families of optimal oocs with lambda 2 we provide a new construction yielding one new and one known infinite family of optimal n w 2 optical orthogonal codes w isin 4 6 our construction relies on various techniques in finite projective spaces involving hyperovals in projective planes and singer groups

asymptotically optimal optical orthogonal codes with new parameters optical orthogonal codes oocs are widely used as spreading codes in optical fiber networks an n w a c ooc with size l is a family of l 0 1 sequences with length n weight w maximum autocorrelation a and maximum cross correlation c in this paper we present two new constructions for oocs with a c 1 which are asymptotically optimal with respect to the johnson bound we first construct an asymptotically optimal mpn m 1 1 ooc with size pn 1 m by using the structure of zpn the ring of integers modulo pn where p is an odd prime with m p 1 and n is a positive integer we then present another asymptotically optimal mp1 pk m 1 1 ooc with size p1 pk 1 m from a product of k finite fields where pi is an odd prime and m is a positive integer such that m pi 1 for 1 i k in particular it is optimal in the case that k 1 and m 1 2 p1 1

an objective 3d large deformation finite element formulation for geometrically exact curved kirchhoff rods the objective of this work is the development of a new finite element formulation for beams according to the kirchhoff theory of thin rods which includes the deformation states of axial tension torsion and bending the proposed formulation accounts for large deformations in three dimensional problem settings consisting of slender prismatic beams with arbitrarily curved initial geometries and arbitrary cross section shapes like in geometrically exact reissner theories the derived deformation measures are geometrically exact in the sense that they are consistent with the strong and weak form of the balance equations and the beam geometry for any configuration and for arbitrarily large translations rotations and strains a novel orthogonal interpolation strategy is applied to the triad field representing the cross section orientation in order to fulfill the kirchhoff constraint of vanishing shear strains in a strong sense and to preserve the objectivity of the spatially discretized problem the continuity requirements resulting from the corresponding weak form are fulfilled by a cubic hermite interpolation thus leading to a c1 continuous representation of the beam centerline fundamental properties such as objectivity path independence consistency and accuracy of the developed beam element are verified by means of suitable numerical examples

performance analysis of optical synchronous cdma communication systems with ppm signaling direct detection optical synchronous code division multiple access cdma systems with m ary pulse position modulation ppm signaling are investigated optical orthogonal codes are used as the signature sequences of our system a union upper bound on the bit error rate is derived taking into account the effect of the background noise multiple user interference and receiver shot noise the performance characteristics are then discussed for a variety of system parameters another upper bound on the probability of error is also obtained based on chernoff inequality this bound is utilized to derive achievable expressions for both the maximum number of users that can communicate simultaneously with asymptotically zero error rate and the channel capacity our results show that under average power and bit error rate constraints there always exists a pulse position multiplicity that permit all the subscribers to communicate simultaneously

mixed finite element methods for elastic rods of arbitrary geometry the boundary value problem for rods having arbitrary geometry and subjected to arbitrary loading is studied within the context of the small strain theory the basic assumptions underlying the rod kinematics are those corresponding to the timoshenko hypotheses in the plane rectilinear case that is plane sections normal to the line of centroids in the undeformed state remain plane but not necessarily normal the problem is formulated in both the standard and mixed variational forms and after establishing the existence and uniqueness of solutions to these equivalent problems the corresponding discrete problems are studied finite element approximations of the mixed problem are shown to be stable and convergent it is shown that the equivalence between the mixed problem and the standard problem with selective reduced integration holds only for the case of rods having constant curvature and torsion though the results of numerical experiments are presented these confirm the convergent behaviour of the mixed problem

new constructions of optimal cyclically permutable constant weight codes three new constructions for families of cyclic constant weight codes are presented all are asymptotically optimum in the sense that in each case as the length of the sequences within the family approaches infinity the ratio of family size to the maximum possible under the johnson upper bound approaches unity

optical orthogonal codes new bounds and an optimal construction a technique for constructing optimal oocs optical orthogonal codes is presented it provides the only known family of optimal with respect to family size oocs having lambda 2 the parameters n omega lambda are respectively p sup 2m 1 p sup m 1 2 where p is any prime and the family size is p sup m 2 three distinct upper bounds on the size of an ooc are presented that for many values of the parameter set n omega lambda improve upon the tightest previously known bound

a new galerkin based approach for accurate non linear normal modes through invariant manifolds a method for producing accurate reduced order models of non linear vibratory systems is presented based on the invariant manifold description of non linear normal modes nnm this approach makes use of polar co ordinates to obtain equations which govern the geometry of the invariant manifold these equations are discretized through a series expansion and galerkin projection over a chosen amplitude and phase domain yielding non linear equations in the expansion coefficients these equations when solved numerically yield an invariant manifold which is accurate to the degree of the expansion and devoid of the limitations which plague typical asymptotic solutions such galerkin based solutions may be used to generate accurate reduced order models for large amplitude strongly non linear motions this procedure is illustrated using two non linear examples a two degree of freedom oscillator and a finite element beam model the solution convergence and manifold geometry are discussed and the resultant reduced order models are shown to possess exceptional accuracy over large amplitude ranges this approach allows the full potential of the invariant manifold formulation to be reached and is suitably general for application to a wide variety of non linear systems

