multi scale lagrangian shock hydrodynamics on q1 p0 finite elements theoretical framework and two dimensional computations abstract a new multi scale stabilized method for q1 p0 finite element computations of lagrangian shock hydrodynamics is presented instabilities of hourglass type are controlled by a stabilizing operator derived using the variational multi scale analysis paradigm the resulting stabilizing term takes the form of a pressure correction with respect to broadly accepted hourglass control approaches the novelty of the method resides in its residual based character the stabilizing residual has a definite physical significance since it embeds a discrete form of the clausius duhem inequality effectively the proposed stabilization samples the production of entropy to counter numerical instabilities the proposed technique is applied to materials with no shear strength e g fluids for which there exists a caloric equation of state and extensions to the case of materials with shear strength e g solids are also envisioned the stabilization operator is incorporated into a mid point predictor multi corrector time integration algorithm which conserves mass momentum and total energy encouraging numerical results in the context of compressible gas dynamics confirm the potential of the method

a conservative three dimensional eulerian method for coupled solid fluid shock capturing a new method is presented for the explicit eulerian finite difference computation of shock capturing problems involving multiple resolved material phases in three dimensions we solve separately for each phase the equations of fluid dynamics or solid mechanics using as interface boundary conditions artificially extended representations of the individual phases for fluids we use a new 3d spatially unsplit implementation of the piecewise parabolic ppm method of colella and woodward for solids we use the 3d spatially unsplit eulerian solid mechanics method of miller and colella vacuum and perfectly incompressible obstacles may also be employed as phases a separate problem is the time evolution of material interfaces which are represented by planar segments constructed with a volume of fluid method the volume fractions are advanced in time using a second order 3d spatially unsplit advection routine with a velocity field determined by solution of interface normal two phase riemann problems from the riemann problem solutions we also determine cross interface momentum and energy fluxes the volume fractions in mixed cells may be arbitrarily small which would ordinarily make the courant friedrichs lewy time step stability limit arbitrarily small as well we overcome this limitation using the mass redistribution formalism to conservatively redistribute generalized mass in the neighborhood of the split cells we present an application of this method to an explosion contained in a metal can a reactive fluid approximating pbx 9404 is encased within an elastic plastic solid approximating copper surrounded by vacuum our implementation is in parallel and with adaptive mesh refinement

asymptotic expansion of a integral involving a bessel function abstract an asymptotic expansion is derived for a quadruple integral involving the bessel function j0 xy zw where each of the integration variables x y z and w belongs to the interval 0 1 and the large variable tends to infinity corresponding results are also obtained for similar integrals in two and three dimensions

asymptotic expansions of integrals of two bessel functions via the generalized hypergeometric and meijer functions abstract asymptotic expansions of certain finite and infinite integrals involving products of two bessel functions of the first kind are obtained by using the generalized hypergeometric and meijer functions the bessel functions involved are of arbitrary generally different orders but of the same argument containing a parameter which tends to infinity these types of integrals arise in various contexts including wave scattering and crystallography and are of general mathematical interest being related to the riemann liouville and hankel integrals the results complete the asymptotic expansions derived previously by two different methods a straightforward approach and the mellin transform technique these asymptotic expansions supply practical algorithms for computing the integrals the leading terms explicitly provide valuable analytical insight into the high frequency behavior of the solutions to the wave scattering problems

nonlinear codes from algebraic curves improving the tsfasman vladut zink bound in the present paper we construct a class of nonlinear codes by making use of higher order derivatives of certain functions of algebraic curves it turns out that the asymptotic bound derived from the goppa geometry codes can be improved for the entire interval 0 1 in particular the tsfasman vladut zink tvz bound is ameliorated for the entire interval 0 1

the second order sharpening of blurred smooth borders the problem is to approximate with local second order accuracy the smooth boundary separating a black and a white region in the plane given discretely located gray values associated with a blurring of that border second order here is with respect to the size ital h of the scale of the prescribed blurring the locally determined approximations are line segments the algorithms discussed here can result in second order accuracy but they may not in certain geometric circumstances typical local curvature estimates based on adjacent line segments do not converge but atypical one does consideration of a class of scaled blurrings leads to a type of blurring of borders which is particularly easy for a computer to undo locally yielding a line which is locally second order accurate some extensions to three and more dimensions are appended

