on the independence of exit time and exit position from small geodesic balls for brownian motions on riemannian manifolds on etudie l independance du temps de sortie premier te et la premiere position de sortie x te d un mouvement brownien x t a partir d une boucle geodesique de rayon sur la variete

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

summable solutions of some partial differential equations and generalised integral means abstract we describe partial differential operators for which we can construct generalised integral means satisfying pizzetti type formulas using these formulas we give a new characterisation of summability of formal power series solutions to some multidimensional partial differential equations in terms of holomorphic properties of generalised integral means of the cauchy data

immersions of compact riemannian manifolds into a ball of a complex space form there are some classical theorems on non immersibility of compact riemannian manifolds with sectional curvature bounded from above given by tompkins o neill chern kuiper and moore see 3 pages 221 226 more recently attention has been paid to the case of immersions into a geodesic ball of a simply connected space form and some conditions of non immersibility in such a ball have been proved in particular estimates for the mean curvature of a complete immersion into a geodesic ball have been obtained by jorge and xavier 11 and a corresponding rigidity theorem for compact hypersurfaces has been proved by markvorsen 14 in this paper we give the kahler analogs of the theorems of jorge and xavier only for the compact case and markvorsen and get some other new results for the kahler case that have no riemannian analog in order to state our results we shall introduce some notation and terminology given a real number let us consider the functions

numerical study of the turbulent flow past an airfoil with trailing edge separation presentation d une methode numerique par volume fini pour la resolution des equations de navier stokes bidimensionnelles incompressibles et stationnaires en coordonnees generales curvilignes application de la methode aux ecoulements turbulents sur des profils avec et sans separation au bord de sortie posterieur comparaison des calculs avec des donnees experimentales

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

focal sets and real hypersurfaces in complex projective space let m be a real submanifold of cpm and let j denote the complex structure we begin by finding a formula for the location of the focal points of m in terms of its second fundamental form this takes a particularly tractable form when m is a complex submanifold or a real hypersurface on which ji is a principal vector for each unit normal to m the rank of the focal map onto a sheet of the focal set of m is also computed in terms of the second fundamental form in the case of a real hypersurface on which je is principal with corresponding principal curvature u if the map onto a sheet of the focal set corresponding to u has constant rank then that sheet is a complex submanifold over which m is a tube of constant radius theorem 1 the other sheets of the focal set of such a hypersurface are given a real manifold structure in theorem 2 these results are then employed as major tools in obtaining two classifications of real hypersurfaces in cpm first there are no totally umbilic real hypersurfaces in cpm but we show theorem 3 let m be a connected real hypersurface in cpm m 3 with at most two distinct principal curvatures at each point then m is an open subset of a geodesic hypersphere secondly we show that there are no einstein real hypersurfaces in cpm and characterize the geodesic hyperspheres and two other classes of hypersurfaces in terms of a slightly less stringent requirement on the ricci tensor in theorem 4 one of the first results in the geometry of submanifolds is that an umbilic hypersurface m in euclidean space must be an open subset of a hyperplane or sphere the proof goes as follows assume that the shape operator is a scalar multiple of the identity a ax and use the codazzi equation to show that x is constant then either x 0 in which case m lies on a hyperplane or the focal points fx x x l x t the unit normal all coincide and m lies on the sphere of radius 1 x centered at the unique focal point this simple idea suggests a plan of attack for classifying hypersurfaces in terms of the nature of the principal curvatures under fairly general conditions the set of focal points corresponding to a principal curvature x can be given a differentiable received by the editors december 19 1980 presented to the society at its annual meeting in san francisco january 10 1981 1980 mathematics subject classificatiom primary 53b25 53c40

