global existence for a quasilinear wave equation outside of star shaped domains abstract we prove global existence of small amplitude solutions of quasilinear dirichlet wave equations outside of star shaped obstacles in 3 1 dimensions we use a variation of the conformal method of christodoulou since the image of the space time obstacle is not static in the einstein diamond our results do not follows directly from local existence theory as did christodoulou s for the nonobstacle case instead we develop weighted estimates that are adapted to the geometry using them and the energy integral method we obtain solutions in the einstein diamond minus the dime dependent obstacle which pull back to solutions in minkowski space minus and obstacle

remarks on the global sobolev inequalities in the minkowski space rn 1 on demontre des inegalites de sobolev globales sur l espace de minkowski r n 1 le theoreme principal est valable sur des tranches a temps fixe

sobolev active contours all previous geometric active contour models that have been formulated as gradient flows of various energies use the same l 2 type inner product to define the notion of gradient recent work has shown that this inner product induces a pathological riemannian metric on the space of smooth curves however there are also undesirable features associated with the gradient flows that this inner product induces in this paper we reformulate the generic geometric active contour model by redefining the notion of gradient in accordance with sobolev type inner products we call the resulting flows sobolev active contours sobolev metrics induce favorable regularity properties in their gradient flows in addition sobolev active contours favor global translations but are not restricted to such motions they are also less susceptible to certain types of local minima in contrast to traditional active contours these properties are particularly useful in tracking applications we demonstrate the general methodology by reformulating some standard edge based and region based active contour models as sobolev active contours and show the substantial improvements gained in segmentation

crystal growth and dendritic solidification we present a numerical method which computes the motion of complex solid liquid boundaries in crystal growth the model we solve includes physical effects such as crystalline anisotropy surface tension molecular kinetics and undercooling the method is based on two ideas first the equations of motion are recast as a single history dependent boundary integral equation on the solid liquid boundary a fast algorithm is used to solve the integral equation efficiently second the boundary is moved by solving a hamiltonjacobi type equation on a fixed domain formulated by osher and sethian for a function in which the boundary is a particular level set this equation is solved by finite difference schemes borrowed from the technology of hyperbolic conservation laws the two ideas are combined by constructing a smooth extension of the normal velocity off the moving boundary in a way suggested by the physics of the problem our numerical experiments show the evolution of complex crystalline shapes development of large spikes and corners dendrite formation and side branching and pieces of solid merging and breaking off freely

solving partial differential equations on irregular domains with moving interfaces with applications to superconformal electrodeposition in semiconductor manufacturing we present a numerical algorithm for solving partial differential equations on irregular domains with moving interfaces instead of the typical approach of solving in a larger rectangular domain our approach performs most calculations only in the desired domain to do so efficiently we have developed a one sided multigrid method to solve the corresponding large sparse linear systems our focus is on the simulation of the electrodeposition process in semiconductor manufacturing in both two and three dimensions our goal is to track the position of the interface between the metal and the electrolyte as the features are filled and to determine which initial configurations and physical parameters lead to superfilling we begin by motivating the set of equations which model the electrodeposition process building on existing models for superconformal electrodeposition we develop a model which naturally arises from a conservation law form of surface additive evolution we then introduce several numerical algorithms including a conservative material transport level set method and our multigrid method for one sided diffusion equations we then analyze the accuracy of our numerical methods finally we compare our result with experiment over a wide range of physical parameters

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

global existence for systems of quasilinear wave equations in 1 4 dimensions abstract hormander proved global existence of solutions for sufficiently small initial data for scalar wave equations in 1 4 dimensions of the form u q u u u where q vanishes to second order and u 2 q 0 0 0 0 without the latter condition only almost global existence may be guaranteed the first author and sogge considered the analog exterior to a star shaped obstacle both results relied on writing the lowest order terms u u 1 2 u 2 and as such do not immediately generalize to systems the current study remedies such and extends both results to the case of multiple speed systems

global existence of null form wave equations on small asymptotically euclidean manifolds abstract we prove the global existence of the small solutions to the cauchy problem for quasilinear wave equations satisfying the null condition on r 3 g where the metric g is a small perturbation of the flat metric and approaches the euclidean metric like 1 x 2 2 with 1 global and almost global existence for systems without the null condition are also discussed for certain small time dependent perturbations of the flat metric in appendix a

almost global existence for quasilinear wave equations in waveguides with neumann boundary conditions in this paper we prove almost global existence of solutions to certain quasilinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides with neumann boundary conditions we use a galerkin method to expand the laplacian of the compact base in terms of its eigenfunctions for those terms corresponding to zero modes we obtain decay using analogs of estimates of klainerman and sideris for the nonzero modes estimates for klein gordon equations which provide better decay are available