second order accurate volume of fluid algorithms for tracking material interfaces we introduce two new volume of fluid interface reconstruction algorithms and compare the accuracy of these algorithms to four other widely used volume of fluid interface reconstruction algorithms we find that when the interface is smooth e g continuous with two continuous derivatives the new methods are second order accurate and the other algorithms are first order accurate we propose a design criteria for a volume of fluid interface reconstruction algorithm to be second order accurate namely that it reproduce lines in two space dimensions or planes in three space dimensions exactly we also introduce a second order unsplit volume of fluid advection algorithm that is based on a second order finite difference method for scalar conservation laws due to bell dawson and shubin we test this advection algorithm by modeling several different interface shapes propagating in two simple incompressible flows and compare the results with the standard second order operator split advection algorithm although both methods are second order accurate when the interface is smooth we find that the unsplit algorithm exhibits noticeably better resolution in regions where the interface has discontinuous derivatives such as at corners

a volume of fluid method based on multidimensional advection and spline interface reconstruction a new volume of fluid method for tracking two dimensional interfaces is presented the method involves a multidimensional advection algorithm based on the use of edge matched flux polygons to integrate the volume fraction evolution equation and a spline based reconstruction algorithm the accuracy and efficiency of the proposed method are analyzed using different tests and the results are compared with those obtained recently by other authors despite its simplicity the proposed method represents a significant improvement and compares favorably with other volume of fluid methods as regards the accuracy and efficiency of both the advection and reconstruction steps

reconstructing volume tracking a new algorithm for the volume tracking of interfaces in two dimensions is presented the algorithm is based upon a well defined second order geometric solution of a volume evolution equation the method utilizes local discrete material volume and velocity data to track interfaces of arbitrarily complex topology a linearity preserving piecewise linear interface geometry approximation ensures that solutions generated retain second order spatial accuracy second order temporal accuracy is achieved by virtue of a multidimensional unsplit time integration scheme we detail our geometrically based solution method in which material volume fluxes are computed systematically with a set of simple geometric tasks we then interrogate the method by testing its ability to track interfaces through large controlled topology changes whereby an initially simple interface configuration is subjected to vortical flows numerical results for these strenuous test problems provide evidence for the algorithm s improved solution quality and accuracy

constrained interpolation remap of divergence free fields abstract a novel constrained interpolation algorithm for remapping of solenoidal face finite element vector fields is presented the algorithm is based on explicit recovery postprocessing and interpolation of a potential for the original vector field and a subsequent application of a curl operator to obtain the desired divergence free finite element field on the new mesh the use of interpolation instead of advection in the remap process offers valuable computational advantages old and new meshes are neither required to have the same connectivity nor to be close to each other slope limiting and upwinding which can be sensitive to grid structure are avoided and replaced by local optimization to control energy of the remapped field the new method is validated using a suite of cyclic remap problems on random and tensor product mesh sequences a comparison with a local remapper based on a constrained transport advection algorithm is also included

self dual doubly even 2 quasi cyclic transitive codes are asymptotically good in this correspondence we prove that the class of binary self dual doubly even 2 quasi cyclic transitive codes is asymptotically good this improves a recent result of bazzi and mitter ieee trans inf theory vol 52 pp 3210 3219 2006 the proof is based on the study of a particular class of codes invariant under dihedral groups using a blend of representation theory and probabilistic arguments the methods are closely related to those used in bazzi and mitter in order to complete the proof a number theoretical result of hasse is needed

