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

compositional modeling in porous media using constant volume flash and flux computation without the need for phase identification abstract the paper deals with the numerical solution of a compositional model describing compressible two phase flow of a mixture composed of several components in porous media with species transfer between the phases the mathematical model is formulated by means of the extended darcy s laws for all phases components continuity equations constitutive relations and appropriate initial and boundary conditions the splitting of components among the phases is described using a new formulation of the local thermodynamic equilibrium which uses volume temperature and moles as specification variables the problem is solved numerically using a combination of the mixed hybrid finite element method for the total flux discretization and the finite volume method for the discretization of transport equations a new approach to numerical flux approximation is proposed which does not require the phase identification and determination of correspondence between the phases on adjacent elements the time discretization is carried out by the backward euler method the resulting large system of nonlinear algebraic equations is solved by the newton raphson iterative method we provide eight examples of different complexity to show reliability and robustness of our approach

stochastic solution of population balance equations for reactor networks this work presents a sequential modular approach to solve a generic network of reactors with a population balance model using a stochastic numerical method full coupling to the gas phase is achieved through operator splitting the convergence of the stochastic particle algorithm in test networks is evaluated as a function of network size recycle fraction and numerical parameters these test cases are used to identify methods through which systematic and statistical error may be reduced including by use of stochastic weighted algorithms the optimal algorithm was subsequently used to solve a one dimensional example of silicon nanoparticle synthesis using a multivariate particle model this example demonstrated the power of stochastic methods in resolving particle structure by investigating the transient and spatial evolution of primary polydispersity degree of sintering and tem style images an algorithm is presented to solve reactor networks with a population balance model a stochastic method is used to solve the population balance equations the convergence and efficiency of the reported algorithms are evaluated the algorithm is applied to simulate silicon nanoparticle synthesis in a 1d reactor particle structure is reported as a function of reactor length and time

a model for steady fluid flow in random three dimensional networks of disc shaped fractures a model for steady fluid flow in three dimensional random networks of fractures has been developed in this model the fractures are disc shaped discontinuities in an impermeable matrix the fracture discs can be arbitrarily located within the rock volume and can have any desired distribution of aperture radius orientation and density thus where the disc model is appropriate it is possible to calculate flow through fracture networks which are statistically similar to those that occur in nature after the boundary conditions and the desired fractures are specified the intersections nodes between these discs elements are identified then steady flow through the network is calculated using a mixed analytical numerical technique in each fracture analytic equations for flow into or out of each node as a function of the average head at each node are developed the equations are based on image theory and the assumption that each node is a source or sink of uniform strength a set of mass balance equations is constructed which equate flow into a node from one of its associated fractures to flow out of the node into the other associated fracture these equations are solved for the average head at each node and flux between fractures can then be calculated by substituting the average head values back into the analytical equations the model has been successfully checked against analytical results for several cases of two and three intersecting fractures we plan to use these techniques to measure the permeability of fracture networks

genotypes of irreducible representations of finite p groups for any characteristic zero coefficient field an irreducible representation of a finite p group can be assigned a roquette p group called the genotype this has already been done by bouc and kronstein in the special cases q and c a genetic invariant of an irrep is invariant under group isomorphism change of coefficient field galois conjugation and under suitable inductions from subquotients it turns out that the genetic invariants are precisely the invariants of the genotype we shall examine relationships between some genetic invariants and the genotype as an application we shall count galois conjugacy classes of certain kinds of irreps

the dade group of a p group let p be a prime number this paper solves the question of the structure of the group d p of endo permutation modules over an arbitrary finite p group p that was open after dade s original papers in 1978 19 20 and it gives a proof of the conjectures proposed in 4 and 10 this leads to a presentation of d p by explicit generators and relations generalizing the presentation obtained by dade when p is abelian

a filtration of the modular representation functor abstract let f and k be algebraically closed fields of characteristics p 0 and 0 respectively for any finite group g we denote by k r f g k z g 0 f g the modular representation algebra of g over k where g 0 f g is the grothendieck group of finitely generated f g modules with respect to exact sequences the usual operations induction inflation restriction and transport of structure with a group isomorphism between the finitely generated modules of group algebras over f induce maps between modular representation algebras making k r f an inflation functor we show that the composition factors of k r f are precisely the simple inflation functors s c v i where c ranges over all nonisomorphic cyclic p groups and v ranges over all nonisomorphic simple k out c modules moreover each composition factor has multiplicity 1 we also give a filtration of k r f

