unique normal forms the nilpotent hamiltonian case the problem we consider in this paper namely the characterization of unique normal forms derives from bifurcation theory in a typical situation one has an unperturbed vector field near a degenerate equilibrium in order to study the effect of generic perturbations suitable coordinates are introduced and the simplified system is said to be in normal form a well known case is the hopf bifurcation where a pair of conjugate eigenvalues cross the imaginary axis using averaging one can in this case compute the periodic orbit that splits off from the equilib um a second familiar example is the takens bogdanov bifurcation where two eigenvalues are zero in all these situations it is necessary to make certain choices both in the definition of what constitutes a normal form and in the computation of the transformation the idea here is to use this second kind of choice to sharpen the very definition of normal form while in standard treatments only the linear part of the field plays a role we show that one can effectively use its non linear part to remove additional terms and thus simplify the problem further the underlying philosophy in this type of game is that

coupled cell networks semigroups lie algebras and normal forms we introduce the concept of a semigroup coupled cell network and show that the collection of semigroup network vector fields forms a lie algebra this implies that near a dynamical equilibrium the local normal form of a semigroup network is a semigroup network itself networks without the semigroup property will support normal forms with a more general network architecture but these normal forms nevertheless possess the same symmetries and synchronous solutions as the original network we explain how to compute lie brackets and normal forms of coupled cell networks and we characterize the sn decomposition that determines the normal form symmetry this paper concludes with a generalization to nonhomogeneous networks with the structure of a semigroupoid

normal forms for hopf zero singularities with nonconservative nonlinear part abstract in this paper we are concerned with the simplest normal form computation of the systems 0 1 x 2 x f x y 2 z 2 y z y f x y 2 z 2 z y z f x y 2 z 2 where f is a formal function with real coefficients and without any constant term these are the classical normal forms of a larger family of systems with hopf zero singularity indeed these are defined such that this family would be a lie subalgebra for the space of all classical normal form vector fields with hopf zero singularity the simplest normal forms and simplest orbital normal forms of this family with nonzero quadratic part are computed we also obtain the simplest parametric normal form of any non degenerate perturbation of this family within the lie subalgebra the symmetry group of the simplest normal forms is also discussed this is a part of our results in decomposing the normal forms of hopf zero singular systems into systems with a first integral and nonconservative systems

computational plasticity for composite structures based on mathematical homogenization theory and practice abstract this paper generalizes the classical mathematical homogenization theory for heterogeneous medium to account for eigenstrains starting from the double scale asymptotic expansion for the displacement and eigenstrain fields we derive a close form expression relating arbitrary eigenstrains to the mechanical fields in the phases the overall structural response is computed using an averaging scheme by which phase concentration factors are computed in the average sense for each micro constituent and history data is updated at two points reinforcement and matrix in the microstructure one for each phase macroscopic history data is stored in the database and then subjected in the post processing stage onto the unit cell in the critical locations for numerical examples considered the cpu time obtained by means of the two point averaging scheme with variational micro history recovery with 30 seconds on sparc 10 51 as opposed to 7 hours using classical mathematical homogenization theory at the same time the maximum error in the microstress field in the critical unit cell was only 3 5 in comparison with the classical mathematical homogenization theory

an improved theory of asymptotic unfoldings abstract an asymptotic unfolding of a dynamical system near a rest point is a system with additional parameters such that every one parameter deformation of the original system can be embedded in the unfolding preserving all properties that can be detected by asymptotic methods asymptotic unfoldings are computed using normal and hypernormal form methods we present a simplified and improved method of computing such unfoldings that can be used in any normal form style

shape optimization using adaptive shape refinement a large part of the computational effort in shape optimization problems is expended in the numerical computation of the gradients for sensitivity information this effort increases dramatically with an increase in the number of variables used to represent the shape an adaptation of the gradient projection algorithm for shape optimization problems is described here along with a method to reduce the intermediate size of the optimization problem by allowing adaptive refinement of the shape the method is demonstrated with a simple representative test case

