an efficient hybrid approach for multiobjective optimization of water distribution systems an efficient hybrid approach for the design of water distribution systems wdss with multiple objectives is described in this paper the objectives are the minimization of the network cost and maximization of the network resilience a self adaptive multiobjective differential evolution samode algorithm has been developed in which control parameters are automatically adapted by means of evolution instead of the presetting of fine tuned parameter values in the proposed method a graph algorithm is first used to decompose a looped wds into a shortest distance tree t or forest and chords the original two objective optimization problem is then approximated by a series of single objective optimization problems of the t to be solved by nonlinear programming nlp thereby providing an approximate pareto optimal front for the original whole network finally the solutions at the approximate front are used to seed the samode algorithm to find an improved front for the original entire network the proposed approach is compared with two other conventional full search optimization methods the samode algorithm and the nsga ii that seed the initial population with purely random solutions based on three case studies a benchmark network and two real world networks with multiple demand loading cases results show that i the proposed nlp samode method consistently generates better quality pareto fronts than the full search methods with significantly improved efficiency and ii the proposed samode algorithm no parameter tuning exhibits better performance than the nsga ii with calibrated parameter values in efficiently offering optimal fronts

enhanced lower bounds for the global optimization of water distribution networks in this paper we address a global optimization approach to the problem of designing a water distribution network that satisfies specified flow demands at stated pressure head requirements the nonlinear nonconvex network problem is transformed into the space of certain design variables by relaxing the nonlinear constraints in the transformed space via suitable polyhedral outer approximations we derive a linear lower bounding problem this problem provides an enhancement of eiger et al s 1994 lower bounding scheme and takes advantage of the monotone concave convex nature of the nonlinear constraints upper bounds are computed by solving a projected linear program that uses the flow conserving solution generated by the lower bounding problem these bounding strategies are embedded within a branch and bound algorithm the partitioning scheme employed reduces the gap from optimality inducing a convergent process to a feasible solution that lies within any prescribed accuracy tolerance of global optimality the approach is illustrated using two standard test problems from the literature for the larger hanoi network problem a better incumbent than previously reported in the literature is obtained and is proven to be within 0 486 of optimality over the specified feasible domain used for this problem

global optimum tree solution for single source looped water distribution networks subjected to a single loading pattern a methodology based on linear programming lp is developed for obtaining the global optimum tree solution for single source looped water distribution networks wdns subjected to a single loading pattern initially a multiple link loop is considered and it is shown that the cost discharge curve is concavoconvex convex for local minima corresponding to trees and concave for discharges in between the logic is then extended to p loop networks for which the cost discharge surface is a p 1 dimensional hypersurface a tree of the looped wdn is initially selected optimized by lp and successively modified considering one loop at a time so that the solution jumps on the hypersurface from one local minimum to a better one the procedure is continued until no further improvement in local optimum solution occurs thus the final solution is the global optimum tree solution the optimization procedure is illustrated through a one source 31 demand node three loop wdn for which only 23 trees out of possible 1048 trees were required to be optimized for obtaining the global optimum tree solution since each link had to carry a minimum specified flow one more iteration was carried out in the end to satisfy the minimum flow constraint even though the tree solution is global optimum the final solution satisfying the minimum flow constraint cannot be claimed to be necessarily the global optimum

a combined nlp differential evolution algorithm approach for the optimization of looped water distribution systems 1 this paper proposes a novel optimization approach for the least cost design of looped water distribution systems wdss three distinct steps are involved in the proposed optimization approach in the first step the shortest distance tree within the looped network is identified using the dijkstra graph theory algorithm for which an extension is proposed to find the shortest distance tree for multisource wdss in the second step a nonlinear programming nlp solver is employed to optimize the pipe diameters for the shortest distance tree chords of the shortest distance tree are allocated the minimum allowable pipe sizes finally in the third step the original looped water network is optimized using a differential evolution de algorithm seeded with diameters in the proximity of the continuous pipe sizes obtained in step two as such the proposed optimization approach combines the traditional deterministic optimization technique of nlp with the emerging evolutionary algorithm de via the proposed network decomposition the proposed methodology has been tested on four looped wdss with the number of decision variables ranging from 21 to 454 results obtained show the proposed approach is able to find optimal solutions with significantly less computational effort than other optimization techniques

