 1995 in press for affine equivalent meshes carry over to the case of isoparametric elements that is the method is stable and convergent provided that a set of three criteria is satisfied and for plane elements at least convergence is at the same rate as in the standard method a procedure for recovering the stress is shown to lead to an approximate stress which converges at the optimal rate to the actual stress with regard to computations a new basis for enhanced strains is introduced and numerical results are presented for this basis as well as for existing bases the results for enhanced strain methods are distinguished by the fact that the constant appearing in asymptotic error estimates is much smaller for these methods than for standard approaches

bounded ultra elliptic solutions of the defocusing nonlinear schrodinger equation abstract an effective integration method is presented for the bounded ultra elliptic solutions of the defocusing nonlinear schrodinger equation the two phase solutions are explicitly parametrized in terms of two physically meaningful variables the energy density and the momentum density cavitation viz a minimum amplitude of zero occurs if and only if the length of the largest spectral band is less than or equal to the sum of the lengths of the two smaller spectral bands in the case of strict inequality there are exactly two cavitation points in each period parallelogram

a discontinuous galerkin formulation for classical and gradient plasticity part 1 formulation and analysis a discontinuous galerkin formulation is developed and analyzed for the cases of classical and gradient plasticity the model of gradient plasticity is based on the von mises yield function in which dependence is on the isotropic hardening parameter and its laplacian the problem takes the form of a variational inequality of the second kind the discontinuous galerkin formulation is shown to be consistent and convergent error estimates are obtained for the cases of semi and fully discrete formulations these mimic the error estimates obtained for classical plasticity with the conventional galerkin formulation

discontinuous galerkin method based on peridynamic theory for linear elasticity modeling of discontinuities shock waves crack surfaces etc in solid mechanics is one of the major research areas in modeling the mechanical behavior of materials among the numerical methods the discontinuous galerkin method dgm poses some advantages in solving these problems in this study a novel formulation for dgm is derived for elastostatics based on the peridynamic theory derivation of the proposed formulation is presented numerical analyses are performed for different problems and the numerical results are compared to that of the known exact solutions of the problems the proposed weak formulation is stable and coercive peridynamic discontinuous galerkin formulation is found to be robust and successful in modeling elastostatic problems copyright 2011 john wiley sons ltd

adaptive stabilization of discontinuous galerkin methods for nonlinear elasticity motivation formulation and numerical examples the goal of this paper is to motivate introduce and demonstrate a novel approach to stabilizing discontinuous galerkin dg methods in nonlinear elasticity problems the stabilization term adapts to the solution of the problem by locally changing the size of a penalty term on the appearance of discontinuities with the goal of better approximating the solution consequently it is called an adaptive stabilization strategy the need for such a strategy is motivated through two and three dimensional examples in nonlinear elasticity the proposed scheme is simple to implement and compute and its performance is demonstrated with two and three dimensional numerical examples the accuracy of the proposed method is compared against a conforming method of the same order and a dg method with a traditional form of stabilization results for trilinear hexahedral elements indicate that the new stabilization strategy is more robust and more accurate when compared to a traditional form of stabilization however conforming trilinear hexahedral elements proved to be more computationally efficient for the examples shown here a two dimensional example with linear triangular elements showed comparable performances between the proposed method and a conforming one

finite elements for materials with strain gradient effects a finite element implementation is reported of the fleck hutchinson phenomenological strain gradient theory this theory fits within the toupin mindlin framework and deals with first order strain gradients and the associated work conjugate higher order stresses in conventional displacement based approaches the interpolation of displacement requires c1 continuity in order to ensure convergence of the finite element procedure for higher order theories mixed type finite elements are developed herein for the fleck hutchinson theory these elements use standard c0 continuous shape functions and can achieve the same convergence as c1 elements these c0 elements use displacements and displacement gradients as nodal degrees of freedom kinematic constraints between displacement gradients are enforced via the lagrange multiplier method the elements developed all pass a patch test the resulting finite element scheme is used to solve some representative linear elastic boundary value problems and the comparative accuracy of various types of element is evaluated copyright 1999 john wiley sons ltd

