an efficient implementation of stress resultant plasticity in analysis of reissner mindlin plates reference epfl article 102718view record in web of science record created on 2007 04 23 modified on 2016 08 08

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

extension of noncommutative soliton hierarchies a linear system which generates a moyal deformed two dimensional soliton equation as an integrability condition can be extended to a three dimensional linear system treating the deformation parameter as an additional coordinate the supplementary integrability conditions result in a first order differential equation with respect to the deformation parameter the flow of which commutes with the flow of the deformed soliton equation in this way a deformed soliton hierarchy can be extended to a bigger hierarchy by including the corresponding deformation equations we prove the extended hierarchy properties for the deformed akns hierarchy and specialize to the cases of deformed nls kdv and mkdv hierarchies corresponding results are also obtained for the deformed kp hierarchy a deformation equation determines a kind of seiberg witten map from classical solutions to solutions of the respective noncommutative deformed equation

stress resultant geometrically nonlinear shell theory with drilling rotations part ii computational aspects abstract in this work we discuss some details of the numerical implementation of the geometrically nonlinear shell theory presented in part i two possibilities to represent finite rotations with an orthogonal matrix and with a rotation vector are examined in detail along with their mutual relationship in both spatial and material description the issues pertinent to the consistent linearization procedure corresponding to these rotation parameterizations are also carefully considered the geometrically nonlinear method of incompatible modes is extended to the nonlinear shell theory under consideration and used to provide a 4 node shell element with enhanced performance a rather extensive set of numerical examples in nonlinear elastostatics is solved in order to corroborate the non locking performance of the incompatible mode based shell elements the examples include not only analyses of simple shell structures undergoing very large displacements and rotations but also cases of strong practical interest such as non smooth shell structures and shell structures with stiffeners

classical dirichlet forms on topological vector spaces closability and a cameron martin formula abstract we prove a sufficient condition for the closability of classical dirichlet forms on l 2 e which is also necessary if all components of the dirichlet form are closable here e is a locally convex topological vector space and a not necessarily quasi invariant probability measure on e the same condition is shown to imply the existence of a closed extension whose domain can be described explicitly in the special case where is quasi invariant with respect to certain vectors in e our result generalises previous theorems on closability in addition we prove a cameron martin type formula for a large class of measures if e is finite dimensional our characterisation of closability is the analogue of the corresponding one dimensional result applications to quantum fields and the connection with the well studied case of abstract wiener spaces are discussed

classical dirichlet forms on topological vector spaces the construction of the associated diffusion process given a minimal classical dirichlet form onl 2 e we construct the associated diffusion process heree is a locally convex topological vector space and is a not necessarily quasi invariant probability measure one the construction is carried out under certain assumptions one and which can be easily verified in many examples in particular we explicitly apply our results to time zero and space time quantum fields with or with out cut off

the r matrix theory and the reduction of poisson manifolds the relation between the r matrix approach to the construction of bi hamiltonian structures and the reduction of poisson manifolds is discussed the crucial role of the reduction process is emphasized by showing on the basis of specific examples that the knowledge of a r matrix may not be sufficient the reduction of the poisson structures related with r from the entire algebra to the lax submanifold may become an obstruction in constructing the bi hamiltonian structures of a specific hierarchy of integrable equations

singular stochastic equations on hilbert spaces harnack inequalities for their transition semigroups we consider stochastic equations in hilbert spaces with singular drift in the framework of g da prato m rockner singular dissipative stochastic equations in hilbert spaces probab theory related fields 124 2 2002 261 303 we prove a harnack inequality in the sense of f y wang logarithmic sobolev inequalities on noncompact riemannian manifolds probab theory related fields 109 1997 417 424 for its transition semigroup and exploit its consequences in particular we prove regularizing and ultraboundedness properties of the transition semigroup as well as that the corresponding kolmogorov operator has at most one infinitesimally invariant measure satisfying some mild integrability conditions finally we prove existence of such a measure for noncontinuous drifts

a trace identity and its application to integrable systems of 1 2 dimensions a trace identity is proposed and it is shown that this identity can be effectively applied to establish the hamiltonian structure of the kp ds hierarchies and a new hierarchy of 1 2 dimensional systems

