polarization phase relationships via multiple morse wavelets ii data analysis three examples are provided of the use of multiple generalized morse wavelets for polarization analysis of three component recordings where phase relationships between components of the signal are transient the example three component signals are i synthetic ii the radial transverse and vertical components of an earthquake and iii the radial transverse and normal components of the solar magnetic field measured by the ulysses spacecraft upstream of an interplanetary shock working in the scale time plane a b the multiple wavelet approach detects coherent motion with elliptical polarization in all three cases our graphical presentations fully take into account restrictions imposed by two factors the minimum usable scale and wraparound effects caused by fourier transform computations and consequently a maximum usable scale

the hilbert spectrum via wavelet projections non stationary signals are increasingly analysed in the time frequency domain to determine the variation of frequency components with time it was recently proposed in this journal that such signals could be analysed by projections onto the time frequency plane giving a set of monocomponent signals these could then be converted to analytic signals using the hilbert transform and their instantaneous frequency calculated which when weighted by the energy yields the hilbert energy spectrum for that projection agglomeration over projections yields the complete hilbert spectrum we show that superior results can be obtained using waveletbased projections the maximal overlap undecimated stationary translation invariant discrete wavelet transform and wavelet packet transforms are used with

a high order hybridizable discontinuous galerkin method with fast convergence to steady state solutions of the gas kinetic equation abstract the mass flow rate of poiseuille flow of rarefied gas through long ducts of two dimensional cross sections with arbitrary shape is critical in the pore network modeling of gas transport in porous media here for the first time the high order hybridizable discontinuous galerkin hdg method is used to find the steady state solution of the linearized bhatnagar gross krook equation on two dimensional triangular meshes the velocity distribution function and its traces are approximated in piecewise polynomial spaces of degree up to 4 on the triangular meshes and mesh skeletons respectively by employing a numerical flux that is derived from the first order upwind scheme and imposing its continuity weakly on the mesh skeletons global systems for unknown traces are obtained with fewer coupled degrees of freedom when compared to the original discontinuous galerkin formulation to achieve fast convergence to the steady state solution a diffusion like equation for flow velocity which is asymptotic preserving into the fluid dynamic limit is solved by the hdg simultaneously on the same meshes the proposed hdg synthetic iterative scheme is proved to be accurate and efficient specifically for flows in the near continuum regime numerical simulations have shown that to achieve the same level of accuracy our scheme could be faster than the conventional iterative scheme by two orders of magnitude also it is faster than the synthetic iterative scheme based on the finite difference discretization in the spatial space by one order of magnitude in addition the implicit hdg method is more efficient than an explicit discontinuous galerkin gas kinetic solver as well as the implicit discontinuous galerkin scheme when the degree of approximating polynomial is larger than 2 the hdg synthetic iterative scheme is ready to be extended to simulate rarefied gas mixtures and the boltzmann collision operator

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

studies of spectral properties of short genes using the wavelet subspace hilbert huang transform wshht abstract this paper presents a new algorithm for the analysis of spectral properties of short genes using the wavelet transform and the hilbert huang transform hht a wavelet subspace algorithm combined with the empirical mode decomposition emd is introduced to create subdivided intrinsic mode functions imfs and a cross correlation analysis is applied to remove pseudo spectral components experiments are carried out on dna sequences with the double base db curve representation and the results show that the signal to noise ratio of buried signals can be enhanced using the proposed method yielding significant patterns that are rarely observed with conventional methods the wavelet subspace hilbert huang transform wshht algorithm is able to correctly identify spectral patterns of very short genes below 70 bp in dna sequences

the discrete multiple wavelet transform and thresholding methods we propose thresholding for multiwavelets considering the coefficient vectors as a whole rather than thresholding individual elements a multivariate universal threshold is obtained using the spl chi sup 2 distribution simulations indicate that using the ghm multiwavelet with appropriate preprocessing our method outperforms univariate thresholding of both ghm and daubechies wavelet decompositions

lattice boltzmann simulations on irregular grids introduction of the natrium library the lattice boltzmann method is a modern approach to simulate fluid flow in its original formulation it is restricted to regular grids second order discretizations and a unity cfl number this paper describes our new off lattice boltzmann solver natrium an extensible and parallel c code to perform lattice boltzmann simulations on irregular grids natrium also allows high order spatial discretizations and non unity cfl numbers to be used we demonstrate how these features can efficiently decrease the number of grid points required in a simulation and thus reduce the computational time compared to the standard lattice boltzmann method we detail the implementation of a recently proposed semi lagrangian lattice boltzmann method and prove its efficiency in comparisons to other state of the art off lattice boltzmann schemes

