generation of coarse scale continuum flow models from detailed fracture characterizations 1 a procedure for developing coarse scale continuum models from detailed fracture descriptions is developed and applied the coarse models are in the form of a generalized dual porosity representation in which matrix rock and fractures exchange fluid locally while large scale flow occurs through the fracture network the methodology developed here introduces local subgrids to resolve dynamics within the matrix and provides appropriate coarse scale parameters describing fracture fracture matrix fracture and matrix matrix flow the geometry of the local subgrids as well as the required parameters for the coarse scale model are determined from local flow solutions using the underlying discrete fracture model the method is applied to two and three dimensional single phase and two phase flow problems and the accuracy of the coarse models is assessed relative to fully resolved discrete fracture simulations for the cases considered it is shown that the technique is capable of generating highly accurate coarse models with many fewer unknowns than the detailed characterizations and speedups of about a factor of 100 are achieved

stochastic analysis of transient saturated flow through heterogeneous fractured porous media a double permeability approach in this paper we use a double porosity double permeability approach to study transient saturated flow in heterogeneous fractured porous media the spatial variabilities in both the fracture and matrix continua motivate us to treat some of the fracture and matrix medium properties as stochastic processes hence flow through heterogeneous fractured porous media is also amenable to stochastic analysis in particular we develop a moment equation based stochastic theory for flow in fractured porous media we derive general equations governing the statistical moments of the pressure heads in such media by perturbation expansions the solutions of these moment equations are the first two moments of the pressure heads these may be used to construct the confidence intervals of the fracture and matrix pressure heads which are measures of uncertainties caused by incomplete knowledge of the fracture and matrix medium heterogeneities the resulting moment equations of pressure heads are coupled and need to be solved sequentially in an iterative manner the two dimensional version of the equations is implemented numerically and illustrated with some examples

the weak metric approximation property we introduce and investigate the weak metric approximation property of banach spaces which is strictly stronger than the approximation property and at least formally weaker than the metric approximation property among others we show that if a banach space has the approximation property and is 1 complemented in its bidual then it has the weak metric approximation property we also study the lifting of the weak metric approximation property from banach spaces to their dual spaces this enables us in particular to show that the subspace of c0 constructed by johnson and schechtman does not have the weak metric approximation property

an explicit formula of bounded feedback stabilizers for feedforward systems abstract this work constitutes continuation of a recent result of the same authors which provides an explicit formula for bounded feedback stabilizers for a wide class of triangular nonlinear systems in the present paper the previous result is extended for nonlinear systems having feedforward structure and whose linearization at the equilibrium is in general uncontrollable

the approximation property in terms of the approximability of weak weak continuous operators abstract by a well known result of grothendieck a banach space x has the approximation property if and only if for every banach space y every weak weak continuous compact operator t x y can be uniformly approximated by finite rank operators from x y we prove the following metric version of this criterion x has the approximation property if and only if for every banach space y every weak weak continuous weakly compact operator t x y can be approximated in the strong operator topology by operators of norm t from x y as application easier alternative proofs are given for recent criteria of approximation property due to lima nygaard and oja

robust adaptive sliding mode control for fuzzy systems with mismatched uncertainties this paper is devoted to design adaptive sliding mode controllers for the takagi sugeno t s fuzzy system with mismatched uncertainties and exogenous disturbances the uncertainties in state matrices are mismatched and norm bounded while the exogenous disturbances are assumed to be bounded with an unknown bound which is estimated by a simple and effective adaptive approach both state and static output feedback sliding mode control problems are considered in terms of linear matrix inequalities lmis both sliding surfaces and sliding mode controllers can be easily obtained via a convex optimization technique finally two simulation examples and a real experiment are utilized to illustrate the applicability and effectiveness of the design procedures proposed in this paper

contaminant transport in fractured porous media steady state solutions by a boundary integral method the problem of steady state transport of a decaying contaminant in a fractured porous rock matrix by two dimensional diffusion and vertical advection is solved using a powerful and readily generalizable numerical method worst case predictions of contaminant penetration are obtained by assuming that the uniform porous medium contains either a single vertical fracture or a periodic array of vertical fractures the method requires construction of appropriate green s functions which are here obtained analytically in both the fracture and matrix regions application of green s theorem in the plane then yields representations for the contaminant concentration in both regions in terms of integrals along their boundaries of known quantities and the unknown fracture matrix interfacial flux this flux is given by a fredholm integral equation which can be solved numerically to great accuracy using a simple discretization technique at sufficiently large distances vertically from the source the concentration is observed to be exponentially decaying although the concentration can in general only be obtained numerically an analytical method is developed which produces a uniformly valid and extremely accurate approximation to its vertical decay length also an assessment of the accuracy of analytical approximations made by various authors to solution of the full problem is provided the parameter space of validity of these simpler psuedo two dimensional models is determined