constrained kp models as integrable matrix hierarchies we formulate the constrained kp hierarchy denoted by ckp k 1 m as an affine sl m k 1 matrix integrable hierarchy generalizing the drinfeld sokolov hierarchy using an algebraic approach including the graded structure of the generalized drinfeld sokolov hierarchy we are able to find several new universal results valid for the ckp hierarchy in particular our method yields a closed expression for the second bracket obtained through dirac reduction of any untwisted affine kac moody current algebra an explicit example is given for the case sl m k 1 for which a closed expression for the general recursion operator is also obtained we show how isospectral flows are characterized and grouped according to the semisimple non regular element e of sl m k 1 and the content of the center of the kernel of e

discretization error for the discrete kirchhoff plate finite element approximation abstract we provide in this work the discretization error estimates that can guide an adaptive mesh refinement for the discrete kirchhoff plate finite elements the proposed developments are built upon the concept of error estimates for classical elasticity and adapted to suit the kirchhoff plate finite elements we give a detailed illustration of the proposed procedures for the discrete kirchhoff triangular plate element along with several different possibilities for constructing the enhancement of test space needed for error estimates the first novelty concerns the consistent displacement field in terms of the third order polynomial for the discrete kirchhoff triangle whereas the second novelty is the use of the argyris triangle with fifth order polynomials for constructing the enhanced test for error estimates we compare the latter against several alternatives that can be used for kirchhoff plates the results of numerical examples are given to illustrate the effectiveness of proposed discretization error estimates

integrable deformations of the mkdv and sg hierarchies and quasigraded lie algebras abstract we construct a new family of quasigraded lie algebras that admit the kostant adler scheme they coincide with special quasigraded deformations of twisted subalgebras of the loop algebras using them we obtain new hierarchies of integrable equations in partial derivatives they coincide with the deformations of integrable hierarchies associated with the loop algebras we consider the case g g l 2 in detail and obtain integrable hierarchies that could be viewed as deformations of mkdv sine gordon and derivative non linear shrodinger hierarchies and some other integrable hierarchies such as the w3 non linear shrodinger hierarchy and its doubled form

a systematic approach to the soliton equations of a discrete eigenvalue problem the ablowitz ladik al problem is a linear vector difference equation whose isospectral flow equations include several important soliton equations e g the discrete nonlinear schrodinger equation iqn qn 1 2qn qn 1 qn 2 qn 1 qn 1 there is an established procedure for describing the soliton hierarchy of the more familiar akns ablowitz kaup newell and segur problem it is based on the notion of a generator for the hierarchy in this paper the soliton equations of the al hierarchy are described and characterized by a generator pair a new continuous spectral problem is introduced and the akns hierarchy is embedded in its hierarchy as a specialization

stable splitting scheme for general form of associated plasticity including different scales of space and time an efficient implementation of the operator split procedure for boundary value solution with plastic flow computation is presented for a general form of associated plasticity model we start with the general form of phenomenological model of plasticity where the yield criterion is not restricted to a simple quadratic form and the elasticity tensor does not have constant entries we then turn to the multi scale model of plasticity which employs the fine scale representation of the plastic deformation along with the homogenization procedure for stress computation we also visit the plasticity model with rate sensitive plastic response where plastic flow computation is carried out at fine scale in time we proved herein the sufficient and necessary conditions for the proposed operator split procedure to converge for any such general form of associated plasticity moreover we presented a systematic manner for constructing the main ingredients for the plastic flow computation and the global newton s iteration such as the consistent elastoplastic tangent

finite deformation plasticity in principal axes from a manifold to the euclidean setting abstract this contribution presents a link between early developments in finite deformation plasticity where the notion of a covariant formulation is introduced and employed and more recent developments where rediscovery of a fundamental work of hill on the method of principal axes led to a very efficient implementation scheme more precisely we demonstrate how to develop a covariant theory of finite deformation plasticity in an invariant form by making use of the elastic principal stretches we also show how to implement principal axis formulation in the framework of manifold to carry out all the necessary manipulations by exploiting the lie derivative formalism and eventually to simplify the final result to the euclidean setting much of our work on numerical implementation reflects the fruitful cross fertilization of ideas with those from theoretical formulation in particular we show how the operator split method which is typically used to simplify the plastic flow computation can also be used to reduce the computational cost related to the special finite element interpolation schemes based on incompatible modes the latter proves to be an indispensable ingredient for accommodating the near incompressibility constraint arising in the finite deformation deviatoric plasticity an important advantage of the proposed formulation as opposed to alternative remedies e g b bar method is that the basic structure of the governing equations need not be modified

