control design of uncertain quantum systems with fuzzy estimators an approach of control design using fuzzy estimators fes is proposed for quantum systems with uncertainties two types of quantum control problems are considered 1 control of a pure state quantum system in the presence of uncertainties and 2 control design of quantum systems with initial mixed states and uncertainties for the first type of tasks a partial feedback control scheme with an fe is presented to design controllers in this scheme an fe is trained to estimate the quantum state for feedback control of a quantum system and controlled projective measurement is used to assist in controlling the system for the second type of quantum control tasks a probabilistic fuzzy estimator pfe is trained to estimate the quantum state for control design of a quantum system with an initial mixed state and a corresponding control algorithm is proposed to design a control law that drives the system from the mixed state to a target pure state two examples of two spin 1 2 systems are also presented and analyzed to demonstrate the process of control design and potential applications of the proposed approach

a probabilistic fuzzy logic system for modeling and control in this paper a probabilistic fuzzy logic system pfls is proposed for the modeling and control problems similar to the ordinary fuzzy logic system fls the pfls consists of the fuzzification inference engine and defuzzification operation to process the fuzzy information different to the fls it uses the probabilistic modeling method to improve the stochastic modeling capability by using a three dimensional membership function mf the pfls is able to handle the effect of random noise and stochastic uncertainties existing in the process a unique defuzzification method is proposed to simplify the complex operation finally the proposed pfls is applied to a function approximation problem and a robotic system it shows a better performance than an ordinary fls in stochastic circumstance

minimizing total tardiness on one machine is np hard the problem of minimizing the total tardiness for a set of independent jobs on one machine is considered lawler has given a pseudo polynomial time algorithm to solve this problem in spite of extensive research efforts for more than a decade the question of whether it can be solved in polynomial time or it is np hard in the ordinary sense remained open in this paper the problem is shown to be np hard in the ordinary sense

quantum risk sensitive estimation and robustness this paper studies a quantum risk sensitive estimation problem and investigates robustness properties of the filter this is a direct extension to the quantum case of analogous classical results all investigations are based on a discrete approximation model of the quantum system under consideration this allows us to study the problem in a simple mathematical setting we close the paper with some examples that demonstrate the robustness of the risk sensitive estimator

ensemble control of bloch equations in this article we study a class of control problems which involves controlling a continuum of dynamical systems with different values of parameters characterizing the system dynamics by using the same control signal we call such problems control of ensembles the motivation for looking into these problems comes from the manipulation of an ensemble of nuclear spins in nuclear magnetic resonance nmr spectroscopy and imaging mri with dispersions in natural frequencies and the strengths of the applied radio frequency rf field from the standpoint of mathematical control theory the challenge is to simultaneously steer a continuum of systems between points of interest with the same control input this raises some new and unexplored questions about controllability of such systems we show that controllability of an ensemble can be understood by the study of the algebra of polynomials defined by the noncommuting vector fields that govern the system dynamics a systematic study of these systems has immediate applications to broad areas of control of ensembles of quantum systems as arising in coherent spectroscopy and quantum information processing the new mathematical structures appearing in such problems are excellent motivation for new developments in control theory

steady state groundwater flow simulation with imprecise parameters a methodology based on fuzzy set theory is developed to incorporate imprecise parameters into steady state groundwater flow models in this case fuzzy numbers are used to represent parameter imprecision as such they are also used as a measure for the uncertainty associated with the hydraulic heads due to the imprecision in the input parameters the imprecise input parameters may come from indirect measurements subjective interpretation and expert judgment of available information in the methodology a finite difference method is combined with level set operations to formulate the fuzzy groundwater flow model this fuzzy modeling technique can handle imprecise parameters in a direct way without generating a large number of realizations two numerical solution methods are used to solve the fuzzy groundwater flow model the groundwater model operator method proposed in this methodology and the iterative algorithm based on conventional interval arithmetics the iterative method is simple but may overestimate the uncertainty of hydraulic heads the groundwater model operator method not only provides the hull of the solution set for the hydraulic heads but also considers the dependence of hydraulic head coefficients which are functions of imprecise parameters sensitivity analysis shows that the dependence of hydraulic head coefficients has a critical impact on the model results and neglecting this dependence may result in significant overestimation of the uncertainty of hydraulic heads a numerical model based on the methodology is tested by comparing it with the analytical solution for a homogeneous radial flow problem it is also applied to a simplified two dimensional heterogeneous flow case to demonstrate the methodology