global solutions for nonlinear wave equations with localized dissipations in exterior domains abstract the cauchy problem for nonlinear wave equations with localized dissipation is considered in exterior domains outside of compact obstacles in three spatial dimensions under the null conditions for the quadratic nonlinear terms the global solutions are shown for sufficiently small data the solutions which have different propagation speeds are considered

scaling of constitutive relationships in unsaturated heterogeneous media a numerical investigation numerical models of groundwater flow in the unsaturated zone require relative conductivity and moisture retention curves at a discretization scale much larger than that at which these constitutive relationships are measured this study seeks to identify simple scaling laws linking parameters of block scale constitutive relationships with the parameters of their measurement scale counterparts represented here using gardner russo models the two parameters of these models saturated conductivity and pore size distribution parameter are viewed as cross correlated regionalized variables with isotropic or anisotropic spatial correlation structures and are simulated using the sequential gaussian method upscaled constitutive curves for steady gravity drainage through three dimensional heterogeneous domains are then constructed by repeating numerical flow experiments for a series of applied infiltration rates and plotting the resulting upscaled relative conductivities and average water saturations against average matric potentials the experiments reveal clear log linear relationships between upscaled relative conductivities and average matric potentials the slopes of which are used to define an upscaled pore size distribution parameter the reciprocal of this quantity which represents an upscaled characteristic capillary length is very well approximated by a spatial power average of its measurement scale values furthermore the averaging exponent is found to be the same as that associated with the upscaling of saturated conductivities over the same flow domains when average matric potentials are normalized using this upscaled characteristic capillary length relative conductivity and moisture saturation values for widely different flow field realizations collapse along well defined curves however for wet conditions the form of these curves differs from that of the models assumed at the measurement scale

finite difference methods for approximating heaviside functions we present a finite difference method for discretizing a heaviside function h u x where u is a level set function u r email protected r that is positive on a bounded region email protected r n there are two variants of our algorithm both of which are adapted from finite difference methods that we proposed for discretizing delta functions in j d towers two methods for discretizing a delta function supported on a level set j comput phys 220 2007 915 931 j d towers discretizing delta functions via finite differences and gradient normalization preprint at http www miracosta edu home jtowers j d towers a convergence rate theorem for finite difference approximations to delta functions j comput phys 227 2008 6591 6597 we consider our approximate heaviside functions as they are used to approximate integrals over w we prove that our first approximate heaviside function leads to second order accurate quadrature algorithms numerical experiments verify this second order accuracy for our second algorithm numerical experiments indicate at least third order accuracy if the integrand f and email protected are sufficiently smooth numerical experiments also indicate that our approximations are effective when used to discretize certain singular source terms in partial differential equations we mostly focus on smooth f and u by this we mean that f is smooth in a neighborhood of w u is smooth in a neighborhood of email protected and the level set u x 0 is a manifold of codimension one however our algorithms still give reasonable results if either f or u has jumps in its derivatives numerical experiments indicate approximately second order accuracy for both algorithms if the regularity of the data is reduced in this way assuming that the level set u x 0 is a manifold numerical experiments indicate that dependence on the placement of w with respect to the grid is quite small for our algorithms specifically a grid shift results in an o h p change in the computed solution where p is the observed rate of convergence

a geometric model for active contours in image processing we propose a new model for active contours based on a geometric partial differential equation our model is intrinsec stable satisfies the maximum principle and permits a rigorous mathematical analysis it enables us to extract smooth shapes we cannot retrieve angles and it can be adapted to find several contours simultaneously moreover as a consequence of the stability we can design robust algorithms which can be engineed with no parameters in applications numerical experiments are presented

computing interface motion in compressible gas dynamics a hamilton jacobi level set formulation of the equations of motion for propagating interfaces has been introduced recently by osher and sethian this formulation allows fronts to self intersect develop singularities and change topology the numerical algorithms based on this approach handle topological merging and breaking naturally work in any number of space dimensions and do not require that the moving front be written as a function instead the moving front is embedded as a particular level set in a fixed domain partial differential equation numerical techniques borrowed from hyperbolic conservation laws are then used to accurately capture the complicated surface motion that satisfies the global entropy condition for propagating fronts given by sethian in this paper we analyze the coupling of this level set formulation to a system of conservation laws for compressible gas dynamics we study both conservative and non conservative differencing of the level set function and compare the two approaches to illustrate the capability of the method we study the compressible rayleigh taylor and kelvin helmholtz instabilities for air air and air helium boundaries we perform numerical convergence studies of the method over a range of parameters and analyze the accuracy of this approach applied to these problems

