coherent state maps related to the bounded positive operators we show that for any bounded positive operator h with the simple spectrum one can canonically define two coherent state maps the algebras generated by annihilation operators defined by these coherent state maps are studied we describe also how the toda isospectral deformation of h deforms the corresponding coherent state maps and the related operator algebras

derived localisation of algebras and modules for any dg algebra a not necessarily commutative and a subset s in h a the homology of a we construct its derived localisation l s a together with a map a l s a well defined in the homotopy category of dg algebras which possesses a universal property similar to that of the ordinary localisation but formulated in homotopy invariant terms even if a is an ordinary ring l s a may have non trivial homology unlike the commutative case the localisation functor does not commute in general with homology but instead there is a spectral sequence relating h l s a and l s h a this spectral sequence collapses when e g s is an ore set or when a is a free ring we prove that l s a could also be regarded as a bousfield localisation of a viewed as a left or right dg module over itself combined with the results of dwyer kan on simplicial localisation this leads to a simple and conceptual proof of the topological group completion theorem further applications include algebraic k theory cyclic and hochschild homology strictification of homotopy unital algebras idempotent ideals the stable homology of various mapping class groups and kontsevich s graph homology

some orthogonal polynomials arising from coherent states we explore in this paper some orthogonal polynomials which are naturally associated with certain families of coherent states often referred to as nonlinear coherent states in the quantum optics literature some examples turn out to be known orthogonal polynomials but in many cases we encounter a general class of new orthogonal polynomials for which we establish several qualitative results

integrable multi boson systems and orthogonal polynomials the strict relation between a certain class of multi boson hamiltonian systems and the corresponding class of orthogonal polynomials is established the correspondence is effectively used to integrate the systems as an explicit example we integrate the class of multi boson systems corresponding to q hahn class polynomials

the second homology group of the mapping class group of an orientable surface in i 7 mumford shows that the picard group p ic is isomorphic to h2 f 2 and conjectures the latter is rank one g 3 we prove this below for g 5 another interpretation of this theorem may be obtained by identifying h2 f as bordism classes of fiber bundles f w4 t where t is a closed oriented surface sect 0 when f is closed every such bundle is bordant to f w t a bundle admitting a section s t w the theorem then says that

a class of vector coherent states defined over matrix domains a general scheme is proposed for constructing vector coherent states in analogy with the well known canonical coherent states and their deformed versions when these latter are expressed as infinite series in powers of a complex variable z in the present scheme the variable z is replaced by matrix valued functions over appropriate domains as particular examples we analyze the quaternionic extensions of the canonical coherent states and the gilmore perelomov and barut girardello coherent states arising from representations of su 1 1 possible physical applications are indicated

second order q difference equations solvable by factorization method by solving an infinite nonlinear system of q difference equations one constructs a chain of q difference operators the eigenproblems for the chain are solved and some applications including the one related to q hahn orthogonal polynomials are discussed it is shown that in the limit q 1 the present method corresponds to the one developed by infeld and hull

sl 2 r symmetry and solvable multiboson systems the one mode and the two mode multiboson systems with sl 2 r symmetry are investigated hamiltonians of these systems are integrated using the theory of orthogonal polynomials the coherent state representation for these systems is constructed

the homotopy type of the cobordism category the embedded cobordism category under study in this paper generalizes the category of conformal surfaces introduced by g segal in s2 in order to formalize the concept of field theories our main result identifies the homotopy type of the classifying space of the embedded d dimensional cobordism category for all d for d 2 our results lead to a new proof of the generalized mumford conjecture somewhat different in spirit from the original one presented in mw

homological stability for the mapping class groups of non orientable surfaces we prove that the homology of the mapping class groups of non orientable surfaces stabilizes with the genus of the surface combining our result with recent work of madsen and weiss we obtain that the classifying space of the stable mapping class group of non orientable surfaces up to homology isomorphism is the infinite loop space of a thom spectrum built from the canonical bundle over the grassmannians of 2 planes in n 2 in particular we show that the stable rational cohomology is a polynomial algebra on generators in degrees 4i this is the non oriented analogue of the mumford conjecture

factorization method for second order functional equations we apply general difference calculus in order to obtain solutions to the functional equations of the second order we show that factorization method can be successfully applied to the functional case this method is equivariant under the change of variables some examples of applications are presented

