a variable stepsize jacobian free exponential integrator for simulating transport in heterogeneous porous media application to wood drying a jacobian free variable stepsize method is developed for the numerical integration of the large stiff systems of differential equations encountered when simulating transport in heterogeneous porous media our method utilises the exponential rosenbrock euler method which is explicit in nature and requires a matrix vector product involving the exponential of the jacobian matrix at each step of the integration process these products can be approximated using krylov subspace methods which permit a large integration stepsize to be utilised without having to precondition the iterations this means that our method is truly jacobian free the jacobian need never be formed or factored during the simulation we assess the performance of the new algorithm for simulating the drying of softwood numerical experiments conducted for both low and high temperature drying demonstrates that the new approach outperforms in terms of accuracy and efficiency existing simulation codes that utilise the backward euler method via a preconditioned newton krylov strategy

calculation of all stabilizing fractional order pd controllers for integrating time delay systems in this paper a simple and effective stabilization method for integrating time delay systems using fractional order pd controllers c s k p k ds m is proposed the presented method is based on finding the stability regions according to the fractional orders of the derivative element in the range of 0 2 these regions are computed by using three stability boundaries real root boundary rrb complex root boundary crb and infinite root boundary irb the method gives the explicit formulae corresponding to these boundaries in terms of fractional order pd controller pd m controller parameters thus the complete set of stabilizing controllers for an arbitrary integrating time delay system can be obtained in order to demonstrate the effectiveness in solution accuracy and the simplicity of this method two simulation studies are given the simulation results indicate that the pd m controllers can provide larger stability regions than the integer order pd controllers

galois representations arising from some compact shimura varieties our aim is to establish some new cases of the global langlands correspondence for glm along the way we obtain a new result on the description of the cohomology of some compact shimura varieties let f be a cm eld with complex conjugation c and

robust decentralized control of perturbed fractional order linear interconnected systems the robust decentralized state feedback stabilization problem for a class of perturbed fractional order linear interconnected systems is investigated the systems considered are subject to structured or unstructured perturbations the decentralized state feedback controllers are designed such that the closed loop perturbed fractional order linear interconnected systems are asymptotically stable by using the definition of positive and negative definite matrices and stability theory of fractional order systems sufficient conditions for robust stabilization of closed loop perturbed fractional order linear interconnected systems are given simulation examples are given to demonstrate the effectiveness of the proposed theoretical results

technical communique fractional order proportional derivative controller for a class of fractional order systems recently fractional order systems fos have attracted more and more attention in various fields but the control design techniques available for the fos suffer from the lack of direct systematic approaches in this paper we focus on a given type of simple model of fos a fractional order proportional derivative fo pd controller is proposed for this class of fos and a practical and systematic tuning procedure has been developed for the proposed fo pd controller synthesis the fairness issue in comparing with other controllers such as the traditional integer order pid io pid controller and the fractional order proportional derivative fo pd controller has been addressed under the same number of design parameters and the same specifications fair comparisons of the three controllers i e io pid fo pd and fo pd via the simulation tests illustrate that the io pid controller designed may not always be stabilizing to achieve flat phase specification while both fo pd and fo pd controllers designed are always stabilizing furthermore the proposed fo pd controller outperforms fo pd controller for the class of fractional order systems

efficient simulation of unsaturated flow using exponential time integration abstract we assess the performance of an exponential integrator for advancing stiff semidiscrete formulations of the unsaturated richards equation in time the scheme is of second order and explicit in nature but requires the action of the matrix function a a 1 e a i on a suitability defined vector v at each time step when the matrix a is large and sparse a v can be approximated by krylov subspace methods that require only matrix vector products with a we prove that despite the use of this approximation the scheme remains second order furthermore we provide a practical variable stepsize implementation of the integrator by deriving an estimate of the local error that requires only a single additional function evaluation numerical experiments performed on two dimensional test problems demonstrate that this implementation outperforms second order variable stepsize implementations of the backward differentiation formulae

