symmetric prismatic tensegrity structures part ii symmetry adapted formulations this paper presents analytical formulations for the symmetry adapted equilibrium force density and geometrical stiffness matrices for prismatic tensegrity structures with dihedral symmetries an analytical expression for the infinitesimal mechanisms is also derived

block diagonalization of laplacian matrices of symmetric graphs via group theory in this article group theory is employed for block diagonalization of laplacian matrices of symmetric graphs the inter relation between group diagonalization methods and algebraic graph methods developed in recent years are established efficient methods are presented for calculating the eigenvalues and eigenvectors of matrices having canonical patterns this is achieved by using concepts from group theory linear algebra and graph theory these methods which can be viewed as extensions to the previously developed approaches are illustrated by applying to the eigensolution of the laplacian matrices of symmetric graphs the methods of this paper can be applied to combinatorial optimization problems such as nodal and element ordering and graph partitioning by calculating the second eigenvalue for the laplacian matrices of the models and the formation of their fiedler vectors considering the graphs as the topological models of skeletal structures the present methods become applicable to the calculation of the buckling loads and the natural frequencies and natural modes of skeletal structures copyright 2006 john wiley sons ltd

multi solution theory of signal processing based on finite element method any function can be approached by finite element to any accuracy because space of finite element of rough division is included in the space of fine division one can get multi solution theory by finite element method the multi solution theory bases on the usually finite element theory will result in a lot oft calculation representation theory of group is used to translate the bases of finite element to orthogonal bases and by this method a multi solution theory is developed bases on finite element method the theory can be applied to two dimension signal compact

quantized abelian principal connections on lorentzian manifolds we construct a covariant functor from a category of abelian principal bundles over globally hyperbolic spacetimes to a category of algebras that describes quantized principal connections we work within an appropriate differential geometric setting by using the bundle of connections and we study the full gauge group namely the group of vertical principal bundle automorphisms properties of our functor are investigated in detail and similar to earlier works it is found that due to topological obstructions the locality property of locally covariant quantum field theory is violated furthermore we prove that for abelian structure groups containing a nontrivial compact factor the gauge invariant borchers uhlmann algebra of the vector dual of the bundle of connections is not separating on gauge equivalence classes of principal connections we introduce a topological generalization of the concept of locally covariant quantum fields as examples we construct for the category of principal u 1 bundles two natural transformations from singular homology functors to the quantum field theory functor that can be interpreted as the chern class and the electric charge in this case we also prove that the electric charges can be consistently set to zero which yields another quantum field theory functor that satisfies all axioms of locally covariant quantum field theory

a natural classification of vibration modes of polygonal ducts based on group theoretic analysis in this work the natural frequencies and mode shapes of polygonal ducts are obtained by a finite element analysis via a group theoretic approach we show that the group theoretic techniques provide a natural setting for the solution of the problem via optimum utilization of the symmetry in the problem the simplifications and insights due to the inherent symmetry is intuitively obvious in simple symmetric structures however a systematic exploitation of this symmetry in more complicated structures is less obvious and is possible perhaps only via useful theorems from group representation theory and the associated projection operator theory we illustrate all the main steps with the help of an example of dihedral groups this example is directly applicable to the problem addressed in this paper the group theoretic approach splits up the original problem into independent subproblems and thereby affects significant computational savings more importantly the approach captures the role of symmetry in the problem and provides insights which are otherwise not obvious the multiplicity of the natural frequencies arising out of the inherent symmetry is determined a priori and neatly separated into different subproblems this suggests a neat physical classification of the mode shapes on a symmetry basis which is unique to this approach the values of the natural frequencies and the mode shapes for triangular square and pentagonal ducts are shown to be in good agreement with the existing results reported in the literature the classification of mode shapes on this symmetry basis is used in the analysis of the polygonal ducts with number of sides varying up to 16

