an effective lie kolchin theorem for quasi unipotent matrices abstract we establish an effective version of the classical lie kolchin theorem namely let a b gl m c be quasi unipotent matrices such that the jordan canonical form of b consists of a single block and suppose that for all k 0 the matrix a b k is also quasi unipotent then a and b have a common eigenvector in particular a b gl m c is a solvable subgroup we give applications of this result to the representation theory of mapping class groups of orientable surfaces

homological and monodromy representations of framed braid groups in this paper we introduce two new classes of representations of the framed braid groups one is the homological representation constructed as the action of a mapping class group on a certain homology group the other is the monodromy representation of the confluent kz equation which is a generalization of the kz equation to have irregular singularities we also give a conjectural equivalence between these two classes of representations

a 3d non newtonian fluid structure interaction model for blood flow in arteries the mathematical modelling and numerical simulation of the human cardiovascular system is playing nowadays an important role in the comprehension of the genesis and development of cardiovascular diseases in this paper we deal with two problems of 3d modelling and simulation in this field which are very often neglected in the literature on the one hand blood flow in arteries is characterized by travelling pressure waves due to the interaction of blood with the vessel wall on the other hand blood exhibits non newtonian properties like shear thinning viscoelasticity and thixotropy the present work is concerned with the coupling of a generalized newtonian fluid accounting for the shear thinning behaviour of blood with an elastic structure describing the vessel wall to capture the pulse wave due to the interaction between blood and the vessel wall we provide an energy estimate for the coupling and compare the numerical results with those obtained with an equivalent fluid structure interaction model using a newtonian fluid

a homological representation formula of colored alexander invariants we give a formula of the colored alexander invariant in terms of the homological representation of the braid groups which we call truncated lawrence s representation this formula generalizes the famous burau representation formula of the alexander polynomial

non linear residually finite groups abstract we give the first example of a non linear residually finite 1 related group a t a t 2 a 2

a relaxation projection method for compressible flows part i the numerical equation of state for the euler equations a new projection method is developed for the euler equations to determine the thermodynamic state in computational cells it consists in the resolution of a mechanical relaxation problem between the various sub volumes present in a computational cell these sub volumes correspond to the ones traveled by the various waves that produce states with different pressures velocities densities and temperatures contrarily to godunov type schemes the relaxed state corresponds to mechanical equilibrium only and remains out of thermal equilibrium the pressure computation with this relaxation process replaces the use of the conventional equation of state eos a simplified relaxation method is also derived and provides a specific eos named the numerical eos the use of the numerical eos gives a cure to spurious pressure oscillations that appear at contact discontinuities for fluids governed by real gas eos it is then extended to the computation of interface problems separating fluids with different eos liquid gas interface for example with the euler equations the resulting method is very robust accurate oscillation free and conservative for the sake of simplicity and efficiency the method is developed in a lagrange projection context and is validated over exact solutions in a companion paper f petitpas e franquet r saurel a relaxation projection method for compressible flows part ii computation of interfaces and multiphase mixtures with stiff mechanical relaxation j comput phys submitted for publication the method is extended to the numerical approximation of a non conservative hyperbolic multiphase flow model for interface computation and shock propagation into mixtures

parameters for which the lawrence krammer representation is reducible we show that the representation introduced by lawrence and krammer to show the linearity of the braid group is generically irreducible however for some values of its two parameters when these are specialized to complex numbers it becomes reducible we construct a representation of degree n n 1 2 of the bmw algebra of type a n 1 as a representation of the braid group on n strands it is equivalent to the lawrence krammer representation where the two parameters of the bmw algebra are related to those appearing in the lawrence krammer representation we give the values of the parameters for which the representation is reducible and give the proper invariant subspaces in some cases we use this representation to show that for these special values of the parameters the bmw algebra of type a n 1 is not semisimple

homological representations of the hecke algebra in this paper a topological construction of representations of thean 1 series of hecke algebras associated with 2 row young diagrams will be given this construction gives the representations in terms of the monodromy representation obtained from a vector bundle on which there is a natural flat connection the fibres of the vector bundle are homology spaces of configuration spaces of points in c with a suitable twisted local coefficient system it is also shown that there is a close correspondence between this construction and the work of tsuchiya and kanie who constructed hecke algebra representations from the monodromy ofn point functions in a conformal field theory onp1 this work has significance in relation to the one variable jones polynomial which can be expressed in terms of characters of the iwahori hecke algebras associated with 2 row young diagrams it gives rise to a topological description of the jones polynomial which will be discussed elsewhere l2

