conformal invariance and finite one dimensional quantum chains based on previous work of cardy 1984 the authors show in a systematic way how using conformal invariance one can determine the anomalous dimensions of various operators from finite quantum chains with different boundary conditions the method is illustrated in the case of the three and four state potts models where the anomalous dimensions of the para fermionic operators are found

corrections to finite size scaling for quantum chains the authors compute the leading order correction to the energy gap at the critical point for the anisotropic ising and the z3 potts quantum chains periodic anti periodic and free boundary conditions are considered for the ising case the corrections are independent of the boundary conditions in the z3 case the correction is the same for anti periodic and free boundary conditions but is 2 5 smaller for the periodic case the authors have no explanation for this phenomenon

conformal invariance and critical dynamics the author discusses the behaviour of dynamic correlation functions under conformal transformations in particular the exact form of the dynamic scaling function at the critical point for an arbitrary isotropic two dimensional model is obtained with either conserved or nonconserved order parameter

the relation between amplitudes and critical exponents in finite size scaling the relation between critical exponents and the amplitude of the correlation length divergence at the critical point of two dimensional systems as a function of finite size is investigated and generalised in two ways correlations more general than those of order order type are included a form appropriate for anisotropic systems is proposed the authors present a exact results for the ising and gaussian models and b numerical results for the symmetric eight vertex baxter continuous q state potts and continuous n component cubic models

pair correlations in the antiperiodic ising strip and conformal invariance an explicit formula for the spatial dependence of the pair correlation function in an ising strip with antiperiodic boundary conditions at the bulk critical temperature is given it follows from the conformal invariance approach of belevin et al 1986 and cardy 1986

on the universality of crossing probabilities in two dimensional percolation six percolation models in two dimensions are studied percolation by sites and by bonds on square hexagonal and triangular lattices rectangles of widtha and heightb are superimposed on the lattices and four functions representing the probabilities of certain crossings from one interval to another on the sides are measured numerically as functions of the ratioa b in the limits set by the sample size and by the conventions and on the range of the ratioa b measured the four functions coincide for the six models we conclude that the values of the four functions can be used as coordinates of the renormalization group fixed point

evaluation of layerwise mixed theories for laminated plates analysis the evaluation of mixed layerwise theories to calculate the in plane and out of plane responses of thick plates in two dimensional modeling of multilayered structures is made the employed models which were proposed by the author in earlier works a priori fulfill the continuity of transverse shear and normal stress components at the interface between two adjacent layers a reissner s mixed variational equation is used to derive the governing equations in terms of introduced stress and displacement variables the interface continuity conditions are imposed by writing the governing equations at a multilayered level the related standard displacement formulations are also discussed for comparison purpose closed form solutions are presented for plates made of orthotropic lamina and bent by harmonic distribution of transverse pressure symmetrically and unsymmetrically laminated as well as sandwich plates have been investigated a comparison with a three dimensional elasticity analysis shows that present mixed layerwise models furnish a better description of the in plane and out of plane response of thick plates with respect to existing layerwise and equivalent single layer theories in particular the proposed models describe with excellent accuracy the transverse shear and normal stress fields unlike available current models these fields are herein determined a priori without requiring implementation of any postprocessing procedures the distribution of the transverse displacement and transverse normal stress in the plate thickness direction are also shown for most of the problems

nonuniversal critical behaviour in planar ising models with extended radially symmetric defects using conformal mapping and finite size scaling the authors determine the local magnetic exponent near a defect characterized by couplings of the form j r j 1 a r in accordance with phenomenological considerations they find that it depends continuously on the amplitude a both for a defect in the interior and on the boundary

finite size scaling in strips antiperiodic boundary conditions the exact values of the universal amplitude a relating the correlation length xi approximately l a to the strip width l at the critical point of ising and 3 state potts models are obtained for the case of antiperiodic or twisted boundary conditions predictions are also made for the finite size scaling behaviour of the interfacial tension