formulation of the high fidelity generalized method of cells with arbitrary cell geometry for refined micromechanics and damage in composites abstract a new parametric formulation for high fidelity generalized method of cells hfgmc is presented for the micromechanical analysis of multiphase periodic composites to this end a linear parametric and geometric mapping is employed to transform arbitrary quadrilateral cell shapes from the physical space to an auxiliary uniform square shapes a complete quadratic displacement expansion is performed in the mapped space thus a new bilinear term is added to the quadratic displacement expansion unlike the original hfgmc for regular array of rectangular cells where this term in not required the continuity of displacements tractions together with the periodicity and equilibrium conditions are imposed in the average sense similar to the original hfgmc formulation using both the physical and mapping variables however the addition of bilinear terms requires the introduction of the first averaged moments of the equilibrium equations in order to demonstrate the ability the new hfgmc formulation spatial stress fields are compared with analytical and numerical solutions of circular and elliptical fibers in an infinite medium furthermore two progressive damage methodologies are coupled with the new hfgmc formulation in order to predict the strain softening and elastic degrading behaviors the first methodology employs a cell extinction approach while the second uses cohesive interfaces between the cells due to the strain softening both damage methodologies require an iterative solution approach of the governing system nonlinear equations damage applications are presented for the transverse loading of composites with square and hexagonal repeating unit cells ruc

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

a continuous method for nonlocal functional differential equations with delayed or advanced arguments abstract in the previous works the authors presented the reproducing kernel method rkm for solving various differential equations however to the best of our knowledge there exist no results for functional differential equations the aim of this paper is to extend the application of reproducing kernel theory to nonlocal functional differential equations with delayed or advanced arguments and give the error estimation for the present method some numerical examples are provided to show the validity of the present method

isoparametric functions on exotic spheres abstract this paper extends widely the work in 11 existence and non existence results of isoparametric functions on exotic spheres and eells kuiper projective planes are established in particular every homotopy n sphere n 4 carries an isoparametric function with certain metric with 2 points as the focal set in strong contrast to the classification of cohomogeneity one actions on homotopy spheres 26 only exotic kervaire spheres admit cohomogeneity one actions besides the standard spheres as an application we improve a beautiful result of berard bergery 2 see also pp 234 235 of 3

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 first order hyperbolic framework for large strain computational solid dynamics an upwind cell centred total lagrangian scheme this paper builds on recent work developed by the authors for the numerical analysis of large strain solid dynamics by introducing an upwind cell centred hexahedral finite volume framework implemented within the open source code openfoam http www openfoam com http www openfoam com in lee gil and bonet 1 a first order hyperbolic system of conservation laws was introduced in terms of the linear momentum and the deformation gradient tensor of the system leading to excellent behaviour in two dimensional bending dominated nearly incompressible scenarios the main aim of this paper is the extension of this algorithm into three dimensions its tailor made implementation into openfoam and the enhancement of the formulation with three key novelties first the introduction of two different strategies in order to ensure the satisfaction of the underlying involutions of the system that is that the deformation gradient tensor must be curl free throughout the deformation process second the use of a discrete angular momentum projection algorithm and a monolithic total variation diminishing runge kutta time integrator combined in order to guarantee the conservation of angular momentum third and for comparison purposes an adapted total lagrangian version of the hyperelastic glace nodal scheme of kluth and despr es 2 is presented a series of challenging numerical examples are examined in order to assess the robustness and accuracy of the proposed algorithm benchmarking it against an ample spectrum of alternative numerical strategies developed by the authors in recent publications

properties of analytic solution and numerical solution of multi pantograph equation this paper deals with the properties of the analytic solution and the numerical solution of the multi pantograph equationu t email protected t email protected i 1 email protected iu q it 0

a second order virtual node algorithm for nearly incompressible linear elasticity in irregular domains we present a cut cell method in r 2 for enforcing dirichlet and neumann boundary conditions with nearly incompressible linear elastic materials in irregular domains virtual nodes on cut uniform grid cells are used to provide geometric flexibility in the domain boundary shape without sacrificing accuracy we use a mixed formulation utilizing a mac type staggered grid with piecewise bilinear displacements centered at cell faces and piecewise constant pressures at cell centers these discretization choices provide the necessary stability in the incompressible limit and the necessary accuracy in cut cells numerical experiments suggest second order accuracy in l we target high resolution problems and present a class of geometric multigrid methods for solving the discrete equations for displacements and pressures that achieves nearly optimal convergence rates independent of grid resolution