analytic wavelet thresholding summary we introduce so called analytic stationary wavelet transform thresholding where using the discrete hilbert transform we create a complex valued analytic vector from which an amplitude vector is defined thresholding of a real valued wavelet coefficient at some transform level is carried out according to the corresponding value in this amplitude vector relevant statistical results follow from properties of the discrete hilbert transform analytic stationary wavelet transform thresholding is found to produce consistently a reduced mean squared error compared to using standard stationary wavelet transform or cycle spinning thresholding for signals with extensive oscillations at some transform levels this improvement is very marked furthermore we show that our thresholding test is invariant to phase shifts in the data whereas if complex wavelet filters are being used the filters must be analytic or anti analytic at each level of the wavelet transform

a local variational theory for the schmidt metric we study local variations of causal curves in a space time with respect to b length or generalized affine parameter length in a convex normal neighbourhood causal curves of maximal metric length are geodesics using variational arguments we show that causal curves of minimal b length in sufficiently small globally hyperbolic sets are geodesics as an application we obtain a generalization of a theorem by schmidt showing that the cluster curve of a partially future imprisoned future inextendible and future b incomplete curve must be a null geodesic we give examples which illustrate that the cluster curve does not have to be closed or incomplete the theory of variations developed in this work provides a starting point for a morse theory of b length

minimax threshold for denoising complex signals with waveshrink for the problem of signal extraction from noisy data waveshrink has proven to be a powerful tool both from an empirical and an asymptotic point of view waveshrink is especially efficient at estimating spatially inhomogeneous signals a key step of the procedure is the selection of the threshold parameter donoho and johnstone 1994 propose a selection of the threshold based on a minimax principle their derivation is specifically for real signals and real wavelet transforms in this paper we propose to extend the use of waveshrink to denoising complex signals with complex wavelet transforms we illustrate the problem of denoising complex signals with an electronic surveillance application

genericity of nondegeneracy for light rays in stationary spacetimes given a lorentzian manifold m g an event p and an observer u in m then p and u are light conjugate if there exists a lightlike geodesic 0 1 m joining p and u whose endpoints are conjugate along using functional analytical techniques we prove that if one fixes p and u in a differentiable manifold m then the set of stationary lorentzian metrics in m for which p and u are not light conjugate is generic in a strong sense the result is obtained by reduction to a finsler geodesic problem via a second order fermat principle for light rays and using a transversality argument in an infinite dimensional banach manifold setup

real nonparametric regression using complex wavelets summary wavelet shrinkage is an effective nonparametric regression technique especially when the underlying curve has irregular features such as spikes or discontinuities the basic idea is simple take the discrete wavelet transform dwt of data consisting of a signal corrupted by noise shrink or remove the wavelet coefficients to remove the noise and then invert the dwt to form an estimate of the true underlying curve various authors have proposed increasingly sophisticated methods of doing this using real valued wavelets complex valued wavelets exist but are rarely used we propose two new shrinkage techniques which use complex valued wavelets extensive simulations show that our methods almost always give significantly more accurate estimates when compared with methods based on real valued wavelets further one of our methods is both simpler and dramatically faster than its competitors in an attempt to understand the excellent performance of this latter method we present a new risk bound on its hard thresholded coefficients

hyperanalytic denoising a new threshold rule for the estimation of a deterministic image immersed in noise is proposed the full estimation procedure is based on a separable wavelet decomposition of the observed image and the estimation is improved by introducing the new threshold to estimate the decomposition coefficients the observed wavelet coefficients are thresholded using the magnitudes of wavelet transforms of a small number of replicates of the image the replicates are calculated by extending the image into a vector valued hyperanalytic signal more than one hyperanalytic signal may be chosen and either the hypercomplex or riesz transforms are used to calculate this object the deterministic and stochastic properties of the observed wavelet coefficients of the hyperanalytic signal at a fixed scale and position index are determined a universal threshold is calculated for the proposed procedure an expression for the risk of an individual coefficient is derived the risk is calculated explicitly when the universal threshold is used and is shown to be less than the risk of universal hard thresholding under certain conditions the proposed method is implemented and the derived theoretical risk reductions substantiated