a modified linear programming gradient method for optimal design of looped water distribution networks a modified linear programming gradient lpg method is presented for solving looped water distribution network problems together with a mathematically rigorous derivation of the lpg model the lpg method of alperovits and shamir is modified in terms of both search direction and step size a quasi newton search direction is proposed instead of the steepest descent direction and the step size is determined by a backtracking line search method instead of a fixed step size the modified method is applied to a numerical example where it provides an improved solution in comparison to the original lpg method

an efficient constraint handling method for genetic algorithms many real world search and optimization problems involve inequality and or equality constraints and are thus posed as constrained optimization problems in trying to solve constrained optimization problems using genetic algorithms gas or classical optimization methods penalty function methods have been the most popular approach because of their simplicity and ease of implementation however since the penalty function approach is generic and applicable to any type of constraint linear or nonlinear their performance is not always satisfactory thus researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization however the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum in this paper ga s population based approach and ability to make pair wise comparison in tournament selection operator are exploited to devise a penalty function approach that does not require any penalty parameter careful comparisons among feasible and infeasible solutions are made so as to provide a search direction towards the feasible region once sufficient feasible solutions are found a niching method along with a controlled mutation operator is used to maintain diversity among feasible solutions this allows a real parameter ga s crossover operator to continuously find better feasible solutions gradually leading the search near the true optimum solution gas with this constraint handling approach have been tested on nine problems commonly used in the literature including an engineering design problem in all cases the proposed approach has been able to repeatedly find solutions closer to the true optimum solution than that reported earlier

the fractional order governing equation of levy motion a governing equation of stable random walks is developed in one dimension this fokker planck equation is similar to and contains as a subset the second order advection dispersion equation ade except that the order a of the highest derivative is fractional e g the 1 65th derivative fundamental solutions are levy s a stable densities that resemble the gaussian except that they spread proportional to time 1 a have heavier tails and incorporate any degree of skewness the measured variance of a plume undergoing levy motion would grow faster than fickian plume at a rate of time 2 a where 0 a 2 the equation is parsimonious since the parameters are not functions of time or distance the scaling behavior of plumes that undergo levy motion is accounted for by the fractional derivatives which are appropriate measures of fractal functions in real space the fractional derivatives are integrodifferential operators so the fractional ade describes a spatially nonlocal process that is ergodic and has analytic solutions for all time and space

local realizations and local polynomial matrix representations of systems we define the local polynomial matrix representations of a controllable matrix pair a b with elements in an arbitrary field f and the local realizations of a nonsingular polynomial matrix whose elements are in f s with respect to a nonempty subset of specm f s we give different characterizations of these local concepts in particular when f c local realizations and left null pairs as defined in gohberg et al i gohberg m a kaashoek f van schagen partially specified matrices and operators classification completion applications bikhauser basel 1995 are closely related moreover global polynomial matrix representations and global realizations as defined in zaballa i zaballa controllability and hermite indices of matrix pairs int j control 68 1 1997 61 86 are particular cases of the same local concepts finally local wiener hopf factorization indices with respect to a nonempty subset of specm f s are defined

approximate controllability of fractional evolution systems with riemann liouville fractional derivatives in this paper we deal with the control systems governed by fractional evolution differential equations involving riemann liouville fractional derivatives in banach spaces our main purpose in this article is to establish suitable assumptions to guarantee the existence and uniqueness results of mild solutions under these conditions the approximate controllability of the associated fractional evolution systems involving riemann liouville fractional derivatives is formulated and proved

a new notion of equivalence for discrete time ar representations we present a new equivalence transformation termed divisor equivalence that has the property of preserving both the finite and the infinite elementary divisor structures of a square non singular polynomial matrix this equivalence relation extends the known notion of strict equivalence which dealt only with matrix pencils to the general polynomial matrix case it is proved that divisor equivalence characterizes in a closed form relation the equivalence classes of polynomial matrices that give rise to fundamentally equivalent discrete time auto regressive representations

