buckling of arbitrary quadrilateral anisotropic plates the problem of buckling of arbitrary quadrilateral anisotropic plates with different boundary conditions under combined in plane loading is considered a rayleigh ritz method combined with a variational formulation and a first order transverse shear deformation theory is used the ritz functions consist of polynomials which include circulation functions that impose various boundary conditions numerical results are obtained for isotropic orthotropic and anisotropic plates with skewed geometries and are compared with existing results that use series solutions and with results generated from finite element simulations

eigenvalue analysis of doubly connected plates with different configurations this paper deals with the vibration and buckling analyses of the first order shear deformable rhombic and square plates using a p type variational method the formulation includes rotary inertia and transverse shear terms the full plate is modeled with a single domain defined by a set of geometric points in the plane of the plate square and rectangular plates with a circular hole at the center are treated as the numerical example for the doubly connected plate and are modeled using one quarter of the geometry and only two elements the symmetry about x and y axes with regards to load and boundary conditions are exploited buckling coefficients and natural frequencies are calculated and compared with results from the published sources and the finite element method

uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory we consider asymptotics for orthogonal polynomials with respect to varying exponential weights wn x dx e nv x dx on the line as n the potentials v are assumed to be real analytic with sufficient growth at infinity the principle results concern plancherel rotach type asymptotics for the orthogonal polynomials down to the axis using these asymptotics we then prove universality for a variety of statistical quantities arising in the theory of random matrix models some of which have been considered recently in 31 and also in 4 an additional application concerns the asymptotics of the recurrence coefficients and leading coefficients for the orthonormal polynomials see also 4 the orthogonal polynomial problem is formulated as a riemann hilbert problem following 19 20 the riemann hilbert problem is analyzed in turn using the steepest descent method introduced in 12 and further developed in 11 13 a critical role in our method is played by the equilibrium measure d v for v as analyzed in 8 1999 john wiley sons inc

dsc ritz method for the free vibration analysis of mindlin plates this paper introduces a novel method for the free vibration analysis of mindlin plates the proposed method takes the advantage of both the local bases of the discrete singular convolution dsc algorithm and the pb 2 ritz boundary functions to arrive at a new approach called dsc ritz method two basis functions are constructed by using dsc delta sequence kernels of the positive type the energy functional of the mindlin plate is represented by the newly constructed basis functions and is minimized under the ritz variational principle extensive numerical experiments are considered by different combinations of boundary conditions of mindlin plates of rectangular and triangular shapes the performance of the proposed method is carefully validated by convergence analysis the frequency parameters agree very well with those in the literature numerical experiments indicate that the proposed dsc ritz method is a very promising new method for vibration analysis of mindlin plates copyright 2004 john wiley sons ltd

formulation of mindlin engesser model for stiffened plate vibration in this paper a mindlin engesser model is developed for the vibration analysis of moderately thick plates with arbitrarily oriented stiffeners the theoretical derivation incorporates the mindlin theory to account for the effects of transverse shear deformation and rotary inertia of plates and the engesser theory to account for the shear deformation of stiffeners with the inclusion of torsion effect in the method of solution the resulting energy functionals are minimized using the ritz procedure with a set of admissible two dimensional functions expressed in the form of simple polynomials the key kinematic feature of these shape functions is that they are boundary oriented and no boundary losses are introduced as in discretization methods with the aim of demonstrating the applicability and versatility of the method numerical examples including plates of various shapes with arbitrarily oriented stiffeners are presented several findings and conclusions regarding the method have been highlighted and discussed

periodic tasep with general initial conditions we consider the one dimensional totally asymmetric simple exclusion process with an arbitrary initial condition in a spatially periodic domain and obtain explicit formulas for the multi point distributions in the space time plane the formulas are given in terms of an integral involving a fredholm determinant we then evaluate the large time large period limit in the relaxation time scale which is the scale such that the system size starts to affect the height fluctuations the limit is obtained assuming certain conditions on the initial condition which we show that the step flat and step flat initial conditions satisfy hence we obtain the limit theorem for these three initial conditions in the periodic model extending the previous work on the step initial condition we also consider uniform random and uniform step random initial conditions

modeling of biological population problems using the element free kp ritz method a degenerate parabolic equation arising in the spatial diffusion of biological population is analyzed using the mesh free kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes effectiveness of the mesh free kp ritz method for biological population model is investigated by numerical examples in this paper the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

painleve equations nonlinear special functions the six painleve equations pi pvi were first discovered about a hundred years ago by painleve and his colleagues in an investigation of nonlinear second order ordinary differential equations recently there has been considerable interest in the painleve equations primarily due to the fact that they arise as reductions of the soliton equations which are solvable by inverse scattering consequently the painleve equations can be regarded as completely integrable equations and possess solutions which can be expressed in terms of solutions of linear integral equations despite being nonlinear equations although first discovered from strictly mathematical considerations the painleve equations have arisen in a variety of important physical applications including statistical mechanics plasma physics nonlinear waves quantum gravity quantum field theory general relativity nonlinear optics and fibre optics the painleve equations may be thought of a nonlinear analogues of the classical special functions they possess hierarchies of rational solutions and one parameter families of solutions expressible in terms of the classical special functions for special values of the parameters further the painleve equations admit symmetries under affine weyl groups which are related to the associated backlund transformations in this paper i discuss some of the remarkable properties which the painleve equations possess including connection formulae backlund transformations associated discrete equations and hierarchies of exact solutions in particular the second painleve equation pii is used to illustrate these properties and some of the applications of pii are also discussed

