the dynamics of repeated impacts with a sinusoidally vibrating table a deceptively simple difference equation is derived which approximately describes the motion of a small ball bouncing vertically on a massive sinusoidally vibrating plate in the case of perfect elastic impacts the equation reduces to the standard mapping which has been extensively studied by physicists in connection with the motions of particles constrained in potential wells it is shown that for sufficiently large excitation velocities and a coefficient of restitution close to one this deterministic dynamical system exhibits large families of irregular non periodic solutions in addition to the expected harmonic and subharmonic motions the physical significance of these and other chaotic motions which appear to occur frequently in non linear oscillations is discussed

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

bilinear modal representations for reduced order modeling of localized piecewise linear oscillators abstract a novel reduced order modeling method for vibration problems of elastic structures with localized piecewise linearity is proposed the focus is placed upon solving nonlinear forced response problems of elastic media with contact nonlinearity such as cracked structures and delaminated plates the modeling framework is based on observations of the proper orthogonal modes computed from nonlinear forced responses and their approximation by a truncated set of linear normal modes with special boundary conditions first it is shown that a set of proper orthogonal modes can form a good basis for constructing a reduced order model that can well capture the nonlinear normal modes next it is shown that the subspace spanned by the set of dominant proper orthogonal modes can be well approximated by a slightly larger set of linear normal modes with special boundary conditions these linear modes are referred to as bi linear modes and are selected by an elaborate methodology which utilizes certain similarities between the bi linear modes and approximations for the dominant proper orthogonal modes these approximations are obtained using interpolated proper orthogonal modes of smaller dimensional models the proposed method is compared with traditional reduced order modeling methods such as component mode synthesis and its advantages are discussed forced response analyses of cracked structures and delaminated plates are provided for demonstrating the accuracy and efficiency of the proposed methodology

a generalization of the aubin lions simon compactness lemma for problems on moving domains abstract this work addresses an extension of the aubin lions simon compactness result to generalized bochner spaces l 2 0 t h t where h t is a family of hilbert spaces parameterized by t a compactness result of this type is needed in the study of the existence of weak solutions to nonlinear evolution problems governed by partial differential equations defined on moving domains we identify the conditions on the regularity of the domain motion in time under which our extension of the aubin lions simon compactness result holds concrete examples of the application of the compactness theorem are presented including a classical problem for the incompressible navier stokes equations defined on a given non cylindrical domain and a class of fluid structure interaction problems for the incompressible navier stokes equations coupled to the elastodynamics of a koiter shell the compactness result presented in this manuscript is crucial in obtaining constructive existence proofs to nonlinear moving boundary problems using rothe s method

an iterated maps approach for dynamic ratchetting in sdof hysteretic damping systems dynamic ratchetting is a phenomenon in which plastic deformation increases in successive cycles in the present paper first various characteristics of dynamic ratchetting are demonstrated based on numerical simulation second iterated maps are developed as a tool for the investigation of dynamic ratchetting in a single degree of freedom sdof system when an elasto perfectly plastic model is employed to represent hysteretic damping a piecewise linear solution can be obtained and used to develop iterated maps a stability investigation in the iterated maps shows that dynamic ratchetting is developed under a stable cycling in this stable cycling dynamic ratchetting occurs when an excitation function loses antiperiodicity shift symmetry

the hilbert phenomenon in chaotic motions abstract it is proved that chaotic dynamical systems have d 1 singularity due to such singularity and its periodicity in hausdorff metric spaces a chaotic dynamical system induces a hilbert iterated system which was discovered at the end of the 19th century this implies that the most puzzling discovery in nature in the 20th century can be put into deep correspondence with that in thoughts in the 19th century all this is verified by the numerical experiments of chaotic vibrations of a beam and a tension slack oscillator

stability and nonlinear dynamics of a vibration system with oblique collisions abstract two moving rigid bodies can contact with each other as the clearance between them is exceeded supposing that the contacting areas are two parallel planes with an oblique angle to the moving direction periodic responses of the system with oblique collision are determined by applying poincare mapping impulse momentum theorem and poisson s hypothesis in this paper first the relations of the body velocities before and after collisions are derived upon an instantaneous collision hypothesis then the existence condition and the stability criterion of the period n motion with single collision are deduced by using the poincare mapping and the floquet theory last numerical simulations are carried out and bifurcation diagrams poincare maps and phase portraits are adopted to prove the stability analysis and illustrate rich dynamical behaviors of the system over a rather broad range of frequency of the external excitation transitions from the single collision period n motion to chaotic one through three ways period doubling bifurcation hopf bifurcation and abruptly transition are revealed