enhanced assumed strain elements and locking in membrane problems abstract the assumptions which guarantee convergence of eas elements first introduced by simo and rifai can be reduced to two postulates specifically the stability condition refers to a relaxed stability of an associated hu washizu principle we investigate the problem of volume locking of membrane problems estimates of a certain type which for instance imply volume locking of the q1 element are fortunately not present with eas elements finally we verify an equivalence of the eas concept with a hellinger reissner method which was observed in numerical computations by andelfinger and ramm

a discontinuous galerkin method for nonlinear shear flexible shells abstract in this paper a discontinuous galerkin method for a nonlinear shear flexible shell theory is proposed that is suitable for both thick and thin shell analysis the proposed method extends recent work on reissner mindlin plates to avoid locking without the use of projection operators such as mixed methods or reduced integration techniques instead the flexibility inherent to discontinuous galerkin methods in the choice of approximation spaces is exploited to satisfy the thin plate compatibility conditions a priori a benefit of this approach is that only generalized displacements appear as unknowns we take advantage of this to craft the method in terms of a discrete energy minimization principle thereby restoring the rayleigh ritz approach in addition to providing a straightforward and elegant derivation of the discrete equilibrium equations the variational character of the method could afford numerous advantages in terms of mesh adaptation and available solution techniques the proposed method is exercised on a set of benchmarks and example problems to assess its performance numerically and to test for shear and membrane locking

criterion for determining clustering versus reentrant melting behavior for bounded interaction potentials we examine in full generality the phase behavior of systems whose constituent particles interact by means of potentials that do not diverge at the origin are free of attractive parts and decay fast enough to zero as the interparticle separation r goes to infinity by employing a mean field density functional theory which is shown to become exact at high temperatures and or densities we establish a criterion that determines whether a given system will freeze at all temperatures or it will display reentrant melting and an upper freezing temperature

on improving the effectiveness of periodic solutions of the nls and dnls equations a method for improving the effectiveness of one phase periodic solutions of integrable equations is suggested which is based on the explicit determination of the locus of the auxiliary spectrum point the method is applied to the nonlinear schrodinger equation and the derivative nonlinear schrodinger equation it is shown that the relations between polynomial p lambda defining the solution in the inverse transform method and its algebraic resolvents play an important role in the theory

phase diagram of highly asymmetric binary hard sphere mixtures we study the phase behavior and structure of highly asymmetric binary hard sphere mixtures by first integrating out the degrees of freedom of the small spheres in the partition function we derive a formal expression for the effective hamiltonian of the large spheres then using an explicit pairwise depletion potential approximation to this effective hamiltonian in computer simulations we determine fluid solid coexistence for size ratios q 0 033 0 05 0 1 0 2 and 1 0 the resulting two phase region becomes very broad in packing fractions of the large spheres as q becomes very small we find a stable isostructural solid solid transition for ql 0 05 and a fluid fluid transition for ql 0 10 however the latter remains metastable with respect to the fluid solid transition for all size ratios we investigate in the limit stackrel ensuremath rightarrow q 0 the phase diagram mimics that of the sticky sphere system as expected the radial distribution function g r and the structure factor s k of the effective one component system show no sharp signature of the onset of the freezing transition and we find that at most points on the fluid solid boundary the value of s k at its first peak is much lower than the value given by the hansen verlet freezing criterion direct simulations of the true binary mixture of hard spheres were performed for qg 0 05 in order to test the predictions from the effective hamiltonian for those packing fractions of the small spheres where direct simulations are possible we find remarkably good agreement between the phase boundaries calculated from the two approaches even up to the symmetric limit q 1 and for very high packings of the large spheres where the solid solid transition occurs in both limits one might expect that an approximation which neglects higher body terms should fail but our results support the notion that the main features of the phase equilibria of asymmetric binary hard sphere mixtures are accounted for by the effective pairwise depletion potential description we also compare our results with those of other theoretical treatments and experiments on colloidal hard sphere mixtures

phase separation of a multiple occupancy lattice gas a binary lattice gas model that allows for multiple occupancy of lattice sites inspired by recent coarse grained descriptions of solutions of interacting polymers is investigated by combining the steepest descent approximation with an exploration of the multidimensional energy landscape and by gibbs ensemble monte carlo simulations the one component version of the model involving on site and nearest neighbour interactions is shown to exhibit microphase separation into two sub lattices with different mean occupation numbers the symmetric two component version of the multiple occupancy lattice gas is shown to exhibit a demixing transition into two phases above a critical mean occupation number