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

minimizing total tardiness in permutation flowshops we consider the permutation flowshop scheduling problem with the objective of minimizing total tardiness presented are several properties that are used to calculate lower bounds on total tardiness of jobs for a given partial sequence and to identify sequences dominated by others we develop a branch and bound algorithm using these bounds and a dominance rule results of computational experiments on randomly generated problems are reported

note on shim and kim s lower bounds for scheduling on identical parallel machines to minimize total tardiness abstract this note introduces a new lower bound for the problem of scheduling on parallel identical machines to minimize total tardiness that is based on the concepts used in the two lower bounds developed by shim and kim shim s o kim y d 2007 scheduling on parallel identical machines to minimize total tardiness european journal of operational research 177 135 146 the note shows that the new lower bound dominates the three lower bounds used in shim and kim s branch and bound algorithm and can be used in place of these lower bounds to lower the enumeration required

transfer function approach to quantum control part i dynamics of quantum feedback systems this paper gives a unified approach to feedback control theory of quantum mechanical systems of bosonic modes described by noncommutative operators a quantum optical closed loop including a plant and controller is developed and its fundamental structural properties are analyzed extensively from a purely quantum mechanical point of view in order to facilitate the use of control theory in microscopic world described by quantum theory in particular an input output description of quantum mechanical systems which is essential in describing the behavior of the feedback systems is fully formulated and developed this would then provide a powerful tool for quantum control and pave an avenue that connects control theory to quantum dynamics this paper is divided into two parts the first part is devoted to the basic formulation of quantum feedback control via quantum communication and local operations on an optical device cavity that can be regarded as a unit of quantum dynamics of bosonic modes the formulation introduced in this paper presents the feature intrinsic in quantum feedback systems based on quantum stochastic differential equations the input output description provides a basis for developing quantum feedback control through the transfer function representation of quantum feedback systems in the follow up paper the quantum mechanical representation of feedback is further elaborated to yield the control theoretical representation of fundamental notions of quantum theory uncertainty principle e g and some applications are presented

more on stochastic models in a recent review article g sposito et al 1986 examined the various stochastic theories which are concerned with transport of solutes in porous media in this short note we expand on their discussion to include several topics which had been omitted we begin by looking at two definitions of probability theory and their relation to the concept of an ensemble an rev ensemble of soils is defined and examined the concept of ergodicity is reviewed and it is pointed out that most stochastic models are theoretically unverifiable the relationship between scale of measurement and stochasticity is briefly reviewed and an equation that combines the two concepts is presented

mechanics of heterogeneous porous media with several spatial scales by extending the theory of homogenization we consider a heterogeneous porous medium whose material structure is characterized by multiple periodicity over several disparate length scales because for geological and engineering applications the driving force e g the pressure gradient and the global motion of primary interest is usually at a scale much larger than the largest of structural periodicity we derive the phenomenological equations of motion by using the perturbation technique of multiple scales all the effective coefficients are defined by boundary value problems on unit cells in smaller scales and no constitutive assumptions are added aside from the basic equations governing the mechanics of the pore fluid and the solid matrix in part i the porous matrix is assumed to be rigid the case of three scales is treated first symmetry and positiveness of the effective darcy permeability tensor are proven extensions to four and more scales are then discussed in part ii we allow the solid matrix to be deformable and deduce the equations of consolidation of a two phase medium the coupling of fluid flow and the quasi static elastic deformation of the matrix is considered when there are three disparate length scales effective coefficients of various kinds are deduced in terms of cell problems on the scale of the pores several general symmetry relations as well as specific properties of a medium composed of layers of porous matrix are discussed

solving the steady state groundwater flow equation for finite linear aquifers using a generalized fourier series approach in two dimensional domains a method to solve steady linear groundwater flow problems using generalized fourier series is developed and particularized for multiple fourier series in two dimensional domains it leads to a linear vector equation whose solution provides a finite number of generalized fourier coefficients approximating the hydraulic head field its implementation is shown and two relevant properties are found for the system matrix it is always symmetric and once computed if additional fourier terms are needed for a better approximation of the hydraulic head field previously computed matrix elements remain invariant i e only new rows and columns are added to the system matrix the method is demonstrated in three simple cases with different geometries and transmissivity fields where solutions are compared with analytical and finite element method results thus the method is verified as an alternative to other flow solvers additionally it provides a direct way to obtain the spectral form of the flow equation solution given a spectral representation of transmissivity and can be easily extended to obtain continuous velocity fields and their approximated spectral expressions copyright 2009 john wiley sons ltd

scheduling on parallel identical machines to minimize total tardiness this paper focuses on the problem of scheduling n independent jobs on m identical parallel machines for the objective of minimizing total tardiness of the jobs we develop dominance properties and lower bounds and develop a branch and bound algorithm using these properties and lower bounds as well as upper bounds obtained from a heuristic algorithm computational experiments are performed on randomly generated test problems and results show that the algorithm solves problems with moderate sizes in a reasonable amount of computation time