a group theoretic approach to the linear free vibration analysis of shells with dihedral symmetry this paper deals with a group theoretic approach to the finite element analysis of linear free vibrations of shells with dihedral symmetry examples of such shell structures are cylindrical shells conical shells shells with circumferential stiffeners corrugated shells spherical shells etc the group theoretic approach is used to exploit the inherent symmetry in the problem for vibration analysis the group theoretic results give the correct symmetry adapted basis for the displacement field the stiffness matrix k and the mass matrix m are identically block diagonalized in this basis the generalized linear eigenvalue problem of free vibration gets split into independent subproblems due to this block diagonalization the simo element is used in the finite element formulation of the shell equilibrium equations numerical results for natural frequencies and natural modes of vibration of several dihedral shell structures are presented the results are shown to be in very good agreement with those reported in the literature the computational advantages and physical insights due to the group theoretic approach are also discussed

symmetry adapted equilibrium matrices a number of authors have previously used group representation theory to block diagonalise the stiffness matrix of a symmetric structure this paper describes how similar techniques can be used to block diagonalise the equilibrium matrix of a symmetric structure this is shown to provide useful insight into the static and kinematic response of such systems in particular it simplifies finding and classifying states of self stress and mechanisms as well as reducing the computational effort required for a force method analysis

a c algebra for quantized principal u 1 connections on globally hyperbolic lorentzian manifolds the aim of this work is to complete our program on the quantization of connections on arbitrary principal u 1 bundles over globally hyperbolic lorentzian manifolds in particular we show that one can assign via a covariant functor to any such bundle an algebra of observables which separates gauge equivalence classes of connections the c algebra we construct generalizes the usual ccr algebras since contrary to the standard field theoretic models it is based on a presymplectic abelian group instead of a symplectic vector space we prove a no go theorem according to which neither this functor nor any of its quotients satisfies the strict axioms of general local covariance as a byproduct we prove that a morphism violates the locality axiom if and only if a certain induced morphism of cohomology groups is non injective we show then that fixing any principal u 1 bundle there exists a suitable category of subbundles for which a quotient of our functor yields a quantum field theory in the sense of haag and kastler we shall provide a physical interpretation of this feature and we obtain some new insights concerning electric charges in locally covariant quantum field theory

a group theoretic approach to the global bifurcation analysis of an axially compressed cylindrical shell abstract the accurate prediction of the buckling load of thin shell structures is an important yet elusive goal it is particularly important in the aerospace industry where thin shell members are commonly used as structural elements due to a lack of adequate analytical results current practices in industry put heavy reliance on experimental testing and empirical data to supplement theoretical analysis see d bushnell computerized buckling analysis of shells martinus nijhoff dordrecht 1985 this paper focuses on recent results of the group theoretic approach to a numerical global postbuckling analysis of a perfect axially compressed cylindrical shell with built in end conditions the built in end conditions obviate the existence of a trivial membrane solution branch the example of an axially compressed cylindrical shell was chosen because it is well known that for thin shells the primary axisymmetric solution branch is riddled with closely spaced symmetry breaking bifurcation points in a numerical arc length continuation scheme the close proximity of the bifurcation points on the primary path manifests itself in severe ill conditioning of the tangent stiffness matrix group theory helps one systematically find an optimal set of basis vectors or symmetry modes which reflect the symmetry of a given solution path the immediate payoff in using these symmetry modes as basis vectors is that the tangent stiffness matrix block diagonalizes and the numerical ill conditioning is avoided thus an efficient and accurate technique for computing solution branches of a specific type and a subsequent diagnosis for symmetry breaking bifurcations is made relatively simple understanding the global behavior of the perfect structure is crucial in identifying critical imperfections and will ultimately diminish the heavy reliance on expensive experimental verification

boundary value problems with symmetry and their approximation by finite elements symmetry and related questions of group theory especially representation theory are well known popular topics among physicists this paper describes how these classical ideas can be put to use in the realm of finite element computations by substituting a family of independent problems on a reduced domain the symmetry cell for the original problem on the whole domain two specific difficulties appear one is how to set boundary conditions on symmetry planes representation theory gives the answer the other is how to proceed with the assembly of finite elements that constitute the symmetry cell to deal with this this paper introduces the concept of index of an element as part of the whole structure which is the number of its distinct symmetrical images the rule for assembly then becomes to perform as usual but to count each element as many times as its index

