the information lost in erasures we consider sources and channels with memory observed through erasure channels in particular we examine the impact of sporadic erasures on the fundamental limits of lossless data compression lossy data compression channel coding and denoising we define the erasure entropy of a collection of random variables as the sum of entropies of the individual variables conditioned on all the rest the erasure entropy measures the information content carried by each symbol knowing its context the erasure entropy rate is shown to be the minimal amount of bits per erasure required to recover the lost information in the limit of small erasure probability when we allow recovery of the erased symbols within a prescribed degree of distortion the fundamental tradeoff is described by the erasure rate distortion function which we characterize we show that in the regime of sporadic erasures knowledge at the encoder of the erasure locations does not lower the rate required to achieve a given distortion when no additional encoded information is available the erased information is reconstructed solely on the basis of its context by a denoiser connections between erasure entropy and discrete denoising are developed the decrease of the capacity of channels with memory due to sporadic memoryless erasures is also characterized in wide generality

adaptive grid generation from harmonic maps on reimannian manifolds abstract in this paper we describe a new method for generation of solution adaptive grids based on harmonic maps on riemannian manifolds the reliability of the method is assured by an existence and uniqueness theorem for one to one maps between multidimensional multiconnected domains we formulate an adaptive riemannian metric consistent with this theorem several examples demonstrating application of the developed procedure are provided

grid generation techniques in computational fluid dynamics revue des differentes methodes on montre que les regions tridimensionnelles sont mieux traitees par fragmentation du champ en sous regions avec generation de grilles dans chaque sous region interet des grilles adaptatives couplees a des solutions physiques

alternating direction adaptive grid generation an alternating direction method has been developed to adaptively resolve numerical solutions to physical problems by moving the points of a coordinate grid with the solution or with the salient quantities derived from it a surface grid is defined over the grid on the physical region grid movement is computed on this abstractly defined solution surface with the use of pointwise weights and is then projected back to determine new locations in the physical region the weights cause clustering relative to the uniform conditions of surface arc length and are formed with magnitudes of quantities that are used for point attraction when the salient quantities have been used to form the surface the gradients are implicitly revolved and surface curvature becomes the primary remaining quantity in each coordinate direction the magnitude of normal curvature is used with arbitrary weights a movement cycle generally consists of a sweep through the coordinate curves in a given direction on a curve by curve basis and then in alternating directions to do the same thing until all directions have been covered

a schur complement formulation for solving free boundary stefan problems of phase change a schur complement formulation that utilizes a linear iterative solver is derived to solve a free boundary stefan problem describing steady state phase change via the isotherm newton approach which employs newton s method to simultaneously and efficiently solve for both interface and field equations this formulation is tested alongside more traditional solution strategies that employ direct or iterative linear solvers on the entire jacobian matrix for a two dimensional sample problem that discretizes the field equations using a galerkin finite element method and employs a deforming grid approach to represent the melt solid interface all methods demonstrate quadratic convergence for sufficiently accurate newton solves but the two approaches utilizing linear iterative solvers show better scaling of computational effort with problem size of these two approaches the schur formulation proves to be more robust converging with significantly smaller krylov subspaces than those required to solve the global system of equations further improvement of performance are made through approximations and preconditioning of the schur complement problem hence the new schur formulation shows promise as an affordable robust and scalable method to solve free boundary stefan problems such models are employed to study a wide array of applications including casting welding glass forming planetary mantle and glacier dynamics thermal energy storage food processing cryosurgery metallurgical solidification and crystal growth

conservative rezoning remapping for general quadrilateral meshes a classic problem in lagrangian numerical hydrodynamics is the conservative transfer of quantities from an old distorted mesh to a new mesh the same problem arises whenever the mesh is changed as for example in adaptive mesh techniques this transfer of information is an interpolation process which is frequently called rezoning or remapping the general problem of conservative rezoning from one arbitrary mesh to another may be formulated as follows m sub k integral integral integral sub v sub k rho r dv that is we compute the mass m sub k of each cell of the new mesh by integrating the known density distribution in the old mesh over the cell volume v sub k a direct intregation is generally prohibitive we show however that is is possible to convert this integral to a surface integral by the appropriate use of the divergence theorem thus greatly reducing the complexity of the problem for two dimensional generall quadrilateral meshes the resulting method is exact and particularly simple

finite element simulation of dynamic wetting flows as an interface formation process a mathematically challenging model of dynamic wetting as a process of interface formation has been for the first time fully incorporated into a numerical code based on the finite element method and applied as a test case to the problem of capillary rise the motivation for this work comes from the fact that as discovered experimentally more than a decade ago the key variable in dynamic wetting flows the dynamic contact angle depends not just on the velocity of the three phase contact line but on the entire flow field geometry hence to describe this effect it becomes necessary to use the mathematical model that has this dependence as its integral part a new physical effect termed the hydrodynamic resist to dynamic wetting is discovered where the influence of the capillary s radius on the dynamic contact angle and hence on the global flow is computed the capabilities of the numerical framework are then demonstrated by comparing the results to experiments on the unsteady capillary rise where excellent agreement is obtained practical recommendations on the spatial resolution required by the numerical scheme for a given set of non dimensional similarity parameters are provided and a comparison to asymptotic results available in limiting cases confirms that the code is converging to the correct solution the appendix gives a user friendly step by step guide specifying the entire implementation and allowing the reader to easily reproduce all presented results including the benchmark calculations

symmetric operations in algebraic cobordism abstract in this article we describe certain new cohomological operations in algebraic cobordisms these operations give the natural obstructions for the cobordism class to be represented by the embedding also they permit to work with algebraic cobordisms and chow groups in a more subtle way than the landweber novikov operations related to 2 torsion effects we describe applications to the computation of the algebraic cobordisms of a pfister quadrics and to the problem of rationality of cycles

streamwise computation of three dimensional incompressible potential flows abstract a new method for the computation of three dimensional incompressible potential flows is presented the dependent variables of this method are the streamwise velocity along a set of chosen streamlines and the coordinates of the chosen streamlines in the cross stream plane since the method computes streamline coordinates directly it can be easily used to generate boundary fitted grids for the computation of three dimensional viscous flows sample computations are presented for i flow through a rectangular diffuser with an offset and with a change in the aspect ratio and ii flow through a duct whose cross section changes from a square to a rhombus

