universality class of replica symmetry breaking scaling behavior and the low temperature fixed point order function of the sherrington kirkpatrick model a scaling theory of replica symmetry breaking rsb in the sherrington kirkpatrick sk model is presented in the framework of critical phenomena for the scaling regime of large rsb orders ensuremath kappa small temperatures t and small homogeneous magnetic fields h we employ the pseudodynamical picture r oppermann m j schmidt and d sherrington phys rev lett 98 127201 2007 where two critical points mathcal c mathcal p 1 and mathcal c mathcal p 2 are associated with the order function s pseudodynamical limits mathrm lim a ensuremath rightarrow ensuremath infty phantom rule 0 2em 0ex q a 1 and mathrm lim a ensuremath rightarrow 0 phantom rule 0 2em 0ex q a 0 at t 0 h 0 1 ensuremath kappa 0 mathcal c mathcal p 1 and mathcal c mathcal p 2 dominated contributions to the free energy functional f q a require an unconventional scaling hypothesis we determine the scaling contributions in accordance with detailed numerical self consistent solutions for up to 200 orders of rsb power laws scaling functions and crossover lines are obtained mathcal c mathcal p 1 dominated behavior is found for the nonequilibrium susceptibility which decays like ensuremath chi 1 ensuremath kappa ensuremath 5 3 f 1 t ensuremath kappa ensuremath 5 3 for the entropy which obeys s t 0 ensuremath sim ensuremath chi 1 2 and for the subclass of diverging parameters a i ensuremath kappa 5 3 f a i t ensuremath kappa ensuremath 5 3 describing parisi box sizes m i t ensuremath equiv a i t t with f 1 ensuremath zeta ensuremath sim ensuremath zeta and f a i ensuremath zeta ensuremath sim 1 ensuremath zeta for ensuremath zeta ensuremath rightarrow ensuremath infty while f 0 is finite mathcal c mathcal p 2 dominated behavior controlled by the magnetic field h while temperature is irrelevant is retrieved in the plateau height or width of the order function q a according to q pl h ensuremath kappa ensuremath 1 f pl h 2 3 ensuremath kappa ensuremath 1 with f pl phantom ensuremath mid ensuremath zeta ensuremath mid ensuremath zeta ensuremath rightarrow ensuremath infty ensuremath sim ensuremath zeta and f pl 0 finite divergent characteristic rsb orders ensuremath kappa mathcal c mathcal p 1 t ensuremath sim t ensuremath 3 5 and ensuremath kappa mathcal c mathcal p 2 h ensuremath sim h ensuremath 2 3 respectively describe the crossover from mean field sk to rsb critical behavior with rational valued exponents extracted with high precision from our rsb data the order function q a is obtained as a fixed point function q a of rsb flow in agreement with integrated fixed point energy and susceptibility distributions

existence of pullback attractors for pullback asymptotically compact processes abstract this paper is concerned with the existence of pullback attractors for evolution processes our aim is to provide results that extend the following results for autonomous evolution processes semigroups i an autonomous evolution process which is bounded dissipative and asymptotically compact has a global attractor ii an autonomous evolution process which is bounded point dissipative and asymptotically compact has a global attractor the extension of such results requires the introduction of new concepts and brings up some important differences between the asymptotic properties of autonomous and non autonomous evolution processes an application to damped wave problem with non autonomous damping is considered

near optimal configurations in mean field disordered systems we present a general technique to compute how the energy of a configuration varies as a function of its overlap with the ground state in the case of optimization problems our approach is based on a generalization of the cavity method to a system interacting with its ground state with this technique we study the random matching problem as well as the mean field diluted spin glass as a by product of this approach we calculate the de almeida thouless transition line of the spin glass on a fixed connectivity random graph

dispersion and wave propagation in discrete and continuous models for granular materials abstract a generalised continuum model for granular media is derived by direct homogenisation of the discrete equations of motion in contrast to previous works on this topic continuum concepts such as stress and moment stress are introduced after homogenisation first a very simple one dimensional model is considered and the continuum version for this model is derived by replacing the difference quotients of the discrete model by differential quotients the dispersion relations of the discrete and the continuous model are derived and compared variational boundary conditions for the continuous model are deduced from the stationarity of the corresponding lagrangian the three dimensional case is treated in an essentially similar fashion the resulting continuum theory is a combination of a cosserat continuum and a higher order deformation gradient continuum the salient features of the theory are illustrated by means of the dispersion relations for planar wave propagation