integrable nonlinear equations and liouville s theorem i a symplectic structure for stationary lax equations of the type l p 0 is constructed wherel is a matrix differential operator of the first order it is shown that the equation has a sufficient for the complete integrability amount of first integrals in involution the well known linearization of the equation by the abelian mapping is obtained in a natural manner in consequent exercising of liouville s procedure

strong uniqueness for sdes in hilbert spaces with nonregular drift we prove pathwise uniqueness for a class of stochastic dierential equations sde on a hilbert space with cylindrical wiener noise whose non linear drift parts are sums of the subdierential of a convex function and a bounded part this generalizes a classical result by one of the authors to innite dimensions our results also generalize

strong solutions to stochastic differential equations with rough coefficients we study strong existence and pathwise uniqueness for stochastic dierential equations in r d with rough coecients

complete integrability of the reduced maxwell bloch equations with permanent dipole abstract we obtain the lax pair hierarchy of commuting flows and backlund transformations for a reduced maxwell bloch rmb system this system is of particular interest for the description of unipolar nonoscillating electromagnetic solitons also called electromagnetic bubbles

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

an integrable reduction of inhomogeneously broadened optical equations abstract we introduce a set of reduced maxwell bloch equations that incorporates the effects of a permanent dipole and inhomogeneous broadening we demonstrate the integrability of this reduction by providing a lax pair which is found using the pseudo potential technique an appropriate backlund transformation is employed to produce a family of solitonic solutions

the kp and more dimensional kdv equations on a 1 2 and a 1 3 the kp equations which are conjugated to completely integrable flows on a 1 2 and a 1 3 are examined these equations fall into different classes determined by the order of the hamiltonians involved more dimensional kdv equations appear in this analysis

a four node corotational quadrilateral elastoplastic shell element using vectorial rotational variables four node corotational quadrilateral elastoplastic shell element summary a four node corotational quadrilateral elastoplastic shell element is presented the local coordinate system of the element is defined by the two bisectors of the diagonal vectors generated from the four corner nodes and their cross product this local coordinate system rotates rigidly with the element but does not deform with the element as a result the element rigid body rotations are excluded in calculating the local nodal variables from the global nodal variables the two smallest components of each nodal orientation vector are defined as rotational variables leading to the desired additive property for all nodal variables in a nonlinear incremental solution procedure different from other existing corotational finite element formulations the resulting element tangent stiffness matrix is symmetric owing to the commutativity of the local nodal variables in calculating the second derivative of strains with respect to these variables for elastoplastic analyses the maxwell huber hencky von mises yield criterion is employed together with the backward euler return mapping method for the evaluation of the elastoplastic stress state the consistent tangent modulus matrix is derived to eliminate locking problems we use the assumed strain method several elastic patch tests and elastoplastic plate shell problems undergoing large deformation are solved to demonstrate the computational efficiency and accuracy of the proposed formulation copyright 2013 john wiley sons ltd

kac moody lie algebras and soliton equations iii stationary equations associated with a1 1 abstract the hamiltonian structure of stationary soliton equations associated with the akns eigenvalue problem is derived in two ways first it is shown to arise from the kostant kirillov symplectic structure on a coadjoint orbit in an infinite dimensional lie algebra second it is obtained as the restriction to a finite dimensional manifold of the infinite dimensional hamiltonian structure associated with a certain eigenvalue problem polynomial in the eigenvalue parameter

the krichever map vector bundles over algebraic curves and heisenberg algebras we study the grassmanniangr x n consisting of equivalence classes of rankn algebraic vector bundles over a riemann surfacex with an holomorphic trivialization at a fixed pointp commutative subalgebras ofgl n h h being the ring of functions holomorphic on a punctured disc aboutp define flows on the grassmannian giving rise to classes of solutions to multi component kp hierarchies these commutative subalgebras correspond to heisenberg algebras in the kac moody algebra associated togl n h one can obtain by the krichever map points ofgr x n and solutions of mckp from coveringsf y x and other geometric data conversely for every point ofgr x n and for every choice of heisenberg algebra we construct using the cotangent bundle ofgr x n an algebraic curve coveringx and other data thus inverting the krichever map we show the explicit relation between the choice of heisenberg algebra and the geometry of the covering space

