general β jacobi corners process and the gaussian free field we prove that the two dimensional gaussian free field describes the asymptotics of global fluctuations of a multilevel extension of the general jacobi random matrix ensembles our approach is based on the connection of the jacobi ensembles to a degeneration of the macdonald processes that parallels the degeneration of the macdonald polynomials to the heckman opdam hypergeometric functions of type a we also discuss the limit 2015 wiley periodicals inc

noncolliding brownian motion with drift and time dependent stieltjes wigert determinantal point process using the determinantal formula of biane bougerol and o connell we give multitime joint probability densities to the noncolliding brownian motion with drift where the number of particles is finite we study a special case such that the initial positions of particles are equidistant with a period a and the values of drift coefficients are well ordered with a scale we show that at each time t 0 the single time probability density of particle system is exactly transformed to the biorthogonal stieltjes wigert matrix model in the chern simons theory introduced by dolivet and tierz here one parameter extensions extensions of the stieltjes wigert polynomials which are themselves q extensions of the hermite polynomials play an essential role the two parameters a and of the process combined with time t are mapped to the parameters q and of the biorthogonal polynomials by the transformation of normalization factor of our probability density the partition function of the chern simons matrix model is readily obtained we study the determinantal structure of the matrix model and prove that at each time t 0 the present noncolliding brownian motion with drift is a determinantal point process in the sense that any correlation function is given by a determinant governed by a single integral kernel called the correlation kernel using the obtained correlation kernel we study time evolution of the noncolliding brownian motion with drift

double vogan diagrams and semisimple symmetric spaces a vogan diagram is a set of involution and painting on a dynkin diagram it selects a real form or equivalently an involution from a complex simple lie algebra we introduce the double vogan diagram which is two sets of vogan diagrams superimposed on an affine dynkin diagram they correspond to pairs of commuting involutions on complex simple lie algebras and therefore provide an independent classification of the simple locally symmetric pairs

a quick proof on the equivalence classes of extended vogan diagrams abstract an extended vogan diagram is an extended dynkin diagram together with a diagram involution such that the vertices fixed by the involution are colored white or black every extended vogan diagram represents an almost compact real form of the affine kac moody lie algebra two extended diagrams are said to be equivalent if they represent isomorphic real forms the equivalence classes of extended vogan diagrams have earlier been classified by the authors in this paper we present a much shorter and instructive argument

cartan automorphisms and vogan superdiagrams the real forms of complex semisimple lie algebras are characterized by cartan involutions and vogan diagrams we extend these notions to the cartan automorphisms and vogan superdiagrams and show that they characterize the real forms of complex contragredient lie superalgebras

height fluctuations in the honeycomb dimer model we study a model of random surfaces arising in the dimer model on the honeycomb lattice for a fixed wire frame boundary condition as the lattice spacing 0 cohn kenyon and propp 3 showed the almost sure convergence of a random surface to a non random limit shape 0 in 12 okounkov and the author showed how to parametrize the limit shapes in terms of analytic functions in particular constructing a natural conformal structure on them we show here that when 0 has no facets for a family of boundary conditions approximating the wire frame the large scale surface fluctuations height fluctuations about 0 converge as 0 to a gaussian free field for the above conformal structure we also show that the local statistics of the fluctuations near a given point x are as conjectured in 3 given by the unique ergodic gibbs measure on plane configurations whose slope is the slope of the tangent plane of 0 at x

consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part i theoretical formulation abstract a derivation of the projected algorithm for general isotropic three invariant plasticity models under plane stress conditions is presented it is obtained by consistently specializing the 3d formulation to the 2d subspace defined by the plane stress condition closed form intrinsic algorithm linearization and a novel expression of the consistent tangent tensor are provided these are also shown to directly emanate from the analogous quantities pertaining to the fully 3d case a detailed discussion of the proposed implementation along with a representative set of numerical examples is provided in the second part of this paper valoroso n rosati l 2008 consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part ii computational issues international journal of solids and structures 46 92 124

the fiber free approach in the evaluation of the tangent stiffness matrix for elastoplastic uniaxial constitutive laws summary it has been shown in a previous paper that the normal stress resultants for an arbitrary polygonal section endowed with a uniaxial elastoplastic law can be computed exactly by means of a general approach it has been denominated fiber free as no fiber discretization of the section is required the aim of this paper was to extend the fiber free approach to the evaluation of the tangent stiffness matrix to allow for the analytical integration of all the basic quantities required by the section state determination occurring in nonlinear frame analysis the numerical examples showed that the general properties of the fiber free approach already discussed with reference to the stress resultants carry over to the tangent stiffness matrix as well namely independent from the complexity of the constitutive law the accuracy in the evaluation of the tangent stiffness matrix allowed by the number of fibers adopted in commercial software for nonlinear frame analysis is even worse than that associated with the computation of the stress resultants copyright 2013 john wiley sons ltd

affine kac moody symmetric spaces related with a1 1 a2 1 a2 2 symmetric spaces associated with lie algebras and lie groups which are riemannian manifolds have recently got a lot of attention in various branches of physics for their role in classical quantum integrable systems transport phenomena etc their infinite dimensional counter parts have recently been discovered which are affine kac moody symmetric spaces in this paper we have algebraically explicitly computed the affine kac moody symmetric spaces associated with affine kac moody algebras a1 1 a2 1 a2 2 we hope these types of spaces will play similar roles as that of symmetric spaces in many physical systems