helicity and the calugareanu invariant the helicity of a localized solenoidal vector field i e the integrated scalar product of the field and its vector potential is known to be a conserved quantity under frozen field distortion of the ambient medium in this paper we present a number of results concerning the helicity of linked and knotted flux tubes particularly as regards the topological interpretation of helicity in terms of the gauss linking number and its limiting form the c lug reanu invariant the helicity of a single knotted flux tube is shown to be intimately related to the c lug reanu invariant and a new and direct derivation of this topological invariant from the invariance of helicity is given helicity is decomposed into writhe and twist contributions the writhe contribution involving the gauss integral for definition see equation 4 8 which admits interpretation in terms of the sum of signed crossings of the knot averaged over all projections part of the twist contribution is shown to be associated with the torsion of the knot and part with what may be described as intrinsic twist of the field lines in the flux tube around the knot see equations 5 13 and 5 15 the generic behaviour associated with the deformation of the knot through a configuration with points of inflexion points at which the curvature vanishes is analysed and the role of the twist parameter is discussed the derivation of the c lug reanu invariant from first principles of fluid mechanics provides a good demonstration of the relevance of fluid dynamical techniques to topological problems

curve shortening flow coupled to lateral diffusion we present and analyze a semi discrete finite element scheme for a system consisting of a geometric evolution equation for a curve and a parabolic equation on the evolving curve more precisely curve shortening flow with a forcing term that depends on a field defined on the curve is coupled with a diffusion equation for that field the scheme is based on ideas of dziuk siam j numer anal 36 6 1808 1830 1999 for the curve shortening flow and dziuk and elliott ima j numer anal 27 2 262 292 2007 for the parabolic equation on the moving curve additional estimates are required in order to show convergence most notably with respect to the length element while in dziuk siam j numer anal 36 6 1808 1830 1999 an estimate of its error was sufficient we here also need to estimate the time derivative of the error which arises from the diffusion equation numerical simulation results support the theoretical findings

performance analysis of direct detection optical cdma communication systems with avalanche photodiodes direct detection optical code division multiple access cdma communication systems with avalanche photodiode apd photodetectors are investigated a chernoff upper bound modified chernoff upper bound and gaussian approximation on the probability of bit error are presented for general apds and arbitrary

nonlinear dynamics of filaments ii nonlinear analysis abstract the linear stability analysis of the full time dependent kirchhoff equations for elastic filaments gives precise information about possible dynamical instabilities the associated dispersion relations derived in the preceding paper provides the selection mechanism for the shapes selected by highly unstable filaments here we perform a nonlinear analysis and derive new amplitude equations which describe the dynamics above the instability threshold the straight filament is studied in detail and the motion is shown to be described by a pair of nonlinear klein gordon equations which couple the local deformation amplitude to the twist density of particular interest is the effect of boundary conditions on the instability threshold it is shown that with suitable choice of boundary conditions the threshold of instability is delayed we also show the existence of pulse like and front like traveling wave solutions

elastic stability of dna configurations i general theory results are presented in the theory of the elastic rod model for dna among which are criteria enabling one to determine whether a calculated equilibrium configuration of a dna segment is stable in the sense that it gives a local minimum to the sum of the segment s elastic energy and the potential of forces acting on it the derived stability criteria are applicable to plasmids and to linear segments subject to strong anchoring end conditions their utility is illustrated with an example from the theory of configurations of the extranucleosomal loop of a dna miniplasmid in a mononucleosome with emphasis placed on the influence that nicking and ligation on one hand and changes in the ratio of elastic coefficients on the other have on the stability of equilibrium configurations in that example the configurations studied are calculated using an extension of the method of explicit solutions to cases in which the elastic rod modeling a dna segment is considered impenetrable and hence excluded volume effects and forces arising from self contact are taken into account

normal modes for non linear vibratory systems a methodology is presented which extends to non linear systems the concept of normal modes of motion which is well developed for linear systems the method is constructive for weakly non linear systems and provides the physical nature of the normal modes along with the non linear differential equations which govern their dynamics it also provides the non linear co ordinate transformation which relates the original system co ordinates to the modal co ordinates using this transformation we demonstrate how an approximate non linear version of superposition can be employed to reconstruct the overall motion from the individual non linear modal dynamics the results presented herein for non linear systems reduce to modal analysis for the linearized system when non linearities are neglected even though the approach is entirely different from the traditional one the tools employed are from the theory of invariant manifolds for dynamical systems and were inspired by the center manifold reduction technique in this paper the basic ideas are outlined a few examples are presented and some natural extensions and applications of the method are briefly described in the conclusions