spatial averaging of unsaturated flow equations under infiltration conditions over areally heterogeneous fields 2 numerical simulations two models for horizontally averaged unsaturated flow have been developed from two different approaches in the first chen et al this issue of these companion papers in this paper the results from both the spatially horizontally averaged richards equation share model and the averaged green ampt model are compared with the results from a three dimensional finite difference model of unsaturated flow which is perceived as the reference solution the results of the averaged green ampt model show very good agreement with the averaged results from the three dimensional model while share model results are applicable only when fluctuations in soil parameters are small with respect to their mean values it is also shown that methods of simple parameter averaging arithmetic or geometric averages with the local richards equation does not yield meaningful results in heterogeneous soils this study suggests that spatially horizontally averaged simplified models such as the averaged green ampt model are attractive alternatives to perturbation models such as the share model in heterogeneous fields due to their simplicity in formulation accuracy in predicting average behaviors and minimal requirement of computer effort the spatially horizontally averaged simplified models can be easily implemented in large scale models such as atmospheric mesoscale models boundary and initial conditions the average saturation at each depth was obtained by areal integration of the local scale water saturation over the specified area under the assumption of independent vertical soil columns at field scales relative occurrence frequency curves of the spatially varying parameters were required for the solution of the average quantities the second model developed was the spatially horizontally averaged richards equation share model this model was developed by using spatial averaging and regular perturbation techniques under the assumption of no source or sink in the study area the share model was expressed as a system of two coupled one dimensional partial differential equations in terms of the mean saturation and the cross covariance of saturation and saturated hydrau

on a global existence theorem of small amplitude solutions for nonlinear wave equations in an exterior domain soit un domaine non borne dans un espace euclidien a n dimensions r n a frontiere compacte et c on considere le probleme mixte u u f t x d 1 d 1 u f t x dans 0 u 0 sur 0 u 0 x u 0 x t u 0 x u 1 x dans f est une fonction non lineaire a valeur reelle et d 1 d 1 u t j x u 1 j 2

stochastic modeling of large scale transient unsaturated flow systems a new framework for modeling large scale transient unsaturated flow systems in spatially variable soils is proposed in order to overcome the problem of limited information about the local details of spatial soil variability a stochastic approach which assumes that local soil properties are realizations of three dimensional random fields is followed for derivation of a large scale model representation structure the three dimensionality of the local flow and the nonlinear dependence of the local flow output on the local soil properties are considered the large scale model structure is derived by averaging the local governing flow equation over the ensemble of realizations of the underlying soil property random fields the resulting mean model representation is in the form of a partial differential equation in which averaged or effective model parameters occur these effective model parameters i e effective hydraulic conductivity and effective specific moisture capacity are evaluated using a quasi linearized fluctuation equation and a spectral representation of stationary processes the large scale model representation considers the large scale effects of soil property variability and has relatively few parameters the general conclusions of this study are that soil property variability produces large scale hysteresis and anisotropy of the effective parameters the potential theoretical and practical ramifications of these results in the area of unsaturated flow modeling need to be investigated the general stochastic modeling framework developed here is applicable not only to unsaturated flow but also to other distributed parameter systems e g saturated flow and transport geothermal and oil reservoir modeling

an axiomatic approach to image interpolation we discuss possible algorithms for interpolating data given in a set of curves and or points in the plane we propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations the absolute minimal lipschitz extension model amle is singled out and studied in more detail we show experiments suggesting a possible application the restoration of images with poor dynamic range

motion of multiple junctions a level set approach abstract a coupled level set method for the motion of multiple junctions is proposed the new method extends the hamilton jacobi level set formulation of osher and sethian it retains the feature of tracking fronts by following level sets and allows the specification of arbitrary velocities on each front the diffusion equation is shown to generate curvature dependent motion and this is used to develop an algorithm to move multiple junctions with curvature dependent speed systems of reaction diffusion equations are shown to possess inherent properties which prohibit efficient numerical solutions when applied to curvature dependent motion

minimal surfaces based object segmentation a geometric approach for 3d object segmentation and representation is presented the segmentation is obtained by deformable surfaces moving towards the objects to be detected in the 3d image the model is based on curvature motion and the computation of surfaces with minimal areas better known as minimal surfaces the space where the surfaces are computed is induced from the 3d image volumetric data in which the objects are to be detected the model links between classical deformable surfaces obtained via energy minimization and intrinsic ones derived from curvature based flows the new approach is stable robust and automatically handles changes in the surface topology during the deformation

binary level set shape optimization model and algorithm for volumetric modulated arc therapy in radiotherapy treatment we introduce in this paper a variational framework for the construction of improved treatment plans in volumetric modulated arc therapy for cancer treatment this framework consists of a shape optimization component from the molding of beam shapes as well as strong constraints from the equipment involved on both beam shapes and intensities we apply the binary level set method to handle complex shape topologies and the fast sweeping method to handle beam intensity constraints the result is a fast flow based algorithm in a simplified setting that guarantees energy decrease we include numerical simulations of clinical cases to demonstrate the efficacy of the approach

