impact of heterogeneous delays on cluster synchronization we investigate cluster synchronization in coupled map networks in the presence of heterogeneous delays we find that while the parity of heterogeneous delays plays a crucial role in determining the mechanism of cluster formation the cluster synchronizability of the network gets affected by the amount of heterogeneity in addition heterogeneity in delays induces a rich cluster pattern as compared to homogeneous delays the complete bipartite network stands as an extreme example of this richness where robust ideal driven clusters observed for the undelayed and homogeneously delayed cases dismantle yielding versatile cluster patterns as heterogeneity in the delay is introduced we provide arguments behind this behavior using a lyapunov function analysis furthermore the interplay between the number of connections in the network and the amount of heterogeneity plays an important role in deciding the cluster formation

the submodule structure of specht modules abstract in this paper we will give a proof of the complete submodule structure of specht modules corresponding to 2 part partitions for the general linear group gl n q in characteristic p coprime to q in non defining characteristic the multiplicities in the specht module s n l l being at most 1 we introduce a partial order on the set of composition factors let e be the lowest integer such that p 1 q qe 1 we explicitly construct the j such that d n j j is a composition factor of s n l l by looking at well defined sets i of exponents of p whose coefficients in the p adic expansion of l j e are relevant we thus parametrise i l n j j the family of such sets i then forms a partially ordered set under inclusion we show that this is isomorphic to the poset of composition factors in s n l l the results in this paper are not to be confused with the results for 2 column partition specht modules in the defining characteristic of the general linear group obtained in a m adamovich phd thesis moscow state university 1992 and discussed in a kleshchev j sheth j algebra 221 1999 705 722 if we were to take q 1modp we would find the same submodule structure as in the corresponding specht modules of the symmetric group cf a kleshchev j sheth j algebra 221 1999 705 722

a new efficient approach to the formulation of mixed finite element models for structural analysis abstract a new finite element formulation is developed based on the hellinger reissner principle with independent strain by dividing the assumed strain into the lower order part and the higher order part the new formulation can be made much more efficient than the standard mixed formulation in addition the present new approach provides a rational way of introducing stabilization matrix to suppress undesirable kinematic modes author

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

assumed strain formulation for triangular c0 plate elements based on a weak form of the kirchhoff constraints application of a weak form of the kirchhoff constraints in the formulation of triangular assumed shear strain c0 plate element is described it is shown that compared to a similar formulation of the quadrilateral elements formulation of the triangles requires some additional considerations which lead to additional terms in the energy expression with those terms performance of the assumed shear strain triangular elements is comparable to that of the quadrilateral elements

a new efficient mixed formulation for thin shell finite element models abstract a nine node shell element is developed by a new and more efficient mixed formulation the new shell element formulation is based on the hellinger reissner principle with independent strain and the concept of degenerate solid shell the new formulation is made more efficient in terms of computing time than the conventional mixed formulation by dividing the assumed strain fields into a lower part and a higher order part numerical results demonstrate that the present nine node element is free of locking even for very thin plates and shells and is also kinematically stable in fact the stiffness matrix associated with the higher order assumed strain plays the role of a stabilization matrix

a hybrid strain finite element for plates and shells this paper describes a new hybrid strain finite element for geometrically linear analysis of plates and shells the formulation for materially linear problems is based on a mixed variational principle having strain and displacement rates as independently varied fields to facilitate extension to materially non linear analysis the variational principle is used in rate form and the plane stress assumption is not imposed a priori in the formulation when desired the plane stress assumption is imposed in a manner similar to imposition of fixed boundary conditions the element geometry is based on a nine noded quadrilateral with biquadratic interpolation of the displacement field the strain field is based on a bilinear interpolation with additional non linear terms chosen on the basis of eigenvalue analysis the element passes the required patch tests does not display either membrane or shear locking effects and is free of communicable spurious modes numerical results are presented for elastic analyses of several standard plate and shell test problems

a functional for shells of arbitrary geometry and a mixed finite element method for parabolic and circular cylindrical shells in this study a higher order shell theory is proposed for arbitrary shell geometries which allows the cross section to rotate with respect to the middle surface and to warp into a non planar surface this new kinematic assumption satisfies the shear free surface boundary condition bc automatically a new internal force expression is obtained based on this kinematic assumption a new functional for arbitrary shell geometries is obtained employing g teaux differential method during this variational process the bc is constructed and introduced to the functional in a systematic way two different mixed elements prsh52 and crsh52 are derived for parabolic and circular cylindrical shells respectively using the new functional the element does not suffer from shear locking the excellent performance of the new elements is verified by applying the method to some test problems copyright 2000 john wiley sons ltd

sublattice synchronization of chaotic networks with delayed couplings synchronization of chaotic units coupled by their time delayed variables is investigated analytically a type of cooperative behavior is found sublattice synchronization although the units of one sublattice are not directly coupled to each other they completely synchronize without time delay the chaotic trajectories of different sublattices are only weakly correlated but not related by generalized synchronization nevertheless the trajectory of one sublattice is predictable from the complete trajectory of the other one the spectra of lyapunov exponents are calculated analytically in the limit of infinite delay times and phase diagrams are derived for different topologies