euler lagrange equations for nonlinearly elastic rods with self contact we derive the euler lagrange equations for nonlinearly elastic rods with self contact the excluded volume constraint is formulated in terms of an upper bound on the global curvature of the centre line this condition is shown to guarantee the global injectivity of the deformation of the elastic rod topological constraints such as a prescribed knot and link class to model knotting and supercoiling phenomena as observed e g in dna molecules are included by using the notion of isotopy and gaussian linking number the bound on the global curvature as a nonsmooth side condition requires the use of clarke s generalized gradients to obtain the explicit structure of the contact forces which appear naturally as lagrange multipliers in the euler lagrange equations transversality conditions are discussed and higher regularity for the strains moments the centre line and the directors is shown

multi scale modal analysis for axisymmetric and spherical symmetric structures with periodic configurations abstract a new modal analysis method with second order two scale sots asymptotic expansion is presented for axisymmetric and spherical symmetric structures the symmetric structures considered are periodically distributed with homogeneous and isotropic constituent materials by the asymptotic expansion of the eigenfunctions the homogenized modal equations the effective materials coefficients the first and second order correctors are obtained the derived homogenized constitutive relationships are the same as the ones which serve to homogenize the corresponding static problems the eigenvalues are also expanded to the second order terms and using the so called corrector equation the correctors of the eigenvalues are expressed in terms of the first and second order correctors of the eigenfunctions the anisotropic materials are obtained by homogenization with different properties in the circumferential direction especially for the two dimensional axisymmetric layered structure the one dimensional plane axisymmetric and spherical symmetric structures the homogenized eigenfunctions and eigenvalues as well as their corresponding correctors are all solved analytically the finite element algorithm is established three typical numerical experiments are carried out and the necessity of the second order correctors is discussed based on the numerical results it is validated that the sots asymptotic expansion homogenization method is effective to identify the eigenvalues of the axisymmetric and spherical symmetric structures with periodic configurations and the original eigenfunctions with periodic oscillation can be reproduced by adding the correctors to the homogenized eigenfunctions

lagrangian aspects of the kirchhoff elastic rod the relation between euler s planar elastic curves and vortex filaments evolving by the localized induction equation lie of hydrodynamics was discovered by hasimoto in 1971 basic facts about an integrable case of kirchhoff elastic rods are described here which amplify the connection between the variational problem for rods and the soliton equation lie in particular it is shown that the centerline of the kirchhoff rod is an equilibrium for a linear combination of the first three conserved hamiltonians in the lie hierarchy

analysis of non linear dynamical systems by the normal form theory abstract a method is proposed for calculating the periodic solutions of non linear mechanical systems with analytical non linearities the jordan normalization procedure for the case of non linear autonomous systems is described and generalized to dampened harmonically excited oscillators non linear modes for hamiltonian systems are introduced normal forms simplify the analysis of bifurcation it is shown how to extend the modal synthesis procedure the proposed non linear modes obtained from free vibrations are used to construct a superposition technique to describe the forced response of harmonically excited systems these results are tested for one and two degrees of freedom systems with cubic non linearities the results are compared with expressions obtained by classical analytical methods averaging or multiple scales methods or runge kutta numerical methods

optical orthogonal signature pattern codes with maximum collision parameter 2 and weight 4 an optical orthogonal signature pattern code oospc finds application in transmitting 2 d images through multicore fiber in code division multiple access cdma communication systems observing a one to one correspondence between an oospc and a certain combinatorial subject called a packing design we present a construction of optimal oospcs with weight 4 and maximum collision parameter 2 which generalizes a well known kohler construction of optimal optical orthogonal codes ooc with weight 4 and maximum collision parameter 2 using this new construction enables one to obtain infinitely many optimal oospcs whose existence was previously unknown we prove that for a multiple n of 4 there exists no optimal oospc of size 6 n with weight 4 and maximum collision parameter 2 together with a report which shows a gap between optimal oocs and optimal oospcs when 6 and n are not coprime we also present a recursive construction of oospcs which are asymptotically optimal with respect to the johnson bound as a by product we obtain an asymptotically optimal m n 4 2 oospc for all positive integers m and n

a high order harmonic balance method for systems with distinct states abstract a pure frequency domain method for the computation of periodic solutions of nonlinear ordinary differential equations odes is proposed in this study the method is particularly suitable for the analysis of systems that feature distinct states i e where the odes involve piecewise defined functions an event driven scheme is used which is based on the direct calculation of the state transition time instants between these states an analytical formulation of the governing nonlinear algebraic system of equations is developed for the case of piecewise polynomial systems moreover it is shown that derivatives of the solution of up to second order can be calculated analytically making the method especially attractive for design studies the methodology is applied to several structural dynamical systems with conservative and dissipative nonlinearities in externally excited and autonomous configurations great performance and robustness of the proposed procedure was ascertained

