continuum modeling of the mechanical and thermal behavior of discrete large structures in the present paper we introduce a rather straightforward construction procedure in order to derive continuum equivalence of discrete truss like repetitive structures once the actual structure is specified the construction procedure can be outlined by the following three steps a all sets of parallel members are identified b unidirectional effective continuum properties are derived for each of these sets and c orthogonal transformations are finally used to determine the contribution of each set to the overall effective continuum properties of the structure here the properties includes mechanical stiffnesses thermal coefficients of thermal expansions and material densities once expanded descriptions of the steps b and c are done the construction procedure will be applied to a wide variety of discrete structures and the results will be compared with those of other existing methods

non gaussian effects on quantum entropies abstract a deduction of generalized quantum entropies within the non gaussian frameworks tsallis and kaniadakis is derived using a generalized combinatorial method and the so called q and calculus in agreement with previous results we also show that for the tsallis formulation the q quantum entropy is well defined for values of the nonextensive parameter q lying in the interval 0 2

finite groups whose element orders are consecutive integers there are various characterizations of groups by conditions on the orders of its elements for example in 8 1 the finite groups all of whose elements have prime power order have been classified in 2 16 181 some simple groups have been characterized by conditions on the orders of its elements and b h neumann 12 has determined all groups whose elements have orders 1 2 and 3 the latter groups are oc3 groups in the sense of the following

shear deformation plate continua of large double layered space structures abstract a simple method is presented to model large rigid jointed lattice structures as continuous elastic media with couple stresses using energy equivalence in our analysis the transition from the discrete system to the continuous media is achieved by expanding the displacements and the rotations of the nodal points in a taylor series about a suitable chosen origin the strain energy of the continuous media with couple stresses is then specialized to obtain shear deformation plate continua equivalent continua for single layered grids double layered grids and three dimensional lattices are then obtained

quantum statistical mechanics for nonextensive systems the traditional basis of description of many particle systems in terms of green functions is here generalized to the case when the system is nonextensive by incorporating the tsallis form of the density matrix indexed by a nonextensive parameter q this is accomplished by expressing the many particle q green function in terms of a parametric contour integral over a kernel multiplied by the usual grand canonical green function which now depends on this parameter we study one and two particle green functions in detail from the one particle green function we deduce some experimentally observable quantities such as the one particle momentum distribution function and the one particle energy distribution function special forms of the two particle green functions are related to physical dynamical structure factors some of which are studied here we deduce different forms of sum rules in the q formalism a diagrammatic representation of the q green functions similar to the traditional ones follows because the equations of motion for both of these are formally similar approximation schemes for one particle q green functions such as hartree and hartree fock schemes are given as examples this extension enables us to predict possible experimental tests for the validity of this framework by expressing some observable quantities in terms of the q averages

what should a statistical mechanics satisfy to reflect nature there is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual boltzmann gibbs prescriptions more specifically ubiquitous natural and artificial systems exhibit generic stationary states which are not ergodic nor close to it in any geometrically simple subset of the a priori allowed phase space in any even extended trivial sense a vast class of such systems appears nevertheless to be tractable within thermostatistical methods completely analogous to the usual ones the question posed in the title arises then naturally some answer to this complex question is advanced in the present review of nonextensive statistical mechanics and its recent connections

equivalent continuum representation of structures composed of repeated elements a procedure for determining the equivalent continuum properties of a structure composed of repeated patterns of discrete elements with both displacement and rotational coordinates is presented these nodal coordinates are transformed to rigid body and strain gradient variables using a polynomial approximation the maximum number of independent variables that may be retained is determined by applying a ranking procedure to the resulting transformation matrix the possibility of introducing errors by requiring the analyst to supply the strain gradient terms directly is reduced by identifying the appropriate variables through the use of the polynomial expansion and the ranking procedure additional constraints may be imposed in this analysis the equivalent continuum parameters result when a further transformation to the appropriate kinematic variables is applied and the strain energy expression is reduced to these variables three dimensional beamand plate like structures are treated the results correspond to findings using other approaches