exponential attractors for the strongly damped wave equation in this paper we study the longtime dynamics to a strongly damped wave equation first in the critical case we prove by the l trajectories method that the related solution semigroup has the exponential attractor second in the subcritical case we give an explicit upper bound of the fractal dimension of the exponential attractor in terms of the data of the equation

pullback attractors for asymptotically compact non autonomous dynamical systems abstract first we introduce the concept of pullback asymptotically compact non autonomous dynamical system as an extension of the similar concept in the autonomous framework our definition is different from that of asymptotic compactness already used in the theory of random and non autonomous dynamical systems as developed by crauel flandoli kloeden schmalfuss amongst others which means the existence of a random or time dependent family of compact attracting sets next we prove a result ensuring the existence of a pullback attractor for a non autonomous dynamical system under the general assumptions of pullback asymptotic compactness and the existence of a pullback absorbing family of sets this attractor is minimal and in most practical applications it is unique finally we illustrate the theory with a 2d navier stokes model in an unbounded domain

existence and upper semicontinuity of random attractors for non autonomous stochastic strongly damped sine gordon equation on unbounded domains abstract in this paper we study the asymptotic behavior of solutions of the non autonomous stochastic strongly damped sine gordon equation driven by multiplicative noise defined on an unbounded domain first we introduce a continuous cocycle for the equation and establish the pullback asymptotic compactness of solutions second we consider the existence and upper semicontinuity of random attractors for the equation

d pullback attractor for a non autonomous wave equation with additive noise on unbounded domains this paper is devoted to investigating the asymptotic behavior of solutions of the wave equation with additive noise as well as a non autonomous term defined on unbounded domains firstly by uniform estimates a closed d pullback absorbing set of dynamical system f produced by the mentioned wave equation is obtained secondly the asymptotical compactness of f is established by the splitting technique finally the existence of ad pullback attractor for corresponding dynamical system f in h 1 r 3 xl 2 r 3 is proved where n 3 particularly we can show that the d pullback attractor is also periodic when the forcing term is periodic

gradient enhanced damage for quasi brittle materials summary conventional continuum damage descriptions of material degeneration suffer from loss of well posedness beyond a certain level of accumulated damage as a consequence numerical solutions are obtained which are unacceptable from a physical point of view the introduction of higher order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models a consistent numerical solution procedure of the governing partial differential equations is presented which is shown to be capable of properly simulating localization phenomena

zero temperature properties of rna secondary structures we analyze different microscopic rna models at zero temperature we discuss both the most simple model which suffers a large degeneracy of the ground state and models in which the degeneracy has been removed in a more or less severe manner we calculate low energy density of states using a coupling perturbing method where the ground state of a modified hamiltonian that repels the original ground state is determined we evaluate scaling exponents starting from measurements of overlaps and energy differences in the case of models without accidental degeneracy of the ground state we are able to clearly establish the existence of a glassy phase with ensuremath theta ensuremath simeq 1 3 87 15 aa 64 60 fr

second gradient constitutive theory for granular material with random packing structure abstract a second gradient constitutive law for granular media is derived in which stress is a function of the second order of strain gradient the constitutive coefficients for granular materials with an isotropic packing structure are derived in explicit terms of inter particle stiffness and particle size in the present constitutive theory the total number of elastic constants for the isotropic granular material is four two of them are the usual lame constants the other two are associated with the second gradient of strain the derived constitutive relationships illustrate the important role of micro scale properties in the macro scale behavior the influence of inter particle stiffness and particle size on the response of material due to the second gradient of strain is discussed this paper also discusses the connection between the second gradient theory and non local theory the second gradient theory can be regarded as the first order approximation of non local theory

implicit gradient elasticity a new formulation of gradient elasticity is derived and implemented pade approximations are used to introduce an implicit relation between non local strains and displacements as a result the finite element interpolation requires only 0 continuous rather than 1 continuous shape functions the underlying energy functional is presented and it is found that the present formulation is of the mixed type whereby the non local strains act as the primary unknowns and the displacements as the auxiliary unknowns the implications on the interpolation are studied finally the influence of the additional length scale parameter on the global response is assessed copyright 2006 john wiley sons ltd