large deviations for increasing sequences on the plane we prove a large deviation principle with explicit rate functions for the length of the longest increasing sequence among poisson points on the plane the rate function for lower tail deviations is derived from a 1977 result of logan and shepp about young diagrams of random permutations for the upper tail we use a coupling with hammersley s particle process and convex analytic techniques along the way we obtain the rate function for the lower tail of a tagged particle in a totally asymmetric hammersley s process

stable distributions in stochastic fragmentation we investigate a class of stochastic fragmentation processes involving stable and unstable fragments we solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small size tail furthermore the entire range of acceptable values of decay exponent consistent with length conservation can be realized we show that the stochastic fragmentation process is non self averaging as moments exhibit significant sample to sample fluctuations additionally we find that the distributions of the moments and of extremal characteristics possess an infinite set of progressively weaker singularities

twenty five years after kls a celebration of non equilibrium statistical mechanics when lenz proposed a simple model for phase transitions in magnetism he couldn t have imagined that the ising model was to become a jewel in field of equilibrium statistical mechanics its role spans the spectrum from a good pedagogical example to a universality class in critical phenomena a quarter century ago katz lebowitz and spohn found a similar treasure by introducing a seemingly trivial modification to the ising lattice gas they took it into the vast realms of non equilibrium statistical mechanics an abundant variety of unexpected behavior emerged and caught many of us by surprise we present a brief review of some of the new insights garnered and some of the outstanding puzzles as well as speculate on the model s role in the future of non equilibrium statistical physics

buckling of arbitrary quadrilateral plates with intermediate supports using the galerkin method abstract a numerical method is developed for the stability analysis of arbitrary quadrilateral shaped elastic plates with internal supports the procedure uses the galerkin method in conjunction with the natural coordinates of the plate as a basis for the analysis of general plates the method is programmed and several numerical exaples are presented to illustrate the scope and efficacy of the procedure local plate buckling loads of skew rhombic trapezoidal and rectangular plates with intermediate line supports are obtained and where possible the results are compared with known solutions in the literature

limiting curves for i i d records we consider the concentration of measure for n i i d two dimensional random variables under the conditioning that they form a record under mild conditions we show that all random variables tend to concentrate as n rightarrow infty around limiting curves which are the solutions of an appropriate variational problem we also show that the same phenomenon occurs without the records conditioning for the longest increasing subsequence in the sample

the asymptotics of monotone subsequences of involutions we compute the limiting distributions of the lengths of the longest monotone subsequences of random signed involutions with or without conditions on the number of fixed points and negated points as the sizes of the involutions tend to infinity the resulting distributions are depending on the number of fixed points 1 the tracy widom distributions for the largest eigenvalues of random goe gue gse matrices 2 the normal distribution or 3 new classes of distributions which interpolate between pairs of the tracy widom distributions we also consider the second rows of the corresponding young diagrams in each case the convergence of moments is also shown the proof is based on the algebraic work of j baik and e rains in 7 which establishes a connection between the statistics of random involutions and a family of orthogonal polynomials and an asymptotic analysis of the orthogonal polynomials which is obtained by extending the riemann hilbert analysis for the orthogonal polynomials by p deift k johansson and baik in 3

discrete painleve equations and their appearance in quantum gravity we discuss an algorithmic approach for both deriving discrete analogues of painleve equations as well as using such equations to characterize similarity reductions of spatially discrete integrable evolution equations as a concrete example we show that a discrete analogue of painleve i can be used to characterize similarity solutions of the kac moerbeke equation it turns out that these similarity solutions also satisfy a special case of painleve iv equation in addition we discuss a methodology for obtaining the relevant continuous limits not only at the level of equations but also at the level of solutions as an example we use the wkb method in the presence of two turning points of the third order to parametrize at the continuous limit the solution of painleve i in terms of the solution of discrete painleve i finally we show that these results are useful for investigating the partition function of the matrix model in 2d quantum gravity associated with the measure exp t1z2 t2z4 t3z6

integrals over grassmannians and random permutations testing the independence of two gaussian populations involves the distribution of the sample canonical correlation coefficients given that the actual correlation is zero the laplace transform as a function of x of this distribution is not only an integral over the grassmannian gr p f n of p dimensional planes in real complex or quaternion n space f n but is also related to a generalized hypergeometric function such integrals are solutions of painleve like equations in the complex case they are solutions to genuine painleve equations these integrals over gr p c n have remarkable expansions in x related to random words of length l formed with an alphabet of p letters 1 p the coefficients of these expansions are given by the probability that a word i contains a subsequence of letters p p 1 1 in that order and ii that the maximal length of the disjoint union of p 1 increasing subsequences of the word is less than or equal tok where k refers to the power of x note that if each letter appears in the word then the maximal length of the disjoint union of p increasing subsequences of the word is automatically l and is thus trivial c 2003 elsevier inc all rights reserved

gaussian fluctuations of jack deformed random young diagrams we introduce a large class of random young diagrams which can be regarded as a natural one parameter deformation of some classical young diagram ensembles a deformation which is related to jack polynomials and jack characters we show that each such a random young diagram converges asymptotically to some limit shape and that the fluctuations around the limit are asymptotically gaussian

