a higher order scheme for two dimensional quasi static crack growth simulations an efficient scheme for the simulation of quasi static crack growth in two dimensional linearly elastic isotropic specimens is presented the crack growth is simulated in a stepwise manner where an extension to the already existing crack is added in each step in a local coordinate system each such extension is represented as a polynomial of some user specified degree n the coefficients of the polynomial describing an extension are found by requiring that the mode ii stress intensity factor is equal to zero at certain points of the extension if a crack grows from a pre existing crack so that a kink develops the leading term describing the crack shape close to the kink will in a local coordinate system be proportional to x 3 2 we therefore allow the crack extensions to contain such a term in addition to the monomial terms the discontinuity in the crack growth direction at a kink the kink angle is determined by requiring that the mode ii stress intensity factor should be equal to zero for an infinitesimal extension of the existing crack to implement the scheme accurate values of the stress intensity factors and t stress are needed in each step of the simulation these fracture parameters are computed using a previously developed integral equation of the second kind c 2007 elsevier b v all rights reserved less

numerical simulation of dilute particle laden flows by wavelet bem fem abstract a wavelet transform based bem and fem numerical scheme was used to simulate laminar viscous flow the velocity vorticity formulation of the navier stokes equations was used the flow simulation algorithm was coupled with a lagrangian particle tracking scheme for dilute suspensions of massless particles and particles without inertia the proposed numerical approach was used to simulate flow and particle paths for two test cases flow over a backward facing step and flow past a circular cylinder we present methods of calculating the pressure and stream function field at the end of each time step the pressure field was used to calculate drag and lift coefficients which enable qualitative comparison of our results with the benchmark the stream function enabled the comparison of streamlines and massless particle paths in steady state low reynolds number value flow fields and thus provided an estimate on the accuracy of the particle tracking algorithm unsteady higher reynolds number value flows were investigated in terms of particle distributions in vortex streets in the wake of the cylinder and behind the step sedimentation of particles without inertia was studied in the flow field behind a backward facing step at reynolds number value 5000

a diagrammatic approach to hecke algebras of the reflection equation hecke algebra deformations of the wreath product cd sn arise in solutions to the yang baxter equations with boundary the reflection equation we use a simple diagrammatic approach to construct bases for these algebras we hence introduce quotient algebras suitable for constructing physical solutions to the reflection equation with a well defined thermodynamic large n limit for all d and n we determine the generic representation theory of these algebras developing a formalism suitable for the analysis of corresponding q spin chain hamiltonian and transfer matrix spectra

karhunen loeve approximation of random fields by generalized fast multipole methods kl approximation of a possibly instationary random field a x l2 dp l d subject to prescribed meanfield ea x a x dp and covariance va x x a x ea x a x ea x dp in a polyhedral domain d rd is analyzed we show how for stationary covariances va x x ga x x with ga z analytic outside of z 0 an m term approximate kl expansion am x of a x can be computed in log linear complexity the approach applies in arbitrary domains d and for nonseparable covariances ca it involves galerkin approximation of the kl eigenvalue problem by discontinuous finite elements of degree p 0 on a quasiuniform possibly unstructured mesh of width h in d plus a generalized fast multipole accelerated krylov eigensolver the approximate kl expansion am x of a x has accuracy o exp bm1 d if ga is analytic at z 0 and accuracy o m k d if ga is ck at zero it is obtained in o mn logn b operations where n o h d

wavelet galerkin schemes for boundary integral equations implementation and quadrature in the present paper we consider the fully discrete wavelet galerkin scheme for the fast solution of boundary integral equations in three dimensions it produces approximate solutions within discretization error accuracy offered by the underlying galerkin method at a computational expense that stays proportional to the number of unknowns we focus on algorithmical details of the scheme in particular on numerical integration of relevant matrix coefficients we illustrate the proposed algorithm by numerical results

comparison between wavelet and fast multipole data sparse approximations for poisson and kinematics boundary domain integral equations the boundary element method applied on non homogenous partial differential equations requires calculation of a fully populated matrix of domain integrals this paper compares two techniques the fast multipole method and the fast wavelet transform which are used to reduce the complexity of such domain matrices the employed fast multipole method utilizes the expansion of integral kernels into series of spherical harmonics the wavelet transform for vectors of arbitrary length based on haar wavelets and variable thresholding limit is used both methods are tested and compared by solving the scalar poisson equation and the velocity vorticity vector kinematics equation the results show comparable accuracy for both methods for a given data storage size wavelets are somewhat better for high and low compression ratios and the fast multipole methods gives better results for moderate compressions considering implementation of the methods the wavelet transform can easily be adapted for any problem while the fast multipole method requires different expansion for each integral kernel

hecke algebraic approach to the reflection equation for spin chains we use the structural similarity of certain coxeter artin systems to the yang baxter and reflection equations to convert representations of these systems into new solutions of the reflection equation we construct certain bethe ansatz states for these solutions using a parametrization suggested by abstract representation theory

every real ellipsoid in mathbb c 2 admits cr umbilical points we prove that every real ellipsoid m c c 2 admits at least four umbilical points which can be compared to the result of webster that a generic real ellipsoid in c with n 3 does not admit any umbilical point

