structural modal interaction with combination internal resonance under wide band random excitation in this paper the non linear interaction of a three degree of freedom structural model subjected to a wide band random excitation is examined the non linearity of the system results in different critical regions of internal resonance and this has a significant effect on the response statistics with reference to the combination internal resonance of the summed type the system response is analyzed by using the fokker planck equation approach together with a non gaussian closure scheme the non gaussian closure is based on the cumulant properties of order greater than three as a first order approximation the scheme yields 209 first order differential equations in first through fourth order joint moments of the response co ordinates the analysis is carried out with the aid of the computer algebra software macsyma the response statistics are determined numerically in the time and frequency internal detuning domains contrary to the gaussian closure scheme the non gaussian closure solution yields a strictly stationary response in addition to a number of complex response characteristics not previously reported in the literature of the area of non linear random vibration these include multiple solutions and jump phenomena jump and collapse in the response mean squares at internal detuning slightly shifted from the exact internal resonance condition at exact internal resonance the system response possesses a unique limit cycle in a stochastic sense the regions of multiple solutions are defined in terms of system parameters damping ratios and non linear coupling parameter and excitation spectral density level

spatially periodic instantons nahm transform and moduli this paper establishes that the nahm transform sending spatially periodic instantons instantons on the product of the real line and a three torus to singular monopoles on the dual three torus is indeed a bijection as suggested by the heuristic in the process we show how the nahm transform intertwines to a fourier mukai transform via kobayashi hitchin correspondences we also prove existence and non existence results

second order poincare inequalities and clts on wiener space we prove infinite dimensional second order poincare inequalities on wiener space thus closing a circle of ideas linking limit theorems for functionals of gaussian fields stein s method and malliavin calculus we provide two applications i to a new second order characterization of clts on a fixed wiener chaos and ii to linear functionals of gaussian subordinated fields

theoretical and experimental study of modal interaction in a two degree of freedom structure abstract fpr a two degree of freedom structure an experimental and theoretical investigation has been made of the primary resonances of the system which occur when the frequency of excitation is near one of the natural frequencies 1 and 2 the additional constraint of 2 2 1 has been included and its profound influence on the response studied the investigation has revealed some characteristics of the response that are the result of both non linearity and more than one degree of freedom the principal one of these being saturation as far as is known this is the first time that saturation has beeb observed and studied in detail in a physical structure

modal interaction of resonantly forced oscillations of two degree of freedom structure an analysis is presented for simultaneous primary resonances of two degree of freedom system with quadratic and cubic nonlinearities to external excitations having the frequencies w 1 and w 2 the relations between the external frequencies of the system are such that they are excited into external resonances in two cases the first case without internal resonances and the second case in the presence of different possibilities of internal resonances one to one two to one three to one one to two and one to three the method of multiple scales mms is used to determine four first order ordinary differential equations which describe the modulation of the amplitudes and phases of both modes in order to use the mms properly we introduce new detuning parameters of both modes it is found analytically that two mode responses can occur at each primary resonance in all cases the steady state solutions and their stability are determined numerical results depicting the resonances are presented

non linear vibrations of free edge thin spherical shells modal interaction rules and 1 1 2 internal resonance this paper is devoted to the derivation and the analysis of vibrations of shallow spherical shell subjected to large amplitude transverse displacement the analog for thin shallow shells of von karman s theory for large deflection of plates is used the validity range of the approximations is assessed by comparing the analytical modal analysis with a numerical solution the specific case of a free edge is considered the governing partial differential equations are expanded onto the natural modes of vibration of the shell the problem is replaced by an infinite set of coupled second order differential equations with quadratic and cubic non linear terms analytical expressions of the non linear coefficients are derived and a number of them are found to vanish as a consequence of the symmetry of revolution of the structure then for all the possible internal resonances a number of rules are deduced thus predicting the activation of the energy exchanges between the involved modes finally a specific mode coupling due to a 1 1 2 internal resonance between two companion modes and an axisymmetric mode is studied 2004 elsevier ltd all rights reserved