optimal 2 d n times m 3 2 1 optical orthogonal codes optical orthogonal codes are commonly used as signature codes for optical code division multiple access systems so far research on 2 d optical orthogonal codes has mainly concentrated on the same autocorrelation and cross correlation constraints in this paper we are concerned about optimal 2 d optical orthogonal codes with the autocorrelation a and the cross correlation 1 some combinatorial constructions for 2 d n m k a 1 optical orthogonal codes are presented when k 3 and a 2 the exact number of codewords of an optimal 2 d n m 3 2 1 optical orthogonal code is determined for any positive integers n 0 1 3 6 9 10 mod 12 and m 2 mod 4

large amplitude non linear normal modes of piecewise linear systems a numerical method for constructing non linear normal modes nnms for piecewise linear autonomous systems is presented these nnms are based on the concept of invariant manifolds and are obtained using a galerkin based solution of the invariant manifold s non linear partial differential equations the accuracy of the constructed non linear modes is checked by the comparison of the motion on the invariant manifold to the exact solution in both time and frequency domains it is found that this construction approach can accurately capture the nnms over a wide range of amplitudes including those with strong non linear effects several interesting dynamic characteristics of the non linear modal motion are found and compared to those of linear modes a two degree of freedom example is used to illustrate the technique the existence stability and bifurcations of the nnms for this example are investigated

general constructions of optimal variable weight optical orthogonal codes variable weight optical orthogonal code ooc was introduced by yang for multimedia optical cdma systems with multiple quality of service qos requirements in this paper four general constructions for optimal cyclic packings and optimal variable weight oocs are presented many new infinite classes of optimal v w 1 q oocs are obtained new infinite classes of optimal v w 1 q oocs for w 4 are easily obtained by the constructions

multiuser detections for optical cdma networks based on expectation maximization algorithm in this paper we introduce new unblind and blind multiuser detectors for an optical code division multiple access system the detectors have two soft and hard stages in the soft stage a soft estimation of the interference is obtained by solving an unconstrained maximum likelihood problem via the iterative expectation maximization em algorithm then the hard stage detects the user information bit by solving a one dimensional boolean constrained problem conditioned on knowing the interference our results reveal that the proposed detectors have very low complexity and are robust against changes in parameters moreover the numerical results illustrate that despite of their simplicities our detectors substantially outperform other well known suboptimum detectors such as multistage and decorrelating detectors

on the geometric flow of kirchhoff elastic rods recently rod theory has been applied to the mathematical modeling of bacterial fibers and biopolymers e g dna to study their mechanical properties and shapes e g supercoiling in static rod theory an elastic rod in equilibrium is the critical point of an elastic energy this induces a natural question of how to find elasticae in this paper we focus on how to find the critical points by means of gradient flows we relate a geometric function of curves to the isotropic kirchhoff elastic energy of rods so that the generalized elastic curves are the centerlines of elastic rods in equilibrium thus the variational problem for rods is formulated in curve geometry this problem turns out to be a generalization of curve straightening flows which induce nonlinear fourth order evolution equations we establish the long time existence of length preserving gradient flow for the geometric energy furthermore by studying the asymptotic behavior we show that the limit curves are the centerlines of the ki

optical orthogonal codes design analysis and applications an optical orthogonal code ooc is a family of 0 1 sequences with good auto and cross correlation properties i e the autocorrelation of each sequence exhibits the thumbtack shape and the cross correlation between any two sequences remains low throughout the use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably the thumbtack shaped autocorrelation facilitates the detection of the desired signal and low profile cross correlation reduces interference from unwanted signals theoretical upper and lower bounds on the maximum possible size of oocs are derived methods for the design and analysis of oocs using tools from projective geometry the greedy algorithm iterative constructions algebraic coding theory block design and various other combinational disciplines are discussed

error analysis for the elastic flow of parametrized curves we analyze a semidiscrete numerical scheme for approximating the evolution of parametric curves by elastic flow in r n the fourth order equation is split into two coupled second order problems which are approximated by linear finite elements we prove error bounds for the resulting scheme and present numerical test calculations that confirm our analysis

on the use of modal derivatives for nonlinear model order reduction summary modal derivative is an approach to compute a reduced basis for model order reduction of large scale nonlinear systems that typically stem from the discretization of partial differential equations in this way a complex nonlinear simulation model can be integrated into an optimization problem or the design of a controller based on the resulting small scale state space model we investigate the approximation properties of modal derivatives analytically and thus lay a theoretical foundation of their use in model order reduction which has been missing so far concentrating on the application field of structural mechanics and structural dynamics we show that the concept of modal derivatives can also be applied as nonlinear extension of the craig bampton family of methods for substructuring we furthermore generalize the approach from a pure projection scheme to a novel reduced order modeling method that replaces all nonlinear terms by quadratic expressions in the reduced state variables this complexity reduction leads to a frequency preserving nonlinear quadratic state space model numerical examples with carefully chosen nonlinear model problems and three dimensional nonlinear elasticity confirm the analytical properties of the modal derivative reduction and show the potential of the proposed novel complexity reduction methods along with the current limitations copyright 2016 john wiley sons ltd

