discrete time techniques for time delay estimation basic aspects of time delay estimation tde based on sampled signals are investigated the direct cross correlation method is analyzed and compared to the average square difference function asdf and the addition only based average magnitude difference function amdf estimators their relative accuracy is theoretically evaluated and previous empirical results are explained it is shown that both the asdf and the amdf based estimators outperform the direct cross correlation based estimator for medium high signal to noise ratios moreover the amdf based estimator which avoids any multiplications significantly reduces the computational complexity of the estimation procedure while offering only a moderate performance loss with respect to the asdf based estimator

error analysis of time delay estimation using a finite integration time correlator a methodology is presented for analyzing the error associated with time delay estimation using a finite integration time correlator processing waveforms received at two separate sensors the type of signal considered is a sinusoid whose amplitude is randomly modulated the signals are assumed to be imbedded in additive gaussian noise before they are correlated the received waveforms are converted to a lower center frequency by mixers whose local oscillators are assumed to contain phase noise by direct calculation in the time domain the variance of the error in the time delay estimate is shown to be a function of integration time signal to noise ratios signal and noise bandwidths and phase noise variance the phase noise is shown to limit the accuracy of the time delay estimate however without phase noise using the methodology the accuracy is shown to approach that obtained by the maximum likelihood estimator

implicit spectrally accurate method for moving boundary problems using immersed boundary conditions concept a fully implicit spectral algorithm for the analysis of moving boundary problem is described the algorithm is based on the concept of immersed boundary conditions ibc i e the computational domain is fixed while the time dependent physical domain is submerged inside the computational domain and is described in the context of the diffusion type problems the physical conditions along the edges of the physical domain are treated as internal constraints the method eliminates the need for adaptive grid generation that follows evolution of the physical domain and provides sharp resolution of the location of the boundary various tests confirm the spectral accuracy in space and the first and second order accuracy in time the computational cost advantage of the ibc method as compared with the more traditional algorithm based on the mapping concept is demonstrated

computations of multi fluid flows abstract full numerical simulations of three dimensional flows of two or more immiscible fluids of different densities and viscosities separated by a sharp interface with finite surface tension are discussed the method used is based on a finite difference approximation of the full navier stokes equations and explicit tracking of the interface between the fluids preliminary simulations of the rayleigh taylor instability and the motion of bubbles are shown

three dimensional front tracking we describe a three dimensional front tracking algorithm discuss its numerical implementation and present studies to validate the correctness of this approach based on the results of the two dimensional computations we expect three dimensional front tracking to significantly improve computational efficiencies for problems dominated by discontinuities in some cases for which the interface computations display considerable numerical sensitivity we expect a greatly enhanced capability

a second order accurate conservative front tracking method in one dimension this paper presents a conservative front tracking method for shocks and contact discontinuities that is second order accurate it is based on a volume of fluid method that treats the moving front with concepts similar to those of an embedded boundary method special care is taken in the centering of the data to ensure the right order of accuracy at the front and a redistribution step guarantees conservation a suite of test problems for tracking both shocks and contact discontinuities is presented that confirms that the method is second order accurate

beamforming design for multiuser two way relaying a unified approach via max min sinr in this paper we develop a unified framework for beamforming designs in non regenerative multiuser two way relaying twr the core of our framework is the solution to the max min signal to interference plus noise ratio sinr problem for multiuser twr we solve this problem using a dinkelbach type algorithm with near optimal performance and superlinear convergence we show that using the max min sinr solution as a corner stone the beamforming designs under various important criteria such as weighted sum rate maximization weighted sum mean square error mse minimization and average bit error rate ber or symbol error rate ser minimization etc can be reformulated into a monotonic program a polyblock outer approximation algorithm is then used to find the desired solutions with guaranteed convergence and optimal performance provided that the core max min sinr solver is optimal furthermore the proposed unified approach can provide important insights for tackling the optimal beamforming designs in other emerging network models and settings for instances we extend the proposed framework to address the beamforming design in collaborative twr and multi pair mimo twr extensive numerical results are presented to demonstrate the merits of the proposed beamforming solutions

an evaluation of roe s scheme generalizations for equilibrium real gas flows the extension of roe s approximate riemann solver to equilibrium real gas is analyzed by means of a general formulation allowing us to clarify the inherent nonuniqueness of the average state and the influence of the functional form of the equation of state several generalizations of roe s scheme are then reviewed and their numerical performances are discussed by computing some 2d steady hypersonic flows the flow solvers are coupled with a newly developed efficient and robust procedure for thermochemical air properties evaluation all of the tested equilibrium solvers achieve very similar results they are found of comparable numerical efficiency the higher performances being associated with vinokur s and liou s solvers it is concluded that equilibrium simulations in 2d are by no means less robust than the perfect gas ones when coupled with the proposed procedure for properties evaluation

node pair finite volume finite element schemes for the euler equation in cylindrical and spherical coordinates a numerical scheme is presented for the solution of the compressible euler equations in both cylindrical and spherical coordinates the unstructured grid solver is based on a mixed finite volume finite element approach equivalence conditions linking the node centered finite volume and the linear lagrangian finite element scheme over unstructured grids are reported and used to devise a common framework for solving the discrete euler equations in both the cylindrical and the spherical reference systems numerical simulations are presented for the explosion and implosion problems with spherical symmetry which are solved in both the axial radial cylindrical coordinates and the radial azimuthal spherical coordinates numerical results are found to be in good agreement with one dimensional simulations over a fine mesh

