numerical simulations for radiation hydrodynamics a finite difference scheme is proposed for two dimensional radiation hydrodynamical equations in the transport limit the scheme is of godunov type in which the set of time averaged flux needed in the scheme is calculated through riemann problems solved in the scheme flow signals are explicitly treated while radiation signals are implicitly treated flow fields and radiation fields are updated simultaneously an iterative approach is proposed to solve the set of nonlinear algebraic equations arising from the implicitness of the scheme the sweeping method used in the scheme significantly reduces the number of iterations or computer cpu time needed a new approach to further accelerate the convergence is proposed which further reduces the number of iterations needed by more than one order no matter how many cells radiation signals propagate in one time step only an extremely small number of iterations are needed in the scheme and each iteration costs only about 0 8 percent of computer cpu time which is needed for one time step of a second order accurate and fully explicit scheme two dimensional problems are treated through a dimensionally split technique therefore iterations for solving the set of algebraic equations are carried out only in each one dimensional sweep through numerical examples it is shown that the scheme keeps the principle advantages of godunov schemes for flow motion in the time scale of flow motion numerical results are the same as those obtained from a second order accurate and fully explicit scheme the acceleration of the convergence proposed in this paper may be directly applied to other hyperbolic systems

topological obstructions to nonnegative curvature we find new obstructions to the existence of complete riemannian metric of nonnegative sectional curvature on manifolds with infinite fundamental groups in particular we construct many examples of vector bundles whose total spaces admit no nonnegatively curved metrics

toward a practical scheme for binary broadcast channels with varying channel quality using dirty paper coding we consider practical schemes for binary dirty paper channels and broadcast channels bcs with two receivers and varying channel quality with the bc application in mind this paper proposes a new design for binary dirty paper coding dpc by exploiting the concept of coset binning the complexity of the system is greatly reduced when compared to the existing works some design challenges of the coset binning approach are identified and addressed the proposed binary dpc system achieves similar performance to the state of the art superposition coding based system while demonstrating significant advantages in terms of complexity and flexibility of system design for binary bcs achieving the capacity generally requires the superposition of a normal channel code and a carefully designed channel code with non uniform bit distribution the non uniform bit distribution is chosen according to the channel conditions therefore to achieve the capacity for binary bcs with varying channel quality it is necessary to use quantization codes of different rates which significantly increases the implementation complexity in this paper we also propose a broadcast scheme that generalizes the concept of binary dpc which we term soft dpc by combining soft dpc with time sharing we achieve a large percentage of the capacity for a wide range of channel quality with little complexity overhead our scheme uses only one fixed pair of codes for users 1 and 2 and a single quantization code which possesses many practical advantages over traditional time sharing and superposition coding solutions and provides strictly better performance

multigrid solution of the euler equations using implicit schemes on utilise une methode multigrille du type factorisation approchee couplee a un schema de direction alternee implicite pour resoudre les equations d euler pour l ecoulement transsonique sur un profil aerodynamique on obtient une convergence tres rapide

on an implicit eno scheme essentially non oscillatory eno schemes which have high order accuracy in regions where solutions are smooth and effectively capture shocks and discontinuities have been developed for numerical solution of hyperbolic equations these methods have traditionally been implemented using explicit euler or explicit runge kutta time marching schemes and consequently suffer from the courant friedrichs lewy cfl time step restriction this restriction is significant for steady state problems and for transient problems with fronts whose speed is slow compared to the propagation speed in the rest of the domain in this paper a novel implicit time marching implementation of the eno roe scheme is developed simulation results which demonstrate the benefits of this implicit implementation are presented

distributed source coding using syndromes discus design and construction we address the problem of compressing correlated distributed sources i e correlated sources which are not co located or which cannot cooperate to directly exploit their correlation we consider the related problem of compressing a source which is correlated with another source that is available only at the decoder this problem has been studied in the information theory literature under the name of the slepian wolf 1973 source coding problem for the lossless coding case and as rate distortion with side information for the lossy coding case we provide a constructive practical framework based on algebraic trellis codes dubbed as distributed source coding using syndromes discus that can be applicable in a variety of settings simulation results are presented for source coding of independent and identically distributed i i d gaussian sources with side information available at the decoder in the form of a noisy version of the source to be coded our results reveal the promise of this approach using trellis based quantization and coset construction the performance of the proposed approach is 2 5 db from the wyner ziv 1976 bound

