fast fe bem algorithms for orthotropic frictional contact summary this paper presents a new and efficient methodology for solving 3d frictional contact problems considering an orthotropic friction law the contact methodology is based on a proposed augmented lagrangian formulation for orthotropic frictional contact problems and a new discrete contact operator which allows to reduce the number of unknowns in a newton like algorithm that accelerates the attainment of the solution a fast uzawa scheme is also proposed on the basis of the steffensen s method both algorithms prove to be very robust and efficient to solve orthotropic frictional contact problems the proposed formalism has the advantage of being very compact and valid for both the fem and the bem numerical results are given to demonstrate the validity of the formulation and algorithms proposed copyright 2013 john wiley sons ltd

an algorithm for computing some heegaard floer homologies in this paper we give an algorithm to compute the hat version of heegaard floer homology of a closed oriented three manifold this method also allows us to compute the filtration coming from a null homologous link in a three manifold

finite affine groups cycle indices hall littlewood polynomials and probabilistic algorithms abstract the study of asymptotic properties of the conjugacy class of a random element of the finite affine group leads one to define a probability measure on the set of all partitions of all positive integers four different probabilistic understandings of this measure are given three using symmetric function theory and one using markov chains this leads to non trivial enumerative results cycle index generating functions are derived and are used to compute the large dimension limiting probabilities that an element of the affine group is separable cyclic or semisimple and to study the convergence to these limits the semisimple limit involves both rogers ramanujan identities this yields the first examples of such computations for a maximal parabolic subgroup of a finite classical group

finite dimensional pointed hopf algebras over finite simple groups of lie type i non semisimple classes in psln q abstract we show that nichols algebras of most simple yetter drinfeld modules over the projective special linear group over a finite field corresponding to non semisimple orbits have infinite dimension we spell out a new criterium to show that a rack collapses

finite element treatment of two dimensional thermoelastic wear problems the present paper concerns the numerical treatment of thermoelastic wear problems the governing equations of thermoelasticity coupled to signorini contact coulomb s friction and archard s wear are formulated as a system of discrete equations this equation system is solved using a bouligand differentiable newton method for five problems of didactic nature

monopoles and lens space surgeries monopole floer homology is used to prove that real projective three space cannot be obtained from dehn surgery on a nontrivial knot in the three sphere to obtain this result we use a surgery long exact sequence for monopole floer homology together with a nonvanishing theorem which shows that monopole floer homology detects the unknot in addition we apply these techniques to give information about knots which admit lens space surgeries and to exhibit families of three manifolds which do not admit taut foliations

link floer homology and the thurston norm we show that link floer homology detects the thurston norm of a link complement as an application we show that the thurston polytope of an alternating link is dual to the newton polytope of its multi variable alexander polynomial to illustrate these techniques we also compute the thurston polytopes of several specific link complements

algorithms for gradient damage models based on a semi smooth newton method in this paper two different algorithms are applied to a model of brittle damage including the gradient of the damage variable both algorithms are based on a modified newton method in the first algorithm the newton method is applied directly to the whole system of equations while in the second algorithm the equilibrium equations and the damage evolution problem are solved uncoupled from each other in a gauss seidel scheme the algorithms are applied to two different formulations of the problem in the first formulation the thermodynamic force work conjugate to the damage variable is kept as an auxiliary variable while in the second formulation this variable is eliminated it turns out that the formulation using the extra variable is more robust in the sense that the algorithms converge even for very large load increments on the other hand the formulation where the extra variable is eliminated is more efficient for small time steps since a smaller system of equations is solved for each increment furthermore it is found that the direct approach is more efficient than the decoupled approach for this problem

the unregularized gradient flow of the symplectic action the symplectic action can be defined on the space of smooth paths in a symplectic manifold p which join two lagrangian submanifolds of p to pursue a new approach to the variational theory of this function we define on a subset of the path space the flow whose trajectories are given by the solutions of the cauchy riemann equation with respect to a suitable almost complex structure on p in particular we prove compactness and transversality results for the set of bounded trajectories