global existence of small solutions to quadratic nonlinear wave equations in an exterior domain abstract we consider the initial boundary value problem for the nonlinear wave equation formula where 2 t b x x formula r b x x r u 0 u 1 are real valued functions 0 is a sufficiently small positive constant in this paper it is shown that small solutions to exist globally in time when n 4 our method in this paper is applicable to the more general nonlinear wave equations such that u f t u t u 2 t u where f is a quadratic nonlinearity in t u part t u 2 t u 1 2 n and n 4

spatial analysis of hydraulic conductivity measured using disc infiltrometers spatial variability of surface hydraulic properties and the extrinsic e g traffic cropping etc and intrinsic e g soil type pore size distribution etc factors associated with these properties are important for infiltration and runoff processes in agricultural fields disc infiltrometers measured infiltration at 296 sites arranged on two parallel transects to examine and differentiate the factors contributing to spatial structure under different field conditions these measurements were made in the corn rows no track interrows and wheel track interrows of the field using four different soil water tensions 0 30 60 and 150 mm unsaturated hydraulic conductivity k and saturated hydraulic conductivity k were maximum in the corn rows and minimum in wheel track inter rows with no track interrows intermediate exponents cz parameters of k and k relationships k k exp av for corn rows and no track interrows were not significantly different from each other but were significantly different from q for the wheel track interrows a t p 0 01 level spatial variability o f k and k values showed some pseudoproportional effect in nugget variance for all three field conditions no track interrows clearly showed an inverse trend for semivariogram o f k with changing tension q values whereas differences were found for corn rows and wheel traffic interrows the spatial structure of y for all three field conditions were mostly white noise under corn rows in addition to random variation a small five row periodic variation at th e p 0 20 level matching the five row traffic configuration was discovered the spatial structure of a was influenced by soil type for the no track interrows spatial structure was absent in wheel track interrows indicating the destruction of pore structure due to compaction

stochastic analysis of unsaturated flow in heterogeneous soils 1 statistically isotropic media steady unsaturated flow with vertical mean infiltration through unbounded heterogeneous porous media is analyzed using a perturbation approximation of the stochastic flow equation which is solved by spectral representation techniques the hydraulic conductivity k is related to the capillary pressure head by k ks exp where ks is the saturated conductivity and is a soil parameter a general formulation is presented for the case with ks and represented as statistically homogeneous spatial random fields in part 1 solutions are developed assuming is constant and representing ks variability by one dimensional and three dimensional isotropic random fields results are obtained for head variances and covariance functions effective hydraulic conductivities variances of the unsaturated hydraulic conductivity flux variances and variance of pressure gradient when the parameter is relatively large corresponding to coarse textured soils the head variance decreases and all of the results demonstrate a trend toward gravitationally dominated one dimensional vertical flow the effective conductivity is dependent on the correlation scale of ln ks and the mean hydraulic gradient

local or global minima flexible dual front active contours most variational active contour models are designed to find local minima of data dependent energy functionals with the hope that reasonable initial placement of the active contour will drive it toward a desirable local minimum as opposed to an undesirable configuration due to noise or complex image structure as such there has been much research into the design of complex region based energy functionals that are less likely to yield undesirable local minima when compared to simpler edge based energy functionals whose sensitivity to noise and texture is significantly worse unfortunately most of these more robust region based energy functionals are applicable to a much narrower class of imagery compared to typical edge based energies due to stronger global assumptions about the underlying image data devising new implementation algorithms for active contours that attempt to capture more global minimizers of already proposed image based energies would allow us to choose an energy that makes sense for a particular class of energy without concern over its sensitivity to local minima such implementations have been proposed for capturing global minima however sometimes the completely global minimum is just as undesirable as a minimum that is too local in this paper we propose a novel fast and flexible dual front implementation of active contours motivated by minimal path techniques and utilizing fast sweeping algorithms which is easily manipulated to yield minima with variable degrees of localness and globalness by simply adjusting the size of active regions the ability to gracefully move from capturing minima that are more local according to the initial placement of the active contour surface to minima that are more global allows this model to more easily obtain desirable minimizers which often are neither the most local nor the most global experiments on various 2d and 3d images and comparisons with some active contour models and region growing methods are also given to illustrate the properties of this model and its performance in a variety of segmentation applications

the lifespan for nonlinear wave equations with multiple propagation speeds in 3d abstract in this paper we consider the cauchy problem for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions on the basis of some klainerman sideris type weighted estimates we get the lifespan of small amplitude solutions for systems with nonlinearities depending on both the unknown functions and their derivatives

on nonlinear elastic waves in 2 d abstract for the cauchy problem of 2 d nonlinear elastic waves of isotropic homogeneous and hyperelastic materials satisfying null conditions assuming the smallness of h 3 r 2 h 2 r 2 norm and the boundedness of h 4 r 2 h 3 r 2 norm for radially symmetric initial data we show the global existence of classical solutions similar results for exterior domain problems are also proved