h control of fractional linear systems abstract in this paper the standard h control problem for continuous time fractional linear time invariant single input single output systems is solved the adopted approach consists of extending to the fractional case the procedure followed within the classical solution for the integer case according to the classical route we first consider the generalization to fractional systems of the standard youla parameterization of all the stabilizing controllers the h optimal controller is then found among the class of stabilizing controllers recasting the control problem into a model matching one the results obtained naturally extend well established results to a fractional setting including both the commensurate and noncommensurate case thus providing a framework where h design can be recast along the well known and fruitful lines of the integer case a worked through example is discussed in detail to illustrate the design procedure

on serre s conjecture for mod l galois representations over totally real fields in 1987 serre conjectured that any mod two dimensional irre ducible odd representation of the absolute galois group of the rationals came from a modular form in a precise way we present a generalisation of this conjecture to 2 dimensional representations of the absolute galois group of a totally real eld where is unramied the hard work is in formulating an analogue of the weight part of serre s conjecture serre furthermore asked whether his conjecture could be rephrased in terms of a mod langlands philosophy using ideas of emerton and vign eras we formulate a mod local global principle for the group d where d is a quaternion algebra over a totally real eld split above and at 0 or 1 innite places and show how it implies the conjecture

multiplicites modulaires et representations de rm gl sb 2 mathbf z sb p et de rm gal overline mathbf q sb p mathbf q sb p en ell p appendice par guy henniart sur l unicite des types pour rm gl sb 2

weights of galois representations associated to hilbert modular forms let f be a totally real field p 3 a rational prime unramified in f and p a place of f over p let gal f f gl2 fp be a two dimensional mod p galois representation which is assumed to be modular of some weight and whose restriction to a decomposition subgroup at p is irreducible we specify a set of weights determined by the restriction of to inertia at p which contains all the modular weights for this proves part of a conjecture of diamond buzzard and jarvis which provides an analogue of serre s epsilon conjecture for hilbert modular forms mod p

design of pid controllers satisfying gain margin and sensitivity constraints on a set of plants this paper presents a method for the design of pid type controllers including those augmented by a filter on the d element satisfying a required gain margin and an upper bound on the complementary sensitivity for a finite set of plants important properties of the method are i it can be applied to plants of any order including non minimum phase plants plants with delay plants characterized by quasi polynomials unstable plants and plants described by measured data ii the sensors associated with the pi terms and the d term can be different i e they can have different transfer function models iii the algorithm relies on explicit equations that can be solved efficiently iv the algorithm can be used in near real time to determine a controller for on line modification of a plant accounting for its uncertainty and closed loop specifications v a single plot can be generated that graphically highlights tradeoffs among the gain margin complementary sensitivity bound low frequency sensitivity and high frequency sensor noise amplification and vi the optimal controller for a practical definition of optimality can readily be identified

conjecture de l inertie moderee de serre on considere k un corps complet pour une valuation discrete de caracteristique nulle et dont le corps residuel est suppose parfait de caracteristique p on appelle e l indice de ramification absolue de k mathcal o k son anneau des entiers et overline k une cloture algebrique soit xk un schema propre et lisse sur k admettant un modele propre et semi stable x sur mathcal o k generalisant les resultats de breuil valables pour e 1 on demontre dans cet article un isomorphisme de periodes reliant le r ieme groupe de cohomologie etale de x overline k a coefficients dans pn et un r ieme groupe de cohomologie log cristalline de la fibre speciale de x nous avons toutefois les restrictions er 1

automorphic lifts of prescribed types we prove a variety of results on the existence of automorphic galois representations lifting a residual automorphic galois representation we prove a result on the structure of deformation rings of local galois representations and deduce from this and the method of khare and wintenberger a result on the existence of modular lifts of specified type for galois representations corresponding to hilbert modular forms of parallel weight 2 we discuss some conjectures on the weights of n dimensional mod p galois representations finally we use recent work of taylor to prove level raising and lowering results for n dimensional automorphic galois representations

