an adaptive spectral dg method for a reduced phase space based level set approach to geometrical optics on curved elements we present an adaptive spectral discontinuous galerkin dg method on curved elements to simulate high frequency wavefronts within a reduced phase space formulation of geometrical optics following recent work the approach is based on the use of level sets defined by functions satisfying the liouville equations in reduced phase space and in particular it relies on the smoothness of these functions to represent them by rapidly convergent spectral expansions in the phase variables the resulting hyperbolic system of equations for the coefficients in these expansions are then amenable to a high order accurate treatment via dg approximations in the present work we significantly expand on the applicability and efficiency of the approach by incorporating mechanisms that allow for its use in scattering simulations and for a reduced overall computational cost with regards to the former we demonstrate that the incorporation of curved elements is necessary to attain any kind of accuracy in calculations that involve scattering off non flat interfaces with regards to efficiency on the other hand we also show that the level set formulation allows for a space p adaptive scheme that under resolves the level set functions away from the wavefront without incurring in a loss of accuracy in the approximation of its location as we show these improvements enable simulations that are beyond the capabilities of previous implementations of these numerical procedures

reconstructing hyperbolic cross trigonometric polynomials by sampling along rank 1 lattices with given fourier coefficients the evaluation of multivariate trigonometric polynomials at the nodes of a rank 1 lattice leads to a one dimensional discrete fourier transform in many applications one is also interested in the reconstruction of the fourier coefficients from samples in the spatial domain we present necessary and sufficient conditions on rank 1 lattices allowing a stable reconstruction of trigonometric polynomials supported on hyperbolic crosses in addition we suggest approaches for determining suitable rank 1 lattices using a component by component algorithm we present numerical results for reconstructing trigonometric polynomials up to spatial dimension 100

exact 3d boundary representation in finite element analysis based on cartesian grids independent of the geometry summary this paper proposes a novel immersed boundary method where the embedded domain is exactly described by using its computer aided design cad boundary representation with non uniform rational b splines nurbs or t splines the common feature with other immersed methods is that the current approach substantially reduces the burden of mesh generation in contrast the exact boundary representation of the embedded domain allows to overcome the major drawback of existing immersed methods that is the inaccurate representation of the physical domain a novel approach to perform the numerical integration in the region of the cut elements that is internal to the physical domain is presented and its accuracy and performance evaluated using numerical tests the applicability performance and optimal convergence of the proposed methodology is assessed by using numerical examples in three dimensions it is also shown that the accuracy of the proposed methodology is independent on the cad technology used to describe the geometry of the embedded domain copyright 2015 john wiley sons ltd

numerical cubature using error correcting codes we present a construction for improving numerical cubature formulas with equal weights and a convolution structure in particular equal weight product formulas using linear error correcting codes the construction is most effective in low degree with extended bch codes using it we obtain several sequences of explicit positive interior cubature formulas with good asymptotics for each fixed degree t as the dimension n to infty using a special quadrature formula for the interval g kuperberg adv in appl math 34 2005 pp 853 870 arxiv math pr 0408360 we obtain an equal weight t cubature formula on the n cube with o n lfloor t 2 rfloor points which is within a constant of the stroud lower bound we also obtain t cubature formulas on the n sphere n ball and gaussian rn with o nt 2 points when t is odd when mu is spherically symmetric and t 5 we obtain o n2 points for each t ge 4 we also obtain explicit positive interior formulas for the n simplex with o nt 1 points for t 3 we obtain o n points these constructions asymptotically improve the nonconstructive tchakaloff bound some related results were recently found independently by victoir siam j numer anal 42 2004 pp 209 227 who also noted that the basic construction more directly uses orthogonal arrays

orthogonal polynomials in transport theories the asymptotical k co behaviour of zeros of the polynomials g v encoun tered in the treatment of direct and inverse problems of scattering in neutron transport as well as radiative transfer theories is investigated in terms of the amplitude kjk of the kth legendre polynomial needed in the expansion of the scattering function the parameters gi describe the anisotropy of scattering of the medium considered in particular it is shown that the asymptotical density of zeros of the polynomials gp v is an inverted semicircle for the anisotropic non multiplying scattering medium

formal state determination following the general results of park and band it is shown that any state of a quantal ensemble allowed by the hilbert space formulation of nonrelativistic quantum mechanics may be determined from the results of measurements under the assumption that all measurements those of energy position and spin projection are in accordance with the projection postulate

