Nonlinear dynamics of dimers on periodic substrates

We study the dynamics of a dimer moving on a periodic one-dimensional substrate as a function of the initial kinetic energy at zero temperature. The aim is to describe, in a simplified picture, the microscopic dynamics of diatomic molecules on periodic surfaces, which is of importance for thin film formation and crystal growth. We find a complex behaviour, characterized by a variety of dynamical regimes, namely oscillatory, “quasi-diffusive” (chaotic) and drift motion. Parametrically resonant excitations of internal vibrations can be induced both by oscillatory and drift motion of the centre of mass. For weakly bound dimers a chaotic regime is found for a whole range of velocities between two non-chaotic phases at low and high kinetic energy. The chaotic features have been monitored by studying the Lyapunov exponents and the power spectra. Moreover, for a short-range interaction, the dimer can dissociate due to the parametric excitation of the internal motion. Received 8 July 2002 / Received in final form 15 November 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: fusco@sci.kun.nl.     

Closed-loop experimental validation of the spatially filtered Shack-Hartmann concept

An experimental validation of the spatially filtered Shack-Hartmann concept (F-SH) is presented that allows aliasing effects to be decreased. This effect is studied by use of an adaptive optical testbed with a focal plane pinhole in front of the wave-front sensor. First, the ability to close the loop on turbulence is demonstrated. Then the performance gain conferred by the device is quantified and compared with end-to-end simulation results. Another property of the F-SH concept, i.e., the reduction of the waffle modes, is highlighted.     

L 2-lower semicontinuity of functionals of quadratic type

Summary A representation formula for the L ²-lower semicontinuous envelope of a quadratic integral of Calculus of Variations is given. Some particular cases are explicited in the details.This paper has been supported by G.N.A.F.A. (Gruppo Nazionale per l'Analisi Funzionale e le sue Applicazioni).     

Non-linear wave propagation in a layered half space

In this paper we consider the one dimensional propagation of weak discontinuities through a layered half space where quasilinear hyperbolic systems in homogeneous conservative form are involved. The amplitude of reflected and transmitted discontinuities across each layer is determined in terms of the initial conditions. The critical time when the incident wave breaks down is discussed. The results are specialized in the case of periodic layering. Physical examples are considered at the end of the paper.     

Mechanosensing of substrate stiffness regulates focal adhesions dynamics in cell

Cell mechanical recognition of extracellular matrix determines the cell activities and functions. Focal adhesions are part of the cell mechanosensing machinery and, operating at the very dynamic interface between cell and extracellular matrix, can operate this recognition and trigger conformational, functional and behavioral modification of the cell. To investigate how the dynamic of assembly and disassembly of focal adhesion are influenced by the substrate mechanics we developed a novel procedure. The analysis consists of the over time tracking of focal adhesion structures in a stable cell line of NIH/3T3 expressing fluorescent pmKate2-paxillin. From collected signals and by their autocorrelation we evaluated the average lifetime and assembly rate of focal adhesion as function of substrate stiffness. Further, by signals cross-correlation we obtained information about the mechanical nature of cytoskeleton and its network. This quantitative approach to focal adhesion dynamics characterization was presented in this study as an investigation tool for cell mechanobiology.     

Slow-motion manifolds,dormant instability,and singular perturbations

If the coexistence of two phases at the transition temperature is kept under observation for a long time, then one observes that the system is not exactly in equilibrium and a very slow evolution driven by surface tension is taking place. Theoretically, one should eventually see a spatially homogeneous state, but the time for settling down is so long that what one actually observes is motion towards a stable state. The complexity of the spatial distribution of the two phases keeps decreasing but appears to be stable for very long periods of time with intermittent periods of fast motion when there are small inclusions of one of the two regions embedded in the other phase. For a simple reaction diffusion model, it is shown that this phenomenon can be explained by investigating the flow on the attractor and the unstable manifolds of equilibria.