conformally invariant gauge fixed actions for 2 d topological gravity we show that invariants of mumford for moduli spaces of curves are obtainable from a gauge fixed action of a topological quantum field theory in two dimensions the method is completely analogous to the relation of donaldson invariants with the topological quantum field theory for gauge theories in four dimensions

viscosity independent numerical errors for lattice boltzmann models from recurrence equations to magic collision numbers we prove for generic steady solutions of the lattice boltzmann lb models that the variation of the numerical errors is set by specific combinations called magic numbers of the relaxation rates associated with the symmetric and anti symmetric collision moments given the governing dimensionless physical parameters such as the reynolds or peclet numbers and the geometry of the computational mesh the numerical errors remain the same for any change of the transport coefficients only when the free kinetic anti symmetric rates and the boundary rules are chosen properly the single relaxation time bgk model has no free collision rate and yields viscosity dependent errors with any boundary scheme for hydrodynamic problems the simplest and most efficient collision operator for invariant errors is the two relaxation times trt model as an example this model is able to compute viscosity independent permeabilities for any porous structure these properties are derived from steady recurrence equations obtained through linear combinations of the lb evolution equations in which the equilibrium and non equilibrium components are directly interconnected via finite difference link wise central operators the explicit dependency of the non equilibrium solution on the relaxation rates is then obtained this allows us first to confirm the governing role of the magic combinations for steady solutions of the stokes equation second to extend this property to steady solutions of the navier stokes and anisotropic advection diffusion equations third to develop a parametrization analysis of the microscopic and macroscopic closure relations prescribed via link wise boundary schemes

low and high order accurate boundary conditions the present contribution focuses on the accuracy of reflection type boundary conditions in the stokesbrinkmandarcy modeling of porous flows solved with the lattice boltzmann method lbm which we operate with the two relaxation time trt collision and the brinkman force based scheme bf called bf trt scheme in parallel we compare it with the stokesbrinkmandarcy linear finite element method fem where the dirichlet boundary conditions are enforced on grid vertices in bulk both bf trt and fem share the same defect in their discretization a correction to the modeled brinkman equation appears given by the discrete laplacian of the velocity proportional resistance force this correction modifies the effective brinkman viscosity playing a crucial role in the triggering of spurious oscillations in the bulk solution while the exact form of this defect is available in lattice aligned straight or diagonal flows in arbitrary flow lattice orientations its approximation is constructed at boundaries we verify that such a brinkman viscosity correction has an even more harmful impact already at the first order it shifts the location of the no slip wall condition supported by traditional lbm boundary schemes such as the bounce back rule for that reason this work develops a new class of boundary schemes to prescribe the dirichlet velocity condition at an arbitrary wall boundary node distance and that supports a higher order accuracy in the accommodation of the trt brinkman solutions for their modeling we consider the standard bf scheme and its improved version called ibf this latter is generalized in this work to suppress or to reduce the viscosity correction in arbitrarily oriented flows our framework extends the one and two point families of linear and parabolic link wise boundary schemes respectively called b li and b mli which avoid the interference of the brinkman viscosity correction in their closure relations the performance of lbm and fem is thoroughly evaluated in three benchmark tests which are run throughout three distinctive permeability regimes the first configuration is a horizontal porous channel studied with a symbolic approach where we construct the exact solutions of fem and bf ibf with different boundary schemes the second problem refers to an inclined porous channel flow which brings in as new challenge the formation of spurious boundary layers in lbm that is numerical artefacts that arise due to a deficient accommodation of the bulk solution by the low accurate boundary scheme the third problem considers a porous flow past a periodic square array of solid cylinders which intensifies the previous two tests with the simulation of a more complex flow pattern the ensemble of numerical tests provides guidelines on the effect of grid resolution and the trt free collision parameter over the accuracy and the quality of the velocity field spanning from stokes to darcy permeability regimes it is shown that with the use of the high order accurate boundary schemes the simple uniform mesh based trt lbm formulation can even surpass the accuracy of fem employing hardworking body fitted meshes

classical yang baxter equations and quantum integrable systems quantum integrable models associated with nondegenerate solutions of classical yang baxter equations related to the simple lie algebras are investigated these models are diagonalized for rational and trigonometric solutions in the cases of sl n gl n o n and sp n algebras the analogy with the quantum inverse scattering method is demonstrated