low lying excitations in the square triangle random tiling model we consider the sub dominant eigenstates of the transfer matrix for the square triangle random tiling model on an infinite strip of width l a numerical algorithm for generation of the corresponding solution of the bethe ansatz is developed numerical finite size scaling analysis of the associated eigenvalues reveals the presence of both integer and non integer critical exponents the analytical value of one of the non integer exponents is found it is also shown numerically that along with the leading correction to the free energy density for some excitations there is a term proportional to

matrix analysis of statically and kinematically indeterminate frameworks abstract the paper is concerned with the structural mechanics of assemblies of bars and pinjoints particularly where they are simultaneously statically and kinematically indeterminate the physical significance of the four linear algebraic vector subspaces of the equilibrium matrix is examined and an algorithm is set up which determines the rank of the matrix and the bases for the four subspaces in particular this algorithm gives full details of any states of self stress and modes of inextensional deformation which an assembly may possess a scheme is devised for the segregation of inextensional modes into rigid body modes up to six of these may be allowed by the foundation constraints and internal mechanisms in some circumstances a state of self stress may impart first order stiffness to an inextensional mode a matrix method for detecting this effect is devised and it is shown that if there is no state of self stress which imparts first order stiffness to a given mode then that mode can undergo rather large distortion which involves either zero change in length of the bars or possibly changes in length of third or higher order in the displacements the significance of negative stiffness as indicated by the matrix method is discussed the paper contains simple examples which illustrate all of the main points of the work

group theoretic exploitations of symmetry in computational solid and structural mechanics the use of group theory in simplifying the study of problems involving symmetry is a well established approach in various branches of physics and chemistry and major applications in these areas date back more than 70 years within the engineering disciplines the search for more systematic and more efficient strategies for exploiting symmetry in the computational problems of solid and structural mechanics has led to the development of group theoretic methods over the past 40 years this paper reviews the advances made in the application of group theory in areas such as bifurcation analysis vibration analysis and finite element analysis and summarizes the various implementation procedures currently available illustrative examples of typical solution procedures are drawn from recent work of the author it is shown how the group theoretic approach through the characteristic vector space decomposition enables considerable simplifications and reductions in computational effort to be achieved in many cases group theoretic considerations also allow valuable insights on the behaviour or properties of a system to be gained before any actual calculations are carried out copyright 2009 john wiley sons ltd

multiple equilibria for unlinked and weakly linked cellular structural forms abstract it is demonstrated that a structural form comprising n unlinked or weakly linked separate identical cells can by its nature suffer an explosion of unstable post buckling states associated with an n fold compound critical point examples of rigid link models and atomic matrix cellular models employing a lennard jones potential are included attention is paid to criteria for the appearance of homogeneous localized but distributed and thoroughly localized solutions for the atomic models generalized coordinates that exploit local and global symmetries of unlinked cells are introduced in a block diagonalization context to clarify the bifurcation structure a discretized lagrangian formulation is introduced to untangle the paths for weakly linked cells

abelian duality on globally hyperbolic spacetimes we study generalized electric magnetic duality in abelian gauge theory by combining techniques from locally covariant quantum field theory and cheeger simons differential cohomology on the category of globally hyperbolic lorentzian manifolds our approach generalizes previous treatments using the hamiltonian formalism in a manifestly covariant way and without the assumption of compact cauchy surfaces we construct semi classical configuration spaces and corresponding presymplectic abelian groups of observables which are quantized by the ccr functor to the category of c algebras we demonstrate explicitly how duality is implemented as a natural isomorphism between quantum field theories we apply this formalism to develop a fully covariant quantum theory of self dual fields

symmetrizing grids radial basis functions and chebyshev and zernike polynomials for the d 4 symmetry group interpolation within a squircle part i a domain is invariant under the eight element d 4 symmetry group if it is unchanged by reflection with respect to the x and y axes and also the diagonal line x y previous treatments of group theory for spectral methods have generally demanded a semester s worth of group theory we show this is unnecessary by providing explicit recipes for creating grids etc we show how to decompose an arbitrary function into six symmetry invariant components and thereby split the interpolation problem into six independent subproblems we also show how to make symmetry invariant basis functions from products of chebyshev polynomials from zernike polynomials and from radial basis functions rbfs of any species these recipes are completely general and apply to any domain that is invariant under the dihedral group d 4 these concepts are illustrated by rbf pseudospectral solutions of the poisson equation in a domain bounded by a squircle the square with rounded corners defined by x 2 y 2 1 0 where here 2 we also apply chebyshev polynomials to compute eigenmodes of the helmholtz equation on the square and show each mode belongs to one and only one of the six d 4 classes