the fermat principle in general relativity and applications in this paper we use a general version of fermat s principle for light rays in general relativity and a curve shortening method to write the morse relations for light rays joining an event with a smooth timelike curve in a lorentzian manifold with boundary the morse relations are obtained under the most general assumptions and one can apply them to have a mathematical description of the gravitational lens effect in a very general context moreover morse relations can be used to check if existing models are corrected

semi lagrangian implicit bhatnagar gross krook collision model for the finite volume discrete boltzmann method in order to increase the accuracy of temporal solutions reduce the computational cost of time marching and improve the stability associated with collisions for the finite volume discrete boltzmann method an advanced implicit bhatnagar gross krook bgk collision model using a semi lagrangian approach is proposed in this paper unlike existing models in which the implicit bgk collision is resolved either by a temporal extrapolation or by a variable transformation the proposed model removes the implicitness by tracing the particle distribution functions pdfs back in time along their characteristic paths during the collision process an interpolation scheme is needed to evaluate the pdfs at the traced back locations by using the first order interpolation the resulting model allows for the straightforward replacement of f eq n 1 by f eq n no matter where it appears after comparing the proposed model with the existing models under different numerical conditions e g different flux schemes and time marching schemes and using the proposed model to successfully modify the variable transformation technique three conclusions can be drawn first the proposed model can improve the accuracy by almost an order of magnitude second it can slightly reduce the computational cost therefore the proposed scheme improves accuracy without extra cost finally the proposed model can significantly improve the t limit compared to the temporal interpolation model while having the same t limit as the variable transformation approach the proposed scheme with a second order interpolation is also developed and tested however that technique displays no advantage over the simple first order interpolation approach both numerical and theoretical analyses are also provided to explain why the developed implicit scheme with simple first order interpolation can outperform the same scheme with second order interpolation as well as the existing temporal extrapolation and variable transformation schemes

a fast iterative scheme for the linearized boltzmann equation iterative schemes to find steady state solutions to the boltzmann equation is efficient for highly rarefied gas flows but can be very slow to converge in the near continuum flow regime in this paper a synthetic iterative scheme is developed to speed up the solution of the linearized boltzmann equation by penalizing the collision operator l into the form l l n delta h n delta h where delta is the gas rarefaction parameter h is the velocity distribution function and n is a tuning parameter controlling the convergence rate the velocity distribution function is first solved by the conventional iterative scheme then it is corrected such that the macroscopic flow velocity is governed by a diffusion type equation that is asymptotic preserving into the navier stokes limit the efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration as well as solving for poiseuille and thermal transpiration flows we find that the fastest convergence of our synthetic scheme for the linearized boltzmann equation is achieved when n delta is close to the average collision frequency the synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near continuum gas flow regimes moreover due to its asymptotic preserving properties the synthetic iterative scheme does not need high spatial resolution in the near continuum flow regime which makes it even faster than the conventional iterative scheme using this synthetic scheme with the fast spectral approximation of the linearized boltzmann collision operator poiseuille and thermal transpiration flows between two parallel plates through channels of circular rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction finally the flow of a ne ar gas mixture is solved based on the linearized boltzmann equation with the lennard jones intermolecular potential for the first time and the difference between these results and those using the hard sphere potential is discussed

a multi dimensional high order discontinuous galerkin method based on gas kinetic theory for viscous flow computations this paper presents a high order discontinuous galerkin dg method based on a multi dimensional gas kinetic evolution model for viscous flow computations generally the dg methods for equations with higher order derivatives must transform the equations into a first order system in order to avoid the so called non conforming problem in the traditional dg framework the inviscid and viscous fluxes are numerically treated differently differently from the traditional dg approaches the current method adopts a kinetic evolution model for both inviscid and viscous flux evaluations uniformly by using a multi dimensional gas kinetic formulation we can obtain a spatial and temporal dependent gas distribution function for the flux integration inside the cell and at the cell interface which is distinguishable from the gaussian quadrature point flux evaluation in the traditional dg method besides the initial higher order non equilibrium states inside each control volume a linear least square lls method is used for the reconstruction of smooth distributions of macroscopic flow variables around each cell interface in order to construct the corresponding equilibrium state instead of separating the space and time integrations and using the multistage runge kutta time stepping method for time accuracy the current method integrates the flux function in space and time analytically which subsequently saves the computational time many test cases in two and three dimensions which include high mach number compressible viscous and heat conducting flows and the low speed high reynolds number laminar flows are presented to demonstrate the performance of the current scheme