capacity bounds and concatenated codes over segmented deletion channels we develop an information theoretic characterization and a practical coding approach for segmented deletion channels compared to channels with independent and identically distributed i i d deletions where each bit is independently deleted with an equal probability the segmentation assumption imposes certain constraints i e in a block of bits of a certain length only a limited number of deletions are allowed to occur this channel model has recently been proposed and motivated by the fact that for practical systems when a deletion error occurs it is more likely that the next one will not appear very soon we first argue that such channels are information stable hence their channel capacity exists then we introduce several upper and lower bounds with two different methods in an attempt to understand the channel capacity behavior the first scheme utilizes certain information provided to the transmitter and or receiver while the second one explores the asymptotic behavior of the bounds when the average bit deletion rate is small in the second part of the paper we consider a practical channel coding approach over a segmented deletion channel specifically we utilize outer ldpc codes concatenated with inner marker codes and develop suitable channel detection algorithms for this scenario different maximum a posteriori map based channel synchronization algorithms operating at the bit and symbol levels are introduced and specific ldpc code designs are explored simulation results clearly indicate the advantages of the proposed approach in particular for the entire range of deletion probabilities less than unity our scheme offers a significantly larger transmission rate compared to the other existing solutions in the literature

schubert calculus for algebraic cobordism we establish a schubert calculus for bott samelson resolutions in the algebraic cobordism ring of a complete flag variety g b extending the results of bressler evens 4 to the algebro geometric setting

coordinate generation with precise controls over mesh properties abstract coordinate generation techniques with precise controls over mesh properties are mathematically developed the controls are precise because mesh properties can be explicitly specified within a local region independent of the mesh elsewhere the local regions can adjoin boundaries where a particular mesh form can greatly simplify a problem or can be used for a smooth juncture between distinct coordinate systems where in effect a branch cut with a prescribed geometry and mesh distribution can be obtained away from boundaries a local region can be given a particular mesh form to model internal objects or to simplify a problem

general curvilinear coordinate systems the basic ideas of the construction and use of numerically generated boundary fitted coordinate systems for the numerical solution of partial differential equations are discussed with such coordinate systems all computation can be done on a fixed square grid in the rectangular transformed region regardless of the shape or movement of the physical boundaries a number of different types of configurations for the transformed region and the basic transformation relations from a cartesian system to a general curvilinear system are given the material of this paper is applicable to all types of coordinate system generation

an isochoric domain deformation method for computing steady free surface flows with conserved volumes abstract the domain deformation method has been applied successfully to steady state free surface flows where the volume of the flow domain is unknown v f de almeida gas liquid counterflow through constricted passages ph d thesis university of minnesota minneapolis mn 1995 p a sackinger p r schunk r r rao a newton raphson pseudo solid domain mapping technique for free and moving boundary problems a finite element implementation j comput phys 125 1996 83 103 l c musson two layer slot coating ph d thesis university of minnesota minneapolis mn 2001 however this method does not handle effectively problems where the volume of the flow domain is known a priori this work extends the original domain deformation method to a new isochoric domain deformation method to account for the volume conservation like in the original domain deformation method the unknown shape of the flow domain is mapped onto a reference domain by using the equations of an elastic pseudo solid the difference with the original method is that this pseudo solid is considered incompressible because of the incompressibility the pseudo pressure of the mapping appears as a lagrange multiplier in the equations and it is determined only up to an arbitrary uniform datum by analyzing the coupled fluid flow mapping problem we show that in the finite element setting such pressure datum can be specified by replacing one continuity equation in the fluid domain

a numerical approach for computing flows by local transformations and domain decomposition using an optimization algorithm this paper presents theoretical information for numerical simulation of two and three dimensional flows based on the concepts of streamlines and local transformation functions associated with domain decomposition in this approach in addition to the pressure the primary unknowns are the local mapping functions between the physical sub domains and transformed domains where the mapped streamlines are parallel straight lines this makes it easy to handle time dependent constitutive equations for complex fluids to solve the governing equations that also involve compatibility equations between sub domains an optimization algorithm is set up in order to compute the unknowns related to the streamlines iteratively applications are given for two dimensional flows between eccentric cylinders using different constitutive equations

boundary fitted coordinate systems for numerical solution of partial differential equations a review a comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given some general mathematical framework and error analysis common to such coordinate systems is also included the general categories of generating systems are those based on conformal mapping orthogonal systems nearly orthogonal systems systems produced as the solution of elliptic and hyperbolic partial differential equations and systems generated algebraically by interpolation among the boundaries also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation dynamically adaptive coordinate systems coupled with the physical solution and time dependent systems that follow moving boundaries are treated references reporting experience using such coordinate systems are reviewed as well as those covering the system development

adaptive gridding for finite difference solutions to heat and mass transfer problems abstract the authors purpose in writing this paper is to review some of their recent work in the calculation of optimal meshes for the solution of parabolic and elliptic partial differential equations pde they first explain our strategies for the adaptive placement of mesh points in addition they make some speculation as to promising avenues for future research in mesh adaptation finally they discuss examples of the application of adaptive gridding to problems of heat and mass transfer they draw these examples from our work in combustion modeling in obtaining numerical solutions of pdes the spatial derivatives are often approximated by discrete representations on a mesh network the accuracy of any numerical solution depends in an important way on the relationship of the location of the mesh points to changes in the dependent variables the authors objective is to investigate finite difference methods in which the mesh networks adapt themselves dynamically to obtain accurate solutions such methods represent an important advance in overcoming a major shortcoming of traditional fixed mesh methods which are often unable to resolve accurately steep fronts or sharp peaks

high level continuity for coordinate generation with precise controls abstract the development of precisely controlled coordinate generation techniques is continued from a first study to include the higher order smoothness which is necessary for three dimensional applications in the first study the controls came from the use of local piecewise linear interpolants in the general multisurface transformation the consequent integration therein resulted in coordinates with continuity up to first derivatives and with the capability to prescribe uniformity either locally or globally for the family of transverse coordinate curves the admission of uniformity placed a constraint upon the general interpolants which was trivially satisfied in the piecewise linear case with smoother piecewise constructions the constraint is used herein along with a requirement for coordinate curves to have the most general possible curvature properties the result is a class of coordinate transformations with continuity extended up to higher derivatives that retains the precise local controls displayed in the first study and that can be used in three or more dimensions

adaptive zoning for singular problems in two dimensions abstract winslow s method for the automatic generation of computation meshes is extended to adaptively vary the zone sizes and orthogonality of grid lines in the resulting mesh through simple analysis and numerical examples the adaptive mesh is shown to give significant increases in accuracy in the computation of singular problems

a new stabilization of adaptive step trapezoid rule based on finite difference interrupts the adaptive step trapezoid rule tr is a generally effective numerical integrator but it is prone to ringing instability and solution stall we introduce a new stabilization algorithm based on finite difference interrupts fdi that reduces ringing and prevents stall unlike previously reported stabilization schemes our algorithm achieves stability and second order accuracy without incurring significant computational cost or spurious diffusion tr with fdi is at least as stable and accurate as existing methods when solving the prototypical scalar problem we demonstrate that it has better stability accuracy and cost when solving the tightly coupled system describing free surface flows of viscoelastic liquids though we demonstrate tr with fdi in the context of a finite element method of lines it is applicable to any tr based algorithm

