formulation of elastostatic hybrid trefftz stress elements abstract the hybrid trefftz stress hts element is derived from the fundamental conditions of linear elastostatics the stress and boundary displacement fields are directly approximated consistent finite element variables are so defined as to obtain boundary integral expressions for the finite element equilibrium and compatibility conditions encoded by dual transformations independent of the constitutive relations reciprocity is preserved in the finite element elasticity relations which are also found to be described by boundary integral arrays when the trefftz constraint is enforced consequent upon duality and reciprocity the resulting boundary integral solving system is symmetric and sparse the energy statements associated with the hybrid trefftz stress element are established and the conditions for the existence uniqueness multiplicity and static and kinematic admissibility of the finite element solutions are presented the hts clement is compared with the displacement frame based hybrid trefftz ht d element of jirousek it is shown that the ht d element is in fact an hybrid stress element the numerical tests performed to assess the relative performances of the hts and ht d elements show that better accuracy levels are obtained using discontinuous boundary approximation bases

schramm loewner evolution theory of the asymptotic behaviors of 2 1 dimensional wolf villain model abstract although extensive analytical and numerical work has focus on investigating the 2 1 dimensional wolf villain wv model some problems concerning its asymptotical behaviors such as the universality class to which it belongs remain controversial the schramm loewner evolution sle theory is an attractive approach to describe the fluctuation phenomena and random processes and has also been applied to the analysis of the stochastic growth of surfaces in this work we applied sle theory to the analysis of the saturated surface to conduct in depth research with a new perspective on the asymptotical behaviors of the 2 1 dimensional wv model on the basis of the analysis of the saturated surface contour lines we determine that the diffusion coefficient calculated for 2 1 dimensional wv model is 2 91 0 01 and that for family model is 2 88 0 01 accordingly we can conclude from the view of sle theory that the 2 1 dimensional wv model similar to the family model also belongs to the edwards wilkinson universality class

influences of large height differences and overhangs on the dynamic scaling behavior of discrete models abstract in order to investigate the influences of large height differences and overhangs on the dynamic scaling behavior of discrete models meanwhile reducing the finite size effects the etching model is modified to reduce large height differences and the overhangs in ballistic deposition surfaces are removed under certain principles numerical simulations are carried out for the modified models and the results show that the modified surfaces lead to good dynamic scaling behavior even on small system length scales the values of the dynamic scaling exponents are in excellent agreement with theoretical predictions of the kardar parisi zhang equation in 1 1 dimensions

conformal invariance of isoheight lines in a two dimensional kardar parisi zhang surface the statistics of isoheight lines in the 2 1 dimensional kardar parisi zhang kpz model is shown to be conformally invariant and equivalent to those of self avoiding random walks this leads to a rich variety of exact analytical results for the kpz dynamics we present direct evidence that the isoheight lines can be described by the family of conformally invariant curves called schramm loewner evolution or sle with diffusivity 8 3 it is shown that the absence of the nonlinear term in the kpz equation will change the diffusivity from 8 3 to 4 indicating that the isoheight lines of the edwards wilkinson surface are also conformally invariant and belong to the universality class of domain walls in the o2 spin model

numerical index of absolute sums of banach spaces abstract we study the numerical index of absolute sums of banach spaces giving general conditions which imply that the numerical index of the sum is less or equal than the infimum of the numerical indices of the summands and we provide some examples where the equality holds covering the already known case of c 0 l 1 and l sums and giving as a new result the case of e sums where e has the rnp and n e 1 in particular for finite dimensional e with n e 1 we also show that the numerical index of a banach space z which contains a dense union of increasing one complemented subspaces is greater or equal than the limit superior of the numerical indices of those subspaces using these results we give a detailed short proof of the already known fact that for a fixed p the numerical indices of all infinite dimensional l p spaces coincide

instability intermittency and multiscaling in discrete growth models of kinetic roughening we show by numerical simulations that discretized versions of commonly studied continuum nonlinear growth equations such as the kardar parisi zhangequation and the lai das sarma villain equation and related atomistic models of epitaxial growth have a generic instability in which isolated pillars or grooves on an otherwise flat interface grow in time when their height or depth exceeds a critical value depending on the details of the model the instability found in the discretized version may or may not be present in the truly continuum growth equation indicating that the behavior of discretized nonlinear growth equations may be very different from that of their continuum counterparts this instability can be controlled either by the introduction of higher order nonlinear terms with appropriate coefficients or by restricting the growth of pillars or grooves by other means a number of such controlled instability models are studied by simulation for appropriate choice of the parameters used for controlling the instability these models exhibit intermittent behavior characterized by multiexponent scaling of height fluctuations over the time interval during which the instability is active the behavior found in this regime is very similar to the turbulent behavior observed in recent simulations of several one and two dimensional atomistic models of epitaxial growth