periodic boundary value problems for neutral multi pantograph equations in this paper a new method is proposed for solving nonlinear neutral multi pantograph equations with periodic boundary conditions by combining the advantages of the homotopy perturbed method hpm and the reproducing kernel method rkm the numerical results obtained show that the present method is reliable

weakly einstein critical metrics of the volume functional on compact manifolds with boundary abstract the goal of this paper is to study weakly einstein critical metrics of the volume functional on a compact manifold m with smooth boundary m here we will give the complete classification for an n dimensional n 3 or 4 weakly einstein critical metric of the volume functional with nonnegative scalar curvature moreover in the higher dimensional case n 5 we will establish a similar result for weakly einstein critical metric under a suitable constraint on the weyl tensor

the diffractive wave trace on manifolds with conic singularities abstract let x g be a compact manifold with conic singularities taking g to be the friedrichs extension of the laplace beltrami operator we examine the singularities of the trace of the half wave group e i t g arising from strictly diffractive closed geodesics under a generic nonconjugacy assumption we compute the principal amplitude of these singularities in terms of invariants associated to the geodesic and data from the cone point this generalizes the classical theorem of duistermaat guillemin on smooth manifolds and a theorem of hillairet on flat surfaces with cone points

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

numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh a finite difference method using a nonuniform triangle mesh is described for the numerical solution of the nonlinear two dimensional poisson equation s 0 where is a function of or its derivatives sis a function of position and or its normal derivative is specified on the boundary the finite difference equations are solved by successive overrelaxation the triangle mesh which is constructed numerically by solving laplace s equation is easily adapted to nonrectangular boundaries and interfaces examples of numerical results are given for the magnetostatic problem with iron and other possible applications are mentioned

a second order virtual node algorithm for stokes flow problems with interfacial forces discontinuous material properties and irregular domains we present numerical methods for the solution of the stokes equations that handle interfacial discontinuities discontinuous material properties and irregular domains the discretization couples a lagrangian representation of the material interface with eulerian representations of the fluid velocity and pressure the methods are efficient easy to implement and yield discretely divergence free velocities that are second order accurate in l for the special case of continuous fluid viscosity we present a method that decouples the stokes equations into three poisson interface problems which we use the techniques in bedrossian 2010 1 to solve we also solve a fourth poisson equation to enforce a discrete divergence free condition in this case we discretize all equations using an embedded approach on a uniform mac grid employing virtual nodes and duplicated cells at the interfaces these additional degrees of freedom allow for accurate resolution of discontinuities in the fluid stress at the material interface in the case of discontinuous viscosity we require a lagrange multiplier term to enforce continuity of the fluid velocity we provide a novel discretization of this term that accurately resolves constant pressure null modes we show that the accurate resolution of these modes significantly improves performance the discrete coupled equations for the velocity pressure and lagrange multipliers are in the form of a symmetric kkt system however if both fluids have the same viscosity then all four linear systems involved are symmetric positive definite with three of the four having the standard 5 point laplace stencil everywhere numerical results indicate second order accuracy for the velocities and first order accuracy for the pressure in the general case for the continuous viscosity case numerical results indicate second order accuracy for both velocities and pressure

numeric solutions for the pantograph type delay differential equation using first boubaker polynomials a numerical method is applied to solve the pantograph equation with proportional delay under the mixed conditions the method is based on the truncated first boubaker series the solution is obtained in terms of first boubaker polynomials also illustrative examples are included to demonstrate the validity and applicability of the technique the results obtained are compared by the known results

exponential stability of a competitive lotka volterra system with delays abstract in this paper the exponential stability of a two species competitive lotka volterra system with discrete delays has been studied by constructing appropriate lyapunov functional and using the linear matrix inequality lmi optimization approach a series of sufficient criteria is obtained which ensure the exponential stability of the positive equilibrium of the given lotka volterra system the results are new and improve some earlier work an illustrative example is given to demonstrate the effectiveness of the obtained results