devising discontinuous galerkin methods for non linear hyperbolic conversation laws abstract in this paper we give a simple introduction to the devising of discontinuous galerkin dg methods for nonlinear hyperbolic conservation laws these methods have recently made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications the dg methods which are extensions of finite volume methods incorporate into a finite element framework the notions of approximate riemann solvers numerical fluxes and slope limiters coined during the remarkable development of the high resolution finite difference and finite volume methods for nonlinear hyperbolic conservation laws we start by stressing the fact that nonlinear hyperbolic conservation laws are usually obtained from well posed problems by neglecting terms modeling nondominant features of the model which nevertheless are essential in crucial small parts of the domain as a consequence the resulting problem becomes ill posed the main difficulty in devising numerical schemes for these conservation laws is thus how to re introduce the neglected physical information in order to approximate the physically relevant solution usually called the entropy solution for the classical case of the entropy solution of the nonlinear hyperbolic scalar conservation law we show how to carry out this process for two prototypical dg methods the first dg method is the so called shock capturing dg method which does not use slope limiters and is implicit the second is the runge kutta dg method which is an explicit method that does not employ a shock capturing term but uses a slope limiter instead we then focus on the runge kutta dg methods and show how to obtain a key stability property which holds independently of the accuracy of the scheme and of the nonlinearity of the conservation law we also show some computational results

directly lower bounding the information capacity for channels with i i d deletions and duplications in this paper we directly lower bound the information capacity for channels with independent identically distributed i i d deletions and duplications our approach differs from previous work in that we focus on the information capacity using ideas from renewal theory rather than focusing on the transmission capacity by analyzing the error probability of some randomly generated code using a combinatorial argument of course the transmission and information capacities are equal but our change of perspective allows for a much simpler analysis that gives more general theoretical results we then apply these results to the binary deletion channel to improve existing lower bounds on its capacity

reliable communication over channels with insertions deletions and substitutions a new block code is introduced which is capable of correcting multiple insertion deletion and substitution errors the code consists of nonlinear inner codes which we call watermark codes concatenated with low density parity check codes over nonbinary fields the inner code allows probabilistic resynchronization and provides soft outputs for the outer decoder which then completes decoding we present codes of rate 0 7 and transmitted length 5000 bits that can correct 30 insertion deletion errors per block we also present codes of rate 3 14 and length 4600 bits that can correct 450 insertion deletion errors per block

simple algebraic technique for nearly orthogonal grid generation rid generation is a very important aspect of solving computational fluid dynamics cfd problems where a set of partial differential equations has to be solved in a given domain it is desirable for the grid to have good orthogonality properties and the grid generator should be able to produce an arbitrary amount of clustering near the body surface when necessary generation of body fitted coordinates meeting these requirements using algebraic techniques are described by eiseman1 and smith 2 it is well known that the most efficient way of dividing the domain for external flow problems is by generating an o type grid for a twodimensional case or an o o topology grid for a three dimensional case since they give the maximum resolution near the body surface with the minimum number of grid points a simple algebraic technique has been developed for generating an o type grid or an o o topology grid for a geometry with sharp edges having a high grid density near the body surface while maintaining orthogonality the present method generates the grid by distributing spacings in the outward normal direction from a closed contour as a function of the rate of change of arc length in that direction this procedure when applied to subsequently generated contours evolves a nearly orthogonal grid with a circular outer boundary a similar procedure applied to a closed three dimensional surface produces a spherical outer boundary thereby generating an o o topology grid

composite three dimensional grids generated by elliptic systems a technique is presented for constructing a boundary conforming grid throughout a general threedimensional flow region as a composite of subregion grids each subregion grid is generated numerically by solving a nonlinear system of elliptic equations the boundary values represent nodal points in a quasi twodimensional grid that covers the curved surface bounding the subregion and are generated numerically by a modified elliptic system a primary feature of the technique is that the composite three dimensional grid remains both continuous and smooth across the surface of juncture between any two adjoining subregions sample results are given for a wing body combination

improved lower bounds for the capacity of i i d deletion and duplication channels this paper considers the capacity of binary deletion channels where bits are deleted independently with probability d it improves significantly upon the best previous framework used to obtain provable lower bounds on this capacity by utilizing a stronger definition of a typical output from the channel the new results give the best known provable bounds on the capacity for all values of d moreover the techniques presented here extend to yield lower bounds for channels with certain types of random insertions namely duplications or combinations of duplications and deletions to demonstrate these techniques in this context two binary channels are analyzed a channel where each transmitted bit is copied with probability nu and a channel where each transmitted bit is copied a geometrically distributed number of times

the schubert calculus braid relations and generalized cohomology let x be the flag variety of a compact lie group and let h be a complex oriented generalized cohomology theory we introduce operators on h x which generalize operators introduced by bernstein gel fand and gel fand for rational cohomology and by demazure for k theory using the becker gottlieb transfer we give a formula for these operators which enables us to prove that they satisfy braid relations only for the two classical cases thereby giving a topological interpretation of a theorem proved by the authors and extended by gutkin one of the central issues in lie theory is the geometry of the flag variety associated to a compact lie group g an important problem concerning the flag variety is the schubert calculus which studies the ring structure of the cohomology of the flag variety work initiated by borel bott and kostant which culminated in a paper by bernstein gel fand and gel fand bgg gave a complete solution to the problem demazure studied the same problem for k theory moreover these techniques have been generalized to the kac moody situation by kac peterson kostant kumar and others this work has focussed on algebro geometric properties of the flag variety here on the other hand we study the flag variety from the point of view of algebraic topology as a consequence not only do we recover the classical results described above but we extend these results to a certain class of cohomology theories those which are complex oriented examples of complex oriented theories include ordinary cohomology k theory complex cobordism and elliptic cohomology since the context we have chosen in very general the proofs are universal and are often simpler than the classical arguments in the work of bgg a crucial role is played by operators ai associated to each simple reflection si of the weyl group of g defined by demazure in k theory these operators ai satisfy the braid relations which are the relations between pairs of simple reflections in this paper we generalize the a to give operators d acting on h g t for any complex oriented theory h we prove that braid relations are satisfied only for cohomology theories with the formal group law of rational cohomology or of k theory theorem received by the editors june 21 1988 1980 mathematics subject classification 1985 revision primary 55n20 57t15 the second author was supported by an nsf graduate fellowship 3 1990 american mathematical society 0002 9947 90 1 00 25 perpage