complex reflection groups braid groups hecke algebras presentations a la coxeter are given for all irreducible nite com plex re ection groups they provide presentations for the corresponding generalized braid groups for all but six cases which allow us to generalize some of the known properties of nite coxeter groups and their associated braid groups such as the computation of the center of the braid group and the construction of deformations of the nite group algebra hecke algebras we introduce monodromy representations of the braid groups which factorize through the hecke algebras extending results of cherednik opdam kohno and others summary introduction complex re ection groups and their presentations a background from complex re ection groups b presentations braid groups and their diagrams a generalities about hyperplane complements b generalities about the braid groups c the braid diagrams proofs of the main theorems for the braid groups b de e r a notation and prerequisites b computation of b de e r and of its center for d c computation of b e e r and of its center hecke algebras a background from di erential equations and monodromy b a family of monodromy representations of the braid group c hecke algebras diagrams and tables appendix generators of the monodromy around a divisor appendix tables to mathematics subject classi cation primary g we thank jean michel peter orlik pierre vogel for useful conversations and the isaac newton institute for its hospitality while the last version of this manuscript was written up the second named author gratefully acknowledges nancial support by the fondation alexander von humboldt for his stays in paris michel brou e gunter malle raphael rouquier

the burau representation of the braid group b_n is unfaithful for large n two fundamental theorems of classical knot theory by j alexander are that every knot is a closed braid and second that a certain procedure see 1 2 for both results assigns to each knot k a polynomial a k in t which only depends on the topological type of the knot once normalized by a power of t to take a positive value at t 0 with this normalization take t to be a transcendental number since 1926 2 it has been known that the function a knots c is not one to one however it has not become clear whether the composite

a velocity pressure streamline diffusion finite element method for navier stokes equations a streamline diffusion finite element method is introduced for the time dependent incompressible navier stokes equations in a bounded domain in r squared and r cubed in the case of a flow with a high reynolds number an error estimate is proved and numerical results are given the method is based on a mixed velocity pressure formulation using the same finite element discretization of space time for the velocity and the pressure spaces which consist of piecewise linear functions together with certain least squares modifications of the galerkin variational formulation giving added stability without sacrificing accuracy

flat connections and brauer type algebras in this paper we introduce a brauer type algebra bg associated with every pseudo reflection group and every coxeter group g when g is a coxeter group of simply laced type we show that bg is isomorphic to the generalized brauer algebra of simply laced type introduced by cohen gijsbers and wales 2005 cgw1 we also prove that bg has a cellular structure and be semisimple for generic parameters when g is a dihedral group or the type h3 coxeter group moreover in the process of construction we introduce a further generalization of the lawrence krammer representation to complex braid groups associated with all pseudo reflection groups

staggered and nonstaggered grids with variable node spacing and local time step ping for the random choice method abstract the staggered grid and random sampling procedure used currently in the random choice method for solving hyperbolic equations like those for one dimensional unsteady flows and two dimensional axisymmetric and planar steady supersonic flows are reviewed and extended to include variable node spacing a nonstaggered grid with variable node spacing more convenient random sampling process and local time stepping are then introduced and there use in significantly reducing computational time and costs in solving certain problems is discussed these methods are easily applied in the random choice method for problems with more dimensions

exact and approximate riemann solvers for real gases a procedure is developed for solving the riemann problem rp for the flow of gases obeying an equation of state eos of the form p p a first method is introduced producing solutions of the exact rp the algorithm is validated by applying it to the classical test case of the shock tube for a perfect gas thereafter the method is applied to gases having eos of the van der waals or virial types with very good resulting accuracy however the procedure is somewhat demanding in computer time therefore some simplifying assumptions are introduced into the computation of simple waves leading to an approximate solution of the rp in most circumstances excellent results are obtained and the computer time is much more competitive however under certain extreme flow conditions it is recommended that a combination of the exact and approximate solvers for the rp be employed

a note on words in braid monoids abstract the purpose of this note is to give a self contained apart from simple facts about coxeter groups and we hope a bit shorter and more understandable account of some results of c1 c2 on normal forms of braids which are themselves based on the papers d1 t in particular a motivation was to give a proof of proposition 5 1 that we use in b m some proofs and results from section 2 onwards seem to be new i thank several people for improvements from earlier versions of the manuscript m geck for pointing out some errors f digne for pointing out that some results don t need the braid group to be of finite type and j y hee for suggesting and providing further improvements in that direction