higher order godunov methods for general systems of hyperbolic conservation laws abstract we describe an extension of higher order godunov methods to general systems of hyperbolic conservation laws this extension allow the method to be applied to problems that are not strictly hyperbolic and exhibit local linear degeneracies in the wave fields the method constructs an approximation of the riemann problem from local wave information a generalization of the engquist osher flux for systems is then used to compute a numerical flux based on this approximation this numerical flux replaces the godunov numerical flux in the algorithm thereby eliminating the need for a global riemann problem solution the additional modifications to the godunov methodology that are needed to treat loss of strict hyperbolicity are described in detail the method is applied to some simple model problems for which the global analytic structure is known the method is also applied to the black oil model for multiphase flow in petroleum reservoirs

duality between source coding and channel coding and its extension to the side information case we explore the information theoretic duality between source coding with side information at the decoder and channel coding with side information at the encoder we begin with a mathematical characterization of the functional duality between classical source and channel coding formulating the precise conditions under which the optimal encoder for one problem is functionally identical to the optimal decoder for the other problem we then extend this functional duality to the case of coding with side information by invoking this duality we are able to generalize the result of wyner and ziv 1976 relating to no rate loss for source coding with side information from gaussian to more arbitrary distributions we consider several examples corresponding to both discrete and continuous valued cases to illustrate our formulation for the gaussian cases of coding with side information we invoke geometric arguments to provide further insights into their duality our geometric treatment inspires the construction and dual use of practical coset codes for a large class of emerging applications for coding with side information such as distributed sensor networks watermarking and information hiding communication systems

an implicit explicit hybrid method for lagrangian hydrodynamics abstract we describe a new implicit explicit hybrid method for solving the equations of hydrodynamics the scheme is an extension of the explicit second order piecewise parabolic method ppm which is unconditionally stable the scheme is thus of the godunov type it is conservative accurate to second order in both space and time and makes use of a nonlinear riemann solver to obtain fluxes of the conserved quantities the hybrid character of the method provides increased accuracy and computational efficiency switching between implicit and explicit formulations occurs smoothly and in a natural way and is performed separately for each characteristic family of waves the method provides high resolution with shocks spread over only one zone and can produce accurate answers to most reasonable problems without the use of an artificial viscosity 1986 academic press inc

a structured fixed rate vector quantizer derived from a variable length scalar quantizer i memoryless sources for pt i see ibid vol 39 no 3 p 851 67 1993 the fixed rate scalar vector quantizer svq for quantizing stationary memoryless sources is extended to a specific type of vector source in which each component is a stationary memoryless scalar subsource independent of the other components algorithms for the design and implementation of the original svq are modified to apply to this case the resulting svq referred to as the extended svq esvq is then used to quantize stationary sources with memory with known autocorrelation function numerical results are presented for the quantization of first order gauss markov sources using this scheme it is shown that the esvq based scheme performs very close to entropy coded transform quantization while maintaining a fixed rate output and outperforms the fixed rate scheme that uses scalar lloyd max quantization of the transform coefficients it is also shown that this scheme performs better than implementable vector quantizers especially at high rates