gradient estimates and applications for sdes in hilbert space with multiplicative noise and dini continuous drift abstract consider the stochastic evolution equation in a separable hilbert space h with a nice multiplicative noise and a locally dini continuous drift we prove that for any initial data the equation has a unique possibly explosive mild solution under a reasonable condition ensuring the non explosion of the solution the strong feller property of the associated markov semigroup is proved gradient estimates and log harnack inequalities are derived for the associated semigroup under certain global conditions which are new even in finite dimensions

well posedness of semilinear stochastic wave equations with holder continuous coefficients abstract we prove that semilinear stochastic abstract wave equations including wave and plate equations are well posed in the strong sense with an holder continuous drift coefficient if 2 3 1 the uniqueness may fail for the corresponding deterministic pde and well posedness is restored by adding an external random forcing of white noise type this shows a kind of regularization by noise for the semilinear wave equation to prove the result we introduce an approach based on backward stochastic differential equations we also establish regularizing properties of the transition semigroup associated to the stochastic wave equation by using control theoretic results

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

comparisons between sine gordon and perturbed nonlinear schrodinger equations for modeling light bullets beyond critical collapse abstract the sine gordon sg equation and perturbed nonlinear schrodinger nls equations are studied numerically for modeling the propagation of two space dimensional 2d localized pulses the so called light bullets in nonlinear dispersive optical media we begin with the 2 1 sg equation obtained as an asymptotic reduction in the two level dissipationless maxwell bloch system followed by the review on the perturbed nls equation in 2d for sg pulse envelopes which is globally well posed and has all the relevant higher order terms to regularize the collapse of standard critical cubic focusing nls the perturbed nls is approximated by truncating the nonlinearity into finite higher order terms undergoing focusing defocusing cycles efficient semi implicit sine pseudospectral discretizations for sg and perturbed nls are proposed with rigorous error estimates numerical comparison results between light bullet solutions of sg and perturbed nls as well as critical nls are reported which validate that the solution of the perturbed nls as well as its finite term truncations are in qualitative and quantitative agreement with the solution of sg for the light bullets propagation even after the critical collapse of cubic focusing nls in contrast standard critical nls is in qualitative agreement with sg only before its collapse as a benefit of such observations pulse propagations are studied via solving the perturbed nls truncated by reasonably many nonlinear terms which is a much cheaper task than solving sg equation directly

a loop group approach to the c neumann problem and moser veselov factorization a geometrical description of continuous and discrete versions of the neumann oscillator in terms of a loop group framework is investigated it is shown that the continuous neumann oscillator can be integrated by the riemann hilbert factorization on the twisted loop group of o 3 lo 3 the solution of the problem is given in terms of a special class of flows on the quotient space lo 3 lo 3 where lo 3 is a subgroup of positive loops in lo 3 it is also shown that the moser veselov algorithm for integrating a discrete version of the neumann oscillator heisenberg xyz chain is induced by a discrete flow in this space the flow can be explicitly integrated by solving the matrix riccati equation in both cases discrete and continuous conservation laws are derived from time invariance of a relation that holds for coefficients of the fourier expansion of the flows

finite elastoplastic deformations of space curved membranes abstract under restriction of an isotropic elastic response of deformed lattice a covariant theory of finite elastoplasticity is developed in principal axes of a pair of deformation tensors in material description the tensor pair consists of the plastic deformation tensor and the total deformation cauchy green tensor the proposed theory is applied to elastoplastic membranes whose reference and current configurations can be arbitrary space curved surfaces pressure insensitive von mises yield criterion and isotropic hardening are considered as a model problem with a particular form of the strain energy function given in terms of elastic principal stretches through an explicit enforcement of the plane stress condition we arrive at a reduced two dimensional problem representation which is set in the membrane tangent plane numerical implementation details are given to show an important role of the operator split methodology in simplifying the state update computation and the computation of the consistent tangent modulus a set of numerical examples illustrates the performance of the presented theory and indicates some of the possible areas of application