controllability of quantum systems with switching control this article focuses on wavefunction controllability of a class of quantum systems with switching control first we present a specific quantum system which is not wavefunction controllable under the action of any one of two controllers with different fixed structures however we prove that the system is wavefunction controllable if the control input is allowed to switch between the two controllers then we present a sufficient condition for wavefunction controllability of a class of quantum systems with switching control and briefly discuss the problem of control design for such quantum control systems finally two illustrative examples are presented to demonstrate a possible control design process for the proposed method

a branch and bound algorithm for the total weighted tardiness problem this paper presents a new branch and bound algorithm for the single machine total weighted tardiness problem it obtains lower bounds using a lagrangian relaxation approach with subproblems that are total weighted completion time problems the well known subgradient optimization technique is replaced by a multiplier adjustment method that leads to an extremely fast bound calculation the method incorporates various devices for checking dynamic programming dominance in the search tree extensive computational results for problems with up to 50 jobs show the superiority of the algorithm over existing methods

stabilizing feedback controls for quantum systems no quantum measurement can give full information on the state of a quantum system hence any quantum feedback control problem is necessarily one with partial observations and can generally be converted into a completely observed control problem for an appropriate quantum filter as in classical stochastic control theory here we study the properties of controlled quantum filtering equations as classical stochastic differential equations we then develop methods using a combination of geometric control and classical probabilistic techniques for global feedback stabilization of a class of quantum filters around a particular eigenstate of the measurement operator

large time behavior of macrodispersion in heterogeneous trending aquifers 1 this paper presents a stochastic analysis of the large time behavior of macrodispersion in a three dimensional heterogeneous aquifer with a linear trend in the mean log hydraulic conductivity to solve the problem analytically focus is placed on the particular case where the linear trend is aligned in the direction of mean hydraulic head gradient a spectral approach based on fourier stieltjes representations for the perturbed quantities is used to develop closed form expressions that describe variability of flow velocity the second order mean flow and asymptotic macrodispersion the impact of the mean log hydraulic conductivity gradient on these results is examined it is found that the asymptotic longitudinal and transverse macrodispersion coefficients decrease with the increasing trend gradient of mean log hydraulic conductivity in the case of finite peclet numbers this feature is a consequence of the reduction in variability of flow velocity with the trend gradient

analysis and synthesis of attractive quantum markovian dynamics we propose a general framework for investigating a large class of stabilization problems in markovian quantum systems building on the notions of invariant and attractive quantum subsystem we characterize attractive subspaces by exploring the structure of the invariant sets for the dynamics our general analysis results are exploited to assess the ability of open loop hamiltonian and output feedback control strategies to synthesize markovian generators which stabilize a target subsystem subspace or pure state in particular we provide an algebraic characterization of the manifold of stabilizable pure states in arbitrary finite dimensional markovian systems that leads to a constructive strategy for designing the relevant controllers implications for stabilization of entangled pure states are addressed by example

spatially constrained fuzzy clustering based sensor placement for spatiotemporal fuzzy control system many industrial processes are spatiotemporal dynamic systems a three dimensional fuzzy logic controller 3 d flc has been recently developed to process the inherent capability of spatiotemporal dynamic systems sensor placement which is always crucial to the control of spatiotemporal dynamic systems is also critical to the design of the 3 d flc in this paper a new sensor placement strategy is developed its main feature is to position the sensor by utilizing the main characteristics of spatial distribution the key technique is to use a spatial constrained fuzzy c means algorithm to extract the characteristics of spatial distribution for an easy implementation a systematic sensor placement design scheme in four steps i e data collection dimension reduction data clustering and sensor locating is developed finally control of a catalytic packed bed reactor is taken as an application to demonstrate the effectiveness of the proposed sensor placement scheme

scale and directional dependence of macrodispersivities in colonnade networks macrodispersion in discrete colonnade network models is investigated using a series of monte carlo type numerical experiments the numerical simulations consider fluid flow and advective transport through a square flow region of a two dimensional network of hexagonal colonnades macrodispersivities are calculated as a function of the scale and orientation of the square flow region within the larger parent geometry particle tracking with flux weighted tracer injection and monitoring is used to generate experimental residence time distributions rtds the method of moments is used to characterize the longitudinal tracer spreading the simulated rtds are utilized to examine the macrodispersive behavior in colonnade networks column diameter 1 m with lognormally distributed fracture apertures b in millimeters the network models are assumed to consist of open fractures with ln b 1 945 and ln b 0 896 this translates to an equivalent continuum log conductivity variance ln k2 of 3 67 based on an ensemble average of 100 realizations the slope for spatial variance versus scale of observation ranges from 3 15 to 3 36 m for varying orientations of the hydraulic gradient for ensemble averaged data the varying orientations appear to have little effect on the macrodispersive behavior for single realization experiments the computed macrodispersivities are directionally dependent at a length scale as large as 30 times the column diameter and probably much beyond the computed asymptotic and preasymptotic macrodispersivities are compared with available stochastic solutions for two dimensional isotropic heterogeneity in the horizontal plane the ensemble based numerical data are in excellent agreement with the solutions of dagan 1984 1988 and gelhar and axness 1983 however for individual realizations nonergodic behavior is clearly apparent in the near source evolving region of transport and the numerical data are quite variable between realizations the study provides important insight on applicability of stochastic continuum theories to discrete colonnade network models having ln k2 much greater than 1