analysis of some quadrilateral nonconforming elements for incompressible elasticity in this work some nonconforming elements on arbitrary quadrilateral meshes in solving incompressible elastic equations are analyzed a uniform optimal convergence rate is established at the incompressible limit nu 0 5 for both displacement and stresses or pressure in the case of incompressible flow

an explicit discontinuous galerkin method for non linear solid dynamics formulation parallel implementation and scalability properties an explicit dynamics spatially discontinuous galerkin dg formulation for non linear solid dynamics is proposed and implemented for parallel computation dg methods have particular appeal in problems involving complex material response e g non local behavior and failure as even in the presence of discontinuities they provide a rigorous means of ensuring both consistency and stability in the proposed method these are guaranteed the former by the use of average numerical fluxes and the latter by the introduction of appropriate quadratic terms in the weak formulation the semi discrete system of ordinary differential equations is integrated in time using a conventional second order central difference explicit scheme a stability criterion for the time integration algorithm accounting for the influence of the dg discretization stability is derived for the equivalent linearized system this approach naturally lends itself to efficient parallel implementation the resulting dg computational framework is implemented in three dimensions via specialized interface elements the versatility robustness and scalability of the overall computational approach are all demonstrated in problems involving stress wave propagation and large plastic deformations copyright 2007 john wiley sons ltd

on a physically stabilized one point finite element formulation for three dimensional finite elasto plasticity abstract in the case of linear elasticity a direct connection between the concept of reduced integration with hourglass stabilization and a mixed method can usually be established in the non linear case this is in general not possible to overcome this difficulty we suggest in this paper a new concept based on a taylor expansion of the constitutively dependent quantities with respect to the centre of the element the push forward of the second linear term of the taylor series for the first piola kirchhoff stress tensor to the current configuration determines the so called hourglass stabilization part of the residual force vector due to the fact that the element uses only one gauss point and the hourglass stabilization part is computed by means of a simple functional evaluation the present element technology is very efficient from the computational point of view in contrast to the 2d case the computation of the jacobi determinant only in the centre of the 3d element does not yield the correct volume if the element shape deviates from being a parallelipiped it is shown in the paper that the error becomes negligibly small for a relatively coarse discretization the formulation is free of volumetric locking and can compete with shell formulations up to an aspect ratio of about hundred for bending dominated problems at least two elements over the thickness are needed in order to compute the onset of plastification correctly the element behaves very robustly in finite elasticity and inelasticity also when large element distortions occur

structure of hard hypersphere fluids in odd dimensions the structural properties of single component fluids of hard hyperspheres in odd space dimensionalities d are studied with an analytical approximation method that generalizes the rational function approximation earlier introduced in the study of hard sphere fluids s b yuste and a santos phys rev a 43 5418 1991 the theory makes use of the exact form of the radial distribution function to first order in density and extends it to finite density by assuming a rational form for a function defined in laplace space the coefficients being determined by simple physical requirements fourier transform in terms of reverse bessel polynomials constitute the mathematical framework of this approximation from which an analytical expression for the static structure factor is obtained in its most elementary form the method recovers the solution of the percus yevick closure to the ornstein zernike equation for hyperspheres at odd dimensions the present formalism allows one to go beyond by yielding solutions with thermodynamic consistency between the virial and compressibility routes to any desired equation of state excellent agreement with available computer simulation data at d 5 and d 7 is obtained

on periodic solutions and their modulations of the manakov system periodic solutions of the manakov system are studied with the aim to establish links between the recent results of wright wright 2013 physica d 264 1 and kamchatnov kamchatnov 2013 europhys lett 103 60003 where one phase solutions have been obtained by different methods and with different parameterizations two types of wave which in the context of the dynamics of two component bose einstein condensates can be called density and polarization waves are determined as particular solutions of the manakov system whitham equations describing modulations of these two types of waves are obtained

soliton dynamics in phase modulated lattices we solve the equations associated with the lax pair of the nonlinear schrodinger equation using a modified procedure of the squared wavefunction method this solution with the aid of the darboux transformation is used to study the soliton dynamics moving in phase modulated lattices it generalizes results from sym s solution and it can describe solitons on lattices with phase modulated profiles as well as with flat phase ones we identify new effects of the phase modulated lattices on soliton steering in comparison with the flat phase lattices