a fast directional algorithm for high frequency electromagnetic scattering this paper is concerned with the fast solution of high frequency electromagnetic scattering problems using the boundary integral formulation we extend the o nlogn directional multilevel algorithm previously proposed for the acoustic scattering case to the vector electromagnetic case we also detail how to incorporate the curl operator of the magnetic field integral equation into the algorithm when combined with a standard iterative method this results in an almost linear complexity solver for the combined field integral equations in addition the butterfly algorithm is utilized to compute the far field pattern and radar cross section with o nlogn complexity

dynamics of field driven interfaces in the two dimensional ising model the time dependent properties of an inclined interface separating up and down spin regions in a two dimensional nearest neighbour ising model evolving under glauber dynamics in a non zero field are studied in the limit of large exchange coupling the model reduces to the single step model for ballistic growth and thence to the asymmetric exclusion process which describes a driven diffusive system of hard core particles on a one dimensional lattice the drift velocity of the interface is found as a function of field temperature and inclination and interface correlation functions are related to sliding tag correlation functions in the particle system the existence of a critical value of the sliding tag velocity implies that there is an inclination dependent easy direction along which temporal interface fluctuations grow subdiffusively this direction is found as is the asymptotic behaviour of the correlation function in all other directions

identities on fractional integrals and various integral transforms in this work we will introduce theorems relating the riemann liouville fractional integral and the weyl fractional integral to some well known integral transforms including laplace transforms stieltjes transforms generalized stieltes transforms hankel transforms and k transforms as applications of the theorems and their results a number of infinite integrals of elementary functions and special functions are evaluated and some illustrative examples are presented

some parseval goldstein type identities involving the fs 2 transform the fc 2 transform and the p4 transform and their applications abstract in the present paper the authors consider several new integral transforms including the f s 2 transform the f c 2 transform and the p 4 transform as generalizations of the classical fourier sine transform the classical fourier cosine transform and the classical stieltjes transform respectively many identities involving these transforms are given by making use of these identities a number of new parseval goldstein type identities are obtained for these and many other well known integral transforms the identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions some examples are also given as illustrations of the results presented here

asymmetric cubature formulas for polynomial integration in the triangle and square we present five new cubature formula in the triangle and square for exact integration of polynomials the points were computed numerically with a cardinal function algorithm which does not impose any symmetry requirements on the points cubature formula are presented which integrate degrees 10 11 and 12 in the triangle and degrees 10 and 12 in the square they have positive weights contain no points outside the domain and have fewer points than previously known results

a cardinal function algorithm for computing multivariate quadrature points we present a new algorithm for numerically computing quadrature formulas for arbitrary domains which exactly integrate a given polynomial space an effective method for constructing quadrature formulas has been to numerically solve a nonlinear set of equations for the quadrature points and their associated weights symmetry conditions are often used to reduce the number of equations and unknowns our algorithm instead relies on the construction of cardinal functions and thus requires that the number of quadrature points n be equal to the dimension of a prescribed lower dimensional polynomial space the cardinal functions allow us to treat the quadrature weights as dependent variables and remove them as well as an equivalent number of equations from the numerical optimization procedure we give results for the triangle where for all degrees d le 25 we find quadrature formulas of this form which have positive weights and contain no points outside the triangle seven of these quadrature formulas improve on previously known results

symmetric quadrature rules on a triangle abstract we present a class of quadrature rules on triangles in r 2 which somewhat similar to gaussian rules on intervals in r 1 have rapid convergence positive weights and symmetry by a scheme combining simple group theory and numerical optimization we obtain quadrature rules of this kind up to the order 30 on triangles this scheme essentially a formalization and generalization of the approach used by lyness and jespersen over 25 years ago can be easily extended to other regions in r 2 and surfaces in higher dimensions such as squares spheres we present example formulae and relevant numerical results

a theorem on widder s potential transform and its applications abstract in the present paper the authors prove a parseval goldstein type theorem involving the classical laplace transform the fourier sine transform and widder s potential transform the theorem is then shown to yield a simple algorithm for evaluating infinite integrals some illustrative examples are also given

five dimensional k optimal lattice rules a major search program is described that has been used to determine a set of five dimensional k optimal lattice rules of enhanced trigonometric degrees up to 12 the program involved a distributed search in which approximately 190 cpu years were shared between more than 1 400 computers in many parts of the world