a higher order approximation to effective conductivity in media of anisotropic random structure properties of the effective conductivity tensor keff are studied by deriving the second order terms in its expansion in the variance 2 of normally distributed log conductivity it is shown that for media of anisotropic structure the components of the effective conductivity tensor are expressed by a functional of the log conductivity covariance that is it depends on the shape of the correlation function and not only on anisotropy ratios variance 2 and space dimensions however the trace of keff is independent of the log conductivity autocovariance and for a given mean conductivity depends only on 2 the dependence of the effective conductivity on the correlation structure is illustrated for gaussian and exponential autocovariances of log conductivity and for two and three dimensional flows

coherent quantum lqg control based on a recently developed notion of physical realizability for quantum linear stochastic systems we formulate a quantum lqg optimal control problem for quantum linear stochastic systems where the controller itself may also be a quantum system and the plant output signal can be fully quantum such a control scheme is often referred to in the quantum control literature as coherent feedback control it distinguishes the present work from previous works on the quantum lqg problem where measurement is performed on the plant and the measurement signals are used as the input to a fully classical controller with no quantum degrees of freedom the difference in our formulation is the presence of additional non linear and linear constraints on the coefficients of the sought after controller rendering the problem as a type of constrained controller design problem due to the presence of these constraints our problem is inherently computationally hard and this also distinguishes it in an important way from the standard lqg problem we propose a numerical procedure for solving this problem based on an alternating projections algorithm and as an initial demonstration of the feasibility of this approach we provide fully quantum controller design examples in which numerical solutions to the problem were successfully obtained for comparison we also consider the case of classical linear controllers that use direct or indirect measurements and show that there exists a fully quantum linear controller which offers an improvement in performance over the classical ones

simulation of contaminant transport in three dimensions 1 the alternating direction galerkin technique the alternating direction galerkin technique for the simulation of advective dispersive transport in three dimensions is developed the technique is designed for high efficiency in handling the large and detailed grids that are often required in simulations of natural groundwater systems it is comparable to an alternating direction finite difference scheme except for two advantages first the capability to handle certain curvilinear grids that may conform to either a flow net geometry or a natural stratigraphy and second the option to enhance solution accuracy through a choice between a finite difference or a finite element representation of the time derivative criteria for controlling numerical dispersion and accuracy can be applied easily three options for the time stepping algorithm are developed and analyzed for stability and their accuracy is investigated for simple flow systems the technique is shown to be far more efficient than a conventional three dimensional finite element model in a companion paper an application to a field scale contaminant transport problem is described

pseudopotential functions in construction of flow nets for contaminant transport modeling construction of flow nets in most hydrogeologic field problems is complicated by nonexistence of orthogonality between streamlines and hydraulic head lines in anisotropic porous media the nonexistence of orthogonality can be circumvented by transformation of the anisotropic porous medium into an isotropic one flow nets are valuable in generation of a numerical solution grid for a contaminant transport equation formulated along the direction of flow and the direction orthogonal to flow effect of flow domain transformation on contaminant transport simulation is not known the flow domain transformation can be avoided by constructing flow nets with streamlines and pseudopotential lines the pseudopotential lines are based on the theory of pseudopotential function a discussion of the theory in isotropic porous media exists in literature to my knowledge this is the first time that the theory is being extended to anisotropic porous media an integration procedure is used to evaluate values of pseudopotential function and hydraulic head along a streamline a comparison of flow nets based on pseudopotential lines and hydraulic head lines indicates that pseudopotential lines are more useful than hydraulic head lines in simulation of contaminant transport in saturated groundwater flow systems

systems control with generalized probabilistic fuzzy reinforcement learning reinforcement learning rl is a valuable learning method when the systems require a selection of control actions whose consequences emerge over long periods for which input output data are not available in most combinations of fuzzy systems and rl the environment is considered to be deterministic in many problems however the consequence of an action may be uncertain or stochastic in nature in this paper we propose a novel rl approach to combine the universal function approximation capability of fuzzy systems with consideration of probability distributions over possible consequences of an action the proposed generalized probabilistic fuzzy rl gpfrl method is a modified version of the actor critic ac learning architecture the learning is enhanced by the introduction of a probability measure into the learning structure where an incremental gradient descent weight updating algorithm provides convergence our results show that the proposed approach is robust under probabilistic uncertainty while also having an enhanced learning speed and good overall performance

