large amplitude motion mechanism and non planar vibration character of stay cables subject to the support motions abstract in this study the shooting method and the continuation technique are applied to investigate the large amplitude motion and non planar motion characteristic of the inclined cable subject to the support motion considering the geometric nonlinearity and the quasi static assumption a spatial discrete model of the cable is formulated which is used to determine the frequency response curves of the cable the effects of the amplitude of the support motion and the inclined angle on the coupling motion of the inclined cable are investigated it is shown that the coupling motion may occur and the motions play a noticeable role on the axial tensions of the cable also the non periodic spatial motions of the cable are examined through direct simulations

determining conductivity by boundary measurements ii interior results abstract in a recent paper the authors showed that an unknown real analytic conductivity gamma may be determined from static boundary measurements in this document they extend this analysis by demonstrating that a similar result holds for piecewise real analytic conductivities in addition for the special case of a layered structure it is shown that a three times continuously differentiable conductivity is identifiable by boundary measurements originator supplied keywords include inversion convergence algorithms estimates coefficients

recovering asymptotics of metrics from fixed energy scattering data from fixed energy scattering data is studied it is shown that if two such metrics g1 g2 have scattering data at some fixed energy which are equal up to smoothing then there exists a diffeomorphism fixing infinity such that g1 g2 is rapidly decreasing given the scattering matrix at two energies it is shown that the asymptotics of a metric and a short range potential can be determined simultaneously these results also hold for a wide class of scattering manifolds

spectra and eigenvectors of scale free networks we study the spectra and eigenvectors of the adjacency matrices of scale free networks when bidirectional interaction is allowed so that the adjacency matrix is real and symmetric the spectral density shows an exponential decay around the center followed by power law long tails at both spectrum edges the largest eigenvalue ensuremath lambda 1 depends on system size n as ensuremath lambda 1 ensuremath sim n 1 4 for large n and the corresponding eigenfunction is strongly localized at the hub the vertex with largest degree the component of the normalized eigenfunction at the hub is of order unity we also find that the mass gap scales as n ensuremath 0 68

localizations on complex networks we study the structural characteristics of complex networks using the representative eigenvectors of the adjacent matrix the probability distribution function of the components of the representative eigenvectors are proposed to describe the localization on networks where the euclidean distance is invalid several quantities are used to describe the localization properties of the representative states such as the participation ratio the structural entropy and the probability distribution function of the nearest neighbor level spacings for spectra of complex networks whole cell networks in the real world and the watts strogatz small world and barabasi albert scale free networks are considered the networks have nontrivial localization properties due to the nontrivial topological structures it is found that the ascending order ranked series of the occurrence probabilities at the nodes behave generally multifractally this characteristic can be used as a structural measure of complex networks

quantum graphs a simple model for chaotic scattering we connect quantum graphs with infinite leads and turn them into scattering systems we show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics typical poles delay time and conductance distributions ericson fluctuations and when considered statistically the ensemble of scattering matrices reproduces quite well the predictions of the appropriately defined random matrix ensembles the underlying classical dynamics can be defined and it provides important parameters which are needed for the quantum theory in particular we derive exact expressions for the scattering matrix and an exact trace formula for the density of resonances in terms of classical orbits analogous to the semiclassical theory of chaotic scattering we use this in order to investigate the origin of the connection between random matrix theory and the underlying classical chaotic dynamics being an exact theory and due to its relative simplicity it offers new insights into this problem which is at the forefront of the research in chaotic scattering and related fields

random matrix analysis of complex networks we study complex networks under random matrix theory rmt framework using nearest neighbor and next nearest neighbor spacing distributions we analyze the eigenvalues of the adjacency matrix of various model networks namely random scale free and small world networks these distributions follow the gaussian orthogonal ensemble statistic of rmt to probe long range correlations in the eigenvalues we study spectral rigidity via the ensuremath delta 3 statistic of rmt as well it follows rmt prediction of linear behavior in semilogarithmic scale with the slope being ensuremath sim 1 ensuremath pi 2 random and scale free networks follow rmt prediction for very large scale a small world network follows it for sufficiently large scale but much less than the random and scale free networks

