on unifying the concepts of scale instrumentation and stochastics in the development of multiphase transport theory a generalized theory of multiphase transport is presented which combines the concepts of scale instrumentation stochastics and time series with the development of transport equations by defining the filtering process as a convolution of a measure p with a field property we are able to exploit the fourier transform to place plausible restrictions on an instrument in frequency space so as to make its measurement relevant to its physical environment an ideal instrument is defined which filters out high frequency noise corresponding to short distances and yet does not alter the structure of low frequencies using ideal instruments we successively filter out lower frequency noise in a multiscale multiphase environment formulas are developed to relate the autocorrelation of a field property on one scale of motion to that on any other scale while taking into account the types of instruments used in the measuring process an equation relating the integral scale on one scale of motion to the integral scale on any other scale of motion is developed power spectra are developed which relate spectra on different scales to the measuring instrument used by successively applying filtering theorems a hierarchy of multiscale transport equations is developed filtered properties in the transport equations are mass averages different properties are allowed to be measured by different instruments and different instruments are allowed on different scales of motion and for different phases the concept of a wide sense stationary ergodic process is introduced to develop mass average autocorrelations and spectra over scales of motion as a function of measuring devices

approximation algorithms for the feedback vertex set problem with applications to constraint satisfaction and bayesian inference a feedback vertex set of an undirected graph is a subset of vertices that intersects with the vertex set of each cycle in the graph given an undirected graph g with n vertices and weights on its vertices polynomial time algorithms are provided for approximating the problem of finding a feedback vertex set of g with smallest weight when the weights of all vertices in g are equal the performance ratio attained by these algorithms is 4 2 n this improves a previous algorithm which achieved an approximation factor of o sqrt log n for this case for general vertex weights the performance ratio becomes min 2 delta 2 4 log 2 n where delta denotes the maximum degree in g for the special case of planar graphs this ratio is reduced to 10 an interesting special case of weighted graphs where a performance ratio of 4 2 n is achieved is the one where a prescribed subset of the vertices so called blackout vertices is not allowed to participate in any feedback vertex set it is shown how these algorithms can improve the search performance for constraint satisfaction problems an application in the area of bayesian inference of graphs with blackout vertices is also presented

sharp l 2 error estimates and superconvergence of mixed finite element methods for non fickian flows in porous media a sharper l2 error estimate is obtained for the non fickian flow of fluid in porous media by means of a mixed ritz volterra projection instead of the mixed ritz projection used in r e ewing y lin and j wang acta math univ comenian n s 70 2001 pp 75 84 moreover local l2 superconvergence for the velocity along the gauss lines and for the pressure at the gauss points is derived for the mixed finite element method via the ritz volterra projection and global l2 superconvergence for the velocity and the pressure is also investigated by virtue of an interpolation postprocessing technique on the basis of the superconvergence estimates some useful a posteriori error estimators are presented for this mixed finite element method

two splitting positive definite mixed finite element methods for parabolic integro differential equations abstract two novel mixed finite element procedures are established for parabolic integro differential equations which can be split into two independent symmetric positive definite sub schemes and do not need to solve a coupled system of equations without requiring the lbb consistency condition the convergence analysis shows that both methods lead to the optimal order l 2 norm error estimate for u and optimal h div norm error estimate for a numerical example is presented to illustrate the theoretical analysis

convergence analysis of compact difference schemes for diffusion equation with nonlocal boundary conditions difference schemes for solving the diffusion equation with nonlocal boundary conditions are considered compact difference is used and the integrals are approximated by the composite simpson scheme convergence of the two compact schemes are derived using the energy method compact difference schemes for solving the diffusion equation with nonlocal boundary conditions are considered in this paper fourth order compact difference is used to approximate the second order spatial derivative and the integrals in the boundary conditions are approximated by the composite simpson quadrature formula the backward euler and crank nicolson schemes are presented as the fully discrete schemes error estimates in the discrete h1 and l norms are given by the energy method showing both schemes are fourth order accurate in space and they have first order and second order accuracy in time respectively numerical results are provided to confirm the theoretical results

geometry of the modulational instability iii homoclinic orbits for the periodic sine gordon equation in this paper the homoclinic geometric structure of the integrable sine gordon equation under periodic boundary conditions is developed specifically focus is given to orbits homoclinic to n tori simple examples of such homoclinic orbits are constructed and a physical interpretation of these states is given a labeling is provided which identifies and catalogues all such orbits these orbits are related in a one to one manner to linearized instabilities explicit formulas for all homoclinic orbits are given in terms of backlund transformations

the bar partial cauchy problem and nonexistence of lipschitz levi flat hypersurfaces in mathbb c p n with n ge 3 in this paper we study the cauchy riemann equation in complex projective spaces specifically we use the modified weight function method to study the bar partial neumann problem on pseudoconvex domains in these spaces the solutions are used to study function theory on pseudoconvex domains via the bar partial cauchy problem we apply our results to prove nonexistence of lipschitz levi flat hypersurfaces in complex projective spaces of dimension at least three which removes the smoothness requirement used in an earlier paper of siu

