fast s box security mechanism research based on the polymorphic cipher in this study we propose a new design method for fast s box construction its security is dependent upon the length of pseudorandom numbers generated by two communication parties as the s box is being built we demonstrate that boolean functions play an important role in the design of both block and stream ciphers to satisfy a variety of cryptographic test methods such as strict avalanche criterion sac bit independence criterion bic and nonlinearity we apply polymorphic cipher pmc theory to the permutation function construction correlations among the test criteria in a real network environment are also evaluated

fluid dynamic description of flocking via the povzner boltzmann equation we introduce and discuss the possible dynamics of groups of indistinguishable agents which are interacting according to their relative positions with the aim of deriving hydrodynamic equations these models are developed to mimic the collective motion of groups of species such as bird flocks fish schools herds of quadrupeds or bacteria colonies our starting model for these interactions is the povzner equation 21 which describes a dilute gas in which binary collisions of elastic spheres depend on their relative positions following the cucker and smale model 9 we will consider binary interactions between agents that are dissipative collisions in which the coefficient of restitution depends on their relative distance under the assumption of weak dissipation it is shown that the povzner equation is modified through a correction in the form of a nonlinear friction type operator using this correction we formally obtain from the povzner equation in a direct way a fluid dynamic description of a system of agents with weak dissipative interactions with a coefficient of restitution that depends on their relative distance

subdivision surfaces a new paradigm for thin shell finite element analysis we develop a new paradigm for thin shell finite element analysis based on the use of subdivision surfaces for i describing the geometry of the shell in its undeformed configuration and ii generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the kirchhoff love theory of thin shells the particular subdivision strategy adopted here is loop s scheme with extensions such as required to account for creases and displacement boundary conditions the displacement fields obtained by subdivision are h2 and consequently have a finite kirchhoff love energy the resulting finite elements contain three nodes and element integrals are computed by a one point quadrature the displacement field of the shell is interpolated from nodal displacements only in particular no nodal rotations are used in the interpolation the interpolation scheme induced by subdivision is non local i e the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements however the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface numerical tests including the belytschko et al 10 obstacle course of benchmark problems demonstrate the high accuracy and optimal convergence of the method

error estimation and adaptive meshing in strongly nonlinear dynamic problems we present work aimed at developing a general framework for mesh adaption in strongly nonlinear possibly dynamic problems we begin by showing that the solutions of the incremental boundary value problem for a wide class of materials including nonlinear elastic materials compressible newtonian fluids and viscoplastic solids obey a minimum principle provided that the constitutive updates are formulated appropriately this minimum principle can be taken as a basis for asymptotic error estimation in particular we chose to monitor the error of a lower order projection of the finite element solution the optimal mesh size distribution then follows from a posteriori error indicators which are purely local i e can be computed element by element we demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

preserving lagrangian structure in nonlinear model reduction with application to structural dynamics this work proposes a model reduction methodology that preserves lagrangian structure and achieves computational efficiency in the presence of high order nonlinearities and arbitrary parameter dependence as such the resulting reduced order model retains key properties such as energy conservation and symplectic time evolution maps we focus on parameterized simple mechanical systems subjected to rayleigh damping and external forces and consider an application to nonlinear structural dynamics to preserve structure the method first approximates the system s lagrangian ingredients the riemannian metric the potential energy function the dissipation function and the external force and subsequently derives reduced order equations of motion by applying the forced euler lagrange equation with these quantities from the algebraic perspective key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness matri

multisymplectic geometry variational integrators and nonlinear pdes this paper presents a geometric variational approach to continuous and discrete mechanics and field theories using multisymplectic geometry we show that the existence of the fundamental geometric structures as well as their preservation along solutions can be obtained directly from the variational principle in particular we prove that a unique multisymplectic structure is obtained by taking the derivative of an action function and use this structure to prove covariant generalizations of conservation of symplecticity and noether s theorem natural discretization schemes for pdes which have these important preservation properties then follow by choosing a discrete action functional in the case of mechanics we recover the variational symplectic integrators of veselov type while for pdes we obtain covariant spacetime integrators which conserve the corresponding discrete multisymplectic form as well as the discrete momentum mappings corresponding to symmetries we show that the usual notion of symplecticity along an infinite dimensional space of fields can be naturally obtained by making a spacetime split all of the aspects of our method are demonstrated with a nonlinear sine gordon equation including computational results and a comparison with other discretization schemes