discretization of three dimensional free surface flows and moving boundary problems via elliptic grid methods based on variational principles abstract a new boundary fitted technique to describe free surface and moving boundary problems is presented we have extended the 2d elliptic grid generator developed by dimakopoulos and tsamopoulos 2003 19 and further advanced by chatzidai et al 2009 18 to 3d geometries the set of equations arises from the fulfillment of the variational principles established by brackbill and saltzman 1982 21 and refined by christodoulou and scriven 1992 22 these account for both smoothness and orthogonality of the grid lines of tessellated physical domains the elliptic grid equations are accompanied by new boundary constraints and conditions which are based either on the equidistribution of the nodes on boundary surfaces or on the existing 2d quasi elliptic grid methodologies the capabilities of the proposed algorithm are first demonstrated in tests with analytically described complex surfaces the sequence in which these tests are presented is chosen to help the reader build up experience on the best choice of the elliptic grid parameters subsequently the mesh equations are coupled with the navier stokes equations in order to reveal the full potential of the proposed methodology in free surface flows more specifically the problem of gas assisted injection in ducts of circular and square cross sections is examined where the fluid domain experiences extreme deformations finally the flow mesh solver is used to calculate the equilibrium shapes of static menisci in capillary tubes

transfinite mappings and their application to grid generation the two essential ingredients of any boundary value problem are the field equations which describe the physics of the problem and a set of relations which specify the geometry of the problem domain mesh generators or grid generators are preprocessors whicd decompose the problem domain into a large number of interconnected finite elements or curvilinear finite difference stencils a number of such techiques have been developed over the past decade to alleviate the frustation and reduce the time involved in the tedious manual subdividing of a complex shaped region or 3 d structure into finite elements our purpose here is to describe how the techniques of bivariate and trivariate blending function interpolation which were originally developed for and applied to geometric problems of computer aided design of sculptured surface and 3 d solids can be adapted and applied to the geometric problems of grid generation in contrast to other techniques which require the numerical solution of complex partial differential equations and hence a great deal of computing the transfinite methods proposed herein are computationally inexpensive

interactive method of variational grid generation abstract in the paper the elliptic variational grid generation technique based on methods of optimal control for distributed systems is presented the interactive nature of the method consists in adaptive changing of the golas of correction steps in the process of grid generation the corrections concern orthogonality and uniformity of the mesh

conformal grid generation this paper treats conformal mapping as it relates to the generation of grids to be used for flow simulation classical and contemporary mapping methods are discussed and compared in some detail numerous suggestions are included to help the reader avoid common pitfalls and the mapping methods believed most promising are identified

assessing the quality of curvilinear coordinate meshes by decomposing the jacobian matrix an algebraic decomposition of the jacobian matrix j x i email protected j which relates physical and computational variables is presented this invertible decomposition parameterizes the mesh by the physically intuitive qualities of cell orientation cell orthogonality cell volume and cell aspect ratio this decompostion can be used to analyze numerically generated curvilinear coordinate meshes and to assess the contribution of the mesh to the truncation error for any specific differential operator and algorithm this is worked out in detail for laplace s equation in nonconservative and conservative forms an analysis by g h k 1 of the mesh contribution to truncation error for the full potential code tair is given in abbreviated form the variables introduced here and their derivatives are also natural lagrange multipliers for adaptive mesh algorithms based on a variational principle

algebraic grid generation three methods are described for transforming grids in bounded two and three dimensional physical domains into a uniform grid in a rectangular computational domain the methods are based on mathematical interpolation functions and do not require the solution of differential equations or the use of complex variables they are simply referred to as algebraic methods and are called transfinite interpolation the multisurface method and the two boundary technique the primary advantage of the methods is that they provide explicit control of physical grid shape and physical grid spacing secondly they require relatively few computations consequently the application of inter active computer graphics in conjunction with the methods is advocated for rapid generation of grids the basic mathematical structure of each method is described and particular attention is given to surface representation parameter variable generation and control function generation physical boundary topology and grid derivative requirements are presented

three dimensional grid generation using poisson equations a method for constructing a boundary fitted grid system for arbitrary three dimensional 3 d configurations is presented the grid generation procedure is formulated through the poison equations a feature of the scheme is that grid lines in the grid system are smothly interconnected between the boundary co ordinates the control of the grid distributions in the interior of the system has implemented by the forcing functions appearing in the poisson equations and by the boundary coordinates reasonable cell sizes and shapes are obtained even for extreme boundary shapes which normally tend to cause poorly controlled grid distributions

an efficient full potential implicit method based on characteristics for supersonic flows la methode utilise la theorie de la propagation de signal caracteristique pour simuler avec precision la structure de l ecoulement qui inclut des ondes de choc et un ecoulement transversal mixte elliptique hyperbolique

solution of viscous internal flows on curvilinear grids generated by the schwarz christoffel transformation abstract a method is presented for combining an accurate orthogonal curvilinear coordinate generation procedure with a fast accurate and stable forward marching viscous flow solution technique to solve for the flow field in arbitrary axisymmetric ducts in this method the coordinates are generated from the plane potential flow streamlines and potential lines using the schwarz christoffel transformation with a composite finite difference formula which is valid everywhere and which treats the poles exactly by analytic integration since the coordinate streamlines approximate the actual streamlines the equations of motion for viscous compressible flow can be parabolized so as to solve for both the boundary layers and core flow in a single streamwise pass the versatility of the method is demonstrated by two examples of viscous compressible swirling flow through complex radial gas turbine passages author

a quasi elliptic transformation for moving boundary problems with large anisotropic deformations we have developed a quasi elliptic set of equations for generating a discretization mesh that optimally conforms to an entire domain that undergoes large deformations in primarily one direction we have applied this method to the axisymmetric problem of the transient displacement of a viscous liquid by a high pressure gas the liquid initially fills completely a tube the diameter of which may be constant or change smoothly suddenly or periodically along its finite length key ingredients for the success of the proposed transformation are limiting the orthogonality requirements on the mesh and employing an improved node distribution function along the deforming boundary the retained orthogonal term along with the penalty method for the imposition of the boundary conditions overcome the inherent restrictions of a conformal transformation producing meshes of high quality this term also eliminates the discontinuous slopes of the coordinate lines that are normal to the free surface these usually arise due to the harmonic transformation around highly deforming surfaces the mathematical anisotropy in the mesh generating equations directly corresponds to the physical one when the initially straight and normal to the axis of symmetry air fluid interface at the tube entrance develops mostly along the axial direction generating a long open bubble moreover the generalized node distribution imposes an optimal discretization of the bubble surface itself combining this scheme with the mixed finite element method produces a powerful tool with extended robustness and accuracy in order to reduce the computational cost the resulting set of equations is solved with a non linear gauss seidel technique and a variable time step specific applications of the proposed scheme are presented