critical behaviour of the two dimensional potts model with a continuous number of states a finite size scaling analysis we investigate the critical behaviour of the two dimensional q state potts model using finite size scaling and transfer matrix methods for the continuous transition range 0 these results for continuous q were obtained from a transfer matrix constructed for a generalized whitney polynomial representing the potts models an effective algorithm to compute the dominant eigenvalues of this essentially nonsymmetric transfer matrix is developed

aggregation and disaggregation in integer programming problems column aggregation of 0 1 programming problems is considered by relaxing the integer requirements in the aggregated problem an easy problem results the solution of which can be used to compute bounds on the loss of accuracy in the objective function value it is shown how these bounds can be improved by identification of valid inequalities and by exploiting primal degeneracy a small example is given to illustrate the procedure

finite size scaling for directed bond percolation with and without cycles on a triangular lattice the authors apply finite size scaling and phenomenological renormalisation group arguments to the problems of directed acyclic directed cyclic and undirected bond percolation on a triangular lattice the results are in good agreement with known estimates and show that the phenomenological renormalisation procedure is sensitive to the difference between global and local directional biases as well as the distinction between locally directed and fully isotropic problems in addition the authors draw tentative comments on the extension to directed problems of the relation a pi eta where a is the inverse correlation length amplitude of a strip of finite width at criticality and eta is the exponent that describes the decay of correlations at the critical point known to hold for various isotropic systems

analytical calculation of two leading exponents of the dilute potts model a potts model on a square lattice with two and four spin interaction and site and bond dilution is shown to be dual to itself the model is mapped onto a vertex problem which in turn is equivalent to a solid on solid model by means of these mappings the dilute potts model can be written as a gaussian like model with staggered and direct periodic fields the leading and next to leading exponents of the potts model are calculated subject to the validity of certain assumptions

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

finite size scaling and the two dimensional xy model shows that the finite size scaling assumption and particularly a conjectured relation involving the exponent eta are valid in the low temperature phase of the 2d xy model order by order in a perturbative expansion of the two point correlation function

error bounds for the aggregated convex programming problem applied mathematical programming problems are often approximations of larger more detailed problems one criterion to evaluate an approximating program is the magnitude of the difference between the optimal objective values of the original and the approximating program the approximation we consider is variable aggregation in a convex program bounds are derived on the difference between the two optimal objective values previous results of geoffrion and zipkin are obtained by specializing our results to linear programming also we apply our bounds to a convex transportation problem

mathematical construction of a reissner mindlin plate theory for composite laminates abstract a reissner mindlin theory for composite laminates without invoking ad hoc kinematic assumptions is constructed using the variational asymptotic method instead of assuming a priori the distribution of three dimensional displacements in terms of two dimensional plate displacements as what is usually done in typical plate theories an exact intrinsic formulation has been achieved by introducing unknown three dimensional warping functions then the variational asymptotic method is applied to systematically decouple the original three dimensional problem into a one dimensional through the thickness analysis and a two dimensional plate analysis the resulting theory is an equivalent single layer reissner mindlin theory with an excellent accuracy comparable to that of higher order layer wise theories the present work is extended from the previous theory developed by the writer and his co workers with several sizable contributions a six more constants 33 in total are introduced to allow maximum freedom to transform the asymptotically correct energy into a reissner mindlin model b the semi definite programming technique is used to seek the optimum reissner mindlin model furthermore it is proved the first time that the recovered three dimensional quantities exactly satisfy the continuity conditions on the interface between different layers and traction boundary conditions on the bottom and top surfaces it is also shown that two of the equilibrium equations of three dimensional elasticity can be satisfied asymptotically and the third one can be satisfied approximately so that the difference between the reissner mindlin model and the second order asymptotical model can be minimized numerical examples are presented to compare with the exact solution as well as the classical lamination theory and the first order shear deformation theory demonstrating that the present theory has an excellent agreement with the exact solution