a numerical study of sparse random matrices a numerical study is presented for the eigensolution statistics of largen n real and symmetric sparse random matrices as a function of the mean numberp of nonzero elements per row the model shows classical percolation and quantum localization transitions atp c 1 andp q 1 respectively in the rigid limitp n we demonstrate that the averaged density of states follows the wigner semicircle law and the corresponding nearest energy level spacing distribution functionp s obeys the wigner surmise in the very sparse matrix limitp n withp p q a singularity e 1 e is found as e 0 and exponential tails develop in the high e regions but thep s distribution remains consistent with level repulsion the localization properties of the model are examined by studying both the eigenvector amplitude and the density fluctuations the valuep q 1 4 is roughly estimated in agreement with previous studies of the anderson transition in dilute bethe lattices

an adaptive hybrid fem fdm method for an inverse scattering problem in scanning acoustic microscopy scanning acoustic microscopy based on focused ultrasound waves is a promising new tool in medical imaging in this work we apply an adaptive hybrid fem fdm finite element methods finite difference methods method to an inverse scattering problem for the time dependent acoustic wave equation where one seeks to reconstruct an unknown sound velocity c x from a single measurement of wave reflection data on a small part of the boundary e g to detect pathological defects in bone typically this corresponds to identifying an unknown object scatterer in a surrounding homogeneous medium the inverse problem is formulated as an optimal control problem where we use an adjoint method to solve the equations of optimality expressing stationarity of an associated augmented lagrangian by a quasi newton method to treat the problem of multiple minima of the objective function the optimization procedure is first performed on a coarse grid to smooth the high frequency error generating a starting point for optimization steps on successively refined meshes local refinement based on the results of previous steps will improve computational efficiency of the method as the main result then an a posteriori error estimate is proved for the error in the lagrangian and a corresponding adaptive method is formulated where the finite element mesh is refined from residual feedback the performance of the adaptive hybrid method and the usefulness of the a posteriori error estimator for problems with limited boundary data are illustrated in three dimensional numerical examples

finding community structure in networks using the eigenvectors of matrices we consider the problem of detecting communities or modules in networks groups of vertices with a higher than average density of edges connecting them previous work indicates that a robust approach to this problem is the maximization of the benefit function known as modularity over possible divisions of a network here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix which plays a role in community detection similar to that played by the graph laplacian in graph partitioning calculations this result leads us to a number of possible algorithms for detecting community structure as well as several other results including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong the algorithms and measures proposed are illustrated with applications to a variety of real world complex networks

multistep greedy algorithm identifies community structure in real world and computer generated networks we have recently introduced a multistep extension of the greedy algorithm for modularity optimization the extension is based on the idea that merging l pairs of communities l 1 at each iteration prevents premature condensation into few large communities here an empirical formula is presented for the choice of the step width l that generates partitions with close to optimal modularity for 17 real world and 1100 computer generated networks furthermore an in depth analysis of the communities of two real world networks the metabolic network of the bacterium e coli and the graph of coappearing words in the titles of papers coauthored by martin karplus provides evidence that the partition obtained by the multistep greedy algorithm is superior to the one generated by the original greedy algorithm not only with respect to modularity but also according to objective criteria in other words the multistep extension of the greedy algorithm reduces the danger of getting trapped in local optima of modularity and generates more reasonable partitions

analysis of weighted networks the connections in many networks are not merely binary entities either present or not but have associated weights that record their strengths relative to one another recent studies of networks have by and large steered clear of such weighted networks which are often perceived as being harder to analyze than their unweighted counterparts here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph allowing us to apply standard techniques for unweighted graphs to weighted ones as well we give a number of examples of the method including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum flow minimum cut theorem