central limit theorems for biorthogonal ensembles and asymptotics of recurrence coefficients we study fluctuations of linear statistics corresponding to smooth functions for certain biorthogonal ensembles we study those biorthogonal ensembles for which the underlying biorthogonal family s

admissible positive systems of affine non twisted kac moody lie algebras abstract we introduce admissible positive systems and hermitian real forms of affine non twisted kac moody lie algebras and show that a real form has admissible positive system if and only if it is hermitian we use the vogan diagrams to classify the hermitian real forms and show that their symmetric spaces carry complex structures

schur dynamics of the schur processes abstract we construct discrete time markov chains that preserve the class of schur processes on partitions and signatures one application is a simple exact sampling algorithm for q volume distributed skew plane partitions with an arbitrary back wall another application is a construction of markov chains on infinite gelfand tsetlin schemes that represent deterministic flows on the space of extreme characters of the infinite dimensional unitary group

static fluctuations of a thick one dimensional interface in the 1 1 directed polymer formulation numerical study we study numerically the geometrical and free energy fluctuations of a static one dimensional 1d interface with a short range elasticity submitted to a quenched random bond gaussian disorder of finite correlation length ensuremath xi g0 and at finite temperature t using the exact mapping from the static 1d interface to the 1 1 directed polymer dp growing in a continuous space we focus our analysis on the disorder free energy of the dp end point a quantity which is strictly zero in the absence of disorder and whose sample to sample fluctuations at a fixed growing time t inherit the statistical translation invariance of the microscopic disorder explored by the dp constructing a new numerical scheme for the integration of the kardar parisi zhang evolution equation obeyed by the free energy we address numerically the time and temperature dependence of the disorder free energy fluctuations at fixed finite ensuremath xi we examine on one hand the amplitude stackrel ifmmode tilde else fi d t and effective correlation length stackrel ifmmode tilde else fi ensuremath xi t of the free energy fluctuations and on the other hand the imprint of the specific microscopic disorder correlator on the large time shape of the free energy two point correlator we observe numerically the crossover to a low temperature regime below a finite characteristic temperature t c ensuremath xi as previously predicted by gaussian variational method computations and scaling arguments and extensively investigated analytically in phys rev e 87 042406 2013 finally we address numerically the time and temperature dependence of the roughness b t which quantifies the dp end point transverse fluctuations and we show how the amplitude stackrel ifmmode tilde else fi d ensuremath infty t ensuremath xi controls the different regimes experienced by b t in agreement with the analytical predictions of a dp toy model approach

polynuclear growth on a flat substrate and edge scaling of goe eigenvalues we consider the polynuclear growth png model in 1 1 dimension with flat initial condition and no extra constraints through the robinson schensted knuth rsk construction one obtains the multilayer png model which consists of a stack of non intersecting lines the top one being the png height the statistics of the lines is translation invariant and at a fixed position the lines define a point process we prove that for large times the edge of this point process suitably scaled has a limit this limit is a pfaffian point process and identical to the one obtained from the edge scaling of the gaussian orthogonal ensemble goe of random matrices our results give further insight to the universality structure within the kpz class of 1 1 dimensional growth models

scale invariance of the png droplet and the airy process we establish that the static height fluctuations of a particular growth model the png droplet converges upon proper rescaling to a limit process which we call the airy process a y the airy process is stationary it has continuous sample paths its single time fixed y distribution is the tracy widom distribution of the largest eigenvalue of a gue random matrix and the airy process has a slow decay of correlations as y 2 roughly the airy process describes the last line of dyson s brownian motion model for random matrices our construction uses a multi layer version of the png model which can be analyzed through fermionic techniques specializing our result to a fixed value of y one reobtains the celebrated result of baik deift and johansson on the length of the longest increasing subsequence of a random permutation

equivalence classes of vogan diagrams abstract a vogan diagram is a dynkin diagram with an involution and the vertices fixed by the involution may be painted they represent real simple lie algebras and two diagrams are said to be equivalent if they represent the same lie algebra in this article we classify the equivalence classes of all vogan diagrams in doing so we find that the underlying dynkin diagrams have certain properties in graph painting we show that this combinatorial property provides an easy classification for most of the simply laced dynkin diagrams

a primal dual algorithm for shakedown analysis of structures abstract the paper describes a primal dual algorithm for shakedown analysis of structures with the use of kinematically admissible finite elements starting from koiter kinematic theorem a primal dual optimization condition is established by adopting static terms as complementary variables newton like iterations are performed to give both upper and quasi lower bounds of the load factor that converge rapidly to the accurate solution of shakedown limit

a periodic hexagon tiling model and non hermitian orthogonal polynomials we study a one parameter family of probability measures on lozenge tilings of large regular hexagons that interpolates between the uniform measure on all possible tilings and a particular fully frozen tiling the description of the asymptotic behavior can be separated into two regimes the low and the high temperature regime our main results are the computations of the disordered regions in both regimes and the limiting densities of the different lozenges there for low temperatures the disordered region consists of two disjoint ellipses in the high temperature regime the two ellipses merge into a single simply connected region at the transition from the low to the high temperature a tacnode appears the key to our asymptotic study is a recent approach introduced by duits and kuijlaars providing a double integral representation for the correlation kernel one of the factors in the integrand is the christoffel darboux kernel associated to polynomials that satisfy non hermitian orthogonality relations with respect to a complex valued weight on a contour in the complex plane we compute the asymptotic behavior of these orthogonal polynomials and the christoffel darboux kernel by means of a riemann hilbert analysis after substituting the resulting asymptotic formulas into the double integral we prove our main results by classical steepest descent arguments

