extensions of the method of poles for code construction the method of poles is a method introduced by franaszek 1969 for constructing a rate 1 1 finite state code from k ary data into a constrained channel of finite type whose capacity is strictly greater than log k the method is based on the computation of a set of states called poles with each pole is associated a set of paths going from this pole to others each set verifies an entropy condition the code produced by the method of poles has a sliding block decoder if each set of paths satisfies moreover an optimization condition based on the sum of the path lengths of the set we give a new optimization condition which guarantees the sliding block window decoding property and has a lower computational complexity than the previous one we also extend the method of poles to the more general case of sofic constrained channels

subdivision based mixed methods for isogeometric analysis of linear and nonlinear nearly incompressible materials this paper addresses the use of isogeometric analysis to solve solid mechanics problems involving nearly incompressible materials the present work is focused on extension of two field mixed variational formulations in both small and large strains to isogeometric analysis inf sup stable displacement pressure combinations for mixed formulations are developed based on the subdivision property of nurbs stability and convergence properties of the proposed displacement pressure combinations are illustrated by computing numerical inf sup constants and error norms the performance of the proposed formulations is assessed by studying several benchmark examples involving nearly incompressible and incompressible elastic and elasto plastic materials in both small and large strain regime

a locking free fem for cavitation computation in nearly incompressible nonlinear elasticity abstract a reduced selective integration finite element method coupled with a gradient flow method is introduced for the cavitation computation in nearly incompressible nonlinear elasticity numerical experiments show that for the iso parametric biquadratic finite element approximation of the displacement field the method is locking free and efficient for the nearly incompressible cavitation computation and has the same optimal convergence rates as in the compressible case for the elastic energy as well as the deformation and stress field if and only if the reduced integration is applied to the bulk energy term using no more than 2 gaussian quadrature nodes in each dimension

an efficient isogeometric solid shell formulation for geometrically nonlinear analysis of elastic shells abstract in this work an isogeometric solid shell model for geometrically nonlinear analyses is proposed it is based on a linear interpolation through the thickness and a nurbs interpolation on the middle surface of the shell for both the geometry and the displacement field the green lagrange strains are linearized along the thickness direction and a modified generalized constitutive matrix is adopted to easily eliminate thickness locking without introducing any additional unknowns and to model multi layered composite shells reduced integration schemes which take into account the high continuity of the shape functions are investigated to avoid interpolation locking and to increase the computational efficiency the relaxation of the constitutive equations at each integration point is adopted in the iterative scheme in order to reconstruct the equilibrium path using large steps and a low number of iterations even for very slender structures this strategy makes it possible to minimize the number of stiffness matrix evaluations and decompositions and it turns out to be particularly convenient in isogeometric analyses

reduced integration at superconvergent points in isogeometric analysis abstract we propose a new reduced integration rule for isogeometric analysis iga based on the concept of variational collocation it has been recently shown that if a discrete space is constructed by smooth and pointwise non negative basis functions there exists a set of points named cauchy galerkin cg points such that collocation performed at these points can reproduce the galerkin solution of various boundary value problems exactly since cg points are not known a priori estimates are necessary in practice and can be found based on superconvergence theory in this contribution we explore the use of estimated cg points i e superconvergent points as numerical quadrature points to obtain an efficient and stable reduced quadrature rule in iga we use the weighted residual formulation as basis for our new quadrature rule so that the proposed approach can be considered intermediate between the standard accurately integrated galerkin variational formulation and the direct evaluation of the strong form in collocation approaches the performance of the method is demonstrated by several examples for odd degrees of discretization we obtain spatial convergence rates and accuracy very close to those of accurately integrated standard galerkin with a quadrature rule of two points per parametric direction independently of the degree

on the maximal displacement of subcritical branching random walks we study the maximal displacement of a one dimensional subcritical branching random walk initiated by a single particle at the origin for each n in mathbb n let m n be the rightmost position reached by the branching random walk up to generation n under the assumption that the offspring distribution has a finite third moment and the jump distribution has mean zero and a finite probability generating function we show that there exists rho 1 such that the function begin aligned g c n rho cn p m n ge cn quad hbox for each c 0 hbox and n in mathbb n end aligned satisfies the following properties there exist 0 underline delta le overline delta infty such that if c underline delta then begin aligned 0 liminf n rightarrow infty g c n le limsup n rightarrow infty g c n le 1 end aligned while if c overline delta then begin aligned lim n rightarrow infty g c n 0 end aligned moreover if the jump distribution has a finite right range r then overline delta r if furthermore the jump distribution is nearly right continuous then there exists kappa in 0 1 such that lim n rightarrow infty g c n kappa for all c underline delta we also show that the tail distribution of m sup n ge 0 m n namely the rightmost position ever reached by the branching random walk has a similar exponential decay without the cutoff at underline delta finally by duality these results imply that the maximal displacement of supercritical branching random walks conditional on extinction has a similar tail behavior