radial distribution function of penetrable sphere fluids to the second order in density the simplest bounded potential is that of penetrable spheres which takes a positive finite value if the two spheres are overlapped being zero otherwise in this paper we derive the cavity function to second order in density and the fourth virial coefficient as functions of t ensuremath equiv k b t where k b is the boltzmann constant and t is the temperature for penetrable sphere fluids the expressions are exact except for the function represented by an elementary diagram inside the core which is approximated by a polynomial form in excellent agreement with accurate results obtained by monte carlo integration comparison with the hypernetted chain hnc and percus yevick py theories shows that the latter is better than the former for t ensuremath lesssim 1 only however even at zero temperature hard sphere limit the py solution is not accurate inside the overlapping region where no practical cancellation of the neglected diagrams takes place the exact fourth virial coefficient is positive for t ensuremath lesssim 0 73 reaches a minimum negative value at t ensuremath approx 1 1 and then goes to zero from below as 1 t 4 for high temperatures these features are captured qualitatively but not quantitatively by the hnc and py predictions in addition in both theories the compressibility route is the best one for t ensuremath lesssim 0 7 while the virial route is preferable if t ensuremath gtrsim 0 7

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 discontinuous galerkin method for the cahn hilliard equation a discontinuous galerkin finite element method has been developed to treat the high order spatial derivatives appearing in the cahn hilliard equation the cahn hilliard equation is a fourth order nonlinear parabolic partial differential equation originally proposed to model phase segregation of binary alloys the developed discontinuous galerkin approach avoids the need for mixed finite element methods coupled equations or interpolation functions with a high degree of continuity that have been employed in the literature to treat the fourth order spatial derivatives the variational formulation of the discontinuous galerkin method its implementation and numerical examples are presented in this communication it is also shown under what conditions the method is stable and an error estimate in an energy type norm is presented the method is evaluated by comparison with a standard finite element treatment in which the cahn hilliard equation is decomposed into two coupled partial differential equations

a discontinuous galerkin method for strain gradient dependent damage study of interpolations and convergence abstract a discontinuous galerkin method has been developed for strain gradient dependent damage the strength of this method lies in the fact that it allows the use of c 0 interpolation functions for continuum theories involving higher order derivatives while in a conventional framework at least c 1 interpolations are required the discontinuous galerkin formulation thereby offers significant potential for engineering computations with strain gradient dependent models when using basis functions with a low degree of continuity jump conditions arise at element edges which are incorporated in the weak form in addition to the formulation itself a detailed study of the convergence properties of the method for various element types is presented and an error analysis is undertaken numerical results of some one and two dimensional problems are presented and discussed

squared wavefunctions approach to periodic solutions of vector nonlinear schrodinger equation we develop a method of squared wavefunctions for the vector nonlinear schrodinger equation the squared wavefunctions of the octet representation of su 3 group give periodic solutions in terms of weierstrass elliptic functions specific limits of the obtained solution are the plane wave the soliton and cnoidal waves which were previously obtained using the ansatz of stationary motion

assumed strain stabilization of the eight node hexahedral element an accurate and robust stabilization based on the assumed strain method and an operator orthogonal to constant strain fields is presented for an eight node hexahedral element with uniform reduced integration the stabilization forces depend only on the element geometry and material properties user specified parameters are not needed yet the assumed strain stabilization is nearly as fast as perturbation type hourglass control in an explicit code it has excellent coarse mesh accuracy for linear elastic bending and is easily incorporated into a nonlinear program the assumed strain field is also used with four point integration which does not require stabilization in addition two forms of the b matrix are studied and it is shown that the mean form is more efficient since it passes the patch test in a simplified form

well posedness and numerical performances of the strain gap method a mixed method of approximation is discussed starting from a suitably modified expression of the hu washizu variational principle in which the independent fields are displacements stresses and strain gaps defined as the difference between compatible strains and strain fields the well posedness of the discrete problem is discussed and necessary and sufficient conditions are provided the analysis of the mixed method reveals that the discrete problem can be split into a reduced problem and in a stress recovery accordingly the discrete stress solution is univocally determined once an interpolating stress subspace is chosen the enhanced assumed strain method by simo and rifai is based on an orthogonality condition between stresses and enhanced strains and coincides with the reduced problem it is shown that the mixed method is stable and converges computational issues in the context of the finite element method are discussed in detail and numerical performances and comparisons are carried out copyright 2001 john wiley sons ltd