monotonic optimization problems and solution approaches problems of maximizing or minimizing monotonic functions of n variables under monotonic constraints are discussed a general framework for monotonic optimization is presented in which a key role is given to a property analogous to the separation property of convex sets the approach is applicable to a wide class of optimization problems including optimization problems dealing with functions representable as differences of increasing functions d i functions

solving shallow water systems in 2d domains using finite volume methods and multimedia sse instructions the goal of this paper is to construct efficient parallel solvers for 2d hyperbolic systems of conservation laws with source terms and nonconservative products the method of lines is applied at every intercell a projected riemann problem along the normal direction is considered which is discretized by means of well balanced roe methods the resulting 2d numerical scheme is explicit and first order accurate in m j castro j a garcia j m gonzalez c pares a parallel 2d finite volume scheme for solving systems of balance laws with nonconservative products application to shallow flows comput methods appl mech engrg 196 2006 2788 2815 a domain decomposition method was used to parallelize the resulting numerical scheme which was implemented in a pc cluster by means of mpi techniques in this paper in order to optimize the computations a new parallelization of simd type is performed at each mpi thread by means of sse streaming simd extensions which are present in common processors more specifically as the most costly part of the calculations performed at each processor consists of a huge number of small matrix and vector computations we use the intel c integrated performance primitives small matrix library to make easy the use of this library which is implemented using assembler and sse instructions we have developed a c wrapper of this library in an efficient way some numerical tests were carried out to validate the performance of the c small matrix wrapper the specific application of the scheme to one layer shallow water systems has been implemented on a pc s cluster the correct behavior of the one layer model is assessed using laboratory data

a stability analysis of a eulerian solution method for moving boundary problems in electrochemical machining we investigate the front tracking method using marker points for the numerical solution of a class of moving boundary problems which arise in connection with certain two dimensional electrochemical machining problems the numerical method is expressed as a system of n nonlinear autonomous ordinary differential equations odes for describing the movement of n marker points on the moving boundary the system has been analysed in some cases with respect to the local stability of equilibrium solutions and to the global stability of nonequilibrium solutions the linearised local stability of the equilibrium solution is investigated in terms of the jacobi matrix for the system of odes closed form expressions for the eigenvalues and the eigenvectors of the jacobi matrix have been derived part of the method comprises the solution of a dirichlet boundary value problem this is carried out using various boundary collocation methods which are investigated the mathematical numerical model has features which are in accordance with those of the physical problem this has also been demonstrated by actual computation of some examples

coupling of the interface tracking and the two fluid models for the simulation of incompressible two phase flow abstract the volume of fluid vof method which uses an interface tracking algorithm for the simulation of the two phase flow is coupled with the two fluid model which is based on time and space averaged equations and cannot track the interface explicitly the idea of the present work is to use the vof method in the parts of the computational domain where the grid density allows surface tracking in the parts of the domain where the flow is too dispersed to be described by the interface tracking algorithms the two fluid model is used the equations of the two fluid model are less accurate than the vof model due to the empirical closures required in the averaged equations however in the case of the sufficiently dispersed flow the two fluid model results are still much closer to the real world than the results of the vof method which do not have any physical meaning when the grid becomes too coarse each model in the present work uses a separate set of equations suitable for description of two dimensional incompressible viscous two phase flow similar discretization techniques are used for both sets of equations and solved with the same numerical method coupling of both models is achieved via the volume fraction of one of the fluids which is used in both models a special criterion for the transition between the models is derived from the interface reconstruction function in the vof method an idealized vortical flow and the rayleigh taylor instability are used as tests of the coupling in both cases the time development causes mixing of the fluids and dispersion of the interface that is beyond the capabilities of the model based on the vof method therefore the two fluid model gradually replaces the interface tracking model in the final stages of the rayleigh taylor instability when both fluids are approaching their final positions and the tractable interface appears again the two fluid model is gradually replaced by the vof method

renormalized meshfree schemes i consistency stability and hybrid methods for conservation laws this paper is devoted to the study of a new kind of meshfree scheme based on a new class of meshfree derivatives the renormalized meshfree derivatives which improve the consistency of the original weighted particle methods the weak renormalized meshfree scheme built from the weak formulation of general conservation laws turns out to be l 2 stable under some geometrical conditions on the distribution of particles and some regularity conditions of the transport field a time discretization is then performed by analogy with finite volume methods and the l 1 l infty and bv stabilities of the obtained time discretized scheme are studied from the same analogy with finite volume methods a hybrid particle scheme is built using the godunov method and is numerically compared to the weak renormalized scheme

