interchanging parameters and integrals in dynamical systems the mapping case we consider dynamical systems with discrete time maps that possess one or more integrals depending upon parameters we show that integrals can be used to replace parameters in the original map so as to construct a different map with different integrals we also highlight a process of reparametrization that can be used to increase the number of parameters in the original map prior to using integrals to replace them properties of the original map and the new map are compared the theory is motivated by and illustrated with examples of a three dimensional trace map and some four dimensional maps previously shown to be integrable

a new family of four dimensional symplectic and integrable mappings abstract we investigate the generalisations of the quispel roberts and thompson qrt family of mappings in the plane leaving a rational quadratic expression invariant to the case of four variables we assume invariance of the rational expression under a cyclic permutation of variables and we impose a symplectic structure with poisson brackets of the weyl type all mappings satisfying these conditions are shown to be integrable either as four dimensional mappings with two explicit integrals which are in involution with respect to the symplectic structure and which can also be inferred from the periodic reductions of the double discrete versions of the modified korteweg devries mkdv and sine gordon sg equations or by reduction to two dimensional mappings with one integral of the symmetric qrt family

why instantons are monopoles it is shown that instantons are hyperbolic monopoles for the loop group with non maximal symmetry breaking at infinity

convergence analysis of moving finite element methods for space fractional differential equations most existent papers have focused on the fixed mesh methods for solving space fractional differential equations however since some classes of space fractional differential equations may have singular or even finite time blowup solutions it is highly needed to develop adaptive mesh methods to solve these problems in this paper the moving finite element methods are studied for a class of time dependent space fractional differential equations the convergence theories of the methods are derived with l 2 norm and numerical examples are provided to support the theoretical results to simplify the analysis a fractional ritz projection operator is introduced and the error estimation of the projection is derived under the moving mesh setting

precise numerical solutions of potential problems using the crank nicolson method we present a numerically precise treatment of the crank nicolson method with an imaginary time evolution operator in order to solve the schrodinger equation the time evolution technique is applied to the inverse iteration method that provides a systematic way to calculate not only eigenvalues of the ground state but also of the excited states this method systematically produces eigenvalues with the accuracy of eleven digits when the cornell potential is used an absolute error estimation technique is implemented based on a power counting rule this method is examined on exactly solvable problems and produces the numerical accuracy down to 10 1 1

on the transport diffusion algorithm and its applications to the navier stokes equations this paper deals with an algorithm for the solution of diffusion and or convection equations where we mixed the method of characteristics and the finite element method globally it looks like one does one step of transport plus one step of diffusion or projection but the mathematics show that it is also an implicit time discretization of thepde in lagrangian form we give an error bound h t h h t in the interesting case that holds also for the navier stokes equations even when the reynolds number is infinite euler equation

a stable finite element method for initial boundary value problems for first order hyperbolic systems a nonstandard finite element method for initial boundary value problems for first order hyperbolic systems in one space dimension with general boundary conditions is analyzed the method can be considered as a generalization of the box scheme we first establish a stability result for the method and then derive several error estimates u x t a x ux x t b x u x t f x t 1 1 o 0 t g kxu l t u x 0 u0 x for x t e i x j 0 1 x 0 where t 0 here aix and 5 x are n x n matrices we assume that aix has n real eigenvalues xx x a2 x a x and that there exist a constant t0 0 and an integer m 0 t0 for all xg furthermore we assume that for each x e there is a nonsingular matrix qix such that

a crank nicolson type space time finite element method for computing on moving meshes in this paper a space time finite element method for evolution problems that is second order accurate in both space and time is proposed for convection dominated problems the elements may be aligned along the characteristics in space time which results in a crank nicolson method along the characteristics the method is also suitable as an alternative to other moving mesh methods for problems in deforming domains numerical examples dealing with diffusion and convection are given

nitsche s method combined with space time finite elements for ale fluid structure interaction problems we propose a weak method for handling the fluid structure interface in finite element fluid structure interaction based on nitsche s method abh math univ hamburg 36 1971 9 we assume transient incompressible newtonian flow and for the structure undamped linear elasticity for the time discretization we use the time continuous energy conserving galerkin method for the structure and for the fluid we employ the time discontinuous galerkin method this means that the velocity becomes piecewise constant on each timestep for the fluid matching the time derivative of the displacements in the solid which is also piecewise constant over a time step we formulate the method and report some numerical examples using space time oriented elements for the fluid in order to mimic lagrangian or ale type simulations

integrable mappings and soliton equations ii abstract some simple solutions of discrete soliton equations are shown to satisfy 2d mappings we show that these belong to a recently introduced 18 parameter family of integrable reversible mappings of the plane thus lending weight to a previous conjecture we also give an example of an integrable mapping occuring in an exactly solvable model in statistical mechanics finally we discuss the notion of generalized reversibility

integrable mappings derived from soliton equations abstract we derive a hierarchy of ibtegrable mappings integrable ordinary difference equations corresponding to solutions of the initial value problem of an integrable partial difference equation with periodic initial data for each n n this hierarchy contains at least one integrable mapping r n r n the integrals of these mappings are constructed using the lax pair of the underlying partial difference equation our approach is illustrated for the integrable partial difference analogues of the sine gordon and the modified korteweg de vries equations