when the law of large numbers fails for increasing subsequences of random permutations let the random variable z n k denote the number of increasing subsequences of length k in a random permutation from s n the symmetric group of permutations of 1 n in a recent paper random structures algorithms 29 2006 277 295 we showed that the weak law of large numbers holds for z n kn if k n o n 2 5 that is limn z n k n ez n k n 1 in probability the method of proof employed there used the second moment method and demonstrated that this method cannot work if the condition k n o n 2 5 does not hold it follows from results concerning the longest increasing subsequence of a random permutation that the law of large numbers cannot hold for z n kn if k n cn 1 2 with c 2 presumably there is a critical exponent l 0 such that the law of large numbers holds if k n o n l with l 0 for some l l 0 several phase transitions concerning increasing subsequences occur at l 1 2 and these would suggest that l 0 1 2 however in this paper we show that the law of large numbers fails for z n kn if lim sup n k n n 4 9 thus the critical exponent if it exists must satisfy l 0 2 5 4 9

affine shuffles shuffles with cuts the whitehouse module and patience sorting abstract type a affine shuffles are compared with riffle shuffles followed by a cut although these probability measures on the symmetric group s n are different they both satisfy a convolution property strong evidence is given that when the underlying parameter q satisfies gcd n q 1 1 the induced measures on conjugacy classes of the symmetric group coincide this gives rise to interesting combinatorics concerning the modular equidistribution by major index of permutations in a given conjugacy class and with a given number of cyclic descents using representation theoretic work on the whitehouse module a formula is obtained for the cycle structure of a riffle shuffle followed by a cut it is proved that the use of cuts does not speed up the convergence rate of riffle shuffles to randomness generating functions for the first pile size in patience sorting from decks with repeated values are derived this relates to random matrices

correlation between eigenvalue spectra and dynamics of neural networks this letter presents a study of the correlation between the eigenvalue spectra of synaptic matrices and the dynamical properties of asymmetric neural networks with associative memories for this type of neural network it was found that there are essentially two different dynamical phases the chaos phase with almost all trajectories converging to a single chaotic attractor and the memory phase with almost all trajectories being attracted toward fixed point attractors acting as memories we found that if a neural network is designed in the chaos phase the eigenvalue spectrum of its synaptic matrix behaves like that of a random matrix i e all eigenvalues lie uniformly distributed within a circle in the complex plan and if it is designed in the memory phase the eigenvalue spectrum will split into two parts one part corresponds to a random background the other part equal in number to the memory attractors the mechanism for these phenomena is discussed in this letter

shape fluctuations and random matrices we study a certain random growth model in two dimensions closely related to the one dimensional totally asymmetric exclusion process the results show that the shape fluctuations appropriately scaled converges in distribution to the tracy widom largest eigenvalue distribution for the gaussian unitary ensemble gue

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

an edge based smoothed finite element method es fem with stabilized discrete shear gap technique for analysis of reissner mindlin plates abstract an edge based smoothed finite element method es fem for static free vibration and buckling analyses of reissner mindlin plates using 3 node triangular elements is studied in this paper the calculation of the system stiffness matrix is performed by using the strain smoothing technique over the smoothing domains associated with edges of elements in order to avoid the transverse shear locking and to improve the accuracy of the present formulation the es fem is incorporated with the discrete shear gap dsg method together with a stabilization technique to give a so called edge based smoothed stabilized discrete shear gap method es dsg the numerical examples demonstrated that the present es dsg method is free of shear locking and achieves the high accuracy compared to the exact solutions and others existing elements in the literature

stability and vibration of shear deformable plates first order and higher order analyses abstract this work presents the highly accurate numerical calculation of the natural frequencies and buckling loads for thick elastic rectangular plates with various combinations of boundary conditions the reissener mindlin first order shear deformation plate theory and the higher order shear deformation plate theory of reddy have been applied to the plate s analysis the governing equations and the boundary conditions are derived using the dynamic version of the principle of minimum of the total energy the solution is obtained by the extended kantorovich method this approach is combined with the exact element method for the vibration and stability analysis of compressed members which provides for the derivation of the exact dynamic stiffness matrix including the effect of in plane and inertia forces the large number of numerical examples demonstrates the applicability and versatility of the present method the results obtained by both shear deformation theories are compared with those obtained by the classical thin plate s theory and with published results many new results are given too

random walk generated by random permutations of 1 2 3 n 1 we study properties of a non markovian random walk x n l l 0 1 2 n evolving in discrete time l on a one dimensional lattice of integers whose moves to the right or to the left are prescribed by the rise and descent sequences characterizing random permutations of n 1 1 2 3 n 1 we determine exactly the probability of finding the end point xn x n n of the trajectory of such a permutation generated random walk pgrw at site x and show that in the limit n it converges to a normal distribution with a smaller compared to the conventional polya random walk diffusion coefficient we formulate as well an auxiliary stochastic process whose distribution is identical to the distribution of the intermediate points x n l l n which enables us to obtain the probability measure of different excursions and to define the asymptotic distribution of the number of turns of the pgrw trajectories

asymptotics of q plancherel measures in this paper we are interested in the asymptotic size of the rows and columns of a random young diagram under a natural deformation of the plancherel measure coming from hecke algebras the first lines of such diagrams are typically of order n so it does not fit in the context of the work of biane int math res notices 4 179 192 2001 and niady probab theory relat fields 136 263 297 2006 using the theory of polynomial functions on young diagrams of kerov and olshanski we are able to compute explicitly the first and second order asymptotics of the length of the first rows our method also works for other measures for example those coming from schur weyl representations