cellular automaton fluids a model for flow in porous media numerical models of fluid flow through porous media can be developed from either microscopic or macroscopic properties the large scale viewpoint is perhaps the most prevalent darcy s law relates the chief macroscopic parameters of interest flow rate permeability viscosity and pressure gradient and may be invoked to solve for any of these parameters when the others are known in practical situations however this solution may not be possible attention is then typically focused on the estimation of permeability and numerous numerical methods based on knowledge of the microscopic pore space geometry have been proposed because the intrinsic inhomogeneity of porous media makes the application of proper boundary conditions difficult microscopic flow calculations have typically been achieved with idealized arrays of geometrically simple pores throats and cracks i propose here an attractive alternative which can freely and accurately model fluid flow in grossly irregular geometries this new method s

stability of the homology of the mapping class groups of orientable surfaces the mapping class group of f fgs r is f rgs wo a where a is the topological group of orientation preserving diffeomorphisms of f which are the identity on df and fix the s punctures when r 0 and 2g s 3 an important feature of f is that it acts properly discontinuously on the teichmiller space us the quotient is the moduli space f of isometry classes of complete hyperbolic metrics of finite area on f since us is homeomorphic to euclidean space and f is virtually torsion free we have

consistent lattice boltzmann modeling of low speed isothermal flows at finite knudsen numbers in slip flow regime ii application to curved boundaries gaseous flows inside microfluidic devices often fall in the slip flow regime according to this theoretical description the navier stokes model remains applicable in bulk while at solid walls a slip velocity boundary model shall be considered physically it is well established that to properly account for the wall curvature the wall slip velocity must be determined by the shear stress rather than the normal component of the velocity derivative alone as commonly applied to planar surfaces it follows that the numerical transcription of this type of boundary condition is generally a challenging task for standard computational fluid dynamics cfd techniques this paper aims to show that the realization of the slip velocity condition on arbitrarily shaped boundaries can be accomplished in a natural way with the lattice boltzmann method lbm to substantiate this conclusion this work undertakes the following three studies first we examine the conditions under which the generic reflection type boundary rules used by lbm become consistent models for the slip velocity boundary condition this effort makes use of the second order chapman enskog expansion method where we address both planar and curved boundaries the analysis also clarifies the capabilities and limitations behind the considered reflection type slip schemes second we revisit the family of parabolic accurate lbm slip boundary schemes originally formulated in phys rev e 96 013311 2017 2470 004510 1103 physreve 96 013311 on the basis of the multireflection framework and discuss their characteristics when operating on curved boundaries as well as the limitations of other less accurate lbm slip boundary formulations such as the linearly accurate slip schemes and the widely popular kinetic based boundary schemes in addition we also discuss the numerical stability of the parabolic slip schemes previously developed providing an heuristic strategy to improve their stable range of operation third we evaluate the performance of the several slip boundary schemes debated in this paper the numerical tests correspond to two classical 2d benchmark flow problems of slip over non planar solid surfaces namely i the velocity profile of the cylindrical couette flow and ii the permeability of a slow rarefied gas over a periodic array of circular cylindrical obstacles the obtained numerical results confirm the competitiveness of the lbm when equipped with slip boundary schemes of parabolic accuracy as cfd tool to simulate slippage phenomena over arbitrarily non planar surfaces indeed although operating on a simple uniform mesh discretization the lbm yields a similar or even superior level of accuracy compared to state of the art fem simulations conducted on hardworking body fitted meshes this conclusion establishes the lbm as a very appealing cfd technique for simulating microfluidic flows in the slip flow regime a result that deserves further exploration in future studies

harmonic stokes flow through periodic porous media a 3d boundary element method abstract our interest is in dynamic filtration through periodic porous saturated media more precisely here we develop a three dimensional numerical model based on boundary element methods to compute the dynamic permeability over a wide range of such media this generalized darcy coefficient is obtained by the homogenization process applied to a periodic deformable porous medium under dynamic solicitations an unusual choice of green functions is made a simple numerical procedure is used for the treatment of the periodic boundary conditions recent advances to treat singular integrals are employed and extended to our case the method is tested on simple examples where theoretical results are available in the static case results are compared with many previous results on periodic arrays of spheres new results are given in the dynamic case the scaling behavior for dynamic permeability in porous media is checked and discussed