a periodically forced piecewise linear oscillator a single degree of freedom non linear oscillator is considered the non linearity is in the restoring force and is piecewise linear with a single change in slope such oscillators provide models for mechanical systems in which components make intermittent contact a limiting case in which one slope approaches infinity an impact oscillator is also considered harmonic subharmonic and chaotic motions are found to exist and the bifurcations leading to them are analyzed

dynamics and bifurcations of nonsmooth systems a survey abstract in this survey we discuss current directions of research in the dynamics of nonsmooth systems with emphasis on bifurcation theory an introduction to the state of the art also for non specialists is complemented by a presentation of the main open problems we illustrate the theory by means of elementary examples the main focus is on piecewise smooth systems which have recently attracted a lot of attention but we also briefly discuss other important classes of nonsmooth systems such as nowhere differentiable ones and differential variational inequalities this extended framework allows us to put the diverse range of papers and surveys in this special issue in a common context a dedicated section is devoted to concrete applications that stimulate the development of the field this survey is concluded by an extensive bibliography

on the roughness induced effective boundary conditions for an incompressible viscous flow abstract we consider the laminar viscous channel flow with the lateral surface of the channel containing surface irregularities it is supposed that a uniform pressure gradient is maintained in the longitudinal direction of the channel after studying the corresponding boundary layers we obtain rigorously the navier friction condition it is valid when the size and amplitude of the imperfections tend to zero furthermore the coefficient in the law is determined through an auxiliary boundary layer type problem and the tangential drag force and the effective mass flow are determined up to order o e3 2 the value of the effective coefficient is shown to be independent with respect to the position of the mean surface in the range of o e

the corresponding phenomena of mechanical and electronic impact oscillator a mechanical impact oscillator and a diode rectifier circuit of an impact oscillator are presented time series and phase portrait analysis are performed for both oscillators the results show that the proposed electronic impact oscillator is in agreement with the mechanical impact oscillator for varying the driving frequency a fixed harmonic input force can generate a periodic or non periodic impact oscillation the phenomena of bifurcation are also observed in both impact oscillators

double impact orbits of periodically forced impact oscillators we consider a periodically forced oscillator which impacts against a rigid constraint the forcing is both sinusoidal and non sinusoidal and is made up of a combination of the first and second harmonics of a fourier series a simple restitution law is used to describe the impact this paper centres around the analysis of double impact periodic solutions that is motions which repeat after every second impact solutions for these double impact orbits are found including non physical orbits and unstable orbits behaviour typical of nonlinear dynamical systems such as period doubling bifurcations are detected and grazing bifurcations which are unique to discontinuous dynamical systems are also observed a combination of analytical and numerical techniques are used to uncover the behaviour of the system at odd multiples of the natural frequency where numerical experiments tell us that stable double impact periodic solutions exist the persistence of these stable double impact orbits are also examined as parameters are varied we conclude by presenting some numerical calculations of two more general cases of impacting systems

type i periodic motions for nonlinear impact oscillators abstract in this paper a general class of nonlinear impact oscillators is considered for subharmonic bifurcation this system can be used to model an inverted pendulum impacting on rigid walls under external periodic excitation and its unperturbed system possesses a pair of homoclinic cycles via the identification given by the impact law and three separate families of periodic orbits inside and outside the homoclinic cycles by discussing the subharmonic orbits inside the homoclinic cycles the subharmonic melnikov method established for smooth dynamical systems is extended to be applicable to the non smooth system

low dimensional maps for piecewise smooth oscillators abstract dynamics of the piecewise smooth nonlinear oscillators is considered for which general methodology of reducing multidimensional flows to low dimensional maps is proposed this includes a definition of piecewise smooth oscillator and creation of a global iterative map providing an exact solution the global map is comprised of local maps which are constructed in the smooth sub regions of phase space to construct this low dimensional map it is proposed to monitor the points of intersections of a chosen boundary between smooth subspaces by a trajectory the dimension reduction is directly related to the dimension of the chosen boundary and the lower its dimension is the larger dimension reduction can be achieved full details are given for a drifting impact oscillator where the five dimensional flow is reduced to one dimensional 1d approximate analytical map first an exact two dimensional map has been formulated and analysed a further reduction to 1d approximate map is introduced and discussed standard nonlinear dynamic analysis reveals a complex behaviour ranging from periodic oscillations to chaos and co existence of multiple attractors accuracy of the constructed maps is examined by comparing with the exact solutions for a wide range of the system parameters

global weak solutions for the two dimensional motion of several rigid bodies in an incompressible viscous fluid we consider the two dimensional motion of several non homogeneous rigid bodies immersed in an incompressible non homogeneous viscous fluid the fluid and the rigid bodies are contained in a fixed open bounded set of r 2 the motion of the fluid is governed by the navier stokes equations for incompressible fluids and the standard conservation laws of linear and angular momentum rule the dynamics of the rigid bodies the time variation of the fluid domain due to the motion of the rigid bodies is not known a priori so we deal with a free boundary value problem the main novelty here is the demonstration of the global existence of weak solutions for this problem more precisely the global character of the solutions we obtain is due to the fact that we do not need any assumption concerning the lack of collisions between several rigid bodies or between a rigid body and the boundary we give estimates of the velocity of the bodies when their mutual distance or the distance to the boundary tends to zero