poles and zeros of matrices of rational functions abstract this expository paper considers the problem of defining poles and zeros with multiplicity including those at infinity for a matrix of rational functions over a field the underlying theme question for the paper is does the number of poles of a matrix equal the number of zeros and what structural meaning underlies such an assertion our approach is motivated by ideas from linear system theory and control engineering control theoretic ideas are not a prerequisite and we hope to encourage specialists in classical linear and commutative algebra to investigate this promising source of new algebra problems

initial value boundary value problems for fractional diffusion wave equations and applications to some inverse problems abstract we consider initial value boundary value problems for fractional diffusion wave equation t u x t l u x t where 0 2 where l is a symmetric uniformly elliptic operator with t independent smooth coefficients first we establish the unique existence of the weak solution and the asymptotic behavior as the time t goes to and the proofs are based on the eigenfunction expansions second for 0 1 we apply the eigenfunction expansions and prove i stability in the backward problem in time ii the uniqueness in determining an initial value and iii the uniqueness of solution by the decay rate as t iv stability in an inverse source problem of determining t dependent factor in the source by observation at one point over 0 t

existence of mild solutions for fractional neutral evolution equations abstract in this paper by using the fractional power of operators and some fixed point theorems we discuss a class of fractional neutral evolution equations with nonlocal conditions and obtain various criteria on the existence and uniqueness of mild solutions in the end we give an example to illustrate the applications of the abstract results

optimisation of gravity fed water distribution network design a critical review abstract this paper surveys the literature on the optimisation of water distribution network design the water distribution network design wdnd optimisation problem entails finding the material and diameter of each pipe in the network so that the total cost of the network is minimised without violating any hydraulic constraints this is a difficult combinatorial optimisation problem in which decision variables are discrete and both cost function and constraints are non linear over the past 30 years a large number of methods especially in the field of meta heuristics have been developed to solve this problem most of which obtain good results on the available benchmark networks in addition to outlining the basic features of each method a detailed computational comparison is presented based on this comparison some issues with the current state of the art in this domain are discussed and some future research directions are suggested additionally the need for an adequate set of benchmark instances is motivated and the minimal requirements for an instance set generator are discussed

structure smith macmillan form and coprime mfds of a rational matrix inside a region p ω abstract the structure of the smith macmillan form of a rational matrix t s inside a region p where is asymmetric with respect to the real axis subset of the finite complex plane c is determined algorithmic procedures based on elementary row and column operations over the euclidean ring r p s consisting of all rational functions with no poles in p are given coprimeness in p of a pair of rational matrices is studied in detail these results lead to constructive procedures for determining the coprime in p matrix fraction descriptions of t a

approximate controllability for a class of fractional stochastic wave equations abstract in this paper we consider the approximate controllability for a class of fractional stochastic wave equations in the sense of riemann liouville fractional derivative based on some special functions we transform the fractional stochastic wave equations into fractional evolution equations further we give an appropriate definition of mild solutions for this type of fractional stochastic wave equations moreover with the aid of fixed point theory we discuss the existence results of the mild solutions of the proposed problem finally we establish the approximate controllability when the corresponding linear system is approximately controllable

implications of head loss path choice in the optimization of water distribution networks the effects of varying the paths used to ensure adequate pressure throughout a water distribution network when using iterative linear programming gradient search techniques for least cost solution of the network are analyzed the path choice is shown to affect how the initial flows are changed i e increased or decreased by the gradient expressions in the flow modification step the long term implication of the difference in the way the flows are changed is a variation in the relative importance in terms of flows of the various links within the system the amount of flow in a particular link in the final solution appears to be dependent on how often that link is included in the pressure defining constraints

regularity theory for time fractional advection diffusion reaction equations abstract we investigate the behavior of the time derivatives of the solution to a linear time fractional advection diffusion reaction equation allowing space and time dependent coefficients as well as initial data that may have low regularity our focus is on proving estimates that are needed for the error analysis of numerical methods the nonlocal nature of the fractional derivative creates substantial difficulties compared with the case of a classical parabolic pde in our analysis we rely on novel energy methods in combination with a fractional gronwall inequality and certain properties of fractional integrals