simple modules over green biset functors we present three examples of green biset functors for which their simple modules can be parametrized these are particular cases of a conjecture by serge bouc classifying the simple modules over a green biset functor a that generalizes the classification of simple biset functors we also prove this conjecture under certain hypothesis for a

tornehave morphisms iii the reduced tornehave morphism and the burnside unit functor abstract we shall show that a morphism anticipated by tornehave induces and helps to explain bouc s isomorphism relating a quotient of the burnside unit functor measuring a difference between real and rational representations of finite 2 groups and a quotient of the kernel of linearization measuring a difference between rhetorical and rational 2 biset functors

obstructions for gluing biset functors abstract we develop an obstruction theory for the existence and uniqueness of a solution to the gluing problem for a biset functor defined on the subquotients of a finite group g the obstruction groups for this theory are the reduced cohomology groups of a category d g whose objects are the sections u v of g where 1 v u g and whose morphisms are defined as a generalization of morphisms in the orbit category using this obstruction theory we calculate the obstruction group for some well known p biset functors such as the dade group functor defined on p groups with p odd

alcahestic subalgebras of the alchemic algebra and a correspondence of simple modules the unified treatment of the five module theoretic notions transfer inflation transport of structure by an isomorphism deflation and restriction is given by the theory of biset functors introduced by bouc in this paper we construct the algebra realizing biset functors as representations the algebra has a presentation similar to the well known mackey algebra we adopt some natural constructions from the theory of mackey functors and give two new constructions of simple biset functors we also obtain a criterion for semisimplicity in terms of the biset functor version of the mark homomorphism the criterion has an elementary generalization to arbitrary finite dimensional algebras over a field

composition factors of functors abstract let x be a family of finite groups satisfying certain conditions and k be a field we study composition factors radicals and socles of biset and related functors defined on x over k for such a functor m and for a group h in x we construct bijections between some classes of maximal respectively simple subfunctors of m and some classes of maximal respectively simple k out h submodules of m h we use these bijections to relate the multiplicity of a simple functor s h v in m to the multiplicity of v in a certain k out h module related to m h we then use these general results to study the structure of one of the important biset and related functors namely the burnside functor b k which assigns to each group g in x its burnside algebra b k g k z b g where b g is the burnside ring of g we find the radical and the socle of b k in most cases of x and k for example if k is of characteristic p 0 and x is a family of finite abelian p groups we find the radical and the socle series of b k considered as a biset functor on x over k we finally study restrictions of functors to nonfull subcategories for example we find some conditions forcing a simple deflation functor to remain simple as a mackey functor for an inflation functor m defined on abelian groups over a field of characteristic zero we also obtain a criterion for m to be semisimple in terms of the images of inflation and induction maps on m

foncteurs d ensembles munis d une double action resume sommaire 1 introduction 2 notations generalites 3 ensembles munis d une double action 3 1 notations 3 2 formule de mackey 3 3 decomposition d un morphisme 3 4 sous categories 3 4 1 ensembles p q libres 3 4 2 groupes reductifs 4 foncteurs simples 5 une theorie de vortex et de source 6 une seconde theorie de vortex et source 7 le foncteur de burnside 7 1 un homomorphisme deb g dans end g 7 2 les sous foncteurs du foncteur de burnside en caracteristique 0 7 2 1 premier exemple 7 2 2 les constantesmg n 7 2 3 lesb groupes 7 2 4 les sous foncteurs deb 7 2 5 exemples deb groupes 8 exemples de foncteurs simples 8 1 le cas des foncteurs de mackey globaux 8 2 les foncteurssh k 8 3 certains foncteurs simples en caracteristique 0 9 l algebreegg end g egg 9 1 une base naturelle 9 2 multiplication 9 3 semi simplicite 10 le foncteur des representations complexes 10 1 caracteres 10 2 sous foncteurs et decomposition 10 3 semi simplicite