a random rule model of surface growth abstract stochastic models of surface growth are usually based on randomly choosing a substrate site to perform iterative steps as in the etching model mello et al 2001 5 in this paper i modify the etching model to perform sequential instead of random substrate scan the randomicity is introduced not in the site selection but in the choice of the rule to be followed in each site the change positively affects the study of dynamic and asymptotic properties by reducing the finite size effect and the short time anomaly and by increasing the saturation time it also has computational benefits better use of the cache memory and the possibility of parallel implementation

critical exponents of the kpz equation via multi surface coding numerical simulations we study the kpz equation in d 2 3 and 4 spatial dimensions by using a restricted solid on solid discretization of the surface we measure the critical exponents very precisely and we show that the rational guess is not appropriate and that d 4 is not the upper critical dimension we are also able to determine very precisely the exponent of the sub leading scaling corrections that turns out to be close to unity in all cases we introduce and use a multi surface coding technique that allows a gain of the order of 30 fold over usual numerical simulations

classification of 2 1 dimensional growing surfaces using schramm loewner evolution statistical behavior and scaling properties of isoheight lines in three different saturated two dimensional grown surfaces with controversial universality classes are investigated using ideas from schramm loewner evolution text sle ensuremath kappa we present some evidence that the isoheight lines in the ballistic deposition bd eden and restricted solid on solid rsos models have conformally invariant properties all in the same universality class as the self avoiding random walk saw equivalently text sle 8 3 this leads to the conclusion that all these discrete growth models fall into the same universality class as the kardar parisi zhang kpz equation in two dimensions

on the numerical index of banach spaces we give a partial answer to the problem of computing the numerical index of lp space 1 p also we give an estimate of the numerical index of the two dimensional real space lp2 1 p for the lp space we show that its numerical index is greater than the lp space one

discrete atomistic model to simulate etching of a crystalline solid a discrete atomistic solid on solid model is proposed to describe dissolution of a crystalline solid by a liquid the model is based on the simple assumption that the probability per unit time of a unit cell being removed is proportional to its exposed area numerical simulations in one dimension demonstrate that the model has very good scaling properties after removal of only about 10 2 monolayers independently of the substrate size the etched surface shows almost time independent short range correlations and the receding surface presents the family vicsek scaling behavior the scaling parameters alpha 0 491 0 002 and beta 0 330 0 001 indicate that the system belongs to the kardar parisi zhang universality class the imposition of periodic boundary conditions on the simulations reduces the effective system size by a factor of 0 68 without changing the exponents alpha and beta surprisingly the periodic condition changes drastically the statistics of the surface height fluctuations and the short range correlations without periodic conditions that statistics is up to 3 standard deviations an asymmetric levy distribution with mu 1 82 0 01 and outside this region the statistics is gaussian with periodic conditions that statistics is gaussian except for large negative fluctuations

diffusion of directed polymers in a random environment we consider a system of random walks or directed polymers interacting weakly with an environment which is random in space and time in spatial dimensionsd 2 we establish that the behavior is diffusive with probability one the diffusion constant is not renormalized by the interaction

the method of fundamental solutions for axisymmetric potential problems in this paper we investigate the application of the method of fundamental solutions mfs to two classes of axisymmetric potential problems in the first the boundary conditions as well as the domain of the problem are axisymmetric and in the second the boundary conditions are arbitrary in both cases the fundamental solutions of the governing equations and their normal derivatives which are required in the formulation of the mfs can be expressed in terms of complete elliptic integrals the method is tested on several axisymmetric problems from the literature and is also applied to an axisymmetric free boundary problem copyright 1999 john wiley sons ltd

stochastic equations for simple discrete models of epitaxial growth we derive continuous stochastic equations governing the asymptotic behavior of growth from a master equation for discrete growth models with local relaxation we consider several simple models of epitaxial growth the family the wolf villain and the das sarma tamborenea models and their modifications i n 1 11 dimensions we derive for each model the corresponding langevin equation and identify leading terms that determine the universality class our results for models with local relaxation are in agreement with recent computer simulations the applicability of the method in 211 dimensions is demonstrated in the case of the family model problems of the procedure in particular regularization in the continuous limit are discussed s1063 651x 96 00710 6