the pearcey process the extended airy kernel describes the space time correlation functions for the airy process which is the limiting process for a polynuclear growth model the airy functions themselves are given by integrals in which the exponents have a cubic singularity arising from the coalescence of two saddle points in an asymptotic analysis pearcey functions are given by integrals in which the exponents have a quartic singularity arising from the coalescence of three saddle points a corresponding pearcey kernel appears in a random matrix model and a brownian motion model for a fixed time this paper derives an extended pearcey kernel by scaling the brownian motion model at several times and a system of partial differential equations whose solution determines associated distribution functions we expect there to be a limiting nonstationary process consisting of infinitely many paths which we call the pearcey process whose space time correlation functions are expressible in terms of this extended kernel

a kinematically exact finite element formulation of planar elastic plastic frames a finite element formulation of finite deformation static analysis of plane elastic plastic frames subjected to static loads is presented in which the only function to be interpolated is the rotation of the centroid axis of the beam one of the advantages of such a formulation is that the problem of the field consistency does not arise exact non linear kinematic relationships of the finite strain beam theory are used which assume the bernoulli hypothesis of plane cross sections finite displacements and rotations as well as finite extensional and bending strains are accounted for the effects of shear strains and non conservative loads are at present neglected yet they can simply be incorporated in the formulation because the potential energy of internal forces does not exist with elastic plastic material the principle of virtual work is introduced as the basis of the finite element formulation a generalized principle of virtual work is proposed in which the displacements rotation extensional and bending strains and the lagrangian multipliers are independent variables by exploiting the special structure of the equations of the problem the displacements the strains and the multipliers are eliminated from the generalized principle of virtual work a novel principle is obtained in which the rotation becomes the only function to be approximated in its finite element implementation it is shown that n 1 point numerical integration must be employed in conjunction with n node interpolation polynomials for the rotation and the lobatto rule is recommended regarding the integration over the cross section it is demonstrated by numerical examples that due to discontinuous integrands no integration order defined as computationally efficient yet accurate enough could be suggested the theoretical findings and a nice performance of the derived finite elements are illustrated by numerical examples

a classification of involutive automorphisms of an affine kac moody lie algebra abstract in this thesis we classify the conjugacy classes of involutions in aut g where g is an affine kac moody lie algebra we distinguish between two kinds of involutions those which preserve the conjugacy class of a borel subalgebra and those which don t we give a complete and non redundant list of representatives of involutions of the first kind and we compute their fixed points sets we prove that any involution of the first kind has a conjugate which leaves invariant the components of the gauss decomposition g n h n we also give a complete list of representatives of the conjugacy classes of involutions of the second kind

on the distribution of the length of the longest increasing subsequence of random permutations let sn be the group of permutations of 1 2 n if 7r e sn we say that 7 i1 7f ik is an increasing subsequence in 7r if il i2 ik and 7r ii 7r i2 7r ik let 1n r be the length of the longest increasing subsequence for example if n 5 and 7r is the permutation 5 1 3 2 4 in one line notation thus 7r 1 5 7r 2 1 then the longest increasing subsequences are 1 2 4 and 1 3 4 and n 3 equip sn with uniform distribution

random skew plane partitions and the pearcey process we study random skew 3d partitions weighted by qvol and specifically the q 1 asymptotics of local correlations near various points of the limit shape we obtain sine kernel asymptotics for correlations in the bulk of the disordered region airy kernel asymptotics near a general point of the frozen boundary and a pearcey kernel asymptotics near a cusp of the frozen boundary

scaling limit for the space time covariance of the stationary totally asymmetric simple exclusion process the totally asymmetric simple exclusion process tasep on the one dimensional lattice with the bernoulli measure as initial conditions 0 1 is stationary in space and time let nt j be the number of particles which have crossed the bond from j to j 1 during the time span 0 t for open image in new window we prove that the fluctuations of nt j for large t are of order t1 3 and we determine the limiting distribution function open image in new window which is a generalization of the gue tracy widom distribution the family open image in new window of distribution functions have been obtained before by baik and rains in the context of the png model with boundary sources which requires the asymptotics of a riemann hilbert problem in our work we arrive at open image in new window through the asymptotics of a fredholm determinant open image in new window is simply related to the scaling function for the space time covariance of the stationary tasep equivalently to the asymptotic transition probability of a single second class particle

asymptotic post buckling fem analysis using corotational formulation finite element asymptotic post buckling analysis being based on fourth order expansions of the strain energy requires that nonlinear structural modeling be accurate to same order at least with respect to the rigid motions of the elements a corotational description is proposed here as a general tool to satisfy this requirement of objectivity by referring each element to a local frame which moves rotates with the element so filtering its rigid motion in this description nonlinearity of the problem derives essentially from the change of reference from the global fixed frame to the local one the strain energy being governed by their relative rotations in finite kinematics this noticeably complicates the algebra for obtaining exact expressions of its variations quite simple basic expressions for the first four corotational derivatives of the strain energy are provided allowing the set up of a fourth order accurate asymptotic analysis starting from standard finite elements based on linear or simplified nonlinear local modelings the formulation is implemented for the analysis of 3d beam assemblages and several numerical results are presented and discussed showing the effectiveness and robustness of the proposed approach in reproducing the nonlinear equilibrium path in both cases of monomodal and coupled multimodal buckling