a new approach to boundary modelling for finite difference applications in solid mechanics procedures for extending the useful scope of the finite difference method in solid mechanics applications are presented the improvements centre around the introduction of the physical nature of the deformations into the equations used to formulate the approximate solution this is accomplished by evaluating the coefficients of taylor series expansions for the displacement approximations in terms of rigid body motions strains and derivatives of strains this procedure is demonstrated with plane stress applications the ability to interpret the derivative approximations physically allows the fictitious nodes typical of the finite difference method to be rationally incorporated into the model as a means of enforcing traction boundary conditions an example problem is solved using both regular and irregular meshes the displacements and stresses compare well with finite element solutions

a large strain finite volume method for orthotropic bodies with general material orientations abstract this paper describes a finite volume method for orthotropic bodies with general principal material directions undergoing large strains and large rotations the governing and constitutive relations are presented and the employed updated lagrangian mathematical model is outlined in order to maintain equivalence with large strain total lagrangian methods the constitutive stiffness tensor is updated transforming the principal material directions to the deformed configuration discretisation is performed using the cell centred finite volume method for unstructured convex polyhedral meshes the current methodology is successfully verified by numerically examining two separate test cases a circular hole in an orthotropic plate subjected to a traction and a rotating orthotropic plate containing a hole subjected to a pressure the numerical predictions have been shown to agree closely with the available analytical solutions in addition a 3 d composite component is examined to demonstrate the capabilities of the developed methodology in terms of a variable material orientation and parallel processing

g deformations and some generalizations of h weyl s tube theorem we prove an invariance theorem for the volumes of tubes about submanifolds in arbitrary analytic riemannian manifolds under g deformations of the second order for locally symmetric spaces or two point homogeneous spaces we give stronger invariance theorems using only g deformations of the first order a11 these results can be viewed as generalizations of the result of h weyl about isometric deformations and the volumes of tubes in spaces of constant curvature they are derived from a new formula for the volume of a tube about a submanifold introduction in 13 h weyl proved his famous tube formula which can be interpreted in the following way let m be a space of constant curvature and let p c m be a topologically embedded submanifold with compact closure then the volumes of tubes about p for all sufeciently small radii r o remain invariant under isometric deformations of p the aim of this paper is to prove an analogous invariance theorem for the volumes of tubes when m is an arbitrary analytic riemannian manifold and the isometric deformations of p c m are replaced by g deformations of the second order in the sense of e cartan for special riemannian manifolds such as locally symmetric spaces or two point homogeneous spaces we are able to prove some stronger invariance theorems involving only g deformations of the first order the latter results can be interpreted as direct generalizations of h weyl s theorem the present paper is an extension of our previous article 8 in which we studied what happens with tubes under deformations of curves as we shall see our secondorder deformation theorem for curves 8 can be extended directly to arbitrary submanifolds as concerns the more special first order deformation theorems our results about submanifolds are not as definitive by far as those for curves many questions for further research remain open in an appendix we consider the analogues of our deformation theorems for the total mean curvatures of the tubes 1 an explicit tube formula let m g be a riemannian manifold of dimension n and let p be a pdimensional connected submanifold topologically embedded in m further we suppose that p has compact closure received by the editors june 20 1985 1980 mathematics subject classifiication primary 53b20 53c40 secondary 53c22 53c25 53c30 53c35

symmetric like riemannian manifolds and geodesic symmetries we treat several classes of riemannian manifolds whose shape operators of geodesic spheres or jacobi operators share some properties with the ones on symmetric spaces

variational iteration method for solving a generalized pantograph equation the variational iteration method is applied to solve the generalized pantograph equation this technique provides a sequence of functions which converges to the exact solution of the problem and is based on the use of lagrange multipliers for identification of optimal value of a parameter in a functional employing this technique it is possible to find the exact solution or an approximate solution of the problem some examples are given to demonstrate the validity and applicability of the method and a comparison is made with existing results