three dimensional quasi static frictional contact by using second order cone linear complementarity problem a new formulation is presented for the three dimensional incremental quasi static problems with unilateral frictional contact under the assumptions of small rotations and small strains a second order cone linear complementarity problem is formulated which consists of complementarity conditions defined by bilinear functions and second order cone constraints the equilibrium configurations are obtained by using a combined smoothing and regularization method for the second order cone complementarity problem copyright 2005 john wiley sons ltd

finding involutions in finite lie type groups of odd characteristic abstract let g be a finite group of lie type in odd characteristic defined over a field with q elements we prove that there is an absolute and explicit constant c such that if g is a classical matrix group of dimension n 2 then at least c log n of its elements are such that some power is an involution with fixed point subspace of dimension in the interval n 3 2 n 3 if g is exceptional or g is classical of small dimension then for each conjugacy class c of involutions we find a very good lower bound for the proportion of elements of g for which some power lies in c

morse theory for lagrangian intersections soit p une variete symplectique compacte et soit l p une sous variete lagrangienne avec 2 p l 0 pour un diffeomorphisme exact de p avec la propriete que l coupe l transversalement on demontre une inegalite de morse reliant l ensemble l l a la cohomologie de l

time discretized variational formulation of non smooth frictional contact the present work extends the non smooth contact class of algorithms introduced by kane et al to the case of friction the formulation specifically addresses contact geometries e g involving multiple collisions between tightly packed non smooth bodies for which neither normals nor gap functions can be properly defined a key aspect of the approach is that the incremental displacements follow from a minimum principle the objective function comprises terms which account for inertia strain energy contact friction and external forcing the euler lagrange equations corresponding to this extended variational principle are shown to be consistent with the equations of motion of solids in frictional contact in addition to its value as a basis for formulating numerical algorithms the variational framework offers theoretical advantages as regards the selection of trajectories in cases of non uniqueness we present numerical and analytical examples which demonstrate the good momentum and energy conservation characteristics of the numerical algorithms as well as the ability of the approach to account for stick and slip conditions

adjoint representations of black box groups psl2 fq abstract given a black box group y encrypting psl 2 f over an unknown field f of unknown odd characteristic p and a global exponent e for y that is an integer e such that y e 1 for all y y we present a las vegas algorithm which constructs a unipotent element in y the running time of our algorithm is polynomial in log e this answers the question posed by babai and beals in 1999 we also find the characteristic of the underlying field in time polynomial in log e and linear in p all our algorithms are randomized furthermore we construct in time polynomial in log e a black box group x encrypting pgl 2 f so 3 f over the same field as y its subgroup y of index 2 isomorphic to y and a polynomial in log e time isomorphism y y a black box field k and polynomial time in log e isomorphisms so 3 k x so 3 k if in addition we know p and the standard explicitly given finite field f q isomorphic to the field on which y is defined then we construct in time polynomial in log e isomorphism so 3 f q so 3 k unlike many papers on black box groups our algorithms make no use of additional oracles other than the black box group operations moreover our result acts as an sl 2 oracle in the black box group theory we implemented our algorithms in gap and tested them for groups such as psl 2 f for f 115756986668303657898962467957 a prime number

proportions of elements with given 2 part order in finite classical groups of odd characteristic for an element g in a group x we say that g has 2 part order 2 b if 2 b is the largest power of 2 dividing the order of g using results of erd os and turan and beals et al we give explicit lower bounds on the proportion of elements of the symmetric group sn with certain 2 part orders some of these lower bounds are constant for example we show that at least 23 5 of the elements in sn n 3 have a certain 2 part order we derive related lower bounds on these proportions for finite classical groups in odd characteristic in particular we show that the proportion of odd order elements in the symplectic and orthogonal groups is at least c n 3 4 where n is the lie rank and c is an explicit constant furthermore we describe how these results can be used to analyze part of yalcinkaya s black box recognition algorithm for finite classical groups in odd characteristic