new results of intersection numbers on moduli spaces of curves we present a series of results we obtained recently about the intersection numbers of tautological classes on moduli spaces of curves including a simple formula of the n point functions for witten s classes an effective recursion formula to compute higher weil petersson volumes several new recursion formulae of intersection numbers and our proof of a conjecture of itzykson and zuber concerning denominators of intersection numbers we also present virasoro and kdv properties of generating functions of general mixed and intersections

consistent lattice boltzmann schemes for the brinkman model of porous flow and infinite chapman enskog expansion we show that a consistent modeling of porous flows needs at least one free collision relaxation rate to avoid a nonlinear dependency of the numerical errors on the viscosity this condition is necessary to get the viscosity independent permeability from the stokes flow and to parametrize properly with nondimensional physical numbers the lattice boltzmann brinkman schemes the two relaxation time trt collision operator controls all coefficients of the higher order corrections in steady solutions with a specific combination of its two collision rates a possibility lacking for the bhatnagar gross krook bgk based single relaxation time schemes the analysis is based on exact recurrence equations of the evolution equation and illustrated for the exact solutions of the brinkman scheme in simply oriented parallel and diagonal channels the apparent viscosity coefficient of the trt stokes brinkman scheme in arbitrary flow is only approximated the compatibility of one dimensional arbitrarily rotated flows with the nonlinear navier stokes equilibrium is examined an explicit dependency for all coefficients on the relaxation rates is presented for the infinite steady state chapman enskog expansion

lattice boltzmann modeling with discontinuous collision components hydrodynamic and advection diffusion equations irrespective of the nature of the modeled conservation laws we establish first the microscopic interface continuity conditions for lattice boltzmann lb multiple relaxation time link wise collision operators with discontinuous components equilibrium functions and or relaxation parameters effective macroscopic continuity conditions are derived for a planar implicit interface between two immiscible fluids described by the simple two phase hydrodynamic model and for an implicit interface boundary between two heterogeneous and anisotropic variably saturated soils described by richard s equation comparing the effective macroscopic conditions to the physical ones we show that the range of the accessible parameters is restricted e g a variation of fluid densities or a heterogeneity of the anisotropic soil properties when the interface is explicitly tracked the interface collision components are derived from the leading order continuity conditions among particular interface solutions a harmonic mean value is found to be an exact lb solution both for the interface kinematic viscosity and for the interface vertical hydraulic conductivity function we construct simple problems with the explicit and implicit interfaces matched exactly by the lb hydrodynamic and or advection diffusion schemes with the aid of special solutions for free collision parameters

vector coherent states from plancherel s theorem clifford algebras and matrix domains as a substantial generalization of the technique for constructing canonical and the related nonlinear and q deformed coherent states we present here a method for constructing vector coherent states vcs in the same spirit these vcs may have a finite or an infinite number of components the resulting formalism which involves an assumption on the existence of a resolution of the identity is broad enough to include all the definitions of coherent states existing in the current literature subject to this restriction as examples we first apply the technique to construct vcs using the plancherel isometry for groups and vcs associated with clifford algebras in particular quaternions as physical examples we discuss vcs for a quantum optical model and finally apply the general technique to build vcs over certain matrix domains

spaces of graphs and surfaces on the work of soren galatius galatius most striking result is easy enough to state let n be the symmetric group on n letters and fn be the free non abelian group with n generators the symmetric group n acts naturally by permutation on the n generators of fn and every permutation gives thus rise to an automorphism of the free group galatius proves that the map n autfn in homology induces an isomorphism in degrees less than n 1 2 the homology of the symmetric groups in these ranges is well understood in particular in common with all finite groups it has no non trivial rational homology by galatius theorem in low degrees this then is also true for autfn h autfn q 0 for 0 2n 3

