generic buckling curves for specially orthotropic rectangular plates using a double affine transformation the classical buckling equation for specially orthotropic plates and the corresponding virtual work theorem are presented in a particularly simple fashion these dual representations are characterized by a single material constant called the generalized rigidity ratio whose range is predicted to be the closed interval from 0 to 1 if this prediction is correct then the numerical results using a ratio greater than 1 in the specially orthotropic plate literature are incorrect when natural boundary conditions are considered a generalized poisson s ratio is introduced thus the buckling results are valid for any specially orthotropic material hence the curves presented in the text are generic rather than specific the solution trends are twofold the buckling coefficients decrease with decreasing generalized rigidity ratio and when applicable they decrease with increasing generalized poisson s ratio since the isotropic plate is one limiting case of the above analysis it is also true that isotropic buckling coefficients decrease with increasing poission s ratio

some numerical results on the block spin transformation for the 2d ising model at the critical point we study the block spin transformation for the 2d ising model at the critical temperaturetc we consider the model with the constraint that the total spin in each block is zero an old argument by cassandro and gallavotti strongly supports the gibbsianness of the transformed measure provided that such model has a critical temperaturet c lower thantc after describing a possible rigorous approach to the problem we present numerical evidence that indeedt c tc and study the dobrushin shlosman uniqueness condition

genotypes of irreducible representations of finite p groups for any characteristic zero coefficient field an irreducible representation of a finite p group can be assigned a roquette p group called the genotype this has already been done by bouc and kronstein in the special cases q and c a genetic invariant of an irrep is invariant under group isomorphism change of coefficient field galois conjugation and under suitable inductions from subquotients it turns out that the genetic invariants are precisely the invariants of the genotype we shall examine relationships between some genetic invariants and the genotype as an application we shall count galois conjugacy classes of certain kinds of irreps

theory and experiments for nonlinear vibrations of imperfect rectangular plates with free edges abstract large amplitude vibrations of completely free rectangular plates are investigated for the first time nonlinear higher order shear deformation theory is used and the nonlinear response to transverse harmonic excitation in the frequency neighborhood of the fundamental mode is studied geometric imperfections are taken into account the numerical analysis is carried out in two steps first the plate displacements and rotations are expanded in terms of chebyshev polynomials and a linear analysis is conducted to obtain the natural frequencies and modes of vibration then the energy functional is discretized by using the natural modes of vibration and a system of nonlinear ordinary differential equations with cubic and quadratic nonlinear terms is obtained a pseudo arc length continuation and collocation scheme is used for bifurcation analysis of periodic solutions moreover to validate the numerical results experimental tests have been conducted for the fundamental vibration mode at several harmonic excitation amplitudes by using a laser doppler vibrometer to characterize the nonlinear response of the plate with imperfections and closed loop control of the excitation the effects of geometric imperfections on the trend of nonlinearity and on natural frequencies are fully discussed and the convergence of the numerical solutions has been verified

geometrical non linear steady state forced periodic vibration of plates part i model and convergence studies a model for the steady state geometrically non linear periodic vibration of thin rectangular plates under harmonic external excitation is presented the equations of motion in the time domain are derived by applying the principle of virtual work and the hierarchical finite element method hfem these equations are transformed into the frequency domain by the harmonic balance method hbm and are solved by a continuation method the convergence properties of the model are discussed by applying it to isotropic and to composite laminated plates

almost gibbsian description of the sign fields of sos fields an example is presented of a measure on a lattice system which has a measure zero set of points configurations where some conditional probability can be discontinuous but does not become a gibbs measure under decimation or other transformations we also discuss some related issues

mathematical properties of renormalization group transformations abstract renormalization group transformations of the type introduced into statistical physics by k g wilson have been widely used with great success for a variety of many body calculations the basic approach consists in integrating out certain degrees of freedom and using a new image hamiltonian to describe the statistical properties of those that remain the mathematical foundations of the procedure however remain somewhat obscure p a pearce and the author have pointed out that there are serious questions about the existence and properties of a thermodynamic limit for renormalization group transformations in particular certain real space transformations show peculiarities in this limit these suggest that there may be serious mathematical problems with renormalization group procedures despite their considerable practical sucess