a family of ans four node exact geometry shell elements in general convected curvilinear coordinates the non conventional exact geometry shell elements based on the timoshenko mindlin kinematics with five displacement degrees of freedom are proposed the term exact geometry exg reflects the fact that coefficients of the first and second fundamental forms of the reference surface and christoffel symbols are taken exactly at every gauss integration point the choice of only displacements as fundamental shell unknowns gives an opportunity to derive strain displacement relationships which are invariant under rigid body shell motions in a convected curvilinear coordinate system this paper presents a newly developed family consisting of three hybrid and one displacement based four node exg shell elements to avoid shear and membrane locking and have no spurious zero energy modes the ans concept is employed the ans interpolations satisfy exactly the plate compatibility equation for in plane strains as a result all exg shell elements developed pass membrane and bending plate patch tests and exhibit a superior performance in the case of distorted coarse mesh configurations copyright 2010 john wiley sons ltd

a finite element formulation with stabilization matrix for geometrically non linear shells an assumed strain finite element formulation with a stabilization matrix is developed for analysis of geometrically non linear problems of isotropic and laminated composite shells the present formulation utilizes the degenerate solid shell concept and assumes an independent strain as well as displacement the assumed independent strain field is divided into a lower order part and a higher order part subsequently the lower order part is set equal to the displacement dependent strain evaluated at the lower order integration points and the remaining higher order part leads to a stabilization matrix the strains and the determinant of the jacobian matrix are assumed to vary linearly in the thickness direction this assumption allows analytical integration through thickness independent of the number of plies a nine node element with a judiciously chosen set of higher order assumed strain field is developed numerical tests involving isotropic and composite shells undergoing large deflections demonstrate the validity of the present formulation

two higher order shell finite elements with stabilization matrix a 32 node three dimensional solid element and a 16 node degenerate solid element that are applicable to analysis of thin shell structural problems are presented in this paper both elements are formulated by using the hellinger reissner principle with independent strain the assumed independent strain field is divided into higherand lower order polynomial terms the element stiffness matrix associated with the higher order assumed strain plays the role of the stabilization matrix various types of the higher order assumed strain are tested for the present elements the resulting finite element models require much less time to compute the element stiffness matrix than the corresponding conventional mixed models or assumed displacement models with a full gaussian quadrature rule numerical results demonstrate that with a properly chosen set of higher order assumed strain the present elements produce reliable and very accurate solutions even for very thin plates and thin shells with deeply curved geometry

on the strain assumption in a finite element model for plates and shells two different methods of assuming independent strain fields are examined for the nine node degenerate solid shell element in the first case the assumed strain field is chosen for the local orthogonal co ordinate systems defined at the gaussian integration points in the second case the independent strain is assumed for a local orthogonal co ordinate system defined at the origin of the parent co ordinates the results of numerical tests involving simple example problems demonstrate that the second method is capable of exactly representing constant stress or moment states even when element geometries are distorted in addition both methods lead to a finite element model which is free of locking

an explicit hybrid stabilized 9 node lagrangian shell element abstract this paper presents an explicit hybrid stabilized 9 node lagrangian shell element in the formulation the stress modes pertinent to the stabilization are contravariant in nature and their products with the displacement derived covariant strain are explicit linear functions of the nodal geometric parameters the element is particularly efficient because the leverage matrix or the stabilization vectors can be constructed without resorting to numerical integration or the gram schmidt orthogonalization accuracy of the element is promising and comparable to the state of the art stabilized and hybrid elements

on extensions of simple modules over symmetric and algebraic groups here and below the cohomology of algebraic groups is the rational cohomology see 13 i 4 this result is quite useful for calculating some ext groups between simple g modules for example it immediately implies that extg l l 0 we would be interested in having a result similar to 1 for the symmetric group 6n for a partition of n we denote by s the corresponding specht module and if is p regular we write d for the corresponding irreducible module over f6n see 11 it is known that the specht modules play a role similar to that of weyl modules for algebraic groups so we are interested in results connecting ext6n d d and hom6n rad s d the first main result of the paper is

submodule structure of some specht modules in this paper we show how homomorphisms between certain permutation modules for the symmetric group s may be used to give information about the submodule structure of specht modules for hook and two rowed diagrams we continue the investigation of the properties of the hook module at characteristic 2 which was begun in 3 4 here we give precise conditions for the module to be completely reducible and to have a unique minimal submodule we also show that the two rowed specht module has a unique minimal submodule over a field of any characteristic let k be any field and x x i xn a set of independent commutative indeterminates we may define the action of s on any polynomal in the elements of x by u xi xu for each u in s we denote by scnprvr the specht module corresponding to a young diagram with n r nodes in the first row and r nodes in the second and by s n rv1 the module for a diagram with n r nodes in the top row and r rows of length 1 then s n rlr and s n r are generated over ks by t and u respectively where