tightness of general c1 p capacities on banach space abstract we prove tightness of c 1 p capacities on a banach space e these capacities are defined in terms of measures on e which are not necessarily gaussian our methods are purely analytic and completely different from earlier approaches which were implemented under more restrictive assumptions

the infinitesimal generator of the stochastic burgers equation we develop a martingale approach for a class of singular stochastic pdes of burgers type including fractional and multi component burgers equations by constructing a domain for their infinitesimal generators it was known that the domain must have trivial intersection with the usual cylinder test functions and to overcome this difficulty we import some ideas from paracontrolled distributions to an infinite dimensional setting in order to construct a domain of controlled functions using the new domain we are able to prove existence and uniqueness for the kolmogorov backward equation and the martingale problem we also extend the uniqueness result for energy solutions of the stochastic burgers equation of gubinelli and perkowski j am math soc 31 2 427 471 2018 to a wider class of equations as applications of our approach we prove that the stochastic burgers equation on the torus is exponentially l 2 ergodic and that the stochastic burgers equation on the real line is ergodic

degenerate sdes with singular drift and applications to heisenberg groups abstract by using the ultracontractivity of a reference diffusion semigroup krylov s estimate is established for a class of degenerate sdes with singular drifts which leads to existence and pathwise uniqueness by means of zvonkin s transformation the main result is applied to singular sdes on generalized heisenberg groups

the problem of selecting the shape functions for a p type finite element abstract the paper addresses the question of the optimal selection of the shape functions for p type finite elements and discusses the effectivity of the conjugate gradient and multilevel iteration method for solving the corresponding linear system the selection of the shape functions is of major importance for the performance of the solver based on iterative methods neither the theory nor practice of the optimal selection of the shape functions is available yet we have seen that the condensation approach which has obvious advantages from the point of parallel computations is a very effective tool for keeping the condition number under the control and is especially advantageous for the conjugate gradient method

a generalized elastoplastic plate theory and its algorithmic implementation in continuum mechanics within specific classes of problems one or two dimensional theories are often simpler to apply than the more complete three dimensional one this is for example the case of thin bodies such as plates or shells which may be studied using appropriate two dimensionai theories within this approach the reduction of the dimension is traded for a loss of information relative to the motion in the transverse direction for example in the case of non linear material behaviour classical plasticity plate theories are usually not able to model the effects related to the spreading of plasticity through the cross section in the present paper we discuss a generalized plasticity plate model which can be used to reproduce some of the three dimensional effects in a two dimensional setting we present the continuous and the discrete time model including both isotropic and kinematic hardening mechanisms moreover the form of the tangent matrix consistent with the discrete model is addressed finally some examples cantilever beam clamped circular plate and clamped square plate under monotonic and cyclic loading are studied numerically using a three dimensional classical plasticity theory a classical plasticity plate theory and the proposed plate theory the generalized plasticity plate model matches the three dimensional response with greater accuracy than the classical plasticity plate model

locking free discontinuous finite elements for the upper bound yield design of thick plates summary this work investigates the formulation of finite elements dedicated to the upper bound kinematic approach of yield design or limit analysis of reissner mindlin thick plates in shear bending interaction the main novelty of this paper is to take full advantage of the fundamental difference between limit analysis and elasticity problems as regards the class of admissible virtual velocity fields in particular it has been demonstrated for 2d plane stress plane strain or 3d limit analysis problems that the use of discontinuous velocity fields presents a lot of advantages when seeking for accurate upper bound estimates for this reason discontinuous interpolations of the transverse velocity and the rotation fields for reissner mindlin plates are proposed the subsequent discrete minimization problem is formulated as a second order cone programming problem and is solved using the industrial software package mosek a comprehensive study of the shear locking phenomenon is also conducted and it is shown that discontinuous elements avoid such a phenomenon quite naturally whereas continuous elements cannot without any specific treatment this particular aspect is confirmed through numerical examples on classical benchmark problems and the so obtained upper bound estimates are confronted to recently developed lower bound equilibrium finite elements for thick plates copyright 2015 john wiley sons ltd