linear precoding for multi pair two way mimo relay systems with max min fairness two way relaying has demonstrated significant gain in spectral efficiency by applying network coding when a pair of source nodes exchange information via a relay node this paper is concerned with the scenario where multiple pairs of users exchange information through a common relay node equipped with multiple antennas we aim to design linear precoding at the relay based on amplify and forward strategy the goal is to maximize the minimum achievable rate among all the users subject to a peak relay power constraint so as to achieve the max min fairness we first convert this nonconvex problem into a series of semidefinite programming problems using bisection search and certain transformation techniques a quasi optimal solution is then obtained by using semidefinite relaxation sdr to reduce the design complexity we further introduce a pair wise zero forcing zf structure that eliminates the interference among different user pairs by applying this structure the precoding design problem is simplified to a power allocation problem which can be optimally solved a simplified power allocation algorithm is also proposed simulation results show that the proposed sdr based precoding not only achieves high minimum user rate but also maintains good sum rate performance when compared with existing schemes it is also shown that the proposed pair wise zf precoding with simplified power allocation strikes a good balance between performance and complexity

lattices which are good for almost everything we define an ensemble of lattices and show that for asymptotically high dimension most of its members are simultaneously good as sphere packings sphere coverings additive white gaussian noise awgn channel codes and mean squared error mse quantization codes these lattices are generated by applying construction a to a random linear code over a prime field of growing size i e by lifting the code to spl ropf sup n

on the symmetric form of systems of conservation laws with entropy abstract this paper reviews the symmetrizability of systems of conservation laws which possess entropy functions symmetric formulations in conservation form for the equations of gas dynamics are presented

nested linear lattice codes for structured multiterminal binning network information theory promises high gains over simple point to point communication techniques at the cost of higher complexity however lack of structured coding schemes limited the practical application of these concepts so far one of the basic elements of a network code is the binning scheme wyner 1974 1978 and other researchers proposed various forms of coset codes for efficient binning yet these schemes were applicable only for lossless source or noiseless channel network coding to extend the algebraic binning approach to lossy source or noisy channel network coding previous work proposed the idea of nested codes or more specifically nested parity check codes for the binary case and nested lattices in the continuous case these ideas connect network information theory with the rich areas of linear codes and lattice codes and have strong potential for practical applications we review these developments and explore their tight relation to concepts such as combined shaping and precoding coding for memories with defects and digital watermarking we also propose a few novel applications adhering to a unified approach

coupling finite elements and finite volumes by lagrange multipliers for explicit dynamic fluid structure interaction this paper proposes a strategy for coupling a finite element description of structures with a finite volume fv description of fluids by means of the lagrange multipliers method for the numerical simulation of fluid structure interaction problems in fast transient dynamics the structural domain uses the classical explicit central difference cd time integration scheme while in the fluid domain a node centered finite volume scheme is adopted which achieves second order accuracy in space and in time by a predictor corrector algorithm combined with a muscl like technique the fv time marching scheme is suitably adapted to enable strong coupling with the cd scheme via lagrange multipliers numerical examples illustrate the effectiveness of the proposed procedure copyright 2010 john wiley sons ltd

a hybrid level set front tracking finite element approach for fluid structure interaction and two phase flow applications we present a hybrid level set front tracking approach suitable for fluid structure interaction and two phase flow applications our approach aims at extending geometrical flexibility of standard mesh moving front tracking methods by introducing an additional implicit level set representation of the geometry under consideration the computational mesh is automatically aligned to the implicitly described geometry by minimizing a nonlinear constrained functional resulting triangulations approximate the geometry accurately while being optimal in a certain sense due to the mesh alignment finite element spaces defined on these triangulations may be easily adjusted to account for special solution properties such as discontinuities across interfaces in order to demonstrate the flexibility of the proposed approach we apply it to a simplified one way coupled fluid structure interaction problem inspired by the flow induced by a moving cardiac valve furthermore we evaluate the approach by solving a two phase flow benchmark problem

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

a self adaptive moving mesh method for the camassa holm equation a self adaptive moving mesh method is proposed for the numerical simulations of the camassa holm equation it is an integrable scheme in the sense that it possesses the exact n soliton solution it is named a self adaptive moving mesh method because the non uniform mesh is driven and adapted automatically by the solution once the non uniform mesh is evolved the solution is determined by solving a tridiagonal linear system due to these two superior features of the method several test problems give very satisfactory results even if by using a small number of grid points

stability of newton tvd runge kutta scheme for one dimensional euler equations with adaptive mesh abstract in this paper we propose a moving mesh method with a newton total variation diminishing tvd runge kutta scheme for the euler equations our scheme improves time discretization in the moving mesh algorithms by analyzing the semi discrete euler equations with the discrete moving mesh equations as constraints the stability of the newton tvd runge kutta scheme is proved thus we can conclude that the proposed algorithm can generate a weak solution to the euler equations finally numerical examples are presented to verify the theoretical results and demonstrate the accuracy of the proposed scheme

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

multiple input multiple output two way relaying a space division approach we propose a novel space division based network coding scheme for multiple input multiple output mimo two way relay channels twrcs in which two multiantenna users exchange information via a multiantenna relay in the proposed scheme the overall signal space at the relay is divided into two subspaces in one subspace the spatial streams of the two users have nearly orthogonal directions and are completely decoded at the relay in the other subspace the signal directions of the two users are nearly parallel and linear functions of the spatial streams are computed at the relay following the principle of physical layer network coding based on the recovered messages and message functions the relay generates and forwards network coded messages to the two users we show that at high signal to noise ratio the proposed scheme achieves the asymptotic sum rate capacity of the mimo twrc within 1 2 log 5 4 0 161 bits per user antenna for any antenna configuration and any channel realization we perform large system analysis to derive the average sum rate of the proposed scheme over rayleigh fading mimo twrcs we show that the average asymptotic sum rate gap to the capacity is at most 0 053 bits per relay antenna it is demonstrated that the proposed scheme significantly outperforms the existing schemes