on semi analytical probabilistic finite element method for homogenization of the periodic fiber reinforced composites the main aim of this paper is a development of the semi analytical probabilistic version of the finite element method fem related to the homogenization problem this approach is based on the global version of the response function method and symbolic integral calculation of basic probabilistic moments of the homogenized tensor and is applied in conjunction with the effective modules method it originates from the generalized stochastic perturbation based fem where taylor expansion with random parameters is not necessary now and is simply replaced with the integration of the response functions the hybrid computational implementation of the system maple with homogenization oriented fem code mcceff is invented to provide probabilistic analysis of the homogenized elasticity tensor for the periodic fiber reinforced composites although numerical illustration deals with a homogenization of a composite with material properties defined as gaussian random variables other composite parameters as well as other probabilistic distributions may be taken into account the methodology is independent of the boundary value problem considered and may be useful for general numerical solutions using finite or boundary elements finite differences or volumes as well as for meshless numerical strategies copyright 2011 john wiley sons ltd

design sensitivity analysis for rate independent elastoplasticity abstract a new incremental direct differentiation method for design sensitivity analysis of structures with rate independent elastoplastic behavior is presented we formulate analytical sensitivity expressions that are consistent with numerical algorithms for elastoplasticity that use implicit methods to integrate the constitutive equations and return mappings to enforce the consistency conditions the sensitivity expressions can be evaluated with only a modest increase in computational expense beyond the cost of simulation combined with the inherent advantages of implicit integration strategies this represents a significant improvement over previous sensitivity formulations for history dependent materials first order sensitivity expressions involving the complete set of design variables including shape design variables are derived for a generic response functional the reduced form of the consistent tangent stiffness matrix obtained at the end of each time or load step in the finite element procedure is used to update the response sensitivities for that time step no iterations are needed in the sensitivity computations a numerical example demonstrates the accuracy and efficiency of the new sensitivity analysis method for an elastoplastic analysis problem explicit sensitivities from the new method are confirmed by finite difference estimates

normal forms symmetry and linearization of dynamical systems we discuss how the presence of a suitable symmetry can guarantee the perturbative linearizability of a dynamical system or a parameter dependent family via the poincare normal form approach we discuss this formally at first and later pay attention to the convergence of the linearizing procedure we also discuss some generalizations of our main result

unique normal forms for planar vector fields soit x un germe d un champ vectoriel analytique ou formel en equilibre a o r 2 avec des valeurs propres purement imaginaires a 0 i a 0 0 alors x est formellement equivalent a precisement un des champs vectoriels polynomiaux suivant ou x 1 2 cos y 1 2 sin pour des coordonnees appropriees x y 7b a 0 a 0 7b a k a 0 k 7b b j a 0 a 1 a j j j 1 b j j 0

construction of darboux coordinates and poincare birkhoff normal forms in noncanonical hamiltonian systems abstract we demonstrate a general method to construct darboux coordinates via normal form expansions in noncanonical hamiltonian system obtained from e g a variational approach to quantum systems the procedure serves as a tool to naturally extract canonical coordinates out of the variational parameters and at the same time to transform the energy functional into its poincare birkhoff normal form the method is general in the sense that it is applicable for arbitrary degrees of freedom in arbitrary orders of the local expansion and it is independent of the precise form of the hamilton operator the method presented allows for the general and systematic investigation of quantum systems in the vicinity of fixed points which e g correspond to ground excited or transition states moreover it directly allows to calculate classical and quantum reaction rates by applying transition state theory

existence and nonexistence of nontrivial solutions of some nonlinear degenerate elliptic equations in connection with the maximizing problem for the functional r u u lq u lp in w01 p 0 we consider the equation div u p 2 u x u q 2 u x x 1 p resp q p e has no nontrivial resp nonnegative nontrivial solution belonging to the class p u w01 p lq xi u q 2u lp p 1 i 1 2 n w01 p provided that is star shaped the crucial point of the proof of our result is to obtain an l estimate of weak solutions and to verify a certain pohozaev type inequality for weak solutions belonging to p