equivalence transformations of rational matrices and applications the known theories of transformations between polynomial matrices are extended to the case of rational matrices specifically equivalence between rational matrices having possibly different dimensions is defined and this has the property of preserving the zero structure of rational matrices in the region c some implications of this new equivalence transformation for linear system theory are also provided

holder continuous solutions for fractional differential equations and maximal regularity abstract we characterize the existence and uniqueness of solutions of an abstract fractional differential equation with infinite delay in holder spaces

optimal design of water distribution networks optimal design of a water distribution network is formulated as a two stage decomposition model the master outer problem is nonsmooth and nonconvex while the inner problem is linear a semi infinite linear dual problem is presented and an equivalent finite linear problem is developed the overall design problem is solved globally by a branch and bound algorithm using nonsmooth optimization and duality theory the algorithm stops with a solution and a global bound such that the difference between this bound and the true global optimum is within a prescribed tolerance the algorithm has been programmed and applied to a number of examples from the literature the results demonstrate its superiority over previous methods

cauchy problem for fractional diffusion equations abstract we consider an evolution equation with the regularized fractional derivative of an order 0 1 with respect to the time variable and a uniformly elliptic operator with variable coefficients acting in the spatial variables such equations describe diffusion on inhomogeneous fractals a fundamental solution of the cauchy problem is constructed and investigated

a two phase decomposition method for optimal design of looped water distribution networks a two phase decomposition method is proposed for the optimal design of new looped water distribution networks as well as for the parallel expansion of existing ones the main feature of the method is that it generates a sequence of improving local optimal solutions the first phase of the method takes a gradient approach with the flow distribution and pumping heads as decision variables and is an extension of the linear programming gradient method proposed by alperovits and shamir 1977 for nonlinear modeling the technique is iterative and produces a local optimal solution in the second phase the link head losses of this local optimal solution are fixed and the resulting concave program is solved for the link flows and pumping heads these then serve to restart the first phase to obtain an improved local optimal solution the whole procedure continues until no further improvement can be achieved some applications and extensions of the method are also discussed

on coprime rational function matrices abstract the concept of coprimeness of matrices with elements in a field of fractions is introduced we focus on the field of rational functions and define when two rational matrices are coprime with respect to different rings the definition of coprimeness at infinity of polynomial matrices is obtained as a particular case moreover the fact that coprimeness is a local property is proved and it is shown how coprimeness changes by performing mobius transformations

some uniqueness and existence results for the initial boundary value problems for the generalized time fractional diffusion equation in this paper some uniqueness and existence results for the solutions of the initial boundary value problems for the generalized time fractional diffusion equation over an open bounded domain gx 0 t email protected r n are given to establish the uniqueness of the solution a maximum principle for the generalized time fractional diffusion equation is used in turn the maximum principle is based on an extremum principle for the caputo dzherbashyan fractional derivative that is considered in the paper too another important consequence of the maximum principle is the continuous dependence of the solution on the problem data to show the existence of the solution the fourier method of the variable separation is used to construct a formal solution under certain conditions the formal solution is shown to be a generalized solution of the initial boundary value problem for the generalized time fractional diffusion equation that turns out to be a classical solution under some additional conditions

a critical study of the linear programming gradient method for optimal design of water supply networks the linear programming gradient lpg method originally proposed by alperovits and shamir 1977 and the subsequent publications based on it are briefly reviewed the optimal solutions obtained by different investigators for a simple two loop network originally taken by alperovits and shamir as an illustrative example are compared and it is shown that they are not even the local optimum solutions the latest modification introduced by kessler and shamir 1989 which incorporates the projected gradient of the objective function is also briefly reviewed and is shown to lead to a truly local optimum solution as claimed by kessler and shamir it is shown that it is preferable initially to suppress the minimum link flow constraint necessary for reliability purposes and introduce it later after obtaining the optimal solution for a branching configuration the philosophy of the lpg method is analyzed it is shown that the lpg method is inefficient at least for optimization of the illustrative two loop network as compared to a heuristic method that initially identifies logically good branching configurations for obtaining the optimal solution