global existence for dirichlet wave equations with quadratic nonlinearities in high dimensions we prove global existence of solutions to quasilinear wave equations with quadratic nonlinearities exterior to nontrapping obstacles in spatial dimensions 4 and higher this generalizes a result of shibata and tsutsumi in spatial dimensions greater than or equal to 6 the technique of proof would allow for more complicated geometries provided that an appropriate local energy decay exists for the associated linear wave equation

dynamic active contours for visual tracking visual tracking using active contours is usually set in a static framework the active contour tracks the object of interest in a given frame of an image sequence a subsequent prediction step ensures good initial placement for the next frame this approach is unnatural the curve evolution gets decoupled from the actual dynamics of the objects to be tracked true dynamical approaches exist all being marker particle based and thus prone to the shortcomings of such particle based implementations in particular topological changes are not handled naturally in this framework the now classical level set approach is tailored for evolutions of manifolds of codimension one however dynamic curve evolution is at least a codimension two problem we propose an efficient level set based approach for dynamic curve evolution which addresses the artificial separation of segmentation and prediction while retaining all the desirable properties of the level set formulation it is based on a new energy minimization functional which for the first time puts dynamics into the geodesic active contour framework

local existence of solution for the initial boundary value problem of fully nonlinear wave equation on considere l existence locale par rapport au temps des solutions pour le probleme aux valeurs limites et initiales d une equation d onde totalement non lineaire

a topology preserving level set method for geometric deformable models active contour and surface models also known as deformable models are powerful image segmentation techniques geometric deformable models implemented using level set methods have advantages over parametric models due to their intrinsic behavior parameterization independence and ease of implementation however a long claimed advantage of geometric deformable models the ability to automatically handle topology changes turns out to be a liability in applications where the object to be segmented has a known topology that must be preserved we present a new class of geometric deformable models designed using a novel topology preserving level set method which achieves topology preservation by applying the simple point concept from digital topology these new models maintain the other advantages of standard geometric deformable models including subpixel accuracy and production of nonintersecting curves or surfaces moreover since the topology preserving constraint is enforced efficiently through local computations the resulting algorithm incurs only nominal computational overhead over standard geometric deformable models several experiments on simulated and real data are provided to demonstrate the performance of this new deformable model algorithm

remarks on global solutions for nonlinear wave equations under the standard null conditions abstract a combination of some weighted energy estimates is applied for the cauchy problem of quasilinear wave equations with the standard null conditions in three spatial dimensions alternative proofs for global solutions are shown including the exterior domain problems

stochastic differential equations and geometric flows in previous years curve evolution applied to a single contour or to the level sets of an image via partial differential equations has emerged as an important tool in image processing and computer vision curve evolution techniques have been utilized in problems such as image smoothing segmentation and shape analysis we give a local stochastic interpretation of the basic curve smoothing equation the so called geometric heat equation and show that this evolution amounts to a tangential diffusion movement of the particles along the contour moreover assuming that a priori information about the shapes of objects in an image is known we present modifications of the geometric heat equation designed to preserve certain features in these shapes while removing noise we also show how these new flows may be applied to smooth noisy curves without destroying their larger scale features in contrast to the original geometric heat flow which tends to circularize any closed curve

on global existence for nonlinear wave equations outside of convex obstacles the authors prove global existence of small solutions to a semilinear wave equation outside of convex obstacles this extends results of christodoulou and klainerman who handled the minkowski space version the proof is a compromise of the methods of christodoulou and klainerman it relies on local estimates proved earlier by smith and sogge together with classical energy decay estimates for the wave equation of morawetz lax and phillips

new characterizations of simple points in 2d 3d and 4d discrete spaces a point of a discrete object is called simple if it can be deleted from this object without altering topology in this article we present new characterizations of simple points which hold in dimensions 2 3 and 4 and which lead to efficient algorithms for detecting such points in order to prove these characterizations we establish two confluence properties of the collapse operation which hold in the neighborhood of a point in spaces of low dimension this work is settled in the framework of cubical complexes which provides a sound topological basis for image analysis and allows to retrieve the main notions and results of digital topology in particular the notion of simple point