exact field driven interface dynamics in the two dimensional stochastic ising model with helicoidal boundary conditions abstract we investigate the interface dynamics of the two dimensional stochastic ising model in an external field under helicoidal boundary conditions at sufficiently low temperatures and fields the dynamics of the interface is described by an exactly solvable high spin asymmetric quantum hamiltonian that is the infinitesimal generator of the zero range process generally the critical dynamics of the interface fluctuations is in the kardar parisi zhang universality class of critical behavior we remark that a whole family of rsos interface models similar to the ising interface model investigated here can be described by exactly solvable restricted high spin quantum x x z type hamiltonians

symmetric quadrature rules for tetrahedra based on a cubic close packed lattice arrangement a family of quadrature rules for integration over tetrahedral volumes is developed the underlying structure of the rules is based on the cubic close packed ccp lattice arrangement using 1 4 10 20 35 and 56 quadrature points the rules are characterized by rapid convergence positive weights and symmetry each rule is an optimal approximation in the sense that lower order terms have zero contribution to the truncation error and the leading order error term is minimized quadrature formulas up to order 9 are presented with relevant numerical examples

rigorous derivation of domain growth kinetics without conservation laws the time evolution of the ising model that describes shrinking domains is studied a singly connected domain of ising spins embedded in a sea of the opposite phase develops att 0 according to a dynamic rule that does not allow its perimeter to increase at long enough times the domain disappears we show that the average lifetime of such a domain is proportional to its area we also consider thet 0 dynamics of a single infinite quadrant the area of the quadrant decreases during the time evolution and we show that the area lost grows linearly with time we solve a first passage time problem as well that is we calculate the average time it takes for the area lost to reach a given value for the first time lastly we map the infinite quadrant model onto a diffusion problem with exclusion in one dimension this latter problem is mapped onto a critical six vertex model

symmetric triangle quadrature rules for arbitrary functions abstract despite extensive research on symmetric polynomial quadrature rules for triangles as well as approaches to their calculation few studies have focused on non polynomial functions particularly on their integration using symmetric triangle rules in this paper we present two approaches to computing symmetric triangle rules for singular integrands by developing rules that can integrate arbitrary functions the first approach is well suited for a moderate amount of points and retains much of the efficiency of polynomial quadrature rules the second approach better addresses large amounts of points though it is less efficient than the first approach we demonstrate the effectiveness of both approaches on singular integrands which can often yield relative errors two orders of magnitude less than those from polynomial quadrature rules

effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for gfem xfem stress approximations around brittle cracks abstract the convergence rates of the conventional generalized extended finite element method gfem xfem in crack modeling are similar to the convergence rates of the finite element method fem laborde et al 2005 and bechet et al 2005 unless the crack tip enrichment functions are applied in a subdomain with fixed dimension independently of the mesh parameter h and also demanding some special care for blending along the transition zone chahine et al 2006 and taracon et al 2009 thus to improve convergence rates more degrees of freedom dof are generated due to the larger quantity of enriched nodes this work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh based smooth partitions of unity pou such pou with higher regularity can be built through the so called c k gfem framework following duarte et al 2006 based on a moving least square of degree zero and considering mesh based smooth weighting functions associated with arbitrary polygonal clouds the purpose herein is to investigate some possible advantages of mesh based smooth pou for modeling discontinuities and singularities in two dimensional problems of linear elastic fracture mechanics in such a fashion that the discretization error associated to stress discontinuities inherent in standard c 0 continuous gfem xfem approximations is eliminated the procedure shares features similar to the standard fem regarding domain partition and numerical integration but as neither the pou nor the enrichment functions are defined in natural domains the integrations are performed using only global coordinates the approximation capabilities of c k gfem discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions considering global measures in terms of strain energy and l 2 norm of displacements the effects on stability are also verified by analyzing the evolution of the condition number the effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved the smoothness of the pou the different types of enrichment functions and the pattern of enrichment the performance of the smooth approximations is compared to the c 0 counterparts built using conventional c 0 fem based pou it is shown that smoothness in the presence of extrinsically applied singular enrichments is important as the information provided by such enrichment is better captured in addition there are no stress jumps around singularities reducing error propagation beyond the neighborhood of the singularity