incremental remapping as a transport advection algorithm there are two fundamentally different strategies for solving the standard transport or continuity equation corresponding to whether it is expressed as a partial differential equation or as an integral statement of conservation the more common approach is to discretize the partial differential equation and to march the solution forward in time the alternative method is to project cell volumes along lagrangian trajectories as far forward or backward in time as desired and then to remap the resulting density distribution onto some target mesh this latter approach is known as remapping remapping has many advantages not the least of which is that the time step is limited only by accuracy considerations but it tends to be expensive and complex in this paper we show that if the time step is made sufficiently short such that trajectories are confined to the nearest neighbor cells then the remapping may be written as a flux form transport algorithm and it becomes nearly as simple and efficient as standard transport schemes the resulting method called incremental remapping retains most of the advantages of general remapping these include a geometric basis for transport b compatibility of associated tracer transport with simple tracer advection i e retention of tracer monotonicity properties and c efficient handling of multiple tracers since each additional tracer adds only a relatively small incremental cost

cellwise conservative unsplit advection for the volume of fluid method we present a cellwise conservative unsplit ccu advection scheme for the volume of fluid method vof in 2d contrary to other schemes based on explicit calculations of the flux balances the ccu advection adopts a cellwise approach where the pre images of the control volumes are traced backwards through the flow map the donating regions of the fluxes are calculated via the streaklines of the grid intersections represented as polygonal chains whose vertices are determined by backward tracing of particles injected in the flow at different times high order accuracy is obtained from the fourth order runge kutta method where intermediate velocities along pathlines are determined with quadratic temporal and bicubic spatial interpolations the volumes of the donating regions are corrected in order to fulfill the discrete continuity of incompressible flows consequently the calculation produces non overlapping donating regions and pre images with conforming edges to their neighbors resulting in the conservativeness and the boundedness liquid volume fraction inside the interval 0 1 of the ccu advection scheme finally the update of the liquid volume fractions is computed from the intersections of the pre image polygons with the reconstructed interfaces the ccu scheme is tested on several benchmark tests for the vof advection together with the standard piecewise linear interface calculation plic the geometrical errors of the ccu compare favorably with other unsplit vof plic schemes finally potential improvements of the vof method with the use of more precise interface representation techniques and the future extension of the ccu scheme to 3d are discussed cellwise vof update through backward tracing of the cell s pre image accuracy enhanced via bicubic spatial interpolation and polygonal chain streakline the ccu advection scheme is fully conservative and bounded no limitation on the courant number geometrical errors dominated by plic interface representation errors

transitive and self dual codes attaining the tsfasman vla spl breve dut 80 zink bound a major problem in coding theory is the question of whether the class of cyclic codes is asymptotically good in this correspondence as a generalization of cyclic codes the notion of transitive codes is introduced see definition 1 4 in section i and it is shown that the class of transitive codes is asymptotically good even more transitive codes attain the tsfasman vlabrevedut 80 zink bound over fq for all squares q l2 it is also shown that self orthogonal and self dual codes attain the tsfasman vlabrevedut 80 zink bound thus improving previous results about self dual codes attaining the gilbert varshamov bound the main tool is a new asymptotically optimal tower e0subee1 subee2sube middotmiddotmiddot of function fields over fq with q lscr2 where all extensions en e0 are galois

a new volume of fluid advection algorithm a new vof advection algorithm is presented termed the stream scheme the algorithm uses a linear piecewise method for free surface reconstruction coupled to a unique fully multidimensional method of cell boundary flux integration the performance of the new algorithm is compared against other vof advection algorithms using a variety of standard advection tests in general the performance of the stream scheme appears superior to existing multidimensional and dimensionally split advection algorithms

a newton krylov solver for remapping based volume of fluid methods a new conservative remapping method is presented here for generating multi dimensional fluxes used for the time integration of hyperbolic equations through single stage unsplit advection a solution to the lagrangian mesh location is generated that converges the volumes of all remapped flux definitions to the volumes of equivalent one dimensional flux definitions at their corresponding cell faces the method is most feasible within localized subdomains of an eulerian solution domain the main utility of the method is the generation of fluxes in the vicinity of discontinuities and sharp gradients that does not introduce physically spuriously extrema while locally conserving mass in generating solutions to lagrangian mesh location by solving a nonlinear equation system the new remap requires the anchoring of the lagrangian mesh removal of degrees of freedom to make the problem definite the method is based on characteristic tracing along trajectories assumed to be linear this paper investigates the convergence and sensitivity of the lagrangian mesh solver to mesh and timestep size in assessing its merit for application in transient cfd codes for single stage unsplit advection volume of fluid methods the new remap suppresses the introduction of undershoots overshoots and wisps in combination with a conservative remapping phase the new method for fixing the location of the lagrangian mesh eliminates the need for heuristic redistribution or clipping procedures for spurious extrema removal