noise reduction in eden models ii surface structure and intrinsic width for pt i see ibid vol 20 p 257 1987 the authors suggest a picture of the intrinsic surface width in eden models and show that it is a major source of corrections to scaling of the surface roughness using the multiple hit noise reduction method they can control the intrinsic width and thereby improve the scaling behaviour systematically as is demonstrated in detailed calculations on the square lattice they calculate the number of excess perimeter sites as a function of time and find that its asymptotic value decays with a power law as a function of increasing hitting number substrate effects and anisotropy become more apparent if noise reduction is applied

three dimensional hybrid trefftz stress elements the stress model of the hybrid trefftz finite element formulation is applied to the linear elastostatic analysis of solids the stresses are approximated in the domain of the element and displacements on its boundary complete linearly independent hierarchical polynomial approximation functions are used in both domain and boundary approximations the displacement basis is defined independently on each inter element surface continuity at the edges and on the corners of the elements is not enforced a priori the stress basis is constrained to solve locally the beltrami governing differential equation it is derived from the associated papkovitch neuber elastic displacement solution generalized variables are used to ensure that the approximations are independent of the geometric description of the elements the solving system is derived directly from the fundamental relations of elastostatics the solving system is symmetric when the same property applies to the local elasticity condition sparse described by boundary integral arrays and well suited to p refinement and parallel processing the numerical implementation of these equations is discussed and numerical tests are presented to illustrate the performance of the finite element formulation copyright 2000 john wiley sons ltd

trefftz method fitting boundary conditions the paper presents various ways of fitting the boundary conditions in the t complete functions method the authors point out the distinct advantages of the orthogonal collocation in comparison to the equidistant collocation and the integral fit the convergence of the collatz error measures and the conditioning of the solution matrices are investigated in detail

generalized finite differences using fundamental solutions summary it is well known that solutions for linear partial differential equations may be given in terms of fundamental solutions the fundamental solutions solve the homogeneous equation exactly and are obtained from the solution of the inhomogeneous equation where the inhomogeneous term is described by a dirac delta distribution fundamental solutions are the building blocks of the boundary element method and of the method of fundamental solutions and are traditionally used to build boundary only global approximations in the domain of interest in this work the same characteristic of the fundamental solutions that of solving the homogeneous equation exactly is used but not to build a global approximation on the contrary local approximations are built in such a manner that it is possible to construct finite difference operators that are free from any form of structured grid copyright q 2009 john wiley sons ltd

trefftz difference schemes on irregular stencils the recently developed flexible local approximation method flame produces accurate difference schemes by replacing the usual taylor expansion with trefftz functions local solutions of the underlying differential equation this paper advances and casts in a general form a significant modification of flame proposed recently by pinheiro and webb a least squares fit instead of the exact match of the approximate solution at the stencil nodes as a consequence of that flame schemes can now be generated on irregular stencils with the number of nodes substantially greater than the number of approximating functions the accuracy of the method is preserved but its robustness is improved for demonstration the paper presents a number of numerical examples in 2d and 3d electrostatic magnetostatic particle interactions scattering of electromagnetic acoustic waves and wave propagation in a photonic crystal the examples explore the role of the grid and stencil size of the number of approximating functions and of the irregularity of the stencils

on the equivalence of the trefftz method and method of fundamental solutions for laplace and biharmonic equations in this paper it is proved that the two approaches known in the literature as the method of fundamental solutions mfs and the trefftz method are mathematically equivalent in spite of their essentially minor and apparent differences in formulation in deriving the equivalence of the trefftz method and the mfs for the laplace and biharmonic problems it is interesting to find that the complete set in the trefftz method for the laplace and biharmonic problems are embedded in the degenerate kernels of the mfs the degenerate scale appears using the mfs when the geometrical matrix is singular the occurring mechanism of the degenerate scale in the mfs is also studied by using circulant the comparison of accuracy and efficiency of the two methods was addressed

a meshless method for kirchhoff plate bending problems in this work a meshless method for the analysis of bending of thin homogeneous plates is presented this meshless method is based on the use of radial basis functions to build an approximation of the general solution of the partial differential equations governing the kirchhoff plate bending problem in order to obtain a symmetric and non singular linear equation system the hermite collocation method is used to assess the formulation a series of plates with different boundary conditions are analysed comparisons are made with other results available in the literature copyright 2001 john wiley sons ltd