geometrically non linear enhanced strain mixed methods and the method of incompatible modes a class of assumed strain mixed finite element methods for fully non linear problems in solid mechanics is presented which when restricted to geometrically linear problems encompasses the classical method of incompatible modes as a particular case the method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part formulated in the context of a three field variational formulation the resulting class of mixed methods provides a possible extension to the non linear regime of well known incompatible mode formulations in addition this class of methods includes non linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements the good performance of the proposed methodology is illustrated in a number of simulations including 2 d 3 d and axisymmetric finite deformation problems in elasticity and elastoplasticity remarkably these methods appear to be specially well suited for problems involving localization of the deformation as illustrated in several numerical examples

explicit isogeometric collocation for the dynamics of three dimensional beams undergoing finite motions abstract we initiate the study of three dimensional shear deformable geometrically exact beam dynamics through explicit isogeometric collocation methods the formulation we propose is based on a natural combination of the chosen finite rotations representation with an explicit geometrically consistent lie group time integrator we focus on extending the integration scheme originally proposed for rigid body dynamics to our nonlinear initial boundary value problem where special attention is required by neumann boundary conditions the overall formulation is simple and only relies on a geometrically consistent procedure to compute the internal forces once control angular and linear accelerations of the beam cross sections are obtained from the previous time step the capabilities of the method are shown through numerical applications involving very large displacements and rotations and different boundary conditions

a simple algorithm for obtaining nearly optimal quadrature rules for nurbs based isogeometric analysis we develop new quadrature rules for isogeometric analysis based on the solution of a local nonlinear problem a simple and robust algorithm is developed to determine the rules which are exact for important b spline spaces of uniform and geometrically stretched knot spacings we consider both periodic and open knot vector configurations and illustrate the efficiency of the rules on selected boundary value problems we find that the rules are almost optimally efficient but much easier to obtain than optimal rules which require the solution of global nonlinear problems that are often ill posed

partial tensor decomposition for decoupling isogeometric galerkin discretizations abstract system matrix assembly for isogeometric i e spline based discretizations of partial differential equations is more challenging than for classical finite elements due to the increased polynomial degrees and the larger and hence more overlapping supports of the basis functions the global tensor product structure of the discrete spaces employed in isogeometric analysis can be exploited to accelerate the computations using sum factorization precomputed look up tables and tensor decomposition we generalize the third approach by considering partial tensor decompositions we show that the resulting new method preserves the global discretization error and that its computational complexity compares favorably to the existing approaches moreover the numerical realization simplifies considerably since it relies on standard techniques from numerical linear algebra

optimal and reduced quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis abstract we continue the study initiated in hughes et al 2010 in search of optimal quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis these rules are optimal in the sense that there exists no other quadrature rule that can exactly integrate the elements of the given spline space with fewer quadrature points we extend the algorithm presented in hughes et al 2010 with an improved starting guess which combined with arbitrary precision arithmetic results in the practical computation of quadrature rules for univariate non uniform splines up to any precision explicit constructions are provided in sixteen digits of accuracy for some of the most commonly used uniform spline spaces defined by open knot vectors we study the efficacy of the proposed rules in the context of full and reduced quadrature applied to two and three dimensional diffusion reaction problems using tensor product and hierarchically refined splines and prove a theorem rigorously establishing the stability and accuracy of the reduced rules

hyperbolic branching brownian motion hyperbolic branching brownian motion is a branching diffusion process in which individual particles follow independent brownian paths in the hyperbolic plane 2 and undergo binary fission s at rate 0 it is shown that there is a phase transition in for 1 8 the number of particles in any compact region of 2 is eventually 0 w p 1 but for 1 8 the number of particles in any open set grows to w p 1 in the subcritical case 1 8 the set of all limit points in 2 the boundary circle at of particle trails is a cantor set while in the supercritical case 1 8 the set has full lebesgue measure for 1 8 it is shown that w p 1 the hausdorff dimension of is 1 1 8 2

sofic systems and encoding data techniques of symbolic dynamics are applied to prove the existence of codes suitable for certain input restricted channels this generalizes the earlier work of adler coppersmith and hassner on the same problem

selective and reduced numerical integrations for nurbs based isogeometric analysis we propose a new approach to construct selective and reduced integration rules for isogeometric analysis based on nurbs elements the notion of an approximation space that approximates the target space is introduced we explore the use of various approximation spaces associated with optimal patch wise numerical quadratures that exactly integrate the polynomials in approximation spaces with the minimum number of quadrature points patch rules exploit the higher continuity of spline basis functions the tendency of smooth spline functions to exhibit numerical locking in nearly incompressible problems when using a full gauss legendre quadrature is alleviated with selective or reduced integration stability and accuracy of the schemes are examined analyzing the discrete spectrum in a generalized eigenvalue problem we propose a local algorithm which is robust and computationally efficient to compute element by element the quadrature points and weights in patch rules the performance of the methods is assessed on several numerical examples in two dimensional elasticity and reissner mindlin shell structures

state splitting for variable length graphs corresp the state splitting algorithm of adler coppersmith and hassner for graphs with edges of fixed length is extended to graphs with edges of variable lengths this has the potential to improve modulation code construction techniques although the ideas of state splitting come from dynamical systems completely graph theoretic terms are used

reduced bezier element quadrature rules for quadratic and cubic splines in isogeometric analysis abstract we explore the use of various element based reduced quadrature strategies for bivariate and trivariate quadratic and cubic spline elements used in isogeometric analysis the rules studied encompass tensor product gauss and gauss lobatto rules and certain so called monomial rules that do no possess a tensor product structure the objective of the study is to determine quadrature strategies which enjoy the same accuracy and stability behavior as full gauss quadrature but with significantly fewer quadrature points several cases emerge that satisfy this objective and also demonstrate superior efficiency compared with standard c 0 continuous finite elements of the same order