grazing bifurcations in an elastic structure excited by harmonic impactor motions abstract in this article non smooth dynamics of an elastic structure excited by a harmonic impactor motion is studied through a combination of experimental numerical and analytical efforts the test apparatus consists of a stainless steel cantilever structure with a tip mass that is impacted by a shaker soft impact between the impactor and the structure is considered and bifurcations with respect to quasi static variation of the shaker excitation frequency are examined in the experiments qualitative changes that can be associated with grazing and corner collision bifurcations are observed aperiodic motions are also observed in the vicinity of the non smooth bifurcation points assuming the system response to be dominated by the structure s fundamental mode a non autonomous single degree of freedom model is developed and used for local analysis and numerical simulations the predicted grazing and corner collision bifurcations are in agreement with the experimental results to study the local bifurcation behavior at the corner collision point and explore the mechanism responsible for the aperiodic motions a derivation is carried out to construct local poincare maps of periodic orbits at a corner collision point such as the one observed in the soft impact oscillator

performance analysis of orthogonal space time block codes over time selective channels and applications to code design of gi systems many existing works on space time block codes stbc assume the channels are block wise constant but this assumption does not always hold in the more general case of time selective channels the channel matrix is no longer orthogonal so inter symbol interference esi is generated and the performance is greatly reduced several decoders have been proposed to eliminate the esi but it remains unclear how and to what extent the performance is affected by the isi in this paper we introduce an approach to analyze the performance of stbc over time selective channels with arbitrary numbers of antennas for which orthogonal stbc s are defined exact error performances are obtained in closed form furthermore the analysis reveals the relationship between the isi and the structure of stbc matrices considering g i systems we then propose one proposition and two design criteria following which it is easy to design or search for better stbc s that have less isi compared with the original code matrix

melnikov method for homoclinic bifurcation in nonlinear impact oscillators based on an inverted pendulum impacting on rigid walls under external periodic excitation a class of nonlinear impact oscillators is discussed for its homoclinic bifurcation the melnikov method established for smooth dynamical systems is extended to be applicable to the nonsmooth one for nonlinear impact systems closed form solutions between impacts are generally unavailable the absence of closed form solutions makes difficulties in estimation of the gap between the stable manifold and unstable manifold in this paper we give a method to compute the melnikov functions up to the n t h order so as to obtain conditions of parameters for the persistence of homoclinic cycles which are formed via the identification given by the impact rule

orthogonal space time block code over time varying flat fading channels channel estimation detection and performance analysis this paper studies the channel estimation detection and performance analysis of mobile wireless communication systems employing space time block codes stbc where the channels exhibit flat rayleigh fading with a significant amount of doppler spread pilot symbol assisted modulation psam is developed to estimate the channels the performance of the channel estimation is evaluated maximum likelihood ml detection is first formulated a linear detector called the symmetric linear sl detector is proposed an interference cancellation ic detector is also developed to improve the performance of the sl detector we derive the closed form analytical expressions for the bit error rate ber or symbol error rate ser of pilot sequence assisted stbc with binary phase shift keying psk quaternary psk 16 quadrature amplitude modulation qam and 64 qam when the sl and ic detectors are used some important design issues in the pilot sequence assisted stbc systems including the selection of pilot spacing and interpolator size are discussed simulation results are presented that verify our analytical results the tradeoffs between the performance and complexity for ml sl and ic detection are also discussed

analysis of a random repeated impact process a simple random repeated impact process similar to the classical random walk process is analyzed the process which consists of a ball bouncing on a randomly vibrating surface is analogous to loss of contact situations which can occur in linkages and vibrating tools it also has relevance to rolling contact where the rolling element may separate from the surface and sustain repeated impacts a coefficient of restitution is used to describe impact and some important assumptions limit the analysis to values of this coefficient greater than 0 8 the markov nature of the process is demonstrated by its one step memory it may be regarded as a discrete markov process imbedded in continuous time a difference equation governing the process is developed and analyzed for the case where the vibrating surface has a gaussian distribution of velocities with the one step transition probability density function a linear weighting function is used to account for the weighting effect of the ball s velocity on the distribution of table velocities at impact the resulting integral equation is solved iteratively to yield the probability density function of ball velocities after impact this information may then be used to predict the magnitudes of the impacts and the time between them

