on the muskat problem with viscosity jump global in time results abstract the muskat problem models the filtration of two incompressible immiscible fluids of different characteristics in porous media in this paper we consider both the 2d and 3d setting of two fluids of different constant densities and different constant viscosities in this situation the related contour equations are non local not only in the evolution system but also in the implicit relation between the amplitude of the vorticity and the free interface among other extra difficulties no maximum principles are available for the amplitude and the slopes of the interface in l we prove global in time existence results for medium size initial stable data in critical spaces we also enhance previous methods by showing smoothing instant analyticity improving the medium size constant in 3d together with sharp decay rates of analytic norms the found technique is twofold giving ill posedness in unstable situations for very low regular solutions

analysis of polynomial phase signals by the integrated generalized ambiguity function the aim of this work is the performance analysis of a method for the detection and parameter estimation of mono or multicomponent polynomial phase signals pps embedded in white gaussian noise and based on a generalized ambiguity function the proposed method is shown to be asymptotically efficient for second order pps and nearly asymptotically efficient for third order ppss the method presents some advantages with respect to similar techniques like the polynomial phase transform for example in terms of i a closer approach to the cramer rao lower bounds ii a lower snr threshold iii a better capability of discriminating multicomponent signals

comments on the cramer rao lower bounds for signals with constant amplitude and polynomial phase for original paper see ieee trans signal processing vol 39 p 749 52 march 1991 different expressions for the cramer rao lower bounds crlbs of constant amplitude polynomial phase signals embedded in white gaussian noise appear in the literature the present paper revisits the derivation of the bounds reported by peleg and porat 1991 and indicates that the resulting expressions depend on the interval over which the signal is defined the proper choice of the interval is the one that centers the signal around zero and results in the minimum lower bounds

on a thin film model with insoluble surfactant abstract this paper studies the existence and asymptotic behavior of global weak solutions for a thin film equation with insoluble surfactant under the influence of gravitational capillary and van der waals forces we prove the existence of global weak solutions for medium sized initial data in large function spaces moreover exponential decay towards the flat equilibrium state is established where an estimate on the decay rate can be computed explicitly

estimating parameters of multiple wideband polynomial phase sources in sensor arrays we consider the problem of estimating the parameters of multiple wideband polynomial phase signal pps sources in sensor arrays a new maximum likelihood ml direction of arrival doa estimator is introduced and the exact cramer rao bound crb is derived for the general case of multiple constant amplitude polynomial phase sources since the proposed exact ml estimator is computationally intensive an approximate solution is proposed originating from the analysis of the log likelihood ll function in the single chirp signal case as a result a new form of spatio temporal matched filter referred to as the chirp beamformer is derived which is applicable to well separated sources that have distinct time frequency or and spatial signatures this beamforming approach requires solving a three dimensional 3 d optimization problem and therefore enjoys essentially simpler implementation than that entailed by the exact ml simulation results are presented illustrating the performance of the estimators and validating our theoretical crb analysis

breakdown of smoothness for the muskat problem in this paper we show that there exists analytic initial data in the stable regime for the muskat problem such that the solution turns to the unstable regime and later breaks down that is no longer belongs to c4

contour dynamics of incompressible 3 d fluids in a porous medium with different densities we consider the problem of the evolution of the interface given by two incompressible fluids through a porous medium which is known as the muskat problem and in two dimensions it is mathematically analogous to the two phase hele shaw cell we focus on a fluid interface given by a jump of densities being the equation of the evolution obtained using darcy s law we prove local well posedness when the smaller density is above stable case and in the unstable case we show ill posedness

product high order ambiguity function for multicomponent polynomial phase signal modeling parameter estimation and performance analysis issues are studied for multicomponent polynomial phase signals ppss embedded in white gaussian noise identifiability issues arising with existing approaches are described first when dealing with multicomponent pps having the same highest order phase coefficients this situation is encountered in applications such as synthetic aperture radar imaging or propagation of polynomial phase signals through channels affected by multipath and is thus worthy of a careful analysis a new approach is proposed based on a transformation called product high order ambiguity function phaf the use of the phaf offers a number of advantages with respect to the high order ambiguity function haf more specifically it removes the identifiability problem and improves noise rejection capabilities performance analysis is carried out using the perturbation method and verified by simulation results