gradient elasticity in statics and dynamics an overview of formulations length scale identification procedures finite element implementations and new results in this paper we discuss various formats of gradient elasticity and their performance in static and dynamic applications gradient elasticity theories provide extensions of the classical equations of elasticity with additional higher order spatial derivatives of strains stresses and or accelerations we focus on the versatile class of gradient elasticity theories whereby the higher order terms are the laplacian of the corresponding lower order terms one of the challenges of formulating gradient elasticity theories is to keep the number of additional constitutive parameters to a minimum we start with discussing the general mindlin theory that in its most general form has 903 constitutive elastic parameters but which were reduced by mindlin to three independent material length scales further simplifications are often possible in particular the aifantis theory has only one additional parameter in statics and opens up a whole new field of analytical and numerical solution procedures we also address how this can be extended to dynamics an overview of length scale identification and quantification procedures is given finite element implementations of the most commonly used versions of gradient elasticity are discussed together with the variationally consistent boundary conditions details are provided for particular formats of gradient elasticity that can be implemented with simple linear finite element shape functions new numerical results show the removal of singularities in statics and dynamics as well as the size dependent mechanical response predicted by gradient elasticity

local and nonlocal continuum modeling of inelastic periodic networks applied to stretching dominated trusses we present a nonlocal continuum model and its numerical implementation to describe the macroscale response of periodic discrete networks via second order homogenization the scale bridging technique is applied to the specific example of stretching dominated elastic and inelastic periodic truss networks experiments on small scale truss structures have highlighted the importance of nodal connections on the effective stiffness and strength therefore we describe the mechanics of trusses by accounting for the stretching of truss members and the deformation of nodes for the representative 2d examples of lattices having square and triangular architectures and for example bar and nodal constitutive laws we show that a simple continuum model based on affinely deforming a representative unit cell is sufficient to reproduce the nonlinear elastic behavior of discrete trusses by contrast localization that arises e g from inelastic deformation requires a refined model this is where the presented nonlocal continuum model is capable of accurately capturing details of localized deformation we illustrate the performance of the model by comparing the results of example finite element simulations using the continuum constitutive model to discrete lattice calculations with elastic plastic bars optimal performance is achieved when the representative unit cell of the continuum model agrees with the actual size of the discrete truss unit cell which accounts for size effects even in regimes where a separation of scales between finite element size and unit cell size does not strictly apply

the dyck bound in the concave 1 dimensional random assignment model we consider models of assignment for random n blue points and n red points on an interval of length 2n in which the cost for connecting a blue point in x to a red point in y is the concave function x y p for 0 1 where the optimal matching is trivially determined here the optimization is non trivial the purpose of this paper is to introduce a special configuration that we call the dyck matching and to study its statistical properties we compute exactly the average cost in the asymptotic limit of large n together with the first subleading correction the scaling is remarkable it is of order n for p 1 2 and it is universal for a wide class of models we conjecture that the average cost of the dyck matching has the same scaling in n as the cost of the optimal matching and we produce numerical data in support of this conjecture we hope to produce a proof of this claim in future work

elastic field of a spherical inclusion with non uniform eigenfields in second strain gradient elasticity in this paper within the complete form of mindlin s second strain gradient theory the elastic field of an isolated spherical inclusion embedded in an infinitely extended homogeneous isotropic medium due to a non uniform distribution of eigenfields is determined these eigenfields in addition to eigenstrain comprise eigen double and eigen triple strains after the derivation of a closed form expression for green s function associated with the problem two different cases of non uniform distribution of the eigenfields are considered as follows i radial distribution i e the distributions of the eigenfields are functions of only the radial distance of points from the centre of inclusion and ii polynomial distribution i e the distributions of the eigenfields are polynomial functions in the cartesian coordinates of points while the obtained solution for the elastic field of the latter case takes the form of an infinite series the solution to the former case is represented in a closed form moreover eshelby s tensors associated with the two mentioned cases are obtained