limiting shapes of ising droplets ising fingers and ising solitons we examine the evolution of an ising ferromagnet endowed with zero temperature single spin flip dynamics a large droplet of one phase in the sea of the opposite phase eventually disappears an interesting behavior occurs in the intermediate regime when the droplet is still very large compared to the lattice spacing but already very small compared to the initial size in this regime the shape of the droplet is essentially deterministic fluctuations are negligible in comparison with characteristic size in two dimensions the shape is also universal that is independent of the initial shape we analytically determine the limiting shape of the ising droplet on the square lattice when the initial state is a semi infinite stripe of one phase in the sea of the opposite phase it evolves into a finger which translates along its axis we determine the limiting shape and the velocity of the ising finger on the square lattice an analog of the ising finger on the cubic lattice is the translating ising soliton we show that far away from the tip the cross section of the ising soliton coincides with the limiting shape of the two dimensional ising droplet and we determine a relation between the cross section area the distance from the tip and the velocity of the soliton

profile driven interfaces in 1 1 dimensions periodic steady states dynamical melting and detachment abstract we study the steady state structure and dynamics of a 2 d ising interface placed in an inhomogeneous external field with a sigmoidal profile which moves with velocity v e in the strong coupling limit the problem maps onto an asymmetric exclusion process involving motion of particles in 1 d with position dependent right and left jump probabilities for small v e the interface is stuck to the field profile as v e increases the profile detaches from the interface at the transition point and beyond the interfacial structure and dynamics are characterized by the kpz exponents for small v e on the other hand the interface is macroscopically smooth with a vanishing roughness exponent the interfacial structure is periodic with a periodicity which depends on the orientation of the interface for a fixed orientation this periodic structure melts as v e is increased we determine the dynamical phase diagram of this system in the v e orientation plane

the index of merit of kth copy integration lattices r2d2lri is an automatic two dimensional cubature algorithm that demonstrates the practical value of using an augmentation sequence consisting of 2 k 2 copy lattices as a basis for numerical integration this paper investigates use of similar embedded augmentation sequences in higher dimensions by developing theoretical results relating to the index of merit of s dimensional 2 k s copy lattices generated from rank 1 simple lattices the theoretical results can be used to guide the search for good augmentation sequences in s dimensions in the sense of high index of merit

dynamics of an anchored toom interface at a sufficiently low noise level the two dimensional toom model north east center majority vote with small errors has two stationary states the authors study the statistical properties of interfaces between these phases with particular attention to a stationary interface maintained in the third quadrant by mixed boundary conditions the fluctuations in this interface are found numerically to be much smaller than in equilibrium interfaces they have exponents 1 4 or 1 3 depending on the symmetry rather than 1 2 the correlations exhibit long range behaviour reminiscent of self organized criticality they construct several approximate theories of the interface which reproduce this behaviour at least qualitatively the most accurate of these leads to a novel nonlinear partial differential equation for the asymptotic probability distribution of the fluctuations along the interface

alternative proposal of the high order gauss quadrature for reference triangle in the generalized finite element method abstract in this paper we propose a new distribution of gaussian points to compute the weak form integrals of the generalized finite element method gfem the relevance of this new distribution is the possibility of evaluating the integrals of oscillatory functions inside the reference triangle in an alternate way a simple scheme of relocation of the quadrature points allows to improve the efficacy of the method a wave propagation problem is solved with the proposed technique and its performance is compared to conventional and other existing proposals in addition we propose a new distribution of gaussian points to the tetrahedral reference element

exclusion process and droplet shape we use a mathematical isomorphism between the one dimensional exclusion process and the two dimensional stochastic ising model in the low temperature limit to describe the typical instantaneous shape of a supercritical droplet we derive specifically the exact asymptotic distribution of the boundaries of a 1 spin region confined to z 2 and subjected to a positive magnetic field in an appropriate scaling the boundary distribution converges to a deterministic continuum limit

numerical cubature from archimedes hat box theorem archimedes hat box theorem states that uniform measure on a sphere projects to uniform measure on an interval this fact can be used to derive simpson s rule we present various constructions of and lower bounds for numerical cubature formulas using moment maps as a generalization of archimedes theorem we realize some well known cubature formulas on simplices as projections of spherical designs we combine cubature formulas on simplices and tori to make new formulas on spheres in particular sn admits a 7 cubature formula and sometimes a 7 design with o n4 points we establish a local lower bound on the density of a positive interior cubature formula on a simplex using the moment map along the way we establish other quadrature and cubature results of independent interest for each t we construct a lattice trigonometric 2t 1 cubature formula in n dimensions with o nt points we derive a variant of the moller lower bound using vector bundles and we show that gaussian quadrature is very sharply locally optimal among positive quadrature formulas