gaussian free field in an interlacing particle system with two jump rates we study the fluctuations of a random surface in a stochastic growth model on a system of interlacing particles placed on a two dimensional lattice there are two different types of particles one with a low jump rate and the other with a high jump rate in the large time limit the random surface has a deterministic shape due to the different jump rates the limit shape and the domain on which it is defined are not smooth the main result is that the fluctuations of the random surface are governed by the gaussian free field 2012 wiley periodicals inc

vogan diagrams of real forms of affine kac moody lie algebras abstract a vogan diagram is actually a dynkin diagram with some additional structure this paper develops theory of vogan diagrams for almost compact real forms of indecomposable nontwisted affine kac moody lie algebras here the equivalence classes of vogan diagrams are in one one correspondence with the isomorphism classes of almost compact real forms

janossy densities of coupled random matrices we explicitly calculate the janossy densities for a special class of finite determinantal random point processes with several types of particles introduced by prahofer and spohn and in the full generality by johansson in connection with the analysis of polynuclear growth models the results of this paper generalize the theorem we proved earlier with borodin about the janossy densities in biorthogonal ensembles in particular our results can be applied to ensembles of random matrices coupled in a chain which provide a very important example of determinantal ensembles we study

maximum distributions of bridges of noncolliding brownian paths one dimensional brownian motion starting from the origin at time t 0 conditioned to return to the origin at time t 1 and to stay positive during time interval 0 t 1 is called the bessel bridge with duration 1 we consider an n particle system of such bessel bridges conditioned never to collide with each other in 0 t 1 which is the continuum limit of the vicious walk model in watermelon configuration with a wall distributions of maximum values of paths attained in the time interval t epsilon 0 1 are studied to characterize the statistics of random patterns of the repulsive paths on the spatiotemporal plane for the outermost path the distribution function of maximum value is exactly determined for general n we show that the present n path system of noncolliding bessel bridges is realized as the positive eigenvalue process of the 2nx2n matrix valued brownian bridge in the symmetry class c using this fact computer simulations are performed and numerical results on the n dependence of the maximum value distributions of the inner paths are reported the present work demonstrates that the extreme value problems of noncolliding paths are related to random matrix theory the representation theory of symmetry and number theory

admissible positive systems of affine kac moody lie algebras the twisted cases abstract we introduce admissible positive systems and hermitian real forms of affine twisted kac moody lie algebras and show that a real form has admissible positive system if and only if it is hermitian we use the vogan diagrams to classify the hermitian real forms and show that their symmetric spaces carry complex structures the affine non twisted kac moody lie algebras have been treated in an earlier work and this article deals with the twisted cases

probing the tails of the ground state energy distribution for the directed polymer in a random medium of dimension d 1 2 3 via a monte carlo procedure in the disorder in order to probe with high precision the tails of the ground state energy distribution of disordered spin systems k orner katzgraber and hartmann have recently proposed an importance sampling monte carlo markov chain in the disorder in this paper we combine their monte carlo procedure in the disorder with exact transfer matrix calculations in each sample to measure the negative tail of ground state energy distribution p d e 0 for the directed polymer in a random medium of dimension d 1 2 3 in d 1 we check the validity of the algorithm by a direct comparison with the exact result namely the tracy widom distribution in dimensions d 2 and d 3 we measure the negative tail up to ten standard deviations which correspond to probabilities of order p d e 0 ensuremath sim 10 ensuremath 22 our results are in agreement with zhang s argument stating that the negative tail exponent ensuremath eta d of the asymptotic behavior mathrm ln phantom rule 0 2em 0ex p d e 0 ensuremath sim ensuremath ensuremath mid e 0 ensuremath mid ensuremath eta d as e 0 ensuremath rightarrow ensuremath ensuremath infty is directly related to the fluctuation exponent ensuremath theta d which governs the fluctuations ensuremath delta e 0 l ensuremath sim l ensuremath theta d of the ground state energy e 0 for polymers of length l via the simple formula ensuremath eta d 1 1 ensuremath ensuremath theta d throughout the paper we comment on the similarities and differences with spin glasses

using multifiber beams to account for shear and torsion applications to concrete structural elements the purpose of this work is to investigate solutions for an enhanced multifiber beam element accounting for shear and torsion higher order interpolations functions are used to avoid any shear locking phenomena and the cross section warping kinematics is extended to non linear behavior using advanced constitutive laws the efficiency of the proposed modeling strategies is tested with experimental results of concrete structural elements subjected to severe loading

statistics of extremal intensities for gaussian interfaces the extremal fourier intensities are studied for stationary edwards wilkinson type gaussian interfaces with power law dispersion we calculate the probability distribution of the maximal intensity and find that generically it does not coincide with the distribution of the integrated power spectrum i e roughness of the surface nor does it obey any of the known extreme statistics limit distributions the fisher tippett gumbel limit distribution is however recovered in three cases i in the nondispersive white noise limit ii for high dimensions and iii when only short wavelength modes are kept in the last two cases the limit distribution emerges in nonconventional scenarios