finite element method for incompressible viscous flows with adaptive hybrid grids a new adaptive finite element numerical method has been developed for the unsteady navier stokes equations of incompressible flow in two dimensions the momentum equations combined with a pressure correction equation are solved employing a nonstaggered grid the solution is advanced in time with an explicit implicit marching scheme an adaptive algorithm has been implemented which refines the grid locally to resolve detected flow features a combination of quadrilateral as well as triangular cells provides a stable and accurate numerical treatment of grid interfaces that are located within regions of high gradients applications of the developed adaptive algorithm include both steady and unsteady flows with low and high reynolds numbers comparisons with analytical as well as experimental data evaluate accuracy and robustness of the method i introduction i ncompressible flows are frequently encountered in engineering applications during the past two decades a significant number of numerical algorithms have been developed for solution of the incompressible navier stokes equations 1 liie lack of pressure term in the continuity equation makes solution of the momentum equations with the divergence free constraint more difficult in the case of incompressible flows the conservation of mass acts as a constraint condition that the velocity field must satisfy whereas in compressible flows the conservation of mass is given through a partial differential equation for the temporal variation of density the infinite speed of sound in the incompressible case requires an implicit treatment of the pressure furthermore spatial discretization for pressure and velocity may produce oscillatory solutions one approach followed is to formulate the equations in terms of a stream function and a vorticity extension of this method to three dimensions is not possible different formulations have been used in three dimensions such as the vorticity velocity approach another approach is to use the compressible flow equations and solve them for low mach numbers the required time step for such computations is very small because the speed of sound approaches infinity at the incompressible limit a method that uses compressible like governing equations is the artificial compressibility approach 2 a time derivative of the pressure is added to the continuity equation and the incompressible flowfield is treated as compressible during the transient stage time accuracy of the simulation is usually not preserved another class of algorithms uses a special poisson equation for the pressure field 5 8 the usual computational procedure is to assume an initial pressure field and then an iterative process is defined until the continuity equation is satisfied a major issue of the corresponding pressure and velocity spatial discretization is oscillations in the pressure field to reject these modes staggered grids have been employed by several of these algorithms 9 10 on the other hand employment of nonstaggered grids11 13 requires dissipation in the algorithms stability of both approaches with high reynolds number flows is an important issue a review of numerical methods for incompressible flows as well as references

novel bounds on the capacity of the binary deletion channel we present novel bounds on the capacity of the independent and identically distributed binary deletion channel four upper bounds are obtained by providing the transmitter and the receiver with genie aided information on suitably defined random processes since some of the proposed bounds involve infinite series we also introduce provable inequalities that lead to more manageable results for most values of the deletion probability these bounds improve the existing ones and significantly narrow the gap with the available lower bounds exploiting the same auxiliary processes we also derive as a by product two simple lower bounds on the channel capacity which for low values of the deletion probability are almost as good as the best existing lower bounds

tracking birth of vortex in flows in order to avoid undesired effects from vortices in many industrial processes it is important to know the set of operating parameters at which the flow does not have recirculation the map of these conditions in the parameter space is called vortex free operating window here we propose an efficient way to construct such window automatically without expensively checking every possible flow states the proposed technique is based on tracking a path in the parameter space at which the local kinematic condition at a stagnation point for vortex birth is satisfied this multiparameter continuation is performed by solving an augmented navier stokes system in the augmented system the birth condition and the governing equations was represented in galerkin s finite element context we used the proposed method in two important coating flows with free surfaces single layer slot coating and forward roll coating

application of a variational method for generating adaptive grids the application of variational methods for generating adaptive grids is not as straightforward as one is led to believe proper scaling suitable weight functions and appropriate clustering on boundaries must be employed to obtain a satisfactory grid this work which is based on the framework developed by brackbill and saltzman provides simple methods for determining scaling and investigates possible options for selecting the weight function and clustering points on the boundaries the concepts developed here are applied to two two dimensional problems a model problem based on burger s equation which contains two length scales and transonic flow past airfoils using the euler equations

the use of solution adaptive grids in solving partial differential equations the grid point distribution used in solving a partial differential equation using a numerical method has a substantial influence on the quality of the solution an adaptive grid which adjusts as the solution changes provides the best results when the number of grid points available for use during the calculation is fixed basic concepts used in generating and applying adaptive grids are reviewed in this paper and examples illustrating applications of these concepts are presented

generation of curvilinear coordinates on multiply connected regions with boundary singularities a new algorithm to generate smooth two dimensional boundary conforming coordinates with grid lines control on multiply connected regions including boundary singularities is devised the technique fits into the category of elliptic grid generators since it is based on the numerical solution of poisson equations the physical domain d is transformed into a topologically equivalent connected rectangular domain d by defining a branch cut inside d control of the grid line spacing over the multiply connected regions is established by appropriately distributing nodal points on the branch cut and on other boundary curves simple and computationally convenient expressions for the control functions present in the poisson system are obtained from this initial distribution of points thus a natural link between clustering properties and the control functions is created fixing the nodal points on the branch cut causes the convergence of the numerical method about the singular boundary points an iterative smoothing process relocating the branch cut is described as a result smooth grids are obtained grid quality analysis shows that coordinate line orthogonality in the new meshes is superior than in similar grids obtained from a well known commercial software the algorithm is successfully tested over a variety of multiply connected domains the computational advantage of this novel grids is revealed by using them to numerically model the vibrations of complexly shaped annular membranes

flows in forward deformable roll coating gaps roll coating is distinguished by the use of one or more gaps between rotating cylinders to meter a continuous liquid layer and to apply it to a continuous flexible substrate of the two rolls that make a forward roll coating gap one is often covered by a layer of deformable elastomer thin films can be obtained without the risk of clashing two hard rolls liquid carried into the converging side of the gap can develop high enough pressure to deform the resilient cover which changes the gap geometry and thus alters the velocity and pressure fields the complete understanding of the flow in this situation is vital to the optimization of this widely used coating method however this elastohydrodynamic action is not well understood the situation is similar to what is called the soft elastohydrodynamic lubrication regime soft ehl however the range of minimum distance between the rotating rolls roll speed and therefore flow rate through the gap in the roll coating process is one to three orders of magnitude larger than the typical values reported in previous work on soft ehl earlier works on deformable roll coating analyzed the action with both the lubrication approximation and the full navier stokes solution and different one dimensional models of roll cover deformation in order to test the accuracy of the past approaches and to evaluate the relationship between the empirical constant used in the one dimensional model to the relevant physical parameters a complete two dimensional formulation has to be employed for both the liquid flow and the solid deformation in this work the flow between a rigid and a deformable rotating roll was examined by solving the complete navier stokes system coupled with a non linear plane strain model of the roll cover deformation the approximate and computationally cheaper approach is evaluated in which the compliant wall is represented by an array of radially oriented hookean springs the equation system was solved by the galerkin finite element method the resulting set of non linear algebraic equations of the fully coupled problem was solved by newton s method with initialization by pseudo arc length continuation as parameters were varied results show how roll deformation affects the total flow rate and forces on the rolls and illustrate how a deformable roll can be used to obtain thin coated layers with much less sensitivity to roll runout than those obtained with rigid rolls