hierarchical computation in the canonical auditory cortical circuit sensory cortical anatomy has identified a canonical microcircuit underlying computations between and within layers this feed forward circuit processes information serially from granular to supragranular and to infragranular layers how this substrate correlates with an auditory cortical processing hierarchy is unclear we recorded simultaneously from all layers in cat primary auditory cortex ai and estimated spectrotemporal receptive fields strfs and associated nonlinearities spike triggered averaged strfs revealed that temporal precision spectrotemporal separability and feature selectivity varied with layer according to a hierarchical processing model strfs from maximally informative dimension mid analysis confirmed hierarchical processing of two cooperative mids identified for each neuron the first comprised the majority of stimulus information in granular layers second mid contributions and nonlinear cooperativity increased in supragranular and infragranular layers the ai microcircuit provides a valid template for three independent hierarchical computation principles increases in processing complexity strf cooperativity and nonlinearity correlate with the synaptic distance from granular layers

bayesian modeling and classification of neural signals identifying and classifying action potential shapes in extracellular neural waveforms have long been the subject of research and although several algorithms for this purpose have been successfully applied their use has been limited by some outstanding problems the first is how to determine shapes of the action potentials in the waveform and second how to decide how many shapes are distinct a harder problem is that action potentials frequently overlap making difficult both the determination of the shapes and the classification of the spikes in this report a solution to each of these problems is obtained by applying bayesian probability theory by defining a probabilistic model of the waveform the probability of both the form and number of spike shapes can be quantified in addition this framework is used to obtain an efficient algorithm for the decomposition of arbitrarily complex overlap sequences this algorithm can extract many times more information than previous methods and facilitates the extracellular investigation of neuronal classes and of interactions within neuronal circuits

polynomial phase estimation by least squares phase unwrapping estimating the coefficients of a noisy polynomial phase signal is important in fields including radar biology and radio communications one approach attempts to perform polynomial regression on the phase of the signal this is complicated by the fact that the phase is wrapped modulo 2 and must be unwrapped before regression can be performed in this paper we consider an estimator that performs phase unwrapping in a least squares manner we call this the least squares unwrapping lsu estimator the lsu estimator can be computed in a reasonable amount of time for data sets of moderate size using existing general purpose algorithms from algebraic number theory under mild conditions on the distribution of the noise we describe the asymptotic properties of this estimator showing that it is strongly consistent and asymptotically normally distributed a key feature is that the lsu estimator is accurate over a far wider range of parameters than many popular existing estimators monte carlo simulations support our theoretical results and demonstrate the excellent statistical performance of the lsu estimator when compared with existing state of the art estimators

interface evolution the hele shaw and muskat problems we study the dynamics of the interface between two incompressible 2 d ows where the evolution equation is obtained from darcy s law the free boundary is given by the discontinuity among the densities and viscosities of the uids this physical scenario is known as the two dimensional muskat problem or the two phase hele shaw ow we prove local existence in sobolev spaces when initially the dierence of the gradients of the pressure in the normal direction has the proper sign an assumption which is also known as the rayleigh taylor condition

a paradifferential approach for well posedness of the muskat problem we study the muskat problem for one fluid or two fluids with or without viscosity jump with or without rigid boundaries and in arbitrary space dimension d of the interface the muskat problem is scaling invariant in the sobolev space h s c mathbb r d where s c 1 frac d 2 employing a paradifferential approach we prove local well posedness for large data in any subcritical sobolev spaces h s mathbb r d s s c moreover the rigid boundaries are only required to be lipschitz and can have arbitrarily large variation the rayleigh taylor stability condition is assumed for the case of two fluids with viscosity jump but is proved to be automatically satisfied for the case of one fluid the starting point of this work is a reformulation solely in terms of the drichlet neumann operator the key elements of proofs are new paralinearization and contraction results for the drichlet neumann operator in rough domains