nonlinear forced vibration of orthotropic rectangular plates using the method of multiple scales the method of multiple scales mms in conjunction with the galerkin method is used to analyze the nonlinear forced and damped response of a rectangular orthotropic plate subjected to a uniformly distributed harmonic transverse loading the effects of damping and in plane loads are considered the analysis considers simply supported as well as clamped plates for each case both movable and immovable edge conditions are considered by using mms all possible resonances such as primary subharmonic and superharmonic reso nances are studied for the undamped response without in plane loading comparisons of the mms results with those obtained by the finite element method show excellent agreement evelopment of composite materials comprising lam inates of orthotropic or multilayered anisotropic materi als recently has been receiving substantially growing research efforts due to the increasing demands for energy efficient high strength minimum weight aircraft designs many re searchers believe that the use of composite materials offers promising alternatives for aircraft designs thin laminated composite plates subjected to transverse periodic loadings could encounter deflections of the order of plate thickness or even higher responses of this kind cannot be predicted by using the linear theory consequently the need to study large amplitude deflection vibrations of composite structures is of paramount importance the literature survey shows that the equations of motion for the large deflection analysis of heterogeneous anisotropic plates using the von karman geometrical nonlinearity were first considered by whitney and leissa 1 based on these equa tions different methods of analysis have been developed by several researchers an excellent number of collections on nonlinear free and forced vibrations of composite plates cov ering the work through 1979 can be found in the comprehen sive book by chia 2 bert3 has conducted a survey on the dynamics of composite plates for the period 1979 81 a re view of the literature on nonlinear vibrations of plates can be found in the review paper by sathyamoorthy4 and the book by nayfeh and mook 5 large deflection analysis of symmetrically laminated rec equations of motion are presented in terms of the lateral displacement and stress function the equations are nondi mensionalized following the transformation introduced by brunelle and oyibo 9 though multimode analysis can be treated the present study is focused on single mode analysis a deflection function representing the first mode and satisfy ing the boundary conditions is assumed and subsequently the stress function is found next the galerkin method is applied to obtain the modal equation which is solved analytically by using the method of multiple scales mms 10 the mms also provides solutions for subharmonic and superharmonic reso nances the effects of damping ratio plate aspect ratio and in plane loading then are studied

an alternate version of pirogov sinai theory a new approach to the pirogov sinai theory of phase transitions is developed not employing the contour models with a parameter the completeness of the phase diagram is proven

nonlinear curvature based model and resonant finite amplitude vibrations of symmetric cross ply laminates abstract moving from a general plate theory a modified general classical laminated plate theory mgclpt exhibiting nonlinear curvatures but still allowing for some worth features of linear curvature models von karman is formulated starting from mgclpt partial differential equations a minimal discretized model suitable for the analysis of resonant finite amplitude vibrations of symmetric cross ply laminates with immovable or movable supports is obtained via the galerkin procedure periodic responses of a single mode model and of a 3 1 internally resonant two mode model excited at primary resonance are obtained via the multiple time scale method the influence of various system parameters thickness ratio plate aspect number of laminae kind of material mode number is addressed and the comparison of nonlinear vibration results as obtained with the mgclpt and the von karman models for different boundary conditions shows some interesting differences

unified aeroelastic flutter theory for very low aspect ratio panels a theory unifying the flutter analyses of orthotropic and isotropic panels having very low aspect ratios and exposed to an inviscid potential flow on the upper surfaces is developed the analysis considers an infinitely long panel of finite width simply supported on the side edges and resting on a spring foundation three dimensional linearized aerodynamic and classical plate theories are used traveling wave modes are utilized as solutions to the panel s aeroelastic equation of motion the resulting aerodynamic integral is evaluated approximately using both numerical and analytical methods the structural and aerodynamic generic variables which are instrumental in establishing this unified theory are derived using affine transformations subsonic as well as supersonic flutter and divergence boundaries are determined the effects of air to panel mass ratios and midplane forces are examined viscous structural damping is found to be destabilizing there is a general agreement between the results of this analysis and those obtained for isotropic panels by previous investigators

rational representations and permutation representations of finite groups we investigate the question which mathbb q valued characters and characters of mathbb q representations of finite groups are mathbb z linear combinations of permutation characters this question is known to reduce to that for quasi elementary groups and we give a solution in that case as one of the applications we exhibit a family of simple groups with rational representations whose smallest multiple that is a permutation representation can be arbitrarily large

two connections between random systems and non gibbsian measures in this contribution we discuss the role disordered or random systems have played in the study of non gibbsian measures this role has two main aspects the distinction between which has not always been fully clear 1 from disordered systems disordered systems can be used as a tool analogies with as well as results and methods from the study of random systems can be employed to investigate non gibbsian properties of a variety of measures of physical and mathematical interest 2 of disordered systems non gibbsianness is a property of various joint measures describing quenched disordered systems we discuss and review this distinction and a number of results related to these issues moreover we discuss the mean field version of the non gibbsian property and present some ideas how a kac limit approach might connect the finite range and the mean field non gibbsian properties