the mapping dynamics of periodic motions for a three piecewise linear system under a periodic excitation in this paper the mapping dynamics of periodic motions for a three piecewise linear system under a periodic excitation is developed and the mapping structures for specified periodic motions are constructed based on the mapping structures an analytical prediction of all possible stable and unstable periodic motions is given the symmetry for the stable asymmetrical periodic motions of such a system is observed however the unstable periodic motions do not have such symmetry the methodology presented in this paper is applicable to other non smooth systems such as friction induced vibration impact oscillator and power control systems in addition the mapping dynamics provides a useful and efficient tool for the co existence of periodic motions and or chaotic motions in nonlinear dynamical systems

bifurcation analysis of an impact oscillator with a one sided elastic constraint near grazing in this paper a linear oscillator undergoing impact with a secondary elastic support is studied experimentally and semi analytically for near grazing conditions the experimentally observed bifurcations are explained with help from simulations based on mapping solutions between locally smooth subspaces smooth as well as nonsmooth bifurcations are observed and the resulting atypical bifurcations are explained often as an interplay between them in order to understand the observed bifurcation scenarios a global analysis is required due to the influence of stable and unstable orbits which are born in distant bifurcations but become important at near grazing conditions the good degree of correspondence between experiment and theory fully justifies the modelling approach

boundary behavior of viscous fluids influence of wall roughness and friction driven boundary conditions we consider a family of solutions to the evolutionary navier stokes system supplemented with the complete slip boundary conditions on domains with rough boundaries we give a complete description of the asymptotic limit by means of convergence arguments and identify a general class of boundary conditions

estimation of clearances and impact forces using vibroimpact response sinusoidal excitation abstract a novel clearance estimation approach has been developed for a randomly excited vibroimpact system the clearance estimates based on this approach were obtained using data from the mechanical analogue of an impact oscillator and simulation using a digital computer and they reasonably agree with the actual clearances

asymmetric type ii periodic motions for nonlinear impact oscillators abstract in this paper a general class of nonlinear impact oscillators is considered for type ii periodic motions this system can be used to model an inverted pendulum impacting on rigid walls under external periodic excitation the unperturbed system possesses a pair of homoclinic cycles and three separate families of periodic orbits inside and outside the homoclinic cycles via the identification given by the impact law by approximating the poincare map to o e directly a general method of melnikov type for detecting the existence of asymmetric type ii subharmonic orbits outside the homoclinic cycles is presented

fluid structure interaction in blood flow capturing non zero longitudinal structure displacement we present a new model and a novel loosely coupled partitioned numerical scheme modeling fluid structure interaction fsi in blood flow allowing non zero longitudinal displacement arterial walls are modeled by a linearly viscoelastic cylindrical koiter shell model capturing both radial and longitudinal displacement fluid flow is modeled by the navier stokes equations for an incompressible viscous fluid the two are fully coupled via kinematic and dynamic coupling conditions our numerical scheme is based on a new modified lie operator splitting that decouples the fluid and structure sub problems in a way that leads to a loosely coupled scheme which is unconditionally stable this was achieved by a clever use of the kinematic coupling condition at the fluid and structure sub problems leading to an implicit coupling between the fluid and structure velocities the proposed scheme is a modification of the recently introduced kinematically coupled scheme for which the newly proposed modified lie splitting significantly increases the accuracy the performance and accuracy of the scheme were studied on a couple of instructive examples including a comparison with a monolithic scheme it was shown that the accuracy of our scheme was comparable to that of the monolithic scheme while our scheme retains all the main advantages of partitioned schemes such as modularity simple implementation and low computational costs

on the convergence of fixed point iterations for the moving geometry in a fluid structure interaction problem abstract in this paper a fluid structure interaction problem for incompressible newtonian fluids is studied we prove the convergence of an iterative process with respect to the computational domain geometry moving according to a viscoelastic deformation in our previous joint works on numerical approximation of similar problems we refer to this approach as the global iterative method 1 2 this iterative approach can be understood as a linearization of the so called geometric nonlinearity of the underlying model the proof of the convergence is based on the banach fixed point theorem where the contractivity of the corresponding mapping is shown using the continuous dependence of the weak solution on the given domain deformation this estimate is obtained by remapping the problem onto a fixed domain and using appropriate divergence free test functions involving the difference of two solutions

orthogonal space time block codes maximum likelihood detection for unknown channels and unstructured interferences space time coding stc schemes for communication systems employing multiple transmit and receive antennas have been attracting increased attention the so called orthogonal space time block codes ostbcs have been of particular interest due to their good performance and low decoding complexity in this paper we take a systematic maximum likelihood ml approach to the decoding of ostbc for unknown propagation channels and unknown noise and interference conditions we derive a low complexity ml decoding algorithm based on cyclic minimization and assisted by a minimum amount of training data furthermore we discuss the design of optimal training sequences and optimal information transfer to an outer decoder numerical examples demonstrate the performance of our algorithm