on iterative techniques for computing flow in large two dimensional discrete fracture networks computation of flow in discrete fracture networks often involves solving for hydraulic head values at all intersection points of a large number of stochastically generated fractures inside a bounded domain for large systems this approach leads to the generation of problems involving highly sparse matrices which must be solved iteratively distributions of fracture lengths spanning over several orders of magnitude and the randomness of fracture orientations and locations lead to coefficient matrices that are devoid of any regular structure in the sparsity pattern in addition to the rapid increase in computational effort with increase in the size of the fracture network the spread in the distribution of fracture parameters such as length and transmissivity dramatically influences the convergence behavior of the system of linear equations an overview of the discrete fracture network dfn methodology for computation of flow is presented along with a comparative study of various krylov subspace iterative methods for the resulting class of sparse matrices the rate of convergence of the iterative techniques is found to exhibit a systematic pattern with respect to changes in statistical parameters of the stochastically generated fracture networks salient features of the observed trends in the convergence pattern are discussed and guidelines for design of dfn algorithms are provided

a residual based a posteriori error estimator for single phase darcy flow in fractured porous media in this paper we develop an a posteriori error estimator for a mixed finite element method for single phase darcy flow in a two dimensional fractured porous media the discrete fracture model is applied to model the fractures by one dimensional fractures in a two dimensional domain we consider raviart thomas mixed finite element method for the approximation of the coupled darcy flows in the fractures and the surrounding porous media we derive a robust residual based a posteriori error estimator for the problem with non intersecting fractures the reliability and efficiency of the a posteriori error estimator are established for the error measured in an energy norm numerical results verifying the robustness of the proposed a posteriori error estimator are given moreover our numerical results indicate that the a posteriori error estimator also works well for the problem with intersecting fractures

rational p biset functors abstract in this paper i give several characterizations of rational biset functors over p groups which are independent of the knowledge of genetic bases for p groups i also introduce a construction of new biset functors from known ones which is similar to the yoneda construction for representable functors and to the dress construction for mackey functors and i show that this construction preserves the class of rational p biset functors this leads to a characterization of rational p biset functors as additive functors from a specific quotient category of the biset category to abelian groups finally i give a description of the largest rational quotient of the burnside p biset functor when p is odd this is simply the functor r q of rational representations but when p 2 it is a non split extension of r q by a specific uniserial functor which happens to be closely related to the functor of units of the burnside ring

discontinuous galerkin finite element convergence for incompressible miscible displacement problems of low regularity in this article we analyze the numerical approximation of incompressible miscible displacement problems with a combined mixed finite element and discontinuous galerkin method under minimal regularity assumptions the main result is that sequences of discrete solutions weakly accumulate at weak solutions of the continuous problem in order to deal with the nonconformity of the method and to avoid overpenalization of jumps across interelement boundaries the careful construction of a reflexive subspace of the space of bounded variation which compactly embeds into l 2 omega and of a lifting operator which is compatible with the nonlinear diffusion coefficient are required an equivalent skew symmetric formulation of the convection and reaction terms of the nonlinear partial differential equation allows us to avoid flux limitation and nonetheless leads to an unconditionally stable and convergent numerical method numerical experiments underline the robustness of the proposed algorithm

accuracy of mixed and control volume finite element approximations to darcy velocity and related quantities the accuracy of the darcy velocity flux and stream function computed from lowest order triangle based control volume and mixed finite element approximations to the two dimensional pressure equation is considered the control volume finite element method similar to integrated finite difference methods and analogous to the interpolation of galerkin finite element results over control volumes is shown to yield a conservative velocity field and smooth streamlines the streamlines and fluxes through the system computed with the control volume finite element approach are compared to those computed from the mixed finite element method which approximates the pressure and velocity variables separately it is shown that for systems with only moderate degrees of heterogeneity the control volume finite element method is the more computationally efficient alternative i e it provides more accurate flow results for a given number of unknowns for more variable or discontinuous permeability fields by contrast such as sand shale systems the mixed finite element method is shown to approximate flow variables more accurately and more realistically than the control volume method with the same number of unknowns