discrete unified gas kinetic scheme for all knudsen number flows low speed isothermal case based on the boltzmann bgk bhatnagar gross krook equation in this paper a discrete unified gas kinetic scheme dugks is developed for low speed isothermal flows the dugks is a finite volume scheme with the discretization of particle velocity space after the introduction of two auxiliary distribution functions with the inclusion of collision effect the dugks becomes a fully explicit scheme for the update of distribution function furthermore the scheme is an asymptotic preserving method where the time step is only determined by the courant friedricks lewy condition in the continuum limit numerical results demonstrate that accurate solutions in both continuum and rarefied flow regimes can be obtained from the current dugks the comparison between the dugks and the well defined lattice boltzmann equation method d2q9 is presented as well

a widely linear complex autoregressive process of order one we propose a simple stochastic process for modeling improper or noncircular complex valued signals the process is a natural extension of a complex valued autoregressive process extended to include a widely linear autoregressive term this process can then capture elliptical as opposed to circular stochastic oscillations in a bivariate signal the process is order one and is more parsimonious than alternative stochastic modeling approaches in the literature we provide conditions for stationarity and derive the form of the covariance and relation sequence of this model we describe how parameter estimation can be efficiently performed both in the time and frequency domain we demonstrate the practical utility of the process in capturing elliptical oscillations that are naturally present in seismic signals

applications of complex valued wavelet transforms to subband decomposition a method for constructing complex valued linear phase fir conjugate quadrature filters and associated wavelet bases is described each filter is derived by replating certain zeros of a real valued fir conjugate quadrature filter by their reciprocal conjugates the derived filters have the same frequency response magnitudes as the original filters and their linear phase property permits the use of symmetrization in subband decomposition to avoid border discontinuities that result from signal periodization subband decomposition and reconstruction using both a length 6 filter associated with a daubechies 1988 wavelet bases and a related length 6 complex valued linear phase filter are compared to illustrate the reduced border effects

noise covariance properties in dual tree wavelet decompositions dual tree wavelet decompositions have recently gained much popularity mainly due to their ability to provide an accurate directional analysis of images combined with a reduced redundancy when the decomposition of a random process is performed which occurs in particular when an additive noise is corrupting the signal to be analyzed it is useful to characterize the statistical properties of the dual tree wavelet coefficients of this process as dual tree decompositions constitute over complete frame expansions correlation structures are introduced among the coefficients even when a white noise is analyzed in this paper we show that it is possible to provide an accurate description of the covariance properties of the dual tree coefficients of a wide sense stationary process the expressions of the cross covariance sequences of the coefficients are derived in the one and two dimensional cases asymptotic results are also provided allowing to predict the behavior of the second order moments for large lag values or at coarse resolution in addition the cross correlations between the primal and dual wavelets which play a primary role in our theoretical analysis are calculated for a number of classical wavelet families simulation results are finally provided to validate these results

local directional denoising denoising of complex valued signals involves the relationships between the real and imaginary parts of the signal the authors introduce the idea of local directional thresholding well suited to signals that are bidirectional overall but unidirectional at any one time such as doppler ultrasound and show its efficacy on synthetic and real data

infinite dimensional morse theory and fermat s principle in general relativity i the following theorem may be viewed as the general relativistic version of fermat s principle among all lightlike curves connecting a given point p to a given timelike curve in a lorentzian manifold the geodesics are characterized by stationary arrival time here arrival time refers to a smooth parametrization of in this article the first steps are taken to make infinite dimensional morse theory applicable to this variational problem the space of trial curves is made into a hilbert manifold by imposing an h2 sobolev condition and fermat s principle is reformulated in this infinite dimensional setting moreover a morse index theorem is presented the mathematical formalism developed here aims at applications to the gravitational lens effect