on twisted lawrence krammer representations abstract lawrence krammer representations are an important family of linear representations of artin tits groups of small type which are known under some assumptions on the parameters to be faithful when the type is spherical or more generally when they are restricted to the artin tits monoid and irreducible when the type is connected here we investigate an analogue of these representations introduced by digne in the spherical cases for every artin tits monoid that appears as the submonoid of fixed points of an artin tits monoid of small type under a group of graph automorphisms and for the corresponding artin tits group under the same assumptions on the parameters as in the small type cases we first show that these so called twisted lawrence krammer representations are faithful and we then prove by computing their formulas when the group of graph automorphisms is of order two or three their irreducibility in all the spherical and connected cases but one

braid groups and the co hopfian property abstract let b n be the braid group on n 4 strands we prove that b n modulo its center is co hopfian we then show that any injective endomorphism of b n is geometric in the sense that it is induced by a homeomorphism of a punctured disk we further prove that any injection from b n to b n 1 is geometric for n 7 additionally we obtain analogous results for mapping class groups of punctured spheres the methods use thurston s theory of surface homeomorphisms and build upon work of ivanov mccarthy

finite element error estimation for quasi newtonian fluid structure interaction problems we consider a monolithic scheme for fluid structure interaction problems involving an incompressible quasi newtonian fluid the monolithic formulation is obtained using the arbitrary lagrangian eulerian ale method with matching conditions at the fluid structure interface the stability and error analysis are performed for the finite element approximation finally some numerical experiments that confirm the theoretical analysis are presented

monodromy of cyclic coverings of the projective line we show that the image of the pure braid group under the monodromy action on the homology of a cyclic covering of degree d of the projective line is an arithmetic group provided the number of ramification points is sufficiently large compared to the degree d and the ramification degrees are co prime to d

bmw algebras of simply laced type abstract it is known that the recently discovered representations of the artin groups of type a n the braid groups can be constructed via bmw algebras we introduce similar algebras of type d n and e n which also lead to the newly found faithful representations of the artin groups of the corresponding types we establish finite dimensionality of these algebras moreover they have ideals i 1 and i 2 with i 2 i 1 such that the quotient with respect to i 1 is the hecke algebra and i 1 i 2 is a module for the corresponding artin group generalizing the lawrence krammer representation finally we give conjectures on the structure the dimension and parabolic subalgebras of the bmw algebra as well as on a generalization of deformations to brauer algebras for simply laced spherical type other than a n

the automorphism group of a free group is not linear a linear group has ascending chain condition on centralizers malcev s p 511 finitely generated linear groups are residually finite malcev s p 453 a solvable linear group is nilpotent by abelian byfinite tits 5 pp 14551461 a linear group either contains a free group of rank two or is solvable by locally finite lubotzky 3 has characterized finitely generated linear groups over a field of characteristic zero by purely group theoretic conditions these conditions appear difficult to check although they have been used to show linearity for certain groups however we do not use his theorem the main result of this paper theorem 5 is that for n 2 3 the automorphism group of a free group of rank n is not a linear group the proof uses the representation theory of algebraic groups to show that a kind of diophantine equation between the irreducible representations of

the braid group b4 is linear we study a linear representation b n gl m z q 1 t 1 with m n n 1 2 we will show that for n 4 this representation is faithful we prove a relation with the new charney length function we formulate a conjecture implying that is faithful for all n

configurations braids and homotopy groups the main results of this article are certain connections between braid groups and the homotopy groups of the 2 sphere the connections are given in terms of brunnian braids over the disk and over the 2 sphere the techniques arise from the natural structure of simplicial and structures on fundamental groups of configuration spaces

two phase flows second order schemes and boundary conditions a second order numerical method suitable to unstructured grids is developed for the solution of two phase flow equations a number of assumptions are introduced justified on physical grounds when the dispersed phase concentration is low their effect is to change the mathematical nature of the system of equations the new numerical method put forward builds on van leer s original ideas the solution of two riemann problems is involved one for the gas phase and a second for the dispersed phase the method is first tested on a one dimensional case with excellent results it is then generalized to two dimensions