stabilization for mapping class groups of 3 manifolds we prove that the homology of the mapping class group of any 3manifold stabilizes under connected sum and boundary connected sum with an arbitrary 3 manifold when both manifolds are compact and orientable the stabilization also holds for the quotient group by twists along spheres and disks and includes as particular cases homological stability for symmetric automorphisms of free groups automorphisms of certain free products and handlebody mapping class groups our methods also apply to manifolds of other dimensions in the case of stabilization by punctures the main result of this paper is a homological stability theorem for mapping class groups of 3 manifolds where the stabilization is by connected sum with an arbitrary 3 manifold more precisely we show that given any two compact connected oriented 3 manifolds n and p with n 6 the homology group hi 0diff n p p rel n z is independent of the number n of copies of p in the connected sum as long as n 2i 2 i e each homology group stabilizes with p we also prove an analogous result for boundary connected sum and a version for the quotient group of the mapping class group by twists along spheres and disks a group closely related to the automorphism group of the fundamental group of the manifold homological stability theorems were first found in the sixties for symmetric groups by nakaoka 36 and linear groups by quillen and now form the foundation of modern algebraic k theory see for example 28 part iv and 42 stability theorems for mapping class groups of surfaces were obtained in the eighties by harer and ivanov 14 25 and recently turned out to be a key ingredient to a solution of the mumford conjecture about the homology of the riemann moduli space 30 the other main examples of families of groups for which stability has been known are braid groups 1 and automorphism groups of free groups 17 18 the present paper extends significantly the class of groups for which homological stability is known to hold it suggests that it is a widespread phenomenon among families of groups containing enough symmetries in addition to the already mentioned stability theorems for mapping class groups of 3 manifolds corollaries of our main result include stability for handlebody subgroups of surface mapping class groups symmetric automorphism groups of free groups and automorphism groups of free products ng for many groups g using similar techniques we obtain stability results also for mapping class groups 0diff m n points rel m for m any m dimensional manifold with boundary m 2 even the case m 2 is new here as well as for the fundamental group 1conf m n of the configuration space of n unordered points in m our paper thus also unifies previous known results as we recover stability for braid groups as 1conf d n symmetric groups as 1conf d n and automorphism groups of free groups as aut nz

assessment of the two relaxation time lattice boltzmann scheme to simulate stokes flow in porous media 1 the recent advances in 3 d imaging of porous structures have generated a tremendous interest in the simulation of complex single and two phase flows lattice boltzmann lb schemes present a powerful tool to solve the flow field directly from the binarized 3 d images however as viscosity often plays an important role the lb scheme should correctly treat viscosity effects this is the case using a lb scheme with two relaxation times trt unlike the broadly used the single relaxation rate bgk where the velocity of the modeled fluid does not vary as the inverse of the viscosity applying the bounce back no slip boundary rule the aim of this work is to apply the lb trt approach to different types of porous media straight channels 2 d model porous media sandstone to solve for the flow field and to evaluate the approach in terms of parameter dependence error and convergence time on the basis of permeability we show that the variation of permeability with the free relaxation parameter of the trt scheme depends on the heterogeneity of the sample and on the numerical resolution the convergence time depends on the applied viscosity and the parameter standing for the speed of sound thus the computation time can be reduced by choosing appropriate values of those parameters two approaches to calculate permeability darcy s law and viscous energy dissipation are proposed and investigated we recommend to use darcy s law as dependence on is less important periodic in the presence of a driving body force and pressure boundary conditions are evaluated in terms of the results

the virtual cohomological dimension of the mapping class group of an orientable surface let f f r be the mapping class group of a surface f of genus g with s punctures and r boundary components the purpose of this paper is to establish cohomology properties of f parallel to those of the arithmetic groups if g is a linear algebraic group defined over q x is the symmetric space associated to g and a is an arithmetic subgroup of g then a is virtually torsion free and acts properly discontinuously on x the rational homology of a is the same as that of x a furthermore there is a bordification of x bs to a manifold with corners 3 and an extension of the action of a to a properly discontinuous action on jf so that the quotient x a is compact the boundary of jf is homotopy equivalent to a wedge of spheres say of dimension d and the virtual cohomological dimension of a is n d 1 where n is the dimension of x in the case of the mapping class group there is no analog for g ivanov unpublished has proven that f is not arithmetic nevertheless f acts properly discontinuously on teichmiiller space r which is homeomorphic to euclidean space of dimension 6 g 6 2 s 3 will play the role of the symmetric space the quotient of 9by f is the moduli space of curves whose rational homology is then identified with that of e harvey har has constructed a borel serre bordification j of 3 by analytic methods in the case where f has punctures we will build g by a different combinatorial method in addition we will explicitly describe inside y a cell complex y of dimension 4 g 4 s onto which j may be f equivariantly retracted thus establishing an analog of the constructions for sl n by serre soul6 sol and ash a this complex will be of the lowest possible dimension because we will use j to prove our main result