free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first order shear deformation theory in this study free vibration of laminated skew plates was investigated discrete singular convolution dsc method is used for numerical solution of vibration problems the straight sided quadrilateral domain is mapped into a square domain in the computational space using a four node element by using the geometric transformation typical results are presented for different geometric parameters and boundary conditions it is concluded from the results that the skew angle have considerable influence on the variations of the frequencies with fibre orientation angle and number of layers in the laminate the results obtained by dsc method are compared with those obtained by analytical and numerical approaches it is shown that reasonable accurate results are obtained present work also indicates that the method of dsc is a promising and potential approach for computational mechanics copyright 2009 john wiley sons ltd

limit theorems for height fluctuations in a class of discrete space and time growth models we introduce a class of one dimensional discrete space discrete time stochastic growth models described by a height function ht x with corner initialization we prove with one exception that the limiting distribution function of ht x suitably centered and normalized equals a fredholm determinant previously encountered in random matrix theory in particular in the universal regime of large x and large t the limiting distribution is the fredholm determinant with airy kernel in the exceptional case called the critical regime the limiting distribution seems not to have previously occurred the proofs use the dual rsk algorithm gessel s theorem the borodin okounkov identity and a novel rigorous saddle point analysis in the fixed x large t regime we find a brownian motion representation this model is equilvalent to the seppalainen johansson model hence some of our results are not new but the proofs are

dynamic stability analysis of composite laminated cylindrical shells via the mesh free kp ritz method abstract in this paper a novel numerical technique is developed for the dynamic stability analysis of composite laminated cylindrical shells under static and periodic axial forces the mesh free kernel particle kp estimate is employed in hybridized form with harmonic functions to approximate the 2 d transverse displacement field a system of mathieu hill equations is obtained through the application of the ritz minimization procedure to the energy expressions the principal instability regions are then analyzed via bolotin s first approximation the mesh free kp ritz method is validated through comparison with existing available numerical data taken from open literature effects of boundary conditions and lamination schemes on the instability regions are also examined in detail

analysis of aeroplane boarding via spacetime geometry and random matrix theory we show that aeroplane boarding can be asymptotically modelled by two dimensional lorentzian geometry boarding time is given by the maximal proper time among curves in the model discrepancies between the model and simulation results are closely related to random matrix theory the models can be used to explain why some commonly practised airline boarding policies are ineffective and even detrimental

edgeworth expansion of the largest eigenvalue distribution function of gaussian orthogonal ensemble in this paper we focus on the large n probability distribution function of the largest eigenvalue in the gaussian orthogonal ensemble of n n matrices goen we prove an edgeworth type theorem for the largest eigenvalue probability distribution function of goen the correction terms to the limiting probability distribution are expressed in terms of the same painleve ii functions appearing in the tracy widom distribution we conclude with a brief discussion of the gsen case

records the maximal layer and uniform distributions in monotone sets abstract consider a nondecreasing nonnegative integrable function f on 0 1 draw an independent sample x 1 y 1 x n y n of size n from the uniform distribution under f and let n n be the number of records in the sample where x i y i is a record when for all j i either x j x i or y j y i we study the dependence upon f of the constant c in the asymptotic formula e n n c n and show that whenever 0 1 f 0 n n e n n 1 in probability the results are related to the expected time analysis of algorithms for finding the collection of all records i e the maximal layer

random walks and random permutations a connection is made between the random turns model of vicious walkers and random permutations indexed by their increasing subsequences consequently the scaled distribution of the maximum displacements in a particular asymmeteric version of the model can be determined to be the same as the scaled distribution of the eigenvalues at the soft edge of the gue random hermitian matrices the scaling of the distribution gives the maximum mean displacement after t time steps as 2t 1 2 with standard deviation proportional to 1 3 the exponent 1 3 is typical of a large class of two dimensional growth problems

buckling and free vibration analyses of stiffened plates using the fsdt mesh free method this paper presents a mesh free galerkin method for the free vibration and stability analyses of stiffened plates via the first order shear deformable theory fsdt the model of a stiffened plate is formed by 1 regarding the plate and the stiffener separately 2 imposing displacement compatible conditions between the plate and the stiffener so that displacement fields of the stiffener can be expressed in terms of the mid surface displacement of the plate and 3 superimposing the strain energy of plate and stiffener because there are no meshes used in this method the stiffeners can be placed anywhere on the plate and need not be placed along the mesh lines several numerical examples are computed by this method to show its accuracy and convergence the present results demonstrate good agreement with the existing solutions given by other researchers and the ansys influences of support size and order of the complete basis functions on the numerical accuracy are also investigated

multi critical unitary random matrix ensembles and the general painleve ii equation we study unitary random matrix ensembles of the form z n detm 2 e ntrvwdm where a 1 2 and v is such that the limiting mean eigenvalue density for n n oc and n n 1 vanishes quadratically at the origin in order to compute the double scaling limits of the eigenvalue correlation kernel near the origin we use the deift zhou steepest descent method applied to the riemann hilbert problem for orthogonal polynomials on the real line with respect to the weight x 2ae nv x here the main focus is on the construction of a local parametrix near the origin with functions associated with a special solution qa of the painleve ii equation q sq 2q3 a we show that qa has no real poles for a 1 2 by proving the solvability of the corresponding riemann hilbert problem we also show that the asymptotics of the recurrence coefficients of the orthogonal polynomials can be expressed in terms of qa in the double scaling limit