analysis and assessment of the no slip and slip boundary conditions for the discrete unified gas kinetic scheme the discrete unified gas kinetic scheme dugks with a force term is a finite volume solver for the boltzmann equation unlike the standard lattice boltzmann method lbm dugks can be applied on nonuniform grids for both the lbm and dugks the boundary conditions need to be processed through the density distribution function so researchers introduced the boundary conditions from the lbm frame into the dugks however the accuracy of these boundary conditions in the dugks has not been studied thoroughly through strict theoretical deduction we find that the bounce back bb scheme leads to a different dependence of the numerical error term in the dugks as compared to the lbm the error term is influenced by the relaxation time and the body force and it can be reduced by lowering the kinetic viscosity unlike the bb scheme the nonequilibrium bounce back scheme has the ability to implement real no slip boundary condition furthermore two slip boundary conditions incorporated with navier s slip model are introduced from the lbm framework into the dugks the tangential momentum change based tmac scheme can be used directly in the dugks because it generates no numerical error term in the dugks for the combination of the bounce back and specular reflection schemes bsr the relation between the slip length and the combination parameter should be modified in accordance with the numerical error term analysis shows that the tmac scheme can simulate a wider range of slip length than the bsr scheme numerical simulations of the couette flow and the poiseuille flow confirm our theoretical analysis

deconvolution bandwidth and the trispectrum abstract in the largest application area of time series analysis geophysical exploration the underlying innovations sequence is of primary interest and must be estimated this sequence is estimated by deconvolving the non gaussian noninvertible time series this involves estimation of a phase shift correction from the time series which can be carried out by maximizing the kurtosis of the series unfortunately the method is hampered by the fact that the time series is typically deficient in power in certain bands of frequencies band limited the consequences of this can be analyzed by studying the trispectrum the third of the polyspectra of the series this reveals two important results first we are able to easily appreciate why for certain types of band limitation kurtosis cannot be used to determine a phase correction second by looking at the inner and outer subvolumes of the support volume for the discrete parameter trispectrum we see that for the standard linear model the trispectrum is no

the monogenic wavelet transform this paper extends the 1 d analytic wavelet transform to the 2 d monogenic wavelet transform the transformation requires care in its specification to ensure suitable transform coefficients are calculated and it is constructed so that the wavelet transform may be considered as both local and monogenic this is consistent with defining the transform as a real wavelet transform of a monogenic signal in analogy with the analytic wavelet transform classes of monogenic wavelets are proposed with suitable local properties it is shown that the monogenic wavelet annihilates anti monogenic signals that the monogenic wavelet transform is phase shift covariant and that the transform magnitude is phase shift invariant a simple form for the magnitude and orientation of the isotropic transform coefficients of a unidirectional signal when observed in a rotated frame of reference is derived the monogenic wavelet ridges of local plane waves are given

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

a finite difference lattice boltzmann method with second order accuracy of time and space for incompressible flow abstract in this paper a kind of finite difference lattice boltzmann method with the second order accuracy of time and space t2s2 fdlbm is proposed in this method a two stage time accurate discretization approach is applied to construct time marching scheme and the spatial gradient operator is discretized by a mixed difference scheme to maintain a second order accuracy in space it is shown that the previous finite difference lattice boltzmann method fdlbm guo and zhao 2003 is a special case of the t2s2 fdlbm through the von neumann analysis the stability of the method is analyzed and two specific t2s2 fdlbms are discussed the two t2s2 fdlbms are applied to simulate some incompressible flows with the non uniform grids compared with other high order fdlbms this two t2s2 fdlbms keep the simplicity of standard lattice boltzmann method compared with the previous fdlbm and lattice boltzmann method the two t2s2 fdlbms are more accurate and more stable the value of the courant friedrichs lewy condition number in our method can be up to 0 9 which also significantly improves the computational efficiency

a generalized demodulation approach to time frequency projections for multicomponent signals in this paper we introduce a flexible approach for the time frequency analysis of multicomponent signals involving the use of analytic vectors and demodulation the demodulated analytic signal is projected onto the time frequency plane so that as closely as possible each component contributes exclusively to a different tile in a wavelet packet tiling of the time frequency plane and at each time instant the contribution to each tile definitely comes from no more than one component a single reverse demodulation is then applied to all projected components the resulting instantaneous frequency of each component in each tile is not constrained to a set polynomial form in time and is readily calculated as is the corresponding hilbert energy spectrum two examples illustrate the method in order better to understand the effect of additive noise the approximate variance of the estimated instantaneous frequency in any tile has been formulated by starting with pure noise and studying its evolving covariance structure through each step of the algorithm the validity and practical utility of the resulting expression for the variance of the estimated instantaneous frequency is demonstrated via a simulation experiment