drift diffusion equations with fractional diffusion and the quasi geostrophic equation motivated by the critical dissipative quasi geostrophic equation we prove that drift diffusion equations with l 2 initial data and minimal assumptions on the drift are locally holder continuous as an application we show that solutions of the quasi geostrophic equation with initial l 2 data and critical diffusion 1 2 are locally smooth for any space dimension

abstract fractional cauchy problems with almost sectorial operators abstract of concern are the cauchy problems for linear and semilinear time fractional evolution equations involving in the linear part a linear operator a whose resolvent satisfies the estimate of growth 1 0 in a sector of the complex plane which occurs when one considers for instance the partial differential operators in the limit domain of dumb bell with a thin handle or in the space of holder continuous functions by constructing a pair of families of operators in terms of the generalized mittag leffler type functions and the resolvent operators associated with a for the first time and a deep analysis on the properties for these families we obtain the existence and uniqueness of mild solutions and classical solutions to the cauchy problems moreover we present three examples to illustrate the feasibility of our results

smith mcmillan factorizations at infinity of rational matrix functions and their control interpretation in this paper the smith mcmillan factorizations at infinity of a transfer function are studied the non uniqueness of these factorizations is characterized via a multiplicative group of bicausal isomorphisms control interpretations are given in terms of system equivalence under some groups of transformations a characterization of the stabilizer of morse group at a b c is given for irreducible systems

a de giorgi nash type theorem for time fractional diffusion equations we study the regularity of weak solutions to linear time fractional diffusion equations in divergence form of arbitrary time order alpha in 0 1 the coefficients are merely assumed to be bounded and measurable and they satisfy a uniform parabolicity condition our main result is a de giorgi nash type theorem which gives an interior holder estimate for bounded weak solutions in terms of the data and the l infty bound of the solution the proof relies on new a priori estimates for time fractional problems and uses de giorgi s technique and the method of non local growth lemmas which has been introduced recently in the context of nonlocal elliptic equations involving operators like the fractional laplacian

infinite elementary divisors of a matrix polynomial and implications a new characterization of infinite poles and zeros in terms of a natural extension of the idea of infinite elementary divisors of a matrix pencil to matrix polynomials is developed it is used to show that two previous descriptions of infinite frequency structure are equivalent subsequently a polynomial matrix transformation which simultaneously preserves the finite and infinite zero structure is presented

analysis of the linear programming gradient method for optimal design of water supply networks a theoretical analysis of the linear programming lp gradient method for optimal design of water distribution networks is presented the method was first proposed by a alperovits and u shamir 1977 and has received much attention in the last 10 years it consists of two stages that are solved in alteration 1 a lp problem is solved for a given feasible flow distribution and 2 a search is conducted in the space of flow variables based on the gradient of the objective function gof in this paper a matrix formulation is given for both stages using well known graph theory matrices it is proven that the mathematical expression of the gof is independent of the choice of the sets of loops and paths along which the head constraints are formulated this is contrary to the claim made by i c goulter et al 1986 the original gof expression is shown to have been an approximation of the steepest direction but still gives good results finally the search procedure is improved by using the projected gradient method

application of a fractional advection dispersion equation abstract a transport equation that uses fractional order dispersion derivatives hasfundamental solutions that are le vy s a stable densities these densities represent plumesthat spread proportional to time 1 a have heavy tails and incorporate any degree ofskewness the equation is parsimonious since the dispersion parameter is not a functionof time or distance the scaling behavior of plumes that undergo le vy motion isaccounted for by the fractional derivative a laboratory tracer test is described by adispersion term of order 1 55 while the cape cod bromide plume is modeled by anequation of order 1 65 to 1 8 1 introduction anomalous or non fickian dispersion has been an activearea of research in the physics community since the introduc tion of continuous time random walks ctrw by montrolland weiss 1965 these random walks extended the predictivecapability of models built on the stochastic process of brown ian motion which is the basis for the classical advection dispersion equation ade the ctrw assign a joint space time distribution called the transition density to individualparticle motions when the tails are heavy enough i e powerlaw non fickian dispersion results for all time scales andspace scales