convergence estimates for a plane elasticity problem solved by the galerkin boundary integral formulation with nurbs abstract a classical mixed boundary value problem of linear elasticity in two dimensions in the galerkin boundary integral formulation is considered we prove a priori error estimates of the solution to this problem by the isogeometric adaptive method using nurbs the estimates include approximation of the boundary of the domain

branching brownian motion seen from its tip it has been conjectured since the work of lalley and sellke ann probab 15 1052 1061 1987 that branching brownian motion seen from its tip e g from its rightmost particle converges to an invariant point process very recently it emerged that this can be proved in several different ways see e g brunet and derrida a branching random walk seen from the tip 2010 poissonian statistics in the extremal process of branching brownian motion 2010 arguin et al the extremal process of branching brownian motion 2011 the structure of this extremal point process turns out to be a poisson point process with exponential intensity in which each atom has been decorated by an independent copy of an auxiliary point process the main goal of the present work is to give a complete description of the limit object via an explicit construction of this decoration point process another proof and description has been obtained independently by arguin et al the extremal process of branching brownian motion 2011

isogeometric collocation using analysis suitable t splines of arbitrary degree abstract this paper deals with the use of analysis suitable t splines of arbitrary degree in combination with isogeometric collocation methods for the solution of second and fourth order boundary value problems in fact analysis suitable t splines appear to be a particularly efficient locally refinable basis for isogeometric collocation able to conserve the cost of only one point evaluation per degree of freedom typical of standard nurbs based isogeometric collocation furthermore t splines allow to easily create highly non uniform meshes without introducing elements with high aspect ratios this makes it possible to avoid the numerical instabilities that may arise in the case of problems characterized by reduced regularity when neumann boundary conditions are imposed in strong form and elements with high aspect ratio are used the local refinement properties of t splines can be also successfully exploited to approximate problems where point loads are applied finally several numerical tests are herein presented in order to confirm all the above mentioned features as well as the good overall convergence properties of the combination of isogeometric collocation and analysis suitable t splines

efficient isogeometric nurbs based solid shell elements mixed formulation and b method abstract in this work solid shell nurbs elements are developed in order to address static problems of slender structures under small perturbations a single layer of elements is considered through the thickness of the shell and the degree of approximation in that direction is chosen to be equal to two a full 3d constitutive relation is assumed the objective is to obtain highly accurate low degree elements to be used in coarse meshes in order to do that we propose a mixed method from which we derive a b projection to deal with locking the main idea is to modify the interpolation of the average stresses and strains through the thickness more precisely we develop two finite elements the first element which is based on the mixed method or equivalently on the b projection is extremely accurate but leads to a fully populated global stiffness matrix to improve the efficiency the second element uses a local least squares type procedure to define a new b projection leading to a sparse global stiffness matrix the quality and efficiency of the methods are assessed through several usual test cases and by comparison with other published techniques

genealogy of extremal particles of branching brownian motion branching brownian motion describes a system of particles that diffuse in space and split into offspring according to a certain random mechanism by virtue of the groundbreaking work by m bramson on the convergence of solutions of the fisher kpp equation to traveling waves the law of the rightmost particle in the limit of large times is rather well understood in this work we address the full statistics of the extremal particles first second third largest etc in particular we prove that in the large t limit such particles descend with overwhelming probability from ancestors having split either within a distance of order 1 from time 0 or within a distance of order 1 from time t the approach relies on characterizing up to a certain level of precision the paths of the extremal particles as a byproduct a heuristic picture of branching brownian motion at the edge emerges which sheds light on the still unknown limiting extremal process 2011 wiley periodicals inc

mixed stress displacement isogeometric collocation for nearly incompressible elasticity and elastoplasticity abstract we propose a mixed stress displacement isogeometric collocation method for nearly incompressible elastic materials and for materials exhibiting von mises plasticity the discretization is based on isogeometric analysis iga with non uniform rational b splines nurbs as basis functions as compared to conventional iga galerkin formulations isogeometric collocation methods offer a high potential of computational cost reduction for higher order discretizations as they eliminate the need for quadrature in the proposed mixed formulation both stress and displacement fields are approximated as primary variables with the aim of treating volumetric locking and instability issues which occur in displacement based isogeometric collocation for nearly incompressible elasticity and von mises plasticity the performance of the proposed approach is demonstrated by several numerical examples

improved numerical integration for locking treatment in isogeometric structural elements part i beams a general mathematical framework is proposed in this paper to define new quadrature rules in the context of bb spline nurbs based isogeometric analysis high order continuity across the elements within a patch turned out to have higher accuracy than c0c0 finite elements as well as a better time efficiency unfortunately a maximum regularity accentuates the shear and membrane locking in thick structural elements the improved selective reduced integration schemes are given for uni dimensional beam problems with basis functions of order two and three and can be easily extended to higher orders the resulting bb spline nurbs finite elements are free from membrane and transverse shear locking moreover no zero energy modes are generated the performance of the approach is evaluated on the classical test of a cantilever beam subjected to a distributed moment and compared to lagrange under integrated finite elements

