finite element approximation to a contact problem for a nonlinear thermoviscoelastic beam abstract in this paper we propose and analyze a finite element method to the solution of a quasi static contact problem between a nonlinear beam and a rigid obstacle error estimates and energy decay are obtained and some numerical simulations described

global attractors for the extensible thermoelastic beam system abstract this work is focused on the dissipative system t t u x x x x u x x x u l 2 0 1 2 x x u f t x x x x t u g describing the dynamics of an extensible thermoelastic beam where the dissipation is entirely contributed by the second equation ruling the evolution of under natural boundary conditions we prove the existence of bounded absorbing sets when the external sources f and g are time independent the related semigroup of solutions is shown to possess the global attractor of optimal regularity for all parameters r the same result holds true when the first equation is replaced by t t u x x t t u x x x x u x x x u l 2 0 1 2 x x u f with 0 in both cases the solutions on the attractor are strong solutions

logarithmic corrections and finite size scaling in the two dimensional 4 state potts model we analyze the scaling and finite size scaling behavior of the two dimensional 4 state potts model we find new multiplicative logarithmic corrections for the susceptibility in addition to the already known ones for the specific heat we also find additive logarithmic corrections to scaling some of which are universal we have checked the theoretical predictions at criticality and off criticality by means of high precision monte carlo data

transfer matrices and partition function zeros for antiferromagnetic potts models iii triangular lattice chromatic polynomial we study the chromatic polynomial pg q for m n triangular lattice strips of widths m 12p 9f with periodic or free transverse boundary conditions respectively and arbitrary lengths n with free longitudinal boundary conditions the chromatic polynomial gives the zero temperature limit of the partition function for the q state potts antiferromagnet we compute the transfer matrix for such strips in the fortuin kasteleyn representation and obtain the corresponding accumulation sets of chromatic zeros in the complex q plane in the limit n we recompute the limiting curve obtained by baxter in the thermodynamic limit m n and find new interesting features with possible physical consequences finally we analyze the isolated limiting points and their relation with the beraha numbers

erratum to mass equidistribution for automorphic forms of cohomological type on gl_ 2 corollary 3 of 4 is not known unconditionally as cohomological automorphic forms on gl2 over an imaginary quadratic field are not known to satisfy the ramanujan conjecture we shall briefly describe the reason for this and discuss what information theorem 1 of 4 does give in the case of imaginary quadratic fields let k be an imaginary quadratic field with nontrivial automorphism c and let be a cuspidal automorphic representation of gl2 ak with unitary central character suppose that and that has langlands parameter wc c gl2 c given by z diag z1 k z1 k for some integer k 2 i e so that is any cohomological representation up to twist it is then known see theorem 1 1 of 1 that for any one may associate a continuous irreducible representation gal k k gl2 q to such that the characteristic polynomial of frobv agrees with the hecke polynomial of v at all places v which do not divide and at which k q and are unramified however because is constructed via an adic limiting process it is not known to arise from a motive and so is not known to be pure to construct one first makes a theta lift from to a holomorphic limit of discrete series representation on sp4 q as in 3 weissauer 6 has proven that if is a holomorphic discrete series representation of sp4 q which is not a cap representation then one may associate a galois representation to it which is pure and locally compatible with at all unramified places so that satisfies ramanujan wherever it is unramified these results are not known for the limit of discrete series representation and to associate a galois representation to it one must apply techniques of taylor 5 which are similar to those used by deligne and serre to associate galois representations to classical weight 1 modular forms these involve multiplying a holomorphic form in by a well understood regular holomorphic form of large weight applying the results of weissauer and recovering from these products by an adic limiting process any archimedean information about the frobenius eigenvalues of is lost during this and neither does one know that arises from a motive as a result the algebraic information we obtain about is insufficient to deduce ramanujan for it we may still draw interesting conclusions from theorem 1 of 4 in the imaginary quadratic case cohomological forms on gl2 k which are base changes from q will satisfy ramanujan and so theorem 1 establishes their equidistribution as their weight becomes large moreover the experimental results of 2 suggest that all

universality of the crossing probability for the potts model for q 1 2 3 4 the universality of the crossing probability pi hs of a system to percolate only in the horizontal direction was investigated numerically by a cluster monte carlo algorithm for the q state potts model for q 2 3 4 and for percolation q 1 we check the percolation through fortuin kasteleyn clusters near the critical point on the square lattice by using representation of the potts model as the correlated site bond percolation model it was shown that probability of a system to percolate only in the horizontal direction pi hs has the universal form pi hs a q q z for q 1 2 3 4 as a function of the scaling variable z b q l 1 nu q p p c q l zeta q here p 1 exp beta is the probability of a bond to be closed a q is the nonuniversal crossing amplitude b q is the nonuniversal metric factor nu q is the correlation length index and zeta q is the additional scaling index the universal function q x approximately equal exp z the nonuniversal scaling factors were found numerically