is measurement based feedback still better for quantum control systems in this paper we put forward a fundamental question concerning feedback control of quantum systems is measurement based feedback control still better than open loop control in contrast to the classical control theory the answer is far from obvious this is because measurement based feedback needs measurement to reduce the system uncertainty whereas the measurement on a quantum system will inevitably increase the system uncertainty in turn in fact there is a complicated tradeoff between the uncertainty introduced and the information gained by the measurement on a quantum system to investigate this fundamental problem we will only focus on a typical model of coherent control mode with and without the decoherence term in the paper by establishing some fundamental limits on the performances of both the open loop and measurement based feedback controls we will demonstrate via simulation that the measurement based feedback control of quantum systems is still superior to the open loop control in some sense for the typical model under consideration

stochastic analysis of spatial variability in two dimensional steady groundwater flow assuming stationary and nonstationary heads two dimensional steady groundwater flow in a confined aquifer with spatially variable transmissivity t is analyzed stochastically using spectral analysis and the theory of intrinsic random functions conditions that ensure a stationary statistically homogeneous head process are derived and using two convenient forms for the covariance function of the ln t process the head covariance function is studied in addition the head variogram is obtained for a particular nonstationary case and the asymptotic head variogram is derived under very general conditions results are compared to those obtained by gelhar 1976 for one and two dimensional phreatic flow and bakr et al 1978 for one and three dimensional confined flow multidimensional flow analysis results in a significantly reduced head variance the head correlation remains high over much greater distances than the ln t correlation the variogram obtained when stationary heads are assumed is identical to that obtained for nonstationary heads for dimensionless lag distances up to 2 times the correlation scale of the log transmissivity the variogram for nonstationary heads continues to grow logarithmically as lag distance increases independent of the form of the input covariance in the nonstationary case the conditions for stationarity are contrasted with the corresponding results obtained for the one and three dimensional cases of gutjahr and gelhar 1981 the head variance calculated from the stationary theory is found to agree with that of previous monte carlo simulations

an alternating direction galerkin technique for simulation of contaminant transport in complex groundwater systems a general contaminant transport simulation technique based on a galerkin finite element representation in space and an alternating direction time stepping scheme is developed the formulation which is in terms of natural coordinates following the principal directions of hydraulic conductivity of the medium decouples the spatial components of the equations leading to tridiagonal matrices the numerical accuracy can be easily controlled in each principal direction through the well established peclet and courant numbers results are found to be comparable to those from the classic finite element scheme but the cost of computation is generally much less because the computational effort varies only linearly with the grid size the technique is thus well suited for transport simulations with complex layered anisotropic groundwater systems requiring large and detailed grids

the spatial and temporal moments of tracer concentration in disordered porous media this study develops a methodology for deriving the spatial and temporal moments of tracer concentration in disordered geological formations and suggests a geostatistical formalism for interpolation and prediction of concentration conditional to concentration measurements the required spatial and temporal moments of the concentration are obtained by a biparticle tracking scheme which yields the bivariate probability distribution function of particle displacements in terms of the input log conductivity random field and the prevailing flow conditions the structure of the moments of the concentration is discussed and we show that 1 the concentration correlation function is anisotropic nonstationary and nonsymmetrical 2 there is a larger correlation between concentrations along the mean flow direction than normal to it 3 the correlation between the concentration at any two points with fixed coordinates on a moving lagrangian coordinate system increases with travel time 4 the correlation function necessarily assumes negative values beyond a certain threshold distance and 5 the concentration variance is finite even when neglecting pore scale dispersion application of the geostatistical prediction algorithm using the concentration spatial temporal moments shows a good potential for reducing prediction uncertainty

weighted tardiness scheduling on parallel machines with proportional weights in this paper we address the problem of scheduling a number of jobs on a bank of parallel machines to minimize the total weighted tardiness under the assumption that the weight of each job is proportional to its processing time the version of the problem that has general weights has been shown to be strongly np complete we prove this version of the problem to be np complete and give a pseudopolynomial time algorithm for solving it we study a family of simple sequencing rules in which the jobs are sequenced in increasing order of i di pi where di is the due date of job i pi its processing time wi its weight and 0 1 this family of sequencing rules generalizes the earliest due date sequencing rule we obtain bounds on the ratio c c iwipi where c and c are the costs of the heuristic and optimal schedules respectively the denominator is the cost of having each job be late by its own processing time it is intended to measure what is or is not a large deviation from optimali

