594 research outputs found
Application of nonsmooth 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
A note on modelling multi-degree of freedom vibro-impact systems using coefficient of restitution models
In this work multi-modal systems subject to impact are considered. Using energy balance techniques for an arbitrary contact interval the effects of modal vibration can be included. The energy balance is used to obtain a relationship between the coefficient of restitution and the modal energy during the contact period. This allows the effects of impact induced vibration to be considered. The subsequent analytical relationships demonstrate that increasing contact duration and excitation of higher modes can reduce the effective value of the coefficient of restitution. It is also shown how this approach can be related to work on energetically consistent impacts
Dynamics of a two degree of freedom vibro-impact system with multiple motion limiting constraints
We consider the dynamics of impact oscillators with multiple degrees of freedom subject to more than one motion limiting constraint or stop. A mathematical formulation for modeling such systems is developed using a modal approach including a modal form of the coefficient of restitution rule. The possible impact configurations for an N degree of freedom system are considered, along with definitions of the impact map for multiply constrained systems. We consider sticking motions that occur when a single mass in the system becomes stuck to an impact stop, and discuss the computational issues related to computing such solutions. Then using the example of a two degree of freedom system with two constraints we describe exact modal solutions for the free flight and sticking motions which occur in this system. Numerical examples of sticking orbits for this system are shown and we discuss identifying the region, S in phase space where these orbits exist. We use bifurcation diagrams to indicate differing regimes of vibro-impacting motion for two different cases; firstly when the stops are both equal and on the same side (i.e. the same sign) and secondly when the stops are unequal and of opposing sign. For these two different constraint configurations we observe qualitatively different dynamical behavior, which is interpreted using impact mappings and two-dimensional parameter space
Use of control to maintain period-1 motions during wind-up or wind-down operations of an impacting driven beam
We consider the dynamical response of a thin beam held fixed at one end while excited by an external driving force. A motion limiting constraint, or stop, causes the beam to impact. During wind-up or wind-down operations, in which the driving frequency is continuously altered, the system can undergo complicated motions close to the value of frequency at which impacts may first occur, the grazing bifurcation. In this region, the beam may experience several impacts within a long period-repeating solution or even chaotic behavior which, in practical terms, may be undesirable to the long-term integrity of the system. The first task is to identify the zones in the space of parameters (forcing amplitude or, alternatively, the gap between the beam and the stop) in which period-1 motions can be guaranteed. In this paper, in the areas in which complicated or chaotic motion occurs, a control strategy is proposed which stabilises unstable period-1 motions. As a consequence, numerical simulations indicate that, for any choice of parameter in the range, simple period-1 motions can be maintained, limiting the number of impacts (together with their velocity)
Sign Rules for Anisotropic Quantum Spin Systems
We present new and exact ``sign rules'' for various spin-s anisotropic
spin-lattice models. It is shown that, after a simple transformation which
utilizes these sign rules, the ground-state wave function of the transformed
Hamiltonian is positive-definite. Using these results exact statements for
various expectation values of off-diagonal operators are presented, and
transitions in the behavior of these expectation values are observed at
particular values of the anisotropy. Furthermore, the effects of sign rules in
variational calculations and quantum Monte Carlo calculations are considered.
They are illustrated by a simple variational treatment of a one-dimensional
anisotropic spin model.Comment: 4 pages, 1 ps-figur
Aspect-ratio dependence of the spin stiffness of a two-dimensional XY model
We calculate the superfluid stiffness of 2D lattice hard-core bosons at
half-filling (equivalent to the S=1/2 XY-model) using the squared winding
number quantum Monte Carlo estimator. For L_x x L_y lattices with aspect ratio
L_x/L_y=R, and L_x,L_y -> infinity, we confirm the recent prediction [N.
Prokof'ev and B.V. Svistunov, Phys. Rev. B 61, 11282 (1999)] that the
finite-temperature stiffness parameters \rho^W_x and \rho^W_y determined from
the winding number differ from each other and from the true superfluid density
\rho_s. Formally, \rho^W_y -> \rho_s in the limit in which L_x -> infinity
first and then L_y -> infinity. In practice we find that \rho^W_y converges
exponentially to \rho_s for R>1. We also confirm that for 3D systems, \rho^W_x
= \rho^W_y = \rho^W_z = \rho_s for any R. In addition, we determine the
Kosterlitz-Thouless transition temperature to be T_KT/J=0.34303(8) for the 2D
model.Comment: 7 pages, 8 figures, 1 table. Minor changes to published versio
On the Emergence of Unstable Modes in an Expanding Domain for Energy-Conserving Wave Equations
Motivated by recent work on instabilities in expanding domains in
reaction-diffusion settings, we propose an analog of such mechanisms in
energy-conserving wave equations. In particular, we consider a nonlinear
Schr{\"o}dinger equation in a finite domain and show how the expansion or
contraction of the domain, under appropriate conditions, can destabilize its
originally stable solutions through the modulational instability mechanism.
Using both real and Fourier spacediagnostics, we monitor and control the
crossing of the instability threshold and, hence, the activation of the
instability. We also consider how the manifestation of this mechanism is
modified in a spatially inhomogeneous setting, namely in the presence of an
external parabolic potential, which is relevant to trapped Bose-Einstein
condensates
Bose-Einstein condensation and superfluidity of dilute Bose gas in a random potential
We develop the dilute Bose gas model with random potential in order to
understand the Bose system in random media such as 4He in porous glass. Using
the random potential taking account of the pore size dependence, we can compare
quantitatively the calculated specific heat with the experimental results,
without free parameters. The agreement is excellent at low temperatures, which
justifies our model. The relation between Bose condensation and superfluidity
is discussed. Our model can predict some unobserved phenomena in this system.Comment: 9 pages, 11 figures, accepted for publication in Phys. Rev.
An experimental study of the impulse response of a vibro-impacting cantilever beam
The dynamics of a vibro-impacting cantilever beam experiment using an impact load cell is considered. The signal recorded from the cell produces spike train -type data. The issues related to the analysis of such data are discussed; particularly the sampling rate and threshold values. For vibro-impact motion of the beam, the duration of impacts is investigated by using a time of contact measure. The implications are discussed for vibro-impact systems mathematically modelled by using instantaneous impact assumptions (coefficient of restitution). Using the load cell to measure impact forces for the beam system is also considered. Then a delay reconstruction of the dynamics of the system by using interspike intervals is considered. It is demonstrated how this process is effected by the influence of noise and the data-acquision process using numerical simulations of the experimental data. It is shown how simple periodic motions can be identified by using a probability density approach and possible future research is highlighted
Isolating Stock Prices Variation with Neural Networks
In this study we aim to define a mapping function that relates the general index value among a set of shares to the prices of individual shares. In more general terms this is problem of defining the relationship between multivariate data distributions and a specific source of variation within these distributions where the source of variation in question represents a quantity of interest related to a particular problem domain. In this respect we aim to learn a complex mapping function that can be used for mapping different values of the quantity of interest to typical novel samples of the distribution. In our investigation we compare the performance of standard neural network based methods like Multilayer Perceptrons (MLPs) and Radial Basis Functions (RBFs) as well as Mixture Density Networks (MDNs) and a latent variable method, the General Topographic Mapping (GTM). As a reference benchmark of the prediction accuracy we consider a simple method based on the average values over certain intervals of the quantity of interest that we are trying to isolate (the so called Sample Average (SA) method). According to the results, MLPs and RBFs outperform MDNs and the GTM for this one-to-many mapping problem
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