physics based preconditioners for flow in fractured porous media discrete fracture models are an attractive alternative to upscaled models for flow in fractured media as they provide a more accurate representation of the flow characteristics a major challenge in discrete fracture simulation is to overcome the large computational cost associated with resolving the individual fractures in large scale simulations in this work two characteristics of the fractured porous media are utilized to construct efficient preconditioners for the discretized flow equations first the preconditioners are tailored to the fracture geometry and presumed flow properties so that the dominant features are well represented there this assures good scalability of the preconditioners in terms of problem size and permeability contrast for fracture dominated problems numerical examples show that such geometric preconditioners are comparable or preferable when compared to state of the art algebraic multigrid preconditioners the robustness of the physics based preconditioner for less favorable fracture conditions is further demonstrated by a systematic degradation of the fracture hierarchy second the preconditioners are physics preserving in the sense that conservative fluxes can be computed even for an inexact pressure solutions this facilitates a scheme where accuracy in the linear solver can be traded for efficiency by terminating the iterative solvers based on error estimates and without sacrificing basic physical modeling principles with the combination of these two properties a novel preconditioner is obtained which bridges the gap between multiscale approximations and iterative linear solvers

a quasi steady state method for solving transient darcy flow in complex 3d fractured networks accounting for matrix to fracture flow modeling natural discrete fracture networks dfn receives more and more attention in applied geosciences from oil and gas industry to geothermal recovery and aquifer management the fractures may be either natural or artificial in case of well stimulation accounting for the flow inside the fracture network and accounting for the transfers between the matrix and the fractures with the same level of accuracy is an important issue for calibrating the well architecture and for setting up optimal resources recovery strategies recently we proposed an original method allowing to model transient pressure diffusion in the fracture network only 1 the matrix was assumed to be impervious a systematic approximation scheme was built allowing to model the initial dfn by a set of n unknowns located at each identified intersection between fractures the higher n the higher the accuracy of the model the main assumption was using a quasi steady state hypothesis that states that the characteristic diffusion time over one single fracture is negligible compared with the characteristic time of the macroscopic problem e g change of boundary conditions in that context the lowest order approximation n 1 has the form of solving a transient problem in a resistor capacitor network a so called pipe network its topology is the same as the network of geometrical intersections between fractures in this paper we generalize this approach in order to account for fluxes from matrix to fractures the quasi steady state hypothesis at the fracture level is still kept then we show that in the case of well separated time scales between matrix and fractures the preceding model needs only to be slightly modified in order to incorporate these fluxes the additional knowledge of the so called matrix to fracture transfer function allows to modify the mass matrix that becomes a time convolution operator this is reminiscent of existing space averaged transient dual porosity models

low rank method for fast solution of generalized smoluchowski equations abstract an efficient method for the fast solution of a new class of generalized smoluchowski equations is developed in contrast to conventional smoluchowski equations with constant rate coefficients that describe the aggregation kinetics the rate coefficients of the generalized smoluchowski equations depend on time the evolution of these coefficients is governed by another set of equations coupled with the aggregation equations the most prominent example of such processes is the ballistic aggregation when aggregates of different sizes have different partial temperatures the conventional approaches fail to deal efficiently with these systems when the number of equations n is large the new method overcomes this difficulty it exploits the low rank approach and drastically decreases computation time instead of o n 2 operations per time step the new method requires only o n r r log n operations where r is the system rank general techniques for an efficient solution of very large systems of ode are discussed in the context of the new approach

new two dimensional slope limiters for discontinuous galerkin methods on arbitrary meshes summary in this paper we introduce an extension of van leer s slope limiter for two dimensional discontinuous galerkin dg methods on arbitrary unstructured quadrangular or triangular grids the aim is to construct a non oscillatory shock capturing dg method for the approximation of hyperbolic conservative laws without adding excessive numerical dispersion unlike some splitting techniques that are limited to linear approximations on rectangular grids in this work the solution is approximated by means of piecewise quadratic functions the main idea of this new reconstructing and limiting technique follows a well known approach where local maximum principle regions are defined by enforcing some constraints on the reconstruction of the solution numerical comparisons with some existing slope limiters on structured as well as on unstructured meshes show a superior accuracy of our proposed slope limiters copyright 2004 john wiley sons ltd