a second strain gradient elasticity theory with second velocity gradient inertia part i constitutive equations and quasi static behavior abstract a multi cell homogenization procedure with four geometrically different groups of cell elements respectively for the bulk the boundary surface the edge lines and the corner points of a body is envisioned which is able not only to extract the effective constitutive properties of a material but also to assess the surface effects produced by the boundary surface on the near bulk material applied to an unbounded material in combination with the thermodynamics energy balance principles this procedure leads to an equivalent continuum constitutively characterized by ordinary double and triple generalized stresses and momenta also applying this procedure to a finite body suitably modelled as a simple material cell system in association with the principle of the virtual power pvp for quasi static actions an equivalent structural system is derived featured by a macro scale pvp having the typical format as for a second strain gradient material model due to the surface effects the latter model does work as a combination of two subsystems i e the bulk material behaving as a cauchy continuum and the boundary surface operating as a membrane like boundary layer each subsystem being in local and global equilibrium by its own further the applied ordinary boundary traction splits into two response dependent parts i e the cauchy traction transmitted to the bulk material and the gurtin murdoch traction acting together with all other boundary tractions upon the boundary layer the role of the boundary layer as a two dimensional manifold enclosing a cauchy continuum is elucidated also with the aid of a discrete model a strain gradient elasticity theory is proposed which includes a minimum total potential energy principle featuring the relevant boundary value problem for quasi static loads and its unique solution a simple application is presented two appendices are included one reports the proof of the global equilibrium of the boundary layer the other is concerned with double and triple stresses the paper is complemented by a companion part ii one on dynamics previous findings by the author polizzotto c 2012 a gradient elasticity theory for second grade materials and higher order inertia int j solids struct 49 2121 2137 are improved and extended

higher order continua derived from discrete media continualisation aspects and boundary conditions abstract in this paper the derivation of higher order continuum models from a discrete medium is addressed with the following aims i for a given discrete model and a given coupling of discrete and continuum degrees of freedom the continuum should be defined uniquely ii the continuum is isotropic and iii boundary conditions are derived consistently with the energy functional and the equations of motion of the continuum firstly a comparison is made between two continualisation methods namely based on the equations of motion and on the energy functional they are shown to give identical results secondly the issue of isotropy is addressed a new approach is developed in which two rather than one layers of neighbouring particles are considered finally the formulation and interpretation of boundary conditions is treated by means of the hamilton ostrogradsky principle boundary conditions are derived that are consistent with the energy functional and the equations of motion a relation between standard stresses and higher order stresses is derived and used to make an interpretation of the higher order stresses an additional result of this study is the non uniqueness of the higher order contributions to the energy

on causality of the gradient elasticity models abstract this paper is concerned with causality of the gradient elasticity models of heterogeneous materials as a rule these models are not strictly causal since they allow an infinite speed of energy transfer by means of either propagating or transient evanescent waves a discussion is presented in this paper of both physical and mathematical implications of this fact this discussion is carried out employing one dimensional 1d second order gradient models a phenomenological enhancement is proposed which makes these models causal the main idea behind this enhancement is that a partial differential equation that governs dynamic behaviour of a causal gradient elasticity model must be of the same order with respect to spatial coordinate and with respect to time the validity of this idea is confirmed in this paper by deriving a second order 1d continuum model for concrete a brief comparison is provided in conclusion of the equations of motion of the 1d second gradient elasticity models and those used in dynamics of thin bars it is shown that the proposed causal model corresponds to the most advanced dynamic models of such bars namely to the timoshenko model for the bending motion and the mindlin model for the longitudinal motion of a bar

regularity and structure of pullback attractors for reaction diffusion type systems without uniqueness abstract in this paper we study the pullback attractor for a general reaction diffusion system for which the uniqueness of solutions is not assumed we first establish some general results for a multi valued dynamical system to have a bi spatial pullback attractor and then we find that the attractor can be backwards compact and composed of all the backwards bounded complete trajectories as an application a general reaction diffusion system is proved to have an invariant h v pullback attractor a a r this attractor is composed of all the backwards compact complete trajectories of the system pullback attracts bounded subsets of h in the topology of v and moreover s a s is precompact in v r a non autonomous fitz hugh nagumo equation is studied as a specific example of the reaction diffusion system