quantum field theories on categories fibered in groupoids we introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes this provides us with a general and flexible framework to study quantum field theories defined on spacetimes with extra geometric structures such as bundles connections and spin structures using right kan extensions we can assign to any such theory an ordinary quantum field theory defined on the category of spacetimes and we shall clarify under which conditions it satisfies the axioms of locally covariant quantum field theory the same constructions can be performed in a homotopy theoretic framework by using homotopy right kan extensions which allows us to obtain first toy models of homotopical quantum field theories resembling some aspects of gauge theories

the generally covariant locality principle a new paradigm for local quantum field theory a new approach to the model independent description of quantum field theories will be introduced in the present work the main feature of this new approach is to incorporate in a local sense the principle of general covariance of general relativity thus giving rise to the concept of a locally covariant quantum field theory such locally covariant quantum field theories will be described mathematically in terms of covariant functors between the categories on one side of globally hyperbolic spacetimes with isometric embeddings as morphisms and on the other side of algebras with unital injective monomorphisms as morphisms moreover locally covariant quantum fields can be described in this framework as natural transformations between certain functors the usual haag kastler framework of nets of operator algebras over a fixed spacetime background manifold together with covariant automorphic actions of the isometry group of the background spacetime can be re gained from this new approach as a special case examples of this new approach are also outlined in case that a locally covariant quantum field theory obeys the time slice axiom one can naturally associate to it certain automorphic actions called relative cauchy evolutions which describe the dynamical reaction of the quantum field theory to a local change of spacetime background metrics the functional derivative of a relative cauchy evolution with respect to the spacetime metric is found to be a divergence free quantity which has as will be demonstrated in an example the significance of an energy momentum tensor up to addition of scalar functions for the locally covariant quantum field theory furthermore we discuss the functorial properties of state spaces of locally covariant quantum field theories that entail the validity of the principle of local definiteness

double link expandohedra a mechanical model for expansion of a virus double link expandohedra are introduced each is constructed from a parent polyhedron by replacing all faces with rigid plates adjacent plates being connected by a pair of spherically jointed bars powerful symmetry techniques are developed for mobility analysis of general double link expandohedra and when combined with numerical calculation and physical model building they demonstrate the existence of generic finite breathing expansion motions in many cases for icosahedrally symmetric trivalent parents with pentagonal and hexagonal faces only fullerene polyhedra the derived expandohedra provide a mechanical model for the experimentally observed swelling of viruses such as cowpea chlorotic mottle virus ccmv a fully symmetric swelling motion a finite mechanism is found for systems based on icosahedral fullerene polyhedra with odd triangulation number t 31 and is conjectured to exist for all odd triangulation numbers

symmetry and states of self stress in triangulated toroidal frames abstract a symmetry extension of maxwell s rule for rigidity of frames shows that every fully triangulated torus has at least six states of self stress with a well defined set of symmetries related to rotational and translational representations in the point group in contrast in trivalent polyhedral toroidal frames i e the duals of the deltahedra the rigid body motions plus the mechanisms are at least equal in number to the bars and their symmetry representation contains that of a set of vector slides along the bars

integrability of the square triangle random tiling model instituut voor theoretische fysica universiteit van amsterdam valckenierstraat 65 1018 xe amsterdam the netherlands received 4 november 1996 it is shown that the square triangle random tiling model is equivalent to an asymmetric limit of the threecoloring model on the honeycomb lattice the latter model is known to be the o n model at t50 andcorresponds to the integrable model connected to the af nea