some families of isoparametric hypersurfaces and rigidity in a complex hyperbolic space the geometric notion of equivalence for submanifolds in a chosen ambient space is that of congruence in this study a certain type of isoparametric hypersurface of a complex hyperbolic space form is shown to have a rigid immersion by utilizing the congruences of a lorentzian hyperbolic space form that lies as an si fiber bundle over the complex hyperbolic space several families of isoparametric hypersurfaces namely tubes and horospheres are constructed whose immersions are rigid

an efficient algorithm for solving generalized pantograph equations with linear functional argument abstract a numerical method for solving the generalized retarded or advanced pantograph equation under initial value conditions is presented to display the validity and applicability of the numerical method four illustrative examples are presented the results reveal that this method is very effective and highly promising when compared with other numerical methods such as adomian decomposition method spline methods and taylor method

stochastic approach for the solution of multi pantograph differential equation arising in cell growth model in this paper a computational technique is introduced for the solution of the first order multi pantograph differential equation mpde through some well known optimization algorithms like sequential quadratic programming sqp and active set technique ast furthermore artificial neural network ann is used for networking of the first order multi pantograph differential equation in used to provide mathematical model based on unsupervised error for equation moreover mathematical modeling has been performed perfectly through multi runs for simulation to justify the better convergence of the solutions also two examples are presented to exhibit the aptitude of the method sqp and ast the comparative study will be made with reported techniques such as variational iteration technique vit 6 and collocation based on bernstein polynomial method bcm 6

a geometric structure preserving discretization scheme for incompressible linearized elasticity abstract in this paper we present a geometric discretization scheme for incompressible linearized elasticity we use ideas from discrete exterior calculus dec to write the action for a discretized elastic body modeled by a simplicial complex after characterizing the configuration manifold of volume preserving discrete deformations we use hamilton s principle on this configuration manifold the discrete euler lagrange equations are obtained without using lagrange multipliers the main difference between our approach and the mixed finite element formulations is that we simultaneously use three different discrete spaces for the displacement field we explicitly derive the governing equations for the two dimensional case where the discrete spaces for the displacement field are constructed by p 1 polynomials over primal meshes for incompressibility constraint p 0 polynomials over dual meshes for the kinetic energy and p 1 polynomials over support volumes for the elastic energy and the discrete space of the pressure field is constructed by p 0 polynomials over primal meshes we test the efficiency and robustness of this geometric scheme using some numerical examples in particular we do not see any volume locking and or checkerboarding of pressure in our numerical examples this suggests that our choice of discrete solution spaces is compatible

a control volume based finite element method for plane micropolar elasticity this paper describes the development of a numerical procedure for predicting deformations and stresses in a loaded two dimensional membrane exhibiting micropolar or cosserat constitutive behaviour the procedure employs a conventional finite element fe mesh together with a dual mesh of interconnected control volumes each of which must satisfy equilibrium a series of patch tests covering a variety of simple strain states are used to validate the procedure that is then employed to predict the stress concentration in a membrane containing a small hole the predictions provided by the procedure are compared with those given previously by fes

collocation methods for nonlinear convolution volterra integral equations with multiple proportional delays in this paper we apply the collocation methods to a class of nonlinear convolution volterra integral equations with multiple proportional delays ncviempds we shall present the existence uniqueness and regularity properties of analytic solution for this type equation and then analyze the convergence and superconvergence properties of the collocation solution the numerical results verify our theoretical analysis

the high fidelity generalized method of cells with arbitrary cell geometry and its relationship to the parametric finite volume micromechanics abstract this contribution is motivated by the recent ijss article titled formulation of the high fidelity generalized method of cells with arbitrary cell geometry for refined micromechanics and damage in composites by haj ali and aboudi in the present discussion we critically compare these authors approach with the parametric finite volume direct averaging micromechanics fvdam theory developed in a sequence of papers dating to 2004 we show that the extension proposed by haj ali and aboudi follows the framework of the parametric fvdam theory and not the original hfgmc model as claimed just as importantly we demonstrate that the proposed extension is fundamentally flawed as it violates accepted principles which every mechanics theory must satisfy namely correct reducibility and coordinate frame indifference direct comparison of predictions generated by the parametric fvdam theory the proposed extension called hfgmc with arbitrary cell geometry and finite element method demonstrates no need for the extension carried out in the specific manner proposed by haj ali and aboudi which in fact produces inferior results