identities for the e2 1 transform and their applications in the present paper the authors introduce the e 2 1 transform with kernel the exponential integral function it is shown that the third iterate of the l 2 transform is the exponential integral transform and some identities involving the new transform the l 2 transform and the widder potential transform are given using the identities parseval goldstein type results involving these transforms are proved some illustrative examples are also given

discontinuous galerkin solver for the shallow water equations in covariant form on the sphere and the ellipsoid abstract a discontinuous galerkin dg method for the solution of the shallow water equations swe on arbitrary 2 dimensional 2d manifolds is presented to this purpose the swe are formulated in covariant form using tensor notation this allows to correctly transform the numerical fluxes between the local coordinate systems of any two neighboring grid cells in particular the covariant form of the numerical diffusion term in the lax friedrichs numerical flux has been derived too this general approach has the advantage that it avoids any coordinate singularity it is tested for the swe on the sphere with several standard test setups beyond this a recently published test case with an analytic solution for linear inertial gravity wave expansion has been performed the derived formalism on arbitrary 2d manifolds allows an easy extension from the sphere to the ellipsoid the comparison of a barotropic instability test case for the earth shows a non negligible difference between the solution on these two bodies the presented approach may be a starting point for the development of a dynamical core for numerical weather and climate prediction models based on the dg method

generalized gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method new gaussian integration schemes are presented for the efficient and accurate evaluation of weak form integrals in the extended finite element method for discontinuous functions we construct gauss like quadrature rules over arbitrarily shaped elements in two dimensions without the need for partitioning the finite element a point elimination algorithm is used in the construction of the quadratures which ensures that the final quadratures have minimal number of gauss points for weakly singular integrands we apply a polar transformation that eliminates the singularity so that the integration can be performed efficiently and accurately numerical examples in elastic fracture using the extended finite element method are presented to illustrate the performance of the new integration techniques

generalized gaussian quadrature rules on arbitrary polygons in this paper we present a numerical algorithm based on group theory and numerical optimization to compute efficient quadrature rules for integration of bivariate polynomials over arbitrary polygons these quadratures have desirable properties such as positivity of weights and interiority of nodes and can readily be used as software libraries where numerical integration within planar polygons is required we have used this algorithm for the construction of symmetric and non symmetric quadrature rules over convex and concave polygons while in the case of symmetric quadratures our results are comparable to available rules the proposed algorithm has the advantage of being flexible enough so that it can be applied to arbitrary planar regions for the integration of generalized classes of functions to demonstrate the efficiency of the new quadrature rules we have tested them for the integration of rational polygonal shape functions over a regular hexagon for a relative error of 10 8 in the computation of stiffness matrix entries one needs at least 198 evaluation points when the region is partitioned whereas 85 points suffice with our quadrature rule copyright 2009 john wiley sons ltd

low temperature dynamics of kinks on ising interfaces the anisotropic motion of an interface driven by its intrinsic curvature or by an external field is investigated in the context of the kinetic ising model in both two and three dimensions we derive in two dimensions 2d a continuum evolution equation for the density of kinks by a time dependent and nonlocal mapping to the asymmetric exclusion process whereas kinks execute random walks biased by the external field and pile up vertically on the physical 2d lattice they execute hard core biased random walks on a transformed 1d lattice their density obeys a nonlinear diffusion equation which can be transformed into the standard expression for the interface velocity v m ensuremath gamma ensuremath gamma ensuremath ensuremath kappa h where m ensuremath gamma ensuremath gamma ensuremath and ensuremath kappa are the interface mobility stiffness and curvature respectively in 3d we obtain the velocity of a curved interface near the 100 orientation from an analysis of the self similar evolution of 2d shrinking terraces we show that this velocity is consistent with the one predicted from the 3d tensorial generalization of the law for anisotropic curvature driven motion in this generalization both the interface stiffness tensor and the curvature tensor are singular at the 100 orientation however their product which determines the interface velocity is smooth in addition we illustrate how this kink based kinetic description provides a useful framework for studying more complex situations by modeling the effect of immobile dilute impurities

identities and parseval type relations for the l2 transform abstract in the present paper the authors introduce identities for the l 2 transform which yield a parseval type relationship for the l 2 transform the parseval type relationship proven in this paper give rise to useful corollaries for evaluating indefinite integrals of special functions some examples are also given as illustrations of the results presented here