a note on the method of poles for code construction the method of poles is a method for constructing a rate 1 1 finite state code from k ary data into a constrained channel s where s is recognized by a given local automaton and s has capacity at least log k we characterize those automata to which the method of poles applies in the case where h s log k the code produced by the method of poles has a sliding block decoder we also give an upper bound on the window length of the decoder that applies when h s spl ges log k

collaborative design of fiber path and shape for complex composite shells based on isogeometric analysis abstract composite shells with complex geometry are widely used in aerospace structures due to the complexity of geometry and curvilinear fiber path the analysis and optimization based on finite element analysis fea for complex variable stiffness vs shells is extremely time consuming by comparing with fea isogeometric analysis iga exhibits higher prediction efficiency of buckling load in this work the formula of geometric stiffness matrix for complex vs shells is derived for the first time based on degenerated shell method using iga which is the basis of performing linear buckling analysis then a new variable curvature quasi linear function vcqlf to describe curvilinear fiber path is proposed which can further expand the design space of vs shells after that two frameworks for shape optimization of complex shells are put forward and then compared and it is found that the one based on loft function can provide representative control variables of shape and effectively reduces the number of design variables for complex shells finally a novel collaborative optimization framework of fiber path and shell shape using iga is established by comparison of traditional methods it is demonstrated that the proposed framework can greatly improve the efficiency of optimization and fully explore the buckling load of complex vs shells

the extremal process of branching brownian motion we prove that the extremal process of branching brownian motion in the limit of large times converges weakly to a cluster point process the limiting process is a randomly shifted poisson cluster process where the positions of the clusters is a poisson process with intensity measure with exponential density the law of the individual clusters is characterized as branching brownian motions conditioned to perform unusually large displacements and its existence is proved the proof combines three main ingredients first the results of bramson on the convergence of solutions of the kolmogorov petrovsky piscounov equation with general initial conditions to standing waves second the integral representations of such waves as first obtained by lalley and sellke in the case of heaviside initial conditions third a proper identification of the tail of the extremal process with an auxiliary process based on the work of chauvin and rouault which fully captures the large time asymptotics of the extremal process the analysis through the auxiliary process is a rigorous formulation of the cavity method developed in the study of mean field spin glasses

studies of refinement and continuity in isogeometric structural analysis we investigate the effects of smoothness of basis functions on solution accuracy within the isogeometric analysis framework we consider two simple one dimensional structural eigenvalue problems and two static shell boundary value problems modeled with trivariate nurbs solids we also develop a local refinement strategy that we utilize in one of the shell analyses we find that increased smoothness that is the k method leads to a significant increase in accuracy for the problems of structural vibrations over the classical c0c0 continuous p method whereas a judicious insertion of c0c0 continuous surfaces about singularities in a mesh otherwise generated by the k method usually outperforms a mesh in which all basis functions attain their maximum level of smoothness we conclude that the potential for the k method is high but smoothness is an issue that is not well understood due to the historical dominance of c0c0 continuous finite elements and therefore further studies are warranted

martingale convergence and the stopped branching random walk we discuss the construction of stopping lines in the branching random walk and thus the existence of a class of supermartingales indexed by sequences of stopping lines applying a method of lyons 1997 and lyons pemantle and peres 1995 concerning size biased branching trees we establish a relationship between stopping lines and certain stopping times consequently we develop conditions under which these supermartingales are also martingales further we prove a generalization of biggins martingale convergence theorem biggins 1977a within this context

an isogeometric method for linear nearly incompressible elasticity with local stress projection abstract in this paper we propose an isogeometric method for solving the linear nearly incompressible elasticity problem the method is similar to the b formulation where the volumetric strain is projected on a lower degree spline space in order to prevent volumetric locking in our method we adopt a local projection on a coarser mesh chosen in order to guarantee optimal convergence moreover the locality of the projector allows to maintain the sparsity of the stiffness matrix that is the efficiency of the method the analysis of the method is based on the inf sup stability of the associated mixed formulation via a macro element technique for spline functions the numerical tests confirm the theory of the method

dispersion optimized quadrature rules for isogeometric analysis modified inner products their dispersion properties and optimally blended schemes abstract this paper introduces optimally blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations to quantify the approximation errors when we modify the inner products we generalize the pythagorean eigenvalue theorem of strang and fix the proposed blended quadrature rules have advantages over alternative integration rules for isogeometric analysis on uniform and non uniform meshes as well as for different polynomial orders and continuity of the basis the optimally blended schemes improve the convergence rate of the method by two orders with respect to the fully integrated galerkin method the proposed technique increases the accuracy and robustness of isogeometric analysis for wave propagation problems

sliding block coding for input restricted channels work on coding arbitrary sequences into a constrained system of sequences called a sofic system is presented such systems model the input constraints for input restricted channels e g run length limits and spectral constraints for the magnetic recording channel in this context it is important that the code be noncatastrophic to ensure that the decoder has limited error propagation a constructive proof is given of the existence of finite state invertible noncatastrophic codes from arbitrary n ary sequences to a sofic system s at constant rate p q provided only that shannon s condition p q