homogeneity with incremental degrees and global stabilisation of a class of high order upper triangular systems the problem of global asymptotic stabilisation is investigated for a class of upper triangular systems with uncontrollable linearisation a notion of generalised homogeneity is introduced in this article providing a new insight and a deeper perspective on how to categorise nonlinear terms into the higher order and equal order terms in a non traditional way the delicate analysis and new categorisation of the vector field make it possible to encompass more general nonlinearities a globally stabilising controller is recursively constructed by a bottom up step by step procedure containing the equal order terms as its indispensable components it is illustrated that the results obtained in this article incorporate and extend existing results for the global stabilisation of upper triangular systems

approximate solutions for diffusive fracture matrix transfer application to storage of dissolved co2 in fractured rocks author s zhou q oldenburg cm spangler lh birkholzer jt abstract 2017 american geophysical union all rights reserved analytical solutions with infinite exponential series are available to calculate the rate of diffusive transfer between low permeability blocks and high permeability zones in the subsurface truncation of these series is often employed by neglecting the early time regime in this paper we present unified form approximate solutions in which the early time and the late time solutions are continuous at a switchover time the early time solutions are based on three term polynomial functions in terms of square root of dimensionless time with the first coefficient dependent only on the dimensionless area to volume ratio the last two coefficients are either determined analytically for isotropic blocks e g spheres and slabs or obtained by fitting the exact solutions and they solely depend on the aspect ratios for rectangular columns and parallelepipeds for the late time solutions only the leading exponential term is needed for isotropic blocks while a few additional exponential terms are needed for highly anisotropic rectangular blocks the optimal switchover time is between 0 157 and 0 229 with highest relative approximation error less than 0 2 the solutions are used to demonstrate the storage of dissolved co2 in fractured reservoirs with low permeability matrix blocks of single and multiple shapes and sizes these approximate solutions are building blocks for development of analytical and numerical tools for hydraulic solute and thermal diffusion processes in low permeability matrix blocks

adaptive fuzzy robust output feedback control of nonlinear systems with unknown dead zones based on a small gain approach in this paper an adaptive fuzzy robust output feedback control problem is considered for a class of single input and single output nonlinear systems in a strict feedback form the considered systems possess the unstructured uncertainties unknown dead zone and the dynamics uncertainties and they do not assume the states being available for the controller design in the controller design fuzzy logic systems are first used to approximate the unstructured uncertainties and by utilizing the information of the bounds of the dead zone slopes and treating the time varying inputs coefficients as a system uncertainty a fuzzy state observer is designed to estimate the unmeasured states by combining a backstepping technique with a nonlinear small gain approach a new adaptive fuzzy robust output feedback control has been developed it is proved that the proposed fuzzy adaptive control approach can guarantee the semiglobal uniform ultimate boundedness for all the solutions of the closed loop systems simulation studies and comparisons with previous methods are included to illustrate the effectiveness of the proposed approach

the strong approximation property we introduce and investigate the strong approximation property of banach spaces which is strictly stronger than the approximation property and at least formally weaker than the weak bounded approximation property among others we show that the weak bounded approximation property is equivalent to a quantitative strengthening of the strong approximation property some recent results on the approximation property of banach spaces and their dual spaces are improved

revisiting the fundamental analytical solutions of heat and mass transfer the kernel of multirate and multidimensional diffusion there are two types of analytical solutions of temperature concentration in and heat mass transfer through boundaries of regularly shaped 1 d 2 d and 3 d blocks these infinite series solutions with either error functions or exponentials exhibit highly irregular but complementary convergence at different dimensionless times td in this paper approximate solutions were developed by combining the error function series solutions for early times and the exponential series solutions for late times and by using time partitioning at the switchover time td0 the combined solutions contain either the leading term of both series for normal accuracy approximations with less than 0 003 relative error or the first two terms for high accuracy approximations with less than 10 7 relative error for 1 d isotropic spheres cylinders slabs and 2 d 3 d rectangular blocks squares cubes rectangles and rectangular parallelepipeds this rapid and uniform convergence for rectangular blocks was achieved by employing the same time partitioning with individual dimensionless times for different directions and the product of their combined 1 d slab solutions the switchover dimensionless time was determined to minimize the maximum approximation errors furthermore the analytical solutions of first order heat mass flux for 2 d 3 d rectangular blocks were derived for normal accuracy approximations these flux equations contain the early time solution with a three term polynomial in td and the late time solution with the limited term exponentials for rectangular blocks the heat mass flux equations and the combined temperature concentration solutions form the ultimate kernel for fast simulations of multirate and multidimensional heat mass transfer in porous fractured media with millions of low permeability blocks of varying shapes and sizes

fuzzy approximation based adaptive backstepping optimal control for a class of nonlinear discrete time systems with dead zone in this paper an adaptive fuzzy optimal control design is addressed for a class of unknown nonlinear discrete time systems the controlled systems are in a strict feedback frame and contain unknown functions and nonsymmetric dead zone for this class of systems the control objective is to design a controller which not only guarantees the stability of the systems but achieves the optimal control performance as well this immediately brings about the difficulties in the controller design to this end the fuzzy logic systems are employed to approximate the unknown functions in the systems based on the utility functions and the critic designs and by applying the backsteppping design technique a reinforcement learning algorithm is used to develop an optimal control signal the adaptation auxiliary signal for unknown dead zone parameters is established to compensate for the effect of nonsymmetric dead zone on the control performance and the updating laws are obtained based on the gradient descent rule the stability of the control systems can be proved based on the difference lyapunov function method the feasibility of the proposed control approach is further demonstrated via two simulation examples