phase separation of penetrable core mixtures a two component system of penetrable particles interacting via a gaussian core potential is considered which may serve as a crude model for binary polymer solutions the pair structure and thermodynamic properties are calculated within the random phase approximation rpa and the hypernetted chain hnc integral equation the analytical rpa predictions are in semi quantitative agreement with the numerical solutions of the hnc approximation which itself is very accurate for gaussian core systems a fluid fluid phase separation is predicted to occur for a broad range of potential parameters the pair structure exhibits a nontrivial clustering behaviour of the minority component similiar conclusions hold for the related model of parabolic core mixtures which is frequently used in dissipative particle dynamics dpd simulations

locking free optimal discontinuous galerkin methods for timoshenko beams in this paper we consider the so called hp version of discontinuous galerkin methods for timoshenko beams we prove that when the numerical traces are properly chosen the methods display optimal convergence uniformly with respect to the thickness of the beam these methods are thus free from shear locking we also prove that when polynomials of degree p are used all the numerical traces superconverge with a rate of order h 2p 1 p 2p 1 numerical experiments verifying the above mentioned theoretical results are shown

a discontinuous galerkin formulation of a model of gradient plasticity at finite strains abstract the work presented here constitutes an extension to the finite strain regime of a discontinuous galerkin based strain gradient plasticity formulation presented in djoko et al j k djoko f ebobisse a t mcbride b d reddy a discontinuous galerkin formulation for classical and gradient plasticity part 1 formulation and analysis comput methods appl mech engrg 196 2007 3881 3897 j k djoko f ebobisse a t mcbride b d reddy a discontinuous galerkin formulation for classical and gradient plasticity part 2 algorithms and numerical analysis comput methods appl mech engrg 197 2007 1 21 the focus here is on algorithmic and computational aspects of the formulation at finite strains the adoption of a logarithmic hyperelastic plastic formulation preserves the essential features of the infinitesimal formulation this key ingredient allows the predictor corrector solution algorithms developed for the infinitesimal gradient formulation to be extended readily to the finite strain regime the use of low order elements is essential to contain the computational expense of the formulation but these elements are prone to locking the method of enhanced assumed strains for geometrically nonlinear problems is utilised to circumvent this limitation the form of the consistent tangent modulus is derived for the case of gradient plasticity two numerical examples are presented to illustrate aspects of the approximation scheme and the algorithm as well as features of the model of gradient plasticity

a formulation for the 4 node quadrilateral element a formulation for the plane 4 node quadrilateral finite element is developed based on the principle of virtual displacements for a deformable body incompatible modes are added to the standard displacement field then expressions for gradient operators are obtained from an expansion of the basis functions into a second order taylor series in the physical co ordinates the internal degrees of freedom of the incompatible modes are eliminated on the element level a modified change of variables is used to integrate the element matrices for a linear elastic material the element stiffness matrix can be separated into two parts these are equivalent to a stiffness matrix obtained from underintegration and a stabilization matrix the formulation includes the cases of plane stress and plane strain as well as the analysis of incompressible materials further the approach is suitable for non linear analysis there an application is given for the calculation of inelastic problems in physically non linear elasticity the element is efficient to implement and it is frame invariant locking effects and zero energy modes are avoided as well as singularities of the stiffness matrix due to geometric distortion a high accuracy is obtained for numerical solutions in displacements and stresses

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

gradient enhanced damage for quasi brittle materials summary conventional continuum damage descriptions of material degeneration suffer from loss of well posedness beyond a certain level of accumulated damage as a consequence numerical solutions are obtained which are unacceptable from a physical point of view the introduction of higher order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models a consistent numerical solution procedure of the governing partial differential equations is presented which is shown to be capable of properly simulating localization phenomena

conditions for equivalence between the hu washizu and related formulations and computational behavior in the incompressible limit the relationship of the hu washizu mixed formulation to other mixed and enhanced formulations is examined in detail in the context of linear elasticity with a view to presenting a unified framework for such formulations the hu washizu formulation is considered in both its classical form and in a modified form that is suited to establishing well posedness in the incompressible limit recently established theoretical results on uniform well posedness are studied computationally by considering a range of numerical examples which illustrate where appropriate the good behavior predicted by the theory as well as the locking behavior that is evident in those problems in which the conditions for stability and convergence are not satisfied 2005 elsevier b v all rights reserved