on functions defined by sums of products of bessel functions various functions defined as infinite series of products of bessel functions of the first kind are studied integral representations are obtained and then used to deduce asymptotic approximations although several methods have been investigated including power series expansions and integral transforms methods based on fourier series emerge as the most useful

second order accurate volume tracking based on remapping for triangular meshes this paper presents a second order accurate piecewise linear volume tracking based on remapping for triangular meshes this approach avoids the complexity of extending unsplit second order volume of fluid algorithms advection methods on triangular meshes the method is based on lagrangian eulerian le methods therefore it does not deal with edge fluxes and corner fluxes flux corrections as is typical in advection algorithms the method is constructed of three parts a lagrangian phase a reconstruction phase and a remapping phase in the lagrangian phase the original eulerian grid is projected along trajectories to obtain lagrangian grids in practice this projection is handled through the time integration of velocity field for grid vertices at each time step the reconstruction is based on truncating the volume material polygon for each lagrangian mixed grid since in piecewise linear approximation the interface is represented by a segment line the polygon material truncation is mainly finding the segment interface finding the segment interface is calculating the line normal and line constant at each multi fluid cell details of applying two normal calculation methods differential and geometric least squares gls methods are given while the gls method exhibits second order accurate approximation in reproducing circular interfaces the differential least squares dls method results in a first order accurate representation of the interface the last part of the algorithm which is remapping of the volume materials from the lagrangian grid to the original one is performed by a series of polygon intersection procedures the behavior of the algorithm is investigated for flow fields with constant interface topology and flow fields inducing large interfacial stretching and tearing second order accuracy is obtained if the velocity integration as well as the reconstruction steps are at least second order accurate

a tower of artin schreier extensions of function fields attaining the drinfeld vladut bound for an algebraic function fieldf having a finite constant field letg f resp n f denote the genus off resp the number of places off of degree one we construct a tower of function fields f 1 subseteq f 2 subseteq f 3 subseteq ldots over mathbb f q 2 such that the ration fi g fi tends to the drinfeld vladut boundq 1

comments on asymptotic expansion of a bessel function integral using hypergeometric functions by l j landau and n j luswili in a recent paper landau and luswili j comput appl math 132 2001 387 used generalized hypergeometric functions to obtain a complete asymptotic expansion for the integral 0 2j sin jv sin d where j is the th order bessel function of the first kind and is a large parameter tending to infinity the purpose of this note is to point out that the same complete asymptotic expansion for this integral as well as another one for a hankel type integral has previously been obtained by stoyanov et al j comput appl math 50 1994 533 by using the same method in addition an alternative simpler representation of the algebraic series contribution to the asymptotic expansion is provided a few errors are also corrected and additional relevant references indicated