numerical algorithms for diffusion reaction problems with non classical conditions abstract parabolic equations with nonlocal boundary conditions have been given considerable attention in recent years in this paper new high order algorithms for the linear diffusion reaction problem are derived the convergence of the new schemes is studied and numerical examples are given to show the efficiency of the new methods to solve linear and nonlinear diffusion reaction equations with these non classical conditions

weighted boundary limits of the generalized kobayashi royden metrics on weakly pseudoconvex domains the purpose of this paper is to study the existence of weighted boundary limits of the generalized kobayashi royden metrics on weakly pseudoconvex domains in cn and to explore the connections between the limits and the levi invariants the main result extends graham s result on strongly pseudoconvex domains to a large class of weakly pseudoconvex domains

stability of the weighted splitting finite difference scheme for a two dimensional parabolic equation with two nonlocal integral conditions nonlocal conditions arise in mathematical models of various physical chemical or biological processes therefore interest in developing computational techniques for the numerical solution of partial differential equations pdes with various types of nonlocal conditions has been growing fast we construct and analyse a weighted splitting finite difference scheme for a two dimensional parabolic equation with nonlocal integral conditions the main attention is paid to the stability of the method we apply the stability analysis technique which is based on the investigation of the spectral structure of the transition matrix of a finite difference scheme we demonstrate that depending on the parameters of the finite difference scheme and nonlocal conditions the proposed method can be stable or unstable the results of numerical experiments with several test problems are also presented and they validate theoretical results

nonlocal reactive transport with physical and chemical heterogeneity localization errors the origin of nonlocality in macroscale models for subsurface chemical transport is illustrated it is argued that media that are either nonperiodic e g media with evolving heterogeneity or periodic viewed on a scale wherein a unit cell is discernible must display some nonlocality in the mean a metaphysical argument suggests that owing to the scarcity of information on natural scales of heterogeneity and on scales of observation associated with an instrument window constitutive theories for the mean concentration should at the outset of any modeling effort always be considered nonlocal the intuitive appeal to nonlocality is reinforced with an analytical derivation of the constitutive theory for a conservative tracer without appeal to any mathematical approximations deng et al 1993 present a first order nonlocal eulerian theory for transport of a conservative solute in an infinite nondeforming domain under steady flow conditions hu et al this issue extended these results to account for nonequilibrium linear sorption with random partition coefficient kd but deterministic constant reaction rate kr these theories are localized herein and comparisons are made between the fully nonlocal fnl nonlocal in time nlt and fully localized fl theories for conservative transport there is little difference between the first order fl and fnl models for spatial moments up to and including the third however for conservative transport the first order nlt model differs significantly from the fnl model in the third spatial moments for reactive transport all spatial moments differ between the fnl and fl models the second transverse horizontal and third longitudinal horizontal moments for the nlt model differ from the fnl model these results suggest that localized first order transport models for conservative tracers are reasonable if only lower order moments are desired however when the chemical reacts with its environment the localization approximation can lead to significant error in all moments and a fnl model will in general be required for accurate simulation

three dimensional stochastic analysis of macrodispersion in aquifers the dispersive mixing resulting from complex flow in three dimensionally heterogeneous porous media is analyzed using stochastic continuum theory stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three dimensional statistically anisotropic input covariance describing the hydraulic conductivity with a statistically isotropic input covariance the longitudinal macrodispersivity is convectively controlled but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term with an arbitrarily oriented anisotropic conductivity covariance all components of the macrodispersivity tensor are convectively controlled and the ratio of transverse to longitudinal dispersivity is of the order of 10 1 in this case the off diagonal components of the dispersivity tensor are significant being numerically larger than the diagonal transverse terms and the transverse dispersion process can be highly anisotropic dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and monte carlo simulations the theory which treats the asymptotic condition of large displacement indicates that a classical gradient transport fickian relationship is valid for large scale displacements

goldilocks domains a weak notion of visibility and applications in this paper we introduce a new class of domains in complex euclidean space called goldilocks domains and study their complex geometry these domains are defined in terms of a lower bound on how fast the kobayashi metric grows and an upper bound on how fast the kobayashi distance grows as one approaches the boundary strongly pseudoconvex domains and weakly pseudoconvex domains of finite type always satisfy this goldilocks condition but we also present families of goldilocks domains that have low boundary regularity or have boundary points of infinite type we will show that the kobayashi metric on these domains behaves in some sense like a negatively curved riemannian metric in particular it satisfies a visibility condition in the sense of eberlein and o neill this behavior allows us to prove a variety of results concerning boundary extension of maps and to establish wolff denjoy theorems for a wide collection of domains c 2017 elsevier inc all rights reserved

equivalence of bicontinuum and second order transport in heterogeneous soils and aquifers the mathematical equivalence of a closed second order transport equation for reactive solutes in saturated heterogeneous porous media e g soils and aquifers and a two region mobile mobile formulation is demonstrated in two ways 1 by averaging the bicontinuum equations and 2 by transforming the second order equation to canonical form the derivation of this equivalence is limited to media with heterogeneities in a plane orthogonal to the flow direction which represents a bidirectional generalization of the stratified case results indicate how the parameters of the bicontinuum formulation can be obtained from statistical descriptions of this heterogeneity and establish a stochastic interpretation for the bicontinuum equations one dimensional analytical solutions of the equivalent transport equations are compared to a three dimensional numerical simulation of transport in a spatially autocorrelated lognormal random conductivity field results indicate that the upscaled equations provide good approximations of the dynamics of the mean resident concentration the flux averaged concentration and their variances