conforming polygonal finite elements summary in this paper conforming finite elements on polygon meshes are developed polygonal finite elements provide greater flexibility in mesh generation and are better suited for applications in solid mechanics which involve a significant change in the topology of the material domain in this study recent advances in meshfree approximations computational geometry and computer graphics are used to construct different trial and test approximations on polygonal elements a particular and notable contribution is the use of meshfree natural neighbour nn basis functions on a canonical element combined with an affine map to construct conforming approximations on convex polygons this numerical formulation enables the construction of conforming approximation on n gons n 3 and hence extends the potential applications of finite elements to convex polygons of arbitrary order numerical experiments on second order elliptic boundary value problems are presented to demonstrate the accuracy and convergence of the proposed method copyright 2004 john wiley sons ltd

identities for the hankel transform and their applications abstract in the present paper the authors show that iterations of the hankel transform with k transform is a constant multiple of the widder transform using these iteration identities several parseval goldstein type theorems for these transforms are given by making use of these results a number of new goldstein type exchange identities are obtained for these and the laplace transform the identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions some examples are also given as illustration of the results presented here

minimal cubature formulae of trigonometric degree in this paper we construct minimal cubature formulae of trigonometric degree we obtain explicit formulae for low dimensions of arbitrary degree and for low degrees in all dimensions a useful tool is a closed form expression for the reproducing kernels in two dimensions

computing almost minimal formulas on the square the main purpose of this paper is to introduce a numerical method for the computation of cubature rules on the square 1 1 2 that are almost minimal i e with few points w r t the degree of precision d in particular for all email protected email protected 55 the sets x d and the weights w k are new new rules are also achieved for degrees 15 d 17 19 and d 23 respectively with 43 54 67 and 96 points

a theorem on the generalized stieltjes transform and its applications abstract this paper presents a proof of parseval goldstein type theorem involving the generalized stieltjes transform and the classical laplace transform the theorem is then shown to yield a number of results about the widder potential transform and the laguerre transform some illustrative examples are also given

three and four dimensional k optimal lattice rules of moderate trigonometric degree a systematic search for optimal lattice rules of specified trigonometric degree d over the hypercube 0 1 sup s has been undertaken the search is restricted to a population k s delta of lattice rules q a this includes those where the dual lattice lambda perpendicular may be generated by s points h for each of which h delta d 1 the underlying theory which suggests that such a restriction might be helpful is presented the general character of the search is described and for s 3 d 29 and s 4 d 23 a list of k optimal rules is given it is not known whether these are also optimal rules in the general sense this matter is discussed

comparison of high order curved finite elements several finite element techniques used in domains with curved boundaries are discussed and compared with particular emphasis in two issues the exact boundary representation of the domain and the consistency of the approximation the influence of the number of integration points on the accuracy of the computation is also studied two dimensional numerical examples solved with continuous and discontinuous galerkin formulations are used to test and compare all these methodologies in every example shown the recently proposed nurbs enhanced finite element method nefem provides the maximum accuracy for a given spatial discretization at least one order of magnitude more accurate than classical isoparametric finite element method fem moreover nefem outperforms cartesian fem and p fem stressing the importance of the geometrical model as well as the relevance of a consistent approximation in finite element simulations

new upper bounds on sphere packings i we continue the study of the linear programming bounds for sphere packing introduced by cohn and elkies we use theta series to give another proof of the principal theorem and present some related results and conjectures this article is in the arxiv as arxiv math mg 0110010

simulation of domain wall dynamics in the 2d anisotropic ising model the authors first show that the movement of a domain wall in a highly anisotropic ising model of spins in two dimensions can be mapped to a random walk movement of labelled walkers in one dimension this movement is correlated in the sense that the transition probability of a given walker labelled i depends upon the current positions of its labelled neighbours i 1 and i 1 a monte carlo simulation of the walk for various numbers of walkers up to a maximum of 50 and for quite long times up to a maximum of 25 104 monte carlo steps yields useful and interesting information about the dynamics they verify that i the centre of mass of the walkers executes an unbiased random walk for all times starting from the lowest times and ii the moment of inertia of the walkers asymptotically reaches a constant value which scales with the number of walkers they also discuss the relation of this work to the dynamics in the 2d ising model identifying phi with the dynamical exponent z the random walk equivalence also provides a geometrical interpretation of the known results for the solid on solid model