iterative linear solvers in a 2d radiation hydrodynamics code computer codes containing both hydrodynamics and radiation play a central role in simulating both astrophysical and inertial confinement fusion icf phenomena a crucial aspect of these codes is that they require an implicit solution of the radiation diffusion equations we present in this paper the results of a comparison of five different linear solvers on a range of complex radiation and radiation hydrodynamics problems the linear solvers used are diagonally scaled conjugate gradient gmres with incomplete lu preconditioning conjugate gradient with incomplete cholesky preconditioning multigrid and multigrid preconditioned conjugate gradient these problems involve shock propagation opacities varying over 5 6 orders of magnitude tabular equations of state and dynamic ale arbitrary lagrangian eulerian meshes we perform a problem size scalability study by comparing linear solver performance over a wide range of problem sizes from 1000 to 100 000 zones the fundamental question we address in this paper is is it more efficient to invert the matrix in many inexpensive steps like diagonally scaled conjugate gradient or in fewer expensive steps like multigrid in addition what is the answer to this question as a function of problem size and is the answer problem dependent we find that the diagonally scaled conjugate gradient method performs poorly with the growth of problem size increasing in both iteration count and overall cpu time with the size of the problem and also increasing for larger time steps for all problems considered the multigrid algorithms scale almost perfectly i e the iteration count is approximately independent of problem size and problem time step for pure radiation flow problems i e no hydrodynamics we see speedups in cpu time of factors of 15 30 for the largest problems when comparing the multigrid solvers relative to diagonal scaled conjugate gradient for the incomplete factorization preconditioners we see a weak dependence of iteration count on problem size the speedups observed for pure radiation flow are typically on the order of 10 relative to diagonal scaled conjugate gradient for radiation hydrodynamics problems we again see multigrid scaling perfectly however for the problems considered we see speedups relative to diagonal scaled conjugate gradient of no more than 10 with incomplete cholesky in fact either equaling or outperforming multigrid we trace these observations to the time step control and the feature of ale to relax distorted zones

volumes of small balls on open manifolds lower bounds and examples question under what curvature assumptions on a complete open manifold is the volume of balls of a fixed radius bounded below independent of the center point xx two theorems establish such assumptions and two examples sharply limit their weakening in particular we give an example of a metric on r4 extending to higher dimensions of positive ricci curvature whose sectional curvatures decay to 0 and such that the volume of balls goes uniformly to 0 as the center goes to infinity 0 introduction the following question came up in discussions of the first author with peter li under what curvature assumptions on a complete open manifold m can one find a constant c m r such that the volume of balls b x r can be bounded from below independent of the midpoint x 0 1 vol b x r c m r note that in the presence of a lower bound on the ricci curvature one needs to prove the above inequality only for some r since the bishop gromov volume comparison theorem gr p 124 then gives a bound c m r for r c n rn in dimension 2 theorem a below is a satisfyingpositive answer since the assumptions do not imply a lower bound on the injectivity radius while any weakening of the assumptions leads to immediate counterexamples theorem a if m2 is complete with curvature k o then there exist c m such that for radii r c m r2 in higher dimensions however we have example 1 there are convex hypersurfaces md in rd 1 such that for d 3 no lower bounds as in 0 1 exist for md in dimensions 2 we therefore assume an upper curvature bound but then one gets uniform control even on the injectivity radius the following theorem has been rediscovered several times received by the editors august 10 1987 1980 mathematics subject classification 1985 revision primary 53c20 secondary 53a07 research supported by nsf grant mcs 7g01780 and the sloan foundation both authors were supported by invitations to the i h e s and the m s r i r 1988 american mathematical society 0002 9947 88 1 00 25 per page

conditions for nonnegative curvature on vector bundles and sphere bundles this paper addresses cheeger and gromoll s question of which vector bundles admit a complete metric of nonnegative curvature and relates their question to the issue of which sphere bundles admit a metric of positive curvature we show that any vector bundle which admits a metric of nonnegative curvature must admit a connection a tensor and a metric on the base space which together satisfy a certain differential inequality on the other hand a slight sharpening of this condition is sufficient for the associated sphere bundle to admit a metric of positive curvature our results sharpen and generalize walschap and strake s conditions under which a vector bundle admits a connection metric of nonnegative curvature

second order discretization in space and time for radiation hydrodynamics second order accurate discretizations for radiation hydrodynamics are currently an area of interest in the high energy density laboratory physics and astrophysics communities second order methods used to solve the hydrodynamics equations and second order methods used to solve the radiation transport equation often differ fundamentally making it difficult to combine them in a second order manner here we present an implicitexplicit imex method for solving the 1d equations of radiation hydrodynamics that is second order accurate in space and time our radiation hydrodynamics model consists of the 1d euler equations coupled with a gray radiation s2 approximation our rh method combines the muscl hancock method for solving the euler equations with the tr bdf2 time integration scheme and the linear discontinuous galerkin finite element spatial discretization scheme for the s2 radiation equations the muscl hancock method is commonly used for hydrodynamic calculations and the linear discontinuous galerkin scheme is the standard for the sn equations of radiative transfer while somewhat similar these schemes vary fundamentally with respect to the treatment of spatial slopes we address the challenges inherent to coupling these different numerical methods and demonstrate how these challenges can be overcome using the method of manufactured solutions we show that the method is second order accurate in space and time for both the equilibrium diffusion and streaming limit and we show that the method is capable of computing radiative shock solutions accurately by comparing our results with semi analytic solutions