a quasi static signorini contact problem for a thermoviscoelastic beam this paper is concerned with the existence uniqueness and numerical solution of a system of equations modelling the evolution of a quasi static thermoviscoelastic beam that may be in contact with two rigid obstacles a finite element approximation is proposed and analysed and some numerical results are given

operator spectrum and exact exponents of the fully packed loop model we develop a coulomb gas description of the critical fluctuations in the fully packed loop model on the honeycomb lattice we identify the complete operator spectrum of this model in terms of electric and magnetic vector charges and we calculate the scaling dimensions of these operators exactly we also study the geometrical properties of loops in this model and we derive exact results for the fractal dimension and the loop size distribution function a review of the many different representations of this model that have recently appeared in the literature is given

monte carlo study of the antiferromagnetic three state potts model with a staggered polarization field on the square lattice using the wang landau monte carlo method we study the antiferromagnetic af three state potts model with a staggered polarization field on the square lattice we obtain two phase transitions one belongs to the ferromagnetic three state potts universality class and the other to the ising universality class the phase diagram obtained is quantitatively consistent with the transfer matrix calculation the ising transition in the large nearest neighbour interaction limit has been made clear by the detailed analysis of the energy density of states

absence of phase transition for antiferromagnetic potts models via the dobrushin uniqueness theorem we prove that theq state potts antiferromagnet on a lattice of maximum coordination numberr exhibits exponential decay of correlations uniformly at all temperatures including zero temperature wheneverq 2r we also prove slightly better bounds for several two dimensional lattices square lattice exponential decay forq 7 triangular lattice q 11 hexagonal lattice q 4 and kagome lattice q 6 the proofs are based on the dobrushin uniqueness theorem

the three state square lattice potts antiferromagnet at zero temperature we study the 3 state square lattice potts antiferromagnet at zero temperature by a monte carlo simulation using the wang swendsen koteck cluster algorithm on lattices up to 1024 1024 we confirm the critical exponents predicted by burton and henley based on the height representation of this model

analysis of dynamic nonlinear thermoviscoelastic beam problems abstract in this paper we study a dynamic contact problem between a nonlinear viscoelastic beam and two rigid obstacles thermal effects are also taken into account and the contact is modeled using the classical signorini condition the existence of solutions is proved by considering approximate problems from a penalization procedure proving some a priori estimates and passing to the limit an exponential decay property is also obtained then fully discrete approximations of the approximate problem are provided using the finite element method for the spatial approximation and the implicit euler scheme for the discretization of the time derivatives a stability property is obtained and a priori error estimates are proved from which under some additional regularity conditions the linear convergence of the algorithm is deduced fully discrete approximations of the signorini problem are then introduced proceeding in a similar way for which a stability property is obtained finally some numerical simulations are performed to demonstrate the accuracy of the approximation and the behavior of the solution

the contact problem in thermoviscoelastic materials abstract we stablish an existence result for the thermoviscoelastic degenerated contact problem the nonlinear stress strain relation we will consider here is given by m l 0 u x 2 dx u x u xt where m is a function satisfying m c 1 0 c 0 m s c s p moreover we show that the solution decays uniformly to zero that is denoting by e t the first order energy associated to the equation we show that there exist positive constants c satisfying e t c e 0 1 t p 2 p where p is a positive number which depends on nonlinear terms of the system

relaxation time for a dimer covering with height representation this paper considers the monte carlo dynamics of random dimer coverings of the square lattice which can be mapped to a rough interface model two kinds of slow modes are identified associated respectively with long wavelength fluctuations of the interface height and with slow drift in time of the system wide mean height within a continuum theory the longest relaxation time for either kind of mode scales as the system sizen for the real discrete model an exactlower bound ofo n is placed on the relaxation time using variational eigenfunctions corresponding to the two kinds of continuum modes

duality and the universality class of the three state potts antiferromagnet on plane quadrangulations we provide a criterion based on graph duality to predict whether the three state potts antiferromagnet on a plane quadrangulation has a zero or finite temperature critical point and its universality class the former case occurs for quadrangulations of self dual type and the zero temperature critical point has central charge c 1 the latter case occurs for quadrangulations of non self dual type and the critical point belongs to the universality class of the three state potts ferromagnet we have tested this criterion against high precision computations on four lattices of each type with very good agreement we have also found that the wang swendsen koteck algorithm has no critical slowing down in the former case and critical slowing down in the latter