connectivity consistent mapping method for 2 d discrete fracture networks 1 we present a new flow computation method in 2 d discrete fracture networks dfn intermediary between the classical dfn flow simulation method and the projection onto continuous grids the method divides the simulation complexity by solving for flows successively at a local mesh scale and at the global domain scale at the local mesh scale flows are determined by classical dfn flow simulations and approximated by an equivalent hydraulic matrix ehm relating heads and flow rates discretized on the mesh borders assembling the equivalent hydraulic matrices provides for a domain scale discretization of the flow equation the equivalent hydraulic matrices transfer the connectivity and flow structure complexities from the local mesh scale to the domain scale compared to existing geometrical mapping or equivalent tensor methods the ehm method broadens the simulation range of flow to all types of 2 d fracture networks both below and above the representative elementary volume rev additional computation linked to the derivation of the local mesh scale equivalent hydraulic matrices increases the accuracy and reliability of the method compared to dfn methods the ehm method first provides a simpler domain scale alternative permeability model second it enhances the simulation capacities to larger fracture networks where flow discretization on the dfn structure yields system sizes too large to be solved using the most advanced multigrid and multifrontal methods we show that the ehm method continuously moves from the dfn method to the tensor representation as a function of the local mesh scale discretization the balance between accuracy and model simplification can be optimally controlled by adjusting the domain scale and local mesh scale discretizations

a stochastic weighted particle method for coagulation advection problems a spatially resolved stochastic weighted particle method for inception coagulation advection problems is presented convergence to a deterministic limit is briefly studied numerical experiments are carried out for two problems with very different coagulation kernels these tests show the method to be robust and confirm the convergence properties the robustness of the weighted particle method is shown to contrast with two direct simulation algorithms which develop instabilities

a new approach to simulating flow in discrete fracture networks with an optimized mesh natural fractured media are highly unpredictable because of existing complex structures at the fracture and at the network levels fractures are by themselves heterogeneous objects of broadly distributed sizes shapes and orientations that are interconnected in large correlated networks with little field data and evidence numerical modeling can provide important information on the underground hydraulic phenomena however it must overcome several barriers first the complex network structure produces a structure difficult to mesh second the absence of a priori homogenization scale along with the double fracture and network heterogeneity levels requires the calculation of large but finely resolved fracture networks resulting in very large simulation domains to tackle these two related issues we reduce the highly complex geometry of the fractures by applying a local transformation that suppresses the cumbersome meshing configurations while keeping the networks fundamental geological and geometrical characteristics we show that the flow properties are marginally affected while the problem complexity i e memory capacity and resolution time can be divided by orders of magnitude the goal of this article is to propose a method of resolution which takes into account the geometrical complexity met in the networks and which makes it possible to treat a few thousand fractures the principal aim of this article is to present a tool to slowly modify the structures of the fracture networks to have a good quality mesh with a marginal loss in precision

implementation of higher order methods for robust and efficient compositional simulation numerical simulation of two phase multicomponent flow in permeable media with species transfer between the phases often requires use of higher order methods unlike first order methods higher order methods may be very sensitive to problem formulation the sensitivity to problem formulation and lack of recognition have hindered the widespread use of higher order methods in various problems including improved oil recovery and sequestration from co 2 injection in this work we offer proper formulation of species balance equations and boundary conditions which overcome problems of formulations used previously that were detrimental to the efficiency of higher order methods we also present proper approximation of phase fluxes in the mixed finite element method our proposals remove major deficiencies in using higher order methods in two phase multicomponent flow numerical examples are presented to demonstrate robustness and efficiency of our approach

an efficient multi point flux approximation method for discrete fracture matrix simulations we consider a control volume discretization with a multi point flux approximation to model discrete fracture matrix systems for anisotropic and fractured porous media in two and three spatial dimensions inspired by a recently introduced approach based on a two point flux approximation we explicitly account for the fractures by representing them as hybrid cells between the matrix cells as well as simplifying the grid generation our hybrid approach excludes small cells in the intersection of the fractures and hence avoids severe time step restrictions associated with small cells excluding the small cells also reduces the condition number of the discretization matrix for examples involving realistic anisotropy ratios in the permeability numerical results show significant improvement compared to existing methods based on two point flux approximations we also investigate the hybrid method by studying the convergence rates for different apertures and fracture matrix permeability ratios finally the effect of removing the cells in the intersections of the fractures are studied together these examples demonstrate the efficiency flexibility and robustness of our new approach