on the muskat problem global in time results in 2d and 3d this paper considers the three dimensional muskat problem in the stable regime we obtain a conservation law which provides an l 2 maximum principle for the fluid interface we also show global in time existence for strong and weak solutions with initial data controlled by explicit constants furthermore we refine the available estimates to obtain global existence and uniqueness for strong solutions with larger initial data than we previously had in 2d finally we provide global in time results in spaces with critical regularity giving solutions with bounded slope and time integrable bounded curvature

global existence singular solutions and ill posedness for the muskat problem the muskat or muskat leibenzon problem describes the evolution of the interface between two immiscible fluids in a porous medium or hele shaw cell under applied pressure gradients or fluid injection extraction in contras t to the hele shaw problem the one phase version of the muskat problem there are few nontrivial exact solutions or analytic results for the muskat problem for the stable forward muskat problem in which the higher viscosity fluid ex pands into the lower viscosity fluid we show global in time existence for initial data that is a small perturbation of a flat interface the initial data in this result ma y contain weak e g curvature singularities for the unstable backwa rd problem in which the higher viscosity fluid contracts we construct singular solution s that start off with smooth initial data but develop a point of infinite curvature at fi nite time c 2004 wiley periodicals inc

a fast algorithm for estimating the parameters of a quadratic fm signal this paper describes a fast algorithm that can be used for estimating the parameters of a quadratic frequency modulated fm signal the proposed algorithm is fast in that it requires only one dimensional 1 d maximizations the optimal maximum likelihood method by contrast requires a three dimensional 3 d maximization which can only be realized with an exhaustive 3 d grid search asymptotic statistical results are derived for all the estimated parameters the amplitude estimate is seen to be optimal whereas the phase parameters are in general suboptimal of the four phase parameter estimates two approach optimality as the signal to noise ratio snr tends to infinity the other two have mean square errors that are within 50 of the theoretical lower bounds for high snr simulations are provided to support the theoretical results extensions to multiple components and higher order fm signals are also discussed

duchon robert solutions for the rayleigh taylor and muskat problems abstract we construct analytic solutions to the euler equations with an interface between two fluids extending work of duchon and robert we also show that the estimates of duchon and robert yield global analytic solutions to the muskat problem with small initial data

estimation of multicomponent polynomial phase signals impinging on a multisensor array using state space modeling this contribution addresses the problem of estimating the parameters of multicomponent polynomial phase signals when impinging on a multisensor array an original approach is proposed based on a state space modelization of the signal and the application of an extended kalman filter for the state estimation the use of a multisensor array allows the exploitation of a spatial information and leads to the consideration of multiple filters with different observation equations computer simulations are used to demonstrate the effectiveness of the proposed algorithm

model based phase unwrapping of 2 d signals a parametric model and a corresponding parameter estimation algorithm for unwrapping 2 d phase functions are presented the proposed algorithm performs global analysis of the observed signal since this analysis is based on parametric model fitting the proposed phase unwrapping algorithm has low sensitivity to phase aliasing due to low sampling rates and noise as well as to local errors in its first step the algorithm fits a 2 d polynomial model to the observed phase the estimated phase is then used as a reference information that directs the actual phase unwrapping process the phase of each sample of the observed field is unwrapped by increasing decreasing it by the multiple of 2 spl pi which is the nearest to the difference between the principle value of the phase and the estimated phase value at this coordinate in practical applications the entire phase function cannot be approximated by a single 2 d polynomial model hence the observed field is segmented and each segment is fit with its own model once the phase model of the observed field has been estimated we can repeat the model based unwrapping procedure described earlier for the case of a single segment and a single model field

non splat singularity for the one phase muskat problem for the water waves equations the existence of splat singularities has been shown in 3 i e the interface self intersects along an arc in finite time the aim of this paper is to show the absence of splat singularities for the incompressible fluid dynamics in porous media