hierarchies of evolution equations associated with certain symmetric spaces hierarchies of evolution equations associated with certain symmetric spaces are presented main examples of such symmetric spaces are hermitian symmetric spaces and the obtained evolution equations include generalized nonlinear schrodinger equations those results are obtained by extending the lie algebra in the ablowitz kaup newell segur scheme from sl 2 c to more general one

hierarchy structure in integrable systems of gauge fields and underlying lie algebras an improved version of nakamura s self dual yang mills hierarchy is presentd and its symmetry contents are studied the new hierarchy as well as the previous one represents a set of commuting dynamical flows in an infinite dimensional manifolds of loop type but includes a large set of dependent variables because of new degrees of freedom the theory acquires a more symmetric form with richer structures for example it allows a large symmetry algebra of riemann hilbert type which is actually a direct sum of two subalgebras left and right this phenomenon is basically the same as observed recently by avan and bellon on the case of principal chiral models in addition to these rather familiar symmeties a new type of symmetries referred to as coordinate transformation type are also introduced generators of the above dynamical flows are all included therein these two types of symmetries altogether form a big lie algebra which lead to more satisfactory understanding of symmetry properties of integrable systems of guage fields

isospectral hamiltonian flows in finite and infinite dimensions i generalized moser systems and moment maps into loop algebras a moment map jr jia gl r is constructed from the poisson manifold j a of rank r perturbations of a fixed n xn matrix a to the dual r f e positive part of the formal loop algebra i r g r c 1 the adler kostant symes theorem is used to give hamiltonians which generate commutative isospectral flows on g r the pull back of these hamiltonians by the moment map gives rise to commutative isospectral hamiltonian flows in j a the latter may be identified with flows on finite dimensional coadjoint orbits in g and linearized on the jacobi variety of an invariant spectral curve xr which generically is an r sheeted riemann surface reductions of j a are derived corresponding to subalgebras of gl r c and sl r c determined as the fixed point set of automorphism groupes generated by involutions i e jdl the classical algebras as well as reductions to twisted subalgebras of s r c the theory is illustrated by a number of examples of finite dimensional isospectral flows defining integrable hamiltonian systems and their embeddings as finite gap solutions to integrable systems of pde s

gauge theory of ba cklund transformations ii abstract a class of gauge transformations is constructed for hamiltonian hierarchies of completely integrable systems on semi simple lie algebras these transformations create or annihilate poles in the scattering data hence create or annihilate solitons in the potential q in that sense they generalize backlund transformations to which they reduce precisely for the 2 2 akns systems to each backlund gauge transformation is associated an automorphism in the weyl group of the lie algebra two proofs are given to show that these backlund gauge transformations preserve the nonlinear evolution equation one proof uses the transformation of the scattering data under the backlund transformation the second proof is purely gauge theoretic

on a non standard algebraic description of integrable nonlinear systems abstract we present a non standard algebraic description of some classical integrable systems in 1 1 dimensions resulting from interchanging the role of space and time variables bi or multi hamiltonian hierarchies obtained this way reduce naturally to the stationary subspaces giving some insight into the recursive structure of stationary flows

on the τ function of matrix hierarchies of integrable equations expressions of the baker and of the functions for algebraic geometrical solutions of the akns d hierarchy of integrable equations are obtained in terms of functions along with a formula connecting them

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

a powerful approach to generate new integrable systems in this paper an effective algorithm to generate integrable systems is given as a result many new integrable equations are derived in a systematic way

hamiltonians and zero curvature equations for integrable partial differential equations we discuss the relationship between two approaches to integrable partial differential equations one using formal affine lie algebras and the other banach lie groups in the first approach integrability of the equations follows from commutativity of hamiltonian flows on the lie algebra while in the second it follows from commutativity of certain flows induced by an action on the banach lie group we show that these two methods are essentially equivalent since one can calculate one type of the flows from the other the classes of solutions encompassed by the two methods however vary significantly we demonstrate this relationship specifically with the nonlinear schrodinger equation

hamiltonian flows for a reduced maxwell bloch system with permanent dipole abstract we place a reduced maxwell bloch rmb system with permanent dipole in a lie algebraic framework that enables us to reveal a hierarchy of systems in involution the first of which is the rmb model this is done in the context of the adler kostant symes theorem we provide the hamiltonian functions for the commuting flows and establish an infinite number of conservation laws

a four node plate bending element based on mindlin reissner plate theory and a mixed interpolation this communication discusses a 4 node plate bending element for linear elastic analysis which is obtained as a special case from a general nonlinear continuum mechanics based 4 node shell element formulation the formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate and shell element

regularization by noise for stochastic hamilton jacobi equations we study regularizing effects of nonlinear stochastic perturbations for fully nonlinear pde more precisely path by path l infty bounds for the second derivative of solutions to such pde are shown these bounds are expressed as solutions to reflected sde and are shown to be optimal