a fully mass conservative iterative impec method for multicomponent compressible flow in porous media abstract in this paper we consider efficient and fully mass conservative numerical methods for the multicomponent compressible single phase darcy flow in porous media compared with the classical implicit pressure explicit concentration impec scheme by which one of the components may be not mass conservative the new scheme enjoys an appealing feature that the conservation of mass is retained for each of the components the pressure velocity system is obtained by the summation of the discrete conservation equation for each component multiplying an unknown parameter which is nonlinearly dependent of the molar concentrations this approach is quite different from the conventional method which is used in the classical impec scheme we utilize a fully mass conservative iterative impec method to solve the nonlinear system for molar concentration pressure and velocity fields the upwind mixed finite element methods are used to solve the pressure velocity system although the peng robinson equation of state eos is utilized to describe the pressure as a function of the molar concentrations our method is suitable for any type of eos under some reasonable conditions the iterative scheme can be proved to be convergent and the molar concentration of each component is positivity preserving several interesting examples of multicomponent compressible flow in porous media are presented to demonstrate the robustness of the new algorithm

characterization of fractured reservoirs using tracer and flow rate data 1 this article introduces a robust method for characterizing fractured reservoirs using tracer and flow rate data the flow rate data are used to infer the interwell connectivity matrix which describes how injected fluids are divided between producers in the reservoir the tracer data are used to find a function called the tracer kernel for each injector producer connection the tracer kernel describes the volume and dispersive properties of the interwell flow path a combination of parametric and nonparametric regression methods was developed to estimate the tracer kernels in situations where data are collected at variable flow rate or variable injected concentration conditions this characterization method was developed to describe enhanced geothermal systems although it works well in general for characterizing incompressible flow in fractured reservoirs e g geothermal carbon sequestration radioactive waste and waterfloods of oil fields where transverse dispersivity can be considered negligible and production takes place at constant bottomhole pressure conditions the inferred metrics can be used to sketch informative field maps and predict tracer breakthrough curves at variable flow rate conditions

an efficient stochastic algorithm for studying coagulation dynamics and gelation phenomena a new class of efficient stochastic algorithms for the numerical treatment of coagulation processes is proposed the algorithms are based on the introduction of fictitious jumps combined with an acceptance rejection technique for distributions depending on particle size the increased efficiency is demonstrated by numerical experiments in particular gelation phenomena are studied

control volume method for numerical simulation of two phase immiscible flow in two and three dimensional discrete fractured media 1 we provide a numerical procedure for the simulation of two phase immiscible and incompressible flow in two and three dimensional discrete fractured media the concept of cross flow equilibrium is used to reduce the fracture dimension from n to n 1 in the calculation of flow in the fractures this concept which is often referred to as the discrete fracture model has a significant effect on the reduction of computational time the spatial discretization is performed with the control volume method this method is locally conservative and allows the use of unstructured grids to represent complex geometries such as discrete fracture configurations the relative permeability is upwinded with a criterion based on the evaluation of the flux direction at the boundaries of the control volumes which is consistent with the physics of fluid flow the system of partial differential equations is decoupled and solved using the implicit pressure explicit saturation impes approach the algorithm has been successfully tested in two and three dimensional numerical simulations of wetting phase fluid injection such as water in discrete fractured media saturated by a nonwetting phase such as nonaqueous phase liquid or oil with mild to high nonlinearity in relative permeability and capillary pressure to the best of our knowledge results for simulations of two phase immiscible and incompressible flow in three dimensional discrete fractured media including capillary and gravity effects are the first to appear in the literature

on the ideals and essential algebras of shifted functors of linear representations abstract we present a study on the shifted green biset functors k r f g of linear f representations with coefficients over k for fields k and f of characteristic zero and a finite group g we provide a criterion for the vanishing of their essential algebras and we prove that the condition of uniqueness of minimal groups for simple modules holds for these functors we give a parametrization of a family of simple k r q g modules we also prove the semisimplicity of the category of c r c g modules by means of an equivalence with a category of modules over a semisimple algebra