practical output tracking of nonlinear systems with uncontrollable unstable linearization the paper focuses on the problem of having the output of nonlinear systems track a prescribed c sup 1 reference signal it is proved that under mild assumptions global practical output tracking is achievable by smooth state feedback although asymptotic output tracking is usually not possible even locally because the linearized system has uncontrollable modes whose eigenvalues are on the right half plane smooth feedback controllers which solve the problem of global practical output tracking are explicitly constructed based on a modified adding a power integrator approach this feedback design method also leads to solutions to challenging benchmark control problems including practical output tracking of an underactuated unstable two degrees of freedom mechanical system

a new coupling term for dual porosity models numerous models are available for simulating dual porosity flow of groundwater heat or solute in a fractured porous medium each approach includes various approximations and results in models of varying complexity one of the simplest models has been proposed by both barenblatt et al 1960 and warren and root 1963 it assumes that the flow exchange of fluid heat or solute between the two porosity systems can be written as a linear function of the difference between averaged driving potentials pressure temperature or concentration this has been called a quasi static formulation because it can be shown to be correct only for long dimensionless time a new formulation of this model is proposed here which retains the original simplicity but is not restricted to very slow transient flows the integral method is used to derive the coupling term for the early parts of the transient regime

the p approximation property in terms of density of finite rank operators abstract we characterize the p approximation property p ap introduced by sinha and karn d p sinha a k karn compact operators whose adjoints factor through subspaces of l p studia math 150 2002 17 33 in terms of density of finite rank operators in the spaces of p compact and of adjoints of p summable operators as application the p ap of dual banach spaces is characterized via density of finite rank operators in the space of quasi p nuclear operators this relates the p ap to saphar s approximation property ap p as another application the p ap is characterized via a trace condition allowing to define the trace functional on certain subspaces of the space of nuclear operators

laplace transform inversion for late time behavior of groundwater flow problems 1 laplace transforms are widely used in solving groundwater flow problems in the groundwater literature it has frequently been asserted or assumed that the late time behavior is governed by the behavior of the laplace transform for small values of the laplace variable careful reading of authoritative monographs on laplace transforms shows that this correspondence does not generally hold in this article the proper asymptotic formula is reviewed and is applied to the problem of water influx into a slab like matrix block in a dual porosity medium in doing so we clear up a long standing discrepancy between the fracture matrix transfer coefficient that has been calculated by laplace methods and the coefficient which has been found by applying fourier methods in the time domain

bounded smooth state feedback and a global separation principle for non affine nonlinear systems abstract in this paper we show that a single input nonlinear system z 0 x g 1 x u g l x u l is globally asymptotically stabilizable by arbitrarily small smooth state feedback if unforced dynamics of are lyapunov stable and satisfies appropriate controllability like rank conditions characterized by the lie bracket of vector fields f0 x and g1 x an explicit smooth state feedback control law is constructed this in turn leads to an analytic resp smooth state feedback control law which solves the problem of global stabilization for analytic resp smooth systems x f x u based on these results we then establish a global separation principle for the system with an output finally we briefly discuss how the results can be extended to a multi input system

adaptive fuzzy control for a class of nonlinear discrete time systems with backlash an adaptive fuzzy controller design is studied for uncertain nonlinear systems in this paper the considered systems are of the discrete time form in a triangular structure and include the backlash and the external disturbance by using the prediction function of future states the systems are transformed into an n step ahead predictor the fuzzy logic systems flss are used to approximate the unknown functions unknown backlash and backlash inversion respectively a discrete time tuning algorithm is developed to estimate the optimal fuzzy parameters compared with the previous works for the discrete time systems with backlash the main contributions of the paper are that 1 the rigorous restriction for the functional estimation error is removed and 2 the external disturbance is bounded but the bound is not required to be known a novel controller and the adaptation laws are constructed by using the discrete taylor series expansion and the difference lyapunov analysis and thus those limitations in the previous works are overcome it is proven that all the signals in the closed loop system are bounded and that the system output can be to follow the reference signal to a bounded compact set a simulation example is provided to illustrate the effectiveness of the proposed approach

backstepping fuzzy adaptive control for a class of quantized nonlinear systems this paper proposes a new adaptive controller for a class of uncertain nonlinear systems with a quantized signal fuzzy logic systems are utilized to approximate nonlinear terms without imposing prior matching conditions required a hysteretic type of quantizer is incorporated to reduce chattering a new adaptive backstepping controller is designed to guarantee that the underlying uncertain nonlinear system is semiglobally uniformly ultimately bounded two numerical examples are presented to demonstrate the effectiveness and potential of the proposed techniques