d2lri a nonadaptive algorithm for two dimensional cubature we describe a nonadaptive automatic cubature routine for integration over a wide variety of two dimensional domains including infinite regions the underlying algorithm first maps the region onto the unit square applies a periodizing sixth order sidi transformation and then generates a sequence of approximations based on embedded lattice rules numerical experiments suggest that the routine is reliable and efficient for a wide range of integrand types and that it is often more effective than other published routines for integrands with a singularity along the boundary and for integration over infinite domains

four dimensional lattice rules generated by skew circulant matrices we introduce the class of skew circulant lattice rules these are s dimensional lattice rules that may be generated by the rows of an s s skew circulant matrix this is a minor variant of the familiar circulant matrix we present briefly some of the underlying theory of these matrices and rules we are particularly interested in finding rules of specified trigonometric degree d we describe some of the results of computer based searches for optimal four dimensional skew circulant rules besides determining optimal rules for d 1 47 we have constructed an infinite sequence of rules q 4 that has a limit rho index of 27 34 0 79 this index is an efficiency measure which cannot exceed 1 and is inversely proportional to the abscissa count

generalized gaussian quadrature rules for systems of arbitrary functions a numerical algorithm is presented for the construction of generalized gaussian quadrature rules originally introduced by s karlin and w studden over three decades ago the quadrature rules to be discussed possess most of the desirable properties of the classical gaussian integration formulae such as positivity of the weights rapid convergence mathematical elegance etc the algorithm is applicable to a wide class of functions including smooth functions not necessarily polynomials as well as functions with end point singularities such as those encountered in the solution of integral equations complex analysis potential theory and several other areas the performance of the algorithm is illustrated with several numerical examples

dynamic scaling and phase transitions in interface growth abstract the dynamic scaling approach is an effective tool for understanding the temporal evolution of fluctuating interfaces the surface width w obeys the scaling form w l t l t l where and are exponents which characterize how the surface width grows with the length scale l and the time t applications of dynamic scaling to a number of surface growth models are discussed the results of a large scale simulation of the ballistic deposition model in three dimensions are presented and compared with recent conjectures the question of universality in interface growth is addressed and a finite temperature generalization of the restricted solid on solid model is studied this model appears to undergo a phase transition from the usual rough phase at high temperatures to a new phase at low temperatures numerical solutions of the generalized langevin equation indicate that there is no phase transition in 2 1 dimensions thus the relation between the continuum equation and the discrete models is still an open question

the representation of lattice quadrature rules as multiple sums we provide a classification of lattice rules applying elementary group theory we assign to each s dimensional lattice rule a rank m and a set of positive integer invariants n sub 1 n sub 2 n sub s the number nu q of abscissas required by the rule is the product n sub 1 n sub 2 n sub s and the rule may be expressed in a canonical form with m independent summations under this classification an n point number theoretic rule in the sense of korobov and conroy is a rank m 1 rule having invariants n 1 1 1 and the product trapezoidal rule using n sup s points in rank m s rule having invariants n n n besides providing a canonical form we give some of the properties of copy rules and of projections into lower dimensions

new identities involving the laplace and the ℒ 2 transforms and their applications in the present paper parseval goldstein type theorems involving the 2 transforms and the laplace transform are proved the theorems are then shown to yield a number of new identities involving several well known integral transforms and special functions using the theorem and its corollaries a number of interesting infinite integrals of elementary and special functions are presented some illustrative examples are also given

fluctuations in the motions of mass and of patterns in one dimensional driven diffusive systems the stochastic spreading of mass fluctuations in systems described by a fluctuating burgers equation increases ast2 3 with time as a consequence the stochastic motion of a mass front a point through which no excess mass current is flowing is shown to increase ast1 3 the same is true for the stochastic displacement of mass points and shock fronts with respect to their average drift provided the initial configuration is fixed an additional average over the stationary distribution of the initial configuration yields stochastic displacements increasing with time ast1 2

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

two tag correlation functions in one dimensional lattice gases correlations between two labelled particles are studied in a one dimensional lattice gas with nearest neighbour hopping fluctuations in the distance between the first particle at time t and the other at time 0 are studied analytically and by monte carlo with unbiased and biased hopping in the latter case the tag tag correlation shows a nonmonotonic dependence on t a stochastic harmonic theory based on an exact mapping to an interface model suggests a scaling form for the correlation as a function of t and the difference between the labels monte carlo data are consistent with scaling in the unbiased case the scaling function given by the harmonic theory seems to be exact