relationships between power law long range interactions and fractional mechanics abstract we investigate the relationships between models of power law long range interactions and mechanics based on fractional derivatives we present the fractional lagrangian density which gives the euler lagrange equation that serves as the equation of motion for fractional power law long range interactions we derive this equation by the fractional variational method in addition we derive a noether like current from the fractional lagrangian density

dynamic continuum modeling of beamlike space structures using finite element matrices subscripts a rational and straight forward method is introduced for developing equivalent continuum models of large beam like periodic lattice structures based on energy equivalence extended timoshenko bean model is chosen to take account of the effects due to couplings between extension transverse shear and bending deformations the procedure for developing continuum models involves utilizing well defined existing finite element matrices directly in caluclating strain and kinetic energies from which equivalent continuum structural and dynamic properties are induced the numerical results of free vibration analysis show that the method developed in this paper gives very reliable dynamic characteristics compared to other methods nomenclature

green functions based on tsallis nonextensive statistical mechanics normalized q expectation value formulation in this paper the green function theory of quantum many particle systems recently presented is reworked within the framework of nonextensive statistical mechanics with a new normalized q expectation values this reformulation introduces a renormalization of temperature of the earlier theory and a self consistency condition the importance of these two features is nontrivial and to emphasize this we explicitly contrast the maximum entropy density matrices derived for an exactly solvable model based on the two types of the constraints the linear response theory is also presented along with its two particle green function version in order to emphasize the importance of the new formalism we collect here the results where both the formalisms have been used to examine the same set of problems this reveals clearly that the new formalism is the method of choice because the numerical results are much more physically meaningful than those found in the old version even though the general features or the answers retain the same characteristics in certain cases in the case where thermodynamic entities are to be examined as in the case of the q dependence of bose einstein condensation the self consistent requirement in the new formalism is numerically much more subtle and thus the earlier results are modified as shown in fig 1

statistical mechanics based on renyi entropy abstract in this work we show that it is possible to obtain a generalized statistical mechanics thermostatistics based on renyi entropy to be maximized with adequate constraints the equilibrium probability distribution thus obtained has a very interesting property indeed it reminds us the statistical distribution proposed by tsallis known to conveniently describe a variety of phenomena in nonextensive systems moreover some examples are worked out in order to illustrate the main features of the herein introduced formalism

effective constitutive relations for large repetitive frame like structures abstract effective mechanical properties for large repetitive frame like structures are derived using straight forward combinations of strength of material orthogonal transformation techniques once the actual structure is identified symmetry considerations are used in order to identify its independent property constants the actual values of these constants are constructed according to a building block format which is carried out in the three consecutive steps a all bask planar lattices are identified b effective continuum properties are derived for each of these planar basic grids using matrix structural analysis methods and c orthogonal transformations are finally used to determine the contribution of each basic set to the overall effective continuum properties of the structure

a q generalization of laplace transforms the laplace transform is generalized by using the q exponential function eqx 1 1 q x 1 1 q that emerges from tsallis non extensive statistical mechanics and some of its properties are obtained the usual transform is recovered as a limiting case q1 the use of the q laplace transform is illustrated by establishing a relation between the classical canonical q partition function and the density of states