on the dynamics of rods in the theory of kirchhoff and clebsch we discuss here the dynamical equations of a theory of elastic rods that is due to kmcm ioff 1 2 and cl bsc 3 4 this properly invariant theory is applicable to motions in which the strains relative to an undistorted configuration remain small although rotations may be large it is constructed to be a first order theory i e a theory that is complete to within an error of order two in an appropriate dimensionless measure of thickness curvature twist and extension in a first order theory of thin rods one can treat the rod as inextensible and we do so here at the outset thus at each time t the arc length parameter s for the axial curve t is employed as a material coordinate i e a parameter whose value at a material point is constant in time and not only the resultant of the shearing forces on a cross section but also the tension in the rod are reactive quantities not given by constitutive equations consider for a moment a rod that is naturally prismatic and dynamically symmetric i e a rod that in an undistorted stress free configuration is a cylinder whose directrix although not necessarily a circle bounds a figure with equal principal moments of inertia a motion of the rod is said to be planar and twist flee i e a motion of pure flexure if it is such that t lies at all times in a fixed plane which contains a principal axis of inertia of each cross section for such a motion we employ a fixed cartesian coordinate system on and for consistency with a discussion of more general motions to be given later in this paper we call the abscissa z and the ordinate x we may write fz s t fx s t for the z and x components of the resultant force f at time t on the cross section with arc length coordinate s the motion of the rod may be described by giving the z x coordinates of the points on t as functions of s and t with o s t the counterclockwise angle from the z axis to the tangent of t at s we have

symmetry breaking and the twisted elastic ring symmetry breaking is considered in the context of a parameter dependent two point boundary value problem describing a twisted elastic ring that arises as a model of dna minicircles we explicitly determine via a perturbation expansion those representatives of a manifold of solutions to a symmetric bvp that persist when the symmetry is broken conditions generating a generic splitting are identified and some degenerate cases are studied in both the generic and degenerate cases the results of the perturbation expansion are used to improve the efficiency of existing algorithms for computing symmetry broken bifurcation diagrams

geodesic finite elements for cosserat rods we introduce geodesic finite elements as a new way to discretize the non linear configuration space of a geometrically exact cosserat rod these geodesic finite elements naturally generalize standard one dimensional finite elements to spaces of functions with values in a riemannian manifold for the special orthogonal group our approach reproduces the interpolation formulas of crisfield and jelenic geodesic finite elements are conforming and lead to objective and path independent problem formulations we introduce geodesic finite elements for general riemannian manifolds discuss the relationship between geodesic finite elements and coefficient vectors and estimate the interpolation error then we use them to find static equilibria of hyperelastic cosserat rods using the riemannian trust region algorithm of absil et al we show numerically that the discretization error depends optimally on the mesh size copyright 2009 john wiley sons ltd

a high order purely frequency based harmonic balance formulation for continuation of periodic solutions combining the harmonic balance method hbm and a continuation method is a well known technique to follow the periodic solutions of dynamical systems when a control parameter is varied however since deriving the algebraic system containing the fourier coefficients can be a highly cumbersome procedure the classical hbm is often limited to polynomial quadratic and cubic nonlinearities and or a few harmonics several variations on the classical hbm such as the incremental hbm or the alternating frequency time domain hbm have been presented in the literature to overcome this shortcoming here we present an alternative approach that can be applied to a very large class of dynamical systems autonomous or forced with smooth equations the main idea is to systematically recast the dynamical system in quadratic polynomial form before applying the hbm once the equations have been rendered quadratic it becomes obvious to derive the algebraic system and solve it by the so called asymptotic numerical method anm continuation technique several classical examples are presented to illustrate the use of this numerical approach

optical orthogonal codes their bounds and new optimal constructions a v k spl lambda sub a spl lambda sub c optical orthogonal code ooc c is a family of 0 1 sequences of length v and weight k satisfying the following two correlation properties 1 spl sigma sub 0 spl les t spl les v 1 x sub t x sub t i spl les spl lambda sub a for any x x sub 0 x sub 1 spl middot spl middot spl middot x sub v 1 spl isin c and any integer i not equivalent 0 mod v and 2 spl sigma sub 0 spl les t spl les v 1 x sub t y sub t i spl les spl lambda sub b for any x x sub 0 x sub 1 spl middot spl middot spl middot x sub v 1 spl isin c y y sub 0 y sub 1 spl middot spl middot spl middot y sub v 1 spl isin c with x spl ne y and any integer i where the subscripts are taken modulo v the study of optical orthogonal codes is motivated by an application in optical code division multiple access communication systems in this paper upper bounds on the size of an optical orthogonal code are discussed several new constructions for optimal optical orthogonal codes with weight k spl ges 4 and correlation constraints spl lambda sub a spl lambda sub c 1 are described by means of optimal cyclic packings many new infinite series of such optimal optical orthogonal codes are thus produced

isoperimetric conjugate points with application to the stability of dna minicircles a conjugate point test determining an index of the constrained second variation in one dimensional isoperimetric calculus of variations problems is described the test is then implemented numerically to determine stability properties of equilibria within a continuum mechanics model of dna minicircles