existence of a weak solution to the fluid structure interaction problem in 3d abstract we study a nonlinear fluid structure interaction problem in which the fluid is described by the three dimensional incompressible navier stokes equations and the elastic structure is modeled by the nonlinear plate equation which includes a generalization of kirchhoff von karman and berger plate models the fluid and the structure are fully coupled via kinematic and dynamic boundary conditions the existence of a weak solution is obtained by designing a hybrid approximation scheme that successfully deals with the nonlinearities of the system we combine time discretization and operator splitting to create two sub problems one piece wise stationary for the fluid and one in the galerkin basis for the plate to guarantee the convergence of approximate solutions to a weak solution a sufficient condition is given on the number of time discretization sub intervals in every step in a form of dependence with number of the galerkin basis functions and nonlinearity order of the plate equation

regularity issues in the problem of fluid structure interaction we investigate the evolution of rigid bodies in a viscous incompressible fluid the flow is governed by the 2d navier stokes equations set in a bounded domain with dirichlet boundary conditions the boundaries of the solids and the domain have holder regularity c1 0 1 first we show the existence and uniqueness of strong solutions up to the collision a key ingredient is a bmo bound on the velocity gradient which substitutes to the standard h2 estimate for smoother domains then we study the asymptotic behaviour of one c1 body falling over a flat surface we show that a collision is possible in finite time if and only if 1 2

existence of weak solutions up to collision for viscous fluid solid systems with slip we study in this paper the movement of a rigid solid inside an incompressible navier stokes flow within a bounded domain we consider the case where slip is allowed at the fluid solid interface through a navier condition taking into account slip at the interface is very natural within this model as classical no slip conditions lead to unrealistic collisional behavior between the solid and the domain boundary we prove for this model existence of weak solutions of leray type up to collision in three dimensions the key point is that due to the slip condition the velocity field is discontinuous across the fluid solid interface this prevents from obtaining global h1 bounds on the velocity which makes many aspects of the theory of weak solutions for dirichlet conditions unadapted

motion of an elastic solid inside an incompressible viscous fluid the motion of an elastic solid inside an incompressible viscous fluid is ubiquitous in nature mathematically such motion is described by a pde system that couples the parabolic and hyperbolic phases the latter inducing a loss of regularity which has left the basic question of existence open until now in this paper we prove the existence and uniqueness of such motions locally in time when the elastic solid is the linear kirchhoff elastic material the solution is found using a topological fixed point theorem that requires the analysis of a linear problem consisting of the coupling between the time dependent navier stokes equations set in lagrangian variables and the linear equations of elastodynamics for which we prove the existence of a unique weak solution we then establish the regularity of the weak solution this regularity is obtained in function spaces that scale in a hyperbolic fashion in both the fluid and solid phases our functional framework is optimal and provides the a priori estimates necessary for us to employ our fixed point procedure

forced vibrations of a beam with one sided amplitude constraint theory and experiment abstract an elastic beam with one sided amplitude constraint subjected to periodic excitation is considered experimental results are obtained and compared with results given by a theoretical model based on a single mode analysis of the beam following the work of moon and shaw 1 this model has been studied in some detail by the author in previous works 2 4 it is a single degree of freedom oscillator with periodic excitation and a piecewise linear restoring force this single mode model is shown to provide good overall qualitative information about the actual physical system it predicts the multiple subharmonic resonances period doublings and some chaotic regimes found experimentally

frequency response characteristics of a multi degree of freedom system with clearances abstract in an earlier study the frequency response characteristics of a single degree of freedom system with a clearance non linearity were studied the current study an extension of the earlier work is concerned with the frequency response characteristics of a multi degree of freedom system with clearances the method of harmonic balance is used to develop approximate analytical solutions of the undamped equations of motion of a multi degree of freedom system composed of three coupled non linear oscillators for primary resonances and a harmonic excitation general formulations are presented which can be used to study both the existence and the stability of the solutions these general formulations are used to discuss a number of modal spacing and modal coupling issues an analysis methodology for multi degree of freedom systems is introduced and illustrated by two special but practical cases a strongly non linear system and a weakly non linear system the results of the analysis of the special cases are validated by using analog simulation it is shown that an analysis of the special cases of the general multi degree of freedom non linear formulation can provide not only an improved understanding of the dynamic behavior of non linear systems but also can be used as the basis for the development of simplified approximate solutions the limitations of the current study and areas for further research are discussed

error rates for rayleigh fading multichannel reception of mpsk signals this paper provides a new closed form expression for calculating the probability that an mpsk signal will lie in a particular decision region when received over n independent and identically distributed rayleigh fading channels corrupted by additive white gaussian noise this expression is applied to provide a unified method to derive the exact symbol error rate and bit error rate for mpsk signals considering n channel diversity reception the n channel diversity reception techniques considered are maximal ratio combining mrc and selection combining mrc with identical channels and dissimilar channels is considered the results for mrc can be extended to provide an approximation for the error rates of mpsk under equal gain combining