influence of solitons in the initial state on chaos in the driven damped sine gordon system abstract the appearance of chaos in the a c driven damped sine gordon equation is studied numerically several transitions from periodic to chaotic behaviour are investigated in detail for flat initial conditions spatial structures breather kink in the initial conditions smooth out many of these transitions and give rise to an interesting symbiosis of time and spatial intermittency this symbiosis appears to be due to the competition between the background tendency towards chaos and the system s preference to maintain a spatial pattern the way that this competition is relieved is also found to depend very strongly on symmetry in the initial conditions

spatial characterization of a hydrogeochemically heterogeneous aquifer using partitioning tracers optimal estimation of aquifer parameters in this paper a distributed parameter extended kalman filter is developed to estimate spatially distributed residual saturation of nonaqueous phase liquids napl and darcy flux and to predict site specific movement of a partitioning tracer plume in a three dimensional heterogeneous aquifer the napl and darcy flux fields are assumed to be time invariant spatial random fields with known spatial correlation structures the extended kalman filter consists of two components 1 a moment propagation algorithm that uses a set of coupled stochastic partial differential equations derived from the advection dispersion retardation equation to predict how the moments propagate through space between measurement times zhang and graham this issue and 2 a moment update algorithm which updates the moments at measurement times because the optimal kalman filtering algorithm is computationally intensive for three dimensional problems a simplified sequential conditioning algorithm is developed that first conditions the darcy flux field using only nonpartitioning tracer measurements and then conditions the napl field using only partitioning tracer measurements the extended kalman filter is applied to a three dimensional domain patterned after the interwell partitioning tracer tests conducted at hill air force base by annable et al 1998 two different cross correlation scenarios and two different sampling networks are investigated

eulerian lagrangian theory of transport in space time nonstationary velocity fields exact nonlocal formalism by conditional moments and weak approximation a unified eulerian lagrangian theory is presented for the transport of a conservative solute in a random velocity field that satisfies locally v x t f x t where f x t is a random function including sources and or the time derivative of head solute concentration satisfies locally the eulerian equation c x t t j x t g x t where j x t is advective solute flux and g x t is a random source independent of f x t we consider the prediction of c x t and j x t by means of their unbiased ensemble moments c x t and j x t conditioned as implied by the subscript on local hydraulic measurements through the use of the latter in obtaining a relatively smooth unbiased estimate x t of v x t these predictors satisfy c x t v t j x t g x t where j x t x t c x t q x t and q x t is a dispersive flux we show that q is given exactly by three space time convolution integrals of conditional lagrangian kernels with q with c and with c for a broad class of v x t fields including fractals this implies that q x t is generally nonlocal and non fickian rendering c x t non gaussian the direct contribution of random variations in f to q depends on c rather than on c we elucidate the nature of the above kernels discuss conditions under which the convolution of and c becomes pseudo fickian with a lagrangian dispersion tensor similar to that derived in 1921 by taylor recall a 1952 result by batchelor which yields an exact expression for c at early time use the latter to conclude that linearizations which predict that c bifurcates at early time when the probability density function of v is unimodal cannot be correct propose instead a weak approximation which leads to a nonlinear integro differential equation for c due to an instantaneous point source and which improves with the quantity and quality of hydraulic data demonstrate that the weak approximation is analogous to the direct interaction closure of turbulence theory offer non fickian and pseudo fickian weak approximations for the second conditional moment of the concentration prediction error demonstrate that it yields the so called two particle covariance as a special case conclude that the conditional variance of c does not become infinite merely as a consequence of disregarding local dispersion and discuss how to estimate explicitly the cumulative release of a contaminant across a compliance surface together with the associated estimation error

numerical solution of parabolic integro differential equations by the discontinuous galerkin method the numerical solution of a parabolic equation with memory is considered the equation is first discretized in time by means of the discontinuous galerkin method with piecewise constant or piecewise linear approximating functions the analysis presented allows variable time steps which as will be shown call then efficiently be selected to match singularities in the solution induced by singularities in the kernel of the memory term or by nonsmooth initial data the combination with finite element discretizat in space is also studied

on diffusion in fractal porous media generalized hydrodynamics and irreversible thermodynamics are used to derive the relation between a general wave vector and frequency dependent diffusion tensor and the power spectral density the results are valid for porous media with evolving heterogeneities an integrodifferential transport equation valid in porous media with evolving heterogeneities is presented

the bergman metric on complete kahler manifolds we use the existence of a bounded uniformly holder continuous plurisubharmonic exhaustion function to characterize the bergman completeness of a complete kahler manifold as an application we proved that any simply connected complete kahler manifold with sectional curvature bounded above by a negative constant is bergman complete

