Experimental evidence of flutter and divergence instabilities induced by dry friction

Flutter and divergence instabilities have been advocated to be possible in elastic structures with Coulomb friction, but no direct experimental evidence has ever been provided. Moreover, the same types of instability can be induced by tangential follower forces, but these are commonly thought to be of extremely difficult, if not impossible, practical realization. Therefore, a clear experimental basis for flutter and divergence induced by friction or follower-loading is still lacking. This is provided for the first time in the present article, showing how a follower force of tangential type can be realized via Coulomb friction and how this, in full agreement with the theory, can induce a blowing-up vibrational motion of increasing amplitude (flutter) or an exponentially growing motion (divergence). In addition, our results show the limits of a treatment based on the linearized equations, so that nonlinearities yield the initial blowing-up vibration of flutter to reach eventually a steady state. The presented results give full evidence to potential problems in the design of mechanical systems subject to friction, open a new perspective in the realization of follower-loading systems and of innovative structures exhibiting 'unusual' dynamical behaviors. © 2011 Elsevier Ltd.

Low-rank optimization with trace norm penalty

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization that makes the trace norm differentiable in the search space and the computation of duality gap numerically tractable. The search space is nonlinear but is equipped with a Riemannian structure that leads to efficient computations. We present a second-order trust-region algorithm with a guaranteed quadratic rate of convergence. Overall, the proposed optimization scheme converges superlinearly to the global solution while maintaining complexity that is linear in the number of rows and columns of the matrix. To compute a set of solutions efficiently for a grid of regularization parameters we propose a predictor-corrector approach that outperforms the naive warm-restart approach on the fixed-rank quotient manifold. The performance of the proposed algorithm is illustrated on problems of low-rank matrix completion and multivariate linear regression. © 2013 Society for Industrial and Applied Mathematics.

A Bayesian wavelet-based multidimensional deconvolution with sub-band emphasis

This paper proposes a new algorithm for waveletbased multidimensional image deconvolution which employs subband-dependent minimization and the dual-tree complex wavelet transform in an iterative Bayesian framework. In addition, this algorithm employs a new prior instead of the popular ℓ1 norm, and is thus able to embed a learning scheme during the iteration which helps it to achieve better deconvolution results and faster convergence. © 2008 IEEE.

Image deconvolution using a Gaussian scale mixtures model to approximate the wavelet sparseness constraint

This paper proposes to use an extended Gaussian Scale Mixtures (GSM) model instead of the conventional ℓ1 norm to approximate the sparseness constraint in the wavelet domain. We combine this new constraint with subband-dependent minimization to formulate an iterative algorithm on two shift-invariant wavelet transforms, the Shannon wavelet transform and dual-tree complex wavelet transform (DTCWT). This extented GSM model introduces spatially varying information into the deconvolution process and thus enables the algorithm to achieve better results with fewer iterations in our experiments. ©2009 IEEE.

Strong flexoelectric behavior in bimesogenic liquid crystals

In this paper, we demonstrate strong flexoelectric coupling in bimesogenic liquid crystals. This strong coupling is determined via the flexoelectro-optic effect in chiral nematic liquid crystals based on bimesogenic mixtures that are doped with low concentrations of high twisting power chiral additive. Two mixtures were examined: one had a pitch length of p∼300nm, the other had a pitch length of p∼600nm. These mixtures exhibit enantiotropic chiral nematic phases close to room temperature. We found that full-intensity modulation, that is, a rotation of the optic axis of 45° between crossed polarizers, could be achieved at significantly lower applied electric fields (E<5Vμm -1) than previously reported. In fact, for the condition of full-intensity modulation, the lowest electric-field strength recorded was E=2Vμm-1. As a result of a combination of the strong flexoelectric coupling and a divergence in the pitch, tilt angles of the optic axis up to 87°, i.e., a rotation of the optic axis through 174°, were observed. Furthermore, the flexoelastic ratios, which may be considered as a figure-of-merit parameter, were calculated from the results and found to be large, ranging from 1.3to2C/Nm for a temperature range of up to 40°C. © 2006 American Institute of Physics.