deformed gaussian orthogonal ensemble description of small world networks the study of spectral behavior of networks has gained enthusiasm over the last few years in particular random matrix theory rmt concepts have proven to be useful in discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the brody type can be used in the present paper we analyze the regular to chaotic behavior of small world sw networks using an extension of the gaussian orthogonal ensemble this rmt ensemble coined the deformed gaussian orthogonal ensemble dgoe supplies a natural foundation of the brody formula sw networks follow goe statistics until a certain range of eigenvalue correlations depending upon the strength of random connections we show that for these regimes of sw networks where spectral correlations do not follow goe beyond a certain range dgoe statistics models the correlations very well the analysis performed in this paper proves the utility of the dgoe in network physics as much as it has been useful in other physical systems

spectra of random graphs with given expected degrees in the study of the spectra of power law graphs there are basically two competing approaches one is to prove analogues of wigner s semicircle law whereas the other predicts that the eigenvalues follow a power law distribution although the semicircle law and the power law have nothing in common we will show that both approaches are essentially correct if one considers the appropriate matrices we will prove that under certain mild conditions the eigenvalues of the normalized laplacian of a random power law graph follow the semicircle law whereas the spectrum of the adjacency matrix of a power law graph obeys the power law our results are based on the analysis of random graphs with given expected degrees and their relations to several key invariants of interest are a number of new values for the exponent where phase transitions for eigenvalue distributions occur the spectrum distributions have direct implications to numerous graph algorithms such as for example randomized algorithms that involve rapidly mixing markov chains

non linear oscillations of a four degree of freedom model of a suspended cable under multiple internal resonance conditions abstract a four degree of freedom model able to capture the main phenomena which are likely to occur in the non planar finite dynamics of an elastic suspended cable subjected to external forcings and support motions is developed from the continuum equations it contains two in plane and two out of plane components one symmetric and one antisymmetric an order two multiple time scales solution is obtained for the case of primary external resonance and three simultaneous internal resonances cable at crossover frequency possible classes of steady state planar non planar unimodal multimodal regular motions of the system are identified and their linearized stability analysis is performed some results are presented to highlight the role played by key perturbations on the onset of various classes the rich behaviour of the system and the influence of some control parameters on the response

multidimensional inverse problems and completeness of the products of solutions to pde a method is given for proving uniqueness theorems for some inverse problems the method is based on a result on completeness of the products of solutions to pde as an example the following uniqueness theorems are proved 1 the scattering amplitude a k known for all s2 and a fixed k 0 determines the compactly supported q x l2 d uniquely 2 the surface data u x y k known for all x y p x x3 0 and a fixed k 0 determine the compactly supported x l2 d d r 3 x x3 0 is arbitrarily small determine aj x j 1 2 uniquely here 2u k2u k2a1x a2 x u x y in r3 a1 l2 d a2 h2 d the same conclusion holds if the surface data are known at two distinct frequencies 4 the surface data u x y k known for all x y p and all k 0 determine v x and h k uniquely here 2 k2 k2 x u x y h k x l2 d h k is fourier transform of a wavelet of compact support 5 the conductivity x w2 2 d x c 0 is uniquely determined by the measurements of u and un on d here n is the outward normal to d d r3 is a bounded domain with a smooth boundary d x u 0 in d 6 necessary and sufficient conditions are given for a function a k s2 k 0 is fixed to be the scattering amplitude corresponding to a local potential from a certain class

laplacian spectra as a diagnostic tool for network structure and dynamics we examine numerically the three way relationships among structure laplacian spectra and frequency synchronization dynamics on complex networks we study the effects of clustering degree distribution and a particular type of coupling asymmetry input normalization all of which are known to have effects on the synchronizability of oscillator networks we find that these topological factors produce marked signatures in the laplacian eigenvalue distribution and in the localization properties of individual eigenvectors using a set of coordinates based on the laplacian eigenvectors as a diagnostic tool for synchronization dynamics we find that the process of frequency synchronization can be visualized as a series of quasi independent transitions involving different normal modes particular features of the partially synchronized state can be understood in terms of the behavior of particular modes or groups of modes for example there are important partially synchronized states in which a set of low lying modes remain unlocked while those in the main spectral peak are locked we find therefore that spectra are correlated with dynamics in ways that go beyond results relating a single threshold to a single extremal eigenvalue