longest increasing subsequences from patience sorting to the baik deift johansson theorem we describe a simple one person card game patience sorting its analysis leads to a broad circle of ideas linking young tableaux with the longest increasing subsequence of a random permutation via the schensted correspondence a recent highlight of this area is the work of baik deift johansson which yields limiting probability laws via hard analysis of toeplitz determinants

buckling of rectangular mindlin plates subjected to partial in plane edge loads using the radial point interpolation method this paper considers the elastic buckling of rectangular mindlin plates that are subjected to partially distributed in plane edge loadings a numerical algorithm based on the radial point interpolation method rpim is proposed for the solution of such plates the pre buckling stresses are first determined using the rpim based on a two dimensional 2 d elastic plane stress problem the buckling load intensity factors for rectangular plates that incorporate these predetermined pre buckling stresses are then computed via the rpim based on the mindlin plate theory numerical examples of the plates with various boundaries and subjected to different partially distributed in plane edge loadings are presented shear locking of the buckling load is studied the results demonstrate the high accuracy of the proposed rpim

pattern recognition using asymmetric attractor neural networks the asymmetric attractor neural networks designed by the monte carlo mc adaptation rule are shown to be promising candidates for pattern recognition in such a neural network with relatively low symmetry when the members of a set of template patterns are stored as fixed point attractors their attraction basins are shown to be isolated islands embedded in a chaotic sea the sizes of these islands can be controlled by a single parameter we show that these properties can be used for effective pattern recognition and rejection in our method the pattern to be identified is attracted to a template pattern or a chaotic attractor if the difference between the pattern to be identified and the template pattern is smaller than a predescribed threshold the pattern is attracted to the template pattern automatically and thus is identified as belonging to this template pattern otherwise it wanders in a chaotic attractor for ever and thus is rejected as an unknown pattern the maximum sizes of these islands allowed by this kind of neural networks are determined by a modified mc adaptation rule which are shown to be able to dramatically enlarge the sizes of the islands we illustrate the use of our method for pattern recognition and rejection with an example of recognizing a set of chinese characters

free vibration and buckling analyses of shear deformable plates based on fsdt meshfree method abstract a meshfree method based on the reproducing kernel particle approximate is employed for the free vibration and buckling analyses of shear deformable plates in this approach the first order mindlin reissner plate theory fsdt is used and the displacement shape functions are constructed using the reproducing kernel approximation satisfying the consistency condition the essential boundary conditions are enforced by a transformation method numerical examples considering various aspect ratios skew angles and boundary conditions are demonstrated to show the validity of the proposed method and satisfactory results were obtained when comparisons are made with the exact and other available numerical results existing in the literature

buckling of thick skew plates the paper considers the elastic buckling of thick skew plates up to now very little work has been done on this subject and the paper aspires to fill this gap based on the principle of stationary total potential energy and the recently developed pb 2 rayleigh ritz method as a solution procedure buckling solutions for skew plates of various aspect ratios skew angles and boundary conditions are determined the tabulation of these results not available thus far should be useful to designers and researchers who may use them as benchmark values to test the validity and convergence of their numerical techniques and softwares for thick plate analysis

geodesics and spanning trees for euclidean first passage percolation the metric d q q on the set q of particle locations of a homogeneous poisson process on r d defined as the infimum of i q i q i 1 1 over sequences in q starting with q and ending with q where denotes euclidean distance has nontrivial geodesics when a 1 the cases 1 are the euclidean first passage percolation fpp models introduced earlier by the authors while the geodesics in the case are exactly the paths from the euclidean minimal spanning trees forests of aldous and steele we compare and contrast results and conjectures for these two situations new results for 1 and any d include inequalities on the fluctuation exponents for the metric x 1 2 and for the geodesies 3 4 in strong enough versions to yield conclusions not yet obtained for lattice fpp almost surely every semiinfinite geodesic has an asymptotic direction and every direction has a semiinfinite geodesic from every q for d 2 and 2 further results follow concerning spanning trees of semiinfinite geodesics and related random surfaces

exact asymptotic results for the bernoulli matching model of sequence alignment finding analytically the statistics of the longest common subsequence lcs of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology we present exact asymptotic results for the distribution of the lcs in a simpler yet nontrivial variant of the original model called the bernoulli matching bm model we show that in the bm model for all c the distribution of the asymptotic length of the lcs suitably scaled is identical to the tracy widom distribution of the largest eigenvalue of a random matrix whose entries are drawn from a gaussian unitary ensemble