on the dimensions of oscillator algebras induced by orthogonal polynomials there is a generalized oscillator algebra associated with every class of orthogonal polynomials n x n 0 on the real line satisfying a three term recurrence relation x n x bn n 1 x bn 1 n 1 x 0 x 1 b 1 0 this note presents necessary and sufficient conditions on bn for such algebras to be of finite dimension as examples we discuss the dimensions of oscillator algebras associated with hermite legendre and gegenbauer polynomials some remarks on the dimensions of oscillator algebras associated with multi boson systems are also presented

systems with intensity dependent conversion integrable by finite orthogonal polynomials we present exact solutions of a class of the nonlinear models which describe the parametric conversion of photons hamiltonians of these models are related to the classes of finite orthogonal polynomials the spectra and exact expressions for eigenvectors of these hamiltonians are obtained

the stable moduli space of riemann surfaces mumford s conjecture d mumford conjectured in 30 that the rational cohomology of the stable moduli space of riemann surfaces is a polynomial algebra generated by certain classes i of di mension 2i for the purpose of calculating rational cohomology one may replace the stable moduli space of riemann surfaces by b 1 where 1 is the group of isotopy classes of automorphisms of a smooth oriented connected surface of large genus tillmann s insight 41 that the plus construction makes b 1 into an infinite loop space led to a stable homo topy version of mumford s conjecture stronger than the original 22 we prove the stronger version relying on harer s stability theorem 15 vassiliev s theorem concerning spaces of functions with moderate singularities 43 42 and methods from homotopy theory

a proof of the smale conjecture diff s3 0 4 the smale conjecture 9 is the assertion that the inclusion of the orthogonal group 0 4 into diff s3 the diffeomorphism group of the 3 sphere with the cw topology is a homotopy equivalence there are many equivalent forms of this conjecture some of which are listed in the appendix to this paper we shall prove

the unstable integral homology of the mapping class groups of a surface with boundary we construct a graph complex calculating the integral homology of the bordered mapping class groups we compute the homology of the bordered mapping class groups of the surfaces s 1 1 s 1 2 and s 2 1 using the circle action on this graph complex we build a double complex and a spectral sequence converging to the homology of the unbordered mapping class groups we compute the homology of the punctured mapping class groups associated to the surfaces s 1 1 and s 2 1 finally we use miller s operad to get the first kudo araki and browder operations on our graph complex we also consider an unstable version of the higher kudo araki dyer lashoff operations

lattice boltzmann and finite difference simulations for the permeability for three dimensional porous media numerical micropermeametry is performed on three dimensional porous samples having a linear size of approximately 3 mm and a resolution of 7 5 microm one of the samples is a microtomographic image of fontainebleau sandstone two of the samples are stochastic reconstructions with the same porosity specific surface area and two point correlation function as the fontainebleau sample the fourth sample is a physical model that mimics the processes of sedimentation compaction and diagenesis of fontainebleau sandstone the permeabilities of these samples are determined by numerically solving at low reynolds numbers the appropriate stokes equations in the pore spaces of the samples the physical diagenesis model appears to reproduce the permeability of the real sandstone sample quite accurately while the permeabilities of the stochastic reconstructions deviate from the latter by at least an order of magnitude this finding confirms earlier qualitative predictions based on local porosity theory two numerical algorithms were used in these simulations one is based on the lattice boltzmann method and the other on conventional finite difference techniques the accuracy of these two methods is discussed and compared also with experiment

direct pore level modeling of incompressible fluid flow in porous media we present a dynamic particle based model for direct pore level modeling of incompressible viscous fluid flow in disordered porous media the model is capable of simulating flow directly in three dimensional high resolution micro ct images of rock samples it is based on moving particle semi implicit mps method we modify this technique in order to improve its stability for flow in porous media problems using the micro ct image of a rock sample the entire medium i e solid and fluid is discretized into particles the incompressible navier stokes equations are then solved for each particle using the mps summations the model handles highly irregular fluid solid boundaries effectively an algorithm to split and merge fluid particles is also introduced to handle the computational load we present a parallel version of the model that runs on distributed memory computer clusters the accuracy of the model is validated against the analytical numerical and experimental data available in the literature the validated model is then used to simulate both unsteady and steady state flow of an incompressible fluid directly in a representative elementary volume rev size micro ct image of a naturally occurring sandstone with email protected resolution we analyze the quality and consistency of the predicted flow behavior and calculate absolute permeability using the steady state flow rate