fem ids for a second order strongly damped wave equation with memory abstract a linear triangular finite element method implicit difference scheme fem ids for the solution of second order strongly damped wave equation sdwe with memory on domain with interfaces is proposed sufficient conditions that guarantee the existence of a unique solution are given the finite element discretization is such that the arbitrary but smooth interface is first approximated by a polygon with a boundary whose vertices all lie on the interface with the interface being at distance from the approximate interface linear interpolation operator incorporating the influence of isproved this together with ritz volterra operator and some auxiliary error estimates in the neighborhood of the interface are used to obtain the convergence estimate of the proposed scheme the scheme is applied to some test examples and the numerical results confirm the computational efficiency of the method

on a singular two dimensional nonlinear evolution equation with nonlocal conditions abstract this paper deals with a nonclassical initial boundary value problem for a two dimensional parabolic equation with bessel operator we prove the existence and uniqueness of the weak solution of the given nonlinear problem we start by solving the associated linear problem after writing this latter in its operator form we establish an a priori bound from which we deduce the uniqueness of the strong solution for the solvability of the associated linear problem we prove that the range of the operator generated by the considered problem is dense on the basis of the obtained results of the linear problem we apply an iterative process to establish the existence and uniqueness of the nonlinear problem

finite difference methods for solution of nonlocal boundary value problems the article is devoted to the construction and investigation of various types of difference schemes relevant to nonlocal boundary value problems stated for multidimensional elliptic equations suitable tools for performing the investigation are developed including difference analogue of green s formula and inequalities corresponding to nonlocal boundary conditions

a nonlinear nonlocal mixed problem for a second order pseudoparabolic equation we study a nonlocal mixed problem for a nonlinear pseudoparabolic equation which can for example model the heat conduction involving a certain thermodynamic temperature and a conductive temperature we prove the existence uniqueness and continuous dependence of a strong solution of the posed problem we first establish for the associated linear problem a priori estimate and prove that the range of the operator generated by the considered problem is dense the technique of deriving the a priori estimate is based on constructing a suitable multiplicator from the resulted energy estimate it is possible to establish the solvability of the linear problem then by applying an iterative process based on the obtained results for the linear problem we establish the existence uniqueness and continuous dependence of the weak solution of the nonlinear problem

exact effective transport dynamics in a one dimensional random environment we study effective transport under linear equilibrium adsorption characterized by a spatially random retardation factor in a stochastic framework we present a methodology to quantify explicitly the impact of spatial disorder on effective transport dynamics we derive an exact effective transport equation which is equivalent to transport under linear kinetic adsorption characterized by a spectrum of adsorption times the distribution of adsorption times is given explicitly in terms of the spatial disorder distribution furthermore we find that effective transport is formally equivalent to a decoupled continuous time random walk this observation and the explicit nature of the presented results allow for a mapping of the static disorder distribution on the transition time distribution

an 8 approximation algorithm for the subset feedback vertex set problem we present an 8 approximation algorithm for the problem of finding a minimum weight subset feedback vertex set or subset fvs in short the input in this problem consists of an undirected graph g v e with vertex weights c v and a subset of vertices s called special vertices a cycle is called interesting if it contains at least one special vertex a subset of vertices is called a subset fvs with respect to s if it intersects every interesting cycle the goal is to find a minimum weight subset fvs the best previous algorithm for the general case provided only a logarithmic approximation factor the minimum weight subset fvs problem generalizes two np complete problems the minimum weight feedback vertex set problem in undirected graphs and the minimum weight multiway vertex cut problem the main tool that we use in our algorithm and its analysis is a new version of multicommodity flow which we call relaxed multicommodity flow relaxed multicommodity flow is a hybrid of multicommodity flow and multiterminal flow

asymptotic behavior of solutions of reaction diffusion equations with nonlocal boundary conditions abstract this paper is concerned with some dynamical property of a reaction diffusion equation with nonlocal boundary condition under some conditions on the kernel in the boundary condition and suitable conditions on the reaction function the asymptotic behavior of the time dependent solution is characterized in relation to a finite or an infinite set of constant steady state solutions this characterization is determined solely by the initial function and it leads to the stability and instability of the various steady state solutions in the case of finite constant steady state solutions the time dependent solution blows up in finite time when the initial function in greater than the largest constant solution also discussed is the decay property of the solution when the kernel function in the boundary condition prossesses alternating sign in its domain

a fast fourier transform stochastic analysis of the contaminant transport problem a three dimensional stochastic analysis of the contaminant transport problem is developed in the spirit of naff 1990 the new derivation is more general and simpler than previous analysis the fast fourier transformation is used extensively to obtain numerical estimates of the mean concentration and various spatial moments data from both the borden and cape cod experiments are used to test the methodology results are comparable to results obtained by other methods and to the experiments themselves

aquifer operator scaling and the effect on solute mixing and dispersion 1 since aquifer parameters may have statistical dependence structures that are present across a huge range of scales the concepts of fractional brownian motion fbm have been used in both analytic and numerical stochastic settings most previous models have used isotropic scaling characterized by a single scalar hurst coefficient any real world anisotropy has been handled by an elliptical stretching random k field we define a d dimensional extension of fbm in which the fractional order integration may take on different orders in the d primary possibly nonorthogonal scaling directions and the degree of connectivity and long range dependence is freely assigned via a probability measure on the unit sphere this approach accounts for the different scaling found in the vertical versus horizontal directions in sedimentary aquifers and allows very general degrees of continuity of k in certain directions it also allows for the representation of fracture networks in a continuum setting the eigenvectors of the scaling matrix describe the primary fracture scaling directions and discrete weights of fractional integration represent fracture continuity that may be limited to a small number of directions in a numerical experiment the motion of solutes through 2 d operator fractional gaussian fields depends very much on transverse hurst coefficients transverse scaling in the range of fractional gaussian noise engenders greater plume mixing and a transition to a fickian regime higher orders of integration in the range of fractional brownian motion are associated with thicker layering of aquifer sediments and more preferential unmixed transport therefore direct representation of the unique directional scaling properties of an aquifer is important for realistic simulation of transport