transversal fluctuations of the asep stochastic six vertex model and hall littlewood gibbsian line ensembles we consider the asep and the stochastic six vertex model started with step initial data after a long time t it is known that the one point height function fluctuations for these systems are of order t1 3 we prove the kpz prediction of t2 3 scaling in space namely we prove tightness and brownian absolute continuity of all subsequential limits as t goes to infinity of the height function with spatial coordinate scaled by t2 3 and fluctuations scaled by t1 3 the starting point for proving these results is a connection discovered recently by borodin bufetov wheeler between the stochastic six vertex height function and the hall littlewood process a certain measure on plane partitions interpreting this process as a line ensemble with a gibbsian resampling invariance we show that the one point tightness of the top curve can be propagated to the tightness of the entire curve

how to improve efficiency and robustness of the newton method in geometrically non linear structural problem discretized via displacement based finite elements abstract in this paper we show how to significantly improve the robustness and the efficiency of the newton method in geometrically non linear structural problems discretized via displacement based finite elements the strategy is based on the relaxation of the constitutive equations at each integration point this leads to an improved iterative scheme which requires a very low number of iterations to converge and can withstand very large steps in step by step analyses the computational cost of each iteration is the same as the original newton method the impressive performances of the proposal are shown by many numerical tests in geometrically non linear analysis the proposed strategy called mip newton seems worthy to replace the standard newton method in any finite element code based on displacement formulations its implementation in existing codes is very easy

an unconditionally convergent algorithm for the evaluation of the ultimate limit state of rc sections subject to axial force and biaxial bending we present a numerical procedure based upon a tangent approach for evaluating the ultimate limit state uls of reinforced concrete rc sections subject to axial force and biaxial bending the rc sections are assumed to be of arbitrary polygonal shape and degree of connection furthermore it is possible to keep fixed a given amount of the total load and to find the uls associated only with the remaining part which can be increased by means of a load multiplier the solution procedure adopts two nested iterative schemes which in turn update the current value of the tentative ultimate load and the associated strain parameters in this second scheme an effective integration procedure is used for evaluating in closed form as explicit functions of the position vectors of the vertices of the section the domain integrals appearing in the definition of the tangent matrix and of the stress resultants under mild hypotheses which are practically satisfied for all cases of engineering interest the existence and uniqueness of the uls load multiplier is ensured and the global convergence of the proposed solution algorithm to such value is proved an extensive set of numerical tests carried out for rectangular l shaped and multicell sections shows the effectiveness of the proposed solution procedure

dynamic analysis of beam structures considering geometric and constitutive nonlinearity abstract a fully geometric and constitutive nonlinear model for the description of the dynamic behavior of beam structures is developed the proposed formulation is based on the geometrically exact formulation for beams due to simo but in this article an intermediate curved reference configuration is considered the resulting deformation map belongs to a nonlinear differential manifold and therefore an appropriated version of newmark s scheme is used in updating the kinematics variables each material point of the cross section is assumed to be composed of several simple materials with their own constitutive laws the mixing rule is used to describe the resulting composite an explicit expression for the objective measure of the strain rate acting on each material point is deduced in this article details about its numerical implementation in the time stepping scheme are also addressed viscosity is included at the constitutive level by means of a thermodynamically consistent visco damage model developed in terms of the material description of the first piola kirchhoff stress vector the constitutive part of the tangent tensor is deduced including the effect of rate dependent inelasticity finally several numerical examples validating the proposed formulation are given

two time distribution function in one dimensional random directed polymers the explicit expression for the two time free energy distribution function in one dimensional random directed polymers is derived in terms of the bethe ansatz replica technique it is shown that such type of the distribution function can be represented in the form of a generalized two dimensional fredholm determinant

analytical integration of elasto plastic uniaxial constitutive laws over arbitrary sections summary we present the preliminary results of a novel approach to the state determination of polygonal sections of arbitrary shape endowed with elasto plastic uniaxial constitutive laws by means of a suitable application of gauss theorem we prove that the normal stress resultants can be computed analytically as sum of finite quantities evaluated solely at the vertices of the section for this reason the proposed approach has been termed fiber free to emphasize the fact that it does not require any subdivision of the section in fibers numerical results show that the fiber approach is grossly inaccurate and that the number of fibers required to achieve a degree of accuracy comparable with that entailed by the fiber free approach is at least one order of magnitude greater than the one commonly suggested in commercial software for nonlinear frame analysis copyright 2012 john wiley sons ltd

two lit trees for lit only σ game abstract a configuration of the lit only game on a finite graph is an assignment of one of two states on or off to all vertices of given a configuration a move of the lit only game on allows the player to choose an on vertex s of and change the states of all neighbors of s given any integer k we say that is k lit if for any configuration the number of on vertices can be reduced to at most k by a finite sequence of moves assume that is a tree with a perfect matching we show that is 1 lit and any tree obtained from by adding a new vertex on an edge of is 2 lit

nurbs plasticity yield surface representation and implicit stress integration for isotropic inelasticity in numerical analysis the failure of engineering materials is controlled through specifying yield envelopes or surfaces that bound the allowable stress in the material however each surface is distinct and requires a specific equation describing the shape of the surface to be formulated in each case these equations impact on the numerical implementation specifically relating to stress integration of the models and therefore a separate algorithm must be constructed for each model this paper presents for the first time a way to construct yield surfaces using techniques from non uniform rational basis spline nurbs surfaces such that any isotropic convex yield envelope can be represented within the same framework these surfaces are combined with an implicit backward euler type stress integration algorithm to provide a flexible numerical framework for computational plasticity the algorithm is inherently stable as the iterative process starts and remains on the yield surface throughout the stress integration the performance of the algorithm is explored using both material point investigations and boundary value analyses demonstrating that the framework can be applied to a variety of plasticity models