iterative implementation of an implicit explicit hybrid scheme for hydrodynamics iterative implementation of an implicit explicit hybrid scheme for solving the euler equations is described in this paper the scheme was proposed by fryxellet al j comput phys 63 283 1986 is of the godunov type in both explicit and implicit regimes is conservative and is accurate to second order in both space and time for all courant numbers only a single level of iterations is involved in the implementation which solves both the implicit relations arising from upstream centered differences for all wave families and the nonlinearity of the euler equations the number of iterations required to reach a converged solution may be significantly reduced by the introduction of the multicolors proposed in this paper only a small number of iterations are needed in the scheme for a simulation with large time steps the multicolors may also be applied to other linear and nonlinear wave equations for numerical solutions

interface and discontinuity aware numerical schemes for plasma 3 t radiation diffusion in two and three dimensions a set of numerical schemes is developed for two and three dimensional time dependent 3 t radiation diffusion equations in systems involving multi materials to resolve sub cell structure interface reconstruction is implemented within any cell that has more than one material therefore the system of 3 t radiation diffusion equations is solved on two and three dimensional polyhedral meshes the focus of the development is on the fully coupling between radiation and material the treatment of nonlinearity in the equations i e in the diffusion terms and source terms treatment of the discontinuity across cell interfaces in material properties the formulations for both transient and steady states the property for large time steps and second order accuracy in both space and time the discontinuity of material properties between different materials is correctly treated based on the governing physics principle for general polyhedral meshes and full nonlinearity the treatment is exact for arbitrarily strong discontinuity the scheme is fully nonlinear for the full nonlinearity in the 3 t diffusion equations three temperatures are fully coupled and are updated simultaneously the scheme is general in two and three dimensions on general polyhedral meshes the features of the scheme are demonstrated through numerical examples for transient problems and steady states the effects of some simplifications of numerical schemes are also shown through numerical examples such as linearization simple average of diffusion coefficient and approximate treatment for the coupling between radiation and material

lower upper implicit schemes with multiple grids for the euler equations on montre qu une methode de surrelaxation successive pour la resolution du schema implicite non factorise est equivalente a une forme modifiee du schema implicite inferieur superieur

channel coding with multilevel phase signals a coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth this is achieved by channel coding with expanded sets of multilevel phase signals in a manner which increases free euclidean distance soft maximum likelihood ml decoding using the viterbi algorithm is assumed following a discussion of channel capacity simple hand designed trellis codes are presented for 8 phase shift keying psk and 16 quadrature amplitude shift keying qask modulation these simple codes achieve coding gains in the order of 3 4 db it is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals which we call mapping by set partitioning based on a new distance measure between binary code sequences which efficiently lower bounds the euclidean distance between the corresponding channel signal sequences a search procedure for more powerful codes is developed codes with coding gains up to 6 db are obtained for a variety of multilevel phase modulation schemes simulation results are presented and an example of carrier phase tracking is discussed

superposition coding for side information channels we present simple practical codes designed for the binary and gaussian dirty paper channels we show that the dirty paper decoding problem can be transformed into an equivalent multiple access decoding problem for which we apply superposition coding our concept is a generalization of the nested lattices approach of zamir shamai and erez in a theoretical setting our constructions are capable of achieving capacity using random component codes and maximum likelihood decoding we also present practical implementations of the constructions and simulation results for both dirty paper channels our results for the gaussian dirty paper channel are on par with the best known results for nested lattices we discuss the binary dirty tape channel for which we present a simple effective coding technique finally we propose a framework for extending our approach to general gel fand pinsker channels