on plate theories and saint venant s principle abstract it is generally known hat the classical germain kirchhoff plate theory is the leading term of the outer asymptotic expansion or interior solution in a small thickness parameter for the linear elastostatics of thin flat isotropic bodies this leading term or the actual outer solution alone cannot satisfy arbitrarily prescribed admissible edge data on the other hand the complementary inner asymptotic expansion or boundary layer solution is determined by a sequence of boundary value problems which are nearly as difficult to solve as the original problem for stress edge data saint venant s principle has been invoked to generate a set of stress boundary conditions for the classical plate theory as well as for higher order terms in the outer expansion giving various thick plate theories without any reference to the inner solution attempts to derive the corresponding boundary conditions for displacement and other types of edge data in the literature for general shape plates have not been successful the present study applies a general method developed by the authors to derive the correct set of boundary conditions for arbitrarily prescribed admissible edge data without an explicit solution of the inner or boundary layer solution for a number of special cases of general interest including cases with displacement edge data our general results also show that to be strictly correct saint venant s principle should be applied only to the leading term outer solution i e the classical plate theory

two dimensional semi infinite multicritical ising models the order parameter correlation functions of the z2 invariant multicritical points in the unitary minimal series of conformal field theory are derived for a semi infinite plane constrained to fixed or free boundary conditions these yield the corresponding universal surface exponents which distinguish the behaviour between even and odd critical models we also make explicit the interplay between duality and boundary conditions

explicit results for the correlation length of the finite sized spherical model of ferromagnetism we report explicit results for the zero field correlation length xi t l of a spherical model ferromagnet confined to geometry ld d infinity d d 2 d or 2 and subjected to twisted boundary conditions in the region of first order phase transition t tc xi under twisted boundary conditions obeys the same scaling law as under periodic boundary conditions though with a different amplitude in the core region t approximately tc the scaling behaviour changes radically as one moves from one set of boundary conditions to the other affected greatly by the pinning of the ground state wavevector k0 of the system

corrections to scaling and self duality in the restricted solid on solid model the corrections to scaling at and above the roughening transition tr in the restricted solid on solid model are studied by means of finite size scaling for semi infinite strips of width 2 to 10 it is shown that at a temperature tsd not far above the roughening temperature where the restricted solid on solid model is invariant under the duality transformation of the five state clock model the fugacity of the sine gordon operator must vanish for the dual truncated planar model this means that the core energy of the vortices diverges between ts and tr the corrections to scaling do not reach their asymptotic behaviour but are dominated by the contributions from the delta phi 4 operator associated with the restriction to steps of height one

numerical analysis of thick plates bending behaviour of a rectangular plate is analysed with the help of a refined higher order theory the theory is based on a higher order displacement model and the three dimensional hooke s laws for plate material giving rise to a more realistic quadratic variation of the transverse shearing strains and linear variation of the transverse normal strain through the plate thickness it is shown that the segmentation method for the numerical analysis of plates simply supported on two opposite edges can be considered to be the most competitive method in terms of efficiency economy reliability and accuracy in such applications

tight bounds for stochastic convex programs variable and row aggregation as a technique of simplifying a mathematical program is utilized to develop bounds for two stage stochastic convex programs with random right hand sides if one is able to utilize the problem structure along with only first moment information a tighter bound than the usual mean model bound based on jensen s inequality may be obtained moreover it is possible to construct examples for which the mean model bound will be arbitrarily poor consequently one can tighten jensen s bound for stochastic programs when the distribution has a compact support this bound may be improved further by partitioning the support using conditional first moments with regard to first moment upper bounds the gassmann ziemba inequality is used for the stochastic convex program to seek a model which can be solved using standard convex programming techniques moreover it allows one to easily construct upper bounds using the solution of the lower bounding problem finally the results are extended to multistage stochastic convex programming problems