determining anisotropic real analytic conductivities by boundary measurements if an electrical potential is applied to the surface of a solid body the current flux across the surface depends on the conductivity in the interior of the body we want to consider the inverse problem of determining the conductivity by these boundary measurements

level density for deformations of the gaussian orthogonal ensemble formulas are derived for the average level density of deformed or transition gaussian orthogonal random matrix ensembles after some general considerations about gaussian ensembles we derive formulas for the average level density for i the transition from the gaussian orthogonal ensemble goe to the poisson ensemble and ii the transition from the goe to m goes

nonlinear interactions and chaotic dynamics of suspended cables with three to one internal resonances abstract nonlinear planar oscillations of suspended cables subjected to external excitations with three to one internal resonances are investigated at first the galerkin method is used to discretize the governing nonlinear integral partial differential equation then the method of multiple scales is applied to obtain the modulation equations in the case of primary resonance the equilibrium solutions the periodic solutions and chaotic solutions of the modulation equations are also investigated the newton raphson method and the pseudo arclength path following algorithm are used to obtain the frequency force response curves the supercritical hopf bifurcations are found in these curves choosing these bifurcations as the initial points and applying the shooting method and the pseudo arclength path following algorithm the periodic solution branches are obtained at the same time the floquet theory is used to determine the stability of the periodic solutions numerical simulations are used to illustrate the cascades of period doubling bifurcations leading to chaos at last the nonlinear responses of the two degree of freedom model are investigated

determining conductivity by boundary measurements a p calderon pose la question est il possible de determiner la conductivite thermique d un objet a partir de mesures statiques de la temperature et du flux de chaleur a la limite on demontre que ces mesures determinent de facon unique la conductivite thermique et toutes ses derivees a la limite

laplacian spectra of and random walks on complex networks are scale free architectures really important we study the laplacian operator of an uncorrelated random network and as an application consider hopping processes diffusion random walks signal propagation etc on networks we develop a strict approach to these problems we derive an exact closed set of integral equations which provide the averages of the laplacian operator s resolvent this enables us to describe the propagation of a signal and random walks on the network we show that the determining parameter in this problem is the minimum degree q m of vertices in the network and that the high degree part of the degree distribution is not that essential the position of the lower edge of the laplacian spectrum c appears to be the same as in the regular bethe lattice with the coordination number q m namely c 0 if q m 2 and c 0 if q m 2 in both of these cases the density of eigenvalues p 0 as c 0 but the limiting behaviors near c are very different in terms of a distance from a starting vertex the hopping propagator is a steady moving gaussian broadening with time this picture qualitatively coincides with that for a regular bethe lattice our analytical results include the spectral density p near c and the long time asymptotics of the autocorrelator and the propagator

random matrix analysis of human eeg data we use random matrix theory to demonstrate the existence of generic and subject independent features of the ensemble of correlation matrices extracted from human eeg data in particular the spectral density as well as the level spacings was analyzed and shown to be generic and subject independent we also investigate number variance distributions in this case we show that when the measured subject is visually stimulated the number variance displays deviations from the random matrix prediction

space time numerical simulation and validation of analytical predictions for nonlinear forced dynamics of suspended cables abstract this paper presents space time numerical simulation and validation of analytical predictions for the finite amplitude forced dynamics of suspended cables the main goal is to complement analytical and numerical solutions accomplishing overall quantitative qualitative comparisons of nonlinear response characteristics by relying on an approximate kinematically non condensed planar modeling a simply supported horizontal cable subject to a primary external resonance and a 1 1 or 1 1 vs 2 1 internal resonance is analyzed to obtain analytical solution a second order multiple scales approach is applied to a complete eigenfunction based series of nonlinear ordinary differential equations of cable damped forced motion accounting for both quadratic cubic geometric nonlinearities and multiple modal contributions local scenarios of cable uncoupled coupled responses and associated stability are predicted based on chosen reduced order models as a cross checking tool numerical simulation of the associated nonlinear partial differential equations describing the dynamics of the actual infinite dimensional system is carried out using a finite difference technique employing a hybrid explicit implicit integration scheme based on system control parameters and initial conditions cable amplitude displacement and tension responses are numerically assessed thoroughly validating the analytically predicted solutions as regards the actual existence the meaningful role and the predominating internal resonance of coexisting competing dynamics some methodological aspects are noticed along with a discussion on the kinematically approximate versus exact as well as planar versus non planar cable modeling