twisting and nonnegative curvature metrics on vector bundles over the round sphere a complete noncompact manifold m with nonnegative sectional curvature is diffeomorphic to the normal bundle of a compact submanifold s called the soul of m when s is a round sphere we show that the clutching map of this bundle is restricted this is used to deduce that there are at most finitely many isomorphism types of such bundles with sectional curvature lying in a fixed interval 0 we also examine the opposite question of how the twisting of the bundle limits the type of possible nonnegative curvature metrics on the bundle it turns out that if the bundle does not admit a nowhere zero section then the normal exponential map is necessarily a diffeomorphism onto m and the ideal boundary of m consists of a single point in their paper cg cheeger and gromoll raised the question of which vector bundles over the round sphere admit complete metrics with nonnegative sectional curvature the significance of this problem is that it attempts to determine to what extent a converse to the soul theorem holds recall that this theorem states that every open i e complete noncompact manifold m with nonnegative curvature km is diffeomorphic to a vector bundle over a compact totally geodesic submanifold s called a soul a natural question then is whether all such vector bundles admit complete metrics with km 0 in ow it was shown that when the soul is a bieberbach manifold nonnegative curvature metrics force the vanishing of the euler class of the vector bundle it follows that among oriented plane bundles over the torus only the trivial one admits such a metric the above case is fairly rigid a priori however since for example any bundle with curvature 0 over such a manifold must also admit a flat metric and the corresponding question for a simply connected base remains open an answer could provide insights on the topological structure of compact manifolds with nonnegative curvature since any open manifold with nonnegative curvature can after modifying its metric be isometrically 1991 mathematics subject classification primary 53c20

an adaptive higher order method for solving the radiation transport equation on unstructured grids a new class of solution methods based on a short characteristics approach embedded in the finite element framework for the solution of the radiation transport equation is developed and tested the order of convergence and the error to runtime ratio are determined in numerical tests furthermore the efficiency of the scheme is demonstrated in the case of a challenging problem from the field of solar physics a quantitative comparison with other methods based either on the characteristics or on the finite element approach is carried out this emphasizes the efficiency and accuracy of our method two different adaptation mechanisms are studied grid adaptation and local variation of the order of the scheme

the metric projection onto the soul we study geometric properties of the metric projection r m s of an open manifold m with nonnegative sectional curvature onto a soul s ir is shown to be c up to codimension 3 in arbitrary codimensions small metric balls around a soul turn out to be convex so that the unit normal bundle of s also admits a metric of nonnegative curvature next we examine how the horizontal curvatures at infinity determine the geometry of m and stu dy the structure of sharafutdinov lines we conclude with regularity properties of the cut and conjugate loci of m the resolution of the soul conjecture of cheeger and gromoll by perelinan showed that the structure of open manifolds with nonnegative sectional curvature is more rigid than expected orne of the key results in 14 is that the metric projection wf m s which maps a point p in m to the point 7r p in s that is closest to p is a riemannian submersioni perelman also observed that this map is at least of class c1 and later it was shown in 9 that 7w is at least c2 and c at almnost every point the existence of such a riemannian submersion combined with the restriction on the sign of the curvature suggests that the geometry of m inust be special the purpose of this paper is to illustrate this in several different directions in fact we show that most natural geometric objects classically used in the study of these spaces are intrinsically related to the structure of the map w the paper is essentially structured as follows after introducing notation and recalling some basic results in sectioni 1 we establish in section 2 the existence of maps similar to w for any submanifold of m homologous and isometric to the soul and use this to prove the existence of convex tubular neighborhoods for them in particular this also proves theorem 2 5 the unit normal bundle vti s admits a metric with nonnegative sectional curvature as a consequence open manifolds with nonnegative curvature provide examples of compact manifolds with the same lower curvatuire bound see also 81 theorem 2 5 also implies that nontrivial plane bundles over a bieberbach maanifold do not admit nonnegatively curved metrics thereby providing a shorter proof of the main result in 13 we are grateful to the referee for pointing out this fact to us properties such as these are established via stanidard submersion techniques but the fact that 7r is not known to be smooth everywhere prevents us fromi using these techniques to study the geometry of m far away from the soul one way around received by the editors august 18 1997 1991 mathematics subject classification primary 53c20