the stable mapping class group and q ℂp in t2 it was shown that the classifying space of the stable mapping class groups after plus construction b has an infinite loop space structure this result and the tools developed in bm to analyse transfer maps are used here to show the following splitting theorem let p p e 0 e p 2 be the adams splitting of the p completed suspension spectrum of p then for some infinite loop space w p b p e 0 e p 3 w p where e i denotes the infinite loop space associated to the spectrum e i the homology of e i is known and as a corollary one obtains large families of torsion classes in the homology of the stable mapping class group this splitting also detects all the miller morita mumford classes our results suggest a homotopy theoretic refinement of the mumford conjecture the above p adic splitting uses a certain infinite loop map b p 1 that induces an isomorphims in rational cohomology precisely if the mumford conjecture is true we suggest that might be a homotopy equivalence

analysis and improvement of brinkman lattice boltzmann schemes bulk boundary interface similarity and distinctness with finite elements in heterogeneous porous media this work focuses on the numerical solution of the stokes brinkman equation for a voxel type porous media grid resolved by one to eight spacings per permeability contrast of 1 to 10 orders in magnitude it is first analytically demonstrated that the lattice boltzmann method lbm and the linear finite element method fem both suffer from the viscosity correction induced by the linear variation of the resistance with the velocity this numerical artefact may lead to an apparent negative viscosity in low permeable blocks inducing spurious velocity oscillations the two relaxation times trt lbm may control this effect thanks to free tunable two rates combination moreover the brinkman force based bf trt schemes may maintain the nondimensional darcy group and produce viscosity independent permeability provided that the spatial distribution ofis fixed independently of the kinematic viscosity such a property is lost not only in the bf bgk scheme but also by partial bounce back trt gray models as shown in this work further we propose a consistent and improved ibf trt model which vanishes viscosity correction via simple specific adjusting of the viscous mode relaxation rate to local permeability value this prevents the model from velocity fluctuations and in parallel improves for effective permeability measurements from porous channel to multidimensions the framework of our exact analysis employs a symbolic approach developed for both lbm and fem in single and stratified unconfined and bounded channels it shows that even with similar bulk discretization bf ibf and fem may manifest quite different velocity profiles on the coarse grids due to their intrinsic contrasts in the setting of interface continuity and no slip conditions while fem enforces them on the grid vertexes the lbm prescribes them implicitly we derive effective lbm continuity conditions and show that the heterogeneous viscosity correction impacts them a property also shared by fem for shear stress but in contrast with fem effective velocity conditions in lbm give rise to slip velocity jumps which depend on i neighbor permeability values ii resolution and iii control parameter ranging its reliable values from poiseuille bounce back solution in open flow to zero in darcy s limit we suggest an upscaling algorithm for from multilayers to multidimensions in random extremely dispersive samples finally on the positive side for lbm besides its overall versatility the implicit boundary layers allow for smooth accommodation of the flat discontinuous darcy profiles quite deficient in fem

multireflection boundary conditions for lattice boltzmann models we present a general framework for several previously introduced boundary conditions for lattice boltzmann models such as the bounce back rule and the linear and quadratic interpolations the objectives are twofold first to give theoretical tools to study the existing link type boundary conditions and their corresponding accuracy second to design boundary conditions for general flows which are third order kinetic accurate using these new boundary conditions couette and poiseuille flows are exact solutions of the lattice boltzmann models for a reynolds number mathrm re 0 stokes limit for arbitrary inclination with the lattice directions numerical comparisons are given for stokes flows in periodic arrays of spheres and cylinders linear periodic array of cylinders between moving plates and for navier stokes flows in periodic arrays of cylinders for mathrm re l200 these results show a significant improvement of the overall accuracy when using the linear interpolations instead of the bounce back reflection up to an order of magnitude on the hydrodynamics fields further improvement is achieved with the new multireflection boundary conditions reaching a level of accuracy close to the quasianalytical reference solutions even for rather modest grid resolutions and few points in the narrowest channels more important the pressure and velocity fields in the vicinity of the obstacles are much smoother with multireflection than with the other boundary conditions finally the good stability of these schemes is highlighted by some simulations of moving obstacles a cylinder between flat walls and a sphere in a cylinder

quantum algebras and q special functions related to coherent states maps of the disc the quantum algebras generated by the coherent states maps of the disc are investigated it is shown that the analytic realization of these algebras leads to a generalized analysis which includes standard analysis as well as q analysis the applications of the analysis to star product quantizations and q special functions theory are given among others the meromorphic continuation of the generalized basic hypergeometric series is found and a reproducing measure is constructed when the series is treated as a reproducing kernel