the hierarchy of multi soliton solutions of the derivative nonlinear schrodinger equation we provide a relatively simple approach to backlund transformations for the derivative nonlinear schrodinger equation by iteration it leads to compact n soliton formulae both with asymptotically vanishing and non vanishing amplitudes the phenomenology of these solutions is discussed and illustrated in some detail

approximation theorem for the self focusing nonlinear schrodinger equation and for the periodic curves in r3 abstract it is shown that any sufficiently smooth periodic solution of the self focusing nonlinear schrodinger equation can be approximated by finite gap ones with an arbitrary small error as a corollary an analogous result for the motion of closed curves in r 3 guided by the filament equation is proved this equation describes the dynamics of very thin filament vortices in a fluid

a new discontinuous galerkin method for kirchhoff love shells abstract discontinuous galerkin methods dg have particular appeal in problems involving high order derivatives since they provide a means of weakly enforcing the continuity of the unknown field derivatives this paper proposes a new discontinuous galerkin method for kirchhoff love shells considering only the membrane and bending response the proposed one field method utilizes the weak enforcement in such a way that the displacements are the only unknowns while the rotation continuity is weakly enforced this work presents the formulation of the new discontinuous galerkin method for linear elastic shells demonstrates the consistency and stability of the proposed framework and establishes the method s convergence rate after a description of the formulation implementation into a finite element code these properties are demonstrated on numerical applications

whitham theory for perturbed korteweg de vries equation abstract original whitham s method of derivation of modulation equations is applied to systems whose dynamics is described by a perturbed korteweg de vries equation two situations are distinguished i the perturbation leads to appearance of right hand sides in the modulation equations so that they become non uniform ii the perturbation leads to modification of the matrix of whitham velocities general form of whitham modulation equations is obtained in both cases the essential difference between them is illustrated by an example of so called generalized korteweg de vries equation method of finding steady state solutions of perturbed whitham equations in the case of dissipative perturbations is considered

a variational multiscale approach to strain localization formulation for multidimensional problems abstract the multiscale approach to strain localization problems developed earlier is generalized to higher dimensions the key idea is the identification of the fine scale field with a component of the displacement that has a large gradient the difference between the total displacement and the fine scale is the coarse scale field the formulation is variationally based with the weak form as the point of departure with suitable assumptions on the space of fine scale fields the weak form is separable into coarse and fine scale parts the weak form of the fine scale problem is used to eliminate the fine scales from the formulation this is achieved by way of a projection onto the fine scale space and allows a reformulation of the full problem in terms of coarse scale components alone in this framework fine scale interpolations are identified that ensure sharp resolution of localized displacement irrespective of the underlying finite element mesh it is demonstrated that by correctly accounting for the microstructural fine scale behavior the formulation results in solutions devoid of pathological mesh sensitivity for problems wherein the detailed structure of the localized displacement is of interest recovery of the fine scale components can be performed to reconstruct the entire displacement field several numerical examples are presented that demonstrate the robustness of the formulation

some geometrical results and estimates for quadrilateral finite elements abstract the concept of the equivalent parallelogram associated with a quadrilateral is introduced the quadrilateral may be regarded as a perturbation of this parallelogram which is most conveniently described by making use of properties of the isoparametric map which defines the quadrilateral the equivalent parallelogram generates a natural means of defining a regular family of quadrilaterals this definition is used together with other properties to obtain in a relatively simple manner estimates in appropriate seminorms or norms of the isoparametric map and its jacobian for use in the determination of finite element interpolation error estimates

locking free quadrilateral continuous discontinuous finite element methods for the reissner mindlin plate we develop a finite element method with continuous displacements and discontinuous rotations for the reissner mindlin plate model on quadrilateral elements to avoid shear locking the rotations mu

effective integration of ultra elliptic solutions of the focusing nonlinear schrodinger equation abstract an effective integration method based on the classical solution of the jacobi inversion problem using kleinian ultra elliptic functions and riemann theta functions is presented for the quasi periodic two phase solutions of the focusing cubic nonlinear schrodinger equation each two phase solution with real quasi periods forms a two real dimensional torus modulo a circle of complex phase factors expressed as a ratio of theta functions associated with the riemann surface of the invariant spectral curve the initial conditions of the dirichlet eigenvalues satisfy reality conditions which are explicitly parametrized by two physically meaningful real variables the squared modulus and a scalar multiple of the wavenumber simple new formulas for the maximum modulus and the minimum modulus are obtained in terms of the imaginary parts of the branch points of the riemann surface