scaling and universality in continuous length combinatorial optimization we consider combinatorial optimization problems defined over random ensembles and study how solution cost increases when the optimal solution undergoes a small perturbation delta for the minimum spanning tree the increase in cost scales as delta2 for the minimum matching and traveling salesman problems in dimension d 2 the increase scales as delta3 this is observed in monte carlo simulations in d 2 3 4 and in theoretical analysis of a mean field model we speculate that the scaling exponent could serve to classify combinatorial optimization problems of this general kind into a small number of distinct categories similar to universality classes in statistical physics

gradient elasticity and nonstandard boundary conditions abstract gradient elasticity for a second gradient model is addressed within a suitable thermodynamic framework apt to account for nonlocality the pertinent thermodynamic restrictions upon the gradient constitutive equations are derived which are shown to include besides the field differential stress strain laws a set of nonstandard boundary conditions consistently with the latter thermodynamic requirements a surface layer with membrane stresses is envisioned in the strained body which together with the above nonstandard boundary conditions make the body constitutively insulated i e no long distance energy flows out of the boundary surface due to nonlocality the total strain energy is shown to include a bulk and surface strain energy a minimum total potential energy principle is provided for the related structural boundary value problem the toupin mindlin polar type strain gradient material model is also addressed and compared with the above one their substantial differences are pointed out particularly for what regards the constitutive equations and the boundary conditions accompanying the solving displacement equilibrium equations a gradient one dimensional bar sample in tension is considered for a few applications of the proposed theory

a new formulation and 0 implementation of dynamically consistent gradient elasticity in his article a special form of gradient elasticity is presented that can be used to describe wave dispersion this new format of gradient elasticity is an appropriate dynamic extension of the earlier static counterpart of the gradient elasticity theory advocated in the early 1990s by aifantis and co workers in order to capture dispersion of propagating waves both higher order inertia and higher order stiffness contributions are included a fact which implies and is denoted as dynamic consistency the two higher order terms are accompanied by two associated length scales to facilitate finite element implementations the model is rewritten such that 0 continuity of the interpolation is sufficient an auxiliary displacement field is introduced which allows the original fourth order equations to be split into two coupled sets of second order equations positive definiteness of the kinetic energy requires that the inertia length scale is larger than the stiffness length scale the governing equations boundary conditions and the discretized system of equations are presented finally dispersive wave propagation in a one dimensional bar is considered in a numerical example copyright 2007 john wiley sons ltd

sufficient and necessary criteria for existence of pullback attractors for non compact random dynamical systems abstract we study pullback attractors of non autonomous non compact dynamical systems generated by differential equations with non autonomous deterministic as well as stochastic forcing terms we first introduce the concepts of pullback attractors and asymptotic compactness for such systems we then prove a sufficient and necessary condition for existence of pullback attractors we also introduce the concept of complete orbits for this sort of systems and use these special solutions to characterize the structures of pullback attractors for random systems containing periodic deterministic forcing terms we show the pullback attractors are also periodic under certain conditions as an application of the abstract theory we prove the existence of a unique pullback attractor for reaction diffusion equations on r n with both deterministic and random external terms since sobolev embeddings are not compact on unbounded domains the uniform estimates on the tails of solutions are employed to establish the asymptotic compactness of solutions

derivation of mindlin s first and second strain gradient elastic theory via simple lattice and continuum models abstract mindlin in his celebrated papers of arch rat mech anal 16 51 78 1964 and int j solids struct 1 417 438 1965 proposed two enhanced strain gradient elastic theories to describe linear elastic behavior of isotropic materials with micro structural effects since then many works dealing with strain gradient elastic theories derived either from lattice models or homogenization approaches have appeared in the literature although elegant none of them reproduces entirely the equation of motion as well as the classical and non classical boundary conditions appearing in mindlin theory in terms of the considered lattice or continuum unit cell furthermore no lattice or continuum models that confirm the second gradient elastic theory of mindlin have been reported in the literature the present work demonstrates two simple one dimensional models that conclude to first and second strain gradient elastic theories being identical to the corresponding ones proposed by mindlin the first is based on the standard continualization of the equation of motion taken for a sequence of mass spring lattices while the second one exploits average processes valid in continuum mechanics furthermore mindlin developed his theory by adding new terms in the expressions of potential and kinetic energy and introducing intrinsic micro structural parameter without however providing explicit expressions that correlate micro structure with macro structure this is accomplished in the present work where in both models the derived internal length scale parameters are correlated to the size of the considered unit cell