positive solutions for a class of equations with a p laplace like operator and weights abstract in this paper we will study the problem of existence of positive solutions to the problem d a r u b r g u 0 a e in 0 r lim r 0 a r u r 0 u r 0 where is an odd increasing homeomorphism of r and g c r is such that g z 0 for all z 0 with g 0 0 the functions a and b that we will refer to as weight functions satisfy a r 0 b r 0 for all r 0 r and are such that a b c 1 0 r l 1 0 r if has the form z z m z and a r r n 1 a r b r r n 1 b r n 2 then solutions of problem d provide solutions with radial symmetry for the problem p div a x m u u b x g u 0 x u 0 x where b 0 r denotes the ball with center 0 and radius r 0 in r n

unique normal forms for vector fields and hamiltonians on construit des formes canoniques pour tous les champs vectoriels resp hamiltoniens en equilibre a 0 r n relativement au groupe des diffeomorphismes formels resp des transformations canoniques tangentiels a l identite

symbolic computation of normal forms for semi simple cases this paper presents a method and computer programs for computing the normal forms of ordinary differential equations whose jacobian matrix evaluated at an equilibrium involves semi simple eigenvalues the method can be used to deal with systems which are not necessarily described on a center manifold an iterative procedure is developed for finding the closed form expressions of the normal forms and associated nonlinear transformations computer programs using a symbolic computer language maple are developed to facilitate the application of the method the programs can be conveniently executed on a main frame a workstation or a pc machine without any interaction a number of examples are presented to demonstrate the applicability of the method and the computation efficiency of the maple programs

design sensitivity analysis for nonlinear thermal systems abstract the lagrange multiplier method and convolution theory are used to formulate design sensitivities for nonlinear transient thermal systems variations of a general design functional are expressed in explicit form with respect to variations in structural shape and the conventional design quantities i e material properties applied loads prescribed boundary conditions and initial conditions the design functional depends on these explicit quantities and the implicit repsonse fields temperature temperature gradient heat flux vector and reaction surface flux a finite element implementation of the methodology illustrates the formulation

versal normal form for nonsemisimple singularities abstract the theory of versal normal form has been playing a role in normal form since the introduction of the concept by v i arnol d in 1 2 but there has been no systematic use of it that is in line with the semidirect character of the group of formal transformations on formal vector fields that is the linear part should be done completely first before one computes the nonlinear terms in this paper we address this issue by giving a complete description of a first order calculation in the case of the two and three dimensional irreducible nilpotent cases which is then followed up by an explicit almost symplectic calculation to find the transformation to versal normal form in a particular fluid dynamics problem and in the celestial mechanics l 4 problem

design sensitivity analysis and optimization of dynamic response abstract the paper presents methods of design sensitivity analysis and optimization of dynamic response of mechanical and structural systems a key feature of the paper is the development of procedures to handle point wise state variable constraints difficulties with a previous treatment where such constraints were transformed to equivalent integral constraints are noted and explained from theoretical as well as engineering standpoints an alternate treatment of such constraints is proposed developed and evaluated in this treatment each point wise state variable constraint is replaced by several constraints that are imposed at all the local max points for the original constraint function the differential equations of motion are formulated in the first order form so as to handle more general problems the direct differentiation and adjoint variable methods of design sensitivity analysis to deal with the point wise constraints are presented with the adjoint variable methods there are two ways of calculating design sensitivity coefficients the first approach uses an impulse load and the second approach uses a step load for the corresponding adjoint equation since the adjoint variable methods are better for a large class of problems an efficient computational algorithm with these methods is presented in detail optimum results for several problems are obtained and compared with those available in the literature the new formulation works extremely well as precise optimum designs are obtained

computation of normal forms via a perturbation technique considering qualitative behavior of a non linear dynamical system often leads to first simplifying the differential equations or finding their normal forms a perturbation technique for computing normal forms is presented this technique associated with the method of multiple scales can be used to systematically find a unique form for a given set of differential equations the technique is discussed in detail through the analysis of hopf bifurcation it is shown that for hopf bifurcation the method only requires solving two dimensional matrix systems for any higher order normal forms of a generaln dimensional system with the aid of the symbolic language maple this approach is straightforward and is computationally efficient and fast furthermore a simple verification scheme is given for verifying the normal forms and associated non linear transformations obtained using any methodology examples are presented to demonstrate the applicability of the perturbation technique and the computation efficiency of the maple program