symmetry preserving return mapping algorithms and incrementally extremal paths a unification of concepts in this work we seek to characterize the conditions under which an elastic plastic stress update algorithm preserves the symmetries inherent to the material response from a numerical standpoint the aim is to determine under what conditions a stress update algorithm produces symmetric consistent tangents when applied to materials obeying normality for the ideally plastic solid we show that only the fully implicit or closest point return mapping algorithm is symmetry preserving for hardening plasticity symmetry cannot be preserved in general unless suitable restrictions are imposed on the constitutive equations we show that these restrictions amount to the existence of a pseudo internal energy function acting as a joint potential for both the direction of plastic flow and the hardening moduli in view of the fact that holonomic methods based on incrementally extremal paths also result in update rules possessing a potential structure and hence in symmetric tangents we address the question of whether any connections exist between the two approaches we show that holonomic methods and the fully implicit algorithm may indeed be brought into correspondence

maximum relative height of elastic interfaces in random media the distribution of the maximal relative height mrh of self affine one dimensional elastic interfaces in a random potential is studied we analyze the ground state configuration at zero driving force and the critical configuration exactly at the depinning threshold both for the random manifold and random periodic universality classes these configurations are sampled by exact numerical methods and their mrh distributions are compared with those with the same roughness exponent and boundary conditions but produced by independent fourier modes with normally distributed amplitudes using pickands theorem we derive an exact analytical description for the right tail of the latter after properly rescaling the mrh distributions we find that corrections from the gaussian independent modes approximation are in general small as previously found for the average width distribution of depinning configurations in the large size limit all corrections are finite except for the ground state in the random periodic class whose mrh distribution becomes for periodic boundary conditions indistinguishable from the airy distribution we find that the mrh distributions are in general sensitive to changes of boundary conditions

airy kernel with two sets of parameters in directed percolation and random matrix theory we introduce a generalization of the extended airy kernel with two sets of real parameters we show that this kernel arises in the edge scaling limit of correlation kernels of determinantal processes related to a directed percolation model and to an ensemble of random matrices

extended vogan diagrams an extended vogan diagram is an extended dynkin diagram with a diagram involution such that the vertices fixed by the involution can be painted or unpainted every extended vogan diagram represents an almost compact real form of some affine kac moody lie algebra two diagrams may represent isomorphic algebras and in this case we say that the diagrams are equivalent in this paper we classify the equivalence classes of extended vogan diagrams and provide a complete list of all diagrams within each class it gives a combinatorial classification of the isomorphic classes of almost compact real forms of the affine kac moody lie algebras

on the formulation of closest point projection algorithms in elastoplasticity part i the variational structure we present in this paper the characterization of the variational structure behind the discrete equations defining the closest point projection approximation in elastoplasticity rate independent and viscoplastic formulations are considered in the infinitesimal and the finite deformation range the later in the context of isotropic finite strain multiplicative plasticity primal variational principles in terms of the stresses and stress like hardening variables are presented first followed by the formulation of dual principles incorporating explicitly the plastic multiplier augmented lagrangian extensions are also presented allowing a complete regularization of the problem in the constrained rate independent limit the variational structure identified in this paper leads to the proper framework for the development of new improved numerical algorithms for the integration of the local constitutive equations of plasticity as it is undertaken in part ii of this work

discrete orthogonal polynomial ensembles and the plancherel measure we consider discrete orthogonal polynomial ensembles which are discrete analogues of the orthogonal polynomial ensembles in random matrix theory these ensembles occur in certain problems in combinatorial probability and can be thought of as probability measures on partitions the meixner ensemble is related to a two dimensional directed growth model and the charlier ensemble is related to the lengths of weakly increasing subsequences in random words the krawtchouk ensemble occurs in connection with zig zag paths in random domino tilings of the aztec diamond and also in a certain simplifled directed flrst passage percolation model we use the charlier ensemble to investigate the asymptotics of weakly increasing subsequences in random words and to prove a conjecture of tracy and widom as a limit of the meixner ensemble or the charlier ensemble we obtain the plancherel measure on partitions and using this we prove a conjecture of baik deift and johansson that under the plancherel measure the distribution of the lengths of the flrst k rows in the partition appropriately scaled converges to the asymptotic joint distribution for the k largest eigenvalues of a random matrix from the gaussian unitary ensemble in this problem a certain discrete kernel which we call the discrete bessel kernel plays an important role

level spacing of random matrices in an external source in an earlier work we had considered a gaussian ensemble of random matrices in the presence of a given external matrix source the measure is no longer unitary invariant and the usual techniques based on orthogonal polynomials or on the coulomb gas representation are not available nevertheless the n point correlation functions are still given in terms of the determinant of a kernel known through an explicit integral representation this kernel is no longer symmetric though and is not readily accessible to standard methods in particular finding the level spacing probability is always a delicate problem in fredholm theory and we have to reconsider the problem within our model we find a new class of universality for the level spacing distribution when the spectrum of the source is ajusted to produce a vanishing gap in the density of the state the problem is solved through coupled non linear differential equations which turn out to form a hamiltonian system as a result we find that the level spacing probability p s behaves like exp c s 8 over 3 for large spacing s this is consistent with the asymptotic behavior exp c s 2 beta 2 whenever the density of state behaves near the edge as rho lambda sim lambda beta