robustness analysis and design of fractional order iλ dμ controllers using the small gain theorem in this paper a simple method is proposed to tune the parameters of fractional integral fractional derivative fife i d controllers based on the bode diagram the proposed technique provides a

on the weights of mod p hilbert modular forms we prove many cases of a conjecture of buzzard diamond and jarvis on the possible weights of mod p hilbert modular forms by making use of modularity lifting theorems and computations in p adic hodge theory

an analogue of serre s conjecture for galois representations and hecke eigenclasses in the mod p cohomology of gl n ℤ

new efficient substepping methods for exponential timestepping exponential integrators are time stepping schemes which exactly solve the linear part of a semilinear ode system this class of schemes requires the approximation of a matrix exponential in every step and one successful modern method is the krylov subspace projection method we investigate the effect of breaking down a single timestep into arbitrary multiple substeps recycling the krylov subspace to minimise costs for these recycling based schemes we analyse the local error investigate them numerically and show they can be applied to a large system with 106 unknowns we also propose a new second order integrator that is found using the extra information from the substeps to form a corrector to increase the overall order of the scheme this scheme is seen to compare favorably with other order two integrators

galois representations with conjectural connections to arithmetic cohomology in this paper we extend a conjecture of a ash and w sinnott relating niveau 1 galois representations to the mod p cohomology of congruence subgroups ofsln z to include galois representations of higher niveau we then present computational evidence for our conjecture in the case n 3 in the form of three dimensional galois representations which appear to correspond to cohomology eigenclasses as predicted by the conjecture our examples include galois representations with nontrivial weight and level as well as irreducible three dimensional representations that are in no obvious way related to lower dimensional representations in addition we prove that certain symmetric square representations are actually attached to cohomology eigenclasses predicted by the conjecture

multiscale finite volume method for compressible multiphase flow in porous media the multiscale finite volume msfv method has been recently developed and tested for multiphase flow problems with simplified physics i e incompressible flow without gravity and capillary effects and proved robust accurate and efficient however applications to practical problems necessitate extensions that enable the method to deal with more complex processes in this paper we present a modified version of the msfv algorithm that provides a suitable and natural framework to include additional physics the algorithm consists of four main steps computation of the local basis functions which are used to extract the coarse scale effective transmissibilities solution of the coarse scale pressure equation reconstruction of conservative fine scale fluxes and solution of the transport equations within this framework we develop a msfv method for compressible multiphase flow the basic idea is to compute the basis functions as in the case of incompressible flow such that they remain independent of the pressure the effects of compressibility are taken into account in the solution of the coarse scale pressure equation and if necessary in the reconstruction of the fine scale fluxes we consider three models with an increasing level of complexity in the flux reconstruction and test them for highly compressible flows tracer transport in gas flow imbibition and drainage of partially saturated reservoirs depletion of gas water reservoirs and flooding of oil gas reservoirs we demonstrate that the msfv method provides accurate solutions for compressible multiphase flow problems whereas slightly compressible flows can be treated with a very simple model a more sophisticate flux reconstruction is needed to obtain accurate fine scale saturation fields in highly compressible flows

pid controller design for robust performance this note is devoted to the problem of synthesizing proportional integral derivative pid controllers for robust performance for a given single input single output plant in the presence of uncertainty first the problem of robust performance design is converted into simultaneous stabilization of a complex polynomial family an extension of the results on pid stabilization is then used to devise a linear programming design procedure for determining all admissible pid gain settings the most important feature of the proposed approach is that it computationally characterizes the entire set of the admissible pid gain values for an arbitrary plant