identification of elastoplastic microscopic material parameters within a homogenization scheme summary a two scale parameter identification approach is investigated the microscopic material parameters of a two scale model are identified by comparing macroscopic simulation data with macroscopic full field measurements of the micro structured specimen gradient based solution strategies are employed for the optimization problem of the two scale parameter identification in particular two approaches for the gradient calculation are investigated the finite difference method is compared with a newly introduced semi analytical scheme the focus lies on the identification of microscopic elastoplastic material parameters the presented identification example with artificial data confirms a reduced computational effort and advantageous convergence for the semi analytical approach within the two scale parameter identification a drawback is the increase in memory requirement copyright 2015 john wiley sons ltd

nonlinear structural design sensivitity analysis for path dependent problems part 1 general theory abstract two procedures direct differentiation and adjoint structure for design sensitivity analysis of nonlinear structural systems with path dependent effects are described in this paper continuum formulation is used and both geometric and material nonlinearities are included in the derivations incremental nonlinear analysis based on the total lagrangian concept is adopted the reference volume concept is used to unify the shape and nonshape design problems to show the generality of the theory the derived expressions are reduced to some special cases that have been treated previously in the literature in part 2 of the paper a few analytical example problems will be solved to demonstrate the use of the design sensitivity analysis theory the theory has also beendiscretized elsewhere using finite element approximations for implementation into structural analysis programs these developments offer a firm foundation for design optimization of complex structural systems

symbolic computation of normal forms for resonant double hopf bifurcations using a perturbation technique abstract this paper presents a perturbation method for computing the normal forms of resonant double hopf bifurcations with the aid of a computer algebraic system this technique based on the method of multiple time scales can be used to deal with general n dimensional systems without the application of center manifold theory explicit iterative formulas have been derived for uniquely determining the coefficients of normal forms and associated non linear transformations up to an arbitrary order user friendly symbolic computer programs written in maple have been developed which can be easily applied for computing the normal forms of a given system examples are presented to show the applicability of the methodology and the convenience of using the computer software

further reductions of normal forms for dynamical systems abstract we propose in this paper a method for obtaining a significant refinement of normal forms for dynamical systems or vector fields with concrete and interesting applications we use lower order nonlinear terms in the normal form for the simplifications of higher order terms our approach is applicable for both the non nilpotent and the nilpotent cases for dynamical systems of dimensions 2 and 3 we give an algorithm that leads to interesting finite order normal forms which are optimal or unique with respect to equivalence by formal near identity transformations we can compute at the same time a formal diffeormorphism that realizes the normalization comparisons with other methods are given for several examples

spectral sequences and parametric normal forms abstract this paper extends recent developments on spectral sequence approach on the simplest normal form theory to parametric cases in this paper the method is first applied to two simple examples parametric single zero and parametric resonant saddle singularities and then to parametric generalized hopf singularity we provide the simplest parametric normal form for these cases

infinitely many radially symmetric solutions for a quasilinear elliptic problem in a ball the authors improve the results of struwe under the hypothesis that f ismerely a locally lipschitz function they are able to deal with cases wherethe growth of f exceeds the sobolev limit exponent in fact their resultssuggest that it is sufficient to have the growth conditions only for u 0 orfor u 0 oru 0 0 our aim here is to extend the results of castro and kurepa to theproblem e

probabilistic entropy in homogenization of the periodic fiber reinforced composites with random elastic parameters summary the purpose of this elaboration is to develop an efficient method for a determination of the probabilistic entropy loss in the homogenization process of the periodic composites with random material characteristics a definition of this entropy convenient for the gaussian continuous distribution is adopted and implemented into the computer algebra system maple homogenization of the fiber reinforced composite with randomly defined young s moduli of the constituents is carried out in the fem and homogenization oriented code based on the four noded plane strain elements probabilistic procedure has triple character and is alternatively based on the monte carlo simulation on the generalized stochastic perturbation based analysis and on the recently developed semi analytical determination of homogenized tensor using the response function method because of this triple usage of the probabilistic methods it is possible to make a detailed comparison of all those techniques especially in view of the entropy variation during the homogenization this procedure may be linked with other homogenization techniques also for various constitutive models and or for the upper and lower bounds on the effective tensor components copyright 2012 john wiley sons ltd