segre classes and kempf laksov formula in algebraic cobordism in this paper we extend to algebraic cobordism the classical damon kempf laksov formula which expresses the chow ring schubert classes of grassmann bundles as schur determinants in chern classes the basic building block of our closed formula which is written as a sum of determinants is represented by a generalisation of segre classes that we introduce and describe

a priori mesh quality estimation via direct relation between truncation error and mesh distortion the purpose of the present work is the derivation and evaluation of a priori mesh quality indicators for structured unstructured as well as hybrid grids emphasis is placed on deriving direct relations between the indicators and mesh distortion the work is based on use of the finite volume discretization for evaluation of first order spatial derivatives the analytic form of the truncation error is derived and applied to elementary types of mesh distortion including typical hybrid grid interfaces the corresponding analytic expressions provide direct relations between computational accuracy and the degree of stretching skewness shearing and non alignment of the mesh

applications and generalizations of variational methods for generating adaptive meshes abstract generating computation meshes for irregular regions have been of interest to a lot of people in many areas of research for a long time one technique that has met with sucess over the long run has been to generate methods using an elliptic equation or a system of elliptic equations the technique in its simplest form uses a system of laplace equations which are solved by direct or iterative methods as people gained more experience with this method source terms were added to the laplace equations to gain additional control of the mesh in variable coefficients of the derivatives were added for further flexibility in this paper the authors work with a method that systematically generates a set of elliptic equations without having to explicitly perturb a set of laplace equations with source terms and variable coefficients this technique uses the variational methods often associated with elliptic equations following this introduction they briefly discuss the variational formulation in two dimensional cartesian geometry then the formulation will be generalized to three dimensions next several three dimensional test problems will be shown after displaying these three dimensional test results the author wil the exhibit an application of the mesh generation technique in two dimensions this application involves generating an adaptive mesh for a supersonic flow past a step in a wind tunnel author

a direct comparison between volume and surface tracking methods with a boundary fitted coordinate transformation and third order upwinding a volume tracking vt and a front tracking ft algorithm are implemented and compared for locating the interface between two immiscible incompressible newtonian fluids in a tube with a periodically varying circular cross section initially the fluids are stationary and stratified in an axisymmetric arrangement so that one is around the axis of the tube core fluid and the other one surrounds it annular fluid a constant pressure gradient sets them in motion with both vt and ft a boundary fitted coordinate transformation is applied and appropriate modifications are made to adopt either method in this geometry the surface tension force is approximated using the continuous surface force method all terms appearing in the continuity and momentum equations are approximated using centered finite differences in space and one sided forward finite differences in time in each time step the incompressibility condition is enforced by a transformed poisson equation which is linear in pressure this equation is solved by either direct lu decomposition or a multigrid iterative solver when the two fluids have the same density the former method is about 3 5 times faster but when they do not the multigrid solver is as much as 10 times faster than the lu decomposition when the interface does not break and the reynolds number remains small the accuracy and rates of convergence of vt and ft are comparable the well known failure of centered finite differences arises as the reynolds number increases and leads to non physical oscillations in the interface and failure of both methods to converge with mesh refinement these problems are resolved and computations with reynolds as large as 500 converged by approximating the convective terms in the momentum equations by third order upwind differences using lagrangian polynomials when the volume of the core fluid or the weber number decrease increasing the importance of interfacial tension and leading to breakup of the interface forming a drop of core fluid the ft method converges faster with mesh refinement than the vt method and upwinding may be required finally examining the generation of spurious currents around a stationary bubble in the tube for ohnesorge numbers between 0 1 and 10 it is found that the maximum velocity remains approximately the same in spite mesh refinements when vt is applied whereas it is of the same order of magnitude for the coarsest mesh and monotonically decreases with mesh refinement when ft is applied

conformal mappings for internal viscous flow problems abstract isolated occlusions in a straight channel or pipe can be described analytically in a fashion that allows efficient accurate computation of nonlinear flow fields through conformal transformations

on lower bounds for the capacity of deletion channels this correspondence considers binary deletion channels where bits are deleted independently with probability d it improves upon the framework used to analyze the capacity of binary deletion channels established by diggavi and grossglauser improving on their lower bounds diggavi and grossglauser considered codebooks with codewords generated by a first order markov chain they only consider typical outputs where an output is typical if an n bit input gives an n 1 d 1 epsi bit output the improvements in this correspondence arise from two considerations first a stronger notion of a typical output from the channel is used which yields better bounds even for the codebooks studied by diggavi and grossglauser second codewords generated by more general processes than first order markov chains are considered

upwind schemes and boundary conditions with applications to euler equations in general geometries abstract a unified treatment of several upwind shock capturing algorithms is presented each algorithm has a riemann initial value problem as its basis the treatment of boundaries involves solving the associated riemann initial boundary value problem the first author s algorithm applied to multidimensional euler equations in general geometries is then presented its worth is verified by various calculations which include mach 8 supersonic flow past a circular cylinder

classification of the deletion correcting capabilities of reed solomon codes of dimension 2 over prime fields deletion correction codes have been used for transmission synchronization and more recently tracing pirated media a generalized reed solomon grs code denoted by grsk l q alpha v is a code of length l over gf q with qk codewords these codes have an efficient decoding algorithm and have been widely used for error correction and detection it was recently demonstrated that grs codes are also capable of correcting deletions we consider a subclass of grs codes with dimension k 2 and q prime and study them with respect to deletion correcting capability we give transformations that either preserve the code or maintain its deletion correction capability we use this to define equivalent codes and then use exhaustive and selective computer searches to find inequivalent codes with the highest deletion correcting capabilities we show that for the class under consideration up to l 3 deletions may be corrected we also show that for lles36 there exist codes with q2 codewords such that receiving only 3 out of t transmitted symbols of a codeword is enough to recover the codeword thus meeting the bound specified above we also specify some nice codes which are associated with the smallest field possible for codes of a given length and deletion correcting capability some of the identified codes are unique with respect to the defined equivalence

a domain decomposition method for the oseen viscoelastic flow equations we study a non overlapping domain decomposition method for the oseen viscoelastic flow problem the data on the interface are transported through newmann and dirichlet boundary conditions for the momentum and constitutive equations respectively the discrete variational formulations of subproblems are presented and investigated for the existence of solutions we show convergence of the domain decomposition solution to a solution of the one domain problem convergence of an iterative algorithm and some numerical results are also presented

comparison of some finite element methods for solving the diffusion convection reaction equation abstract in this paper we describe several finite element methods for solving the diffusion convection reaction equation none of them is new although the presentation is non standard in an effort to emphasize the similarities and differences between them in particular it is shown that the classical supg method is very similar to an explicit version of the characteristic galerkin method whereas the taylor galerkin method has a stabilization effect similar to a sub grid scale model which is in turn related to the introduction of bubble functions