the extremal process of critical points of the pure p spin spherical spin glass model recently sharp results concerning the critical points of the hamiltonian of the p spin spherical spin glass model have been obtained by means of moments computations in particular these moments computations allow for the evaluation of the leading term of the ground state i e of the global minimum in this paper we study the extremal point process of critical points that is the point process associated to all critical values in the vicinity of the ground state we show that the latter converges in distribution to a poisson point process of exponential intensity in particular we identify the correct centering of the ground state and prove the convergence in distribution of the centered minimum to a minus gumbel variable these results are identical to what one obtains for a sequence of i i d variables correctly normalized namely we show that the model is in the universality class of rem

optimal quadrature for univariate and tensor product splines abstract numerical integration is a core subroutine in many engineering applications including the finite element method fem isogeometric analysis is a fem technology that uses smooth b spline and nurbs basis functions traditionally gaussian quadrature was used for numerical integration but this yields suboptimal performance this is attributed to the fact that gaussian quadrature rules do not take inter element smoothness of the spline basis into account resulting in over integration the equations for exact quadrature are well known but prove notoriously hard to solve due to their nonlinear nature these generalized gauss rules were first introduced in hughes et al 2010 in the context of isogeometric analysis where newton iteration was utilized to study and tabulate several cases later homotopy continuation barto and calo 2015 was used as an alternative strategy for finding these rules in this paper we describe an algorithm to generalize on both of these techniques it is optimal in the sense that it will integrate a space of dimension n using no more than n 1 2 quadrature points the algorithm works on arbitrary nonuniform knot vectors of any polynomial degree and continuity and is demonstrated on polynomial orders up to 15 it extends to 2d and 3d integrals by tensor product

order reduction method for locking free isogeometric analysis of timoshenko beams the order reduction or method is proposed to provide an effective and efficient locking free formulation in the isogeometric analysis of plane curved timoshenko beams the shear and membrane strains are represented by the reduced order b spline basis functions and the locking phenomenon can be prevented the modified strains are equivalent to the original ones in the sense of the least square approximation different order reduction strategies are discussed and it is suggested to use multiple sets of lower order b spline basis functions to improve the accuracy the theoretical analysis of the formulation and the computational cost is carried out to assess the efficiency of the or method the performance of the proposed method is tested by the straight beam curved beams with constant and varied curvatures problems and compared with other methods such as the selective and reduced integration method the local discrete shear gap method and the local b method without strain smoothing the numerical results show that the proposed method is competitive which leads to an efficient locking free formulation

isogeometric thickness stretchable shell efficient formulation for nonlinear dynamic problems an isogeometric shell element with through thickness stretch is introduced and applied to quasi static and dynamic problems the shell element supports full three dimensional constitutive laws ie the plane stress assumption is not required an updated lagrangian rate formulation is adopted and biquadratic spline based interpolation functions are used for in plane interpolation the concept of fiber mass scaling is proposed to lower the highest eigenfrequencies to improve the performance of the formulation clamped and unclamped knot vectors are compared and the advantages of using unclamped knot vectors are demonstrated the shell element is validated using several benchmark tests which indicate good performance of the proposed formulation

a branching random walk seen from the tip we show that all the time dependent statistical properties of the rightmost points of a branching brownian motion can be extracted from the traveling wave solutions of the fisher kpp equation the distribution of all the distances between the rightmost points has a long time limit which can be understood as the delay of the fisher kpp traveling waves when the initial condition is modified the limiting measure exhibits the surprising property of superposability the statistical properties of the distances between the rightmost points of the union of two realizations of the branching brownian motion shifted by arbitrary amounts are the same as those of a single realization we discuss the extension of our results to more general branching random walks

a simplified kirchhoff love large deformation model for elastic shells and its effective isogeometric formulation abstract isogeometric kirchhoff love elements have received an increasing attention in geometrically nonlinear analysis of elastic shells nevertheless some difficulties still remain among the others the highly nonlinear expression of the strain measure which leads to a complicated and costly computation of the discrete operators and the existence of locking which prevents the use of coarse meshes for slender shells and low order nurbs are key issues that need to be addressed in this work exploiting the hypothesis of small membrane strains we propose a simplified strain measure with a third order polynomial dependence on the displacement variables which allows an efficient evaluation of the discrete quantities numerical results show practically no difference to the original model even for very large displacements and composite structures patch wise reduced integrations are then investigated to deal with membrane locking in large deformation problems an optimal integration scheme for third order c 2 nurbs in terms of accuracy and efficiency is identified finally the recently proposed newton method with mixed integration points is used for the solution of the discrete nonlinear equations with a great reduction of the iterative burden with respect to the standard newton scheme

the method of poles a coding method for constrained channels a method for solving coding problems involving channels restricted by finite state constraints is presented the method was introduced by p a franaszek 1969 and is based on the computation of a set of principal states it is proved that state independent decoding is guaranteed the main result is that the transducer constructed using the method is a local automaton in its output the method is also related to recent work in symbolic dynamics by r l adler 1987 b marcus 1985 and others typical applications are coding methods for magnetic storage