novel theory for polynomial and rational matrices at infinity part 2 rational matrices the development reported in part 1 of this series is continued by presenting a unifying theory for rational matrices at infinity the cornerstone for the development is again the homogeneous form for polynomial and rational matrices it is shown that when a rational matrix is factorized in matrix fraction description mfd redundancy at infinity may be introduced this redundancy can be characterized precisely as the common divisor of the numerator and the denominator matrices at infinity moreover when the numerator and the denominator matrices are completely coprime the determinantal degree of the denominator is the mcmillan degree of the rational matrix

on matrix polynomials with the same finite and infinite elementary divisors abstract a criterion is presented that characterizes when two matrix polynomials of any size rank and degree have the same finite and infinite elementary divisors this characterization inherits a coprimeness condition of the extended unimodular equivalence defined by pugh and shelton 17 in the set of real or complex matrix polynomials satisfying the constraint that the difference between the number of rows and columns is constant this extended unimodular equivalence is first generalized to matrices of any size with elements in any principal ideal domain

maximum principle for the generalized time fractional diffusion equation abstract in the paper a maximum principle for the generalized time fractional diffusion equation over an open bounded domain g 0 t g r n is formulated and proved the proof of the maximum principle is based on an extremum principle for the caputo dzherbashyan fractional derivative that is given in the paper too the maximum principle is then applied to show that the initial boundary value problem for the generalized time fractional diffusion equation possesses at most one classical solution and this solution continuously depends on the initial and boundary conditions

spectral equivalence of matrix polynomials and the index sum theorem abstract the concept of linearization is fundamental for theory applications and spectral computations related to matrix polynomials however recent research on several important classes of structured matrix polynomials arising in applications has revealed that the strategy of using linearizations to develop structure preserving numerical algorithms that compute the eigenvalues of structured matrix polynomials can be too restrictive because some structured polynomials do not have any linearization with the same structure this phenomenon strongly suggests that linearizations should sometimes be replaced by other low degree matrix polynomials in applied numerical computations motivated by this fact we introduce equivalence relations that allow the possibility of matrix polynomials with coefficients in an arbitrary field to be equivalent with the same spectral structure but have different sizes and degrees these equivalence relations are directly modeled on the notion of linearization and consequently inherit the simplicity applicability and most relevant properties of linearizations simultaneously though they are much more flexible in the possible degrees of equivalent polynomials this flexibility allows us to define in a unified way the notions of quadratification and l ification to introduce the concept of companion form of arbitrary degree and to provide concrete and simple examples of these notions that generalize in a natural and smooth way the classical first and second frobenius companion forms the properties of l ifications are studied in depth in this process a fundamental result on matrix polynomials the index sum theorem is recovered and extended to arbitrary fields although this result is known in the systems theory literature for real matrix polynomials it has remained unnoticed by many researchers it establishes that the sum of the finite and infinite partial multiplicities together with the left and right minimal indices of any matrix polynomial is equal to the rank times the degree of the polynomial the index sum theorem turns out to be a key tool for obtaining a number of significant results on the possible sizes and degrees of l ifications and companion forms on the minimal index preservation properties of companion forms of arbitrary degree as well as on obstructions to the existence of structured companion forms for structured matrix polynomials of even degree this paper presents many new results blended together with results already known in the literature but extended here to the most general setting of matrix polynomials of arbitrary sizes and degrees over arbitrary fields therefore we have written the paper in an expository and self contained style that makes it accessible to a wide variety of readers

