Zeta-functions of renormalizable sub-Lorenz templates

We describe the Williams zeta-functions and the twist zeta-functions of sub-Lorenz templates generated by renormalizable Lorenz maps, in terms of the corresponding zeta-functions of the sub-Lorenz templates generated by the renormalized map and by the map that determines the renormalization type.     

Computational study and analysis of the kinetic isotope effects of the rearrangement of cis-bicyclo[4.2.0]oct-7-ene to cis,cis-cycloocta-1,3-diene

[reaction: see text] On the basis of KIE experiments, the ring opening of cis-bicyclo[4.2.0.]oct-7-ene has been suggested as an anti-Woodward-Hoffmann reaction candidate. We hereby report the results of a high-level computational study of the alternate reaction pathways which proves that the energy profiles show a clear preference for the conrotatory (W-H allowed) ring opening followed by double-bond isomerization. Computed KIE values for the aforementioned mechanism are in good agreement with the experimental values.     

A Non-Linear SGS Model Based On The Spatial Velocity Increment

A new subgrid scale (SGS) modelling concept for large-eddy simulation (LES) of incompressible flow is proposed based on the three-dimensional spatial velocity increment δ u _i . The new model is inspired by the structure function formulation developed by Métais and Lesieur [39] and applied in the context of the scale similarity type formulation. First, the similarity between the SGS stress tensor τ _ij and the velocity increment tensor Q _ij = δ u _i δ u _j is analyzed analytically and numerically using a priori tests of fully developed pipe flow at Re _τ = 180. Both forward and backward energy transfers between resolved and unresolved scales of the flow are well predicted with a SGS model based on Q _ij . Secondly, a posteriori tests are performed for two families of turbulent shear flows. LES of fully developed pipe flow up to Re _τ = 520 and LES of round turbulent jet at Re _D = 25000 carried out with a dynamic version of the model provide promising results that confirm the power of this approach for wall-bounded and free shear flows.     

Parametric amplification of the dynamic radiation force of acoustic waves in fluids

We report on parametric amplification in dynamic radiation force produced by a bichromatic acoustic beam in a fluid. To explain this effect we develop a theory taking into account the nonlinearity of the fluid. The theory is validated through an experiment to measure the dynamic radiation force on an acrylic sphere. Results exhibit an amplification of 66 dB in water and 80 dB in alcohol as the difference of the frequencies is increased from 10 Hz to 240 kHz.     

Near infrared emission spectroscopy induced by ultrasonic irradiation

Near infrared emission caused by ultrasonic excitation is demonstrated for the first time in this work. The instrument is constituted of an acousto-optical tunable filter-based spectrometer, an ultrasonic processor connected to a titanium alloy ultrasonic probe and a cylindrical borosilicate flask containing the sample to be excited. The radiation emitted by the sample is collected by a concave mirror and sent to the spectrometer. The effects of the position of the probe extremity in relation to a lateral entrance of the borosilicate flask and of the ultrasonic power on the emission signal were studied. The best results were obtained by positioning the probe extremity up to 2mm from the reflexive body (lateral entrance) using 30% of the full ultrasonic incident power and acquiring spectra after 5 min of sonication. The NIR emission spectra resulting from the ultrasonic excitation were in agreement with that obtained by thermal excitation. The proposed technique was utilized to study different poly(dimethylsiloxane) samples having different viscosities.     

Observability of continuous Petri nets with infinite server semantics

Timed continuous Petri net (contPN) systems with infinite server semantics are nonlinear systems, particularly a subclass of piecewise linear (PWL) systems. This paper addresses several problems regarding the state observability of these systems. We assume that the initial marking/state is not known and by measuring the marking of some places we want to estimate all the others. First, a study of the different linear systems corresponding to a continuous Petri net system is performed. It is shown that in some cases, some of them are redundant, and so can be disregarded. The notion of distinguishable modes is introduced which helps us in giving a necessary and sufficient criterion for the observability in infinitesimal time. Structural observability, i.e., observability for all possible values of firing rates of transitions, is studied and it is proved that in some cases it can be reduced to a linear problem, even if the system is nonlinear. Using results from linear structured systems, the concept of weak structural or generic observability is considered.     

A bound on the treewidth of planar even-hole-free graphs

The class of planar graphs has unbounded treewidth, since the k×k grid, ∀k∈N, is planar and has treewidth k. So, it is of interest to determine subclasses of planar graphs which have bounded treewidth. In this paper, we show that if G is an even-hole-free planar graph, then it does not contain a 9×9 grid minor. As a result, we have that even-hole-free planar graphs have treewidth at most 49.     

Periodic problem for a nonlinear‐damped wave equation on the boundary

In this work we investigate the existence of periodic solutions in t for the following problem: We employ elliptic regularization and monotone method. We consider $\mbox{\boldmath{$\Omega$}}\mbox{\boldmath{$\subset$}}{\mathbb{R}}^{{{n}}} \ (n\geqslant 1)$ an open bounded set that has regular boundary Γ and Q=Ω ×(0,T), T>0, a cylinder of ${\mathbb{R}}^{n+1}$ with lateral boundary Σ = Γ × (0,T). Copyright © 2009 John Wiley & Sons, Ltd.     

Random telegraph signals with time dependent capture and emission probabilities: Analytical and numerical results

In this work, we study the noise spectra of random telegraph signals (RTS) with time dependent capture and emission probabilities. The capture and emission probabilities are made time dependent by cyclo-stationary excitation. Rigorous analytical calculations are performed to derive the model equations, and Monte Carlo simulations are performed to explore the noise behavior and validate the analytical model. Two study cases are explored: input signals modeled by periodic square wave and sinusoidal waves. We present clear situations where the integrated noise power is smaller than stationary case for a suitable choice of parameters in both cyclo-stationary inputs studied.