parallelization of a fuzzy control algorithm using quantum computation quantum computation is proposed for the parallelization of a fuzzy logic control flc algorithm quantum computation speeds up the fuzzy inference since serial operations between matrices of large dimensionality are now replaced by a one step quantum addition or a quantum subtraction the unitarity properties of the algorithm prove that the flc stands for a simulator of a quantum computing machine

a quasi linear theory of non fickian and fickian subsurface dispersion 1 theoretical analysis with application to isotropic media a theory is presented which accounts for nonlinearity caused by the deviation of plume particles from their mean trajectory in three dimensional statistically homogeneous but anisotropic porous media under an exponential covariance of log hydraulic conductivities existing linear theories predict that in the absence of local dispersion transverse dispersivities tend asymptotically to zero as fickian conditions are reached according to our new quasi linear theory these dispersivities ascend to peak values and then diminish gradually toward nonzero fickian asymptotes which are proportional to y4 when the log hydraulic conductivity variance y2 is much less than 1 all existing theories agree that in isotropic media the asymptotic longitudinal dispersivity is proportional to y2 when y2 1 and all are nominally restricted to mildly heterogeneous media in which this inequality is satisfied however the quasi linear theory appears to be less prone to error than linear theories when extended to strongly heterogeneous media because it deals with the above nonlinearity without formally limiting y2 it predicts that when y 1 in isotropic media both the longitudinal and transverse dispersivities ascend monotonically toward fickian asymptotes proportional to y

flow in heterogeneous media displaying a linear trend in the log conductivity the purpose of this study is to derive a general solution for the problem of flow in nonstationary geological formations where the nonstationary manifests itself in the form of a spatial trend in the mean log conductivity a stochastic frame of reference is adopted to account for the spatial variability of the hydraulic conductivity for a complete stochastic description we derive the expected values and spatial covariances of the hydraulic head and the fluid flux vector as well as a relation between the expected values of the head and the fluxes these expressions are obtained using a perturbation expansion of the log conductivity about its nonstationary mean and they are correct to the first order in the variance of the log conductivity the expressions we derive are applicable for any space dimensionality and for arbitrary orientation of the trend in space a general methodology is outlined for derivation of these expressions for any type of spatial covariance and for demonstration explicit results are obtained for a gaussian isotropic covariance 16 refs 6 figs

robust incoherent control of qubit systems via switching and optimisation a robust incoherent quantum control scheme via projective measurements plus unitary transformations is proposed for driving a qubit system from an unknown initial mixed state to an arbitrary target pure state this scheme consists of two main steps projective measurement on the initial mixed state and optimal control between two pure states the first step projects the initial state into an eigenstate of the qubit system by projective measurement and guarantees that the proposed scheme is robust to different initial mixed states the second step finds a set of suitable optimal controls to drive the qubit system from the conditional eigenstate to the target pure state the connection between the two steps is accomplished by a switching strategy to accomplish the second step two approaches are presented in detail these approaches are time optimal transition with unbounded control and bang bang control with minimal switches the minimal time and minimal number of switches in these approaches can be calcu

feedback stabilization of isospectral control systems on complex flag manifolds application to quantum ensembles the convex set of density operators of an n level quantum mechanical system foliated as a complex flag manifold where each leaf is identified with the adjoint unitary orbit of the eigenvalues of a density matrix for an isospectral bilinear control system evolving on such an orbit the state feedback stabilization problem admits a natural lyapunov based time varying feedback design a global description of the domain of attraction of the closed loop system can be provided based on a ldquoroot spacerdquo like structure of the cone of density operators the converging conditions are time independent but depend on the topology of the flag manifold it is shown that the closed loop must have a number of equilibria at least equal to the euler characteristic of the manifold thus imposing topological obstructions to global stabilizability

macrodispersivity tensor for nonreactive solute transport in isotropic and anisotropic fractal porous media analytical solutions using spectral stochastic theory macrodispersivity tensors are developed for one two and three dimensional isotropic and anisotropic fractal porous media since natural geologic aquifers are always bounded we introduce the concept of a maximum length scale lmax in the one dimensional case the asymptotic long time longitudinal macrodispersivity a is proportional to lmax2 and in the multidimensional cases a lmax in the multidimensional cases as the fractal dimension increases a decreases because a larger fractal dimension means the tortuosity of solute particles is larger leading to more mixing in the transverse direction which in turn reduces longitudinal spreading the transverse macrodispersivities are shown to be analogous to traditional spectral stochastic results in the multidimensional cases lmax is shown to be controlled by the aquifer thickness as a result ergodic conditions may be reached in relatively thin aquifers allowing the use of the asymptotic macrodispersivity expressions obtained here for single realizations