minimum light number of lit only σ game on a tree let t be a tree with leaves each vertex of t is assigned a state either lit or off an assignment of states to all the vertices of t is called a configuration the lit only s game allows the player to pick a lit vertex and change the states of all its neighbours we prove that for any initial configuration one can make a sequence of allowable moves to arrive at a configuration in which the number of lit vertices is no greater than email protected email protected we also give examples to show that the bound email protected email protected cannot be relaxed to email protected email protected

large n limit of gaussian random matrices with external source part i we continue the study of the hermitian random matrix ensemble with external source open image in new window where a has two distinct eigenvalues a of equal multiplicity this model exhibits a phase transition for the value a 1 since the eigenvalues of m accumulate on two intervals for a 1 and on one interval for 0 1 was treated in part i where it was proved that local eigenvalue correlations have the universal limiting behavior which is known for unitarily invariant random matrices that is limiting eigenvalue correlations are expressed in terms of the sine kernel in the bulk of the spectrum and in terms of the airy kernel at the edge in this paper we establish the same results for the case 0 a 1 as in part i we apply the deift zhou steepest descent analysis to a 3 3 matrix riemann hilbert problem due to the different structure of an underlying riemann surface the analysis includes an additional step involving a global opening of lenses which is a new phenomenon in the steepest descent analysis of riemann hilbert problems

dominos and the gaussian free field we define a scaling limit of the height function on the domino tiling model dimer model on simply connected regions in z 2 and show that it is the massless free field a gaussian process with independent coefficients when expanded in the eigenbasis of the laplacian

limit shapes and the complex burgers equation in this paper we study surfaces in r 3 that arise as limit shapes in random surface models related to planar dimers these limit shapes are surface tension minimizers that is they minimize a functional of the form h dx dy among all lipschitz functions h taking given values on the boundary of the domain the surface tension has singularities and is not strictly convex which leads to formation of facets and edges in the limit shapes we find a change of variables that reduces the euler lagrange equation for the variational problem to the complex inviscid burgers equation complex hopf equation the equation can thus be solved in terms of an arbitrary holomorphic function which is somewhat similar in spirit to weierstrass parametrization of minimal surfaces we further show that for a natural dense set of boundary conditions the holomorphic function in question is in fact algebraic the tools of algebraic geometry can thus be brought in to study the minimizers and especially the formation of their singularities this is illustrated by several explicitly computed examples

invariants of real forms of affine kac moody lie algebras abstract the theory of vogan diagrams which are dynkin diagrams with an overlay of certain additional information allows one to give a rapid classification of finite dimensional real semisimple lie algebras and to make use of this classification in practice this paper develops a corresponding theory of vogan diagrams for almost compact real forms of indecomposable nontwisted affine kac moody lie algebras in this case also the equivalence classes of vogan diagrams correspond to the isomorphism classes of almost compact real forms although the real forms of such algebras had already been classified the theory of vogan diagrams introduces invariants for such algebras and makes it possible to locate a given real form within the classification

quantum flag manifolds quantum symmetric spaces and their associated universal k matrices abstract let u be a connected simply connected compact lie group with complexification g let u and g be the associated lie algebras let be the dynkin diagram of g with underlying set i and let u q u be the associated quantized universal enveloping algebra of u for some 0 q distinct from 1 let o q u be the coquasitriangular quantized function hopf algebra of u whose drinfeld double o q g r we view as the quantized function algebra of g considered as a real algebraic group we show how the datum of an involution of and a invariant function i r can be used to deform o q g r into a algebra o q id g r by a modification of the drinfeld double construction we then show how by a generalized theory of universal k matrices a specific subalgebra of o q id g r admits homomorphisms into both u q u and o q u the images being coideal subalgebras of respectively u q u and o q u we illustrate the theory by showing that two main classes of examples arise by such coideals namely quantum flag manifolds and quantum symmetric spaces except possibly for certain exceptional cases in the former case this connects to work of the first author and neshveyev while for the latter case we heavily rely on recent results of balagovic and kolb

statistical self similarity of one dimensional growth processes abstract for one dimensional growth processes we consider the distribution of the height above a given point of the substrate and study its scale invariance in the limit of large times we argue that for self similar growth from a single seed the universal distribution is the tracy widom distribution from the theory of random matrices and that for the growth from a flat substrate it is some other only numerically determined distribution in particular for the polynuclear growth model in the droplet geometry the height maps onto the longest increasing subsequence of a random permutation from which the height distribution is identified as the tracy widom distribution

limit process of stationary tasep near the characteristic line the totally asymmetric simple exclusion process tasep on input amssym bbb z with the bernoulli measure as an initial condition 0 1 is stationary it is known that along the characteristic line the current fluctuates at an order of t1 3 the limiting distribution has also been obtained explicitly in this paper we determine the limiting multipoint distribution of the current fluctuations moving away from the characteristics by the order t2 3 the main tool is the analysis of a related directed last percolation model we also discuss the process limit in tandem queues in equilibrium 2010 wiley periodicals inc