simulation models with correct statistical properties for rayleigh fading channels in this paper new sum of sinusoids statistical simulation models are proposed for rayleigh fading channels these new models employ random path gain random initial phase and conditional random doppler frequency for all individual sinusoids it is shown that the autocorrelations and cross correlations of the quadrature components and the autocorrelation of the complex envelope of the new simulators match the desired ones exactly even if the number of sinusoids is as small as a single digit integer moreover the probability density functions of the envelope and phase the level crossing rate the average fade duration and the autocorrelation of the squared fading envelope which contains fourth order statistics of the new simulators asymptotically approach the correct ones as the number of sinusoids approaches infinity while good convergence is achieved even when the number of sinusoids is as small as eight the new simulators can be directly used to generate multiple uncorrelated fading waveforms for frequency selective fading channels multiple input multiple output channels and diversity combining scenarios statistical properties of one of the new simulators are evaluated by numerical results finding good agreements

numerical scheme of locating the periodic response of non smooth non autonomous systems of high dimension abstract the paper presents a numerical scheme of locating the periodic response of high dimensional systems with non smooth characters such as clearances constraints frictions the basic idea comes from the fact that an asymptotic stable periodic response of the system attracts its transient response and it may be extracted from the transient response somehow the paper thus suggests a novel iteration scheme to extrapolate the periodic response from a short time history of the transient response by curve fitting compared with the current schemes such as shooting incremental harmonic balancing and their improved forms the present scheme makes full use of the information within the transient response and the system characters so that the computational efficiency has increased by an order and the numerical convergence depending on the initial iteration has greatly improved

global dynamics of a vibro impacting linear oscillator abstract the steady state vibro impacting responses of one dimensional harmonically excited linear oscillators are studied by using a modern dynamical systems approach allied with numerical simulation the steady state motions are attracting sets in the system phase space and capture initial conditions in their domains of attraction unlike the free harmonically excited oscillator the phase space of a vibro impacting system may be inhabited by many attracting sets for example there are sub harmonic multi impact periodic orbits and chaotic steady state responses in order to build a qualitative understanding of vibro impact response an attempt is made to build generic topological models of their phase spaces for physically significant parameter ranges use is made of the poincare section or stroboscopic mapping technique essentially following an initial impact forwards or backwards in time to subsequent or previous impacts using a computer the qualitative understanding gained from the analysis and simulations is discussed in an engineering context

relevance of the slip condition for fluid flows near an irregular boundary we consider the navier stokes equation in a domain with a rough boundary the roughness is modeled by a small amplitude and small wavelength oscillation with typical scale varepsilon ll 1 for periodic oscillation it is well known that the best homogenized that is regular in varepsilon boundary condition is of navier type such result still holds for random stationary irregularities as shown recently by the first author 5 15 we study here arbitrary irregularity patterns

stability and dynamics of a harmonically excited elastic perfectly plastic oscillator this paper deals with the stability and the dynamics of a harmonically excited elastic perfectly plastic oscillator the hysteretical system is written as a non smooth forced autonomous system it is shown that the dimension of the phase space can be reduced using adapted variables free vibrations of such a system are then considered for the damped system the extended direct method of liapounov is applied to this non smooth mechanical system and the asymptotic stability of the origin is proven in the new phase space the forced vibration of such an oscillator is treated by numerical approach by using the time locating techniques the stability of the limit cycles is analytically investigated with a perturbation approach the boundary between elastoplastic shakedown and alternating plasticity is given in closed form it is shown that this boundary corresponds to a bifurcation boundary for the undamped system period doubling bifurcation finally the equivalent damping of this hysteretic system is characterized from dynamical properties

stability and bifurcation analysis for oscillators with motion limiting constraints abstract the stability and bifurcation analysis is presented for a class of non linear single degree of freedom vibrating systems excited by harmonic forcing the common characteristic of these systems is that their damping and stiffness parameters can change abruptly at certain displacement values the most general n periodic steady state solutions with an arbitrary number of contacts per response cycle are analyzed it is shown that when the damping is positive the change of stability of the steady state response cannot happen through a hopf bifurcation