influence of complex coefficients on the stability of difference scheme for parabolic equations with non local conditions abstract the stability of a finite difference scheme for schrodinger kuramoto tsuzuki and parabolic equations subject to non local conditions with complex coefficients is dealt with the stability conditions which have to be met by complex coefficients in non local conditions have been determined the main result of this study is that complex coefficients together with non local conditions cause new effects on the stability of difference scheme numerical experiment has revealed additional regularities in the stability conditions

numerical solutions of reaction diffusion equations with nonlocal boundary conditions abstract the purpose of this paper is to present some iterative methods for numerical solutions of a class of nonlinear reaction diffusion equations with nonlocal boundary conditions using the finite difference method and the method of upper and lower solutions we present some monotone iterative schemes for both the time dependent and the steady state finite difference systems each monotone iterative scheme gives a computational algorithm for numerical solutions and an existence comparison theorem for the corresponding finite difference system the existence comparison theorems are used to investigate the asymptotic behavior of the discrete time dependent solution in relation to the discrete maximal and minimal solutions of the steady state problem numerical results are given to a model problem where the solution of the continuous problem is explicitly known and its values at the mesh points are used to compare with the numerical solutions obtained by the monotone iterative schemes

the two level finite difference schemes for the heat equation with nonlocal initial condition abstract in this paper the two level finite difference schemes for the one dimensional heat equation with a nonlocal initial condition are analyzed as the main result we obtain conditions for the numerical stability of the schemes in addition we revise the stability conditions obtained in 21 for the crank nicolson scheme we present several numerical examples that confirm the theoretical results within linear as well as nonlinear problems in some particular cases it is shown that for small regions of the time step size values the explicit ftcs scheme is stable while certain implicit methods such as crank nicolson scheme are not

inertial effects in dispersion in porous media 1 in this work we develop the macroscale transport equation for dispersion of a nonreactive chemical species with a particular focus on the influence of inertial contributions at moderate reynolds numbers our starting point is the continuum level description of transport written at the subpore scale volume averaging is used to upscale these equations to develop the macroscale solute balance that applies at the darcy scale we develop a fully transient version of the ancillary closure problem that predicts the total dispersion tensor and we solve the closure using finite fourier transforms the result of this effort is a nonlocal macroscale transport equation where the nonlocal dispersion depends upon the microscale geometry of the pore space and the physical characteristics of the fluid both the longitudinal and transverse components of the total dispersion tensor are computed for a simple three dimensional unit cell the computational results indicate that a simple three dimensional periodic unit cell is able to capture the correct behavior for the longitudinal dispersion in the range 101 pep 2 5 105 although the magnitude of the longitudinal dispersion coefficient is underpredicted by up to a factor of about 4 for the transverse dispersion coefficient the simple unit cell provides much less satisfactory results when compared with experimental data the inertial effects for the longitudinal dispersion coefficient were relatively small but for the transverse dispersion coefficient inertial effects were predicted to increase the transverse dispersion coefficient up to 40 times that which would be predicted for stokes flow

numerical algorithm for parabolic problems with non classical conditions the parabolic problems with non classical conditions are discussed in a reproducing kernel space in this paper a reproducing kernel space is constructed in which the non classical conditions of the parabolic problems are satisfied based on the reproducing kernel space a new technique for solving the non classical parabolic problems is presented some examples are displayed to demonstrate the validity and applicability of the proposed method

macroscopic balance equations in soils and aquifers the case of space and time dependent instrumental response macroscopic balance equations for mass and linear momentum in soils and aquifers are derived in the relativist concept under the condition that all physical variables are associated with a single instrumental weighting function that depends on both position and time the resulting balance equations differ in concept from expressions obtained recently in the representative elementary volume rev approach by exhibiting additional terms that depend on the time and space derivatives of the instrumental weighting function these terms indicate that mass and linear momentum balance at the macroscopic scale are not preserved unless the weighting function has space time invariance properties over the period and spatial domain of measurement

fixed parameter tractability for subset feedback set problems with parity constraints the subset feedback set problem which is a generalization of the well known feedback vertex set problem is that we are given an undirected graph g with a vertex subset s and a positive integer k and the goal is to find a vertex set x of size at most k such that g x has no s cycle where an s cycle is a cycle having at least one vertex of s it was recently shown that this problem is fixed parameter tractable where k is the parameter in this paper we further generalize this problem to one with the parity constraints and show the fixed parameter tractability 1 for a parameter k there exists a fixed parameter algorithm that either finds a vertex set x of size k such that g x has no s cycle of even length or concludes that such a vertex set does not exist 2 for a parameter k there exists a fixed parameter algorithm that either finds a vertex set x of size k such that g x has no s cycle of odd length or concludes that such a vertex set does not exist