a boundary element formulation for wear modeling on 3d contact and rolling contact problems the present work shows a new numerical treatment for wear simulation on 3d contact and rolling contact problems this formulation is based on the boundary element method bem for computing the elastic influence coefficients and on projection functions over the augmented lagrangian for contact restrictions fulfillment the constitutive equations of the potential contact zone are signorini s contact conditions coulomb s law of friction and holm archard s law of wear the proposed methodology is applied to predict wear on different contact and rolling contact problems results are validated with numerical solutions and semi analytical models presented in the literature the bem considers only the degrees of freedom involved on these kind of problems those on the solids surfaces reducing the number of unknowns and obtaining a very good approximation on contact tractions using a low number of elements together with the formulation an acceleration strategy is presented allowing to reduce the times of resolution

cobordisms of sutured manifolds and the functoriality of link floer homology abstract it has been a central open problem in heegaard floer theory whether cobordisms of links induce homomorphisms on the associated link floer homology groups we provide an affirmative answer by introducing a natural notion of cobordism between sutured manifolds and showing that such a cobordism induces a map on sutured floer homology this map is a common generalization of the hat version of the closed 3 manifold cobordism map in heegaard floer theory and the contact gluing map defined by honda kazez and matic we show that sutured floer homology together with the above cobordism maps forms a type of tqft in the sense of atiyah applied to the sutured manifold cobordism complementary to a decorated link cobordism our theory gives rise to the desired map on link floer homology hence link floer homology is a categorification of the multi variable alexander polynomial we outline an alternative definition of the contact gluing map using only the contact element and handle maps finally we show that a weinstein sutured manifold cobordism preserves the contact element

some applications of gabai s internal hierarchy any haken 3 manifold possibly with boundary consisting of tori can be transformed into a surface s 1 by a series of splitting and regluing along incompressible surfaces this fact was proved by gabai as an application of his sutured manifold theory the first half of this paper provides a few technical details in the proof in the second half of this paper some applications of gabai s theorem to heegaard floer homology are given we refine the known results about the thurson norm and fibrations we also give some classification results for floer simple knots in manifolds with positive b 1

2 blocks with abelian defect groups we give a classification up to morita equivalence of 2 blocks of quasi simple groups with abelian defect groups as a consequence we show that donovan s conjecture holds for elementary abelian 2 groups and that the entries of the cartan matrices are bounded in terms of the defect for arbitrary abelian 2 groups we also show that a block with defect groups of the form c2m c2m for m 2 has one of two morita equivalence types and hence is morita equivalent to the brauer correspondent block of the normaliser of a defect group this completes the analysis of the morita equivalence types of 2 blocks with abelian defect groups of rank 2 from which we conclude that donovan s conjecture holds for such 2 groups a further application is the completion of the determination of the number of irreducible characters in a block with abelian defect groups of order 16 the proof uses the classification of finite simple groups

abundant p singular elements in finite classical groups abstract in 1995 isaacs kantor and spaltenstein proved that for a finite simple classical group g defined over a field with q elements and for a prime divisor p of g distinct from the characteristic the proportion of p singular elements in g elements with order divisible by p is at least a constant multiple of 1 1 p e where e is the order of q modulo p motivated by algorithmic applications we define a subfamily of p singular elements called p abundant elements which leave invariant certain large subspaces of the natural g module we find explicit upper and lower bounds for the proportion of p abundant elements in g and prove that it approaches a positive limiting value as the dimension of g tends to infinity it turns out that the limiting proportion of p abundant elements is at least a constant multiple of the isaacs kantor spaltenstein lower bound for the proportion of all p singular elements

the contact invariant in sutured floer homology we describe an invariant of a contact 3 manifold with convex boundary as an element of juhasz s sutured floer homology our invariant generalizes the contact invariant in heegaard floer homology in the closed case due to ozsvath and szabo

new second order cone linear complementarity formulation and semi smooth newton algorithm for finite element analysis of 3d frictional contact problem we propose a new second order cone linear complementarity problem soclcp formulation for the numerical finite element analysis of three dimensional 3d frictional contact problems by the parametric variational principle specifically we develop a regularization technique to resolve the multi valued difficulty involved in the frictional contact law and use a second order cone complementarity condition to handle the regularized coulomb friction law in contact analysis the governing equations of the 3d frictional contact problem is represented by an soclcp via the parametric variational principle and the finite element method which avoids the polyhedral approximation to the coulomb friction cone so that the problem to be solved has much smaller size and the solution has better accuracy in this paper we reformulate the soclcp as a semi smooth system of equations via a one parametric class of second order cone complementarity functions and then apply the non smooth newton method for solving this system numerical results confirm the effectiveness and robustness of the soclcp approach developed