parametric approximation of isotropic and anisotropic elastic flow for closed and open curves deckelnick and dziuk math comput 78 266 645 671 2009 proved a stability bound for a continuous in time semidiscrete parametric finite element approximation of the elastic flow of closed curves in mathbb r d d geq2 we extend these ideas in considering an alternative finite element approximation of the same flow that retains some of the features of the formulations in barrett et al j comput phys 222 1 441 462 2007 siam j sci comput 31 1 225 253 2008 ima j numer anal 30 1 4 60 2010 in particular an equidistribution mesh property for this new approximation we obtain also a stability bound for a continuous in time semidiscrete scheme apart from the isotropic situation we also consider the case of an anisotropic elastic energy in addition to the evolution of closed curves we also consider the isotropic and anisotropic elastic flow of a single open curve in the plane and in higher codimension that satisfies various boundary conditions

nonlinear dynamics and loop formation in kirchhoff rods with implications to the mechanics of dna and cables the paper contributes a general dynamical formulation and numerical solution procedure for studying nonlinear and three dimensional dynamics of kirchhoff rods target applications include the dynamic formation of dna loops and supercoils as well as loops hockles in marine cables the formulation accommodates non homogeneous and non isotropic inextensible rods both with and without coupling of tension and torsion the utility of this formulation is illustrated by studying the dynamics and quasi static response of a clamped clamped rod subject to compression and or twist for slow loading rates the computed quasi static responses converge to published equilibrium solutions for a benchmark problem as loading rates increase new behaviors are observed including hysteresis in the neighborhood of equilibrium bifurcations the addition of chirality in the form of tension torsion coupling has a pronounced influence on the computed looped geometries this finding has implications for dna loops formed by dna protein binding as well as loop formation in helically wound wire and synthetic cables

numerical computation of nonlinear normal modes in mechanical engineering this paper reviews the recent advances in computational methods for nonlinear normal modes nnms different algorithms for the computation of undamped and damped nnms are presented and their respective advantages and limitations are discussed the methods are illustrated using various applications ranging from low dimensional weakly nonlinear systems to strongly nonlinear industrial structures

numerical solution of a bending torsion model for elastic rods aiming at simulating elastic rods we discretize a rod model based on a general theory of hyperelasticity for inextensible and unshearable rods after reviewing this model and discussing topological effects of periodic rods we prove convergence of the discretized functionals and stability of a corresponding discrete flow our experiments numerically confirm thresholds e g for michell s instability and indicate a complex energy landscape in particular in the presence of impermeability

nonlinear normal modes for vibratory systems under harmonic excitation this paper considers the use of numerically constructed invariant manifolds to determine the response of nonlinear vibratory systems that are subjected to harmonic excitation the approach is an extension of the nonlinear normal mode nnm formulation previously developed by the authors for free oscillations wherein an auxiliary system that models the excitation is used to augment the equations of motion in this manner the excitation is simply treated as an additional system state yielding a system with an extra degree of freedom dof whose response is known a reduced order model for the forced system is then determined by the usual nnm procedure and an efficient galerkin based solution method is used to numerically construct the attendant invariant manifolds the technique is illustrated by determining the frequency response for a simple 2 dof mass spring system with cubic nonlinearities and for a discretized beam model with 12 dof the results show that this method provides very accurate responses over a range of frequencies near resonances

a method for nonlinear modal analysis and synthesis application to harmonically forced and self excited mechanical systems abstract the recently developed generalized fourier galerkin method is complemented by a numerical continuation with respect to the kinetic energy which extends the framework to the investigation of modal interactions resulting in folds of the nonlinear modes in order to enhance the practicability regarding the investigation of complex large scale systems it is proposed to provide analytical gradients and exploit sparsity of the nonlinear part of the governing algebraic equations a novel reduced order model rom is developed for those regimes where internal resonances are absent the approach allows for an accurate approximation of the multi harmonic content of the resonant mode and accounts for the contributions of the off resonant modes in their linearized forms the rom facilitates the efficient analysis of self excited limit cycle oscillations frequency response functions and the direct tracing of forced resonances the rom is equipped with a large parameter space including parameters associated with linear damping and near resonant harmonic forcing terms an important objective of this paper is to demonstrate the broad applicability of the proposed overall methodology this is achieved by selected numerical examples including finite element models of structures with strongly nonlinear non conservative contact constraints

a generalized bose chowla family of optical orthogonal codes and distinct difference sets a new construction of optical orthogonal codes is provided in this correspondence which is a generalization of the well known construction of distinct difference set dds by bose and chowla this construction is optimal with respect to the johnson bound and has parameters n qa 1 omega q and lambda 1