an efficient adaptive mesh redistribution method for a non linear dirac equation this paper presents an efficient adaptive mesh redistribution method to solve a non linear dirac nld equation our algorithm is formed by three parts the nld evolution the iterative mesh redistribution of the coarse mesh and the local uniform refinement of the final coarse mesh at each time level the equidistribution principle is first employed to iteratively redistribute coarse mesh points and the scalar monitor function is subsequently interpolated on the coarse mesh in order to do one new iteration and improve the grid adaptivity after an adaptive coarse mesh is generated ideally and finally each coarse mesh interval is equally divided into some fine cells to give an adaptive fine mesh of the physical domain and then the solution vector is remapped on the resulting new fine mesh by an affine method the nld equation is finally solved by using a high resolution shock capturing method on the fixed non uniform fine mesh extensive numerical experiments demonstrate that the proposed adaptive mesh method gives the third order rate of convergence and yields an efficient and fast nld solver that tracks and resolves both small local and large solution gradients automatically

spectrally accurate immersed boundary conditions method for three dimensional flows a three dimensional spectrally accurate algorithm based on the immersed boundary conditions ibc concept has been developed for the analysis of flows in channels bounded by rough boundaries the algorithm is based on the velocityvorticity formulation and uses a fixed computational domain with the flow domain immersed in its interior the geometry of the boundaries is expressed in terms of double fourier expansions and boundary conditions enter the algorithm in the form of constraints the spatial discretization uses fourier expansions in the stream wise and span wise directions and chebyshev expansions in the wall normal direction the algorithm can use either the fixed flow rate constraint or the fixed pressure gradient constraint a direct implementation of the former constraint is described an efficient solver which takes advantage of the structure of the coefficient matrix has been developed it is demonstrated that the applicability of the algorithm can be extended to more extreme geometries using the over determined formulation various tests confirm the spectral accuracy of the algorithm

hp multilevel monte carlo methods for uncertainty quantification of compressible navier stokes equations we propose a novel hp multilevel monte carlo method for the quantification of uncertainties in the compressible navier stokes equations using the discontinuous galerkin method as deterministic

an algorithm for aligning a quadrilateral grid with internal boundaries we present a new numerical algorithm that aligns a quadrilateral grid with internal alignment curves iacs these iacs can be used to delineate internal interfaces discontinuities in material properties internal boundaries or major features of a flow field the adaptive iac grid generation algorithm readjusts a predefined reference grid to create a nearby grid where the mesh cell edges are aligned with the iacs on an aligned grid numerical discretizations of partial differential equations can be formulated to satisfy the interfacial relations such as matching fluxes across the discontinuity to reduce the numerical errors introduced by the discontinuity we present examples to demonstrate the effectiveness of the iac grid generation algorithm for multiple embedded interfaces in a quadrilateral grid

invariant domains and second order continuous finite element approximation for scalar conservation equations we propose a technique for approximating nonlinear scalar conservation equations that uses continuous finite elements and is formally at least second order accurate in space and maximum principle preserving the method is explicit in time uses unstructured continuous finite elements in space and works in any space dimension the stability and accuracy of the method are achieved by adapting the artificial viscosity

self adjusting grid methods for one dimensional hyperbolic conservation laws it is shown how to automatically adjust the grid to follow the dynamics of the numerical solution of hyperbolic conservation laws the grid motion is determined by averaging the local characteristic velocities of the equations with respect to the amplitudes of the signals the resulting algorithm is a simple extension of many currently popular godunov type methods computer codes using one of these methods can be easily modified to add the moving mesh as an option numerical examples are given that illustrate the improved accuracy of godunov s and roe s methods on a self adjusting mesh

numerical simulation of crystal growth in three dimensions using a sharp interface finite element method a sharp interface numerical model is presented to simulate thermally driven crystal growth in three dimensional space the model is formulated using the finite element method and works directly with primitive variables it solves the energy equation in a fixed volume mesh while explicitly tracking the motion of the solid liquid interface the three dimensional interface is represented by connected planar triangles that form a surface mesh to accurately capture the morphology of the growing dendrite the surface mesh is updated every few time steps so that the quality of the triangles is maintained and the size of the triangles is always kept in a range associated with the element size of the fixed volume mesh the interface curvature is calculated by a least squares paraboloid fitting to neighbouring nodes the model is validated through a comparison with an exact solution of a three dimensional stefan problem a mesh refinement study a mesh orientation test and a comparison with solvability theory it is shown that the interface position is tracked to second order accuracy simulations are performed under different combinations of the undercooling and surface energy the effects of these parameters on the growth and morphology of the dendrites are studied copyright 2006 john wiley sons ltd