infinite flag varieties and conjugacy theorems abstract we study the orbit of a highest weight vector in an integrable highest weight module of the group g associated to a kac moody algebra unk a we obtain applications to the geometric structure of the associated flag varieties and to the algebraic structure of unk a in particular we prove conjugacy theorems for cartan and borel subalgebras of unk a so that the cartan matrix a is an invariant of unk a

frame elements with mixed formulation for singular section response mixed formulations of frame elements offer significant advantages over more traditional displacement formulations particularly under large cyclic inelastic deformations including the effects of shear this paper complements the recent proposal of a consistent variational basis for the mixed formulation of frame elements by supplying the explicit definition of the stress field over the cross section the paper also addresses the numerical stability of the element state determination algorithm in the presence of an ill conditioned or even singular section stiffness matrix the proposed algorithm is based on the eigendecomposition of the section stiffness matrix and uses the sherman morrison woodbury formula and the moore penrose pseudoinverse to avoid the inversion of ill conditioned matrices in the element state determination in the extreme case of uniform tension or uniform flexure the section flexibility matrix is split into an elastic and a plastic component before eigendecomposition with the proposed method the inelastic response of the element under multiple perfectly plastic hinges can be successfully traced numerical examples demonstrate the capabilities of the approach copyright 2008 john wiley sons ltd

differential equations for dyson processes we call a dyson process any process on ensembles of matrices in which the entries undergo diffusion we are interested in the distribution of the eigenvalues or singular values of such matrices in the original dyson process it was the ensemble of n n hermitian matrices and the eigenvalues describe n curves given sets x1 xm the probability that for each k no curve passes through xk at time k is given by the fredholm determinant of a certain matrix kernel the extended hermite kernel for this reason we call this dyson process the hermite process similarly when the entries of a complex matrix undergo diffusion we call the evolution of its singular values the laguerre process for which there is a corresponding extended laguerre kernel scaling the hermite process at the edge leads to the airy process which was introduced by prahofer and spohn as the limiting stationary process for a polynuclear growth model and in the bulk to the sine process scaling the laguerre process at the edge leads to the bessel process

stationary states of crystal growth in three dimensions a new markov process describing crystal growth in three dimensions is introduced states of the process are configurations of the crystal surface which has a terrace edge kink structure the states are continuous along edges but discrete across edges in accordance with the very different rates for the two types of captures of particles stationary distributions describing steady crystal growth are found in general to our knowledge these are the first examples of stationary distributions for layered crystal growth in three dimensions the steady growth rate and other quantities are obtained explicitly for two interacting edges for many interacting edges growth behavior is determined a in various asymptotic regimes including thermodynamic limits b via simulations and c using series cluster expansions in the slope of the surface the first three coefficients being computed the theoretical growth rates show a marked dependence on surface dimensions this may contribute to the size dependence and dispersion in the observed growth rate of small crystals

finite order automorphisms on contragredient lie superalgebras abstract we add combinatorial data to the dynkin diagrams to classify all finite order automorphisms on contragredient lie superalgebras and study their invariant subalgebras

fluctuations of particle systems determined by schur generating functions abstract we develop a new toolbox for the analysis of the global behavior of stochastic discrete particle systems we introduce and study the notion of the schur generating function of a random discrete configuration our main result provides a central limit theorem clt for such a configuration given certain conditions on the schur generating function as applications of this approach we prove clt s for several probabilistic models coming from asymptotic representation theory and statistical physics including random lozenge and domino tilings non intersecting random walks decompositions of tensor products of representations of unitary groups

universal distributions for growth processes in 1 1 dimensions and random matrices we develop a scaling theory for kardar parisi zhang growth in one dimension by a detailed study of the polynuclear growth model in particular we identify three universal distributions for shape fluctuations and their dependence on the macroscopic shape these distribution functions are computed using the partition function of gaussian random matrices in a cosine potential

satake diagrams of affine kac moody algebras satake diagrams of affine kac moody algebras untwisted and twisted are obtained from their dynkin diagrams these diagrams give a classification of restricted root systems associated with these algebras in the case of simple lie algebras these root systems and satake diagrams correspond to symmetric spaces which have recently found many physical applications in quantum integrable systems quantum transport problems random matrix theories etc we hope these types of root systems may have similar applications in theoretical physics in future and may correspond to symmetric spaces analogue of affine kac moody algebras if they exist

asymptotics of plancherel measures for symmetric groups 1 1 plancherel measures given a finite group g by the corresponding plancherel measure we mean the probability measure on the set g of irreducible representations of g which assigns to a representation g the weight dim g for the symmetric group s n the set s n is the set of partitions of the number n which we shall identify with young diagrams with n squares throughout this paper the plancherel measure on partitions arises naturally in representation theoretic combinatorial and probabilistic problems for example the plancherel distribution of the first part of a partition coincides with the distribution of the longest increasing subsequence of a uniformly distributed random permutation 31 we denote the plancherel measure on partitions of n by mn

universal singularity at the closure of a gap in a random matrix theory we consider a hamiltonian h h 0 v in which h 0 is a given non random hermitian matrix and v is an n times n hermitian random matrix with a gaussian probability distribution we had shown before that dyson s universality of the short range correlations between energy levels holds at generic points of the spectrum independently of h 0 we consider here the case in which the spectrum of h 0 is such that there is a gap in the average density of eigenvalues of h which is thus split into two pieces when the spectrum of h 0 is tuned so that the gap closes a new class of universality appears for the energy correlations in the vicinity of this singular point