constant rate pcps for circuit sat with sublinear query complexity the pcp theorem arora et al 1998 arora and safra 1998 says that every np proof can be encoded to another proof namely a probabilistically checkable proof pcp which can be tested by a verifier that queries only a small part of the pcp a natural question is how large is the blow up incurred by this encoding that is how long is the pcp compared to the original np proof the state of the art work of ben sasson and sudan 2008 and dinur 2007 shows that one can encode proofs of length n by pcps of length n poly log n that can be verified using a constant number of queries in this work we show that if the query complexity is relaxed to ne then one can construct pcps of length o n for circuit sat and pcps of length o tlog t for any language in ntime t more specifically for any e 0 we present nonuniform probabilistically checkable proofs pcps of length 2o 1 e n that can be checked using ne queries for circuit sat instances of size n our pcps have perfect completeness and constant soundness this is the first constant rate pcp construction that achieves constant soundness with nontrivial query complexity o n our proof replaces the low degree polynomials in algebraic pcp constructions with tensors of transitive algebraic geometry ag codes we show that the automorphisms of an ag code can be used to simulate the role of affine transformations that are crucial in earlier high rate algebraic pcp constructions using this observation we conclude that any asymptotically good family of transitive ag codes over a constant sized alphabet leads to a family of constant rate pcps with polynomially small query complexity such codes are constructed in the appendix to this article for the first time for every message length building on an earlier construction for infinitely many message lengths by stichtenoth 2006

excellent nonlinear codes from algebraic function fields the gilbert varshamov gv bound for asymptotic families of codes over f sub q has been improved by tsfasman vla spl breve dut 80 and zink tvz in 1982 and only recently further improvements have been obtained by xing elkies and niederreiter o spl uml zbudak by considering also nonlinear codes these improvements involve higher derivations in function fields and are very computational we give in this correspondence a much simpler proof for those improvements our construction of asymptotically good nonlinear codes is very similar to goppa s construction of algebraic geometry codes

is the class of cyclic codes asymptotically good there is the long standing question whether the class of cyclic codes is asymptotically good by an old result of lin and weldon long bose chaudhuri hocquenhem bch codes are asymptotically bad berman proved that cyclic codes are asymptotically bad if only finitely many primes are involved in the lengths of the codes we investigate further classes of cyclic codes which also turn out to be asymptotically bad based on reduction arguments we give some evidence that there are asymptotically good sequences of binary cyclic codes in which all lengths are prime numbers provided there is any asymptotically good sequence of binary cyclic codes

integral evaluation using the mellin transform and generalized hypergeometric functions tutorial and applications to antenna problems this is a tutorial presentation of the mellin transform mt method for the exact calculation of one dimensional definite integrals and an illustration of the application of this method to antenna electromagnetics problems once the basics have been mastered one quickly realizes that the mt method is extremely powerful often yielding closed form expressions very difficult to come up with other methods or to deduce from the usual tables of integrals yet as opposed to other methods the mt method is very straightforward to apply it usually requires laborious calculations but little ingenuity in fact the mt method is used by mathematica to symbolically calculate definite integrals the first part of this paper is a step by step tutorial proceeding from first principles it includes basic information on mellin barnes integrals and generalized hypergeometric functions and summarizes the key ideas of the mt method in the remaining parts the mt method is applied to three examples from the antenna area the results here are believed to be new at least in the antenna electromagnetics literature in our first example we obtain a closed form expression as a generalized hypergeometric function for the power radiated by a constant current circular loop antenna this quantity has been extensively discussed recently our second example concerns the admittance of a 2 d slot antenna in both these examples the exact closed form expressions are applied to improve upon existing formulas in standard antenna textbooks in our third example finally we obtain a very simple expression for an integral arising in recent unpublished studies of unbounded biaxially anisotropic media

efficient simulation of surface tension dominated flows through enhanced interface geometry interrogation in this paper three improvements for modelling surface tension dominated interfacial flows using interface tracking based solution algorithms are presented we have developed an improved approach to curvature estimation for incorporation into modern mesh based surface tension models such as the continuum surface force csf and sharp surface force ssf models the scheme involves generating samples of curvature estimates from the multitude of height functions that can be generated from vof representations of interfaces and applying quality statistics based on interface orientation and smoothness to choose optimal candidates from the samples in this manner the orientation dependence of past schemes for height function based curvature estimation is ameliorated the use of compact stencils for efficient computation can be maintained and robustness is enhanced even in the presence of noticeable subgrid scale disturbances in the interface representation for surface tension dominated flows the explicit capillary timestep restriction is relaxed through timescale separated slope limiting that identifies spurious modes in curvature evolution and omits them from contributing to surface force computations thus promoting efficiency in simulation through the use of less timesteps efficiency in flow simulation is further promoted by incorporating awareness of interface location into multigrid preconditioning for krylov subspace based solution of elliptic problems this use of interface cognizance in solving problems such as the helmholtz equation and the poisson equation enables multigrid like convergence in discontinuous coefficient elliptic problems without the expense of constructing the galerkin coarse grid operator the key improvements in the surface tension modelling and the numerical linear algebra are also applicable to level set based interfacial flow simulation