lattice and trellis quantization with lattice and trellis bounded codebooks high rate theory for memoryless sources high rate lattice and trellis quantizers for nonuniform sources are introduced and analyzed the performance of these quantizers is determined by two separable quantities the granular gain and the boundary gain which are determined by the shapes of the granular cells and of the support region respectively the granular gain and boundary gain are the duals of shaping and coding gain in data transmission applications using this duality it is shown for gaussian sources that the ultimate achievable boundary gain with high rate lattice bounded lattice codebooks is the same as the ultimate gain that can be obtained from variable rate entropy coding it is observed that if lattice codebooks can achieve the ultimate granular gain of 0 255 b per dimension then lattice bounded lattice codebooks can approach the rate distortion limit the performance of lattice quantizers is compared to that of optimum vector quantizers

on optimal shaping of multidimensional constellations a scheme for the optimal shaping of multidimensional constellations is proposed this scheme is motivated by a type of structured vector quantizer for memoryless sources and results in n sphere shaping of n dimensional cubic lattice based constellations because n sphere shaping is optimal in n dimensions shaping gains higher than those of n dimensional voronoi constellations can be realized while optimal shaping for a large n can realize most of the 1 53 db total shaping gain it has the undesirable effect of increasing the size and the peak to average power ratio of the constituent 2d constellation this limits its usefulness for many real world channels which have nonlinearities the proposed scheme alleviates this problem by achieving optimal constellation shapes for a given limit on the constellation expansion ratio or the peak to average power ratio of the constituent 2d constellation results of calderbank and ozarow 1990 on nonequiprobable signaling are used to reduce the complexity of this scheme and make it independent of the data rate with essentially no effect on the shaping gain comparisons with forney s 1989 trellis shaping scheme are also provided

obstructions to nonnegative curvature and rational homotopy theory we establish a link between rational homotopy theory and the problem which vector bundles admit a complete riemannian metric of nonnegative sectional curvature as an application we show for a large class of simply connected nonnegatively curved manifolds that if c lies in the class and t is a torus of positive dimension then most vector bundles over c x t admit no complete nonnegatively curved metrics

second order accurate interface and discontinuity aware diffusion solvers in two and three dimensions a numerical scheme is developed for two and three dimensional time dependent diffusion equations in numerical simulations involving mixed cells the focus of the development is on the formulations for both transient and steady states the property for large time steps second order accuracy in both space and time the correct treatment of the discontinuity in material properties and the handling of mixed cells for a mixed cell interfaces between materials are reconstructed within the cell so that each of resulting sub cells contains only one material and the material properties of each sub cell are known diffusion equations are solved on the resulting polyhedral mesh even if the original mesh is structured the discontinuity of material properties between different materials is correctly treated based on governing physics principles the treatment is exact for arbitrarily strong discontinuity the formulae for effective diffusion coefficients across interfaces between materials are derived for general polyhedral meshes the scheme is general in two and three dimensions since the scheme to be developed in this paper is intended for multi physics code with adaptive mesh refinement amr we present the scheme on mesh generated from amr the correctness and features of the scheme are demonstrated for transient problems and steady states in one two and three dimensional simulations for heat conduction and radiation heat transfer the test problems involve dramatically different materials

a new lagrangian method for steady supersonic flow computation i godunov scheme abstract this paper studies the problem of steady two dimensional supersonic flow of an inviscid compressible fluid using the new lagrangian formulation of hui and van roessel in which the stream function and the lagrangian time are used as independent variables a shock capturing method is developed by applying the first order godunov scheme to the conservation form equations of this formulation the method is fast and robust furthermore extensive comparisons with exact solutions and with the second order godunov scheme of glaz and wardlaw based on the eulerian formulation show that the first order lagrangian method generally attains the same level of accuracy as the second order eulerian method and is even better in resolving slip line discontinuities

systematic lossy source channel coding the fundamental limits of systematic communication are analyzed in systematic transmission the decoder has access to a noisy version of the uncoded raw data analog or digital the coded version of the data is used to reduce the average reproduced distortion d below that provided by the uncoded systematic link and or increase the rate of information transmission unlike the case of arbitrarily reliable error correction d spl rarr 0 for symmetric sources channels where systematic codes are known to do as well as nonsystematic codes we demonstrate that the systematic structure may degrade the performance for nonvanishing d we characterize the achievable average distortion and we find necessary and sufficient conditions under which systematic communication does not incur loss of optimality the wyner ziv 1976 rate distortion theorem plays a fundamental role in our setting the general result is applied to several scenarios for a gaussian bandlimited source and a gaussian channel the invariance of the bandwidth signal to noise ratio snr in decibels product is established and the optimality of systematic transmission is demonstrated bernoulli sources transmitted over binary symmetric channels and over certain gaussian channels are also analyzed it is shown that if nonnegligible bit error rate is tolerated systematic encoding is strictly suboptimal