freezing transition of the random bond rna model statistical properties of the pairing weights to characterize the pairing specificity of rna secondary structures as a function of temperature we analyze the statistics of the pairing weights as follows for each base i of the sequence of length n we consider the n 1 pairing weights w i j with the other bases j not equal i of the sequence we numerically compute the probability distributions p1 w of the maximal weight w i max max j w i j the probability distribution pi y 2 of the parameter y2 i summation operator j w i 2 j as well as the average values of the moments y k i summation operator j w i k j we find that there are two important temperatures t c t gap the distribution p1 w vanishes at some value w 0 t 1 and accordingly the moments y k i decay exponentially as w 0 t k in k for t t gap the distributions p1 w and pi y2 present the characteristic derrida flyvbjerg singularities at w 1n and y 2 1 n for n 1 2 in particular there exists a temperature dependent exponent mu t that governs the singularities p1 w approximately 1 w mu t 1 and pi y2 approximately 1 y 2 mu t 1 as well as the power law decay of the moments y k i approximately 1k mu t the exponent mu t grows from the value mu t 0 0 up to mu t gap approximately 2 the study of spatial properties indicates that the critical temperature t c where the large scale roughness exponent changes from the low temperature value zeta approximately 0 67 to the high temperature value zeta approximately 0 5 corresponds to the exponent mu t c 1 for t t c there exists frozen pairs of all sizes whereas for t c t t gap there exists frozen pairs but only up to some characteristic length diverging as xi t approximately 1 t c t nu with nu approximately 2 the similarities and differences with the weight statistics in levy sums and in derrida s random energy model are discussed

existence and continuity of bi spatial random attractors and application to stochastic semilinear laplacian equations abstract a concept of a bi spatial random attractor for a random dynamical system is introduced a unified result about existence and upper semi continuity for a family of bi spatial random attractors is obtained if a family of random systems is convergent uniformly absorbing in an initial space and uniformly omega compact in both initial and terminate spaces the upper semi continuity result improves all existing results even for single spatial attractors as an application of the abstract result it is shown that every semilinear laplacian equation on the entire space perturbed by a multiplicative and stochastic noise possesses an l 2 l q random attractor with q 2 moreover it is proved that the family of obtained attractors is upper semi continuous at any density of noises and the family of attractors for the corresponding compact systems is both upper and lower semi continuous at infinity under the topology of both spaces

asymptotic behavior of stochastic wave equations with critical exponents on mathbb r 3 the existence of a random attractor in h 1 3 x l 2 3 is proved for the damped semilinear stochastic wave equation defined on the entire space 3 the nonlinearity is allowed to have a cubic growth rate which is referred to as the critical exponent the uniform pullback estimates on the tails of solutions for large space variables are established the pullback asymptotic compactness of the random dynamical system is proved by using these tail estimates and the energy equation method

gradient dependent plasticity formulation and algorithmic aspects a plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure hardening parameter but also on the laplacian thereof the consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity to properly solve the set of non linear differential equations the plastic multiplier is discretized in addition to the usual discretization of the displacements for appropriate boundary conditions this formulation can also be derived from a variational principle accordingly the theory is complete

backwards compact attractors and periodic attractors for non autonomous damped wave equations on an unbounded domain abstract we study the backwards dynamics for the wave equation defined on the whole 3d euclid space with a positively bounded coefficient of the damping and a time dependent force we introduce a backwards compact attractor which is the minimal one among the backwards compact and pullback attracting sets we prove that a backwards compact attractor is equivalent to a pullback attractor invariant that is backwards compact i e the union of the attractor over the past time is pre compact we also establish a sufficient and necessary criterion of the existence of a backwards compact attractor and show the relationship of a periodic attractor as an application of these abstract results we prove that the non autonomous wave equation has a backwards compact attractor under some backwards assumptions of the non autonomous force moreover we establish the backwards compactness from some periodicity assumptions more precisely if the force is assumed only to be periodic then a backwards compact attractor exists and if the damped coefficient is further assumed to be periodic then the attractor is both periodic and backwards compact