modeling extreme waves based on equations of potential flow with a free surface a method for numerical investigation of nonlinear wave dynamics based on direct hydrodynamical modeling of 1 d potential periodic surface waves is created the model is a part of an interactive wind wave model using a non stationary conformal mapping the principal equations are rewritten in a surface following coordinate system and reduced to two simple evolutionary equations for the elevation and the velocity potential of the surface fourier expansion is used to approximate these equations high accuracy was confirmed by validation of the non stationary model against known solutions and by comparison between the results obtained with different resolution in the horizontal the method developed is applied to the simulation of waves evolution with different initial conditions numerical experiments with initially monochromatic waves with different steepness show that the model is able to simulate breaking conditions when the surface becomes a multi valued function of the horizontal coordinate an estimate of the critical initial wave height that divides between non breaking and eventually breaking waves is obtained simulations of nonlinear evolution of a wave field is represented initially by two modes with close wave numbers amplitude modulation and a wave field with a phase modulation both runs result in the appearance of large and very steep waves these also break if the initial amplitudes are sufficiently large

error analysis and bounds in time delay estimation we have analyzed the error propagation in the classical delay estimation based on the identification of the maximum of the cross correlation between the input signals the resulting error propagation model has the form of a linear combination of the errors additional to the signal samples these errors are weighted by the derivative of the input signals at the sampling instants based on the error propagation model we have further found an upper bound to the square of the estimation error the use of the model is demonstrated by two simple examples

a boundary integral approach to unstable solidification we consider the supercooled stefan problem with a general anisotropic curvature and velocity dependent boundary condition on the moving interface we present numerical methods based on an integral equation formulation and including a new algorithm for moving curves with curvature dependent velocity these methods compute a periodic interface with o t accuracy where t is the time step previous work has been limited to short time spans and achieved slightly less than o t12 accuracy accurate numerical results are seen to agree with the predictions of linear stability theory this agreement has eluded previous authors because their numerical methods suffered from grid effects and their linear stability theory was incorrect we study the long time evolution of an unstable interface our computations exhibit the beginnings of a sidebranching instability when the boundary condition includes anisotropy and tip splitting in the isotropic case

compute compress and forward exploiting asymmetry of wireless relay networks compute and forward cf harnesses interference in a wireless network by allowing relays to compute combinations of source messages the computed message combinations at relays are correlated and so directly forwarding these combinations to a destination generally incurs information redundancy and spectrum inefficiency to address this issue we propose a novel relay strategy termed compute compress and forward ccf in ccf source messages are encoded using nested lattice codes constructed on a chain of nested coding and shaping lattices a key difference of ccf from cf is an extra compressing stage inserted in between the computing and forwarding stages of a relay so as to reduce the forwarding information rate of the relay the compressing stage at each relay consists of two operations first to quantize the computed message combination on an appropriately chosen lattice referred to as a quantization lattice and then to take modulo on another lattice referred to as a modulo lattice we study the design of the quantization and modulo lattices and propose successive recovering algorithms to ensure the recoverability of source messages at destination based on that we formulate a sum rate maximization problem that is in general an np hard mixed integer program a low complexity algorithm is proposed to give a suboptimal solution numerical results are presented to demonstrate the superiority of ccf over the existing cf schemes

nurbs representational strategies for tracking moving boundaries and topological changes during phase evolution abstract nucleation growth coalescence and separation are topological and shape changing events common to many physical problems including those aimed at modeling microstructural phase evolution the common computational approaches to these problems rely on implicitly representing the geometric boundary of microstructural phases through level sets and phase fields since explicit geometrical representations necessitate rediscretization in mesh or grid based solution approaches in this paper we develop an isogeometric explicit boundary tracking procedure that utilizes non uniform rational b splines nurbs to model both topology and shape changing events such as phase nucleation growth separation and dissolution the computational algorithms developed in the paper rely on a constructive solid geometry csg inspired representation of phases that permits parametric immersion of void inclusion phase boundaries in the underlying matrix phase the representation also enables dynamically capturing topological and shape changing events without modifying the underlying discretizations the developed procedure is demonstrated through multiphysics examples that capture phase coalescence and separation caused by interactions of electrical field and surface energy under a constraint on mass conservation

mixing in the stokes flow in a cylindrical container kinematic features of three dimensional mixing by advection of passive particles in time periodic flows are the primary subject of this study a classification of periodic points providing important information about the mixing properties of a flow is presented and the dynamics of the poincare map in the vicinity of periodic points is analysed for all identified types three examples of stokes flow in a finite cylindrical cavity with discontinuous periodic motion of its end walls are used to illustrate the determination of both periodic lines and isolated periodic points in the flow domain the stable and unstable manifolds of points on the periodic lines create two surfaces in the flow a numerical technique based on tracking of a material surface is presented to study the manifold surfaces and their intersections it is illustrated with numerical examples that flows with periodic lines possess only quasi two dimensional mechanisms of chaotic advection

temporal evolution of periodic disturbances in two layer couette flow the time dependent motion for a two layer couette flow consisting of fluids of different viscosities is simulated numerically by using an algorithm based on the volume of fluid vof method interfacial tension is included via a continuous surface force csf algorithm the algorithm is fine tuned to handle the motion which is driven by a shear induced interfacial instability due to the viscosity stratification the code is validated against linear theory two prototypical situations are presented one at a moderately high reynolds number and the other at a lower reynolds number the initial condition is seeded with the eigenmode of largest growth rate with amplitudes that are varied from those that capture the linear regime to larger values for nonlinear regimes issues of free surface advection and viscosity interpolation are discussed the onset of nonlinearity occurs at the interface and is quadratic followed by wave steepening