conservative and bounded volume of fluid advection on unstructured grids abstract this paper presents a novel eulerian lagrangian piecewise linear interface calculation plic volume of fluid vof advection method which is three dimensional unsplit and discretely conservative and bounded the approach is developed with reference to a collocated node based finite volume two phase flow solver that utilizes the median dual mesh constructed from non convex polyhedra the proposed advection algorithm satisfies conservation and boundedness of the liquid volume fraction irrespective of the underlying flux polyhedron geometry which differs from contemporary unsplit vof schemes that prescribe topologically complicated flux polyhedron geometries in efforts to satisfy conservation instead of prescribing complicated flux polyhedron geometries which are prone to topological failures our vof advection scheme the non intersecting flux polyhedron advection nifpa method builds the flux polyhedron iteratively such that its intersection with neighboring flux polyhedra and any other unavailable volume is empty and its total volume matches the calculated flux volume during each iteration a candidate nominal flux polyhedron is extruded using an iteration dependent scalar the candidate is subsequently intersected with the volume guaranteed available to it at the time of the flux calculation to generate the candidate flux polyhedron the difference in the volume of the candidate flux polyhedron and the actual flux volume is used to calculate extrusion during the next iteration the choice in nominal flux polyhedron impacts the cost and accuracy of the scheme however it does not impact the methods underlying conservation and boundedness as such various robust nominal flux polyhedron are proposed and tested using canonical periodic kinematic test cases zalesak s disk and two and three dimensional deformation the tests are conducted on the median duals of a quadrilateral and triangular primal mesh in two dimensions and on the median duals of a hexahedral wedge and tetrahedral primal mesh in three dimensions comparisons are made with the adaptation of a conventional unsplit vof advection scheme to our collocated node based flow solver depending on the choice in the nominal flux polyhedron the nifpa scheme presented accuracies ranging from zeroth to second order and calculation times that differed by orders of magnitude for the nominal flux polyhedra which demonstrate second order accuracy on all tests and meshes the nifpa method s cost was comparable to the traditional topologically complex second order accurate vof advection scheme

a plic vof method suited for adaptive moving grids this paper presents a new variant of the volume of fluid vof color function c advection algorithm based on the piecewise linear interface construction plic method suitable for use on general moving grids from several existing methods for reconstructing the linear interface we adopted the least squares volume of fluid interface reconstruction algorithm lvira which can be easily implemented on general grids the distinguishing step in the advection algorithm that takes into account the grid movement is the construction of the donating region containing the fluid passing through corresponding cell faces in a single time step the donating regions are constructed utilizing fluid velocity in cell corners relative to grid corner velocities the method is conservative as it complies with the space conservation law scl and requires a proper definition of the grid velocities and fluxes due to the grid movement the accuracy of the presented advection algorithm is assessed with standard test cases it is comparable with other plic based algorithms on fixed grids while the applicability on adaptive moving grids enables a considerable reduction in the number of grid cells

comment on two dimensional highly directive currents on large circular loops j math phys 41 6130 2000 margetis and fikioris apparently unaware of the earlier results available in the literature used an elaborate mellin transform technique to obtain an asymptotic approximation for a particular case of a bessel function integral here the earlier more general results are pointed out

an improvement of the gilbert varshamov bound over nonprime fields the gilbert varshamov bound guarantees the existence of families of codes over the finite field bbf ell with good asymptotic parameters we show that this bound can be improved for all nonprime fields bbf ell with ell geq 49 except possibly ell 125 we observe that the same improvement even holds within the class of transitive codes and within the class of self orthogonal codes