finite difference schemes for incompressible flow based on local pressure boundary conditions in this paper we discuss the derivation and use of local pressure boundary conditions for finite difference schemes for the unsteady incompressible navier stokes equations in the velocity pressure formulation their use is especially well suited for the computation of moderate to large reynolds number flows we explore the similarities between the implementation and use of local pressure boundary conditions and local vorticity boundary conditions in the design of numerical schemes for incompressible flow in 2d in their respective formulations when these local numerical boundary conditions are coupled with a fully explicit convectively stable time stepping procedure the resulting methods are simple to implement and highly efficient unlike the vorticity formulation the use of the local pressure boundary condition approach is readily applicable to 3d flows the simplicity of the local pressure boundary condition approach and its easy adaptation to more general flow settings make the resulting scheme an attractive alternative to the more popular methods for solving the navier stokes equations in the velocity pressure formulation we present numerical results of a second order finite difference scheme on a nonstaggered grid using local pressure boundary conditions stability and accuracy of the scheme applied to stokes flow is demonstrated using normal mode analysis also described is the extension of the method to variable density flows

on the numerical radius of operators in lebesgue spaces we show that the absolute numerical index of the space lp is p 1pq 1q where 1p 1q 1 in other words we prove that sup x p 1 tx d x lp x p 1 p 1pq 1q t for every t l lp and that this inequality is the best possible when the dimension of lp is greater than one we also give lower bounds for the best constant of equivalence between the numerical radius and the operator norm in lp for atomless when restricting to rank one operators or narrow operators

flooding transition in the topography of toppling surfaces of stochastic and rotational sandpile models a continuous phase transition occurs in the topography of toppling surfaces of stochastic and rotational sandpile models when they are flooded with liquid say water the toppling surfaces are extracted from the sandpile avalanches that appear due to sudden burst of toppling activity in the steady state of these sandpile models though a wide distribution of critical flooding heights exists a critical point is defined by merging the flooding thresholds of all the toppling surfaces the criticality of the transition is characterized by power law distributionofislandareainthecriticalregime afinitesizescalingtheoryisdevelopedandverifiedbycalculating several new critical exponents the flooding transition is found to be an interesting phase transition and does not belong to the percolation universality class the universality class of this transition is found to depend on the degree of self affinity of the toppling surfaces characterized by the hurst exponent h and the fractal dimension df of critical spanning islands the toppling surfaces of different stochastic sandpile models are found to have a single hurst exponent whereas those of different rotational sandpile models have another hurst exponent as a consequence the universality class of different sandpile models remains preserved within the same symmetry of the models

a simple mesh generator in matlab creating a mesh is the first step in a wide range of applications including scientific computing and computer graphics an unstructured simplex mesh requires a choice of meshpoints vertex nodes

schramm loewner evolution theory of the asymptotic behaviors of 2 1 dimensional das sarma tamborenea model abstract a mass of theoretical analysis and numerical calculation on 2 1 dimensional das sarma tamborenea model have been carried out over the years a problem about asymptotical behaviors that this model belongs to which universality classes is still interesting and controversial the schramm loewner evolution theory is an innovative point of view to describe the conformal invariance of contour lines of saturated rough surfaces in this paper we used sle theory to analyze the conformal invariance of the 2 1 dimensional dt model a noise reduction technique was also utilized to get better scaling behavior the results show that the contour lines of 2 1 dimensional dt model satisfy the property of conformal invariance and belongs to 4 universality class the relation d f 1 8 is also satisfied for the fractal dimension and diffusion coefficient of the contour lines

controlled instability and multiscaling in models of epitaxial growth we show that discretized versions of commonly studied nonlinear growth equations have a generic instability in which isolated pillars or grooves on an otherwise flat interface grow in time when their height or depth exceeds a critical value controlling this instability by the introduction of higher order nonlinear terms leads io intermittent behavior characterized by multiexponent scaling of height fluctuations similar to the turbulent behavior found in recent simulations of one dimensional atomistic models of epitaxial growth

critical properties of island perimeters in the flooding transition of stochastic and rotational sandpile models critical properties of external perimeters of islands that appear at the flooding transition in the toppling surfaces defined by the toppling number si of each sand column of stochastic and rotational sandpile models are studied a set of new critical exponents are estimated by extensive numerical simulation and finite size scaling analysis the values of the critical exponents are found different for these sandpile models several scaling relations among the critical exponents and the hurst exponent describing the self affinity of the toppling surfaces are established and verified the critical exponents obtained here are also found connected to the exponents describing the avalanche size distribution