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

approximation of the buckling problem for reissner mindlin plates this paper deals with the approximation of the buckling coefficients and modes of a clamped plate modeled by the reissner mindlin equations these coefficients are the reciprocals of the eigenvalues of a noncompact operator we give a spectral characterization of this operator and show that the relevant buckling coefficients correspond to isolated nondefective eigenvalues then we consider the numerical computation of these coefficients and their corresponding modes for the finite element approximation of reissner mindlin equations it is well known that some kind of reduced integration or mixed interpolation has to be used to avoid locking in particular we consider duran liberman elements which have been already proved to be locking free for load and vibration problems we adapt the classical approximation theory for noncompact operators to obtain optimal order error estimates for the eigenfunctions and a double order for the eigenvalues these estimates are valid with constants independent of the plate thickness we report some numerical experiments confirming the theoretical results finally we refine the analysis in the case of a uniformly compressed plate

fredholm determinants jimbo miwa ueno τ functions and representation theory the authors show that a wide class of fredholm determinants arising in the representation theory of big groups such as the infinite dimensional unitary group solve painleve equations their methods are based on the theory of integrable operators and the theory of riemann hilbert problems 2002 wiley periodicals inc

random words toeplitz determinants and integrable systems ii this paper connects the analysis of the length of the longest weakly increasing subsequence of inhomogeneous random words to a riemnn hilbert problem and an associated system of integrable partial differential equations in particular we show that the poissonization of the distribution function of this length can be identified as the jimbo miwa ueno tau function

developments in random matrix theory in this introduction to the journal of physics a special issue on random matrix theory we give a review of the main historical developments in random matrix theory a short summary of the papers that appear in this special issue is also given

exact solvability and asymptotic aspects of generalized xx0 spin chains abstract building on our earlier work saeedian et al 2018 we introduce and study generalized xx0 models we explicitly construct a long range interacting spin chain referred to as the selberg model and study the correlation functions of the selberg and xx0 models using a matrix integral representation of the generalized xx0 model and applying asymptotic analysis in non intersecting brownian motion the phase structure of the selberg model is determined we find that tails of the tracy widom distribution of gaussian unitary ensemble govern a discrete to continuous third order phase transition in selberg model the same method also reproduces the gross witten phase transition of the original xx0 model finally we conjecture universal features for the phase structure of the generalized xx0 model

random sorting networks local statistics via random matrix laws this paper finds the bulk local limit of the swap process of uniformly random sorting networks the limit object is defined through a deterministic procedure a local version of the edelman greene algorithm applied to a two dimensional determinantal point process with explicit kernel the latter describes the asymptotic joint law near 0 of the eigenvalues of the corners in the antisymmetric gaussian unitary ensemble in particular the limiting law of the first time a given swap appears in a random sorting network is identified with the limiting distribution of the closest to 0 eigenvalue in the antisymmetric gue moreover the asymptotic gap in the bulk between appearances of a given swap is the gaudin mehta law the limiting universal distribution for gaps between eigenvalues of real symmetric random matrices the proofs rely on the determinantal structure and a double contour integral representation for the kernel of random poissonized young tableaux of arbitrary shape

buckling of rectangular mindlin plates with internal line supports this paper considers the elastic buckling of rectangular mindlin plates under normal inplane forces the plates may have any number of internal line straight or curved supports that span between any two edges based on the energy functional derived from the incremental total potential energy approach the newly developed pb 2 rayleigh ritz method is applied for solution the special feature of this method is the pb 2 ritz function which consists of the product of 1 a two dimensional polynomial function and 2 a basic function formed from taking the product of the equations of the boundaries and internal line supports with each equation raised to appropriate powers as shown herein the method is convenient for analysts since no discretization is required and very accurate results can be obtained buckling load intensity factors for rectangular plates with various boundary conditions and various thickness and aspect ratios are tabulated for designers these may also serve as benchmark values for the testing of other numerical methods

unitary matrix models as exactly solvable string theories models of unitary matrices are solved exactly in a double scaling limit using orthogonal polynomials on a circle exact differential equations are found for the scaling functions of these models for the simplest model k 1 the painlev e ii equation with constant 0 is obtained there are possible nonperturbative phase transitions in these models the scaling function is of the form mathit n mathrm ensuremath 1 2 mathit k 1 ifmmode times else texttimes fi f mathit n 2 mathit k 2 mathit k 1 ensuremath lambda mathit x ensuremath lambda for the kth multicritical point the specific heat is mathit f 2 and is therefore manifestly positive equations are given for k 2 and 3 with a discussion of asymptotic behavior

the element free kp ritz method for free vibration analysis of conical shell panels in this paper the free vibration of conical panels is analyzed by the mesh free kp ritz method both 1 d and 2 d versions of the kp ritz approach are formulated for conical panels for conical panels with two simply supported straight edges the 1 d kp ritz version is used where the kernel particle estimation is employed in hybridized form with harmonic functions to approximate the 2 d displacement field for conical panels having arbitrary boundary conditions the displacement field is approximated by the 2 d kp ritz version with 2 d form of kernel particle functions employed the classical thin shell theory based on love s hypothesis is employed in the present analyses and based on the kernel particle concept and ritz technique the eigenequations of the frequencies of the conical panels are obtained to validate the accuracy of stability of the present method convergence studies were carried out based on the influences of the support size and the number of nodes comparisons were also made with existing results available in the open literature this study also examines in detail the effects of variation in the semi vertex angle and boundary conditions on the frequency characteristics of conical panels

tracy widom distributions in critical unitary random matrix ensembles and the coupled painleve ii system we study fredholm determinants of the painleve ii and painleve xxxiv kernels in certain critical unitary random matrix ensembles these determinants describe special gap probabilities of eigenvalues we obtain tracy widom formulas for the fredholm determinants which are explicitly given in terms of integrals involving a family of distinguished solutions to the coupled painleve ii system in dimension four moreover the large gap asymptotics for these fredholm determinants are derived where the constant terms are given explicitly in terms of the riemann zeta function