mathematical aspects of variational grid generation ii abstract variational grid generation techniques are now used to produce grids suitable for solving numerical partial differential equations in irregular geometries in this paper the existence and uniqueness of solutions of the volume and smoothness problems that are used in variational grid generation are studied an analysis of the euler lagrange el equations near the identity shows that the volume problem is difficult these variational problems use a reference grid to specify the properties of the desired grid replication of reference grid properties is analyzed examples are given that show the effectiveness of the reference grid concept

schubert calculus in complex cobordism we study the structure of the complex cobordism ring of the flag variety of a compact connected lie group an explicit procedure for determining products of basis elements is obtained generalizing the work of bernstein gel fand gel fand on ordinary cohomology and of kostant kumar on k theory bott samelson resolutions are used to replace the classical basis of schubert cells

capacity bounds for sticky channels the capacity of sticky channels a subclass of insertion channels where each symbol may be duplicated multiple times is considered the primary result is to provide nearly tight numerical upper and lower bounds for the independent and identically distributed i i d duplication channel

degeneracy loci classes in k theory determinantal and pfaffian formula abstract we prove a determinantal formula that describes the k theoretic degeneracy loci classes for grassmann bundles we further prove pfaffian formulas for symplectic and odd orthogonal grassmann bundles the former generalizes damon kempf laksov s determinantal formula and the latter generalize pragacz kazarian s formulas for the chow ring

k theoretic chern class formulas for vexillary degeneracy loci abstract using raising operators and geometric arguments we establish formulas for the k theory classes of degeneracy loci in classical types we also find new determinantal and pfaffian expressions for classical cases considered by giambelli the loci where a generic matrix drops rank and where a generic symmetric or skew symmetric matrix drops rank in an appendix we construct a k theoretic euler class for even rank vector bundles with quadratic form refining the chow theoretic class introduced by edidin and graham we also establish a relation between top chern classes of maximal isotropic subbundles which is used in proving the type d degeneracy locus formulas

discretization of free surface flows and other moving boundary problems a system of elliptic partial differential equations and boundary conditions has been developed for generating boundary fitted element discretizations of two dimensional free and moving boundary problems terms in the differential equations are scaled for dimensional homogeneity and adjustable weighting of orthogonality smoothness and concentration of the coordinate mesh they govern grid points become finite element nodes mapped isoparametrically or subparametrically from a simple or patched computational domain concentration terms contain control functions and parameters that influence node spacing along each coordinate independently overall control is by patchwise parameters and functions successful selection of these to follow deforming flow regions is straightforward and is illustrated by analysis of steady and transient slide coating flows

elliptic grid generation various types of generating systems for boundary conforming coordinate systems based on the numerical solution of systems of elliptic partial differential equations are discussed particular emphasis is given to the determination of functions in these equations which control the distribution of the curvilinear coordinate lines in the field

marangoni benard convection with a deformable free surface computations of marangoni convection are usually performed in two or three dimensional domains with rigid boundaries in two dimensions allowing the free surface to deform can result in a solution set with a qualitatively different bifurcation structure we describe a finite element technique for calculating bifurcations that arise due to thermal gradients in a two dimensional domain with a deformable free surface the fluid is assumed to be newtonian to conform to the boussinesq approximation and to have a surface tension that varies linearly with temperature an orthogonal mapping from the physical domain to a reference domain is employed which is determined as the solution to a pair of elliptic partial differential equations the mapping equations and the equilibrium equations for the velocity pressure and temperature fields and their appropriate nonlinear boundary conditions are discretized using the finite element method and solved simultaneously by newton iteration contact angles other than 90 degrees are shown to disconnect the transcritical bifurcations to flows with an even number of cells in the expected manner the loss of stability to single cell flows is associated with the breaking of a reflectional symmetry about the middle of the domain and therefore occurs at a pitchfork bifurcation point for contact angles both equal to and less than 90 degrees

grid evolution in time asymptotic problems the selection of the proper coordinate system in solving any fluid flow or heat transfer problem is a very important consideration a new technique of moving mesh points in physical space is introduced so as to reduce the error in a computed asymptotic solution relative to that obtained using a fixed mesh the technique has been used to solve the simple viscous burgers equation in one and two dimensions substantial error reductions are demonstrated the treatment of boundary points and the effect of using different error criteria in generating grids are discussed

a newton raphson pseudo solid domain mapping technique for free and moving boundary problems an implicit pseudo solid domain mapping technique is described that facilitates finite element analysis of free and moving boundary problems the technique is based on an implicit full newton strategy free of restrictions on mesh structure this leads to many advantages over existing domain mapping techniques the fully coupled approach using newton s method is particularly effective for problems with strong coupling between the internal bulk physics and the governing physics at unknown free boundary locations it is also useful when the distinguishing conditions which constrain the free boundary shape provide only an implicit dependence on the boundary location unstructured meshes allow for efficient resolution of internal and boundary layers and other regions of strong local variations in the solution and they also reduce the amount of user interaction required to define a problem since the meshes may be generated automatically the technique is readily applied to steady or transient problems in complex geometries of two and three dimensions examples are shown that include free and moving boundary problems from solidification and capillary hydrodynamics

coordinate system control adaptive meshes the discussion of the formulation and properties of the adaptive mesh algorithm is as complete as space permits as should be clear from the discussion adaptive gridding is most useful for singular perturbation problems where localized regions with large gradients develop spontaneously often choosing the correct weight function is not trivial and sometimes it is appropriate to cause the mesh to respond to structure in several dependent variables simultaneously

the numerical differentiation of discrete functions using polynomial interpolation methods a fortran subroutine package called dermod has been written for calculating numerical approximations for the spatial derivatives of a function defined only on a discrete set of data points the routines are designed to complement many existing codes for solving ordinary and partial differential equations and for the interpolation of tabular data we describe some new numerical differentiation algorithms discuss a mapping procedure for nonuniform grids and explain the program methodology used in designing the software

automatic algebraic coordinate generation a computer software system has been developed to automatically generate two dimensional coordinates from algebraic transformations for topologically complex regions a smooth assembly of the transformations can be used to automatically produce a composite mesh where a general gridded format is retained the algebraic mesh generation system consists of a collection of operator subroutines which are applied to an established data structure and which automatically perform the necessary parts of mesh construction from a sequence of multisurface transformations the system operators are discussed taking into account the data base the order of application direct surface generators geometric surface operators surface generators from existing surfaces transverse operators mesh operators assembly operators and data visualization operators attention is given to applications related to airfoils

generation of orthogonal and nearly orthogonal coordinates with gridcontrol near boundaries a numerical procedure is presented for the generation of boundary fitted curvilinear coordinates with controllable mesh spacing and orthogonality the technique is based on a straightforward two step procedure involving the solution of poisson s equation the method is capable of generating orthogonal grids with partial control of the mesh spacing or nearly orthogonal grids with strict control of the mesh spacing the inhomogeneous terms in the poisson equations are automatically adjusted during the grid generation the technique is applicable to two dimensional simply connected regions typical of airfoils cascades diffusers and inlets