finite size scaling of the quantum ising chain with periodic free and antiperiodic boundary conditions the authors give exact results for the energy spectrum of a chain of n ising spins in a transverse field with periodic free and antiperiodic boundary conditions the dependence of the energy gaps on boundary conditions is compatible with predictions of conformal invariance for correlation lengths in two dimensional strips the feasibility of calculating surface critical indices using phenomenological renormalisation with free boundary conditions and the convergence for large n are discussed

enhanced first order theory based on mixed formulation and transverse normal effect abstract an accurate prediction of displacements and stresses for laminated and sandwich plates is presented using an enhanced first order plate theory based on the mixed variational theorem efsdtm developed in this paper in the mixed formulation transverse shear stresses based on an efficient higher order plate theory ehopt developed by cho and parmerter cho m parmerter r r 1993 efficient higher order composite plate theory for general lamination configurations aiaa journal 31 1299 1306 are utilized and modified to satisfy prescribed lateral conditions and displacements are assumed to be those of a first order shear deformation theory fsdt relationships between the modified ehopt and the fsdt are systematically derived via both the mixed variational theorem and the least square approximation of difference between in plane stresses including the transverse normal stress effect it is shown that the transverse normal stress effect should be considered in predicting the in plane stresses when the poisson effect is dominant the developed efsdtm preserves the computational advantage of the classical fsdt while allowing for important local through the thickness variations of displacements and stresses through the recovery procedure the accuracy and efficiency of the present theory are assessed by comparing its results with various plate models as well as the three dimensional exact solutions for thick laminated and sandwich plates

finite size corrections for ground states of the xxz heisenberg chain the method of de vega and woynarovitch 1985 is used to calculate finite size corrections to the ground state energy in different sectors for the xxz heisenberg chain finite size scaling amplitudes and correction to scaling exponents in the critical region are derived using conformal invariance a scaling dimension x pi gamma 2 pi is extracted corresponding to the electric field operator in the 8 vertex model this confirms a conjecture of baxter and kelland 1974 finite size scaling properties near the kosterlitz thouless critical point delta 1 are discussed

critical exponents of two dimensional potts and bond percolation models critical exponents of the two dimensional q state potts model are calculated by means of finite size scaling and transfer matrix techniques for continuous q results for the temperature exponent agree accurately with the conjecture of den nijs 1979 the magnetic exponent is found to behave in accordance with the conjecture of nienhuis et al 1980

conformal invariance in incommensurate phases we study finite size corrections to the free energy of free fermion models on a torus with periodic twisted and fixed boundary conditions inside the critical striped incommensurate phase the free energy densityf n m on ann m square lattice with periodic or twisted boundary conditions scales asf n m f a s nm we derive exactly the finite size scaling fss amplitudesa s as a function of the aspect ratios m n these amplitudes are universal because they do not depend on details of the free fermion hamiltonian we establish an equivalence between the fss amplitudes of the free fermion model and the coulomb gas system with electric and magnetic defect lines the twist angle generates magnetic defect lines while electric defect lines are generated by competition between domain wall separation and system size the fss behavior of the free fermion model is consistent with predictions of the theory of conformal invariance with the conformal chargec l for instance the fss amplitude on an infinite cylinder with fixed boundary conditions is found to be one quarter of that with periodic boundary conditions finally we conjecture the exact form of the fss amplitudes for an interacting fermion model on a torus numerical calculations employing the bethe ansatz confirm our conjecture in the infinite cylinder limit

universal amplitudes in finite size scaling generalisation to arbitrary dimensionality the relationship between the correlation length and critical exponents in finite width strips in two dimensions is generalised to cylindrical geometries of arbitrary dimensionality d for d not 2 these correspond however to curved spaces the result is verified for the spherical model