adaptive osher type scheme for the euler equations with highly nonlinear equations of state abstract for the numerical simulation of detonation of condensed phase explosives a complex equation of state eos such as the jones wilkins lee jwl eos or the cochran chan c c eos are widely used however when a conservative scheme is used for solving the euler equations with such equations of state a spurious solution across the contact discontinuity a well known phenomenon in multi fluid systems arises even for single materials in this work we develop a generalised osher type scheme in an adaptive primitive conservative framework to overcome the aforementioned difficulties resulting numerical solutions are compared with the exact solutions and with the numerical solutions from the godunov method in conjunction with the exact riemann solver for the euler equations with mie gruneisen form of equations of state such as the jwl and the c c equations of state the adaptive scheme is extended to second order and its empirical convergence rates are presented verifying second order accuracy for smooth solutions through a suite of several tests problems in one and two space dimensions we illustrate the failure of conservative schemes and the capability of the methods of this paper to overcome the difficulties

braid groups are linear in a previous work 11 the author considered a representation of the braid group p bn glm z ql1 t l m n n 1 2 and proved it to be faithful for n 4 bigelow 3 then proved the same representation to be faithful for all n by a beautiful topological argument the present paper gives a different proof of the faithfulness for all n we establish a relation between the charney length in the braid group and exponents of t a certain bn invariant subset of the module is constructed whose properties resemble those of convex cones we relate line segments in this set with the thurston normal form of a braid

quivers floer cohomology and braid group actions we consider the derived categories of modules over a certain family a m of graded rings and floer cohomology of lagrangian intersections in the symplectic manifolds which are the milnor fibres of simple singularities of type a m we show that each of these two rather different objects encodes the topology of curves on an m 1 punctured disc we prove that the braid group b m 1 acts faithfully on the derived category of a m modules and that it injects into the symplectic mapping class group of milnor fibers the philosophy behind our results is as follows using floer cohomology one should be able to associate to the milnor fibre a triangulated category its construction has not been carried out in detail this triangulated category should contain a full subcategory which is equivalent up to a slight difference in the grading to the derived category of a m modules the full embedding would connect the two occurrences of the braid group thus explaining the similarity between them

a knot invariant via representation spaces a beautiful construction of a casson on the representation spaces corresponding to a heegard splitting of an oriented homology 3 sphere m gives rise to an integer invariant m of m this invariant generalizes the rohlin invariant and gives stricking corollaries in low dimension al topology defined as an intersection number of appropriate subspaces this invariant m can be roughly thought of as the number of conjugacy classes of irreducible representations of n m into su2 counted with signs a detailed discussion of this invariant can be found in an expose by s akbulut and j mccarthy 1 further works on casson s invariant include the generalizations by k walker as well as s boyer and a nicas to rational homology 3 spheres 14 3 and by s cappell r lee and e miller to representatio ns into sun 4 the works of c taubes 13 and a flore 6 interpret casson s invariant as the euler number of the instanton homology or flore homology of m in this paper analogous to casson s original construction we will define an intersection number of the representation spaces corresponding to a braid representative of a knot k in s this intersection number turns out to be an integer knot invariant see theorem 1 8 the representations of the knot group s k used in our construction seem to be mysterious they are representations of s3 k into su2 such that all meridians of k are represented by trace zero matrices call such a representation of the knot group a trace free representation then roughly speaking our knot invariant h k is the number of conjugacy classes of irreducible trace free representations of s3 k counted with signs our knot invariant h k can be computed via knot diagrams it turns out that our algorithm of computing h k by using the skein model is the same as the algorithm of computing sgn k given by j h conway 5

the lawrence krammer bigelow representations of the braid groups via uq sl2 abstract we construct representations of the braid groups b n on n strands on free z q 1 s 1 modules w n l using generic verma modules for an integral version of u q sl 2 we prove that the w n 2 are isomorphic to the faithful lawrence krammer bigelow representations of b n after appropriate identification of parameters of laurent polynomial rings by constructing explicit integral bases and isomorphism we also prove that the b n representations w n l are irreducible over the fractional field q q s