modelling the transition between fixed and mobile bed conditions in two phase free surface flows in a two phase free surface flow the transition from a mobile bed condition to a fixed bed one and vice versa occurs at a sharp interface across which the relevant system of partial differential equations changes abruptly this leads to the possibility of conceiving a new type of riemann problem rp which we have called composite riemann problem crp where not only the initial constant values of the variables but also the system of equations change from left to right of a discontinuity in this paper we present a strategy for solving a crp by reducing it to a standard rp of a single composite system of equations this can be obtained by combining the two original systems by means of a suitable weighting function namely the erodibility variable and the introduction of an appropriate differential equation for this quantity in this way the crp problem can be analyzed theoretically with standard methods and the features of the solutions can be clearly identified in particular a stationary contact wave is able to correctly describe the sharp transition between mobile and fixed bed conditions a finite volume scheme based on the multiple averages generalized roe approach rosatti and begnudelli 2013 22 was used to numerically solve the fixed mobile crp several test cases demonstrate the effectiveness exact well balanceness and high accuracy of the scheme when applied to problems that fall within the physical range of applicability of the relevant mathematical model

compute and forward harnessing interference through structured codes interference is usually viewed as an obstacle to communication in wireless networks this paper proposes a new strategy compute and forward that exploits interference to obtain significantly higher rates between users in a network the key idea is that relays should decode linear functions of transmitted messages according to their observed channel coefficients rather than ignoring the interference as noise after decoding these linear equations the relays simply send them towards the destinations which given enough equations can recover their desired messages the underlying codes are based on nested lattices whose algebraic structure ensures that integer combinations of codewords can be decoded reliably encoders map messages from a finite field to a lattice and decoders recover equations of lattice points which are then mapped back to equations over the finite field this scheme is applicable even if the transmitters lack channel state information

towards the asymptotic sum capacity of the mimo cellular two way relay channel in this paper we consider the transceiver and relay design for the multiple input multiple output mimo cellular two way relay channel ctwrc where a multi antenna base station bs exchanges information with multiple multiantenna mobile stations via a multi antenna relay station rs we propose a novel two way relaying scheme to approach the sum capacity of the mimo ctwrc a key contribution of this work is a new nonlinear lattice based precoding technique to precompensate the interstream interference so as to achieve efficient interference free lattice decoding at the relay we derive sufficient conditions for the proposed scheme to asymptotically achieve the sum capacity of the mimo ctwrc in the high signal to noise ratio snr regime to fully exploit the potential of the proposed scheme we also investigate the optimal power allocation at the bs and the rs to maximize the weighted sum rate of the mimo ctwrc in the general snr regime it is shown that the problem can be formulated as a monotonic program and a polyblock outer approximation algorithm is developed to find the globally optimal solution with guaranteed convergence we demonstrate by numerical results that the proposed scheme significantly outperforms the existing schemes and closely approaches the sum capacity of the mimo ctwrc in the high snr regime

volume of fluid interface tracking with smoothed surface stress methods for three dimensional flows motivated by the need for three dimensional methods for interface calculations that can deal with topology changes we describe a numerical scheme built from a volume of fluid interface tracking technique that uses a piecewise linear interface calculation in each cell momentum balance is computed using explicit finite volume finite differences on a regular cubic grid surface tension is implemented by the continuous surface stress or continuous surface force method examples and verifications of the method are given by comparing simulations to analytical results and experiments for sedimenting droplet arrays and capillary waves at finite reynolds number in the case of a pinching pendant drop both three dimensional and axisymmetric simulations are compared to experiments agreement is found both before and after the reconnections

numerical methods for tracking interfaces an overview is given of special numerical methods for tracking discontinuous fronts and interfaces these methods include surface tracking methods based on connected marker points along the interface volume tracking methods that track the volume occupied by the solution regions bounded by the interfaces and moving mesh methods where the underlying mesh is aligned and moved with the interface the pros and cons of the current methods are discussed and a new method is proposed that overcomes some of the difficulties encountered in approximating equations with multiple interacting interfaces

monotonic optimization framework for coordinated beamforming in multicell networks intercell interference is the major limiting factor in wireless multicell networks recently it has been shown that significant performance gains can be achieved by cooperation among base stations different degrees of cooperation are possible in this paper cooperation in the form of intercell interference management is considered the base stations are equipped with multiple antennas while the mobile terminals only have a single antenna the base stations jointly coordinate beamforming and scheduling and thus perform a weaker form of cooperation among base stations than suggested in recently proposed joint transmission techniques the terminals treat intercell interference as noise the corresponding resource allocation problem is cast as a utility maximization problem which includes common performance objectives such as the arithmetic mean the geometric mean and the max min operation of achievable user rates the resulting utility maximization problem is a nonconvex optimization problem after a suitable reformulation the problem can be solved to global optimality using the framework of monotonic optimization although the numerical complexity of the proposed method is exponential the reformulation step leads to an optimization problem which only scales in the number of mobile terminals instead of the entire set of physical layer parameters in essence the proposed framework represents a powerful tool for computing benchmarks for certain scenarios and utility functions under jointly optimal beamforming and scheduling