localization transition on complex networks via spectral statistics the spectral statistics of complex networks are numerically studied the features of the anderson metal insulator transition are found to be similar for a wide range of different networks a metal insulator transition as a function of the disorder can be observed for different classes of complex networks for which the average connectivity is small the critical index of the transition corresponds to the mean field expectation when the connectivity is higher the amount of disorder needed to reach a certain degree of localization is proportional to the average connectivity though a precise transition cannot be identified the absence of a clear transition at high connectivity is probably due to the very compact structure of the highly connected networks resulting in a small diameter even for a large number of sites

description of chaos order transition with random matrices within the maximum entropy principle the deformed gaussian orthogonal ensemble introduced earlier is developed here for large dimensional matrices both the spacing and eigenvector distributions are studied and compared to other ones suggested for the chaos order transition problem the concept of a universal lower entropy with respect to the gaussian orthogonal ensemble entropy is proved very useful

multiple internal resonances and non planar dynamics of shallow suspended cables to the harmonic excitations abstract in the present study the nonlinear response of a shallow suspended cable with multiple internal resonances to the primary resonance excitation is investigated the method of multiple scales is applied directly to the nonlinear equations of motion and associated boundary conditions to obtain the modulation equations and approximate solutions of the cable frequency response curves and force response curves are used to study the equilibrium solution and its stability the effects of the excitation amplitude on the frequency response curves of the cable are also analyzed moreover the chaotic dynamics of the shallow suspended cable is investigated by means of numerical simulations

non linear responses of suspended cables to primary resonance excitations we investigate the non linear forced responses of shallow suspended cables we consider the following cases 1 primary resonance of a single in plane mode and 2 primary resonance of a single out of plane mode in both cases we assume that the excited mode is not involved in an autoparametric resonance with any other mode we analyze the system by following two approaches in the first we discretize the equations of motion using the galerkin procedure and then apply the method of multiple scales to the resulting system of non linear ordinary differential equations to obtain approximate solutions discretization approach in the second we apply the method of multiple scales directly to the non linear integral partial differential equations of motion and associated boundary conditions to determine approximate solutions direct approach we then compare results obtained with both approaches and discuss the influence of the number of modes retained in the discretization procedure on the predicted solutions

boundary control wave field continuation and inverse problems for the wave equation abstract we consider the problem of the wave field continuation and recovering of coefficients for the wave equation in a bounded domain in r n n 1 the inverse data is a response operator mapping neumann boundary data into dirichlet ones the reconstruction procedure is local this means that observing boundary response for larger times we may recover coefficients deeper in the domain the approach is based upon ideas and results of the boundary control theory yielding some natural multidimensional analogs of the classical gel fand levitan krein equations

an optimization approach to a three dimensional acoustic inverse problem in the time domain an optimization approach to a three dimensional acoustic inverse problem is considered in the time domain the velocity and the density are reconstructed by minimizing an objective functional by introducing a dual function the gradient of the objective functional is found with an explicit expression the parameters are then reconstructed by an iterative algorithm the conjugate gradient method the uniqueness of the solution is also proved

a formulation for higher dimensional inverse problems for the wave equation abstract two particular inverse scattering problems are of special interest the first concerns the discovery of a perturbation in the speed of sound by analyzing the return signal from a blast wave set off above it the second concerns the determination of a potential from the back scattering of plane waves in one dimensional problems the two cases are very closely related in higher dimensions the situation becomes much more complicated we present here a new approach to four such classical higher dimensional inverse problems for determining the coefficients of a partial differential equation including the two mentioned the idea stems from the work of deift and trubowitz 1 in one space dimension no conclusive theorem is found but the approach provides an algorithm for iteration which might lead to an existence theorem and which will be explored numerically elsewhere