constructions of binary constant weight cyclic codes and cyclically permutable codes a general theorem is proved showing how to obtain a constant weight binary cyclic code from a p ary linear cyclic code where p is a prime by using a representation of gf p as cyclic shifts of a binary p tuple based on this theorem constructions are given for four classes of binary constant weight codes the first two classes are shown to achieve the johnson upper bound on minimum distance asymptotically for long block lengths the other two classes are shown similarly to meet asymptotically the low rate plotkin upper bound on minimum distance a simple method is given for selecting virtually the maximum number of cyclically distinct codewords with full cyclic order from reed solomon codes and from berlekamp justesen maximum distance separable codes two correspondingly optimum classes of constant weight cyclically permutable codes are constructed it is shown that cyclically permutable codes provide a natural solution to the problem of constructing protocol sequence sets for the m active out of t users collision channel without feedback

elastic stability of dna configurations ii supercoiled plasmids with self contact configurations of protein free dna miniplasmids are calculated with the effects of impenetrability and self contact forces taken into account by using exact solutions of kirchhoff s equations of equilibrium for elastic rods of circular cross section bifurcation diagrams are presented as graphs of excess link ensuremath delta mathcal l versus writhe w and the stability criteria derived in paper i of this series are employed in a search for regions of such diagrams that correspond to configurations that are stable in the sense that they give local minima to elastic energy primary bifurcation branches that originate at circular configurations are composed of configurations with mathrm d m symmetry m 2 3 dots among the results obtained are the following i there are configurations with mathrm c 2 symmetry forming secondary bifurcation branches which emerge from the primary branch with m 3 and bifurcation of such secondary branches gives rise to tertiary branches of configurations without symmetry ii whether or not self contact occurs a noncircular configuration in the primary branch with m 2 called branch ensuremath alpha is stable when for it the derivative d ensuremath delta mathcal l d mathcal w computed along that branch is strictly positive iii for configurations not in ensuremath alpha the condition d ensuremath delta mathcal l d mathcal w g0 is not sufficient for stability in fact each nonplanar contact free configuration that is in a branch other than ensuremath alpha is unstable a rule relating the number of points of self contact and the occurrence of intervals of such contact to the magnitude of ensuremath delta mathcal l which in paper i was found to hold for segments of dna subject to strong anchoring end conditions is here observed to hold for computed configurations of protein free miniplasmids

a dynamic lagrangian frequency time method for the vibration of dry friction damped systems abstract a new frequency time domain procedure the dynamic lagrangian mixed frequency time method dlft is proposed to calculate the non linear steady state response to periodic excitation of structural systems subject to dry friction damping in this formulation the dynamic lagrangians are defined as the non linear contact forces obtained from the equations of motion in the frequency domain with the adjunction of a penalization on the difference between the interface displacements calculate by the non linear solver in the frequency domain and those calculated in the time domain from the non linear contact forces thus accounting for coulomb friction and non penetration conditions the dynamic lagrangians allow one to solve for the non linear forces between two points in contact without using artifacts such as springs the new dlft method is thus particularly well suited to handling finite element models of structures in frictional contact as it does not require a special model for the contact interface dynamic lagrangians are also better suited to frequency domain friction problems than the traditional time domain method of augmented lagrangians furthermore a reduction of the non linear system to relative interface displacements is introduced to decrease the computation time the dlft method is validated for a beam in contact with a flexible dry friction element connected to ground for frictional constraints that feature two dimensional relative motion results are also obtained for a large scale structural system with a large number of one dimensional dry friction dampers the dlft method is shown to be accurate and fast and it does not suffer from convergence problems at least in the examples studied

a new recursive construction for optical orthogonal codes we present a new recursive construction for n spl omega spl lambda sub a spl lambda sub c optical orthogonal codes for the case of spl lambda sub a spl lambda sub c spl lambda this recursive construction enlarges the original family with spl lambda unchanged and produces a new family of asymptotically optimal codes if the original family is asymptotically optimal we call a code asymptotically optimal following the definition of o moreno et al see ibid vol 41 p 448 55 1995 if as n the length of code goes to infinity the ratio of the number of codewords to the corresponding johnson bound approaches unity

combinatorial constructions for optimal two dimensional optical orthogonal codes optical orthogonal codes oocs have been designed for ocdma a one dimensional 1 d optical orthogonal code 1 d ooc is a set of one dimensional binary sequences having good auto and cross correlations one limitation of 1 d ooc is that the length of the sequence increases rapidly when the number of users or the weight of the code is increased which means large bandwidth expansion is required if a big number of codewords is needed to lessen this problem two dimensional 2 d coding also called multiwavelength oocs was invested a two dimensional 2 d optical orthogonal code 2 d ooc is a set of utimesv matrices with 0 1 elements having good auto and cross correlations recently many researchers are working on constructions and designs of 2 d oocs in this paper we shall reveal the combinatorial properties of 2 d oocs and give an equivalent combinatorial description of a 2 d ooc based on this we are able to use combinatorial methods to obtain many optimal 2 d oocs