two scale computational modelling of water flow in unsaturated soils containing irregular shaped inclusions the focus of this paper is two dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix when the inclusions are small a two scale richards equation based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation defined at each point in the macroscopic domain governing the flow in the inclusions this paper is devoted to a number of advances in the numerical implementation of this model namely by treating the micro scale as a two dimensional problem our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries and if necessary modified to account for additional phenomena e g imposing the macroscopic gradient on the micro scale via a linear approximation of the macroscopic variable along the microscopic boundary this is achieved with the help of an exponential integrator for advancing the solution in time this time integration method completely avoids generation of the jacobian matrix of the system and hence eases the computation when solving the two scale model in a completely coupled manner numerical simulations are presented for a two dimensional infiltration problem

technical communique h design with fractional order pdµ controllers this article focuses on h performance design for fractional order systems with time delay using fractional order proportional derivative pd m controllers first the stabilizing parameters region in proportional derivative plane of pd m controller for a fixed derivative order is determined in terms of a graphical stability criterion applicable to fractional order time delay systems then in the stabilizing region the pairs of proportional and derivative gains of pd m controller are calculated for a range of frequencies which satisfy the h norm constraint of complementary sensitivity function and define the h boundary curve finally by changing the derivative order of pd m controller we observe the relationship between the h curve and the derivative order examples are followed to illustrate the design procedure

modularity of certain potentially barsotti tate galois representations where is the reduction of p these results were subject to hypotheses on the local behavior of p at x i e the restriction of p to a decomposition group at x and to irreducibility hypotheses on 1p in this paper we build on the methods of 461 451 and 121 and relax the hypotheses on local behavior in particular we treat certain adic representations which are not semistable at x but potentially semistable we do this using results of 61 generalizing a theorem of ramakrishna 321 see fontaine mazur 22 131 for a slightly different point of view the results in 61 show that certain potentially barsotti tate deformation problems are smooth allowing us to define certain universal deformations for with the necessary galoistheoretic properties to apply wiles method to carry out the proof that these deformations are indeed realized in the cohomology of modular curves i e that the universal deformation rings are hecke algebras we need to identify the corresponding cohomology groups and prove they have the modular theoretic properties needed to apply wiles method as in 151 and 121 the identification is made by matching local behavior of automorphic representations and galois representations via the local langlands correspondence together with fontaine s theory at the prime we work directly with cohomology of modular curves instead of

h sub spl infin design with first order controllers the problem of determining all first order controllers c s x 1s x2 s x3 which stabilize a given single input single output siso linear time invariant lti plant of arbitrary order has been recently solved in this note these results are extended to determine the subset of controllers which also satisfy various robustness and performance specifications which can be formulated as specific hinfin norm constraints the problem is solved by converting the hinfin problem into the simultaneous stabilization of the closed loop characteristic polynomial and a family of related complex polynomials the stability boundary of each of these polynomials can be computed explicitly for fixed x3 by solving linear equations the union of the resulting stability regions yields the set of all x1 and x2 which simultaneously satisfy the hinfin condition and closed loop stability for a fixed x3 the entire three dimensional set meeting specifications is obtained by sweeping x3 over the stabilizing range

an algorithm for stabilization of fractional order time delay systems using fractional order pid controllers this technical note presents a solution to the problem of stabilizing a given fractional order system with time delay using fractional order pllambdadmu controllers it is based on determining a set of global stability regions in the kp ki kd space corresponding to the fractional orders lambda and mu in the range of 0 2 and then choosing the biggest global stability region in this set this method can be also used to find the set of stabilizing controllers that guarantees prespecified gain and phase margin requirements the algorithm is simple and has reliable result which is illustrated by an example and hence is practically useful in the analysis and design of fractional order control systems

fractional order systems and pi sup spl lambda d sup spl mu controllers dynamic systems of an arbitrary real order fractional order systems are considered the concept of a fractional order pi sup spl lambda d sup spl mu controller involving fractional order integrator and fractional order differentiator is proposed the laplace transform formula for a new function of the mittag leffler type made it possible to obtain explicit analytical expressions for the unit step and unit impulse response of a linear fractional order system with fractional order controller for both open and closed loops an example demonstrating the use of the obtained formulas and the advantages of the proposed pi sup spl lambda d sup spl mu controllers is given