calculation of internodal transmissivities in finite difference models of flow in heterogeneous porous media we present an analytical and numerical investigation of the finite difference computation of the equivalent conductivity of heterogeneous porous media the customary harmonic scheme to evaluate finite difference internodal transmissivities produces a systematic bias in the numerical results unless an extremely fine grid is used in order to quantify such effects we have developed an analytical approach in the form of a series expansion of the equivalent numerical conductivity in powers of the conductivity variance this leads to an expression of the numerical answer as a function of the grid block size the calculation confirms the existence of a strong bias and of a very slow convergence we propose a simple method to correct it which is well suited for upscaling numerical experiments performed with more contrasting heterogeneous media show similar results this allows the use of coarser gridding and consequently an appreciable speedup in the numerical simulation approach

biset functors and genetic sections for p groups abstract in this note i show that if f is a biset functor defined over finite p groups then for each finite p group p there is a direct summand of f p admitting a natural direct sum decomposition indexed by the irreducible rational representations of p or equivalently by the equivalence classes of origins in p or also by equivalence classes of genetic sections of p this leads to a description of the torsion part of the group of relative syzygies in the dade group of p and to a conjecture on the structure of the torsion part of the whole dade group of p

multicomponent fluid flow by discontinuous galerkin and mixed methods in unfractured and fractured media 1 a discrete fracture model for the flow of compressible multicomponent fluids in homogeneous heterogeneous and fractured media is presented in single phase in the numerical model we combine the mixed finite element mfe and the discontinuous galerkin dg methods we use the cross flow equilibrium concept to approximate the fractured matrix mass transfer the discrete fracture model is numerically superior to the single porosity model and overcomes limitations of the dual porosity models including the use of a shape factor the mfe method provides a direct and accurate approximation for the velocity field which is crucial for the convective terms in the flow equations the dg method associated with a slope limiter is used to approximate the species balance equations this method can capture the sharp moving fronts the calculation of the fracture fracture flux across three and higher intersecting fracture branches is a challenge in this work we provide an accurate approximation of these fluxes by using the mfe formulation numerical examples in unfractured and fractured media illustrate the efficiency and robustness of the proposed numerical model

a monte carlo simulation of coagulation a monte carlo simulation technique is described for the study of the coagulation of suspended particles the method is computationally efficient since the particle trajectories are not used to determine coagulations instead pairs of particles are assigned probabilities to coagulate and the evolution is computed as a stochastic markov game we also describe a simple analytic method to obtain the stationary distribution of sizes for the various mechanisms of relative particle motion it is demonstrated that the simulation yields the correct stationary size distribution independent of initial condition

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

a new event driven constant volume method for solution of the time evolution of particle size distribution direct simulation monte carlo dsmc method is an important approach for numerical solution of the population balance equation which characterizes the dynamic evolution of particle size distribution in dispersed systems one sample of the whole system i e subsystem is taken into account in most dsmc methods it means that a spatially isotropic whole system is considered and simulation particles having same number weight are tracked a new event driven constant volume edcv method for population balance modeling is proposed to describe the dynamic evolution in dispersed systems under influence of coagulation breakage nucleation surface growth dissolution condensation evaporation and deposition settling the method adopts the concept of differentially weighting simulation particles and several schemes of sample restoration are developed to maintain simulation particle number within prescribed bounds at the same time the constant volume computational domain is tracked by comparing of several popular monte carlo methods it is concluded that the proposed edcv method exhibits comparatively high precision and efficiency

rhetorical biset functors rational p biset functors and their semisimplicity in characteristic zero rhetorical biset functors can be defined for any family of finite groups that is closed under subquotients up to isomorphism the rhetorical p biset functors almost coincide with the rational p biset functors we show that over a field with characteristic zero the rhetorical biset functors are semisimple and furthermore they admit a character theory involving primitive characters of automorphism groups of cyclic groups