almost global existence for quasilinear wave equations in three space dimensions this article studies almost global existence for solutions of quadratically quasi linear systems of wave equations in three space dimensions the approach here uses only the classical invariance of the wave operator under translations spatial rotations and scaling using these techniques we can handle wave equations in minkowski space or dirichlet wave equations in the exterior of a smooth star shaped obstacle we can also apply our methods to systems of quasilinear wave equations having different wave speeds this extends our work 11 for the semilinear case previous almost global ex istence theorems for quasilinear equations in three space dimensions were for the non obstacle case in 9 john and klainerman proved almost global existence on minkowski space for quadratic quasilinear equations using the lorentz invariance of the wave operator in addition to the symmetries listed above subsequently in 14 klainerman and sideris obtained the same result for a class of quadratic divergence form nonlinearities without relying on lorentz invariance this line of thought was refined and applied to prove global in time results for null form equa tions related to the theory of elasticity in sideris 22 23 and for multiple speed systems of null form quasilinear equations in sideris and tu 24 and yokoyama 29 the main difference between our approach and the earlier ones is that we ex ploit the 0 x 1 decay of solutions of wave equations with sufficiently decaying initial data as much as we involve the stronger 0 t l decay here of course x x x2 x is the spatial component and t the time component of a space time vector t x g m x e3 establishing 0 x 1 decay is considerably easier and can be achieved using only the invariance with respect to translations and spatial rotation a weighted l2 space time estimate for inhomogeneous wave equations proposition 3 1 below from 11 is important in making the spatial decay useful for the long time existence argument for semilinear systems one can show almost global existence from small data using only this spatial decay 11 for quasilinear systems however we also have to show that both first and second derivatives of u decay like 1 t fortunately we can do this using a variant of some l1 l estimates of john h rmander

global smooth solutions of 3 d null form wave equations in exterior domains with neumann boundary conditions abstract the paper is devoted to investigating long time behavior of smooth small data solutions to 3 d quasilinear wave equations outside of compact convex obstacles with neumann boundary conditions concretely speaking when the surface of a 3 d compact convex obstacle is smooth and the quasilinear wave equation fulfills the null condition we prove that the smooth small data solution exists globally provided that the neumann boundary condition on the exterior domain is given one of the main ingredients in the current paper is the establishment of local energy decay estimates of the solution itself as an application of the main result the global stability to 3 d static compressible chaplygin gases in exterior domain is shown under the initial irrotational perturbation with small amplitude

determining soil hydraulic properties by parameter estimation on the selection of a model for the hydraulic properties parameter estimation procedures involving solution of the inverse flow problem pertinent to a transient experiment constitute a powerful method of determining the soil hydraulic properties one of the problems associated with these procedures is the selection of an appropriate model to describe the soil hydraulic properties three different models were considered those of van genuchten vg and brooks and corey bc model and the exponential model of gardner for the hydraulic conductivity soil water pressure relationships coupled with a new expression for the soil water content soil water pressure relationship gr model for a given model the soil hydraulic properties were determined from simulated and measured outflow experiments supplemented with water content at a soil water pressure head of 15 000 cm h2o using the parameter estimation procedure of kool et al 1985a and data from two soils a hypothetical sandy loam soil assumed to be described by the vg model and a silt loam soil model validation tests were performed and the most appropriate model was selected from the candidate models by discrimination tests using the akaike information criterion aic in the case of the hypothetical sandy loam the vg model was found to be the most accurate and most consistent with the data the performance of both the bc and the gr models in terms of the aic was less good but very similar to each other in the case of the silt loam soil the vg model with additional parameter m which accounts for the correlation between pores and for the flow path tortuosity m 2 02 rather than a constant m 0 5 was found to be most accurate and most consistent with the data the performance of the bc and the gr models was similar when m was considered as an unknown parameter instead of a constant

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

statistical analysis of spatial variability in unsaturated flow parameters core scale estimates of soil parameters of the gardner russo and van gemachten models of the hydraulic conductivity and water retention functions were obtained for 417 undisturbed soil cores taken from a wall of a trench 20 m long 2 5 m deep using a procedure based on inverse problem methodology these estimates were used to evaluate the first two statistical moments of the underlying random space functions rsfs using the restricted maximum likelihood estimation procedure coupled with the weighted least squares procedure to estimate parameters of models of the covariance and the drift functions of the pertinent rsfs the fitted models were used to evaluate the mean and covariance functions of the hydraulic conductivity and water rentention functions for given water saturations covariance functions of log saturated conductivity log ks and the shape parameters of the gardner russo and van genuchten models exhibited statistical anisotropy characterized by aspect ratios that vary between 3 to 4 correlation scales of log ks were larger than those of the shape parameters consequently the product of the variance of log unsaturated conductivity and its correlation scale remained essentially invariant for a considerable range of water saturation the implications of these results regarding stochastic modeling of transport in heterogeneous porous formations and possible applications of the results of this study are discussed briefly