formulation and comparison of algorithms for frictional contact problems this paper presents two algorithms for solving the discrete quasi static small displacement linear elastic contact problem with coulomb friction the algorithms are adoptions of a newton method for solving b differentiable equations and an interior point method for solving smooth constrained equations for the application of the former method the contact problem is formulated as a system of b differentiable equations involving the projection operator onto sets with simple structure for the application of the latter method the contact problem is formulated as a system of smooth equations involving complementarity conditions and with the non negativity of variables treated as constraints the two algorithms are numerically tested for two dimensional problems containing up to 100 contact nodes and up to 100 time increments results show that at the present stage of development the newton method is superior both in robustness and speed additional comparison is made with a commercial finite element code

a theory of friction a rather general theory of friction inspired from the classical theory of plasticity is proposed it includes the contact impenetrability condition as a by product

heegaard floer homology and concordance bounds on the thurston norm we prove that twisted correction terms in heegaard floer homology provide lower bounds on the thurston norm of certain cohomology classes determined by the strong concordance class of a 2 component link l in s 3 we then specialise this procedure to knots in s 2 times s 1 and obtain a lower bound on their geometric winding number furthermore we produce an obstruction for a knot in s 3 to have untwisting number 1 we then provide an infinite family of null homologous knots with increasing geometric winding number on which the bound is sharp

holomorphic disks and knot invariants abstract we define a floer homology invariant for knots in an oriented three manifold closely related to the heegaard floer homologies for three manifolds defined in an earlier paper we set up basic properties of these invariants including an euler characteristic calculation and a description of the behavior under connected sums then we establish a relationship with hf for surgeries along the knot applications include calculation of hf of three manifolds obtained by surgeries on some special knots in s 3 and also calculation of hf for certain simple three manifolds which fiber over the circle

holomorphic disks and topological invariants for closed three manifolds the aim of this article is to introduce certain topological invariants for closed oriented three manifolds y equipped with a spiny structure given a heegaard splitting of y u 0o u u 1 these theories are variants of the lagrangian floer homology for the g fold symmetric product of relative to certain totally real subspaces associated to u 0 and u 1

black box exceptional groups of lie type ii abstract if a black box group g is known to be isomorphic to an exceptional simple group g of lie type of twisted rank 1 other than any f 4 2 2 e or d 4 3 2 e over a field of known size q and if suitable sl 2 and discrete log oracles are available when q is odd then a polynomial time las vegas algorithm is given that produces a constructive isomorphism between g and g

estimating proportions of elements in finite groups of lie type abstract we show that certain closure properties on subsets q of a finite group g of lie type enable the ratio q g to be determined by finding the proportions of elements of q in the maximal tori of g and the proportions of certain related subsets of the weyl group we prove fundamental results about these subsets q including those necessary for moving between these groups and their automorphism groups normal subgroups and central quotients as a sample application of these new techniques we derive upper and lower bounds for the proportion of elements with order divisible by certain natural sets of primes for the finite classical groups thereby improving existing results

black box exceptional groups of lie type if a black box group is known to be isomorphic to an exceptional simple group of lie type of twisted rank 1 other than any f4 q over a field of known size a las vegas algorithm is given to produce a constructive isomorphism in view of its timing this algorithm yields an upgrade of all known nearly linear time monte carlo permutation group algorithms to las vegas algorithms when the input group has no composition factor isomorphic to any group f4 q or g2 q

a newton method for three dimensional fretting problems the present paper concerns the numerical treatment of fretting problems using a finite element analysis the governing equations resulting from a formal finite element discretization of an elastic body with a potential contact surface are considered in a quasi static setting the constitutive equations of the potential contact surface are signorini s contact conditions coulomb s law of friction and archard s law of wear using a backward euler time discretization and an approach based on projections the governing equations are written as an augmented lagrangian formulation which is implemented and solved using a newton algorithm for three dimensional fretting problems of didactic nature details concerning the implementation are provided