scaling of clusters and winding angle statistics of isoheight lines in two dimensional kardar parisi zhang surfaces we investigate the statistics of iso height lines of 2 1 dimensional kardar parisi zhang model at different level sets around the mean height in the saturation regime we find that the exponent describing the distribution of the height cluster size behaves differently for level cuts above and below the mean height while the fractal dimensions of the height clusters and their perimeters remain unchanged the winding angle statistics also confirms again the conformal invariance of these contour lines in the same universality class of self avoiding random walks saws the study of surfaces their static statistical properties as well as growth and evolution dynamics and their morphological properties has been attracting an ever increasing amount of interest over the last two decades a method of characterizing surfaces is by looking at their iso height contour lines and the islands that are generated by a cut through the surface at a certain constant height such a situation can be found in the patterns exhibited by topographical islands and continents these islands and their coastlines have some fractal features with a fractal dimension related to the roughness exponent given by the structure function h h x h x r 2 i r 2 where h x is the height of interface as a function of its position theoretical modeling of the growth processes started with the work by edwards and wilkinson ew 1 who suggested that one might describe the dynamics of the height fluctuations by a simple linear diffusion equation kardar parisi and zhang kpz 2 realized that there is a relevant term proportional to the square of the height gradient which represents a correction for lateral growth the kpz equation is given by

a class of difference schemes with flexible local approximation solutions of many physical problems have salient local features that are qualitatively known a priori for example singularities at point sources edge and corners boundary layers derivative jumps at material interfaces strong dipole field components near polarized spherical particles cusps of electronic wavefunctions at the nuclei electrostatic double layers around colloidal particles etc the known methods capable of providing flexible local approximation of such features include the generalized finite element partition of unity method special variational difference schemes in broken sobolev spaces and a few other specialized techniques in the proposed new class of flexible local approximation methods flame a desirable set of local approximating functions such as cylindrical or spherical harmonics plane waves harmonic polynomials etc defines a finite difference scheme on a chosen grid stencil one motivation is to minimize the notorious staircase effect at curved and slanted interface boundaries however the new approach has much broader applications as illustrative examples the paper presents arbitrarily high order 3 point schemes for the 1d schrodinger equation and a 1d singular equation schemes for electrostatic interactions of colloidal particles electromagnetic wave propagation and scattering plasmon resonances moreover many classical finite difference schemes including the collatz mehrstellen schemes are direct particular cases of flame

geometrical exponents of contour loops on synthetic multifractal rough surfaces multiplicative hierarchical cascade p model in this paper we study many geometrical properties of contour loops to characterize the morphology of synthetic multifractal rough surfaces which are generated by multiplicative hierarchical cascading processes to this end two different classes of multifractal rough surfaces are numerically simulated as the first group singular measure multifractal rough surfaces are generated by using the p model the smoothened multifractal rough surface then is simulated by convolving the first group with a so called hurst exponent h the generalized multifractal dimension of isoheight lines contours d q correlation exponent of contours x l cumulative distributions of areas and perimeters are calculated for both synthetic multifractal rough surfaces our results show that for both mentioned classes hyperscaling relations for contour loops are the same as that of monofractal systems in contrast to singular measure multifractal rough surfaces h plays a leading role in smoothened multifractal rough surfaces all computed geometrical exponents for the first class depend not only on its hurst exponent but also on the set of p values but in spite of multifractal nature of smoothened surfaces second class the corresponding geometrical exponents are controlled by h the same as what happens for monofractal rough surfaces

meshfree explicit local radial basis function collocation method for diffusion problems this paper formulates a simple explicit local version of the classical meshless radial basis function collocation kansa method the formulation copes with the diffusion equation applicable in the solution of a broad spectrum of scientific and engineering problems the method is structured on multiquadrics radial basis functions instead of global the collocation is made locally over a set of overlapping domains of influence and the time stepping is performed in an explicit way only small systems of linear equations with the dimension of the number of nodes included in the domain of influence have to be solved for each node the computational effort thus grows roughly linearly with the number of the nodes the developed approach thus overcomes the principal large scale problem bottleneck of the original kansa method two test cases are elaborated the first is the boundary value problem nafems test associated with the steady temperature field with simultaneous involvement of the dirichlet neumann and robin boundary conditions on a rectangle the second is the initial value problem associated with the dirichlet jump problem on a square the accuracy of the method is assessed in terms of the average and maximum errors with respect to the density of nodes number of nodes in the domain of influence multiquadrics free parameter and timestep length on uniform and nonuniform node arrangements the developed meshless method outperforms the classical finite difference method in terms of accuracy in all situations except immediately after the dirichlet jump where the approximation properties appear similar