triangular sos models and cubic crystal shapes a solid on solid sos model in a field h conjugate to the orientation of the surface is exactly solved with the aid of pfaffians the free energy h directly gives the equilibrium shape of a finite crystal the phase diagram exhibits rough and smooth phases corresponding to rounded and flat portions of the crystal surface the solid on solid model undergoes transitions of the pokrovsky talapov type 1979 characterised by a specific heat exponent alpha 1 2 one special point of the phase diagram corresponds to the appearance of a facet via an alpha 0 transition height height correlations are derived along a special line in the phase diagram with the aid of the known equivalence of this sos model with an ising model several exponents can be translated from one model to the other this enables one to derive the topology of the phase diagram of the antiferromagnetic triangular ising model with first and second neighbour couplings in a field

spanning forests and the q state potts model in the limit q 0 we study the q state potts model with nearest neighbor coupling v e j 1 in the limit q v 0 with the ratio w v q held fixed combinatorially this limit gives rise to the generating polynomial of spanning forests physically it provides information about the potts model phase diagram in the neighborhood of q v 0 0 we have studied this model on the square and triangular lattices using a transfer matrix approach at both real and complex values of w for both lattices we have computed the symbolic transfer matrices for cylindrical strips of widths 2 l 10 as well as the limiting curves b of partition function zeros in the complex w plane for real w we find two distinct phases separated by a transition point w w0 where w0 1 4 resp w0 0 1753 0 0002 for the square resp triangular lattice for w w0 we find a non critical disordered phase that is compatible with the predicted asymptotic freedom as w for w w0 our results are compatible with a massless berker kadanoff phase with central charge c 2 and leading thermal scaling dimension xt 1 2 marginally irrelevant operator at w w0 we find a first order critical point the first derivative of the free energy is discontinuous at w0 while the correlation length diverges as w w0 and is infinite at w w0 the critical ehavior at w w0 seems to be the same for both lattices and it differs from that of the berker kadanoff phase our results suggest that the central charge is c 1 the leading thermal scaling dimension is xt 1 0 and the critical exponents are 1 d 1 2 and 1

antiferromagnetic potts models on the square lattice a high precision monte carlo study we study the antiferromagnetic q state potts model on the square lattice for q 3 and q 4 using the wang swendsen koteck wsk monte carlo algorithm and a powerful finite size scaling extrapolation method for q 3 we obtain good control up to correlation length 5000 the data are consistent with ae2 p 1 a1e as with p 1 the staggered susceptibility behaves as stagg 5 3 for q 4 the model is disordered 2 even at zero temperature in appendices we prove a correlation inequality for potts antiferromagnets on a bipartite lattice and we prove ergodicity of the wsk algorithm at zero temperature for potts antiferromagnets on a bipartite lattice

finite difference approximate solutions for the strongly damped extensible beam equations approximate solutions are considered for the strongly damped extensible beam equations using the method of lines and an implicit finite difference scheme existence and stability of the corresponding methods are studied and error estimates are also obtained energy conservation and decay properties of the finite difference approximate solutions are shown using the discrete energy method numerical results are also given in order to check the properties of analytical solutions

a dynamic thermoviscoelastic contact problem with the second sound effect abstract this paper deals with a contact problem describing the mechanical and thermal evolution of a damped extensible thermoviscoelastic beam under the cattaneo law relating the heat flux to the gradient of the temperature the beam is rigidly clamped at its left end whereas the right end of the beam moves vertically between reactive stops like a nonlinear spring existence and uniqueness of the solution is proved as well as the exponential decay of the related energy then fully discrete approximations are introduced by using the classical finite element method and the implicit euler scheme to approximate the spatial variable and to discretize the time derivatives respectively an a priori error estimates result is proved from which the linear convergence of the algorithm is deduced the case where the two stops are rigid is also studied from the point of view of the existence and longtime behavior of the solutions finally some numerical simulations are presented to demonstrate the accuracy of the approximation and the behavior of the solution

a numerical method for a nonlinear system of integro differential equations arising in thermoviscoelasticity this paper deals with the numerical solution of nonlinear integro differential equations modelling a one dimensional quasi static contact problem in thermoviscoelasticity a finite element approximation is proposed and analysed and some numerical results are given

transfer matrices and partition function zeros for antiferromagnetic potts models i general theory and square lattice chromatic polynomial we study the chromatic polynomials zero temperature antiferromagnetic potts model partition functions p g q for m n rectangular subsets of the square lattice with m 8 free or periodic transverse boundary conditions and n arbitrary free longitudinal boundary conditions using a transfer matrix in the fortuin kasteleyn representation in particular we extract the limiting curves of partition function zeros when n which arise from the crossing in modulus of dominant eigenvalues beraha kahane weiss theorem we also provide evidence that the beraha numbers b2 b3 b4 b5 are limiting points of partition function zeros as n whenever the strip width m is 7 periodic transverse b c or 8 free transverse b c along the way we prove that a noninteger beraha number except perhaps b10 cannot be a chromatic root of any graph