spatial epidemics critical behavior in one dimension in the simple mean field sis and sir epidemic models infection is transmitted from infectious to susceptible members of a finite population by independent p coin tosses spatial variants of these models are considered in which finite populations of size n are situated at the sites of a lattice and infectious contacts are limited to individuals at neighboring sites scaling laws for these models are given when the infection parameter p is such that the epidemics are critical it is shown that in all cases there is a critical threshold for the numbers initially infected below the threshold the epidemic evolves in essentially the same manner as its branching envelope but at the threshold evolves like a branching process with a size dependent drift the corresponding scaling limits are super brownian motions and dawson watanabe processes with killing respectively

a conditional limit theorem for the frontier of a branching brownian motion on demontre un theoreme limite faible qui relie le comportement pour une grande duree du maximum d un mouvement brownien ramifie a la valeur limite d une certaine martingale associee

monomial cubature rules since stroud a compilation a bibliography of references to cubature rules which have appeared since the publication of stroud s book 1971 is presented the standard regions that are treated in this paper are the n cube the n simplex the n sphere and the entire space

on the maximal displacement of critical branching random walk we consider a branching random walk initiated by a single particle at location 0 in which particles alternately reproduce according to the law of a galton watson process and disperse according to the law of a driftless random walk on the integers when the offspring distribution has mean 1 the branching process is critical and therefore dies out with probability 1 we prove that if the particle jump distribution has mean zero positive finite variance eta 2 and finite 4 varepsilon moment and if the offspring distribution has positive variance sigma 2 and finite third moment then the distribution of the rightmost position m reached by a particle of the branching random walk satisfies p m ge x sim 6 eta 2 sigma 2 x 2 as x rightarrow infty we also prove a conditional limit theorem for the distribution of the rightmost particle location at time n given that the process survives for n generations

hourglass control in linear and nonlinear problems abstract mesh stabilization techniques for controlling the hourglass modes in under integrated hexahedral and quadrilateral elements are described it is shown that the orthogonal hourglass techniques previously developed can be obtained from simple requirements that insure the consistency of the finite element equations in the sense that the gradients of linear fields are evaluated correctly it is also shown that this leads to an hourglass control that satisfies the patch test the nature of the parameters which relate the generalized stresses and strains for controlling hourglass modes is examined by means of a mixed variational principle and some guidelines for their selection are discussed finally effective means of implementing these hourglass procedure in computer codes are described applications to both the laplace equation and the equations of solid mechanics in 2 and 3 dimensions are considered

codes circulaires automates locaux et entropie abstract the theory of codes and finite automata is applied to prove the existence of codes suitable for coding arbitrary sequences into a constrained system of sequences called system of finite type the techniques are different from those used by adler coppersmith hassner and marcus in earlier work on the same problem

fast formation of isogeometric galerkin matrices by weighted quadrature abstract in this paper we propose an algorithm for the formation of matrices of isogeometric galerkin methods the algorithm is based on three ideas the first is that we perform the external loop over the rows of the matrix the second is that we calculate the row entries by weighted quadrature the third is that we exploit the local tensor product structure of the basis functions while all ingredients have a fundamental role for computational efficiency the major conceptual change of paradigm with respect to the standard implementation is the idea of using weighted quadrature the test function is incorporated in the integration weight while the trial function the geometry parametrization and the pdes coefficients form the integrand function this approach is very effective in reducing the computational cost while maintaining the optimal order of approximation of the method analysis of the cost is confirmed by numerical testing where we show that for p large enough the time required by the floating point operations is less than the time spent in unavoidable memory operations the sparse matrix allocation and memory write the proposed algorithm allows significant time saving when assembling isogeometric galerkin matrices for all the degrees of the test spline space and paves the way for a use of high degree k refinement in isogeometric analysis

an unsteady 3d isogeometrical boundary element analysis applied to nonlinear gravity waves abstract in this paper we describe a three dimensional isogeometric analysis based on the boundary element method iga bem in the time domain we show the capabilities and accuracy of the method for the simulation of non linear gravity waves the flow is assumed to be inviscid and irrotational and this leads to a mixed boundary value problem governed by the laplace s equation the boundary integral equation is solved at each time step and the time marching scheme is performed with a fourth order runge kutta method the hydrodynamic force is calculated with an auxiliary boundary equation in the simulations the analysis suitable t spline and nurbs basis are used to approximate both the geometry and the bem variables in the context of the bezier extraction framework the main advantages of this approach are 1 the control of the continuity and smoothness of the t spline and nurbs basis which makes the model numerically stable without the need of artificial smooth techniques 2 the high geometrical approximation of the non rational splines 3 the refinement capabilities without affecting the geometry and bem variables and 4 and the direct integration with computer aided geometrical design tools some numerical benchmark examples are analysed to demonstrate the accuracy and the stability of the method in addition we report simulations of waves generated by the movement of submerged foils which have implications in some wave generator systems installed in surf parks

locking free isogeometric collocation formulation for three dimensional geometrically exact shear deformable beams with arbitrary initial curvature abstract this paper presents a displacement based and a mixed isogeometric collocation formulations for three dimensional geometrically exact shear deformable beams with arbitrarily curved initial geometry strong forms of both formulations are consistently linearized with respect to the underlying configuration manifold high efficiency is achieved by using a geometrically consistent kinematic model in which incremental rotations are parametrized through the spatial rotation vector several numerical tests demonstrate that the proposed mixed formulation is totally locking free for any choice of approximation degree mixed formulation also exhibits higher robustness in the incremental iterative algorithm elimination of shear locking and low computational cost assured by the combination of isogeometric collocation with a consistent kinematic model result in a very efficient accurate and geometrically powerful method able to handle geometrically complex beam problems