existence of a weak solution to a fluid elastic structure interaction problem with the navier slip boundary condition abstract we study a nonlinear moving boundary fluid structure interaction fsi problem between an incompressible viscous newtonian fluid modeled by the 2d navier stokes equations and an elastic structure modeled by the shell or plate equations the fluid and structure are coupled via the navier slip boundary condition and balance of contact forces at the fluid structure interface the slip boundary condition might be more realistic than the classical no slip boundary condition in situations e g when the structure is rough and in modeling fsi dynamics near or at a contact cardiovascular tissue and cell seeded tissue constructs which consist of grooves in tissue scaffolds that are lined with cells are examples of rough elastic interfaces interacting with an incompressible viscous fluid the problem of heart valve closure is an example of a fsi problem with a contact involving elastic interfaces we prove the existence of a weak solution to this class of problems by designing a constructive proof based on the time discretization via operator splitting this is the first existence result for fluid structure interaction problems involving elastic structures satisfying the navier slip boundary condition

non periodic motion caused by grazing incidence in an impact oscillator the motion of a single degree of freedom periodically forced oscillator subjected to a rigid amplitude constraint is considered using analytical methods the singularities caused by grazing impact are studied it is shown that as a stable periodic orbit comes to grazing impact under the control of a single parameter a special type of bifurcation occurs the motion after the bifurcation may be non periodic and a criterion for this based on orientation and eigenvalues is given

experimental bifurcation analysis of an impact oscillator tuning a non invasive control scheme abstract we investigate a non invasive locally stabilizing control scheme necessary for an experimental bifurcation analysis our test rig comprises a harmonically forced impact oscillator with hardening spring nonlinearity controlled by electromagnetic actuators and serves as a prototype for electromagnetic bearings and other machinery with build in actuators we propose a sequence of experiments that allows one to choose optimal control gains filter parameters and settings for a continuation method without a priori study of a model depending on the algorithm for estimating the jacobian required by newton s method we find two almost disjoint sets of suitable control parameters control based continuation succeeds reliably in producing the full bifurcation diagram including both stable and unstable equilibrium states for an appropriately tuned controller

application of non smooth modelling techniques to the dynamics of a flexible impacting beam non smooth modelling techniques have been successfully applied to lumped mass type structures for modelling phenomena such as vibro impact and friction oscillators in this paper the application of these techniques to continuous elements using the example of a cantilever beam is considered employing a galerkin reduction to form an n degree of freedom modal model a technique for modelling impact phenomena using a non smooth dynamics approach is demonstrated numerical simulations computed using the non smooth model are compared with experimentally recorded data for a flexible beam constrained to impact on one side a method for dealing with sticking motions when numerically simulating the beam motion is presented in addition choosing the dimension of the model based on power spectra of experimentally recorded time series is discussed

kinematic splitting algorithm for fluid structure interaction in hemodynamics abstract in this paper we study a kinematic splitting algorithm for fluid structure interaction problems this algorithm belongs to the class of loosely coupled fluid structure interaction schemes we will present stability analysis for a coupled problem of non newtonian shear dependent fluids in moving domains with viscoelastic boundaries fluid flow is described by the conservation laws with nonlinearities in convective and diffusive terms for simplicity of presentation the structure is modelled by the generalized string equation but the results presented in the paper may be generalized to more complex structure models the arbitrary lagrangian eulerian approach is used in order to take into account moving computational domain numerical experiments including numerical error analysis and comparison of hemodynamic parameters for newtonian and non newtonian fluids demonstrate reliability of the proposed scheme

optimal design and placement of pilot symbols for channel estimation the problem of designing and placing pilot symbols for the estimation of frequency selective random channels is considered the channel is assumed to be a block fading model with finite impulse response fir for both single input single output siso and multiple input multiple output mimo channels under the assumption of independent and identical distributed channel taps the cramer rao bound crb on the mean square error mse of semi blind channel estimators is derived and minimized with respect to pilot symbols and their placement it is shown that the optimal strategy is to place pilot symbols satisfying certain orthogonality condition in such a way that data and pilot symbols with higher power are in the middle of the packet the results also indicate that the optimal pilot placements are independent of channel probability distribution for constant modulus symbols we show that the quasi periodic placement and its generalization in the multiuser case turn out to be optimal we further consider estimating channels with correlated taps and show that the previous placement strategy is also optimal among orthogonal pilot sequences

torus doubling bifurcations and strange nonchaotic attractors in a vibro impact system whether strange nonchaotic attractors snas can occur typically in dynamical systems other than quasiperiodically driven systems has been an open problem here we show that the snas can be induced by the interruption of torus doubling bifurcation in a periodically driven vibro impact system it is found that the creation of snas occurs due to the collision of doubled torus with some unstable periodic orbits based on the poincare map technique two types of codimension 3 bifurcations are represented and typical torus doubling bifurcations can occur in the neighborhood of these bifurcation points we use the singular continuous fourier spectrum and its scaling to verify the strangeness nondifferentiability of the attractors the implicitly transcendental map is used to calculate the largest lyapunov exponent by qr based algorithm which ensures that the underlying dynamics with nonpositive lyapunov exponents is nonchaotic the associated mechanism is described for the creation of snas through detecting unstable periodic orbits from poincare map series