duality of ordinary and extraordinary surface critical behaviour in the two dimensional potts model the dual relationship between semi infinite two dimensional q state potts models with free and fixed spin boundary conditions is used to study the surface critical behaviour at the bulk critical temperature with fixed boundary spins i e the extraordinary transition both the magnetisation and energy densities have singularities of the same form mod t tc mod 2 alpha as the bulk free energy at t tc both the spin spin and energy energy correlations decay as r 4 parallel to the surface

kosterlitz thouless transition in three state mixed potts ferro antiferromagnets we study three state potts spins on a square lattice in which all bonds are ferromagnetic along one of the lattice directions and antiferromagnetic along th eo ther numerical transfer matrix methods are used on infinite strips of width l sites 4 l 14 based on the analysis of the ratio of scaled mass gaps inverse correlation lengths and scaled domain wall free energies we provide strong evidence that a critical kosterlitz thouless phase is present whose upper limit is in our best estimate tc 0 29 0 01 from an analysis of the extremely anisotropic nature of excitations below tc w e argue that the critical phase extends all the way down to t 0 while domain walls parallel to the ferromagnetic direction are soft for the whole extent of the critical phase those along the antiferromagnetic direction seem to undergo a softening transition at a finite temperature assuming a bulk correlation length varying for t t c a s t a exp b t tc 1 2 we attempt finite size scaling plots of our finite width correlation lengths our best results are for tc 0 50 0 01 we propose a scenario in which such inconsistency is attributed to the extreme narrowness of the critical region

asymptotic construction of reissner like composite plate theory with accurate strain recovery abstract the focus of this paper is to develop an asymptotically correct theory for composite laminated plates when each lamina exhibits monoclinic material symmetry the development starts with formulation of the three dimensional 3 d anisotropic elasticity problem in which the deformation of the reference surface is expressed in terms of intrinsic two dimensional 2 d variables the variational asymptotic method is then used to rigorously split this 3 d problem into a linear one dimensional normal line analysis and a nonlinear 2 d plate analysis accounting for classical as well as transverse shear deformation the normal line analysis provides a constitutive law between the generalized 2 d strains and stress resultants as well as recovering relations to approximately but accurately express the 3 d displacement strain and stress fields in terms of plate variables calculated in the plate analysis it is known that more than one theory may exist that is asymptotically correct to a given order this nonuniqueness is used to cast a strain energy functional that is asymptotically correct through the second order into a simple reissner like plate theory although it is not possible in general to construct an asymptotically correct reissner like composite plate theory an optimization procedure is used to drive the present theory as close to being asymptotically correct as possible while maintaining the beauty of the reissner like formulation numerical results are presented to compare with the exact solution as well as a previous similar yet very different theory the present theory has excellent agreement with the previous theory and exact results

finite size scaling for percolation on elongated lattices in two and three dimensions we derive scaling laws for the percolation properties of an elongated lattice i e those with dimensions of l d ensuremath 1 ifmmode times else texttimes fi mathrm nl in d dimensions where n denotes the aspect ratio of the lattice based on statistical arguments it is shown that in the direction of the extension the percolation threshold scales approximately as mathrm ln n 1 a in both two and three dimensions extensive monte carlo simulations of the site percolation model confirm this scaling behavior it is further shown that the density of the incipient infinite cluster at the percolation threshold scales differently in two and three dimensions

a refined asymptotic theory and computational model for multilayered composite plates abstract the asymptotic theory of multilayered composite plates developed recently is refined to embrace the shear deformation theory the derivation is based on application of asymptotic expansion to the hellinger reissner variational functional in which the displacements and transverse stresses are taken to be the functions subject to variation by introducing rotations as auxiliary variables in the asymptotic formulation the shear deformation theory of laminated plates arises naturally as the first order approximation to the three dimensional theory higher order corrections are determined in an adaptive and hierarchic way the computational model is constructed on the basis of the asymptotic expressions of the h r functional in conjunction with the finite element method in which the displacements and transverse stresses may be interpolated independently through successive ntegration the transverse stress degrees of freedom are condensed at the element level resulting in rotations and midplane displacements as basic unknowns in the system equations in the model the lateral boundary conditions are satisfied exactly the edge conditions associated with each level are shown to be similar to the ones in the 2d theory of mindlin s plates which can be easily implemented in the computation the performance of the model is illustrated by example problems