a preconditioning strategy for linear systems arising from nonsymmetric schemes in isogeometric analysis abstract in the context of isogeometric analysis we consider two discretization approaches that make the resulting stiffness matrix nonsymmetric even if the differential operator is self adjoint these are the collocation method and the recently developed weighted quadrature for the galerkin discretization in this paper we are interested in the solution of the linear systems arising from the discretization of the poisson problem using one of these approaches in sangalli and tani 2016 a well established direct solver for linear systems with tensor structure was used as a preconditioner in the context of galerkin isogeometric analysis yielding promising results in particular this preconditioner is robust with respect to the mesh size h and the spline degree p in the present work we discuss how a similar approach can be applied to the considered nonsymmetric linear systems the efficiency of the proposed preconditioning strategy is assessed with numerical experiments on two dimensional and three dimensional problems

exponential and double exponential tails for maximum of two dimensional discrete gaussian free field we study the tail behavior for the maximum of discrete gaussian free field on a 2d box with dirichlet boundary condition after centering by its expectation we show that it exhibits an exponential decay for the right tail and a double exponential decay for the left tail in particular our result implies that the variance of the maximum is of order 1 improving an o log n bound by chatterjee chaos concentration and multiple valleys 2008 and confirming a folklore conjecture an important ingredient for our proof is a result of bramson and zeitouni commun pure appl math 2010 who proved the tightness of the centered maximum together with an evaluation of the expectation up to an additive constant

effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear deformable beams with varying curvature and torsion abstract we present a displacement based and a mixed isogeometric collocation iga c formulation for free form three dimensional shear deformable beams with high and rapidly varying curvature and torsion when such complex shapes are concerned the approach used to build the iga geometric model becomes relevant although iga c has been so far successfully applied to a wide range of problems the effects that different parameterization and knot placement techniques may have on the accuracy of collocation based formulations is still an unexplored field to fill this gap primal and mixed formulations are used combining two parameterization methods chord length and equally spaced with two knot placement techniques uniformly spaced and de boor with respect to the space varying frenet local frame we derive the strong form of the governing equations in a compact form through the definition of two matrix operators conveniently used to perform first and second order derivatives of the vector fields involved in the formulations this approach is very efficient and easy to implement within a collocation based scheme several challenging numerical experiments allow to test the different considered parameterizations and knot placement techniques revealing in particular that with the primal formulation an equally spaced parameterization is definitively the most recommended choice and it should always be used with an approximation degree of at least p 6 although some caution must be adopted when very high jacobians and small curvatures occur the same holds for the mixed formulation with the difference that p 4 is enough to yield accurate results

isogeometric collocation for the reissner mindlin shell problem abstract we present an isogeometric collocation formulation for the reissner mindlin shell problem after recalling the necessary basics on differential geometry and the shell governing equations we show that the standard approach of expressing the equilibrium equations in terms of the primal variables is not a suitable way for shells due to the complexity of the underlying equations we then propose an alternative approach based on a stepwise formulation and show its numerical implementation within an isogeometric collocation framework the formulation is tested successfully on a set of benchmark examples which comprise important aspects like locking and boundary layers these test show that locking effects can be conveniently avoided by using high polynomial degrees an accompanying study on the computational time also confirms that high polynomial degrees are preferable in terms of computational efficiency

gaussian quadrature rules for c1 quintic splines with uniform knot vectors abstract we provide explicit quadrature rules for spaces of c 1 quintic splines with uniform knot sequences over finite domains the quadrature nodes and weights are derived via an explicit recursion that avoids numerical solvers each rule is optimal that is requires the minimal number of nodes for a given function space for each of n subintervals generically only two nodes are required which reduces the evaluation cost by 2 3 when compared to the classical gaussian quadrature for polynomials over each knot span numerical experiments show fast convergence as n grows to the two third quadrature rule of hughes et al 2010 for infinite domains

efficient quadrature for nurbs based isogeometric analysis abstract we initiate the study of efficient quadrature rules for nurbs based isogeometric analysis a rule of thumb emerges the half point rule indicating that optimal rules involve a number of points roughly equal to half the number of degrees of freedom or equivalently half the number of basis functions of the space under consideration the half point rule is independent of the polynomial order of the basis efficient rules require taking into account the precise smoothness of basis functions across element boundaries several rules of practical interest are obtained and a numerical procedure for determining efficient rules is presented we compare the cost of quadrature for typical situations arising in structural mechanics and fluid dynamics the new rules represent improvements over those used previously in isogeometric analysis