the influence of the non newtonian properties of blood on the flow in large arteries unsteady flow in a 90 curved tube a numerical and experimental investigation of unsteady entry ow in a 903 curved tube is presented to study the impact of the non newtonian properties of blood on the velocity distribution the time dependent ow rate for the newtonian and the nonnewtonian blood analog uid were identical for the numerical computation a carreau yasuda model was employed to accommodate the shear thinning behavior of the xanthan gum solution the viscoelastic properties were not taken into account the experimental results indicate that signi cant di erences between the newtonian and non newtonian uid are present the numerical results for both the newtonian and the non newtonian uid agree well with the experimental results since viscoelasticity was not included in the numerical code shear thinning behavior of the blood analog uid seems to be the dominant non newtonian property even under unsteady ow conditions finally a comparison between the non newtonian uid model and a newtonian uid at a rescaled reynolds number is presented the rescaled reynolds number based on a characteristic rather than the high shear rate viscosity of the xanthan gum solution was about three times as low as the original reynolds number comparison reveals that the character of ow of the non newtonian uid is simulated quite well by using the appropriate reynolds number 1999 elsevier science ltd all rights reserved

finite complex reflection arrangements are k pi 1 let v be a finite dimensional complex vector space and w gl v be a finite complex reflection group let v reg be the complement in v of the reflecting hyperplanes we prove that v reg is a k 1 space this was predicted by a classical conjecture originally stated by brieskorn for complexified real reflection groups the complexified real case follows from a theorem of deligne and after contributions by nakamura and orliksolomon only six exceptional cases remained open in addition to solving these six cases our approach is applicable to most previously known cases including complexified real groups for which we obtain a new proof based on new geometric objects we also address a number of questions about 1 w v the braid group of w this includes a description of periodic elements in terms of a braid analog of springer s theory of regular elements

braid groups and hodge theory this paper gives an account of the unitary representations of the braid group that arise via the hodge theory of cyclic branched coverings of mathbb p 1 highlighting their connections with ergodic theory complex reflection groups moduli spaces of 1 forms and open problems in surface topology

a multiphase godunov method for compressible multifluid and multiphase flows we propose a new model and a solution method for two phase compressible flows the model involves six equations obtained from conservation principles applied to each phase completed by a seventh equation for the evolution of the volume fraction this equation is necessary to close the overall system the model is valid for fluid mixtures as well as for pure fluids the system of partial differential equations is hyperbolic hyperbolicity is obtained because each phase is considered to be compressible two difficulties arise for the solution one of the equations is written in non conservative form non conservative terms exist in the momentum and energy equations we propose robust and accurate discretisation of these terms the method solves the same system at each mesh point with the same algorithm it allows the simulation of interface problems between pure fluids as well as multiphase mixtures several test cases where fluids have compressible behavior are shown as well as some other test problems where one of the phases is incompressible the method provides reliable results is able to compute strong shock waves and deals with complex equations of state

numerical solution to rarefaction or shock wave duct area change interaction conclusion it may be said that vt rj prescribed by eq 5 gives the best correlation with measurement for k and further substantiates the claim of so and hwang1 that the solution eqs 3 7 represents the best solution for self preserving turbulent round jets furthermore eqs 3 7 also represent the solutions for incompressible heated round jets if the turbulent prandtl number prt is assumed to be constant then eq 3 with the exponent r 2 i2 replaced by ri2pr vn2 becomes the solution of the temperature equation since eqs 1 and 2 are equally applicable for incompressible heated round jets eqs 8 11 also represent solutions for such flows therefore the present results are just as valid for nonisothermal round jets

on injective homomorphisms for pure braid groups and associated lie algebras abstract the purpose of this article is to record the center of the lie algebra obtained from the descending central series of artin s pure braid group a lie algebra analyzed in work of kohno t kohno linear representations of braid groups and classical yang baxter equations in contemp math vol 78 1988 pp 339 363 t kohno vassiliev invariants and the de rham complex on the space of knots in symplectic geometry and quantization in contemp math vol 179 amer math soc providence ri 1994 pp 123 138 t kohno serie de poincare koszul associee aux groupes de tresses pures invent math 82 1985 57 75 and falk and randell m falk r randell the lower central series of a fiber type arrangement invent math 82 1985 77 88 the structure of this center gives a lie algebraic criterion for testing whether a homomorphism out of the classical pure braid group is faithful which is analogous to a criterion used to test whether certain morphisms out of free groups are faithful f r cohen j wu on braid groups free groups and the loop space of the 2 sphere in algebraic topology categorical decomposition techniques in progr math vol 215 birkhauser basel 2003 braid groups free groups and the loop space of the 2 sphere math at 0409307 however it is as unclear whether this criterion for faithfulness can be applied to any open cases concerning representations of p n such as the gassner representation