umbilical points on three dimensional strictly pseudoconvex cr manifolds i manifolds with u 1 action the question of existence of umbilical points in the cr sense on compact three dimensional strictly pseudoconvex cr manifolds was raised in the seminal paper by chern and moser acta math 133 219 271 1974 in the present paper we consider compact three dimensional strictly pseudoconvex cr manifolds that possess a free transverse action by the circle group u 1 we show that every such cr manifold m has at least one orbit of umbilical points provided that the riemann surface x m u 1 is not a torus in particular every compact circular and strictly pseudoconvex hypersurface in mathbb c 2 has at least one circle of umbilical points the existence of umbilical points in the case where x is a torus is left open in general but it is shown that if such an m has additional symmetries in a certain sense then it must possess umbilical points as well

new solutions of reflection equation derived from type b bmw algebras we use b type knot theory to find new solutions of sklyanin s reflection equation in a systematic way this generalizes the well known baxterization of birman wenzl algebras and should describe integrable systems which are restricted to a half plane

compression techniques for boundary integral equations asymptotically optimal complexity estimates matrix compression techniques in the context of wavelet galerkin schemes for boundary integral equations are developed and analyzed that exhibit optimal complexity in the following sense the fully discrete scheme produces approximate solutions within discretization error accuracy offered by the underlying galerkin method at a computational expense that is proven to stay proportional to the number of unknowns key issues are the second compression which reduces the near field complexity significantly and an additional a posteriori compression the latter is based on a general result concerning an optimal work balance that applies in particular to the quadrature used to compute the compressed stiffness matrix with sufficient accuracy in linear time

on the fast matrix multiplication in the boundary element method by panel clustering the boundary element method bem leads to a system of linear equations with a full matrix while fem yields sparse matrices this fact seems to require much computational work for the definition of the matrix for the solution of the system and in particular for the matrix vector multiplication which always occurs as an elementary in this paper a method for the approximate matrix vector multiplication is described which requires much less arithmetical work in addition the storage requirements are strongly reduced

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

collocation methods for poisson s equation in this paper we provide an analysis on the collocation methods cm which uses a large scale of admissible functions such as orthogonal polynomials trigonometric functions radial basis functions and particular solutions etc the admissible functions can be chosen to be piecewise i e different functions are used in different subdomains the key idea is that the collocation method can be regarded as the least squares method involving integration approximation and optimal convergence rates can be easily achieved based on the traditional analysis of the finite element method the key analysis is to prove the uniformly vh elliptic inequality and some inverse inequalities used this paper explores the interesting fact that for the collocation methods given in this paper the integration rules only affect on the uniformly vh elliptic inequality but not on the solution accuracy the advantage of the cm is to formulate easily the associated algebraic equations which can be solved from the collocation equations directly by the least squares method thus to greatly reduce the condition number of the associated matrix moreover the new effective condition number is proposed to provide a better upper bound of condition number and to show a good stability for real problems solved by the collocation methods note that the boundary approximation method in li z c li combined methods for elliptic equations with singularities interfaces and infinities kluwer academic publishers boston london 1998 is a special case of the cm where the admissible functions satisfy the equations exactly numerical experiments are also carried for poisson s problem to support the analysis made

on the riemann mapping theorem we prove a generalization of the riemann mapping theorem if a bounded simply connected domain q with connected smooth boundary has the spherical boundary then it is biholomorphic to the unit ball

a hierarchical o n force calculation algorithm a novel code for the approximate computation of long range forces between n mutually interacting bodies is presented the code is based on a hierarchical tree of cubic cells and features mutual cell cell interactions which are calculated via a cartesian taylor expansion in a symmetric way such that total momentum is conserved the code benefits from an improved and simple multipole acceptance criterion that reduces the force error and the computational effort for n 104 the computational costs are found empirically to rise sublinearly with n for applications in stellar dynamics this is the first competitive code with complexity o n it is faster than the standard tree code by a factor of 10 or more

integrable boundary conditions for multi species asep the first result of the present paper is to provide classes of explicitsolutions for integrable boundary matrices for the multi species asep with anarbitrary number of species all the solutions we have obtained can be seen as representations of a newalgebra that contains the boundary hecke algebra the boundary hecke algebra isnot sufficient to build these solutions this is the second result of ourpaper

hecke algebra solutions to the reflection equation we construct solutions to sklyanin s reflection equation in the case in which the bulk yang baxter solution is of hecke algebra type each solution constitutes an extension of the hecke algebra together with a spectral parameter dependent boundary operator k theta we solve for the defining relations of the extension and for the spectral parameter dependence of the boundary operator the problem of finding concrete matrix solutions to the reflection equation is thus reduced to that of constructing finite dimensional representations of the hecke algebra extension this problem is solved in the generic case by establishing isomorphism with an affine hecke algebra quotient whose representation theory is known

on spin systems related to the temperley lieb algebra the spectrum of the transfer matrices constructed from the spectral parameter dependent temperley lieb r matrix is found using functional relations identical to those of the spin 1 2 xxz magnet

the dual reciprocity boundary element method drbem for two dimensional sine gordon equation this paper presents the dual reciprocity boundary element method drbem for solving two dimensional sine gordon sg equation the integral equation formulation employs the fundamental solution of the laplace equation and hence a domain integral arises in the boundary integral equation furthermore the time derivatives are approximated by the time stepping method and the domain integral also appears from these approximations the domain integral is transformed into boundary integral by using the dual reciprocity method drm the linear radial basis function rbf is employed for drm the dynamics of line solitons and ring solitons of circular and elliptic shapes are studied numerical results are presented for some problems involving line and ring solitons to demonstrate the usefulness and accuracy of this approach