well posedness of the muskat problem with h2 initial data abstract we study the dynamics of the interface between two incompressible fluids in a two dimensional porous medium whose flow is modeled by the muskat equations for the two phase muskat problem we establish global well posedness and decay to equilibrium for small h 2 perturbations of the rest state for the one phase muskat problem we prove local well posedness for h 2 initial data of arbitrary size finally we show that solutions to the muskat equations instantaneously become infinitely smooth

rayleigh taylor breakdown for the muskat problem with applications to water waves the muskat problem models the evolution of the interface between two different fluids in porous media the rayleigh taylor condition is natural to reach linear stability of the muskat problem we show that the rayleigh taylor condition may hold initially but break down in finite time as a consequence of the method used we prove the existence of water waves turning

a low complexity blind estimator of narrowband polynomial phase signals consider the problem of estimating the parameters of multiple polynomial phase signals observed by a sensor array in practice it is difficult to maintain a precisely calibrated array the array manifold is then assumed to be unknown and the estimation is referred to as blind estimation to date only an approximated maximum likelihood estimator amle was suggested for blindly estimating the polynomial coefficients of each signal however this estimator requires a multidimensional search over the entire coefficient space instead we propose an estimation approach which is based on two steps first the signals are separated using a blind source separation technique which exploits the constant modulus property of the signals then the coefficients of each polynomial are estimated using a least squares method applied to the unwrapped phase of the estimated signal this estimator does not involve any search in the coefficient spaces the computational complexity of the proposed estimator increases linearly with respect to the polynomial order whereas that of the amle increases exponentially simulation results show that the proposed estimator achieves the cramer rao lower bound at moderate or high signal to noise ratio

absence of splash singularities for surface quasi geostrophic sharp fronts and the muskat problem in this paper for both the sharp front surface quasi geostrophic equation and the muskat problem we rule out the splash singularity blow up scenario in other words we prove that the contours evolving from either of these systems cannot intersect at a single point while the free boundary remains smooth splash singularities have been shown to hold for the free boundary incompressible euler equation in the form of the water waves contour evolution problem our result confirms the numerical simulations in earlier work in which it was shown that the curvature blows up because the contours collapse at a point here we prove that maintaining control of the curvature will remove the possibility of pointwise interphase collapse another conclusion that we provide is a better understanding of earlier work in which squirt singularities are ruled out in this case a positive volume of fluid between the contours cannot be ejected in finite time

viscous fingering an optimal bound on the growth rate of the mixing zone we consider the flow of two immiscible fluids of different mobility in a porous medium if the more mobile fluid displaces the other a macroscopically sharp interface is unstable by growing a network of fingers on a mesoscopic scale the two phases mix on a macroscopic scale we are interested in the evolution of this mixing zone we show that the effect of a large but finite mobility ratio lambda is strong enough to limit the growth rate of the mixing zone this is done by rigorously deriving an a priori estimate for the saffman taylor model in this geometry of an infinite channel the estimate essentially states that the mobility ratio lambda itself in the nondimensionalized setting with unit velocity imposed at infinity is the optimal bound on the velocity by which the penetrating phase progresses in direction of the channel since the introduction of diffusion limited aggregation various stochastic algorithms simulating this two phase flow have been developed the generated clusters which

a note on interface dynamics for convection in porous media we studied the fluid interface problem through porous media given by two incompressible 2 d fluids of different densities this problem is mathematically analogous to the dynamics interface for convection in porous media where the free boundary evolves between fluids with different temperatures we found a new formula for the evolution equation of the free boundary parameterized as a function in the periodic case in this formula there is not a principal value in the non local integral operator involved in the equation giving a simpler system using this formulation we perform numerical simulations in the stable case denser fluid below which shows a strong regularity effect in the periodic interface