a new approach to the word and conjugacy problems in the braid groups abstract a new presentation of the n string braid group b n is studied using it a new solution to the word problem in b n is obtained which retains most of the desirable features of the garside thurston solution and at the same time makes possible certain computational improvements we also give a related solution to the conjugacy problem but the improvements in its complexity are not clear at this writing

the lower central series of a fiber type arrangement for a certain class fiber type of arrangements including the supersolvable ones of jambu and terao 3 we prove a formula relating the poincare polynomial of the complement with the ranks of successive quotients in the lower central series of the fundamental group such a formula was proved by kohno 5 for the single family of examplesa l

residual finiteness growths of virtually special groups let g be a virtually special group then the residual finiteness growth of g is at most linear this result cannot be found by embedding g into a special linear group indeed the special linear group mathrm sl k mathbb z for k 2 has residual finiteness growth n k 1

the infimum supremum and geodesic length of a braid conjugacy class abstract algorithmic solutions to the conjugacy problem in the braid groups bn n 2 3 4 were given in earlier work this note concerns the computation of two integer class invariants known as inf and sup a key issue in both algorithms is the number m of times one must cycle resp decycle in order to either increase inf resp decrease sup or to be sure that it is already maximal resp minimal for the class our main result is to prove that m is bounded above by n2 n 2 1 in the situation stated by e a elrifai and h r morton 1994 quart j math oxford45 479 497 and by n 2 in the situation stated by authors 1998 adv math 139 322 353 it follows immediately that the computation of inf and sup is polynomial in both word length and braid index in both algorithms the integers inf and sup determine but are not determined by the shortest geodesic length for elements in a conjugacy class and so we also obtain a polynomial time algorithm for computing this length

on lawrence krammer representations lawrence krammer representations or simply lk representations for short are linear representations of artin tits groups of small type over the ring z x 1 y 1 which are of particular interest since they are known to be faithful when the type is spherical and irreducible when the type is spherical and connected here we define and study lk representations over an arbitrary commutative ring r under some conditions on r and on the parameters of an lk representation which generalize the classical settings we recover the faithfulness property and give a new proof of irreducibility that works for every non necessarily spherical connected type we then study the equivalence of distinct lk representations of a given artin tits group for distinct choices of parameters finally we generalize to our setting the known classification of lk representations in the spherical cases and proceed with their classification in the affine cases

unitary braid group representations a large class of braid group representations are proven unitary which means a hermitian bilinear form left invariant by the representation under consideration exists this generalizes and improves known results on the burau and gassner representations the elementary methods are naturally suggested by the study of monodromy invariant hermitian forms applications to conformal quantum field theory in two dimensions are mentioned

generalized flux vector splitting and roe average for an equilibrium real gas abstract the flux vector splittings of steger warming and van leer and roe s approximate riemann solver are generalized to arbitrary equilibrium gas laws comparisons with other formulations are made

reading the dual garside length of braids from homological and quantum representations we show that lawrence s representation and linear representations of the braid groups from generic highest weight representations of u q mathfrak sl 2 detect the dual garside length of braids in a simple and natural way that is by expressing a representation as a matrix over a laurent polynomial ring using a certain natural basis the span of the variable is equal to a constant multiple of the dual garside length

fully discrete error estimation for a quasi newtonian fluid structure interaction problem we consider an incompressible quasi newtonian fluid structure interaction fsi problem formulated in a monolithic framework where the matching conditions at the moving interface are satisfied the fully discretized fsi system is discussed with detailed analysis for the stability and error estimate as well as numerical experiments that confirm the theoretical results

on the linear representation of braid groups we give a new derivative of the burau and gassner representations of the braid and pure braid groups various applications are explored

krammer representations for complex braid groups abstract let b be the generalized braid group associated to some finite complex reflection group w we define a representation of b of dimension the number of reflections of the corresponding reflection group which generalizes the krammer representation of the classical braid groups and is thus a good candidate in view of proving the linearity of b we decompose this representation in irreducible components and compute its zariski closure as well as its restriction to parabolic subgroups we prove that it is faithful when w is a coxeter group of type ade and odd dihedral types and conjecture its faithfulness when w has a single class of reflections if true this conjecture would imply various group theoretic properties for these groups that we prove separately to be true for the other groups