a symmetry extension of maxwell s rule for rigidity of frames a symmetry extension of maxwell s rule for rigidity of frames is found this rule subsumes and strengthens maxwell s 1864 rule by requiring that the internal and external degrees of freedom of a pin jointed structure are not only numerically equal but are also equisymmetric a number of special cases of maxwell s original rule are studied to show the improved insight that the symmetry adapted version can give

linear yang mills theory as a homotopy aqft it is observed that the shifted poisson structure antibracket on the solution complex of klein gordon and linear yang mills theory on globally hyperbolic lorentzian manifolds admits retarded advanced trivializations analogs of retarded advanced green s operators quantization of the associated unshifted poisson structure determines a unique up to equivalence homotopy algebraic quantum field theory aqft i e a functor that assigns differential graded algebras of observables and fulfills homotopical analogs of the aqft axioms for klein gordon theory the construction is equivalent to the standard one while for linear yang mills it is richer and reproduces the brst bv field content gauge fields ghosts and antifields

symmetric prismatic tensegrity structures part i configuration and stability this paper presents a simple and efficient method to determine the self equilibrated configurations of prismatic tensegrity structures nodes and members of which have dihedral symmetry it is demonstrated that stability of this class of structures is not only directly related to the connectivity of members but is also sensitive to their geometry height radius ratio and is also dependent on the level of self stress and stiffness of members a catalogue of the structures with relatively small number of members is presented based on the stability investigations

superselection sectors and general covariance i this paper is devoted to the analysis of charged superselection sectors in the framework of the locally covariant quantum field theories we shall analyze sharply localizable charges and use net cohomology of j e roberts as a main tool we show that to any 4 dimensional globally hyperbolic spacetime a unique up to equivalence symmetric tensor mathrm c category with conjugates in case of finite statistics is attached to any embedding between different spacetimes the corresponding categories can be embedded contravariantly in such a way that all the charged quantum numbers of sectors are preserved this entails that to any spacetime is associated a unique gauge group up to isomorphisms and that to any embedding between two spacetimes there corresponds a group morphism between the related gauge groups this form of covariance between sectors also brings to light the issue whether local and global sectors are the same we conjecture this holds that at least on simply connected spacetimes it is argued that the possible failure might be related to the presence of topological charges our analysis seems to describe theories which have a well defined short distance asymptotic behaviour

the stack of yang mills fields on lorentzian manifolds we provide an abstract definition and an explicit construction of the stack of non abelian yang mills fields on globally hyperbolic lorentzian manifolds we also formulate a stacky version of the yang mills cauchy problem and show that its well posedness is equivalent to a whole family of parametrized pde problems our work is based on the homotopy theoretical approach to stacks proposed in hollander isr j math 163 93 124 2008 which we shall extend by further constructions that are relevant for our purposes in particular we will clarify the concretification of mapping stacks to classifying stacks such as bgcon

model independent comparison between factorization algebras and algebraic quantum field theory on lorentzian manifolds this paper investigates the relationship between algebraic quantum field theories and factorization algebras on globally hyperbolic lorentzian manifolds functorial constructions that map between these two types of theories in both directions are developed under certain natural hypotheses including suitable variants of the local constancy and descent axioms the main result is an equivalence theorem between cauchy constant and additive algebraic quantum field theories and cauchy constant additive and time orderable prefactorization algebras a concept of involution for the latter class of prefactorization algebras is introduced via transfer this involves cauchy constancy explicitly and does not extend to generic time orderable prefactorization algebras

finite symmetric systems and their analysis abstract symmetry of linear mechanical systems permits one to substantially reduce the effort in their analysis classification and structural analysis of the finite linear symmetric systems models are studied in this paper there are two variants of the symmetry approach mechanical and algebraic in accordance with the former a symmetric system is replaced by one or several small nonsymmetric subsystems which are subjected to special loads obtained from the initial set the total response of the original symmetric system is found by special superposition of partial responses of these subsystems the algebraic approach is based on the explicit block diagonal decomposition of the matrix equation corresponding to a symmetric system while both approaches have the same efficiency the latter is easier to implement and describe it is presented here the condtions under which the symmetry technique may be utilized do not include symmetry of the applied loads specifically symmetry of those loads which form the right side of the associated equations nevertheless if the loads are symmetric the efficiency of the symmetry approach substantially increases group theory which is widely used in this paper is the mathematical tool for the study of symmetry and all necessary notions are introduced