hypernormal form theory foundations and algorithms abstract hypernormal forms unique normal forms simplest normal forms are investigated both from the standpoint of foundational theory and algorithms suitable for use with computer algebra the baider theory of the campbell hausdorff group is refined by a study of its subgroups to determine the smallest substages into which the hypernormalization process can be divided this leads to a linear algebra algorithm to compute the generators needed for each substage with the least amount of work a concrete interpretation of jan sanders spectral sequence for hypernormal forms is presented examples are given and a proof is given for a little known theorem of belitskii expressing the hypernormal form space in the inner product style as the kernel of a higher order differential operator

multiscale analytical sensitivity analysis for composite materials we describe a methodology aimed at determining the sensitivity of the global structural behaviour such deformation or vibration modes with respect to the local characteristics such as material constants of micro constituents an analytical gradient computation which involves the direct differentiation of the multiple scale strong forms with respect to the design parameters is developed comparison of the multiple scale sensitivity analysis masa to the central finite difference cfd approximation in terms of accuracy and computation efficiency is carried out we demonstrate the robustness of the masa approach compared to the cfd approximation which has been found to be highly sensitive to the choice of the step size whose optimal value is problem dependent copyright 2001 john wiley sons ltd

existence and uniqueness for a class of quasilinear elliptic boundary value problems abstract we prove existence and uniqueness of positive solutions for the boundary value problem r n 1 u r n 1 f u u 0 u 1 0 where x x p 2x f x xp 1 may not be decreasing on 0 and is a large parameter

on sufficient conditions for the existence of radially symmetric solutions of the p laplace equation abstract we consider the dirichlet problem for the p laplace equation with a nonlinear source new a priori estimates for solutions are established in particular we obtain an explicit formula which shows the dependence of the existence of a weak bounded radially symmetric solution on the dimension of the problem

sensitivity and randomness in homogenization of periodic fiber reinforced composites via the response function method the main issue this paper addresses is the derivation and implementation of a general homogenization method including the simultaneous determination of sensitivity gradients and probabilistic moments of the effective elasticity tensor this is possible with an application of the perturbation method based on taylor expansion and with the effective modules method the computational procedure is implemented using plane strain analysis carried out with the finite element method program mcceff and the symbolic computations system maple the sensitivity gradients and probabilistic moments are commonly determined on the basis of partial derivatives for the homogenized elasticity tensor calculated using the response function method with respect to some composite parameters they are subjected separately to a normalization procedure in deterministic analysis and the relevant algebraic combinations for the stochastic case this enriched homogenization procedure is tested on a periodic fiber reinforced two component composite where the material parameters are taken as design variables and then the input random quantities the results of computational analysis are compared against the results of the central finite difference approach in the case of sensitivity gradients determination as well as the direct monte carlo simulation approach this numerical methodology may be further applied not only in the context of the homogenization method but also to extend various discrete computational techniques such as boundary finite element and finite difference together with various meshless methods

variational principle for shape design sensitivity analysis in this paper the adjoint method of design sensitivity analysis is stated as a general variational principle that is applicable to a wide range of problems the principle gives a very simple and straightforward method of obtaining the design sensitivity expression for a functional dependent on the state fields the sensitivity expression involves certain adjoint fields and explicit design variations of the functional and the governing equations for the primary state fields the principle is stated in terms of an augmented functional that is defined by adding to the response functional whose sensitivity is desired the equilibrium equation of the primary problem then explicit design variation of the augmented functional gives the total design variation of the response functional stationarity of the augmented functional with respect to the state fields defines the adjoint problem for the response functional the principle is proved and applied to several classes of linear and nonlinear problems such as field problems structural problems and dynamic response problems it is shown that the design sensitivity expressions derived in the literature using long procedures are obtained quite routinely by use of the principle