exponential rosenbrock type methods we introduce a new class of exponential integrators for the numerical integration of large scale systems of stiff differential equations these so called rosenbrock type methods linearize the flow in each time step and make use of the matrix exponential and related functions of the jacobian in contrast to standard integrators the methods are fully explicit and do not require the numerical solution of linear systems we analyze the convergence properties of these integrators in a semigroup framework of semilinear evolution equations in banach spaces in particular we derive an abstract stability and convergence result for variable step sizes this analysis further provides the required order conditions and thus allows us to construct pairs of embedded methods we present a third order method with two stages and a fourth order method with three stages respectively the application of the required matrix functions to vectors are computed by krylov subspace approximations we briefly discuss these implementation issues and we give numerical examples that demonstrate the efficiency of the new integrators

brief synthesis of h pid controllers a parametric approach this paper considers the problem of synthesizing proportional integral derivative pid controllers for which the closed loop system is internally stable and the h norm of a related transfer function is less than a prescribed level for a given single input single output plant it is shown that the problem to be solved can be translated into simultaneous stabilization of the closed loop characteristic polynomial and a family of complex polynomials it calls for a generalization of the hermite biehler theorem applicable to complex polynomials it is shown that the earlier pid stabilization results are a special case of the results developed here then a linear programming characterization of all admissible h pid controllers for a given plant is obtained this characterization besides being computationally efficient reveals important structural properties of h pid controllers for example it is shown that for a fixed proportional gain the set of admissible integral and derivative gains lie in a union of convex sets

a numerical scheme for two dimensional optimal control problems with memory effect a new formulation for multi dimensional fractional optimal control problems is presented in this article the fractional derivatives which are coming from the formulation of the problem are defined in the riemann liouville sense some terminal conditions are imposed on the state and control variables whose dimensions need not be the same a numerical scheme is described by using the grunwald letnikov definition to approximate the riemann liouville fractional derivatives the set of fractional differential equations which are obtained after the discretization of the time domain are solved within the grunwald letnikov approximation to obtain the state and the control variable numerically a two dimensional fractional optimal control problem is studied as an example to demonstrate the performance of the scheme

on a conjecture of conrad diamond and taylor we prove a conjecture of conrad diamond and taylor on the size of certain deformation rings parametrizing potentially barsotti tate ga lois representations to achieve this we extend results of breuil and m ezard classifying galois lattices in semistable representations in terms of strongly divisible modules to the potentially crystalline case in hodge tate weights 0 1 we then use these strongly divisible modules to compute the desired deformation rings as a corollary we obtain new results on the modularity of potentially barsotti tate representations

characterization of pid and lead lag compensators satisfying given h sub spl infin specifications this note deals with the problem of characterizing a class of second order three parameter controllers including proportional integral derivative pid and lead lag compensators satisfying given h sub spl infin closed loop specifications design characterizations of similar form as in the recent work on pid control are derived for a larger class of compensators using simple geometric considerations specifically it is shown that given the value of one parameter i the region of the plane defined by the other two parameters where the considered h sub spl infin constraint is satisfied consists of the union of disjoint convex sets whose number can be bounded by means of the pancake cutting formula and ii the closed loop pole distribution can be related to them an example illustrates how the method can be applied to design a pid controller in the case of bounded sensitivity

weight cycling and serre type conjectures for unitary groups we prove that for forms of u 3 which are compact at infinity and split at places dividing a prime p in generic situations the serre weights of a mod p modular galois representation which is irreducible when restricted to each decomposition group above p are exactly those previously predicted by herzig we do this by combining explicit computations in p adic hodge theory based on a formalism of strongly divisible modules and breuil modules with descent data which we develop here with a technique that we call weight cycling