pathological behavior of renormalization group maps at high fields and above the transition temperature we show that decimation transformations applied to high q potts models result in non gibbsian measures even for temperatures higher than the transition temperature we also show that majority transformations applied to the ising model in a very strong field at low temperatures produce non gibbsian measures this shows that pathological behavior of renormalization group transformations is even more widespread than previous examples already suggested

regularity properties and pathologies of position space renormalization group transformations scope and limitations of gibbsian theory we reconsider the conceptual foundations of the renormalization group rg formalism and prove some rigorous theorems on the regularity properties and possible pathologies of the rg map our main results apply to local in position space rg maps acting on systems of bounded spins compact single spin space regarding regularity we show that the rg map defined on a suitable space of interactions formal hamiltonians is always single valued and lipschitz continuous on its domain of definition this rules out a recently proposed scenario for the rg description of first order phase transitions on the pathological side we make rigorous some arguments of griffiths pearce and israel and prove in several cases that the renormalized measure is not a gibbs measure for any reasonable interaction this means that the rg map is ill defined and that the conventional rg description of first order phase transitions is not universally valid for decimation or kadanoff transformations applied to the ising model in dimension d 3 these pathologies occur in a full neighborhood 0 h e of the low temperature part of the first order phase transition surface for block averaging transformations applied to the ising model in dimension d 2 the pathologies occur at low temperatures for arbitrary magnetic field strength pathologies may also occur in the critical region for ising models in dimension d 4 we discuss the heuristic and numerical evidence on rg pathologies in the light of our rigorous theorems in addition we discuss critically the concept of gibbs measure which is at the heart of present day classical statistical mechanics we provide a careful and we hope pedagogical overview of the theory of gibbsian measures as well as the less familiar non gibbsian measures emphasizing the distinction between these two objects and the possible occurrence of the latter in different physical situations we give a rather complete catalogue of the known examples of such occurrences the main message of this paper is that despite a well established tradition gibbsiannessshould not be taken for granted

a finite element method for nonlinear forced vibrations of rectangular plates the finite element method has been extended to determine the response of large amplitu de forced vibrations of thin plates a harmonic force matrix of a rectangular element under uniform harmonic excitation is developed for nonlinear forced vibration analysis in plane deformation and inertia are both considered in the formulation results obtained are compared with simple elliptic response perturbation and other approximation solutions nomenclature a nondimensional amplitude of vibration wmax z b nondimensional forcing amplitude factor a b plate length and width c d extensional and bending stiffness matrices c ratio of volumes under plate mode shape and square of mode shape e young s modulus e midsurface strains f0 amplitude of uniform harmonic pressure f ff2 linearizing functions h plate thickness k element linear stiffness matrix k element nonlinear stiffness matrix length of loaded plate element m element mass matrix

majority rule at low temperatures on the square and triangular lattices we consider the majority rule renormalization group transformation applied to nearest neighbor ising models for the square lattice with 2 by 2 blocks we prove that if the temperature is sufficiently low then the transformation is not defined we use the methods of van enter fewrnandez and sokal who proved the renormalized measure is not gibbsian for 7 by 7 blocks if the temperature is too low for the triangular lattice we prove that a zero temperature majorityrule transformation may be defined the resulting renormalized hamiltonian is local with 14 different types of interactions

a unified approach to phase diagrams in field theory and statistical mechanics we construct the phase diagram of any system which admits a low temperature polymer or cluster expansion such an expansion turns the system into a hard core interacting contour model with small but not necessarily positive activities the method uses some of zahradnik s ideas z1 but applies equally well to systems with complex interactions we give two applications first to low temperaturep 2 models with complex couplings and second to a computation of asymptotics of partition functions in periodic volumes if the index of a supersymmetric field theory is known the second application would help determine the number of phases in infinite volume

renormalization group at criticality and complete analyticity of constrained models a numerical study we study the majority rule transformation applied to the gibbs measure for the 2d ising model at the critical point the aim is to show that the renormalized hamiltonian is well defined in the sense that the renormalized measure is gibbsian we analyze the validity of dobrushin shlosman uniqueness dsu finite size condition for the constrained models corresponding to different configurations of the image system it is known that dsu implies in our 2d case complete analyticity from which as recently shown by haller and kennedy gibbsianness follows we introduce a monte carlo algorithm to compute an upper bound to vasserstein distance appearing in dsu between finite volume gibbs measures with different boundary conditions we get strong numerical evidence that indeed the dsu condition is verified for a large enough volumev for all constrained models