first order design sensitivities for transient conduction problems by an adjoint method an adjoint approach is presented for the design sensitivity analysis of transient conduction problems variations of a general design functional are expressed in explicit form with respect to all design quantities i e material properties shape applied thermal loads including convection and initial conditions the methodology incorporates the mutual energy between the real and adjoint thermal problems and a geometric mapping to describe shape variations finite element implementation of the method is discussed and an example is provided some potential difficulties that might be encountered when using the adjoint method with the finite element method are addressed these involve the application of impulse loadings and dirac temperature fields in the adjoint loadings

on hopf bifurcation and control for a delay systems abstract hopf bifurcation of a delay differential equation modeling two enterprise interaction mechanism is investigated for the demands of computer simulation applications the discrete time two enterprise interaction model is proposed by using the forward euler scheme by discussing the characteristic equation of linearized part the local stability criterion of the positive fixed point is presented time lag is selected as the bifurcation parameter then it is demonstrated that variation of time lag may result in hopf bifurcation furthermore derivations for the directions and stability of hopf bifurcation are also given for the purpose of controlling hopf bifurcation a time delayed feedback control scheme is proposed finally we simulate the main results

sensitivity analysis of linear elastic systems using domain parameterization and a mixed mutual energy principle abstract a unified approach for explicit structural design sensitivity analysis of linear elastic systems is presented first order sensitivity expression involving the complete set of design variable including shape design parameters are derived for general response functional both direct differentiation and adjoint variable methods are developed in a general variational context a domain parameterization method related to the mixed eulerian lagrangian kinematic description is introduced for the treatment of shape variation problems this approach is an alternative to the material derivative methods presented elsewhere in the literature the adjoint variable derivation is based on a mixed energy principle the mutual hu washizu energy principle which is formally stated and proved the design sensitivity derivation based on this principle unifies and extends several of the adjoint variable methods found in the literature the derivations presented here are extended to nonlinear systems in a subsequent paper the sensitivity expressions are valid for use with force displacement or mixed approximate solutions of the elasticity equations other formulations are generally only consistent with displacement solution methods numerical implementation of the design sensitivity methods is discussed and illustrative examples are included

filtration preserving mappings and centralizers within graded lie algebras we use spectral sequence techniques to compute centralizers of elements within graded lie algebras and the methods are then applied to the calculation of unique normal forms of elements within one parameter matrix lie algebras a finiteness criterion for unique normal forms is presented

on the existence of sign changing bound state solutions of a quasilinear equation abstract in this paper we establish the existence of bound state solutions having a prescribed number of sign changes for p m u f u 0 x r n n m 1 where m u u m 2 u our result is new even for the case of the laplacian m 2

finite deformation plasticity for composite structures computational models and adaptive strategies abstract we develop computational models and adaptive modeling strategies for obtaining an approximate solution to a boundary value problem describing the finite deformation plasticity of heterogeneous structures a nearly optimal mathematical model consists of an averaging scheme based on approximating eigenstrains and elastic concentration factors in each micro phase by a constant in the portion of the macro domain where modeling errors are small whereas elsewhere a more detailed mathematical model based on a piecewise constant approximation of eigenstrains and elastic concentration factors is utilized the methodology is developed within the framework of statistically homogeneous composite material and local periodicity assumptions

on a class of semilinear elliptic systems abstract this paper deals with the existence of positive solutions to a dirichlet problem for the superlinear elliptic system u f v v g u on a ball where is a positive parameter and f 0 g 0 may be negative

normal form theory and spectral sequences abstract the concept of unique normal form is formulated in terms of a spectral sequence as an illustration of this technique some results of baider and churchill concerning the normal form of the anharmonic oscillator are reproduced the aim of this paper is to show that spectral sequences give us a natural framework in which to formulate normal form theory

infinitely many radial solutions for a p laplacian problem p superlinear at the origin abstract we prove the existence of infinitely many radial solutions for a p laplacian dirichlet problem which is p superlinear at the origin the main tool that we use is the shooting method we extend for more general nonlinearities the results of j iaia in j iaia radial solutions to a p laplacian dirichlet problem appl anal 58 1995 335 350 previous developments require a behavior of the nonlinearity at zero and infinity while our main result only needs a condition of the nonlinearity at zero