the homomorphic analytic signal this paper introduces an alternative form of analytic signal that is formed using homomorphic signal processing techniques it may be generated for signals that demonstrate redundancy in their pole zero distributions such as phase signals and real signals the analytic signal is formed by manipulating the positions of the signal s nonminimum phase poles and zeros to create a minimum phase signal a factorization of real signals is presented that demonstrates the properties of the homomorphic analytic signal and a new definition of instantaneous frequency is developed examples are given to verify the theory and comparisons with the linear analytic signal and instantaneous frequency are made

computing the discrete time analytic signal via fft starting with a real valued n point discrete time signal frequency domain algorithms are provided for computing 1 the complex valued standard n point discrete time analytic signal of the same sample rate 2 the complex valued decimated n 2 point discrete time analytic signal of half the original sample rate and 3 the complex valued interpolated nm point discrete time analytic signal of m times the original sample rate special adjustment of the transform end points are shown to be necessary in order to generate proper discrete time analytic signals

implicit gas kinetic unified algorithm based on multi block docking grid for multi body reentry flows covering all flow regimes based on the previous researches of the gas kinetic unified algorithm gkua for flows from highly rarefied free molecule transition to continuum a new implicit scheme of cell centered finite volume method is presented for directly solving the unified boltzmann model equation covering various flow regimes in view of the difficulty in generating the single block grid system with high quality for complex irregular bodies a multi block docking grid generation method is designed on the basis of data transmission between blocks and the data structure is constructed for processing arbitrary connection relations between blocks with high efficiency and reliability as a result the gas kinetic unified algorithm with the implicit scheme and multi block docking grid has been firstly established and used to solve the reentry flow problems around the multi bodies covering all flow regimes with the whole range of knudsen numbers from 10 to 3 7e6 the implicit and explicit schemes are applied to computing and analyzing the supersonic flows in near continuum and continuum regimes around a circular cylinder with careful comparison each other it is shown that the present algorithm and modelling possess much higher computational efficiency and faster converging properties the flow problems including two and three side by side cylinders are simulated from highly rarefied to near continuum flow regimes and the present computed results are found in good agreement with the related dsmc simulation and theoretical analysis solutions which verify the good accuracy and reliability of the present method it is observed that the spacing of the multi body is smaller the cylindrical throat obstruction is greater with the flow field of single body asymmetrical more obviously and the normal force coefficient bigger while in the near continuum transitional flow regime of near space flying surroundings the spacing of the multi body increases to six times of the diameter of the single body the interference effects of the multi bodies tend to be negligible the computing practice has confirmed that it is feasible for the present method to compute the aerodynamics and reveal flow mechanism around complex multi body vehicles covering all flow regimes from the gas kinetic point of view of solving the unified boltzmann model velocity distribution function equation

on the analytic wavelet transform an exact and general expression for the analytic wavelet transform of a real valued signal is constructed resolving the time dependent effects of nonnegligible amplitude and frequency modulation the analytic signal is first locally represented as a modulated oscillation demodulated by its own instantaneous frequency and then taylor expanded at each point in time the terms in this expansion called the instantaneous modulation functions are time varying functions which quantify at increasingly higher orders the local departures of the signal from a uniform sinusoidal oscillation closed form expressions for these functions are found in terms of bell polynomials and derivatives of the signal s instantaneous frequency and bandwidth the analytic wavelet transform is shown to depend upon the interaction between the signal s instantaneous modulation functions and frequency domain derivatives of the wavelet inducing a hierarchy of departures of the transform away from a perfect representation of the signal the form of these deviation terms suggests a set of conditions for matching the wavelet properties to suit the variability of the signal in which case our expressions simplify considerably one may then quantify the time varying bias associated with signal estimation via wavelet ridge analysis and choose wavelets to minimize this bias