universal amplitude exponent relations for interfaces and conformal mappings the author considers the finite size fs scaling behaviour of the transverse correlation lengths xi sub n for an interface confined in a strip geometry exactly at a second order fluctuation dominated wetting transition he shows that the dimensionless amplitude ratios a sub n sigma l2 kbt xi sub n with sigma the surface stiffness coefficient are related to the short distance expansion critical exponent theta by a sub n pi 2n n theta 1 2 for all fluctuation dominated wetting transitions provided the binding potential v y in the capillary wave model is conformally mapped from the semi infinite plane he argues that the existence of this amplitude exponent relation reflects the conformal invariance of the capillary wave model lagrange density and lists a number of one point functions which can be shown to exhibit this invariance explicitly

dynamic critical behaviour of semi infinite systems conformal invariance and mirror theory the critical dynamics of the d dimensional semi infinite systems is studied at bulk critical temperature as a result of the conformal invariance the dynamic response and correlation functions depend only on the real distance r the image distance r and the time t mirror theory assuming the non conserved order parameter with o n symmetry the authors evaluate the response and correlation functions exactly in the large n limit and also to first order in epsilon 4 d the authors results satisfy the mirror theory for the various types of the phase transitions including the ordinary special anisotropic special and extraordinary transitions

a study of transverse normal stress effect on vibration of multilayered plates and shells this paper evaluates transverse normal stress zzeffect on vibration of multilayered structures to this purpose a mixed plate model initially introduced by toledano and murakami has been extended to dynamics analysis of double curved shells these models allow both continuous interlaminar transverse shear and normal stresses as well as the zigzag form of the displacement distribution in the shell thickness directions to be modelled governing equations have been derived by employing a reissner s mixed theorem classical models on the basis of standard displacement formulations have been considered for comparison purposes the evaluations of transverse stress effects have been conducted by comparing constant linear and higher order distributions of transverse displacement components in the plate thickness directions free vibrational response of layered simply supported plates cylindrical and spherical shells made of isotropic as well as orthotropic layers has been analyzed the numerical investigation carried out and comparison with earlier results has concluded that 1 the possibility of describing interlaminar continuous transverse normal stress makes the mixed theories more attractive with respect to other available modelling 2 any refinements of classical models are meaningless unless the effects of interlaminar continuous transverse shear and normal stresses are both taken into account in a multilayered shell theory

hunting for the central charge of the virasoro algebra six and eight state spin models in two dimensions conformal invariance has important implications for the finite size scaling properties of the spectra of transfer matrices and quantum chains at the critical point some relations between the finite size scaling amplitudes are obtained which can be used as a test of conformal invariance and implicitly to distinguished between second order and first order phase transitions the numerical values of the scaling amplitudes give the scale dimensions of various operators six and eight state self dual quantum chains with cubic symmetries are considered at the critical point for three values of the coupling constant the systems are found to be conformal invariant and estimates for several critical exponents are obtained based on the approximate values of the critical exponent one tries to find the values of the corresponding central charges of the virasoro algebras

finite size effects in conformal field theories and non local operators in one dimensional quantum systems the authors generalise the well known connection between critical exponents and finite size effects in conformal field theories to non local operators and find the long wave asymptotics of vacuum expectation values of some non local operators in one dimensional quantum systems

critical off critical interface in the ising quantum chain and conformal invariance the low energy excitation spectrum of an ising quantum chain in a transverse field which is critical h j 1 for 1 or n or l 2 and off critical h not j for l 2 n or l is calculated up to o l 1 interface critical exponents are determined numerically in the odd sector and exactly in the even sector using finite size scaling one gets an ordinary surface transition when h j and an extraordinary surface transition when h j the gap exponent relation is verified the mass gaps and the level degeneracy are in agreement with conformal invariance