time needed to board an airplane a power law and the structure behind it a simple model for the boarding of an airplane is studied passengers have reserved seats but enter the airplane in arbitrary order queues are formed along the aisle as some passengers have to wait to reach the seats for which they have reservation we label a passenger by the number of his or her reserved seat in most cases the boarding process is much slower than for the optimal situation where passenger and seat orders are identical we study this dynamical system by calculating the average boarding time when all permutations of n passengers are given equal weight to first order the boarding time for a given permutation ordering of the passengers is given by the number s of sequences of monotonically increasing values in the permutation we show that the distribution of s is symmetric on 1 n which leads to an average boarding time n 1 2 we have found an exact expression for s and have shown that the full distribution of s approaches a normal distribution as n increases however there are significant corrections to the first order results due to certain correlations between passenger ordering and the substrate seat ordering this occurs for some cases in which the sequence of the seats is partially mirrored in the passenger ordering these cases with correlations have a boarding time that is lower than predicted by the first order results the large number of cases with reduced boarding times have been classified we also give some indicative results on the geometry of the correlations with sorting into geometry groups with increasing n both the number of correlation types and the number of cases belonging to each type increase rapidly using enumeration we find that as a result of these correlations the average boarding time behaves like n with 0 69 as compared with 1 0 for the first order approximation

on the long time behavior of the doubly infinite toda lattice under initial data decaying at infinity we provide rigorous analysis of the long time behavior of the doubly infinite toda lattice under initial data that decay at infinity in the absence of solitions we solve approximately and for large times the riemann hilbert matrix factorization problem equivalent to the related inverse scattering problem with the help of the beals coifman formula by reducing it to a simpler one through a series of contour deformations in the spirit of the deift zhou method

lengths of monotone subsequences in a mallows permutation we study the length of the longest increasing and longest decreasing subsequences of random permutations drawn from the mallows measure under this measure the probability of a permutation uppi in s n is proportional to q mathrm inv uppi where q is a real parameter and mathrm inv uppi is the number of inversions in uppi the case q 1 corresponds to uniformly random permutations the mallows measure was introduced by mallows in connection with ranking problems in statistics we determine the typical order of magnitude of the lengths of the longest increasing and decreasing subsequences as well as large deviation bounds for them we also provide a simple bound on the variance of these lengths and prove a law of large numbers for the length of the longest increasing subsequence assuming without loss of generality that q 1 our results apply when q is a function of n satisfying n 1 q rightarrow infty the case that n 1 q o 1 was considered previously by mueller and starr in our parameter range the typical length of the longest increasing subsequence is of order n sqrt 1 q whereas the typical length of the longest decreasing subsequence has four possible behaviors according to the precise dependence of n and q we show also that in the graphical representation of a mallows distributed permutation most points are found in a symmetric strip around the diagonal whose width is of order 1 1 q this suggests a connection between the longest increasing subsequence in the mallows model and the model of last passage percolation in a strip

optimal back to front airplane boarding the problem of finding an optimal back to front airplane boarding policy is explored using a mathematical model that is related to the 1 1 polynuclear growth model with concave boundary conditions and to causal sets in gravity we study all airplane configurations and boarding group sizes optimal boarding policies for various airplane configurations are presented detailed calculations are provided along with simulations that support the main conclusions of the theory we show that the effectiveness of back to front policies undergoes a phase transition when passing from lightly congested airplanes to heavily congested airplanes the phase transition also affects the nature of the optimal or near optimal policies under what we consider to be realistic conditions optimal back to front policies lead to a modest 8 char21 12 phantom rule 0 16em 0ex improvement in boarding time over random no policy boarding using two boarding groups having more than two groups is not effective

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

on the solvability of painleve ii and iv we introduce a rigorous methodology for studying the riemann hilbert problems associated with certain integrable nonlinear ordinary differential equations for concreteness we investigate the painleve ii and painleve iv equations we show that the cauchy problems for these equations admit in general global meromorphic in t solutions furthermore for special relations among the monodromy data and for t on stokes lines these solutions are bounded for finite t

analyzing two dimensional sine gordon equation with the mesh free reproducing kernel particle ritz method abstract we consider an analysis of the non linear two dimensional sine gordon sg equation the analysis is performed using the mesh free reproducing kernel particle ritz method kp ritz method the mesh free kernel particle estimate is employed to approximate the 2d displacement field a system of discrete equations is obtained through application of the ritz minimization procedure to the energy expressions to validate the accuracy of the results and stability of the present method convergence studies were carried out based on influences of support size and number of nodes the present results were compared with results reported in extant literature and were found to be in good agreement with the literature

asymptotics for toeplitz determinants perturbation of symbols with a gap we study the determinants of toeplitz matrices as the size of the matrices tends to infinity in the particular case where the symbol has two jump discontinuities and tends to zero on an arc of the unit circle at a sufficiently fast rate we generalize an asymptotic expansion by widom indiana univ math j 21 277 283 1971 which was known for symbols supported on an arc we highlight applications of our results in the circular unitary ensemble and in the study of fredholm determinants associated to the sine kernel

painleve ii asymptotics near the leading edge of the oscillatory zone for the korteweg de vries equation in the small dispersion limit in the small dispersion limit solutions to the korteweg de vries equation develop an interval of fast oscillations after a certain time we obtain a universal asymptotic expansion for the korteweg de vries solution near the leading edge of the oscillatory zone up to second order corrections this expansion involves the hastings mcleod solution of the painleve ii equation we prove our results using the riemann hilbert approach c 2009 wiley periodicals inc