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

stability of the discretized pantograph differential equation in this paper we study discretizations of the general pantograph equation y t ay t by 6 t cy o t t 0 y o yo where a b c and yo are complex numbers and where 0 and 0 are strictly increasing functions on the nonnegative reals with 6 0 q o 0 and 0 t t 0 t t for positive t our purpose is an analysis of the stability of the numerical solution with trapezoidal rule discretizations and we will identify conditions on a b c and the stepsize which imply that the solution sequence yn i is bounded or that it tends to zero algebraically as a negative power of n

mimetic finite difference method for the stokes problem on polygonal meshes various approaches to extend finite element methods to non traditional elements general polygons pyramids polyhedra etc have been developed over the last decade the construction of basis functions for such elements is a challenging task and may require extensive geometrical analysis the mimetic finite difference mfd method works on general polygonal meshes and has many similarities with low order finite element methods both schemes try to preserve the fundamental properties of the underlying physical and mathematical models the essential difference between the two schemes is that the mfd method uses only the surface representation of discrete unknowns to build the stiffness and mass matrices since no extension of basis functions inside the mesh elements is required practical implementation of the mfd method is simple for polygonal meshes that may include degenerate and non convex elements in this article we present a new mfd method for the stokes problem on arbitrary polygonal meshes and analyze its stability the method is developed for the general case of tensor coefficients which allows us to apply it to a linear elasticity problem as well numerical experiments show for the velocity variable second order convergence in a discrete l 2 norm and first order convergence in a discrete h 1 norm for the pressure variable first order convergence is shown in the l 2 norm

analysis of a model representing stage structured population growth with state dependent time delay a stage structured model of population growth is proposed where the time to ma turity is itself state dependent it is shown that under appropriate assumptions all solutions are positive and bounded criteria for the existence of positive equilibria and further conditions for the uniqueness of the equilibria are given the stability of the equilibria are also discussed in addition an attracting region is determined for solutions such that this region collapses to the unique positive equilibrium in the state independent case

e approximate polynomial solutions for the multi pantograph equation with variable coefficients abstract in this paper we present a new method to obtain analytical approximate polynomial solutions for the multi pantograph equation this method allows us to determine an approximate polynomial solution of the nonlinear multi pantograph equation with variable coefficients and to specify the maximal error of the approximation relative to the exact solution of the problem two numerical examples are given to illustrate the validity and the applicability of the method a comparison with previous results is also presented

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

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

discussion paper has renaming the high fidelity generalized method of cells been justified abstract the high fidelity generalized method of cells hfgmc has been originally developed by aboudi 2001 aboudi et al 2001 as a micromechanical method for periodic multi phase composite media a computational implementation of the hfgmc equations has been proposed by bansal and pindera 2004 to enhance numerical efficiency still with direct reference to the hfgmc formulation later the same computational implementation is recast as a new method called finite volume direct averaging micromechanics fvdam starting by bansal and pindera 2006 the current discussion paper has two aims the first is to show that the fvdam is not a new method and that it has the same assumptions and identical governing equations as those originally derived by the hfgmc the only difference is in the solution procedure where intermediate dependent variables in the form of average displacements at the interfaces are used instead of directly solving for the unknown micro variables the coefficients of the displacement polynomials thus renaming the hfgmc micromodel to fvdam has not been justified in fact haj ali and aboudi 2009 have shown that the same reduction of variables can be achieved by a simple static condensation carried out at the global system of equations instead of introducing intermediate variables the second aim of this paper is to address misrepresentations in a recent discussion paper by the fvdam authors claiming in part that the hfgmc method using parametric geometry of the subcells should follow their formulation termed parametric fvdam we show that the latter is limited to an incomplete quadratic expansion of the displacement and an approximation in the form of a priori constant jacobian of the parametric mapping however the hfgmc with arbitrary cell geometry haj ali and aboudi 2010 has been formulated in a direct and general manner i e retaining the full quadratic expansion of the displacement together with the complete jacobian thus the parametric fvdam is a special case of the parametric hfgmc i e when the jacobian is sampled and evaluated only at one point namely the origin of the parametric coordinate system the intended new contribution of haj ali and aboudi 2010 to refined micromechanics and progressive damage has been completely ignored by the fvdam discussion paper therefore in order to maintain scientific clarity it is strongly advocated to preserve the original name of the hfgmc method regardless of the different computational implementations used for solving the governing equations for both orthogonal and parametric geometries of the subcells