molecular dynamics boundary conditions for regular crystal lattices we present a method for deriving molecular dynamics boundary conditions for use in multiple scale simulations that can be applied at a planar boundary for any solid that has a periodically repeating crystal lattice the method is based on a linearization in the vicinity of the boundary and utilizes a fourier and laplace transforms in space and time to eliminate the degrees of freedom associated with atoms outside the boundary this method is straightforward to implement numerically and thus can be automated for a general crystal lattice we show that this method reproduces the known kernel for a 1d linear chain and apply the approach to obtain the damping kernel matrices for two real crystal lattices the graphene and diamond structures of carbon

positive radial solutions for dirichlet problems with mean curvature operators in minkowski space abstract in this paper by using leray schauder degree arguments and critical point theory for convex lower semicontinuous perturbations of c 1 functionals we obtain existence of classical positive radial solutions for dirichlet problems of type div v 1 v 2 f x v 0 in b r v 0 on b r here b r x r n x r and f 0 r 0 r is a continuous function which is positive on 0 r 0

a mixed eulerian lagrangian displacement model for large deformation analysis in solid mechanics abstract a new mixed kinematic description for large deformation solid mechanics is presented the novel aspect of the new model is that both the initial and current configurations are treated as unknown large deformation statements of the principles of virtual work and stationary potential energy are formulated with the new description and presented in incremental form suitable for iterative finite element solutions the well known total lagrangian and updated lagrangian descriptions are shown to be special cases of the mixed formulation the new description is advantageous in situations where it is difficult to select an appropriate material discretization prior to analysis applications to large deformation frictional contact and fracture mechanics are presented to demonstrate the utility of the new kinematic description

on the representations and formula presented equivariant normal form for solenoidal hopf zero singularities abstract in this paper we deal with the solenoidal conservative lie algebra associated to the classical normal form of hopf zero singular system we concentrate on the study of some representations and z 2 equivariant normal form for such singular differential equations first we list some of the representations that this lie algebra admits the vector fields from this lie algebra could be expressed by the set of ordinary differential equations where the first two of them are in the canonical form of a one degree of freedom hamiltonian system and the third one depends upon the first two variables this representation is governed by the associated poisson algebra to one sub family of this lie algebra euler s form vector potential and clebsch representation are other representations of this lie algebra that we list here we also study the non potential property of vector fields with hopf zero singularity from this lie algebra finally we examine the unique normal form with non zero cubic terms of this family in the presence of the symmetry group z 2 the theoretical results of normal form theory are illustrated with the modified chua s oscillator

adjoint design sensitivity analysis of reduced atomic systems using generalized langevin equation for lattice structures an efficient adjoint design sensitivity analysis method is developed for reduced atomic systems a reduced atomic system and the adjoint system are constructed in a locally confined region utilizing generalized langevin equation gle for periodic lattice structures due to the translational symmetry of lattice structures the size of time history kernel function that accounts for the boundary effects of the reduced atomic systems could be reduced to a single atom s degrees of freedom for the problems of highly nonlinear design variables the finite difference method is impractical for its inefficiency and inaccuracy however the adjoint method is very efficient regardless of the number of design variables since one additional time integration is required for the adjoint gle through numerical examples the derived adjoint sensitivity turns out to be accurate and efficient through the comparison with finite difference sensitivity

existence and uniqueness of fast decay entire solutions of quasilinear elliptic equations we prove the existence and uniqueness of fast decay solutions and clarify the structure of positive radial solutions of the quasilinear elliptic equation mu f u 0 in rn where m denotes the m laplace operator and f has a supercritical growth for small u 0 and a subcritical growth for large u our proofs use only elementary arguments based on several variational identities and a maximum principle of peletier and serrin

embedding and splitting ordinary differential equations in normal form abstract we introduce an embedding of real or complex n dimensional space k n as an algebraic variety v which is determined by the action of a linear one parameter group every analytic vector field on k n corresponds to some embedded vector field on v for a symmetric vector field this embedded vector field splits into a reduced system and a direct sum of non autonomous linear systems examples and applications are mostly concerned with poincare dulac normal forms embeddings provide a natural setting for perturbations of symmetric systems in particular of systems in normal form up to some degree