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)

High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States

In this article, we prove that exact representations of dimer and plaquette valence-bond ket ground states for quantum Heisenberg antiferromagnets may be formed via the usual coupled cluster method (CCM) from independent-spin product (e.g. N\'eel) model states. We show that we are able to provide good results for both the ground-state energy and the sublattice magnetization for dimer and plaquette valence-bond phases within the CCM. As a first example, we investigate the spin-half $J_1$--$J_2$ model for the linear chain, and we show that we are able to reproduce exactly the dimerized ground (ket) state at $J_2/J_1=0.5$. The dimerized phase is stable over a range of values for $J_2/J_1$ around 0.5. We present evidence of symmetry breaking by considering the ket- and bra-state correlation coefficients as a function of $J_2/J_1$. We then consider the Shastry-Sutherland model and demonstrate that the CCM can span the correct ground states in both the N\'eel and the dimerized phases. Finally, we consider a spin-half system with nearest-neighbor bonds for an underlying lattice corresponding to the magnetic material CaV$_4$O$_9$ (CAVO). We show that we are able to provide excellent results for the ground-state energy in each of the plaquette-ordered, N\'eel-ordered, and dimerized regimes of this model. The exact plaquette and dimer ground states are reproduced by the CCM ket state in their relevant limits.Comment: 34 pages, 13 figures, 2 table

Exploiting Evolution for an Adaptive Drift-Robust Classifier in Chemical Sensing

Gas chemical sensors are strongly affected by drift, i.e., changes in sensors' response with time, that may turn statistical models commonly used for classification completely useless after a period of time. This paper presents a new classifier that embeds an adaptive stage able to reduce drift effects. The proposed system exploits a state-of-the-art evolutionary strategy to iteratively tweak the coefficients of a linear transformation able to transparently transform raw measures in order to mitigate the negative effects of the drift. The system operates continuously. The optimal correction strategy is learnt without a-priori models or other hypothesis on the behavior of physical-chemical sensors. Experimental results demonstrate the efficacy of the approach on a real problem

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

A class of ansatz wave functions for 1D spin systems and their relation to DMRG

We investigate the density matrix renormalization group (DMRG) discovered by White and show that in the case where the renormalization eventually converges to a fixed point the DMRG ground state can be simply written as a ``matrix product'' form. This ground state can also be rederived through a simple variational ansatz making no reference to the DMRG construction. We also show how to construct the ``matrix product'' states and how to calculate their properties, including the excitation spectrum. This paper provides details of many results announced in an earlier letter.Comment: RevTeX, 49 pages including 4 figures (macro included). Uuencoded with uufiles. A complete postscript file is available at http://fy.chalmers.se/~tfksr/prb.dmrg.p

Quantum lattice dynamical effects on the single-particle excitations in 1D Mott and Peierls insulators

As a generic model describing quasi-one-dimensional Mott and Peierls insulators, we investigate the Holstein-Hubbard model for half-filled bands using numerical techniques. Combining Lanczos diagonalization with Chebyshev moment expansion we calculate exactly the photoemission and inverse photoemission spectra and use these to establish the phase diagram of the model. While polaronic features emerge only at strong electron-phonon couplings, pronounced phonon signatures, such as multi-quanta band states, can be found in the Mott insulating regime as well. In order to corroborate the Mott to Peierls transition scenario, we determine the spin and charge excitation gaps by a finite-size scaling analysis based on density-matrix renormalization group calculations.Comment: 5 pages, 5 figure

Tumori maligni delle ghiandole salivari della laringe: un'unica review istituzionale

I tumori a istotipo salivare della laringe sono molto rari, con pochi report in letteratura in merito al loro andamento clinico. Nel presente manoscritto discutiamo un'esperienza di 10 anni presso una singola struttura. Abbiamo condotto una review retrospettiva della casistica di un centro di oncologia della testa e del collo di terzo livello. I pazienti sono stati individuati mediante analisi di un database e sono stati revisionati da un Anatomo Patologo testa collo. I dati inerenti la clinica, le modalità di trattamento e gli esiti sono stati prelevati da archivi elettronici. Sono stati inclusi sei pazienti nello studio, con un range di età dai 44 ai 69 anni. Tutti e sei erano affetti da neoplasie maligne a istotipo salivare della laringe. Gli istotipi includevano: tre carcinomi adenoido-cistici (2 sopraglottico, 1 sottoglottico), un carcinoma mucoepidermoidale (sopraglottico), un carcinoma epiteliale-mioepiteliale (sopraglottico), e un adenocarcinoma (transglottico). Tutti sono stati sottoposti a trattamento chirurgico (2 chirurgie laser, 4 open) e 5 dei 6 pazienti sono stati successivamente sottoposti a terapia adjuvante (4 a radioterapia, 1 a radio-chemioterapia concomitante). Un paziente era fumatore; nessun paziente aveva storia di abuso di alcolici. A un follow-up con mediana di 4,5 anni nessuno dei pazienti ha presentato recidiva o metastasi locali o a distanza. I tumori a istotipo salivare della laringe si presentano solitamente in pazienti della seconda/terza età, e possono essere trattati con successo mediante approcci multimodali, con un ottimo controllo locoregionale di malattia