orthogonal polynomials in stein s method stein s method provides a way of finding approximations to the distribution say of a random variable which at the same time gives estimates of the approximation error involved in essence the method is based on a defining equation or equivalently an operator of the distribution and a related stein equation up to now it was not clear which equation to take one could think of a lot of equations we show how for a broad class of distributions there is one convenient equation we give a systematic treatment including the stein equation and its solution a key tool in stein s theory is the generator method developed by barbour and we suggest employing the generator of a markov process for the operator of the stein equation for a given distribution there may be various markov processes which fit in barbour s method and up to now it was still not clear which markov process to take to obtain good results we show how for a broad class of distributions there is a special markov process a birth and death process or a diffusion which takes a leading role in the analysis furthermore a key role is played by the classical orthogonal polynomials it turns out that the defining operator is based on a hypergeometric difference or differential equation which lies at the heart of the classical orthogonal polynomials furthermore the spectral representation of the transition probabilities of the markov process involved are in terms of orthogonal polynomials closely related to the distribution to be approximated this systematic treatment together with the introduction of orthogonal polynomials in the analysis seems to be new furthermore some earlier uncovered examples like the beta the student s t and the hypergeometric distribution are now worked out

structurally nonlinear fluttering airfoil in turbulent flow the dynamics and response of a structurally nonlinear two dimensional airfoil in turbulent flow are investigated numerically the solution is analyzed in terms of probability density function pdf response mean square power spectral density and lyapunov exponent both the longitudinal and vertical components of turbulence are considered it is shown that turbulent flow due to its longitudinal component diminishes the stability of the aeroelastic system by advancing the flutter point and decreasing the damping thus confirming results from previous work where only the longitudinal component was modeled furthermore the shift in flutter airspeed is strongly dependent on the random stiffness terms it is also observed that turbulence may advance the airspeed at which the pitch angle marginal pdf changes from uni to bimodal compared with the nonexcited deterministic case whereas the heave transition appears to be postponed this observation is attributed to the nonlinearity considered a cubic stiffness in torsion finally in terms of response mean square the system appears to he more sensitive to the presence of the longitudinal excitation component at pre rather than at postinstability airspeeds

fluctuations of eigenvalues and second order poincare inequalities linear statistics of eigenvalues in many familiar classes of random matrices are known to obey gaussian central limit theorems the proofs of such results are usually rather difficult involving hard computations specific to the model in question in this article we attempt to formulate a unified technique for deriving such results via relatively soft arguments in the process we introduce a notion of second order poincare inequalities just as ordinary poincare inequalities give variance bounds second order poincare inequalities give central limit theorems the proof of the main result employs stein s method of normal approximation a number of examples are worked out some of which are new one of the new results is a clt for the spectrum of gaussian toeplitz matrices

moduli spaces of instantons on the taub nut space we present adhm nahm data for instantons on the taub nut space and encode these data in terms of bow diagrams we study the moduli spaces of the instantons and present these spaces as finite hyperkahler quotients as an example we find an explicit expression for the metric on the moduli space of one su 2 instanton

combination parametric resonance leading to periodic and chaotic response in two degree of freedom systems with quadratic non linearities the dynamic response of a parametrically excited non linear system with two degrees of freedom is studied the system of equations which describes the compliant motion of a robotic manipulator exhibits internal resonance and is excited at a frequency near a primary resonance the effect of coupling is studied in detail non zero periodic motions are observed to co exist with a stable equilibrium state over a range of detuning near the resonant frequency loss of stability of the periodic response is observed at points of vertical tangency corresponding to a jump in the response while for some of the cases hopf bifurcation in the response corresponding to amplitude modulated motions is observed in the latter case period doubling of the amplitude of response is observed with a monotonic change in detuning eventually leading to chaotic motion in the system near exact tuning to the parametric resonance a quenching of the chaotic motion is found leaving only the stable zero equilibrium state for the system over some detuning interval