on well posedness of the muskat problem with surface tension abstract we consider the muskat problem with surface tension for one fluid or two fluids with or without viscosity jump with infinite depth or lipschitz rigid boundaries and in arbitrary dimension d of the interface the problem is nonlocal quasilinear and to leading order is scaling invariant in the sobolev space h s c r d with s c 1 d 2 we prove local well posedness for large data in all subcritical sobolev spaces h s r d s s c allowing for initial interfaces whose curvatures are unbounded and furthermore when d 1 not locally square integrable to the best of our knowledge this is the first large data well posedness result that covers all subcritical sobolev spaces for the muskat problem with surface tension we reformulate the problem in terms of the dirichlet neumann operator and use a paradifferential approach to reduce the problem to an explicit parabolic equation which is of independent interest

analysis of multicomponent polynomial phase signals while the theory of estimation of monocomponent polynomial phase signals is well established the theoretical and methodical treatment of multicomponent polynomial phase signals mc ppss is limited in this paper we investigate several aspects of parameter estimation for mc ppss and derive the crameacuter rao bound we show the limits of existing techniques and then propose a nonlinear least squares nls approach we also motivate the use the nelder mead simplex algorithm for minimizing the nonlinear cost function the slight increase in computational complexity is a tradeoff for improved mean square error performance which is evidenced by simulation results

aircraft flight parameter estimation based on passive acoustic techniques using the polynomial wigner ville distribution the acoustic signal from an overflying aircraft as heard by a stationary observer is used to estimate an aircraft s constant height ground speed range and acoustic frequency central to the success of this flight parameter estimation scheme is the need for an accurate estimate of the instantaneous frequency of the observed acoustic signal in this paper the polynomial wigner ville distribution is used in this application as the instantaneous frequency estimator its performance and the issue of the optimal time domain window length are addressed

an estimation algorithm for 2 d polynomial phase signals we consider nonhomogeneous 2 d signals that can be represented by a constant modulus polynomial phase model a novel 2 d phase differencing operator is introduced and used to develop a computationally efficient estimation algorithm for the parameters of this model the operation of the algorithm is illustrated using an example

generalized high order phase function for parameter estimation of polynomial phase signal the high order phase function hpf has been introduced recently to estimate the parameters of a polynomial phase signal pps in this correspondence we generalize the standard hpf by introducing multiple time instants thus the standard hpf can be treated as a special example of the generalized hpf with identical time instants we propose a procedure for finding time instants minimizing the mean square error mse the proposed method achieves better performances than the high order ambiguity function haf and polynomial wigner ville distribution pwvd the theoretical analysis as well as the monte carlo simulations verify the advantages such as lower mse and lower snr threshold for the pps

optimal parameter selection in the phase differencing algorithm for 2 d phase estimation a parametric model and a corresponding algorithm for estimating two dimensional 2 d phase functions were presented in a previous paper the performance of the phase estimation algorithm and hence the performance of any algorithm that employs it strongly depends on the choice of the two free parameters of the algorithm in this correspondence we systematically analyze the performance of the phase estimation algorithm and derive rules for selecting the algorithm parameters such that the mean squared error in estimating the signal phase is minimized it is shown analytically and verified using monte carlo simulations that this choice of parameters results in unbiased estimates of the phase and spatial frequency functions the variances of both the estimated phase and frequency functions are very close to the corresponding cramer rao lower bounds

parameter estimation of 2 d random amplitude polynomial phase signals phase information has fundamental importance in many two dimensional 2 d signal processing problems in this paper we consider 2 d signals with random amplitude and a continuous deterministic phase the signal is represented by a random amplitude polynomial phase model a computationally efficient estimation algorithm for the signal parameters is presented the algorithm is based on the properties of the mean phase differencing operator which is introduced and analyzed assuming that the signal is observed in additive white gaussian noise and that the amplitude field is gaussian as well we derive the cramer rao lower bound crb on the error variance in jointly estimating the model parameters the performance of the algorithm in the presence of additive white gaussian noise is illustrated by numerical examples and compared with the crb