stochastic analysis of unsaturated flow one dimensional monte carlo simulations and comparisons with spectral perturbation analysis and field observations a numerical experiment was designed to study the stochastic behavior of one dimensional transient unsaturated flow in a monte carlo setting soil hydraulic properties log saturated hydraulic conductivity ln ks pore size distribution parameter and the specific water capacity c are assumed to be statistically homogeneous random fields described by exponential correlation functions with identical correlation lengths fifty realizations of each soil hydraulic property with statistical properties obtained from a field experiment are generated by using a nearest neighbor model numerical solutions of the one dimensional flow equation are used repeatedly to obtain realizations of soil water pressure head and flux q corresponding to the realizations of in ks and c the dependence of and q on the statistical properties of ln ks and c and the magnitude of the hydraulic head gradient g prevailing at the lower boundary are investigated in addition results of monte carlo analysis and spectral perturbation analyses are compared with field observations the greatest variability of and q are observed when soil hydraulic properties are uncorrelated and have large variances and integral scales and when g at the lower boundary is unity the monte carlo and spectral perturbation analyses tend to agree reasonably well for the flow domains in which ergodicity of local soil hydraulic properties is assured results of the monte carlo and spectral perturbation analyses are also supported by field observations

effective soil water characteristics and ensemble soil water profiles in heterogeneous soils one dimensional vertical flows through spatially heterogeneous areas are studied with numerical solutions for a variety of soil types to ascertain the behavior of the ensemble soil heterogeneity is treated using the distributions of parameters describing the characteristic relations of conductivity water content and pressure head values of the critical parameters taken from a modified brooks corey or van genuchten model have previously 7lsqb smith and diekkruger 1992 been shown in two extensive data sets to exhibit little interdependence the static ensemble characteristics except for saturated and residual water content parameters are shown to have regular bias compared to a soil with the mean characteristic parameters the measured data also are shown not to support the popular similar media heterogeneity model using both analytic approximate flow models and an ensemble solution of richards equation the effective dynamic ensemble characteristics in three example soils are studied as suggested in previous studies such effective characteristics are conditional to flow conditions and are here shown to be quite different from ensemble static characteristics this indicates that irrespective of the sample size effective soil dynamic characteristics are not measurable for samples possessing significant heterogeneity

effective hydraulic parameters for steady state vertical flow in heterogeneous soils 1 in hydroclimate and land atmospheric interaction models effective hydraulic properties are needed at large grid scales in this study the effective soil hydraulic parameters of the areally heterogeneous soil formation are derived by conceptualizing the heterogeneous soil formation as an equivalent homogeneous medium and assuming that the equivalent homogeneous soil will approximately discharge the same total amount of flux and produce same average pressure head profile in the formation as compared to previous effective hydraulic property studies a specific feature of this study is that the derived effective hydraulic parameters are mean gradient dependent i e vary across depth although areal soil heterogeneity was formulated as parallel homogeneous stream tubes in this study our results appear to be consistent with the previous findings of mean gradient unsaturated hydraulic conductivity yeh et al 1985a 1985b three widely used hydraulic conductivity models were employed in this study i e the gardner model the brooks and corey model and the van genuchten model we examined the impact of parameter correlation boundary condition surface pressure head and elevation above the water table on the effective saturated hydraulic conductivity and shape parameter the correlation between the saturated hydraulic conductivity ks and the shape parameter increases the effective saturated hydraulic conductivity while it does not affect the effective the effective is usually smaller than the mean value of while the effective ks can be smaller or larger than the mean value depending on no correlation or full correlation between ks and fields respectively an important observation of this study is that gardner and van genuchten functions resulted in effective parameters whereas it is difficult to define effective parameters for the brooks corey model since this model uses a piecewise continuous profile for hydraulic conductivity

cross correlated random field generation with the direct fourier transform method this paper presents a computer algorithm that is capable of cogenerating pairs of three dimensional cross correlated random fields the algorithm produces random fields of real variables by the inverse fourier transform of a randomized discrete three dimensional spectral representations of the variables the randomization is done in the spectral domain in a way that preserves the direct power and cross spectral density structure two types of cross spectra were examined one type specifies a linear relationship between the two fields which produces the same correlation scales for both variables but different variances the second cross spectrum is obtained from a specified transfer function and the two power spectra and it produces fields with different correlation scales for both models the degree of correlation is specified by the coherency a delay vector can also be specified to produce an out of phase correlation between the two fields the algorithm is very efficient computationally is relatively easy to use and does not produce the lineation problems that can be encountered with the turning bands method perhaps most important this random field generator is capable of co generating cross correlated random fields

general quasilinear wave equations with localized dissipation in exterior domains abstract we show that the method of commuting vector fields can be applied to quasilinear wave equations with localized dissipations in general exterior domains this allows us to show long time existence for general quasilinear wave equations with quadratic nonlinearities moreover by assuming that the dissipation is effective in a certain neighborhood of the boundary we need not place any assumption on the geometry of the domain

computing minimal surfaces via level set curvature flow given a fixed closed curve or curves in r sp3 there is an associated problem of finding a surface with mean curvature zero which has that curve or curves as its boundary in this paper a new approach to numerically solving the minimal surface problem is introduced the surface is represented as a level set of a global function phi r sp3 to r the family of surfaces evolve in time according to mean curvature flow a solution is found when a steady state condition is achieved a new system of interpolatory boundary conditions are used to maintain the connection between the surface and the fixed boundary contour several computer surfaces are shown including examples of topological changes