hybrid simulation combining two space time discretization of the discrete velocity boltzmann equation abstract despite the efficiency and low dissipation of the stream collide scheme of the discrete velocity boltzmann equation which is nowadays implemented in many lattice boltzmann solvers a major drawback exists over alternative discretization schemes i e finite volume or finite difference that is the limitation to cartesian uniform grids in this paper an algorithm is presented that combines the positive features of each scheme in a hybrid lattice boltzmann method in particular the node based streaming of the distribution functions is coupled with a second order finite volume discretization of the advection term of the boltzmann equation under the bhatnagar gross krook approximation the algorithm is established on a multi domain configuration with the individual schemes being solved on separate sub domains and connected by an overlapping interface of at least 2 grid cells a critical parameter in the coupling is the cfl number equal to unity which is imposed by the stream collide algorithm nevertheless a semi implicit treatment of the collision term in the finite volume formulation allows us to obtain a stable solution for this condition the algorithm is validated in the scope of three different test cases on a 2d periodic mesh it is shown that the accuracy of the combined discretization schemes agrees with the order of each separate scheme involved the overall numerical error of the hybrid algorithm in the macroscopic quantities is contained between the error of the two individual algorithms finally we demonstrate how such a coupling can be used to adapt to anisotropic flows with some gradual mesh refinement in the fv domain

numerical simulation of flows from free molecular regime to continuum regime by a dvm with streaming and collision processes a discrete velocity method dvm with streaming and collision processes is presented in this work for simulation of flows from free molecular regime to continuum regime the present scheme can be considered as a semi lagrangian like scheme at first we follow the conventional dvm to discretize the phase velocity space by a number of discrete velocities then for each discrete velocity the kinetic equation with bgk shakhov model is integrated in space and time within one time step as a result a simple algebraic formulation can be obtained and its solution can be marched in time by the streaming and collision processes however differently from the conventional semi lagrangian scheme the present scheme uses the muscl approach with van albada limiter in the process of reconstructing the distribution function at the surrounding points of the cell center and the transport distance is controlled in order to avoid extrapolation this makes the present scheme be capable of simulating the hypersonic rarefied flows in addition as compared to the unified gas kinetic scheme ugks the present scheme is simpler and easier for implementation thus the computational efficiency can be improved accordingly to validate the proposed numerical scheme test examples from free molecular regime to continuum regime are simulated numerical results showed that the present scheme can predict the flow properties accurately even for hypersonic rarefied flows

performance evaluation of the general characteristics based off lattice boltzmann scheme and dugks for low speed continuum flows the general characteristics based off lattice boltzmann scheme proposed by bardow et al 1 hereafter bardow s scheme and the discrete unified gas kinetic scheme dugks 2 are two methods that successfully overcome the time step restriction by the collision time which is commonly seen in many other kinetic schemes in this work we first perform a theoretical analysis of the two schemes in the finite volume framework by comparing their numerical flux evaluations it is found that the effect of collision term is considered in the evaluation of the cell interface distribution function in both schemes which explains why they can overcome the time step restriction and can give accurate results even as the time step is much larger than the collision time the difference between the two schemes lies in the treatment of the integral of the collision term when evaluating the cell interface distribution function in which bardow s scheme uses the rectangular rule while dugks uses the trapezoidal rule the performance of the two schemes i e accuracy stability and efficiency are then compared by simulating several two dimensional flows including the unsteady taylorgreen vortex flow the steady lid driven cavity flow and the laminar boundary layer problem it is observed that dugks can give more accurate results than bardow s scheme with a same mesh size furthermore the numerical stability of bardow s scheme decreases as the courantfriedrichslewy cfl number approaches to 1 while the stability of dugks is not affected by the cfl number apparently as long as cfl 1 it is also observed that dugks is twice as expensive as the bardow s scheme with the same mesh size

weighted l2 stability of a discrete kinetic approximation for the incompressible navier stokes equations on bounded domains abstract this paper is concerned with the stability of a discrete kinetic approximation with a boundary scheme introduced by the authors in a previous work we prove the weighted l 2 stability of the approximation by using an identity on three point difference schemes for convection equations with the weighted l 2 stability the convergence of the discrete kinetic approximation can be directly established moreover the present stability analysis particularly the identity on three point difference schemes may be adapted to other kinetic methods numerical experiments are conducted to verify our stability results

functional regularity properties for light rays in general relativity in this note we consider some functionals restricted to the nonholonomic constraint satisfied by lightlike curves in lorentzian manifolds these functionals are related to the arrival time map whose critical points are light rays in general relativity and they have been used in the variational theory of light rays in some recent literatures we exhibit an explicit example showing that from a functional point of view the constraint above does not have sufficient regularity nevertheless we show that up to a continuous change in coordinates the used functionals restricted to the constraint have just the regularity that one needs to develop lusternik schnirelmann theory or morse theory