interplay of degree correlations and cluster synchronization we study the evolution of coupled chaotic dynamics on networks and investigate the role of degree degree correlation in the networks cluster synchronizability we find that an increase in the disassortativity can lead to an increase or a decrease in the cluster synchronizability depending on the degree distribution and average connectivity of the network networks with heterogeneous degree distribution exhibit significant changes in cluster synchronizability as well as in the phenomena behind cluster synchronization as compared to those of homogeneous networks interestingly cluster synchronizability of a network may be very different from global synchronizability due to the presence of the driven phenomenon behind the cluster formation furthermore we show how degeneracy at the zero eigenvalues provides an understanding of the occurrence of the driven phenomenon behind the synchronization in disassortative networks the results demonstrate the importance of degree degree correlations in determining cluster synchronization behavior of complex networks and hence have potential applications in understanding and predicting dynamical behavior of complex systems ranging from brain to social systems

synchronized clusters in coupled map networks i numerical studies we study the synchronization of coupled maps on a variety of networks including regular one and two dimensional networks scale free networks small world networks tree networks and random networks for small coupling strengths nodes show turbulent behavior but form phase synchronized clusters as coupling increases when nodes show synchronized behavior we observe two interesting phenomena first there are some nodes of the floating type that show intermittent behavior between getting attached to some clusters and evolving independently second we identify two different ways of cluster formation namely self organized clusters which have mostly intracluster couplings and driven clusters which have mostly intercluster couplings the synchronized clusters may be of dominant self organized type dominant driven type or mixed type depending on the type of network and the parameters of the dynamics we define different states of the coupled dynamics by considering the number and type of synchronized clusters for the local dynamics governed by the logistic map we study the phase diagram in the plane of the coupling constant and the logistic map parameter ensuremath mu for large coupling strengths and nonlinear coupling we find that the scale free networks and the caley tree networks lead to better cluster formation than the other types of networks with the same average connectivity for most of our study we use the number of connections of the order of the number of nodes as the number of connections increases the number of nodes forming clusters and the size of the clusters in general increase

the application of geometrically exact shell elements to b spline surfaces abstract in the present study we propose a framework that directly links a general tensor based geometrically exact shell finite element to b spline surface geometric modeling four node and 9 node assumed strain elements based on the partial mixed hellinger reissner variational functional and a 4 node assumed natural strain ans element are implemented in b spline surface representation bubble functions are included in the basis functions to improve the performance of the developed elements the bi cubic rectangular b spline tensor patch is employed to generate the general form of parameterized shell surfaces by using the b spline function the present general tensor based shell elements can handle the arbitrary geometry of the free form surfaces numerical results demonstrate the efficient linkage concept between surface modeling of computer aided geometric design cagd and finite element shell analysis in static and dynamic examples

finite element formulation by parametrized hybrid variational principles variable stiffness and removal of locking in this paper a new one parameter hybrid functional is obtained as a special case of felippa and militello s parametrized variational principles the functional contains stress strain and compatible displacement as the primary fields it will be proved that some of the existing variable stiffness formulations fall into the framework of the new functional novel applications of the functional are also suggested mainly for removal of locking solid element destabilized 8 node and stabilized 9 plate elements are designed all of them can handle thin plate shell analysis in particular a prominent method is devised for constructing stabilization vectors the vectors are explicit linear functions of the nodal coordinates and can be implemented without resorting to gram schmidt orthogonalization or numerical integration results of the new elements in popular benchmark tests are encouraging

cluster and group synchronization in delay coupled networks we investigate the stability of synchronized states in delay coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics using a master stability approach we find that the master stability function shows a discrete rotational symmetry depending on the number of groups the coupling matrices that permit solutions on group or cluster synchronization manifolds show a very similar symmetry in their eigenvalue spectrum which helps to simplify the evaluation of the master stability function our theory allows for the characterization of stability of different patterns of synchronized dynamics in networks with multiple delay times multiple coupling functions but also with multiple kinds of local dynamics in the networks nodes we illustrate our results by calculating stability in the example of delay coupled semiconductor lasers and in a model for neuronal spiking dynamics

a consistent control of spurious singular modes in the 9 node lagrange element for the laplace and mindlin plate equations abstract when 2 2 quadrature is used with the 9 node lagrange element which is essential in c 0 plate elements to avoid locking spurious singular modes appear on the element level which can lead to singularity or near singularity of the global equations here these modes are controlled by a procedure that introduces additional generalized stresses and strains so that the spurious modes are eliminated and the consistency of the resulting finite difference equations is not impaired hence the procedure passes the patch test applications to the diffusion and mindlin plate equations are presented results show that h 3 convergence in the l 2 norm is almost retained

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

a new approach to the finite element modelling of beams with warping effect as a first step toward developing a finite element formulation that can model coupling among extensional bending and torsional behaviour of beams a new method is proposed to properly represent the warping of arbitrary cross sections the basic approach is to introduce a small warping displacement superimposed over flat cross sections of a shear flexible beam in a deformed configuration numerical tests involving simple isotropic beams undergoing a small elastic displacement demonstrate the validity of the new approach the present approach can be extended to composite beams as well as isotropic beams experiencing a large deflection or finite rotation