a new look at proper orthogonal decomposition we investigate some basic properties of the proper orthogonal decomposition pod method as it is applied to data compression and model reduction of finite dimensional nonlinear systems first we provide an analysis of the errors involved in solving a nonlinear ode initial value problem using a pod reduced order model then we study the effects of small perturbations in the ensemble of data from which the pod reduced order model is constructed on the reduced order model we explain why in some applications this sensitivity is a concern while in others it is not we also provide an analysis of computational complexity of solving an ode initial value problem and study the computational savings obtained by using a pod reduced order model we provide several examples to illustrate our theoretical results

a matrix deim technique for model reduction of nonlinear parametrized problems in cardiac mechanics abstract when relying on newton iterations to solve nonlinear problems in the context of reduced basis rb methods the assembling of the rb arrays during the online stage depends on the dimension of the underlying high fidelity approximation this is more of an issue when dealing with fully nonlinear problems for which the global jacobian matrix has to be entirely reassembled at each newton step in this paper the discrete empirical interpolation method deim and its matrix version mdeim are combined to evaluate both the residual vector and the jacobian matrix very efficiently in the case of complex parametrized nonlinear mechanical problems we compare this strategy with the classical deim approach and we derive a posteriori error estimates on the solution accounting for the contribution of deim mdeim errors the effectiveness of the proposed framework is assessed on quasi static nonlinear problems in particular we consider a nonlinear elasticity problem defined on a cube and a mechanical model describing heart contraction for an idealized left ventricle geometry the latter is a coupled problem in which the activation of the heart contraction is given by the solution of an electrophysiology model our numerical results show that mdeim is preferable to the classical deim both in terms of efficiency and accuracy

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

dimensional model reduction in non linear finite element dynamics of solids and structures a general approach to the dimensional reduction of non linear finite element models of solid dynamics is presented for the newmark implicit time discretization the computationally most expensive phase is the repeated solution of the system of linear equations for displacement increments to deal with this it is shown how the problem can be formulated in an approximation ritz basis of much smaller dimension similarly the explicit newmark algorithm can be also written in a reduced dimension basis and the computation time savings in that case follow from an increase in the stable time step length in addition the empirical eigenvectors are proposed as the basis in which to expand the incremental problem this basis achieves approximation optimality by using computational data for the response of the full model in time to construct a reduced basis which reproduces the full system in a statistical sense because of this global time viewpoint the basis need not be updated as with reduced bases computed from a linearization of the full finite element model if the dynamics of a finite element model is expressed in terms of a small number of basis vectors the asymptotic cost of the solution with the reduced model is lowered and optimal scalability of the computational algorithm with the size of the model is achieved at the same time numerical experiments indicate that by using reduced models substantial savings can be achieved even in the pre asymptotic range furthermore the algorithm parallelizes very efficiently the method we present is expected to become a useful tool in applications requiring a large number of repeated non linear solid dynamics simulations such as convergence studies design optimization and design of controllers of mechanical systems

variational integrators and the newmark algorithm for conservative and dissipative mechanical systems the purpose of this work is twofold first we demonstrate analytically that the classical newmark family as well as related integration algorithms are variational in the sense of the veselov formulation of discrete mechanics such variational algorithms are well known to be symplectic and momentum preserving and to often have excellent global energy behavior this analytical result is veried through numerical examples and is believed to be one of the primary reasons that this class of algorithms performs so well second we develop algorithms for mechanical systems with forcing and in particular for dissipative systems in this case we develop integrators that are based on a discretization of the lagrange d alembert principle as well as on a variational formulation of dissipation it is demonstrated that these types of structured integrators have good numerical behavior in terms of obtaining the correct amounts by which the energy changes over the integration run

structure preserving model reduction of port hamiltonian systems by moment matching at infinity model reduction of port hamiltonian systems by means of the krylov methods is considered aiming at port hamiltonian structure preservation it is shown how to employ the arnoldi method for model reduction in a particular coordinate system in order to preserve not only a specific number of the markov parameters but also the port hamiltonian structure for the reduced order model furthermore it is shown how the lanczos method can be applied in a structure preserving manner to a subclass of port hamiltonian systems which is characterized by an algebraic condition in fact for the same subclass of port hamiltonian systems the arnoldi method and the lanczos method turn out to be equivalent in the sense of producing reduced order port hamiltonian models with the same transfer function