feedback control of quantum state reduction feedback control of quantum mechanical systems must take into account the probabilistic nature of quantum measurement we formulate quantum feedback control as a problem of stochastic nonlinear control by considering separately a quantum filtering problem and a state feedback control problem for the filter we explore the use of stochastic lyapunov techniques for the design of feedback controllers for quantum spin systems and demonstrate the possibility of stabilizing one outcome of a quantum measurement with unit probability

simulation of contaminant plumes with large dispersive contrast evaluation of alternating direction galerkin models the evolution of narrow sharply defined contaminant plumes corresponding in shape to those often observed in the field is examined it is shown that the transverse dispersion mechanism consistent with such shapes can be as low as of the order of molecular diffusion and that dispersivity contrasts of as much as 4 orders of magnitude are possible even at the lowest physically realistic values of transverse dispersion parameters however transverse mass spreading is capable of significantly retarding the advance of the plume front the principal direction and alternating direction galerkin models together are found to be capable of handling all cases of dispersive contrast including those with dispersivity ratio of infinity the models are formulated in curvilinear coordinates with certain restrictions on the element deformation a three way comparison between principal direction alternating direction galerkin and conventional finite element models is performed with respect to accuracy and efficiency the effects of longitudinal and transverse numerical dispersion occuring in the various models are examined and related to the discretization visual indications of the presence of numerical error are discussed

using the nonstationary spectral method to analyze flow through heterogeneous trending media this paper describes a nonstationary spectral theory for analyzing flow in a heterogeneous porous medium with a systematic trend in log hydraulic conductivity this theory relies on a linearization of the groundwater flow equation but does not require the stationarity assumptions used in classical spectral theories the nonstationary theory is illustrated with a two dimensional analysis of a linear trend aligned with the mean flow direction in this case closed form solutions can be obtained for the effective hydraulic conductivity head covariance and log conductivity head cross covariance the effective hydraulic conductivity decreases from the geometrical mean as the mean slope of the log conductivity increases trending leads to a reduction of head variance and a structural change in the head covariance and the log conductivity head cross covariance such changes have important implications for measurement conditioning or cokriging methods which rely on the head covariance and log conductivity head covariance the nonstationary spectral analysis is also compared with classical spectral analysis this comparison indicates that the classical spectral method correctly predicts the normalized head covariance in a linear trending media the stationary spectral method fails to capture the qualitative influence of trends on the effective hydraulic conductivity and the log conductivity head cross covariance although the magnitude of the error is relatively small for realistic values of the mean log conductivity slope the stationary and nonstationary results are the same when there is no trend in log conductivity the trending conductivity example illustrates that the nonstationary spectral method has all the capabilities of the classical spectral approach while not requiring as many restrictive assumptions

h infty control of linear quantum stochastic systems the purpose of this paper is to formulate and solve a h infin controller synthesis problem for a class of noncommutative linear stochastic systems which includes many examples of interest in quantum technology the paper includes results on the class of such systems for which the quantum commutation relations are preserved such a requirement must be satisfied in a physical quantum system a quantum version of standard classical dissipativity results are presented and from this a quantum version of the strict bounded real lemma is derived this enables a quantum version of the two riccati solution to the h infin control problem to be presented this result leads to controllers which may be realized using purely quantum purely classical or a mixture of quantum and classical elements this issue of physical realizability of the controller is examined in detail and necessary and sufficient conditions are given our results are constructive in the sense that we provide explicit formulas for the hamiltonian function and coupling operator corresponding to the controller

stochastic modeling of groundwater flow by unconditional and conditional probabilities 2 the solute transport the problem of solute transport in a heterogeneous formation whose transmissivity or hydraulic conductivity are subject to uncertainty is studied for two and three dimensional flows approximate closed form solutions are derived for the case of a solute pulse in an average uniform flow through a formation of unconditional stationary random transmissivity the solute concentration regarded as a random variable is determined in terms of its expectation and variance and is found to be subject to a high degree of uncertainty the uncertainty is greatly reduced if the solute input zone is large compared to the transmissivity integral scale in any case the concentration expectation does not obey a diffusion type equation in the case of two dimensional flows unless the solute body has traveled a distance larger than a few tens transmissivity integral scales this distance may be exceedingly large in many conceivable applications