riemannian submersions from compact four manifolds we show that under certain conditions a nontrivial riemannian submersion from positively curved four manifolds does not exist this gives a partial answer to a conjecture due to fred wilhelm we also prove a rigidity theorem for riemannian submersions with totally geodesic fibers from compact four dimensional einstein manifolds

a high order godunov scheme for steady supersonic gas dynamics abstract a high order extension of godunov s method is developed for the equations of steady supersonic flow sample calculations show that the method resolves smooth flow accurately and represents strong shock waves with very little diffusion and no post shock oscillation

writing on dirty paper corresp a channel with output y x s z is examined the state s sim n 0 qi and the noise z sim n 0 ni are multivariate gaussian random variables i is the identity matrix the input x in r n satisfies the power constraint l n sum i 1 n x i 2 leq p if s is unknown to both transmitter and receiver then the capacity is frac 1 2 ln 1 p n q nats per channel use however if the state s is known to the encoder the capacity is shown to be c ast frac 1 2 ln 1 p n independent of q this is also the capacity of a standard gaussian channel with signal to noise power ratio p n therefore the state s does not affect the capacity of the channel even though s is unknown to the receiver it is shown that the optimal transmitter adapts its signal to the state s rather than attempting to cancel it

successive refinement for the wyner ziv problem and layered code design we examine successive refinement for the wyner ziv problem described in a recent paper by steinberg and merhav where the authors showed that if the side information for all stages is identical then the jointly gaussian source with squared error distortion measure is successively refinable we first extend this result to the case where the difference between the source and the side information is gaussian and independent of the side information as a byproduct we give an alternative proof that the wyner ziv problem for these sources has no rate loss a result that was recently shown by pradhan et al through invoking the duality between the gaussian wyner ziv problem and the costa problem we then perform layered wyner ziv code design for this general type of source based on nested scalar quantization bit plane coding and low density parity check ldpc code based slepian wolf coding source coding with side information we show that density evolution can be used to analyze the slepian wolf code performance provided that certain symmetry conditions which have been dubbed dual symmetry are satisfied by the hypothetical channel between the source and the side information we also show that the dual symmetry condition is indeed satisfied by the hypothetical channel in our slepian wolf coding setup this justifies the use of density evolution in our ldpc code based slepian wolf code design for wyner ziv coding for the jointly gaussian source our layered coder performs 1 29 to 3 45 db from the wyner ziv bound for rates ranging from 0 47 to 4 68 bits per sample when the side information is laplacian and the source equals the side information plus an independent gaussian noise term our layered coder performs 1 33 to 3 90 db from the wyner ziv bound for rates ranging from 0 48 to 4 64 bits per sample

trellis coded quantization of memoryless and gauss markov sources trellis coded quantization tcq is developed and applied to the encoding of memoryless and gauss markov sources the theoretical justification for the approach is alphabet constrained rate distortion theory which is a dual to the channel capacity argument that motivates trellis coded modulation tcm the authors adopt the notions of signal set expansion set partitioning and branch labeling of tcm but modify the techniques to account for the source distribution to design tcq coders of low complexity with excellent mean squared error mse performance for a memoryless uniform source tcq provides an mse within 0 21 db of the distortion rate bound at all positive integral rates the performance is superior to that promised by the coefficient of quantization for all of the best lattices known in dimensions 24 or less for a memoryless gaussian source the tcq performance at rates of 0 5 1 and 2 b sample is superior to all previous results the authors found in the literature the encoding complexity of tcq is very modest tcq is incorporated into a predictive coding structure for the encoding of gauss markov sources simulation results for first second and third order gauss markov sources are presented