improvement of the scaled corrector method for bifurcation analysis using symmetry exploiting block diagonalization in the nonlinear bifurcation analysis for large scaled structures the standard eigenanalysis of the tangent stiffness matrix yields important information but at the same time demands a large amount of computational cost the scaled corrector method was developed as a numerically efficient eigenanalysis free bifurcation analysis strategy which exploits byproducts of the numerical iteration for path tracing this method however has a problem in its accuracy especially when eigenvalues are nearly or exactly coincidental as a remedy for this we propose a new bifurcation analysis method through the implementation of bifurcation mechanism of a symmetric structure into the scaled corrector method the bifurcation mode is accurately approximated by decomposing a scaled corrector vector into a number of vectors by means of block diagonalization method in group theoretic bifurcation theory and in turn by choosing the predominant one among these vectors in order to demonstrate the usefulness of this method it is applied to the bifurcation analysis of reticulated regular hexagonal truss domes to compute accurately the locations of double bifurcation points and nearly coincidental bifurcation points and associated bifurcation modes

block diagonalization analysis of symmetric plates abstract this paper presents a block diagonalization method to solve stiffness equations of isotropic symmetric plates by means of a suitable local coordinate transformation chosen based on group theory the stiffness matrix is decomposed into a block diagonal form the stiffness equation in the local coordinate is solved block by block thus realizing numerical efficiency and greatly reducing the requisite amount of computer memory the efficiency has been further upgraded with the aid of the concept of augmented orbit this method is applied to a square isotropic plate subject to asymmetric loads to show its usefulness

lower order symmetric mechanism modes and bifurcation behavior of deployable bar structures with cyclic symmetry abstract kinematic bifurcation is generally unavoidable for deployable structures stating at one critical point along the compatibility path a deployable structure could exhibit unexpected motions it can either keep transforming along the primary path or get into one of the bifurcation paths in this study a group theoretic approach which is applicable for bifurcation analyses on symmetric deployable bar structures is developed with the aid of symmetry groups and their irreducible representations the key issue is to decompose the compatibility matrix of a deployable structure into block matrices in the symmetry adapted coordinate system and then extract new mechanism modes with lower order symmetries these symmetric mechanisms are associated with independent bifurcation paths and can identify the feasibility of the paths further using the prediction correction algorithm the lower order symmetric mechanisms are utilized to lead the structure smoothly transform into expected bifurcation paths to verify the effectiveness of the proposed approach several 2d linkages and 3d deployable structures are analyzed which possess inherent cyclic symmetries numerical results indicate that the proposed approach can effectively trace the complex and independent bifurcation paths

an orthogonal self stress matrix for efficient analysis of cyclically symmetric space truss structures via force method abstract the analysis of structures is normally carried out through displacement method while the force method is considered as an alternative approach for this purpose and used on occasion the generation of compatibility conditions the transpose of self stress matrix is one of the major and complicated parts of any structural analysis using force method in this paper an efficient method is proposed for producing orthogonal self stress matrix related to space truss structures with cyclic symmetry this is actually performed by eigen decomposition of a special matrix having the same null basis as in equilibrium matrix then the advantages of the obtained compatibility conditions are demonstrated with respect to different formulations such as standard force method eigen force method and integrated force method finally the efficiency of the presented method is comprehensively compared with three well known numerical methods and tested on a set of practical examples the results indicate clearly the significant superiority of the proposed approach in terms of both computational time and the accuracy of the results

some computational aspects of a group theoretic finite element approach to the buckling and postbuckling analyses of plates and shells of revolution abstract progress in the application of group theoretic methods to the nonlinear bifurcation analysis of symmetric structures has provided new hope in understanding the global postbuckling behavior of symmetric thin shell structures however what is still lacking in the computational mechanics community is a general purpose fe code with a group theoretic capability designed to take optimal advantage of existing symmetry this paper addresses some of the important issues associated with developing such a code the long term goal being to provide structural analysts with new numerical tools for doing careful global analyses of imperfection sensitive structures which may eventually lead to more accurate predictions of the maximum load carrying capacity of thin imperfection sensitive shell structures