on the dagan model of solute transport in groundwater foundational aspects the convection dispersion equation cde developed by dagan 1984 to predict the ensemble average concentration of a conservative solute in groundwater has been used successfully to interpret recent tracer experiments in a sand aquifer at the borden site in canada this successful application encouraged further investigation of the dagan model in respect to its physical basis and predictive characteristics it is shown in the present paper which deals with the first topic that the dagan model cde can be derived through an extension of the cumulant expansion technique applied previously by chu and sposito 1980 to develop a mean cde for solute transport in homogeneous porous media this technique also leads directly to the mean cde developed by gelhar and axness 1983 as an asymptotic large time limit and to model dispersion coefficients derived by mather on and de marsily 1980 and guven and moiz 1986 the dagan cde then is considered in detail in respect to which conceptualization of the solute concentration resident or flux the model may utilize in predictive applications general mathematical expressions relating the two conceptualizations are derived for an arbitrary solute transport problem and then are applied to the dagan model for point and prism source inputs finally the dagan model is interpreted physically using data from the recent tracer experiments of roberts and mackay 1986 at the borden site it is shown that model predictions of resident and flux concentrations are numerically indistinguishable on any time scale over which field solute concentration measurements typically are made the model prediction of dispersion coefficients on the other hand leads to dramatic differences in predicted plume behavior depending on whether finite time expressions or their asymptotic limits are used according to the dagan model the asymptotic transverse dispersion coefficient cannot replace the time dependent coefficient on any realistic time scale for solute movement at the borden site

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 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

on spectral measure and monte carlo approaches to flow in heterogeneous media a pedagogical approach to the spectral integral method as applied to flow problems is presented the deterministic fourier analog to the random spectral integral is highlighted thus illustrating the close ties between the two the general solution to the deterministic flow problem is used to illustrate that a weakly stationary conductivity field does not in general lead to a weakly stationary head field several alternative monte carlo methods are presented and compared to illustrate the problems associated with dropping terms of the form h from the flow equation where and h are respectively perturbations in the conductivity and head fields

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

high resolution monte carlo simulation of flow and conservative transport in heterogeneous porous media 1 methodology and flow results in this the first of two papers concerned with the use of numerical simulation to examine flow and transport parameters in heterogeneous porous media via monte carlo methods various aspects of the modelling effort are examined in particular the need to save on core memory causes one to use only specific realizations that have certain initial characteristics in effect these transport simulations are conditioned by these characteristics also the need to independently estimate length scales for the generated fields is discussed the statistical uniformity of the flow field is investigated by plotting the variance of the seepage velocity for vector components in the x y and z directions finally specific features of the velocity field itself are illuminated in this first paper in particular these data give one the opportunity to investigate the effective hydraulic conductivity in a flow field which is approximately statistically uniform comparisons are made with first and second order perturbation analyses the mean cloud velocity is examined to ascertain whether it is identical to the mean seepage velocity of the model finally the variance in the cloud centroid velocity is examined for the effect of source size and differing strengths of local transverse dispersion

stochastic models of subsurface flow infinite versus finite domains and stationarity stochastic solutions of the differential equation describing one dimensional flow through a porous medium with spatially variable hydraulic conductivity which is represented by a stationary statistically homogeneous random process are developed using several techniques the analytical approximations using first order analysis propagation of error covariance differential equations and variogram analysis all yield consistent results which demonstrate the important effects of boundary conditions and conditioning using the theory of intrinsic random functions stochastic solutions are developed for the case when the logarithm of the hydraulic conductivity is a three dimensional stationary random field in contrast to the one dimensional case it is found that the resulting three dimensional head perturbation will be locally stationary under very general conditions results from the one dimensional analytical solutions are found to be in agreement with previous monte carlo simulations for a flow system of finite length the solution based on linearization in the logarithm of hydraulic conductivity proved to be very robust showing reasonable agreement with monte carlo results even for the largest input standard deviation of lnk 4 6

a three dimensional fuzzy control methodology for a class of distributed parameter systems the traditional fuzzy set is two dimensional 2 d with one dimension for the universe of discourse of the variable and the other for its membership degree this 2 d fuzzy set is not able to handle the spatial information the traditional fuzzy logic controller flc developed from this 2 d fuzzy set should not be able to control the distributed parameter system that has the tempo spatial nature a three dimensional 3 d fuzzy set is defined to be made of a traditional fuzzy set and an extra dimension for spatial information based on concept of the 3 d fuzzy set a new fuzzy control methodology is proposed to control the distributed parameter system similar to the traditional flc it still consists of fuzzification rule inference and defuzzification operations different to the traditional flc it uses multiple sensors to provide 3 d fuzzy inputs and possesses the inference mechanism with 3 d nature that can fuse these inputs into a so called ldquospatial membership function rdquo thus a simple 2 d rule base can still be used for two obvious advantages one is that rules will not increase as sensors increase for the spatial measurement the other is that computation of this 3 d fuzzy inference can be significantly reduced for real world applications using only a few more sensors the proposed flc is able to process the distributed parameter system with little complexity increased from the traditional flc the 3 d flc is successfully applied to a catalytic packed bed reactor and compared with the traditional flc the results demonstrate its effectiveness to the nonlinear unknown distributed parameter process and its potential to a wide range of engineering applications