a simple riemann solver and high order godunov schemes for hyperbolic systems of conservation laws a simple approximate riemann solver for hyperbolic systems of conservation laws is developed for its use in godunov schemes the solver is based on characteristic formulations and is illustrated through euler and ideal magnetohydrodynamical mhd equations the procedure of a high order godunov scheme incorporated with the riemann solver for one dimensional hyperbolic systems of conservation laws is described in detail the correctness of the scheme is shown by comparison with the piecewise parabolic method for euler equations and by comparison with exact solutions of riemann problems for ideal mhd equations the robustness of the scheme is demonstrated through numerical examples involving more than one strong shock at the same time it is shown that the scheme offers the principle advantages of godunov schemes robust operation in the presence of strong waves thin shock fronts thin contact and slip surface discontinuities

asymptotic preserving and positive schemes for radiation hydrodynamics in view of radiation hydrodynamics computations we propose an implicit and positive numerical scheme that captures the diffusion limit of the two moments approximate model for the radiative transfer even on coarses grids the positivity of the scheme is equivalent to say that the scheme preserves the limited flux property various test cases show the accuracy and robustness of the scheme

flux limiters in the coupling of radiation and hydrodynamic models two numerical approximations to radiative heat transfer problem based on asymptotic and entropy approaches are proposed for hydrodynamics radiation coupling we compare the radiative fluxes between the two approaches and we show that the coupling based on the entropy approach is flux limited while the other approach does not preserve this condition relaxation schemes are considered for the hydrodynamic part and an iterative procedure is used for radiation the new splitting algorithm avoids the use of riemann solvers and newton iterations numerical examples are carried out on two and three dimensional problems

a second order iterative implicit explicit hybrid scheme for hyperbolic systems of conservation laws an iterative implicit explicit hybrid scheme is proposed for hyperbolic systems of conservation laws each wave in a system may be implicitly or explicitly or partially implicitly and partially explicitly treated depending on its associated courant number in each numerical cell and the scheme is able to smoothly switch between implicit and explicit calculations the scheme is of godunov type in both explicit and implicit regimes is in a strict conservation form and is accurate to second order in both space and time for all courant numbers the computer code for the scheme is easy to vectorize multicolors proposed in this paper may reduce the number of iterations required to reach a converged solution by several orders for a large time step the feature of the scheme is shown through numerical examples

strongly nonnegative curvature we prove that all currently known examples of manifolds with nonnegative sectional curvature satisfy a stronger condition their curvature operator can be modified with a 4 form to become positive semidefinite

an implicit explicit eulerian godunov scheme for compressible flow a hybrid implicit explicit scheme is developed for eulerian hydrodynamics the hybridization is a continuous switch and operates on each characteristic field separately the explicit scheme is a version of the second order godunov scheme the implicit method is only first order accurate in time but leads to a block tridiagonal matrix inversion for efficiency and is unconditionally stable for the case of linear advection the methodology is described for the cases of linear advection for nonlinear scalar problems and for gas dynamics an important element of our work is the use of a modified engquist osher flux function in place of the godunov flux several numerical results are presented to demonstrate the properties of the method especially stable numerical shocks at very high cfl numbers and second order accurate steady states

the ceo problem multiterminal source coding we consider a new problem in multiterminal source coding motivated by the following decentralized communication estimation task a firm s chief executive officer ceo is interested in the data sequence x t sub t 1 sup spl infin which cannot be observed directly perhaps because it represents tactical decisions by a competing firm the ceo deploys a team of l agents who observe independently corrupted versions of x t sub t 1 sup spl infin because x t is only one among many pressing matters to which the ceo must attend the combined data rate at which the agents may communicate information about their observations to the ceo is limited to say r bits per second if the agents were permitted to confer and pool their data then in the limit as l spl rarr spl infin they usually would be able to smooth out their independent observation noises entirely then they could use their r bits per second to provide the ceo with a representation of x t with fidelity d r where d spl middot is the distortion rate function of x t in particular with such data pooling d can be made arbitrarily small if r exceeds the entropy rate h of x t suppose however that the agents are not permitted to convene agent i having to send data based solely on his own noisy observations y sub i t we show that then there does not exist a finite value of r for which even infinitely many agents can make d arbitrarily small furthermore in this isolated agents case we determine the asymptotic behavior of the minimal error frequency in the limit as l and then r tend to infinity