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

uniform decay estimates and the lorentz invariance of the classical wave equation on etudie le comportement asymptotique des solutions de u 0 ou t 2 1 2 n 2 pour des conditions initiales u 0 u t g x en t 0 avec g reguliere a support compact dans r n

global solutions of nonlinear hyperbolic equations for small initial data on considere des systemes quasilineaires d equations hyperboliques d ordre 2 qui sont des deformations non lineaires de l equation d onde on etudie l existence globale et le comportement asymptotique des solutions du probleme de cauchy quand la donnee initiale est suffisamment petite

magnification of label maps with a topology preserving level set method image segmentation aims at partitioning an image into multiple segments the application of this procedure produces a label map also referred to as segmentation map that classifies the pixels of the original image in contrast to natural images label maps are nominal scale images typically represented as integer valued images nominal scaled label maps can also appear as a representation of the raw data in areas such as in geostatistics in some applications the original resolution of a label map does not suffice and a larger size map has to be generated in this paper we present a magnification algorithm for label maps and nominal images the main property of our method is that it preserves the topology during the magnification process which means that no isolated pixel vanishes to the best of our knowledge apart from nearest neighbor interpolation the problem of label map magnification has not previously been addressed in the literature the main idea of the proposed method is to accomplish a boundary refinement by smoothing the regions boundaries on a finer grid the method relies on well known methods namely the fundamental operations of morphological image processing erosion and dilation and the level set method the level set method is well suited for our purposes since it does not depend on a parametrization and it is numerically stable the topological flexibility of the level set method often found to be an advantage in applications is a drawback here since the topology of the original label map should be preserved however using the so called simple point criterion from digital topology one can adapt the conventional level set method so that the topology will not be modified throughout the magnification procedure

global existence of null form wave equations in exterior domains we provide a proof of global existence of solutions to quasilinear wave equations satisfying the null condition in certain exterior domains in particular our proof does not require estimation of the fundamental solution for the free wave equation we instead rely upon a class of keel smith sogge estimates for the perturbed wave equation using this a notable simplification is made as compared to previous works concerning wave equations in exterior domains one no longer needs to distinguish the scaling vector field from the other admissible vector fields

almost global existence for nonlinear wave equations in an exterior domain in two space dimensions in this paper we deal with the exterior problem for a system of nonlinear wave equations in two space dimensions assuming that the initial data is small and smooth we establish the same type of lower bound of the lifespan for the problem as that for the cauchy problem despite of the weak decay property of the solution in two space dimensions

a variational approach for the segmentation of the left ventricle in cardiac image analysis in this paper we propose a level set method to segment mr cardiac images our approach is based on a coupled propagation of two cardiac contours and integrates visual information with anatomical constraints the visual information is expressed through a gradient vector flow based boundary component and a region term that aims at best separating the cardiac contours regions according to their global intensity properties in order to deal with misleading visual support an anatomical constraint is considered that couples the propagation of the cardiac contours according to their relative distance the resulting motion equations are implemented using a level set approach and a fast and stable numerical approximation scheme the additive operator splitting encouraging experimental results are provided using real data

stochastic analysis of steady state unsaturated flow in heterogeneous media comparison of the brooks corey and gardner russo models existing stochastic models of unsaturated flow and transport are usually developed using the simple gardner russo constitutive relationship though it is generally accepted that the more complex van genuchten and brooks corey relationships may perform better in describing experimental data in this paper we develop first order stochastic models for gravity dominated flow in second order stationary media with both the brooks corey and the gardner russo constitutive relationships these models also account for the spatial variability in effective water content while the spatial variability is generally neglected in most existing stochastic models analytical solutions are obtained for the case of one dimensional gravity dominated flow on the basis of the solutions we illustrate the differences between results from these two constitutive models through some one dimensional examples it is found that the impacts of the constitutive models on the statistical moments of suction head effective water content unsaturated hydraulic conductivity and velocity depend on the saturation ranges for example the mean head and the mean effective water content for the brooks corey model differ in a great manner with their counterparts for the gardner russo model near the dry and wet limits while the differences are small at the intermediate range of saturation this finding is confirmed with some two dimensional examples it is also found that the brook corey model has certain advantages over the gardner russo model in analyzing unsaturated flow in heterogeneous media for example the stochastic model developed based on the brooks corey function requires the coefficient of variation of head and soil parameter bc to be small 1 whereas that based on the gardner russo function assumes the one point cross covariance of head and olgr to be small 1 illustrative examples reveal that the latter condition may be violated because the one point covariance is found to increase rapidly to beyond unity as the soil becomes dry whereas the former may be readily satisfied