the interaction between quasilinear elastodynamics and the navier stokes equations the interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations coupled to one another along the moving material interface through the continuity of the velocity and traction vectors we prove the existence and uniqueness locally in time of strong solutions in sobolev spaces for quasilinear elastodynamics coupled to the incompressible navier stokes equations unlike our approach in 5 for the case of linear elastodynamics we cannot employ a fixed point argument on the nonlinear system itself and are instead forced to regularize it by a particular parabolic artificial viscosity term we proceed to show that with this specific regularization we obtain a time interval of existence which is independent of the artificial viscosity together with a priori estimates we identify the global solution in both phases as well as the interface motion as a weak limit in strong norms of our sequence of regularized problems

kinematic splitting algorithm for fluid structure interaction in hemodynamics abstract in this paper we study a kinematic splitting algorithm for fluid structure interaction problems this algorithm belongs to the class of loosely coupled fluid structure interaction schemes we will present stability analysis for a coupled problem of non newtonian shear dependent fluids in moving domains with viscoelastic boundaries fluid flow is described by the conservation laws with nonlinearities in convective and diffusive terms for simplicity of presentation the structure is modelled by the generalized string equation but the results presented in the paper may be generalized to more complex structure models the arbitrary lagrangian eulerian approach is used in order to take into account moving computational domain numerical experiments including numerical error analysis and comparison of hemodynamic parameters for newtonian and non newtonian fluids demonstrate reliability of the proposed scheme

interaction of rarefaction waves with area enlargements in ducts the interaction of a rarefaction wave with a gradual monotonic area enlargement of finite length in a duct is studied both analytically and numerically an analytical quasisteady flow analysis is presented first to obtain asymptotic solutions for the flow at late times after all transient disturbances from the interaction process have subsided analytical results are presented and discussed for the boundary between the two possible predicted asymptotic wave patterns and the corresponding asymptotic strengths of the transmitted reflected and other waves as a function of both the incident rarefaction wave strength and area enlargement ratio for perfect diatomic gases and air finally numerical results obtained using the random choice method are presented and discussed for the complete nonstationary rarefaction wave interaction with the area enlargement these results show clearly how the transmitted reflected and other waves develop and evolve with time until they eventually attain constant strengths in agreement with the quasisteady flow predictions for the asymptotic wave patterns

analysis of a streamline diffusion finite element method for the stokes and navier stokes equations for the stokes equations with convection and the incompressible navier stokes equations the authors analyze a streamline diffusion finite element method that is capable of balancing both the convection and the pressure thus allowing the use of arbitrary pairs of velocity pressure spaces for the linear problem the authors obtain for all mesh peclet numbers optimal error estimates in natural norms including in particular the l 2 norm of the pressure the same holds for the nonlinear problem which close to a regular branch of solutions i e the linearized operator is an isomorphism of the norm of the inverse of which still depends on the reynolds number consequently the dependence of the error constants on the reynolds number is not completely resolved in this case

on the jones polynomial of closed 3 braids in j 2 vaughan jones introduced a new polynomial vl t which is an invariant of the isotopy type of an oriented knot or link l c s 3 the polynomial can be computed from an arbitrary representation of l as a closed braid i e from an element in one of the artin braid groups b n 1 2 3 it is very powerful distinguishing the trefoil and its mirror image the unknot and the kinoshita terasaka knot and any two members of the infinite sequence of whitehead links all of which have homeomorphic complements in an early version of j 2 before the results reported here were complete jones had conjectured that his polynomial was injective on closed 3 braids in this note we use trace identities in the burau matrix representation of b 3 to construct myriad counterexamples to that conjecture at the same time we also disprove a second conjecture of jones from j 23 that a link l is amphicheiral if vl t vl t 1 the 2 variable generalized jones polynomial introduced in f y h l m o also fails to distinguish any of our link pairs finally our examples answer in the negative a question of morton who asked whether the alexander polynomial is a complete invariant of the link obtained by adjoining the braid axis to a closed 3 braid link in the monograph mu murasugi began a classification of closed 3 braid links work which was extended by hartley in h from the partial results in mu and h it seemed reasonable to conjecture that omitting various obvious exceptional cases links with braid index 3 composite links and torus links the link type of a closed 3 braid is determined by its conjugacy class in bj up to the equivalences which correspond to orientation changes this conjecture remains open when we began this work we had hoped to settle it expecting that the conjugacy class of a braid was determined by the jones or alexander polynomial of the associated closed braid however this is far from the truth the problem of characterizing all of the 3 braids whose closures have a given jones or alexander or 2 variable polynomial seems to be very non trivial and possibly even to be too complicate to have an interesting solution