an isogeometric formulation of the koiter s theory for buckling and initial post buckling analysis of composite shells abstract numerical formulations of the koiter theory allow the efficient prediction through a reduced model of the behavior of shell structures when failure is dominated by buckling in this work we propose an isogeometric version of the method based on a solid shell model a nurbs interpolation is employed on the middle surface of the shell to accurately describe the geometry and the high continuity typical of the displacement field in buckling problems and to directly link the cad model to the structural one a linear interpolation is then adopted through the thickness together with a modified generalized constitutive matrix which allows us to easily eliminate thickness locking and model multi layered composites reduced integration schemes which take into account the continuity of the shape functions are used to avoid interpolation locking and make the integration faster a mixed integration point strategy makes it possible to transform the displacement model into a mixed stress displacement one required by the koiter method to obtain accurate predictions without introducing stress interpolation functions the result is an efficient numerical tool for buckling and initial post buckling analysis of composite shells characterized by a low number of dofs and integration points and by a simple and quick construction of the reduced model

the genealogy of branching brownian motion with absorption we consider a system of particles which perform branching brownian motion with negative drift and are killed upon reaching zero in the near critical regime where the total population stays roughly constant with approximately n particles we show that the characteristic time scale for the evolution of this population is of order logn 3 in the sense that when time is measured in these units the scaled number of particles converges to a variant of neveu s continuous state branching process furthermore the genealogy of the particles is then governed by a coalescent process known as the bolthausen sznitman coalescent this validates the non rigorous predictions by brunet derrida muller and munier for a closely related model

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

b and f projection methods for nearly incompressible linear and non linear elasticity and plasticity using higher order nurbs elements abstract this paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of isogeometric analysis after reviewing some fundamentals of isogeometric analysis we investigate the use of higher order non uniform rational b splines nurbs within the b projection method the higher continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results a new non linear f projection method based on a modified minimum potential energy principle and inspired by the b method is proposed for the large deformation case it leads to a symmetric formulation for which the consistent linearized operator for fully non linear elasticity is derived and used in a newton raphson iterative procedure the performance of the methods is assessed on several numerical examples and results obtained are shown to compare favorably with other published techniques

codes and local constraints etude du probleme de l existance et de la construction de codes dont les elements des mots satisfont certaines contraintes concernant les sequences de lettres qu ils peuvent contenir l equivalence entre les notions de maximalite et de completude pour ces codes est etudiee

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

tightness for a family of recursion equations in this paper we study the tightness of solutions for a fam ily of recursive equations these equations arise naturally in the study of random walks on tree like structures examples include the maxi mal displacement of branching random walk in one dimension and the cover time of symmetric simple random walk on regular binary trees recursion equations associated with the distribution functions of these quantities have been used to establish weak laws of large numbers here we use these recursion equations to establish the tightness of the corre sponding sequences of distribution functions after appropriate centering we phrase our results in a fairly general context which we hope will fa cilitate their application in other settings

efficient mass and stiffness matrix assembly via weighted gaussian quadrature rules for b splines abstract calabro et al 2017 changed the paradigm of the mass and stiffness computation from the traditional element wise assembly to a row wise concept showing that the latter one offers integration that may be orders of magnitude faster considering a b spline basis function as a non negative measure each mass matrix row is integrated by its own quadrature rule with respect to that measure each rule is easy to compute as it leads to a linear system of equations however the quadrature rules are of the newton cotes type that is they require a number of quadrature points that is equal to the dimension of the spline space in this work we propose weighted quadrature rules of gaussian type which require the minimum number of quadrature points while guaranteeing exactness of integration with respect to the weight function the weighted gaussian rules arise as solutions of non linear systems of equations we derive rules for the mass and stiffness matrices for uniform c 1 quadratic and c 2 cubic isogeometric discretizations in each parameter direction our rules require locally only p 1 quadrature points p being the polynomial degree while the nodes cannot be reused for various weight functions as in calabro et al 2017 the computational cost of the mass and stiffness matrix assembly is comparable

simple a posteriori error estimators in adaptive isogeometric analysis in this article we propose two simple a posteriori error estimators for solving second order elliptic problems using adaptive isogeometric analysis the idea is based on a serendipity11according to wikipedia serendipity means a fortunate happenstance or pleasant surprise it was coined by horace walpole in 1754 one aspect of walpole s original definition of serendipity is the need for an individual to be sagacious enough to link together apparently innocuous facts in order to come to a valuable conclusion we feel that this applies for the present discovery but it is of course up to the readers to judge pairing of discrete approximation spaces s h p k m s h p 1 k 1 m where the space s h p 1 k 1 m is considered as an enrichment of the original basis of s h p k m by means of the k refinement a typical unique feature available in isogeometric analysis the space s h p 1 k 1 m is used to obtain a higher order accurate isogeometric finite element approximation and using this approximation we propose two simple a posteriori error estimators the proposed a posteriori error based adaptive h refinement methodology using lr b splines is tested on classical elliptic benchmark problems the numerical tests illustrate the optimal convergence rates obtained for the unknown as well as the effectiveness of the proposed error estimators

reduced integration and the shear flexible beam element the timoshenko beam element is studied in an investigation of shear locking in the development of c 0 continuous elements using shear flexible or penalty function type formulations a penalty type argument is used to degenerate thick elements to thin elements and the various approximations of the shear related energy terms act as different types of constraints depending on the formulation two types of constraints may emerge which are classified as true or spurious formulations that ensure only true constraints in the extreme penalty limit cases display superior performance in the thick element situation the argument is extended to a shallow curved timoshenko beam and another mechanism inplane locking arises if all energy terms corresponding to the membrane energy are exactly integrated