continuous discontinuous finite element approximations of fourth order elliptic problems in structural and continuum mechanics with applications to thin beams and plates and strain gradient elasticity abstract a new finite element method for fourth order elliptic partial differential equations is presented and applied to thin bending theory problems in structural mechanics and to a strain gradient theory problem the method combines concepts from the continuous galerkin cg method the discontinuous galerkin dg method and stabilization techniques a brief review of the cg method the dg method and stabilization techniques highlights the advantages and disadvantages of these methods and suggests a new approach for the solution of fourth order elliptic problems a continuous discontinuous galerkin c dg method is proposed which uses c 0 continuous interpolation functions and is formulated in the primary variable only the advantage of this formulation over a more traditional mixed approach is that the introduction of additional unknowns and related difficulties can be avoided in the context of thin bending theory the c dg method leads to a formulation where displacements are the only degrees of freedom and no rotational degrees of freedom need to be considered the main feature of the c dg method is the weak enforcement of continuity of first and higher order derivatives through stabilizing terms on interior boundaries consistency stability and convergence of the method are shown analytically numerical experiments verify the theoretical results and applications are presented for bernoulli euler beam bending poisson kirchhoff plate bending and a shear layer problem using toupin mindlin strain gradient theory

discontinuous galerkin methods for non linear elasticity this paper presents the formulation and a partial analysis of a class of discontinuous galerkin methods for quasistatic non linear elasticity problems these methods are endowed with several salient features the equations that define the numerical scheme are the euler lagrange equations of a one field variational principle a trait that provides an elegant and simple derivation of the method in consonance with general discontinuous galerkin formulations it is possible within this framework to choose different numerical fluxes numerical evidence suggests the absence of locking at near incompressible conditions in the finite deformations regime when piecewise linear elements are adopted finally a conceivable surprising characteristic is that as demonstrated with numerical examples these methods provide a given accuracy level for a comparable and often lower computational cost than conforming formulations stabilization is occasionally needed for discontinuous galerkin methods in linear elliptic problems in this paper we propose a sufficient condition for the stability of each linearized non linear elastic problem that naturally includes material and geometric parameters the latter needed to account for buckling we then prove that when a similar condition is satisfied by the discrete problem the method provides stable linearized deformed configurations upon the addition of a standard stabilization term we conclude by discussing the complexity of the implementation and propose a computationally efficient approach that avoids looping over both elements and element faces several numerical examples are then presented in two and three dimensions that illustrate the performance of a selected discontinuous galerkin method within the class copyright 2006 john wiley sons ltd

a discontinuous galerkin formulation for a strain gradient dependent damage model abstract the numerical solution of strain gradient dependent continuum problems has been dogged by continuity demands on the basis functions for most commonly accepted models solutions using the finite element method demand c 1 continuity of the shape functions here recent developments in discontinuous galerkin methods are explored and exploited for the solution of a prototype non linear strain gradient dependent continuum model a formulation is developed that allows the rigorous solution of a strain gradient damage model using standard c 0 shape functions the formulation is tested in one dimension for the simplest possible finite element formulation continuous piecewise linear displacement and constant on elements internal variable numerical results are shown to compare excellently with a benchmark solution the results are remarkable given the simplicity of the proposed formulation

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

periodic solutions and whitham equations for the ab system effective formulae for the single phase periodic solution of the ab system are obtained the solution depends on a complete set of four complex parameters riemann invariants the derivation of whitham equations which describe a slow evolution of the modulated periodic solution is presented the general theory is illustrated by application to the problem of soliton creation on the front of a sharp pulse

on elliptic solutions of a coupled nonlinear schrodinger system abstract an explicit formula is obtained for single phase bounded elliptic solutions of the manakov system of integrable coupled nonlinear schrodinger equations in terms of the weierstrass sigma function with a real quasiperiod the parametrization is effective in the sense that the reality conditions are completely characterized for each of the three possible couplings focusing focusing defocusing defocusing and focusing defocusing the manakov soliton is recovered in the soliton limit and the small wave modulation limit is shown to satisfy the linearized dispersion relation of planewave solutions