a min max theorem on feedback vertex sets we establish a necessary and sufficient condition for the linear system x hx e x 0 associated with a bipartite tournament to be totally dual integral whereh is the cycle vertex incidence matrix ande is the all one vector the consequence is a min max relation on packing and covering cycles together with strongly polynomial time algorithms for the feedback vertex set problem and the cycle packing problem on the corresponding bipartite tournaments in addition we show that the feedback vertex set problem on general bipartite tournaments isnp complete and approximable within 3 5 based on the min max theorem

a quantitative analysis of oka s lemma in this paper we will examine a strong form of oka s lemma which provides sufficient conditions for compact and subelliptic estimates for the overline partial neumann operator on lipschitz domains on smooth domains the condition for subellipticity is equivalent to d angelo finite type and the condition for compactness is equivalent to catlin s condition p as an application we will prove regularity for the overline partial neumann operator in the sobolev space ws 0 leq s frac 1 2 on c2 domains

the method of lines for solution of the one dimensional wave equation subject to an integral conservation condition hyperbolic partial differential equations with an integral condition serve as models in many branches of physics and technology recently much attention has been expended in studying these equations and there has been a considerable mathematical interest in them in this work the solution of the one dimensional nonlocal hyperbolic equation is presented by the method of lines the method of lines mol is a general way of viewing a partial differential equation as a system of ordinary differential equations the partial derivatives with respect to the space variables are discretized to obtain a system of odes in the time variable and then a proper initial value software can be used to solve this ode system we propose two forms of mol for solving the described problem several numerical examples and also some comparisons with finite difference methods will be investigated to confirm the efficiency of this procedure

a numerical approach for a semilinear parabolic equation with a nonlocal boundary condition a semilinear reaction diffusion problem with a nonlocal boundary condition is studied this paper presents a new and very easy implementable numerical algorithm for computations this is based on a suitable linearization in time and on the principle of linear superposition any method for the space discretization fem was taken in this analysis can be chosen the derived algorithm is implicit and it does not need any iteration scheme to get a solution with the nonlocal boundary condition stability analysis has been performed and the optimal error estimates have been derived numerical results have been compared with other known techniques

numerical solution of a parabolic equation subject to specification of energy in this paper special attention is devoted to one particular problem the diffusion equation subject to the specification of mass in a portion of the domain which has been studied quite extensively both analytically and numerically in recent years parabolic partial differential equations with a non local constraint in place of one of the standard boundary specifications feature in the mathematical modeling of many phenomena in this paper the application of the method of lines mol to such problems is considered the mol semi discretization approach will be used to transform the model partial differential equation into a system of first order linear ordinary differential equations odes the mol is a method of solving pdes by discretizing the equation with respect to all but one variable usually time the spatial partial derivative is approximated by a finite difference method the solution of the resulting system of first order odes satisfies a recurrence relation which involves a matrix exponential function numerical techniques are developed by approximating the exponential matrix function in this recurrence relation the matrix exponential function is approximated by a rational approximation consisting of four parameters new parallel algorithms are developed using the resulting approximation numerical experiments on two challenging examples are presented to illustrate the performance of the algorithms

plurisubharmonic approximation and boundary values of plurisubharmonic functions we study the problem of approximating plurisubharmonic functions on a bounded domain omega by continuous plurisubharmonic functions defined on neighborhoods of omega over bar it turns out that t

role of boundary conditions in convergence and nonlocality of solutions to stochastic flow problems in bounded domains steady flow through a heterogeneous porous medium in a bounded domain is investigated using a recursive perturbation scheme the effect of boundary conditions on a two dimensional flow with arbitrary variation of the mean flow allowing large gradients is investigated using analytical expressions for the head and velocity covariance functions boundary conditions were decomposed into deterministic and stochastic components two flow cases with the same zero order and different first order boundary conditions were analyzed boundary conditions are deterministic for the first case and random for the second significant differences between the two cases indicate random or absence of randomness processes must be modeled at boundaries first order solutions for the head and velocity covariance functions for a bounded rectangular domain are derived the resulting integral kernels involve greens functions and they are evaluated by numerical integration boundary conditions for higher order problems influence the absolute value and shape of the kernels and therefore of the head and velocity variance and covariance functions it is found that the validity of the perturbation scheme is dependent on the magnitude of the kernels and not only on the condition f2 1 where f is the variance of the log hydraulic conductivity assumed gaussian and weakly homogeneous in space the type of boundary conditions affects the values of the kernels and therefore determine the convergence limits for the problem milder head gradients also allow larger values of f2 nonlocality is also contingent on boundary type weakly homogeneous log fluctuating conductivity fields give rise to head and velocity covariances which are not weakly homogeneous the inhomogeneous fields are obtained from a linear filter of the solution to the problem without stochasticity higher gradient regions induce higher head and velocity variances in the presence of space varying gradients nonlocal effects are most important away from the boundaries lpar center of the domain small local head gradients result in small head and velocity gradients and therefore where observations are made in stagnation regions data should be analyzed taking into account this effect the results may be used to interpret experimental data for columns or data taken where conditions do not fit the average uniform flow assumption and when processes at the boundaries influence the flow and therefore the mixing of contaminants