layer stripping solutions of multidimensional inverse scattering problems a layer stripping procedure for solving three dimensional schrodinger equation inverse scattering problems is developed this method operates by recursively reconstructing the potential from the jump in the scattered field at the wave front and then using the reconstructed potential to propagate the wave front and the scattered field further into the inhomogeneous region it is thus a generalization of algorithms that have been developed for one dimensional inverse scattering problems although the procedure has not yet been numerically tested the corresponding one dimensional algorithms have performed well on synthetic data the procedure is applied to a two dimensional inverse seismic problem connections between simplifications of this method and born approximation inverse scattering methods are also noted

identification of small amplitude perturbations in the electromagnetic parameters from partial dynamic boundary measurements we consider the inverse problem of reconstructing small amplitude perturbations in the conductivity for the wave equation from partial on part of the boundary dynamic boundary measurements through construction of appropriate test functions by a geometrical control method we provide a rigorous derivation of the inverse fourier transform of the perturbations in the conductivity as the leading order of an appropriate averaging of the partial dynamic boundary perturbations this asymptotic formula is generalized to the full time dependent maxwell s equations our formulae may be expected to lead to very effective computational identification algorithms aimed at determining electromagnetic parameters of an object based on partial dynamic boundary measurements

spectral analysis of deformed random networks we study spectral behavior of sparsely connected random networks under the random matrix framework subnetworks without any connection among them form a network having perfect community structure as connections among the subnetworks are introduced the spacing distribution shows a transition from the poisson statistics to the gaussian orthogonal ensemble statistics of random matrix theory the eigenvalue density distribution shows a transition to the wigner s semicircular behavior for a completely deformed network the range for which spectral rigidity measured by the dyson mehta ensuremath delta 3 statistics follows the gaussian orthogonal ensemble statistics depends upon the deformation of the network from the perfect community structure the spacing distribution is particularly useful to track very slight deformations of the network from a perfect community structure whereas the density distribution and the ensuremath delta 3 statistics remain identical to the undeformed network on the other hand the ensuremath delta 3 statistics is useful for the larger deformation strengths finally we analyze the spectrum of a protein protein interaction network for helicobacter and compare the spectral behavior with those of the model networks

universality in complex networks random matrix analysis we apply random matrix theory to complex networks we show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks namely scale free small world and random networks follow universal gaussian orthogonal ensemble statistics of random matrix theory second we show an analogy between the onset of small world behavior quantified by the structural properties of networks and the transition from poisson to gaussian orthogonal ensemble statistics quantified by brody parameter characterizing a spectral property we also present our analysis for a protein protein interaction network in budding yeast

on the spectrum of the normalized graph laplacian we investigate how the spectrum of the normalized geometric graph laplacian is affected by operations like motif dougling graph splitting or joining the multiplicity of the eigenvalue 1 or equivalently the dimension of the kernel of the adjacency matrix of the graph is of particular interest this multiplicity can be increased for instance by motif doubling

community detection as an inference problem we express community detection as an inference problem of determining the most likely arrangement of communities we then apply belief propagation and mean field theory to this problem and show that this leads to fast accurate algorithms for community detection

an inverse boundary problem for the schrodinger operator with magnetic field the problem under consideration in this article is the inverse boundary spectral problem for the schrodinger operator with magnetic field the operator is considered on a compact riemannian manifold with nonzero boundary so that the corresponding unperturbed operator is the laplace beltrami operator on the manifold it is shown that boundary spectral data determine the potential and the boundary impedance uniquely while the magnetic field may be found to within the group of gauge transformations

statistics of atmospheric correlations for a large class of quantum systems the statistical properties of their spectrum show remarkable agreement with random matrix predictions recent advances show that the scope of random matrix theory is much wider in this work we show that the random matrix approach can be beneficially applied to a completely different classical domain namely to the empirical correlation matrices obtained from the analysis of the basic atmospheric parameters that characterize the state of atmosphere we show that the spectrum of atmospheric correlation matrices satisfy the random matrix prescription in particular the eigenmodes of the atmospheric empirical correlation matrices that have physical significance are marked by deviations from the eigenvector distribution