a singular value decomposition svd based generalized finite difference gfd method for close interaction moving boundary flow problems in this paper we present a study on a singular value decomposition svd based generalized finite difference gfd method and a nodal selection scheme for moving body boundary flow problems formulated on a hybrid cartesian cum meshfree grid system the present study shows that the svd based method is more robust and accurate than the conventional least squares based gfd scheme a nodal selection scheme is also introduced to overcome the problem of numerical instability associated with the clustering of computational nodes such nodal clustering occurs dynamically when moving bodies or boundaries approach within close proximity of each other resulting in the overlap of their meshfree grids the nodal scheme is applied to close interaction flow problems as exemplified by the squeezing action of a circular cylinder through a very narrow slot and the close proximity bypass interaction of two oscillating circular cylinders

singularity confinement and algebraic integrability two important notions of integrability for discrete mappings algebraic integrability and singularity confinement have been used for discrete mappings algebraic integrability is related to the existence of sufficiently many conserved quantities and singularity confinement is associated with the local analysis of singularities in this article the relationship between these two notions is explored for birational autonomous mappings the main result of this article is that algebraically integrable mappings are shown to have the singularity confinement property using this result the proof of the nonexistence of algebraic conserved quantities for a class of discrete systems is given

the classification of monopoles for the classical groups by studying a construction of nahm we compute the moduli spaces of monopoles with maximal symmetry breaking at infinity forsu n so n andsp n these are found to be equivalent to spaces of holomorphic maps from 1 into flag manifolds

integrable mappings of the plane preserving biquadratic invariant curves we provide a general framework to construct integrable mappings of the plane that preserve a one parameter family b x y k of biquadratic invariant curves where parametrization by k is very general these mappings are reversible by construction i e they are the composition of two involutions and can be shown to be measure preserving they generalize integrable maps previously given by mcmillan and quispel roberts and thompson by considering a transformation of the case of the symmetric biquadratic to a canonical form we provide a normal form for the symmetric integrable map acting on each invariant curve we give a lax pair for a large subclass of our symmetric integrable maps including at least a 10 parameter subfamily of the 12 parameter symmetric quispel roberts thompson maps

instantons in two and four dimensions it is shown that yang mills instantons in four dimensions can naturally be identified with the instantons of a two dimensional theory with values in the loop group

instantons and jumping lines we study the behaviour under deformation of holomorphic bundles of rank 2 over 1 this is then applied to the description of the moduli space tilde m n of framed su 2 instantons of chargen tilde m n is shown to map to n with equidimensional fibers we use this to provide a stratification of tilde m n and compute the strata explicitly to codimension 4 this then yields 1 tilde m n 2 and for the standard moduli spacem n 1 m n 0 forn odd 2 forn even

monopoles and geodesics using the holomorphic geometry of the space of straight lines in euclidean 3 space it is shown that every static monopole of chargek may be constructed canonically from an algebraic curve by means of the atiyah ward ansatz a k

continuous finite elements in space and time for the heat equation on analyse une nouvelle methode variationnelle pour l approximation de l equation de la chaleur a l aide des elements finis continus dans l espace et le temps on presente les estimations d erreurs et les resultats d experiences numeriques

a computational framework for fluid structure interaction finite element formulation and applications abstract this work is concerned with the modelling of the interaction of fluid flow with flexibly supported rigid bodies the fluid flow considered is governed by the incompressible navier stokes equations and modelled by employing stabilised low order velocity pressure finite elements the motion of the fluid domain is accounted for by an arbitrary lagrangian eulerian ale strategy the rigid body motion excited by the fluid flow is restricted by the elastic and damping properties of the supports for the temporal discretisation the discrete implicit generalised method is employed the resulting strongly coupled set of nonlinear equations is solved by means of a novel partitioned solution procedure which is based on the newton raphson methodology and incorporates full linearisation of the overall incremental problem the strong coupling is resolved and optimal convergence of the residuals is achieved several numerical examples are presented to demonstrate the robustness and efficiency of the methodology the examples clearly capture the phenomena of vortex induced oscillations and galloping

integrable mappings of the plane preserving biquadratic invariant curves iii abstract we provide a new condition of foliation that enables the construction of very general integrable mappings of the plane preserving a biquadratic family of curves

growth and integrability in discrete systems we introduce a new discrete integrability criterion inspired from the recent findings of ablowitz and collaborators this criterion is based on the study of the growth of some characteristic of the solutions of a mapping using nevanlinna theory since the practical implementation of the latter does not always lead to a clear cut answer we complement the growth criterion by the singularity confinement property this combination turns out to be particularly efficient its application allows us to recover the known forms of the discrete painleve equations and to show that no new ones may exist within a given parametrization

nahm s equations and the classification of monopoles solutions of nahm s system of ordinary differential equations are produced by variational methods this leads to an explicit parametrisation of the solutions to the bogomolny equation over 3