exact block diagonalization of large eigenvalue problems for structures with symmetry we consider large eigenvalue problems for skeletal structures with symmetry we present an algorithm based upon a novel combination of group theoretic ideas and substructuring techniques that block diagonalizes such systems exactly and efficiently the procedure requires only the structural matrices of a repeating substructure together with the symmetry modes which are obtained from symmetry considerations alone we first present a simple paradigmatic example and then follow with several non trivial applications involving large lattice structures

prismatic tensegrity structures with additional cables integral symmetric states of self stress and cable controlled reconfiguration procedure abstract a simple energy method is put forward to determine the prestress distribution for symmetric tensegrity structures with multiple states of self stress and a class of prismatic tensegrities with additional cables are introduced to show the accuracy of presented method for the purpose of modifying structural shape as well as mechanical properties a cable controlled reconfiguration procedure is subsequently proposed for these structures by defining the length adjustments as the control parameters the reconfiguration procedure is regarded as a quasi static process consisting of a sequence of equilibrium configurations with varying control parameters then the nonlinear iterative algorithm based on the tangent stiffness of the structure is presented to simulate and follow this reconfiguration process by way of example a particular class of reconfigurations coined symmetrical reconfigurations are investigated carefully and the key features as well as the potential applications are given

analysis of symmetric or partially symmetric structures this paper combines group theoretic methods with substructuring techniques to treat the symmetric or partially symmetric structures subjected to arbitrary loads first for a given substructure module whose symmetry group is g it gives a method to find the generalized displacements associated with irreducible representations of g based on some concepts presented in this paper and then points out that for these displacements the analysis problem for a substructure module can be divided into a series of uncoupled subproblems for each subproblem the triangularization as well as condensation can be carried out individually finally a simplified calculation formula of condensed stiffness coefficients for the original displacements is established in which only the coefficients relating to the displacements in the basic region are necessary to be calculated a series of computer programs has been developed by the methods presented in this paper 1 4 these programs enable us to reduce the cpu time and save the memory noticeably

exploitation of symmetry in graphs with applications to finite and boundary elements analysis summary we present explicit and parametric forms of transformation matrices for three well known and widely used symmetry groups s2 c2v and c4v group representation theory is the most powerful method for exploiting symmetry we propose an efficient algorithm for systematic generation of reducible representations that can be combined linearly to obtain the projection operators the exact column spaces of these projection operators are calculated and integrated through special orderings leading to exact explicit and parametric forms of transformation matrices the transformation matrices could be used directly for block diagonalization of single variable scalar field problems another algorithm is proposed to extend the application of the method to nonscalar and multivariable field problems finally the generality and efficiency of the proposed method in relation to computation times and the accuracy of results are illustrated through examples from spectral decomposition free vibration buckling of fems and boundary element analysis of a symmetric field copyright 2012 john wiley sons ltd

a cohomological perspective on algebraic quantum field theory algebraic quantum field theory is considered from the perspective of the hochschild cohomology bicomplex this is a framework for studying deformations and symmetries deformation is a possible approach to the fundamental challenge of constructing interacting qft models symmetry is the primary tool for understanding the structure and properties of a qft model

tiles and colors tiling models are classical statistical models in which different geometric shapes the tiles are packed together such that they cover space completely in this paper we discuss a class of two dimensional tiling models in which the tiles are rectangles and isosceles triangles some of these models have been solved recently by means of bethe ansatz we discuss the question why only these models in a larger family are solvable and we search for the yang baxter structure behind their integrability in this quest we find the bethe ansatz solution of the problem of coloring the edges of the square lattice in four colors such that edges of the same color never meet in the same vertex

structural computations with the singular value decomposition of the equilibrium matrix abstract the singular value decomposition of the equilibrium matrix makes it possible to answer any question of a static kinematic or static kinematic nature for any structural assembly within a unified computational framework the paper introduces this decomposition relates it to the physical properties of a given assembly and derives formulae for stresses displacements etc a simple example illustrates the calculations