time delay estimation via cross correlation in the presence of large estimation errors the estimate of the difference in time of arrival of a common random signal received at two sensors each of which also receives uncorrelated noise is examined for both small and large estimation errors it is shown that as the post integration signal to noise ratio decreases the correlator exhibits a thresholding effect that is the probability of a large error an anomalous estimate increases rapidly approximate theoretical results for the probability of an anomaly are presented and are verified experimentally the variance of the time delay estimate is examined for both a gated mode in which the time delay corresponding to the correlation peak closest to the true time delay is used as the estimate of time delay and an ungated mode in which the time delay corresponding to the largest peak over the full range of the correlator delay times is used as the estimate the observed variance for both modes is compared with the theoretical variance based on a small error analysis for the gated modes the signal to noise ratio below which the observed variance begins to differ significantly from the small error theory can be reliably predicted from a linearity criterion it is shown however that the expected variance for the ungated mode can depart from the small error theory at a higher signal to noise ratio than for the gated modes thus the variance due to anomalies can be the most important factor in determining the region of applicability of the small error analysis

pressure based compressible calculation method utilizing total variation diminishing schemes a pressure based implicit procedure to solve the euler and navier stokes equations on a nonorthogonal mesh with collocated finite volume formulation is described the boundedness criteria for this procedure are determined from total variation diminishing tvd schemes which are based on characteristic variables and are applied to the fluxes of the convected quantities including mass flow rate the procedure incorporates the e eddy viscosity turbulence model the algorithm is first tested for inviscid flows at different mach numbers ranging from subsonic to supersonic on a bump in a channel geometry where the results are compared with other existing numerical solutions the method is then validated against experiment and another numerical solution for the case of turbulent transonic flow through a gas turbine rotor blade cascade for which wind tunnel experimental data exist

an adaptive method of lines with error control for parabolic equations of the reaction diffusion type abstract a piecewise linear finite element based method of lines is presented for the numerical solution of coupled parabolic partial differential equations which model biological and physicochemical reaction diffusion processes in one space dimension the vertial lines emanating from the space nodes in this method change at automatically selected times when in order to control a norm of the space discretization error adaptive spatial regridding occurs the regridding algorithm is an extension of one described previously by the authors 7 and is implemented in the program femol 1 which uses the lsodi package 14 15 of hindmarsh and painter to integrate the ordinary differential equations in time along the vertical lines computational results show that the method is efficient that a posteriori estimates of the space discretization error are accurate and that the adaptive procedure reliably controls the space discretization error

a simplified adaptive mesh technique derived from the moving finite element method an adaptive mesh technique is derived as a constrained minimization of the functional used in the moving finite element mfe method the result is a matrix equation for mesh velocities alone i e a pure adaptive mesh prescription the method retains many attractive features of mfe including the ability to independently control mesh motion through penalty terms

on the determination of the position of extrema of sampled correlators the problem of determination of the position of the extremum of a continuous correlator function from its samples if the spectrum of the correlator is not bandlimited is discussed searching for the position of the extremum by fitting a parabola through three samples around that extremum leads to clustering of the estimates around values corresponding with the sampling moments

some aspects of high speed blunt body flow computations with roe scheme this paper discusses some aspects of three dimensional supersonic and hypersonic inviscid blunt body flow computations the method used is based on the solution of the euler equations employing an explicit upwind total variation diminishing formulation of the roe riemann solver within the cell centered finite volume approach a comparative study of various total variation diminishing limiters and entropy fixes is carried out to identify the most appropriate combination the effect of using cell spacing in the total variation diminishing extrapolations is highlighted furthermore a mach number dependence and grid sensitivity study is carried out on various total variation diminishing limiters scaled with mesh spacing local time stepping and code parallelization has been employed to accelerate convergence in terms of effective wall clock times

space time discontinuous galerkin finite element method for two fluid flows a novel numerical method for two fluid flow computations is presented which combines the space time discontinuous galerkin finite element discretization with the level set method and cut cell based interface tracking the space time discontinuous galerkin stdg finite element method offers high accuracy an inherent ability to handle discontinuities and a very local stencil making it relatively easy to combine with local hp refinement the front tracking is incorporated via cut cell mesh refinement to ensure a sharp interface between the fluids to compute the interface dynamics the level set method lsm is used because of its ability to deal with merging and breakup also the lsm is easy to extend to higher dimensions small cells arising from the cut cell refinement are merged to improve the stability and performance the interface conditions are incorporated in the numerical flux at the interface and the stdg discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative the numerical method is applied to one and two dimensional two fluid test problems using the euler equations

two phase flows on interface refined grids modeled with vof staggered finite volumes and spline interpolants abstract a two phase 2d model that combines the volume of fluid vof method with implicit staggered finite volumes discretization of the navier stokes equation is presented staggered finite volumes are developed on the basis of nonconforming crouzeix raviart finite elements where all components of the velocity lie in the middle of the element edges and the pressure degrees of freedom are found in the centers of mass of the elements staggered finite volumes extend marker and cell mac regular staggered grids to unstructured mesh a linear saddle point problem resulting from either the discretization or the newton method is solved for all unknown pressures and velocities interface is represented with spline interpolants which follow the vof distribution adaptive mesh refinement is used to obtain a high level of uniform refining at the domain of dependence of the interface the aligned grid is obtained by irregular refining of the cells which are intersected by a curve the boundaries of its elements coincide with the slope segments going through the intersections of the curve with the underlying regular elements boundary the deformable computational grids are used only to discretize the navier stokes equation the advection of volume fractions is done on the advection mesh which corresponds to highest regular refining on the computational grid approximation of the surface tension on spline interpolants offers a straightforward way to describe correctly the pressure jumps on interface fitted staggered grids this allows deletion of the anomalous currents around a statical bubble and their effective reduction in real simulations on the aligned grid the continuity of the viscous stress is modeled exactly due to the finite volume approach using the proposed numerical techniques single bubble rise is analyzed