the significance of heterogeneity of evolving scales to transport in porous formations flow takes place in a heterogeneous formation of spatially variable conductivity which is modeled as a stationary space random function to model the variability at the regional scale the formation is viewed as one of a two dimensional horizontal structure a constant head gradient is applied on the formation boundary such that the flow is uniform in the mean a plume of inert solute is injected at t 0 in a volume v0 under ergodic conditions the plume centroid moves with the constant mean flow velocity u and a longitudinal macrodispersion coefficient dl may be defined as half of the time rate of change of the plume second spatial moment with respect to the centroid for a log conductivity covariance cy of finite integral scale i at first order in the variance y2 and for a travel distance l ut i dl y2ui and transport is coined as fickian ergodicity of the moments is ensured if l i where l is the initial plume scale some field observations have suggested that heterogeneity may be of evolving scales and that the macrodispersion coefficient may grow with l without reaching a constant limit anomalous diffusion to model such a behavior previous studies have assumed that cy is stationary but of unbounded integral scale with cy ar 1 0 for large lag r under ergodic conditions it was found that asymptotically dl aul1 i e non fickian behavior and anomalous dispersion the present study claims that an ergodic behavior is not possible for a given finite plume of initial size l since the basic requirement that l i cannot be satisfied for cy of unbounded scale for instance the centroid does not move any more with u but is random figure 1 owing to the large scale heterogeneity in such a situation the actual effective dispersion coefficient dl is defined as half the rate of change of the mean second spatial moment with respect to the plume centroid in each realization this is the accessible entity in a given experiment we show that in contrast with dl the behavior of dl is controlled by l and it has the fickian limit dl aul1 figure 3 we also discuss the case in which y is of stationary increments and is characterized by its variogram y then u and dl can be defined only if y is truncated equivalently an infrared cutoff is carried out in the spectrum of y however for a bounded u it is shown that dl depends only on y furthermore for y ar dl aul2l 1 i e dispersion is fickian for 0 1 whereas for 1 2 transport is non fickian since 2 dl cannot grow faster than l ut this is in contrast with a recently proposed model neuman 1990 in which the dispersion coefficient is independent of the plume size and it grows approximately like l1 5

a galerkin method for two dimensional hyperbolic integro differential equation with purely integral conditions the present paper is devoted to the solution for two dimensional hyperbolic integro differential equations subject to purely integral conditions first it is demonstrated the existence and uniqueness of the solution under certain conditions for the numerical approach a galerkin method based on least squares is proposed the numerical examples illustrate the technique and show the efficiency of the proposed method

the complexity of multiterminal cuts in the multiterminal cut problem one is given an edge weighted graph and a subset of the vertices called terminals and is asked for a minimum weight set of edges that separates each terminal from all the others when the number k of terminals is two this is simply the mincut max flow problem and can be solved in polynomial time it is shown that the problem becomes np hard as soon as k 3 but can be solved in polynomial time for planar graphs for any fixed k the planar problem is np hard however if k is not fixed a simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of 2 2 k of the optimal cut weight is also described

a monte carlo assessment of eulerian flow and transport perturbation models monte carlo studies of flow and transport in two dimensional synthetic conductivity fields are employed to evaluate first order flow and eulerian transport theories hydraulic conductivity is assumed to obey fractional brownian motion fbm statistics with infinite integral scale or to have an exponential covariance structure with finite integral scale the flow problem is solved via a block centered finite difference scheme and a random walk approach is employed to solve the transport equation for a conservative tracer the model is tested for mass conservation and convergence of computed statistics and found to yield accurate results it is then used to address several issues in the context of flow and transport the validity of the first order relation between the fluctuating velocity covariance and the fluctuating log conductivity is examined the simulations show that for exponential covariance this approximation is justified in the mean flow direction for log conductivity variance f2 of the order of unity however as f2 increases the relation for the transverse velocity component deviates from the fully nonlinear monte carlo results eulerian transport models neglect triplet correlation functions that appear in the nonlocal macroscopic flux the relative importance of the triplet correlation term for conservative chemicals is examined this term appears to be small relative to the convolution flux term in mildly heterogeneous media as f2 increases or the integral scale grows the triplet correlation becomes significant in purely convective transport the triplet correlation term is significant if the heterogeneity is evolving the exact nonlocal macroscale flux for the purely convective case significantly differs from that of the convective dispersive transport this is in agreement with recent theoretical analysis and numerical studies and it suggests that neglecting local scale dispersion may lead to large errors localization errors in the flux term are evaluated using monte carlo simulations the nonlocal in time model significantly differs from the fully nonlocal model for small variance and integral scale there is a slight difference between the fully localized flux and the fully nonlocal convolution flux this is also in agreement with recent theories that suggest that moments through the second for the two models are nearly identical for conservative tracers the fully localized model does not perform well in the purely convective cases