tabu search algorithms for water network optimization abstract in this paper we propose a tabu search algorithm to find the least cost design of looped water distribution networks the mathematical nature of this optimization problem a nonlinear mixed integer problem is at the origin of a multitude of contributions to the literature in the last 25 years in fact exact optimization methods have not been found for this type of problem and in the past classical optimization methods like linear and nonlinear programming were tried at the cost of drastic simplifications tabu search is a valuable heuristic technique for solving problems cast in combinatorial form this is based on the human memory process and uses an iterative neighborhood search procedure in an attempt to avoid becoming trapped in local optima the use of such a heuristic procedure to solve the aforementioned problem needs particular tailoring to produce high quality solutions in this paper we present the essential features of the algorithm and the results obtained when it is applied to some of the classical water distribution network case studies appearing in the literature the results are very promising and demonstrate the usefulness of tabu search algorithms in solving this kind of optimization problem

local wiener hopf factorization and indices over arbitrary fields abstract in this paper a generalization to arbitrary fields of the usual wiener hopf equivalence of complex valued rational matrix functions is given and the left local wiener hopf factorization indices defined in our previous work a amparan s marcaida i zaballa local realizations and local polynomial matrix representations of systems linear algebra appl 425 2007 757 775 are proved to form a complete system of invariants for this equivalence relation for the case when the field is algebraically closed a reduced form of a controllable matrix pair under the feedback equivalence is presented for which the controllability indices can be written as sums of the local controllability indices a amparan s marcaida i zaballa on the existence of linear systems with prescribed invariants for system similarity linear algebra appl 413 2006 510 533

a novel high order space time spectral method for the time fractional fokker planck equation the fractional fokker planck equation is an important physical model for simulating anomalous diffusions with external forces because of the nonlocal property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations in this paper a space time spectral method is presented for the numerical solution of the time fractional fokker planck initial boundary value problem the proposed method employs the jacobi polynomials for the temporal discretization and fourier like basis functions for the spatial discretization due to the diagonalizable trait of the fourier like basis functions this leads to a reduced representation of the inner product in the galerkin analysis we prove that the time fractional fokker planck equation attains the same approximation order as the time fractional diffusion equation developed in x li and c xu siam j numer anal 47 2009 pp 2108 2131 by using the present method that indicates an e

a diameter sensitive flow entropy method for reliability consideration in water distribution system design flow entropy is a measure of uniformity of pipe flows in water distribution systems by maximizing flow entropy one can identify reliable layouts or connectivity in networks in order to overcome the disadvantage of the common definition of flow entropy that does not consider the impact of pipe diameter on reliability an extended definition of flow entropy termed as diameter sensitive flow entropy is proposed this new methodology is then assessed by using other reliability methods including monte carlo simulation a pipe failure probability model and a surrogate measure resilience index integrated with water demand and pipe failure uncertainty the reliability assessment is based on a sample of wds designs derived from an optimization process for each of the two benchmark networks correlation analysis is used to evaluate quantitatively the relationship between entropy and reliability to ensure reliability a comparative analysis between the flow entropy and the new method is conducted the results demonstrate that the diameter sensitive flow entropy shows consistently much stronger correlation with the three reliability measures than simple flow entropy therefore the new flow entropy method can be taken as a better surrogate measure for reliability and could be potentially integrated into the optimal design problem of wdss sensitivity analysis results show that the velocity parameters used in the new flow entropy has no significant impact on the relationship between diameter sensitive flow entropy and reliability

global optimization of nonlinear network design a novel approach for obtaining globally optimal solutions to design of networks with nonlinear resistances and potential driven flows is proposed the approach is applicable to networks where the potential loss on an edge in the network is governed by a convex and strictly monotonically increasing function of flow rate we introduce a relaxation of the potential loss constraint and formulate the design problem as a mixed integer nonlinear program a linearization based approach with tailored cuts is proposed that improves the computational efficiency over a standard implementation we have also implemented a simple heuristic approach for finding feasible solutions at the root node and during the search process the algorithm has been implemented with ibm ilog cplex and is shown to be computationally effective on a number of examples from the literature

existence and regularity of solutions to time fractional diffusion equations we investigate some initialboundary value problems for time fractional diffusion equations of order 0 1 such equations model anomalous diffusion on fractals the existence of solution irrelevant to is established only if the external force function f is weighted hlder continuous which is weaker than hlder continuous some interesting versions of maximal and spatial regularity criteria depending on the fractional exponent are also discussed