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

finite size studies of the ashkin teller model the authors study the ashkin teller model in the time continuous hamiltonian version finite size scaling is used to calculate the magnetic gamma m electric gamma p and thermal alpha and nu critical exponents for several values of the coupling constant lambda the results confirm the believed extended scaling relations and suggest a conjecture relating the mass gap amplitudes and critical indices in the hamiltonian context

aggregation and disaggregation techniques and methodology in optimization a fundamental issue in the use of optimization models is the tradeoff between the level of detail and the ease of using and solving the model aggregation and disaggregation techniques have proven to be valuable tools for manipulating data and determining the appropriate policies to employ for this tradeoff furthermore aggregation and disaggregation techniques offer promise for solving large scale optimization models supply a set of promising methodologies for studying the underlying structure of both univariate and multivariate data sets and provide a set of tools for manipulating data for different levels of decision makers in this paper we develop a general framework for aggregation and disaggregation methodology survey previous work regarding aggregation and disaggregation techniques for optimization problems illuminate the appropriate role of aggregation and disaggregation methodology for optimization applications and propose future research directions

restatement of first order shear deformation theory for laminated plates abstract a restatement of the first order shear deformation theory of plates is offered and verified numerically by exact 3 d elasticity results based on a more appropriate physical assumption the restated theory innovatively interprets its variables and applies elasticity equations in a more pertinent manner it assumes physically that only in some average sense does a straight line originally normal to the midplane remain straight and rotate relative to the normal of the midplane after deformation hence the in plane displacement is still approximated in an average sense as linear and the transverse deflection as constant through the plate thickness the associated nominal uniform transverse shear strain directly derived from these displacement field assumptions is identified as the weighted average transverse shear strain through the plate thickness with the corresponding transverse shear stress as the weighting function while the actual transverse shear strain is permitted to vary through the thickness and satisfies the constitutive law with its stress counterpart likewise the average rotation of the line is identified as its weighted average value instead of the one evaluated from a linear regression of the inplane displacement with the least square method examination of bending energy and transverse shear energy supports this interpretation in addition an effective transverse shear stiffness parameter is identified and proven appropriate this restated first order shear deformation theory yields accurate local as well as global response predictions without employing a shear correction factor

reconstruction of first order shear deformation shell theory for laminated and sandwich shells a first order shear deformation shell theory fsdt based on general curvilinear coordinates has been reconstructed through a strain energy transformation based on the definition of the mean displacements the transverse shear strains that are constant through the thickness are improved to vary through the thickness it is assumed that the displacements and in surface strains of three dimensional theory are approximated by those of fsdt relationship between fsdt and three dimensional theory has been systematically established in the averaged least square sense this relationship provides the closed form recovering relations for three dimensional variables expressed in terms of fsdt relations the present approach has been applied to a higher order zigzag shell theory comparisons of displacements and stresses of laminated and sandwich shells using the present theory are made with the original fsdt and three dimensional exact solutions

tests of hyperuniversality for self avoiding walks a universal combination of amplitudes for the end to end distance of n step self avoiding walks and for the number of n step self avoiding polygons is estimated numerically for various lattices in d 2 universality of this amplitude combination is confirmed to good accuracy while in d 3 the data are consistent with universality but the error limits are rather large for finite width square lattice strips the authors calculate universal critical point correlation amplitudes by fixed fugacity monte carlo simulations in addition these amplitudes are calculated analytically either exactly or approximately by cardy s conformal mapping approach numerical values agree well with the theoretical predictions