a picture of the global bifurcation diagram in ecological interacting and diffusing systems abstract this paper concerns global phenomena of pattern formation in stationary reaction diffusion equations possessing turing s diffusion induced instability which appear typically in mathematical biology global bifurcation diagrams with respect to two diffusion parameters are presented by integrating two complementary approaches analytical and numerical simple and double bifurcation analysis using group theoretic methods for the compact lie group d x results from singular perturbations when one diffusion constant is sufficiently small and a global existence theorem on primary bifurcated branches when the other diffusion is sufficiently large are the main analytical results a new numerical method is used to trace all bifurcating branches we examine interrelations between those local and semi global results under the light of global pictures obtained by numerical studies a variety of interesting and new diagrams near double eigenvalues are observed coexistence of multiple stable stationary states and global extension and deformation of local double structures are one of the main conclusions

relating nets and factorization algebras of observables free field theories in this paper we relate two mathematical frameworks that make perturbative quantum field theory rigorous perturbative algebraic quantum field theory paqft and the factorization algebras framework developed by costello and gwilliam to make the comparison as explicit as possible we use the free scalar field as our running example while giving proofs that apply to any field theory whose equations of motion are green hyperbolic which includes for instance free fermions the main claim is that for such free theories there is a natural transformation intertwining the two constructions in fact both approaches encode equivalent information if one assumes the time slice axiom the key technical ingredient is to use time ordered products as an intermediate step between a net of associative algebras and a factorization algebra

when is a symmetric body bar structure isostatic body bar frameworks provide a special class of frameworks which are well understood generically with a full combinatorial theory for rigidity given a symmetric body bar framework this paper exploits group representation theory to provide necessary conditions for rigidity in the form of very simply stated restrictions on the numbers of those structural components that are unshifted by the symmetry operations of the framework we give some initial results and conjectures for when these conditions are also sufficient for rigidity

modified stiffness iteration to pinpoint multiple bifurcation points abstract a modified stiffness iteration to precisely compute a bifurcation point with multiple zero eigenvalues is presented the iteration combines the direct pinpointing iteration for simple bifurcation points with a procedure to modify the tangent stiffness matrix based on pertinent congruent transformation to reduce the multiple eigenvalues to single ones two different transformation matrices are employed to modify the stiffness matrix one is a non orthogonal transformation matrix amplifying the values of the entries in a certain row and a column of the stiffness matrix the other is an orthogonal one which is chosen with reference to the symmetry of the system under consideration the use of the non orthogonal transformation matrix is a key idea termed stiffness amplification method in this paper whereas the orthogonal matrix is based on block diagonalization which is becoming popular in group theoretic analysis of symmetric structures extensive numerical examples show the robustness and usefulness of the proposed iteration method for pinpointing multiple bifurcation points

maxwell laman counts for bar joint frameworks in normed spaces abstract the rigidity matrix is a fundamental tool for studying the infinitesimal rigidity properties of euclidean bar joint frameworks in this paper we generalise this tool and introduce a rigidity matrix for bar joint frameworks in arbitrary finite dimensional real normed vector spaces using this new matrix we derive necessary maxwell laman type counting conditions for a well positioned bar joint framework in a real normed vector space to be infinitesimally rigid moreover we derive symmetry extended counting conditions for a bar joint framework with a non trivial symmetry group to be isostatic i e minimally infinitesimally rigid these conditions imply very simply stated restrictions on the number of those structural components that are fixed by the various symmetry operations of the framework finally we offer some observations and conjectures regarding combinatorial characterisations of symmetric isostatic bar joint frameworks in r 2 p where the unit ball p is a quadrilateral

littlewood richardson coefficients for grothendieck polynomials from integrability abstract we study the littlewood richardson coefficients of double grothendieck polynomials indexed by grassmannian permutations geometrically these are the structure constants of the equivariant k theory ring of grassmannians representing the double grothendieck polynomials as partition functions of an integrable vertex model we use its yang baxter equation to derive a series of product rules for the former polynomials and their duals the littlewood richardson coefficients that arise can all be expressed in terms of puzzles without gashes which generalize previous puzzles obtained by knutson tao and vakil