a variational characterization of a hyperelastic rod with hard self contact abstract we consider an elastic rod modeled as a curve in space with an impenetrable surrounding tube of radius subject to a general class of boundary conditions the impossibility of self intersection is then imposed as a family of scalar constraints on the physical separation of nonlocal pairs of points on the rod thus the usual variational formulation of energy minimization is considered in a context of nonconvex nonsmooth optimization we show the existence of minimizers within suitably defined homotopy classes associated with both the centerline and the frame along the rod the principle results are then concerned with derivation of first order necessary conditions for optimality and some consequences of these for the contact forces and for regularity

a variational rod model with a singular nonlocal potential the classical theory of elastic rods does not account for the possibility that large deformations may involve distinct points along the rod occupying the same physical space we develop an elastic rod model with a pairwise repulsive potential such that if two non adjacent points along the rod are close in physical space there is an energy barrier which prevents contact while for points nearby along the rod the potential is describable classically this framework is developed to prove the existence of minimizers within each homotopy class where the idea of topological homotopy of a curve is generalized to elastic rods as framed curves finally the relevant first order optimality conditions are derived and used to investigate the regularity of minimizers

nonlinear dynamics of filaments i dynamical instabilities abstract the kirchhoff model provides a well established mathematical framework to study both computationaly and theoretically the dynamics of thin filaments within the approximations of linear elasticity theory the study of static solutions to these equations has a long history and the usual approach to describing their instabilities is to study the time dependent version of the kirchhoff model in the euler angle frame here we study the linear stability of the full time independent equations by introducing a new are length preserving perturbation scheme as an application we consider the instabilities of various stationary solutions such as the planar ring and straight rod subjected to twisting perturbations this scheme gives a direct proof of the existence of dynamical instabilities and provides the selection mechanism for the shape of unstable filaments

complicated dynamics of a linear oscillator with a light essentially nonlinear attachment abstract we study the dynamics of a two degree of freedom dof nonlinear system consisting of a grounded linear oscillator coupled to a light mass by means of an essentially nonlinear nonlinearizable stiffness we consider first the undamped system and perform a numerical study based on non smooth transformations to determine its periodic solutions in a frequency energy plot it is found that there is a sequence of periodic solutions bifurcating or emanating from the main backbone curve of the plot we then study analytically the periodic orbits of the undamped system using a complexification averaging technique in order to determine the frequency contents of the various branches of solutions and to understand the types of oscillation performed by the system at the different regimes of the motion the transient responses of the weakly damped system are then examined and numerical wavelet transforms are used to study the time evolutions of their harmonic components we show that the structure of periodic orbits of the undamped system greatly influences the damped dynamics as it causes complicated transitions between modes in the damped transient motion in addition there is the possibility of strong passive energy transfer energy pumping from the linear oscillator to the nonlinear attachment if certain periodic orbits of the undamped dynamics are excited by the initial conditions

constructions of optimal 2 d optical orthogonal codes via generalized cyclotomic classes optical orthogonal codes oocs are widely used as spreading codes in optical fiber networks in this paper a bound on the code size of 2 d oocs with both at most one pulse per wavelength am oppw and at most one pulse per time slot am oppts is derived accordingly two constructions of optimal 2 d oocs with both am oppw and am oppts are proposed via the generalized cyclotomic classes furthermore optimal 2 d ooc with am oppw can be also constructed by adding more codewords into the 2 d oocs with both am oppw and am oppts

construction of optimal 2d optical codes using n w 2 2 optical orthogonal codes two dimensional 2d wavelength time coding schemes have recently been studied for optical code division multiple access in this paper we propose a new family of 2d codes which use synchronized quadratic congruence sequences for wavelength hopping and n w 2 2 optical orthogonal codes for time spreading the new 2d codes provide larger asymptotically optimal code cardinality than other 2d codes by relaxing the maximum cross correlation function from one to two our study shows that the heavier code weight supported by our 2d codes results in better code performance than some of previously proposed 2d codes of the maximum cross correlation functions of one and two the new codes potentially support more subscribers and heavier bursty asynchronous traffic with gradual performance degradation as traffic load increases

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

nonlinear normal modes for damped geometrically nonlinear systems application to reduced order modelling of harmonically forced structures in order to build efficient reduced order models roms for geometrically nonlinear vibrations of thin structures a normal form procedure is computed for a general class of nonlinear oscillators with quadratic and cubic nonlinearities the linear perturbation brought by considering a modal viscous damping term is especially addressed in the formulation a special attention is focused on how all the linear modal damping terms are gathered together in order to define a precise decay of energy onto the invariant manifolds also defined as nonlinear normal modes nnms then this time independent formulation is used to reduce the dynamics governing the oscillations of a structure excited by an external harmonic force the validity of the proposed roms is systematically discussed and compared with other available methods in particular it is shown that large values of the modal damping of the slave modes may change the type of nonlinearity hardening softening behaviour of the directly excited master mode two examples are used to illustrate the main features of the method a two degrees of freedom dof system allows presentation of the main results through a simple example then a water filled circular cylindrical shell with external resonant forcing is considered in order to show the ability of the method to substantially reduce the dynamics of a continuous structure 2006 elsevier ltd all rights reserved