hyperkahler quotient construction of bps monopole moduli spaces we use the hyperkahler quotient of flat space to obtain some monopole moduli space metrics in explicit form using this new description we discuss their topology completeness and isometries we construct the moduli space metrics in the limit when some monopoles become massless which corresponds to non maximal symmetry breaking of the gauge group we also introduce a new family of hyperkahler metrics which depending on the mass parameter being positive or negative tend to either the asymptotic metric on the moduli space of many su 2 monopoles or to previously unknown metrics these new metrics are singular or complete depending on the particular choice of the level set of the moment map the singular metrics are of relevance to the moduli spaces of vacua of three dimensional gauge theories for higher rank gauge groups finally we make a few comments concerning the existence of closed or bound orbits on some of these manifolds and the integrability of the geodesic flow

a non linear analysis of the interactions between parametric and external excitations abstract solutions of a non linear equation having a form often encountered in the study of structural dynamics and in which both parametric and external excitation is present have been obtained analytically and numerically all the asymptotic analytical results can be verified by numerical integration for small values of some other solutions obtained numerically cannot be approximated by conventional asymptotic methods both types of solutions can exist simultaneously in these situations the initial conditions determine which solution describes the actual response of the system the solutions that can be predicted only by numerical means exhibit period multiplications i e the response has a period that is an integral multiple of the period of the excitation and chaos in fact in a certain range of one set of initial conditions can lead to period doubling in the response while another set can lead to a response very close to the asymptotic prediction very flexible structures can exhibit non linear characteristics in their response at very small amplitudes of the excitation the present results serve to illustrate some of the extraordinary behavior that such structures can exhibit and suggest that it may be extremely difficult to develop control systems for them

on the construction of monopoles for the classical groups forg a classical group an equivalence is exhibited between a g monopoles over 3 with maximal symmetry breaking at infinity b families of rank g algebraic curves int 1 along with divisors on those curves satisfying certain constraints c solutions of nahm s equations over rank g intervals satisfying the appropriate boundary conditions a and b are linked by twistor techniques b and c via the krichever method for solving non linear differential equations and a and c via the adhmn construction providing a unified picture of techniques for solution amongst other things an asymptotic formula for the higgs field of the monopole is computed

on the construction of monopoles we show that any self dual su 2 monopole may be constructed either by ward s twistor method or nahm s use of the adhm construction the common factor in both approaches is an algebraic curve whose jacobian is used to linearize the non linear ordinary differential equations which arise in nahm s method we derive the non singularity condition for the monopole in terms of this curve and apply the result to prove the regularity of axially symmetric solutions

stein s method on wiener chaos we combine malliavin calculus with stein s method in order to derive explicit bounds in the gaussian and gamma approximations of random variables in a fixed wiener chaos of a general gaussian process our approach generalizes refines and unifies the central and non central limit theorems for multiple wiener ito integrals recently proved in several papers from 2005 to 2007 by nourdin nualart ortiz latorre peccati and tudor we apply our techniques to prove berry esseen bounds in the breuer major clt for subordinated functionals of fractional brownian motion by using the well known mehler s formula for ornstein uhlenbeck semigroups we also recover a technical result recently proved by chatterjee concerning the gaussian approximation of functionals of finite dimensional gaussian vectors

hardening softening behaviour in non linear oscillations of structural systems using non linear normal modes the definition of a non linear normal mode nnm as an invariant manifold in phase space is used in conservative cases it is shown that normal form theory allows one to compute all nnms as well as the attendant dynamics onto the manifolds in a single operation then a single mode motion is studied the aim of the present work is to show that too severe truncature using a single linear mode can lead to erroneous results using single non linear mode motion predicts the correct behaviour hence the nonlinear change of co ordinates allowing one to pass from the linear modal variables to the normal ones linked to the nnms defines a framework to properly truncate non linear vibration pdes two examples are studied a discrete system a mass connected to two springs and a continuous one a linear euler bernoulli beam resting on a non linear elastic foundation for the latter a comparison is given between the developed method and previously published results