fast k dimensional tree algorithms for nearest neighbor search with application to vector quantization encoding fast search algorithms are proposed and studied for vector quantization encoding using the k dimensional k d tree structure here the emphasis is on the optimal design of the k d tree for efficient nearest neighbor search in multidimensional space under a bucket voronoi intersection search framework efficient optimization criteria and procedures are proposed for designing the k d tree for the case when the test data distribution is available as in vector quantization application in the form of training data as well as for the case when the test data distribution is not available and only the voronoi intersection information is to be used the criteria and bucket voronoi intersection search procedure are studied in the context of vector quantization encoding of speech waveform they are empirically observed to achieve constant search complexity for o log n tree depths and are found to be more efficient in reducing the search complexity a geometric interpretation is given for the maximum product criterion explaining reasons for its inefficiency with respect to the optimization criteria

parameter estimation of multicomponent 2d polynomial phase signals using the 2d phaf based approach this paper considers parameter estimation of multicomponent 2d polynomial phase signals mc 2d ppss the main contributions included are i derivation of the cramer rao lower bound crlb for mc 2d ppss ii two dimensional product high order ambiguity function 2d phaf based estimation procedure recently proposed by barbarossa for the estimation of third order mc 2d ppss is extended to signals of arbitrary orders iii procedure for optimal lag set selection in the proposed 2d phaf has been proposed iv since the 2d phaf is characterized by large mean squared error mse for higher order signals refinement procedure is introduced that is able to improve the estimation accuracy and to reduce mse up to the crlb the proposed estimator has been used for target focusing in radar images

asymptotic statistical analysis of the high order ambiguity function for parameter estimation of polynomial phase signals the high order ambiguity function haf is a nonlinear operator designed to detect estimate and classify complex signals whose phase is a polynomial function of time the haf algorithm introduced by peleg and porat 1991 estimates the phase parameters of polynomial phase signals measured in noise the purpose of this correspondence is to analyze the asymptotic accuracy of the haf algorithm in the case of additive white gaussian noise it is shown that the asymptotic variances of the estimates are close to the cramer rao bound crb for high snr however the ratio of the asymptotic variance and the crb has a polynomial growth in the noise variance

improving polynomial phase parameter estimation by using nonuniformly spaced signal sample methods this paper investigates the computationally efficient parameter estimation of polynomial phase signals embedded in noise many authors have previously proposed multilinear analysis methods which operate on uniformly spaced samples of the signal such methods include the higher order ambiguity functions hafs the polynomial wigner ville distributions pwvds and the higher order phase hp functions this paper investigates the use of multilinear methods which operate on nonuniformly spaced signal samples it is seen that the relaxation of the requirement to use uniformly spaced samples in the analysis can lead to significant performance improvements a theoretical analysis and simulations are presented in support of these claims

dynamics near unstable interfacial fluids we study three examples of unstable interfacial fluid motions vortex sheets with surface tension hele shaw flows with surface tension and vortex patches in all three cases the nonlinear dynamics of a large class of smooth perturbations is proven to be characterized by the corresponding fastest linear growing mode s up to the time scale of log frac 1 delta where delta is the magnitude of the initial perturbation in all three cases the analysis is based on an unified analytical framework that includes precise bounds on the growth of the linearized operator given by an explicit solution formula as well as a special sharp nonlinear energy growth estimate our main contribution is establishing this nonlinear energy growth estimate for each interface problem in certain high energy norms

a hybrid cpf haf estimation of polynomial phase signals detailed statistical analysis in this paper we consider parameter estimation of high order polynomial phase signals ppss we propose an approach that combines the cubic phase function cpf and the high order ambiguity function haf and is referred to as the hybrid cpf haf method in the proposed method the phase differentiation is first applied on the observed pps to produce a cubic phase signal whose parameters are in turn estimated by the cpf the performance analysis carried out in the paper considers up to the tenth order ppss and is supported by numerical examples revealing that the proposed approach outperforms the haf in terms of the accuracy and signal to noise ratio threshold extensions to multicomponent and multidimensional ppss are also considered all supported by numerical examples specifically when multicomponent ppss are considered the product version of the cpf haf outperforms the product haf phaf that fails to estimate parameters of components whose pps order exceeds three