braids mapping class groups and categorical delooping dehn twists around simple closed curves in oriented surfaces satisfy the braid relations this gives rise to a group theoretic map phi beta 2g to gamma g 1 from the braid group to the mapping class group we prove here that this map is trivial in homology with any trivial coefficients in degrees less than g 2 in particular this proves an old conjecture of j harer the main tool is categorical delooping in the spirit of tillmann in invent math 130 257 175 1997 by extending the homomorphism to a functor of monoidal 2 categories phi is seen to induce a map of double loop spaces on the plus construction of the classifying spaces any such map is null homotopic in an appendix we show that geometrically defined homomorphisms from the braid group to the mapping class group behave similarly in stable homology

coarse and fine grid numerical behavior of mrt trt lattice boltzmann schemes in regular and random sphere packings we analyze the intrinsic impact of free tunable combinations of the relaxation rates controlling viscosity independent accuracy of the multiple relaxation times mrt lattice boltzmann models preserving all mrt degrees of freedom we formulate the parametrization conditions which enable the mrt schemes to provide viscosity independent truncation errors for steady state solutions and support them with the second and third order accurate linear and parabolic respectively boundary schemes the parabolic schemes demonstrate the advanced accuracy with weak dependency on the relaxation rates as confirmed by the simulations with the d3q15 model in three regular arrays sc bcc fcc of touching spheres yet the low order bounce back boundary rule remains appealing for pore scale simulations where the precise distance to the boundaries is undetermined however the effective accuracy of the bounce back crucially depends on the free tunable combinations of the relaxation rates we find that the combinations of the kinematic viscosity rate with the available ghost antisymmetric collision mode rates mainly impact the accuracy of the bounce back scheme as the first step we reduce them to the one combination presented by so called magic parameter in the frame of the two relaxation times trt model and study its impact on the accuracy of the drag force permeability computations with the d3q19 velocity set in two different dense random packings of 8000 spheres each we also run the simulations in the regular bcc and fcc packings of the same porosity for the broad range of the discretization resolutions ranging from 5 to 750 lattice nodes per sphere diameter a special attention is given to the discretization procedure resulting in significantly reduced scatter of the data obtained at low resolutions the results reveal the identical dependency versus the discretization resolution in all four packings regular and random while very small values overestimate the drag measurements several fold on the coarse grids 1 may overestimate the permeability at the same extent in low resolution region we provide practical guidelines extending previously known solutions for the straight diagonal poiseuille flow analysis of the high resolution region reveals the collapse of the solutions obtained with all the considered values with the average rate of 1 3 followed by their common smooth first order convergence with the rate of 1 0 as the best towards the reference solutions provided by the parabolic schemes high quality power law fits estimate that the bounce back would reach their accuracy obtained at about 200 nodes per sphere for two order magnitude higher grid resolution the parametrization conditions enable the mrt lbe to provide viscosity independent truncation spatial errors these schemes are supported with the high order accurate boundary conditions confirmed in touching arrays of spheres the effect of free relaxation rates on drag force computations is examined for bounce back and high order conditions random and regular packings demonstrate identical numerical errors for various relaxation rates and resolutions for low resolution we provide practical guidelines while high resolutions revealed first order convergence to reference drag

the homology of the mapping class group 1 2 h btg a h mg q in this paper we will show that m g btg and b i l sg get more and more complicated as the genus g tends to infinity more precisely we will prove theorem 1 1 let q z2 z4 z6 denote the polynomial algebra of generators z2n in dimension in n 1 2 3 there are classes y2 y4 y2n with y2n in the 2nth cohomology group h 2n b i sg z such that the homomorphism of algebras sending z2n toy2n

on the homotopy of the stable mapping class group by considering all surfaces and their mapping class groups at once it is shown that the classifying space of the stable mapping class group after plus construction b has the homotopy type of an infinite loop space the main new tool is a generalized group completion theorem for simplicial categories the first deloop of b coincides with that of miller m induced by the pairs of pants multiplication the classical representation of the mapping class group onto siegel s modular group is shown to induce a map of infinite loop spaces from b to k theory it is then a direct consequence of a theorem by charney and cohen cc that there is a space y such that b im j 1 2 y where im j 1 2 is the image of j localized away from the prime 2