critical behaviour and logarithmic corrections of a quantum model with three spin interaction extended finite size scaling and series expansion methods are used to determine the critical properties of the one dimensional quantum ising model with three spin interaction by supposing the presence of logarithmic corrections the universality class of the model is investigated the results obtained by different methods support the conjecture that the model belongs to the same universality class as the four state potts model

proper generalized decomposition and layer wise approach for the modeling of composite plate structures abstract in the framework of the design of laminated and sandwich structures the computation of local quantities needs a layer wise approach but the computational cost of such approach increases with the number of layers in this work the introduction of the proper generalized decomposition pgd is presented for the layer wise modeling of heterogeneous structures in order to reduce the number of unknowns the displacement field is approximated as a sum of separated functions of the in plane coordinates x y and the transverse coordinate z this choice yields to an iterative process that consists of solving a 2d and 1d problem successively at each iteration in the thickness direction a fourth order expansion in each layer is considered for the in plane description classical finite element method is used after a preliminary study to show the relevance of the present approach mechanical tests for thin to thick laminated and sandwich plates with various boundary conditions are presented the results are compared with elasticity reference solutions

a critical amplitude relation for one dimensional quantum transitions and determination of the exponent eta a new critical amplitude relation which holds for one dimensional quantum ground state transitions is presented the relation yields an estimate of the sound velocity which appears in the conformal field theory as an a priori unknown parameter with the use of this relation the exponent eta can be explicitly determined from only the scaling fit of the off critical energy gap the relation is confirmed in the transverse ising model the s 1 2 anisotropic xy model and the three state potts model

finite size scaling of the free energy levels in the ising and potts q 3 universality the finite size scaling of the free energy levels of privman and fisher 1984 is tested numerically on two dimensional lattice strips in the ising and q 3 potts universality the universal amplitudes and the free energy per site are obtained

on cardy s formula for the critical crossing probability in 2d percolation cardy s formula for the probability r of crossing a rectangular critical percolation system in the vertical direction with free boundaries on the two sides is written explicitly in terms of the aspect ratio r heightlwidth the first three terms are given by n 24 33i r 4 2 e r 3 e 7n 13 e 3zr 3 i which with n 1 nv i r m sufficient to determine x to high accuracy for all r

conformal invariance and surface defects in the two dimensional ising model exact results the surface critical behavior of the two dimensional ising model with homogeneous perturbations in the surface interactions is studied on the one dimensional quantum version a transfer matrix method leads to an eigenvalue equation for the excitation energies the spectrum at the bulk critical point is obtained using anl 1 expansion wherel is the length of the ising chain it exhibits the towerlike structure which is characteristic of conformal models in the case of irrelevant surface perturbations h s j s 0 as well as for the relevant perturbationh s 0 for which the surface is ordered at the bulk critical point leading to an extraordinary surface transition the exponents are deduced from the gap amplitudes and confirmed by exact finite size scaling calculations both cases are finally related through a duality transformation

bending vibration and buckling of simply supported thick multilayered orthotropic plates an evaluation of a new displacement model abstract based upon a piecewise linear displacement field which allows the contact conditions for the displacements and the transverse shearing stresses at the interfaces to be satisfied simultaneously the non linear in the von karman sense equations of motion for thick multilayered orthotropic plates are developed successively the equations are specified to the linear boundary value problem of the bending and to the linear eigenvalue problems of the undamped vibration and buckling of rectangular plates in order to assess the accuracy of the proposed theory the sample problem of the bending free undamped vibration and buckling of a three layered symmetric cross ply square plate simply supported on all edges is investigated for purposes of comparison numerical results from the exact elasticity theory the classical lamination kirchhoff theory and the shear deformation theory timoshenko and mindlin with three different values of the shear correction factor are also presented it is found that the proposed approach is very efficient in predicting the global responses deflection natural frequencies and buckling loads of thick multilayered plates and models effects such as the distortion of the deformed normals not attainable from the classical lamination theory as well as the shear deformation theory