a numerical method for two phase flow with an unstable interface abstract the random choice method is used to compute the oil water interface for two dimensional porous media equations the equations used are a pair of coupled equations the elliptic pressure equation and the hyperbolic saturation equation the equations do not include the dispersive capillary pressure term and the computation does not introduce numerical diffusion the method resolves saturation discontinuities sharply the main conclusion of this paper is that the random choice is a correct numerical procedure for this problem even in the highly fingered case two methods of inducing fingers are considered deterministically through choice of cauchy data and heterogeneity through maximizing the randomness of the random choice method

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

achieving 1 2 log 1 snr on the awgn channel with lattice encoding and decoding we address an open question regarding whether a lattice code with lattice decoding as opposed to maximum likelihood ml decoding can achieve the additive white gaussian noise awgn channel capacity we first demonstrate how minimum mean square error mmse scaling along with dithering lattice randomization techniques can transform the power constrained awgn channel into a modulo lattice additive noise channel whose effective noise is reduced by a factor of spl radic 1 snr snr for the resulting channel a uniform input maximizes mutual information which in the limit of large lattice dimension becomes 1 2 log 1 snr i e the full capacity of the original power constrained awgn channel we then show that capacity may also be achieved using nested lattice codes the coarse lattice serving for shaping via the modulo lattice transformation the fine lattice for channel coding we show that such pairs exist for any desired nesting ratio i e for any signal to noise ratio snr furthermore for the modulo lattice additive noise channel lattice decoding is optimal finally we show that the error exponent of the proposed scheme is lower bounded by the poltyrev exponent

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

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

time delay estimation of chirp signals in the fractional fourier domain a new time delay estimator is presented in this paper it is evaluated based on the delay property of the fractional fourier transform with less computation and is suitable for chirp signals the statistical analysis in terms of signal to noise ratio snr and estimation accuracy for this estimation is also studied the proposed method for the time delay yields a variance which is theoretically equal to the cramer rao lower bound the validity of this estimation method is demonstrated via simulations

asymptotic capacity of the separated mimo two way relay channel a multiple input multiple output two way relay channel consisting of two communication nodes and a full duplex relay node in which no direct link exists between the two communication nodes is considered we propose an achievable scheme that employs horizontally encoded lattice codes combined with generalized singular value decomposition based precoding for the first phase the second phase of the proposed scheme follows the fundamentals of the previous scheme which uses vertically encoded structural bining with the only difference that the added codeword of the two codewords from the communication nodes instead of those two individual codewords is decoded and retransmitted in the proposed scheme we show that the proposed scheme achieves the cut set bound asymptotically as the signal to noise ratios of the channels tend to infinity

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

new perspectives for maximum likelihood time delay estimation this paper introduces a new realization for maximum likelihood time delay estimation tde that illuminates the relationships between maximum likelihood tde and other methods we obtain the result by deriving the likelihood function using a fundamental method that appears to be new to the field of array processing this method is a natural complement to the generalized karhunen loeve expansion

moving mesh methods with locally varying time steps the time steps associated with moving mesh methods are proportional to the smallest mesh size in space and as a result they are very small at each time level for some practical problems the physical phenomena develop dynamically singular or nearly singular solutions in fairly localized regions and therefore the smallest time step at each time level occurs only in these localized regions in this work we will develop a local time stepping algorithm for the moving mesh methods the principal idea will be demonstrated by investigating the nonlinear hyperbolic conservation laws numerical experiments are carried out to demonstrate the efficiency and robustness of the proposed methods

an approximate riemann solver for shallow water equations and heat advection in horizontal centrifugal casting an approximate riemann solver was developed for solving modified shallow water equations swe and energy transport describing the average flow dynamics of a single layer spreading inside a horizontally rotating cylinder the numerical model was particularly developed for simulating the horizontal centrifugal casting hsc of the outer shell of a work roll the swe were derived in the rotating frame of reference therefore fictitious forces the centrifugal force and the coriolis force were considered in addition other forces such as the bed shear force the force of gravity the wind shear force and forces arising from the variable liquid solid interface were taken into account the jacobian matrix of the nonlinear hyperbolic system of pdes was decomposed into a set of eigenvalues and corresponding eigenvectors using standard and corrected roe averages a harten hyman entropy fix was used to prevent expansion shocks entropy violating solutions typically occurring during transonic rarefactions source terms were applied as a stationary discontinuity and were physically bounded and well balanced for steady states producing non oscillatory solutions each wave was upwinded using the explicit godunov s method the high resolution corrections with flux limiters were used to achieve second order of accuracy and dispersion free solutions at discontinuities in addition to the riemann solver a central scheme fv model was used to solve the heat diffusion inside the cylinder mold and partially solidified liquid layer coupled with the solidification model several simulations were performed results were analyzed and discussed