an induction theorem for the unit groups of burnside rings of 2 groups abstract let g be a 2 group and b g denote the group of units of the burnside ring of g for each subquotient h k of g there is a generalized induction map from b h k to b g defined as the composition of inflation and multiplicative induction maps we prove that the product of generalized induction maps b h k b g is surjective when the product is taken over the set of all subquotients that are isomorphic to the trivial group or a dihedral 2 group of order 2 n with n 4 as an application we give an algebraic proof for a theorem by tornehave the unit group for the burnside ring of a 2 group aarhus universitet preprint series 1983 84 41 may 1984 which states that tom dieck s exponential map from the real representation ring of g to b g is surjective we also give a sufficient condition for the surjectivity of the exponential map from the burnside ring of g to b g

a mixed finite element technique based on implicit discretization of faults for permeability upscaling in fault damage zones 1 natural fault damage zones fdzs are often composed of complex arrays containing many thin faults to account for fdzs in large scale models it is necessary to represent the flow effects of these many small faults by some form of upscaling the explicit discretization of the geometry and topology of these thin faults and of the rock matrix typically leads to meshes comprising large numbers of elements making it difficult to solve the flow equations efficiently this paper proposes a practical technique based on the mixed finite element method mfem permitting the permeability upscaling in two dimensional fault damage zones that contain thin and isotropic low permeability faults this technique utilizes an implicit discretization scheme that is similar in principle to those used for discrete fracture networks the scheme described here treats flow across faults accurately but unlike the schemes used for fractures it neglects the flow along the faults because intrafault volumetric flow in thin faults is very small this approach allows for a simpler numerical discretization and a reduction in numerical calculation effort the scheme can be readily implemented in a standard mixed finite element code compared with the same mfem based on an explicit discretization scheme the two techniques are shown to produce results that agree closely the implicit technique is shown to be more efficient than the explicit technique for a typical fault damage zone model this technique is readily extendable to three dimensions

application of the mixed hybrid finite element approximation in a groundwater flow model luxury or necessity selected groundwater flow scenarios are used in a two way comparison between the mixed hybrid finite element method and the standard finite element method also called the conforming finite element method the simulations presented are performed in the bidimensional case with a triangular space discretization because of its practical interest for hydrogeologists the basic idea of the mixed procedure is to approximate both the hydraulic potential and the velocity simultaneously and to satisfy an exact water balance for each element by contrast the conforming finite element method calculates the potential field everywhere and then calculates the velocity by differentiation of the potential the conventional approach results in an elementwise constant velocity which can be subject to significant problems because of the normal component discontinuity of the velocity the mixed hybrid finite element method provides velocities everywhere in the field as well as potentials at the center of each element and each edge moreover the normal component of the velocity field is continuous between adjacent elements the results of the simulations are presented in the form of streamlines to avoid the problem of velocity discontinuity the method of cordes and kinzelbach 1992 is used it allows the construction of a continuous velocity field from potentials obtained by the conforming finite element method the comparison studies show that the mixed hybrid finite element is superior to the conforming method in terms of accuracy it is also superior to the conforming method in terms of computational effort the potential fields obtained by the mixed hybrid and the conforming finite element methods are the same

the functor of rational representations for p groups abstract let k be a field of characteristic p 0 let c p k be the category whose objects are the finite p groups morphisms are the k linear combinations of bisets and composition of morphisms is obtained by k linear extension from the usual product of bisets let f p k denote the category of k linear functors from c p k to the category of k vector spaces this paper investigates the structure of the functor kr q mapping a p group p to kr q p k z r q p as an object of f p k where r q p is the grothendieck group of the category of finite dimensional q p modules the main result is an explicit description of the lattice of all subfunctors of kr q in particular for p odd it is shown that kr q is a uniserial object in f p k for p 2 the lattice of subfunctors of kr q can be described as the lattice of closed subsets of a graph whose vertices are the 2 groups of normal 2 rank 1 in both cases a composition series of kr q is obtained which leads to a formula giving the dimension of the evaluations sq k p of the simple objects sq k of f p k associated to p groups q of normal p rank 1 different from cp this formula can be phrased in terms of rational representations of p but also in terms of the geometry of the lattice of subgroups of p using the notions of basic subgroups and origins for example if p 2 the dimension of s 1 k p is equal to the number of absolutely irreducible q p modules