hammersley s interacting particle process and longest increasing subsequences in a famous paper 8 hammersley investigated the lengthl n of the longest increasing subsequence of a randomn permutation implicit in that paper is a certain one dimensional continuous space interacting particle process by studying a hydrodynamical limit for hammersley s process we show by fairly soft arguments that limn 1 2 el n 2 this is a known result but previous proofs 14 11 relied on hard analysis of combinatorial asymptotics

integral formulas for the asymmetric simple exclusion process in this paper we obtain general integral formulas for probabilities in the asymmetric simple exclusion process asep on the integer lattice mathbb z with nearest neighbor hopping rates p to the right and q 1 p to the left for the most part we consider an n particle system but for certain of these formulas we can take the n to infty limit first we obtain for the n particle system a formula for the probability of a configuration at time t given the initial configuration for this we use bethe ansatz ideas to solve the master equation extending a result of schutz for the case n 2 the main results of the paper derived from this are integral formulas for the probability for given initial configuration that the mth left most particle is at x at time t in one of these formulas we can take the n to infty limit and it gives the probability for an infinite system where the initial configuration is bounded on one side for the special case of the totally asymmetric simple exclusion process tasep our formulas reduce to the known ones

higher order analogues of the tracy widom distribution and the painleve ii hierarchy we study fredholm determinants related to a family of kernels which describe the edge eigenvalue behavior in unitary random matrix models with critical edge points the kernels are natural higher order analogues of the airy kernel and

first passage percolation has sublinear distance variance let 0 1 the distance dist 0 from the origin to a vertex 2 has variance bounded by c log where c c a b d is a constant which may only depend on a b and d some related variants are also discussed

emergence of a singularity for toeplitz determinants and painleve v we obtain asymptotic expansions for toeplitz determinants corresponding to a family of symbols depending on a parameter t for t positive the symbols are regular so that the determinants obey szeg s strong limit theorem if t 0 the symbol possesses a fisher hartwig singularity letting t 0 we analyze the emergence of a fisher hartwig singularity and a transition between the two different types of asymptotic behavior for toeplitz determinants this transition is described by a special painleve v transcendent a particular case of our result complements the classical description of wu mccoy tracy and barouch of the behavior of a 2 spin correlation function for a large distance between spins in the two dimensional ising model as the phase transition occurs

the random average process and random walk in a space time random environment in one dimension we study space time fluctuations around a characteristic line for a one dimensional interacting system known as the random average process the state of this system is a real valued function on the integers new values of the function are created by averaging previous values with random weights the fluctuations analyzed occur on the scale n1 4 where n is the ratio of macroscopic and microscopic scales in the system the limits of the fluctuations are described by a family of gaussian processes in cases of known product form invariant distributions this limit is a two parameter process whose time marginals are fractional brownian motions with hurst parameter 1 4 along the way we study the limits of quenched mean processes for a random walk in a space time random environment these limits also happen at scale n1 4 and are described by certain gaussian processes that we identify in particular when we look at a backward quenched mean process the limit process is the solution of a stochastic heat equation

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

buckling of moderately thick arbitrarily shaped plates with intermediate point supports using a simple hp cloud method abstract this paper presents the simple hp cloud meshless method for the stability analysis of moderately thick plates with various shapes subjected to uniaxial and biaxial in plane compressive and pure shear loads to allow the effect of transverse shear deformation on the critical buckling load of the plate the mindlin s plate theory is employed simple hp cloud method is applied for constructing the cloud shape functions and for discretization of the domain shepard functions are also used for the partition of unity and complete polynomials are utilized for the enrichment functions part the simple hp cloud method has kronecker delta property so contrary to most of meshless methods the essential boundary conditions can be imposed directly constructing the stiffness and geometry matrices leads to an eigenvalue problem that should be solved to determine the critical buckling load of the plate numerical results are verified against the results reported elsewhere to illustrate the accuracy and effectiveness of the present method to show the applications of simple hp cloud method in the buckling analysis of moderately thick plates local buckling coefficients of various shapes of plates rectangular skew trapezoidal triangular circular semi circular hexagonal and general shape with different boundary conditions are determined also local buckling coefficients of plates with point supports and intermediate support are calculated

large deformations of the tracy widom distribution i non oscillatory asymptotics we analyze the left tail asymptotics of deformed tracy widom distribution functions describing the fluctuations of the largest eigenvalue in invariant random matrix ensembles after removing each soft edge eigenvalue independently with probability 1 gamma in 0 1 as gamma varies a transition from tracy widom statistics gamma 1 to classical weibull statistics gamma 0 was observed in the physics literature by bohigas et al phys rev e 79 031117 2009 we provide a description of this transition by rigorously computing the leading order left tail asymptotics of the thinned goe gue and gse tracy widom distributions in this paper we obtain the asymptotic behavior in the non oscillatory region with gamma in 0 1 fixed for the goe gue and gse distributions and gamma uparrow 1 at a controlled rate for the gue distribution this is the first step in an ongoing program to completely describe the transition between tracy widom and weibull statistics as a corollary to our results we obtain a new total integral formula involving the ablowitz segur solution to the second painleve equation