the operational significance of the continuum hypothesis in the theory of water movement through soils and aquifers the operational meaning of the representative elementary volume rev concept on which current foundational theories of water movement through porous media are based is analyzed critically it is concluded that the rev concept as applied to real porous media is both unnecessarily restrictive and experimentally unverifiable in its place a relativist concept is proposed in which macroscopic physical variables are defined as convolution products of microscopic properties of a porous medium with weighting functions that represent the appropriate measuring instruments the effects of resolution and precision differences among experimental measuring devices now recognized as critical in the assessment of spatial variability in the properties of soils and aquifers can be incorporated naturally within the relativist concept but are excluded a priori in the rev concept the relativist point of view unlike the rev concept has a clear operational meaning and in principle extends theoretical validity to all local measurements made on porous media it is sufficient mathematically to derive conventional macroscopic balance equations for mass and linear momentum as well as a differential equation for the isothermal transport of water through an unsaturated anisotropic deformable soil or aquifer

monte carlo studies of flow and transport in fractal conductivity fields comparison with stochastic perturbation theory a monte carlo simulation of flow and transport is employed to study tracer migration in porous media with evolving scales of heterogeneity fractal media transport is studied with both conservative and reactive chemicals in media that possess physical as well as chemical heterogeneity linear kinetic equations are assumed to relate the sorbed phase and the aqueous phase concentrations the fluctuating log conductivity possesses the power law spectrum of a fractional brownian motion fbm chemical heterogeneity is represented as spatially varying reaction rates that also are assumed to obey fbm statistics and may be correlated to the conductivity field the model is based on a finite difference approximation to the flow problem and a random walk particle tracking approach for solving the solute transport equation the model is used to make comparisons with the nonlocal transport equations recently developed by deng et al 1993 and hu et al 1995 1997 the results presented herein support these nonlocal models for a wide range of heterogeneous systems however the infinite integral scale associated with the fractal conductivity has a significant effect on the prediction of the nonlocal theories this suggests that integral scale should play a role in stochastic eulerian perturbation theories the importance of the local scale dispersion depends to a great extent on the magnitude of the local dispersivities the effect of neglecting local dispersion decreases with the decrease in local dispersivity

a two grid block centered finite difference method for nonlinear non fickian flow model in this paper a two grid block centered finite difference scheme is introduced and analyzed to solve the nonlinear parabolic integro differential equation arising in modeling non fickian flow in porous media this method is considered where the nonlinear problem is solved only on a coarse grid of size h and a linear problem is solved on a fine grid of size h error estimates are established on non uniform rectangular grid which show that the discrete l l2 and l2 h1 errors are o t h 2 h 3 finally some numerical experiments are presented to show the efficiency of the two grid method and verify that the convergence rates are in agreement with the theoretical analysis

a meshless method on non fickian flows with mixing length growth in porous media based on radial basis functions a comparative study the present study aims to introduce a solution for parabolic integro differential equations arising in heat conduction in materials with memory which naturally occur in many applications two radial basis functions rbfs collocation schemes are employed for solving this equation the first method tested is an unsymmetric method and the second one which appears to be more efficient is a symmetric one the convergence of these two schemes is accelerated as we use the cartesian nodes as the center nodes

volume averaging for determining the effective dispersion tensor closure using periodic unit cells and comparison with ensemble averaging in this work we use the method of volume averaging to determine the effective dispersion tensor for a heterogeneous porous medium closure for the averaged equation is obtained by solution of a concentration deviation equation over a periodic unit cell our purpose is to show how the method of volume averaging with closure can be rectified with the results obtained by other upscaling methods under particular conditions although this rectification is something that is generally believed to be true there has been very little research that explores this issue explicitly we show that under certain limiting but mild assumptions the closure problem provides a fourier series solution for the effective dispersion tensor when second order spatial stationarity is imposed on the velocity field the method yields a simple fourier series that converges to an integral form in the limit as the period of the unit cell approaches infinity this limiting result is identical to the quasi fickian forms that have been developed previously via ensemble averaging by deng et al 1993 and recently by fiori and dagan 2000 except in the definition of the averaging operation as a second objective we have conducted a numerical study to evaluate the influence of the size of the averaging volume on the effective dispersion tensor and its volume averaged statistics this second objective is complimentary in many ways to recent research reported by rubin et al 1999 via ensemble averaging and by wang and kitanidis 1999 via volume averaging on the block averaged effective dispersion tensor the variability of the effective dispersion tensor from realization to realization is assessed by computing the volume averaged effective dispersion tensor for an ensemble of finite fields with the same ensemble statistics ensembles were generated using three different sizes of unit cells all three unit cell sizes yield similar results for the value of the mean effective dispersion tensor however the coefficient of variation depends strongly upon the size of the unit cell and our results are consistent with those developed by fiori 1998 from the ensemble averaging perspective this implies that in applications the actual value of the effective dispersion tensor may be significantly different than expected on the basis of unconditioned hydraulic conductivity statistics and this variation should be considered when applying macrodispersion to real world systems

the boundary penalty method for the diffusion equation subject to the specification of mass in this paper we concern with a new boundary penalty finite element method for the one dimensional time dependent diffusion equation subject to the specification of mass instead of solving the diffusion equation directly we will use the finite element method to solve a boundary penalty problem which is derived from the diffusion equation and analyse the error estimate of the semi discrete and fully discrete approximations when the penalty parameter e is sufficiently small the numerical experiments show that our method is very effective and supports our analysis