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

approximate solution of multi pantograph equation with variable coefficients this paper deals with the approximate solution of multi pantograph equation with nonhomogenous term in terms of taylor polynomials the technique we have used is based on a taylor matrix method in addition some numerical examples are presented to show the properties of the given method and the results are discussed

a dynamical zeta function for pseudo riemannian foliations we investigate a generalization of geodesic random walks to pseudo riemannian foliations the main application we have in mind is to consider the logarithm of the associated zeta function as grand canonical partition function in a theory unifying aspects of general relativity quantum mechanics and dynamical systems

exponential basis functions in solution of problems with fully incompressible materials in this paper exponential basis functions ebfs satisfying the governing equations of elastic problems with incompressible materials are introduced due to similarity between elasticity problems and steady state fluid problems the bases found for the former problems are used for latter problems we discuss on using single field form known as displacement velocity based formulation and also on using a two field form known as u p formulation in the first formulation we find the pressure bases through performing a limit analysis using a fictitious bulk modulus while in the second formulation the bases are found directly by considering the pressure as a separate variable in the second formulation we directly apply the condition of incompressibility it is shown that both formulations yield identical bases meaning that the first one may be used in a standard approach however it is also shown that when the incompressibility condition is applied by a laplacian of pressure in the second formulation some additional spurious ebfs may be obtained having defined appropriate bases we follow the solution strategy recently introduced by the authors for other engineering problems some well known benchmark problems are solved to show the capabilities of the method

solving generalized pantograph equations by shifted orthonormal bernstein polynomials abstract in this paper we introduce shifted orthonormal bernstein polynomials sobps and derive the operational matrices of integration and delays for these polynomials then we apply them to convert the pantograph equations to a system of linear equations an important property of this method is that the condition number of the coefficient matrix of the system is small which confirms that our method is stable error analysis and comparison with other methods are given to confirm the validity efficiency and applicability of the proposed method

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

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

jost maps ball homogeneous and harmonic manifolds abstract given a real number e 0 small enough an associated jost map j e between two riemannian manifolds is defined then we prove that connected riemannian manifolds for which the center of mass of each small geodesic ball is the center of the ball i e for which the identity is a j e map are ball homogeneous in the analytic case we characterize such manifolds in terms of the euclidean laplacian and we show that they have constant scalar curvature under some restriction on the ricci curvature we prove that riemannian analytic manifolds for which the center of mass of each small geodesic ball is the center of the ball are locally and weakly harmonic

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

a taylor method for numerical solution of generalized pantograph equations with linear functional argument this paper is concerned with a generalization of a functional differential equation known as the pantograph equation which contains a linear functional argument in this paper we introduce a numerical method based on the taylor polynomials for the approximate solution of the pantograph equation with retarded case or advanced case the method is illustrated by studying the initial value problems the results obtained are compared by the known results

a new collocation method for approximate solution of the pantograph functional differential equations with proportional delay the paper presents a new numerical method for solving functional differential equations with proportional delays of the first and higher orders the method consists of replacing the initial equation by an approximate equation which has an exact analytic solution with a set of free parameters these free parameters are determined by the use of the collocation procedure some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results the numerical results show that the proposed method is of a high accuracy and is efficient for solving a wide class of functional differential equations with proportional delays including equations of neutral type the method is applicable to both initial and boundary value problems