on the elliptic mesh generation in domains containing multiple inclusions and undergoing large deformations we present an improved method to generate a sequence of structured meshes even when the physical domain contains deforming inclusions this method belongs to the class of arbitrary lagrangian eulerian ale methods for solving moving boundary problems its tools are either a separate mappings of the domain boundaries and enforcing the node distribution on lines emanating from singular points or b domain decomposition and separate mappings of each subdomain using suitable coordinate systems the latter is shown to be more versatile and general in both cases a set of elliptic equations is used to generate the grid extending in this way the method advanced by dimakopoulos and tsamopoulos y dimakopoulos j a tsamopoulos a quasi elliptic transformation for moving boundary problems with large anisotropic deformations j comput phys 192 2003 494 522 we shall present examples where this earlier method and all other mesh generating methods which are based on a conformal mapping or solving a quasi elliptic set of pdes fail to produce an acceptable mesh and accurate solutions in such geometries furthermore in contrast to other methods appropriate boundary conditions and constraints such as orthogonality of specific mesh lines and prespecified node distributions on them can be easily implemented along a specific part of the domain or its boundary hence no attractive terms at specific corners or singular points are needed to increase the mesh resolution around the moving interfaces while keeping low the memory requirements and the computational time a local mesh refinement technique has been incorporated as well the method is demonstrated in two challenging examples where no remeshing is required in spite of the large domain deformations in the first one the transient growth of two bubbles embedded in a viscoelastic filament undergoing stretching in the axial direction is examined while in the second one the linear and non linear dynamics of two bubbles in a viscous medium are determined in an acoustic field the large elasticity of the filament in the first case or the large inertia in the second case coupled with the externally induced large deformations of the liquid domain requires the accurate calculation which is achieved by the method we propose herein the governing equations are solved using the finite element galerkin method with appropriate modifications to solve the hyperbolic constitutive equation of a viscoelastic fluid these are coupled with an implicit euler method for time integration or with arnoldi s algorithm for normal mode analysis

the moving finite element method applications to general partial differential equations with multiple large gradients abstract the moving finite element mfe method has been reduced to practice in the automatic solution program dyla for general systems of transient partial differential equations pdes in 1 d several test examples are presented which illustrate the unique node movement and systematic control features which are intrinsic in the mfe method computational dilemmas of numerical diffusion gibbs overshooting and undershooting zone tangling and grid remap or re connection aliasing which occur frequently in conventional pde methods are essentially eliminated in the mfe method arbitrarily large gradients or shocks can be solved with extremely high resolution and accuracy for non coincident or even counterdirected propagating wavefronts boundary layers of arbitrarily small dimensions are solved with high accuracy simultaneously with the large scale structures in reactive and non reactive fluid calculations the mfe method requires a small fraction of the grid nodes which are used in conventional pde solution methods because the nodes migrate continuously and systematically to those positions where they are most needed in order to yield accurate pde solutions on entire problem domains courant friedrichs lewy time step limits are exceeded by wide margins by factors of two to several thousand finally the extension of the mfe method to 2 d is briefly discussed

a front tracking method for viscous incompressible multi fluid flows abstract a method to simulate unsteady multi fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described the flow field is discretized by a conservative finite difference approximation on a stationary grid and the interface is explicitly represented by a separate unstructured grid that moves through the stationary grid since the interface deforms continuously it is necessary to restructure its grid as the calculations proceed in addition to keeping the density and viscosity stratification sharp the tracked interface provides a natural way to include surface tension effects both two and three dimensional full numerical simulations of bubble motion are presented

on one dimensional stretching functions for finite difference calculations abstract the class of one dimensional stretching functions used in finite difference calculations is studied for solutions containing a highly localized region of rapid variation simple criteria for a stretching function are derived using a truncation error analysis these criteria are used to investigate two types of stretching functions one is an interior stretching function for which the location and slope of an interior clustering region are specified the simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine it was first employed by thomas et al aiaa j 10 1972 887 the other type of function is a two sided stretching function for which the arbitrary slopes at the two ends of the one dimensional interval are specified the simplest such general function is found to be one based on the inverse tangent the special case where the slopes were both equal and greater than one was first employed by roberts the general two sided function has many applications in the construction of finite difference grids examples of such applications are found in the listed references

design of low density parity check codes for modulation and detection a coding and modulation technique is studied where the coded bits of an irregular low density parity check ldpc code are passed directly to a modulator at the receiver the variable nodes of the ldpc decoder graph are connected to detector nodes and iterative decoding is accomplished by viewing the variable and detector nodes as one decoder the code is optimized by performing a curve fitting on extrinsic information transfer charts design examples are given for additive white gaussian noise channels as well as multiple input multiple output mimo fading channels where the receiver but not the transmitter knows the channel for the mimo channels the technique operates within 1 25 db of capacity for various antenna configurations and thereby outperforms a scheme employing a parallel concatenated turbo code by wide margins when there are more transmit than receive antennas

a general mapping procedure for variable area duct acoustics a general mapping procedure is described and applied to the study of noise propagation in variable area ducts the mapping provides a boundary fitted co ordinate system which is ideal for the finite difference solution of acoustic fields with irregular boundaries without the burden of large matrices required by finite element methods the procedure is first described in general and then applied to a particular two dimensional geometry under current experimental investigation this method should be ideally suited to the study of high frequency noise propagation in variable area ducts and in cases where the far field is included in the calculation procedure moreover the current approach can be directly extended to three dimensions resulting in numerical calculation over a rectangular parallelepiped in the transformed plane

entropy computations via analytic depoissonization we investigate the basic question of information theory namely evaluation of shannon entropy and a more general renyi 1961 entropy for some discrete distributions e g binomial negative binomial etc we aim at establishing analytic methods i e those in which complex analysis plays a pivotal role for such computations which often yield estimates of unparalleled precision the main analytic tool used here is that of analytic poissonization and depoissonization we illustrate our approach on the entropy evaluation of the binomial distribution that is we prove that for binomial n p distribution shannon s h sub n becomes h sub n spl ap 1 2 ln n 1 2 ln spl radic 2 spl pi p 1 p spl sigma sub k spl ges 1 a sub k n sup k where a sub k are explicitly computable constants moreover we argue that analytic methods e g complex asymptotics such as rice s method and singularity analysis mellin transforms poissonization and depoissonization can offer new tools for information theory especially for studying second order asymptotics e g redundancy in fact there has been a resurgence of interest and a few successful applications of analytic methods to a variety of problems of information theory therefore we propose to name such investigations as analytic information theory

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100