solving of the coefficient inverse problem for a nonlinear singularly perturbed two dimensional reaction diffusion equation with the location of moving front data abstract asymptotic numerical approach to solving the coefficient inverse problem for a nonlinear singularly perturbed two dimensional reaction diffusion equation by knowing the location of moving front data is proposed asymptotic analysis of the direct problem allows to reduce the original two dimensional parabolic problem to a series of more simple equations with lower dimension for the determination of moving front parameters it enables to associate the observed location of the moving front to the parameters which have to be identified numerical examples show the effectiveness of the proposed method

property c and an inverse problem for a hyperbolic equation let utt u q x t u 0 in d 0 t where d r3 is a bounded domain with a smooth boundary d t d d diam d q x t c 0 t l d suppose that for every u d f x t c1 d 0 t the value un d h s t is known where n is the outer normal to d u solves and and satisfies the initial conditions u ut 0 at t 0 then q x t is uniquely determined by the data f h f c1 d 0 t in the subset s of d 0 t consisting of the lines which make 45 with the t axis and which meet the planes t 0 and t t outside d 0 t provided that q x t is known outside s here d is the closure of d

an inverse initial boundary value problem for the wave equation in the presence of imperfections of small volume we consider for the wave equation the inverse problem of identifying locations and certain properties of the shapes of small conductivity inhomogeneities in a homogeneous background medium from dynamic boundary measurements on part of the boundary and for a finite interval in time using as weights particular background solutions constructed by a geometrical control method we develop an asymptotic method based on appropriate averaging of the partial dynamic boundary measurements our approach is expected to lead to very effective computational identification algorithms

superstatistical generalizations of wishart laguerre ensembles of random matrices using beck and cohen s superstatistics we introduce in a systematic way a family of generalised wishart laguerre ensembles of random matrices with dyson index 1 2 and 4 the entries of the data matrix are gaussian random variables whose variancesfluctuate from one sample to another according to a certain probability density f and a single deformation parameter three superstatistical classes for f are usually considered 2 inverse 2 and log normal distributions while the first class already considered by two of the authors leads to a power law decay of the spectral density we here introduce and solve exactly a superposition of wishart laguerre ensembles with inverse 2 distribution the corresponding macroscopic spectral density is given by a deformation of the semi circle and marcenko pastur laws on a non compact support with exponential tails after discussing in detail the validity of wigner s surmise in the wishart laguerre class we introduce a generalised dependent surmise with stretched exponential tails which well approximates the individual level spacing distribution in the bulk the analytical results are in excellent agreement with numerical simulations to illustrate our findings we compare the 2 and inverse 2 class to empirical data from financial covariance matrices

unfolding of the spectrum for chaotic and mixed systems abstract random matrix theory rmt is capable of making predictions for the spectral fluctuations of a physical system only after removing the influence of the level density by unfolding the spectra when the level density is known unfolding is done by using the integrated level density to transform the eigenvalues into dimensionless variables with unit mean spacing when it is not known as in most practical cases one usually approximates the level staircase function by a polynomial we here study the effect of unfolding procedure on the spectral fluctuation of two systems for which the level density is known asymptotically the first is a time reversal invariant chaotic system which is modeled in rmt by a gaussian orthogonal ensemble goe the second is the case of chaotic systems in which m quantum numbers remain almost undistorted in the early stage of the stochastic transition the hamiltonian of a system may be represented by a block diagonal matrix with m blocks of the same size in which each block is a goe unfolding is done once by using the asymptotic level densities for the eigenvalues of the m blocks and once by representing the integrated level density in terms of polynomials of different orders we find that the spacing distribution of the eigenvalues shows a little sensitivity to the unfolding method on the other hand the variance of level number 2 l is sensitive to the choice of the unfolding function unfolding that utilizes low order polynomials enhances 2 l relative to the theoretical value while the use of high order polynomial reduces it the optimal value of the order of the unfolding polynomial depends on the dimension of the corresponding ensemble

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