on well posedness for a free boundary fluid structure model we address a fluid structure interaction model describing the motion of an elastic body immersed in an incompressible fluid we establish a priori estimates for the local existence of solutions for a class of initial data which also guarantees uniqueness

continuous and discontinuous grazing bifurcations in impacting oscillators this paper seeks to formulate conditions for the persistence of a local attractor in the immediate vicinity of periodic and quasiperiodic grazing trajectories in an impacting mechanical system a local analysis based on the discontinuity mapping approach is employed to derive a normal form description of the dynamics near the grazing trajectory in agreement with previous studies of grazing periodic trajectories it is found that the catastrophic loss of a local attractor and strong instability characteristic of grazing bifurcations is directly associated with the repeated application of a square root term that appears to lowest order in the normal form expansion specifically it is found that the square root term is absent in the description of the dynamics normal to a quasiperiodic trajectory covering a co dimension one invariant torus resulting in a piecewise linear description of the normal dynamics and at most a weak instability in contrast for co dimension two or higher the square root term is generically present in the normal dynamics here however the quasiperiodicity of the grazing motion implies that there is no upper limit to the time between impacts on nearby trajectories suggesting the persistence of a local attractor for some interval about the parameter value corresponding to grazing the results of the analysis are illustrated through a series of model examples

existence of a solution to a fluid multi layered structure interaction problem abstract we study a nonlinear unsteady moving boundary fluid structure interaction fsi problem in which the structure is composed of two layers a thick layer and a thin layer which serves as a fluid structure interface with mass the fluid flow which is driven by the time dependent dynamic pressure data is modeled by the navier stokes equations for an incompressible viscous fluid defined on a 2d cylinder the elastodynamics of the cylinder wall is governed by the 1d linear wave equation modeling the thin structural layer and by the 2d equations of linear elasticity modeling the thick structural layer we prove existence of a weak solution to this nonlinear fsi problem as long as the cylinder radius is greater than zero the spaces of weak solutions presented in this manuscript reveal a striking new feature the presence of a thin fluid structure interface with mass regularizes solutions of the coupled problem

stable loosely coupled type algorithm for fluid structure interaction in blood flow we introduce a novel loosely coupled type algorithm for fluid structure interaction between blood flow and thin vascular walls this algorithm successfully deals with the difficulties associated with the added mass effect which is known to be the cause of numerical instabilities in fluid structure interaction problems involving fluid and structure of comparable densities our algorithm is based on a time discretization via operator splitting which is applied in a novel way to separate the fluid sub problem from the structure elastodynamics sub problem in contrast with traditional loosely coupled schemes no iterations are necessary between the fluid and structure sub problems this is due to the fact that our novel splitting strategy uses the added mass effect to stabilize rather than to destabilize the numerical algorithm this stabilizing effect is obtained by employing the kinematic lateral boundary condition to establish a tight link between the velocities of the fluid and of the structure in each sub problem the stability of the scheme is discussed on a simplified benchmark problem and we use energy arguments to show that the proposed scheme is unconditionally stable due to the crucial role played by the kinematic lateral boundary condition the proposed algorithm is named the kinematically coupled scheme

existence of a weak solution to a nonlinear fluid structure interaction problem modeling the flow of an incompressible viscous fluid in a cylinder with deformable walls we study a nonlinear unsteady moving boundary fluid structure interaction fsi problem arising in modeling blood flow through elastic and viscoelastic arteries the fluid flow which is driven by the time dependent pressure data is governed by two dimensional incompressible navier stokes equations while the elastodynamics of the cylindrical wall is modeled by the one dimensional cylindrical koiter shell model two cases are considered the linearly viscoelastic and the linearly elastic koiter shell the fluid and structure are fully coupled two way coupling via the kinematic and dynamic lateral boundary conditions describing continuity of velocity the no slip condition and the balance of contact forces at the fluid structure interface we prove the existence of weak solutions to the two fsi problems the viscoelastic and the elastic case as long as the cylinder radius is greater than zero the proof is based on a novel semi discrete operator splitting numerical scheme known as the kinematically coupled scheme introduced in guidoboni et al j comput phys 228 18 6916 6937 2009 to numerically solve the underlying fsi problems the backbone of the kinematically coupled scheme is the well known marchuk yanenko scheme also known as the lie splitting scheme we effectively prove convergence of that numerical scheme to a solution of the corresponding fsi problem

analysis of the coupled navier stokes biot problem abstract we analyze a weak formulation of the coupled problem defining the interaction between a free fluid and a poroelastic structure the problem is governed by the time dependent incompressible navier stokes equations and the biot equations under a small data assumption existence and uniqueness results are proved and a priori estimates are provided