τ functions and zero curvature equations of toda akns type the connection between functions and zero curvature equations for the homogeneous construction of the basic module l 0 over the simplest affine kac moody algebra a 1 1 is studied

from akns to derivative nls hierarchies via deformations of associative products using deformations of associative products derivative nonlinear schrodinger dnls hierarchies are recovered as akns type hierarchies since the latter can also be formulated as gelfand dickey type lax hierarchies a recently developed method to obtain functional representations can be applied we actually consider hierarchies with dependent variables in any possibly noncommutative associative algebra e g an algebra of matrices of functions this also covers the case of hierarchies of coupled derivative nls equations

modified non abelian toda field equations and twisted quasigraded lie algebras we construct a new family of quasigraded lie algebras that admit the kostant adler scheme they coincide with special quasigraded deformations of twisted subalgebras of the loop algebras using them we obtain new hierarchies of integrable equations in partial derivatives which we call modified non abelian toda field hierarchies

the patch test a condition for assessing fem convergence this paper discusses various forms of the irons patch test and shows again that its satisfaction is a necessary convergence condition being equivalent to consistency further it is shown that the test can be applied for verification of stability requirements thus providing also a sufficient condition of convergence the patch test is useful in testing the order of asymptotic convergence and the satisfaction of the test gives a guide for development of certain incompatible element forms

kac moody lie algebras and soliton equations ii lax equations associated with a1 1 the soliton equations associated with sl 2 eigenvalue problems polynomial in the eigenvalue parameter are given a unified treatment they are shown to be generated by a single family of commuting hamiltonians on a subalgebra of the loop algebra of sl 2 the conserved densities and fluxes of the usual anks hierarchy are identified with conserved densities and fluxes for the polynomial eigenvalue problems the hamiltonian structures of the soliton equations associated with the polynomial eigenvalue problems are given a unified treatment

estimates for invariant probability measures of degenerate spdes with singular and path dependent drifts in terms of a nice reference probability measure integrability conditions on the path dependent drift are presented for infinite dimensional degenerate pdes to have regular positive solutions to this end the corresponding stochastic partial differential equations are proved to possess the weak existence and uniqueness of solutions as well as the existence uniqueness and entropy estimates of invariant probability measures when the reference measure satisfies the log sobolev inequality sobolev estimates are derived for the density of invariant probability measures some results are new even for non degenerate sdes with path independent drifts the main results are applied to nonlinear functional spdes and degenerate functional sdes spdes

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

the symmetries of solitons in this article we will retrace one of the great mathematical adventures of this century the discovery of the soliton and the gradual explanation of its remarkable properties in terms of hidden symmetries we will take an historical approach starting with a famous numerical experiment carried out by fermi pasta and ulam on one of the first electronic computers and with zabusky and kruskal s insightful explanation of the surprising results of that experiment and of a follow up experiment of their own in terms of a new concept they called solitons solitons however raised even more questions than they answered in particular the evolution equations that govern solitons were found to be hamiltonian and have infinitely many conserved quantities pointing to the existence of many non obvious symmetries we will cover next the elegant approach to solitons in terms of the inverse scattering transform and lax pairs and finally explain how those ideas led step by step to the discovery that loop groups acting by dressing transformations give a conceptually satisfying explanation of the secret soliton symmetries

backlund transformations between the akns and dnls hierarchies starting from the functional representation of the ablowitz kaup newell segur akns and derivative nonlinear schr dinger dnls hierarchies and using the chains of the miura like transformations we derive a set of b cklund transformations that link solutions of these systems it is shown that the extended akns and dnls hierarchies possess a common set of tau functions and their connection with the ablowitz ladik hierarchy is established these results are another manifestation of the already known fact that the akns and dnls hierarchies are closely related and can be viewed as particular cases of a more general system