experimental investigation of structural linear and autoparametric interactions under random excitation when the first normal mode is externally excited by a band limited random excitation the system mean square response is found to be linearly proportional to the excitation spectal density up to a certain level above which the two normal modes exhibit discontinuity when the second normal mode is externally excited for small levels of excitation spectral density the response is dominated by the second normal mode for higher levels of excitation spectral density the first normal mode attends and interacts with the second normal mode

variational inequalities with examples and an application to the central limit theorem upper bounds for the distance in variation between an arbitrary probability measure and the standard normal one are established via some integrodifferential functionals including information the results are illustrated by gamma and t distributions moreover as a by product another proof of the central limit theorem is obtained

a new method of normal approximation we introduce a new version of stein s method that reduces a large class of normal approximation problems to variance bounding exercises thus making a connection between central limit theorems and concentration of measure unlike skorokhod embeddings the object whose variance must be bounded has an explicit formula that makes it possible to carry out the program more easily as an application we derive a general clt for functions that are obtained as combinations of many local contributions where the definition of local itself depends on the data several examples are given including the solution to a nearest neighbor clt problem posed by p bickel

stochastic response of nonlinear structures with parameter random fluctuations the random response of a nonlinear structural system is examined when its parameters are experiencing random fluctuations with time the treatment is based on the recent developments in the mathematical theory of stochastic differential equations these include the ito stochastic calculus and the fokker planck equation approach to derive a general differential equation that describes the evolution of the statistical moments of the response coordinates the differential equation is found to constitute an infinite coupled set of differential equations that are closed via two different closure schemes the system response is determined in the neighborhood of internal resonance condition and for various random intensities of the system parameters it is found that the random modal interaction is governed mainly by the internal resonance ratio and the stiffness fluctuation intensity the effect of the random damping fluctuation on the system response is found to be very small compared to the stiffness fluctuation effect

canonical transformations for hyperkahler structures and hyperhamiltonian dynamics we discuss generalizations of the well known concept of canonical transformations for symplectic structures to the case of hyperkahler structures different characterizations which are equivalent in the symplectic case give rise to non equivalent notions in the hyperkahler framework we will thus distinguish between hyperkahler and canonical transformations we also discuss the properties of hyperhamiltonian dynamics in this respect

forcing induced asymmetry on dynamical systems with cubic non linearities abstract the present work investigates the dynamics of a class of two degree of freedom oscillators with cubic non linearity in the restoring forces these oscillators are under the action of an external load including constant and harmonic components initially a perturbation analysis is applied to the equations of motion demonstrating the effect of the asymmetry induced by the constant loading component on the classical 1 1 and 1 3 internal resonances as well as on the possibility of the appearance of a first order 1 2 internal resonance next sets of slow flow equations governing the amplitudes and phases of vibration are derived for the special case of no internal resonance and for the most complicated case corresponding to 1 1 internal resonance the analytical findings are then complemented by numerical results obtained by examining the dynamics of a two degree of freedom mechanical system first the effect of certain system parameters on the existence and stability of constant and periodic solutions of the slow flow equations is illustrated by presenting a sequence of response diagrams finally the dynamics of the system used as an example is investigated further by direct integration of the slow flow equations this shows the existence of a period doubling sequence culminating into a continual interchange between quasiperiodic and chaotic response it also demonstrates a new transition scenario from phase locked to phase entrained and drift response

nahm s equations and the classification of monopoles solutions of nahm s system of ordinary differential equations are produced by variational methods this leads to an explicit parametrisation of the solutions to the bogomolny equation over 3