analytical investigation of structurally stable configurations in shape memory alloy actuated plates strains produced by active materials embedded in plates have been extensively used to manipulate the shape of surface like engineering structures shape memory alloys smas are active materials that provide a significant amount of strain under large stresses a characteristic of great utility in such morphing structures in this work an analytical approach to approximate the deformation of plates with sma constituents is developed via the rayleigh ritz method an additive set of kinematically admissible displacement fields with unknown coefficients is used to describe the plate displacement field the total potential energy is then calculated using the displacement field loading conditions and constitutive relations for the plate layer s composed of sma wire meshes dense sma films and or elastic material the unknown coefficients are then found via minimization of the total potential energy this approach provides closed form expressions for the approximate deformation of the plates including multistable configurations the response of circular sma based plates is studied herein the results show that temperature fields with a linear variation in the radial direction induce multistable configurations in which the plate gaussian curvature is determined by the direction of the temperature gradient an alternative inversion of the proposed approach is used to directly compute the temperature field required to morph a plate towards a prescribed goal shape the obtained closed form expressions show good agreement with detailed non linear finite element analysis simulations the proposed approach provides analysts with a low computational cost and relatively simple implementation to assess the potentially stable configurations of sma based plates under given loading conditions knowledge of such stable configurations is very valuable in the design of sma based morphing structures c 2015 elsevier ltd all rights reserved

path integral approach to the nonextensive canonical density matrix abstract feynman s path integral is herein generalized to the nonextensive canonical density matrix based on tsallis entropy this generalization is done in two ways by using unnormalized and normalized constraints firstly we consider the path integral formulation with unnormalized constraints and this generalization is worked out through two different ways which are shown to be equivalent these formulations with unnormalized constraints are solutions to the two generalized bloch equations proposed in this work the first form of the generalized bloch equation is linear but with a temperature dependent effective hamiltonian the second form is nonlinear and resembles the anomalous correlated diffusion equation porous medium equation furthermore we can extend these results to the prescription of field theory using integral representations the second development is dedicated to analyzing the path integral formulation with normalized constraints to illustrate the methods introduced here we analyze the free particle case and a non interacting scalar field the results herein obtained are expected to be useful in the discussion of generic nonextensive contexts

equivalent continuum models of large platelike lattice structures abstract a new continuum method based on the concept of energy equivalence is introduced to represent a large platelike periodic lattice structure as an equivalent continuum plate the procedure for developing an equivalent continuum plate involves the use of existing well defined finite element matrices for easy calculation of strain and kinetic energies contained in a representative lattice cell of the lattice plate the strain and kinetic energies contained in the representative lattice cell of lattice plate and the finite element of equivalent continuum plate are expressed in terms of continuum degrees of freedom introduced in this paper with corresponding reduced stiffness and mass matrices the structural properties of the equivalent continuum plate are then obtained by simply equating the reduced stiffness and mass matrices for the equivalent continuum plate to those for the lattice plate free vibration analyses for the continuum plates are conducted to evaluate the continuum method proposed in this paper numerical tests show that the present continuum method gives very reliable structural and dynamic properties compared with other well recognized continuum methods

tsallis nonextensive statistics with normalized q expectation values thermodynamical stability and simple illustrations abstract we prove that the specific heat c q q is nonnegative for q 0 1 in the tsallis generalized canonical ensemble with normalized q expectation values in this way we show the thermodynamic stability for this ensemble we also analyze the behavior of some thermodynamic functions such as internal energy and specific heat in the classical and quantum cases considering a spectrum of energy e n e n r e r 0

static and vibration analyses of general wing structures using equivalent plate models an efficient method using equivalent plate model is developed for studying the static and vibration analyses of general built up wing structures composed of skins spars and ribs the model includes the transverse shear effects by treating the built up wing as a plate following the reissner mindlin theory the so called first order shear deformation theory fsdt the ritz method is used with the legendre polynomials being employed as the trial functions this is in contrast to previous equivalent plate model methods which have used simple polynomials known to be prone to numerical ill conditioning as the trial functions the present developments are evaluated by comparing the results with those obtained using msc nastran for a set of examples these examples are i free vibration analysis of a clamped trapezoidal plate with a uniform thickness and b non uniform thickness varying as an airfoil ii free vibration and static analyses including skin stress distribution of a general built up wing and iii free vibration and static analyses of a swept back box wing the results obtained by the present equivalent plate model are in good agreement with those obtained by the finite element method

finite groups with consecutive nonlinear character degrees abstract the aim of this paper is to investigate structure of the finite groups whose nonlinear irreducible character degrees are consecutive integers