comparison of wave propagation characteristics of the cosserat continuum model and corresponding discrete lattice models a comparison is made between two dimensional elastic discrete lattices and a corresponding cosserat continuum firstly it is demonstrated how the equations of motion of the cosserat model can be retrieved from those of a lattice model for this purpose two lattice geometries are elaborated a 7 cell hexagonal lattice and a 9 cell square lattice for both lattices the individual cells have two translational spring interactions and a rotational spring interaction with their neighbouring cells secondly the dispersion relations for the lattice models and the cosserat continuum model are examined in order to determine up to which wavelength of the deformation field the cosserat model accurately represents the underlying discrete micro structure the effect of the lattice anisotropy and inhomogeneity on this accuracy is also discussed

regularity of random attractors for a degenerate parabolic equations driven by additive noises abstract we study the regularity of random attractors for a class of stochastic degenerate parabolic equations with the leading term involving a diffusion variable which many be non smooth or unbounded without any restrictions on the upper growth order p of the nonlinearity except that p 2 we show that the associated random dynamical system admits a unique compact random attractor in the space d 0 1 2 d n l d n for any 2 2 p 2 where d n is an arbitrary bounded or unbounded domain in r n n 2

a variational principle for gradient plasticity abstract we elaborate on a generalized plasticity model which belongs to the class of gradient models suggested earlier by aifantis and co workers the generalization of the conventional theory of plasticity has been accomplished by the inclusion of higher order spatial gradients of the equivalent plastic strain in the yield condition first it is shown how these gradients affect the critical condition for the onset of localization and allow for a wavelength selection analysis leading to estimates for the width and or spacing of shear bands due to the presence of higher order gradients additional boundary conditions for the equivalent plastic strain are required this question and also the associated problem of the formulation and solution of general boundary value problems were left open in the previous work we demonstrate here that upon assuming a certain type of additional boundary conditions the structural symmetries of the gradient dependent constitutive model are such that there exists a variational principle for the displacement rates and the rate of the equivalent plastic strain the variational principle can serve as a basis for the numerical solution of boundary value problems in the sense of the finite element method explicit expressions for the tangent stillness matrix and the generalized nodal point forces are given

dependence of rna secondary structure on the energy model we analyze a microscopic rna model which includes two widely used models as limiting cases namely it contains terms for bond as well as for stacking energies we numerically investigate possible changes in the qualitative and quantitative behavior while going from one model to the other in particular we test whether a transition occurs when continuously moving from one model to the other for this we calculate various thermodynamic quantities at both zero temperature and finite temperatures all calculations can be done efficiently in polynomial time by a dynamic programming algorithm we do not find a sign for the transition between the models but the critical exponent ensuremath nu of the correlation length describing the phase transition in all models to an ordered low temperature phase seems to depend continuously on the model finally we apply the ensuremath epsilon coupling method to study low energy excitations the exponent ensuremath theta describing the energy scaling of the excitations seems to depend not much on the energy model

on the generalized virial theorem and eshelby tensors the formal relationships between the scalar and tensorial virials and eshelby tensors have been presently investigated the key idea is to evaluate the eshelby stress from discrete or atomistic simulations for a structured body conceived as a numerical homogenization method to reconstitute the macroscopic continuum behavior in multiscale modelling approaches extending first the writing of the scalar virial to a material format it is shown that the average of the elaborated scalar material virial is the trace of the material eshelby stress the spatial and material virials are further related to eachother in the framework of hyperelasticity and a tensorial extension of the material virial is provided interpretation of those results from the microscopic point of view shows that eshelby stress may be identified and calculated at the discrete level from the average of the virial tensor consideration of the material version of the virial theorem further leads to express eshelby stress versus the average of the internal tensorial material virial and of the kinetic energy the average scalar virial is further identified to the grand potential in a thermodynamic context a definition of the material scalar virial for a second order continuum is lastly proposed based on the identification of a second order eshelby stress and in line with the second order cauchy born rule