hamiltonian structure for the modulation equations of a sine gordon wavetrain on etudie l equation sinus gordon e 2 t 2 x 2 u sin u 0 ou e est un petit parametre on construit une solution asymptotique sous la forme d un train d onde n phase variant lentement

estimation principal components and hamiltonian systems in this paper we show how symplectic geometry can be used to analyse a fundamental problem in estimation theory the fitting of lines and planes to a data set in n dimensions symplectic methods yield information not only on the critical point structure of the maximum likelihood estimation mle function see byrnes and willems 7 but also on the asymmetries in the distribution of the data points in n space

structure preserving model reduction for mechanical systems this paper focuses on methods of constructing of reduced order models of mechanical systems which preserve the lagrangian structure of the original system these methods may be used in combination with standard spatial decomposition methods such as the karhunen loeve expansion balancing and wavelet decompositions the model reduction procedure is implemented for three dimensional finite element models of elasticity and we show that using the standard newmark implicit integrator significant savings are obtained in the computational costs of simulation in particular simulation of the reduced model scales linearly in the number of degrees of freedom and parallelizes well

asynchronous variational integrators we describe a class of asynchronous variational integrators avi for nonlinear elastodynamics the avis are characterized by the following distinguishing attributes i the algorithms permit the selection of independent time steps in each element and the local time steps need not bear an integral relation to each other ii the algorithms derive from a spacetime form of a discrete version of hamilton s principle as a consequence of this variational structure the algorithms conserve local energy and momenta exactly subject to solvability of the local time steps numerical tests reveal that even when local energy balance is not enforced exactly the global and local energy behavior of the avis is quite remarkable a property which can probably be traced to the symplectic nature of the algorithm

emergent behavior in flocks we provide a model for both continuous and discrete time describing the evolution of a flock our model is parameterized by a constant beta capturing the rate of decay which in our model is polynomial of the influence between birds in the flock as they separate in space our main result shows that when beta 1 2 convergence of the flock to a common velocity is guaranteed while for betages1 2 convergence is guaranteed under some condition on the initial positions and velocities of the birds only

modal reduction of mathematical models of biological molecules this paper reports a detailed study of modal reduction based on either linear normal mode lnm analysis or proper orthogonal decomposition pod for modeling a single a d glucopyranose monomer as well as a chain of monomers attached to a moving atomic force microscope afm under harmonic excitations also a modal reduction method combining pod and component modal synthesis is developed the accuracy and efficiency of these methods are reported the focus of this study is to determine to what extent these methods can reduce the time and cost of molecular modeling and simultaneously provide the required accuracy it has been demonstrated that a linear reduced order model is valid for small amplitude excitation and low frequency excitation it is found that a nonlinear reduced order model based on pod modes provides a good approximation even for large excitation while the nonlinear reduced order model using linear eigenmodes as the basis vectors is less effective for modeling molecules with a strong nonlinearity the reduced order model based on component modal synthesis using pod modes for each component also gives a good approximation with the reduction in the dimension of the system using these methods the computational time and cost can be reduced significantly

discontinuous galerkin method for a nonlocal hydrodynamic model of flocking dynamics abstract in this paper we devise an efficient and robust numerical method for a nonlocal nonlinear model of flocking dynamics the governing equations are a hydrodynamic limit of the model of cucker and smale which consists of the compressible euler equations with added nonlinear nonlocal interaction terms the numerical scheme is based on the discontinuous galerkin method a semi implicit scheme is used in the time discretization which requires only the solution of one linear system per time level while retaining the stability of an implicit scheme a crucial point is the construction of a suitable linearization of the nonlocal terms which does not result in fill in of the system matrices element wise and inter element artificial diffusion is added to the scheme along with a postprocessing procedure to deal with near vacuum states that typically arise in the solution we demonstrate the efficiency and robustness of the scheme on numerical experiments in 1d and 2d

reconstruction equations and the karhunen loeve expansion for systems with symmetry we present a method for applying the karhunen loeve decomposition to systems with continuous symmetry the techniques in this paper contribute to the general procedure of removing variables associated with the symmetry of a problem and related ideas have been used in previous works both to identify coherent structures in solutions of pdes and to derive low order models via galerkin projection the main result of this paper is to derive a simple and easily implementable set of reconstruction equationswhich close the system of odes produced by galerkin projection the geometric interpretation of the method closely parallels techniques used in geometric phases and reconstruction techniques in geometric mechanics we apply the method to the kuramoto sivashinsky equation and are able to derive accurate models of considerably lower dimension than are possible with the traditional karhunen loeve expansion