Hydrodynamic Fluctuations in Laminar Fluid Flow. I. Fluctuating Orr-Sommerfeld Equation

In recent years it has become evident that fluctuating hydrodynamics predicts that fluctuations in nonequilibrium states are always spatially long ranged. In this paper we consider the application of fluctuating hydrodynamics to laminar fluid flow, using plane Couette flow as a representative example. Specifically, fluctuating hydrodynamics yields a stochastic Orr-Sommerfeld equation for the wall-normal velocity fluctuations, where spontaneous thermal noise acts as a random source.This stochastic equation needs to be solved subject to appropriate boundary conditions. We show how an exact solution can be obtained from an expansion in terms of the eigenfunctions of the Orr-Sommerfeld hydrodynamic operator. We demonstrate the presence of a flow-induced enhancement of the wall-normal velocity fluctuations and a resulting flow-induced energy amplification and provide a quantitative analysis how these quantities depend on wave number and Reynolds number.     

Dissipative localized States with shieldlike phase structure

A novel type of parametrically excited dissipative solitons is unveiled. It differs from the well-known solitons with constant phase by an intrinsically dynamical evolving shell-type phase front. Analytical and numerical characterizations are proposed, displaying quite a good agreement. In one spatial dimension, the system shows three types of stationary solitons with shell-like structure whereas in two spatial dimensions it displays only one, characterized by a π-phase jump far from the soliton position.     

Intracavity system design for IR multiphoton dissociation

An intracavity system for the infrared multiple photon dissociation (IRMPD) of molecules with high dissociation energy threshold has been designed and implemented. The system design based on a TEA CO₂ laser with a cavity folded in V-shape included the analysis of its stability varying the cavity dimensions as well as the analysis of the positions of the beam waists and of the beam size at them. The intracavity energy as a function of the total sample pressure has been measured and the laser-operation threshold has been determined. Intracavity IRMPD has been compared to traditional IRMPD performed in an irradiation geometry in which the radiation is focused into a photoreactor placed outside the laser cavity. Dissociation volumes in intracavity irradiation have resulted an order of magnitude larger than those obtained in experiments performed with the photoreactor outside the laser cavity.     

Generalized hyper-heuristics for solving 2D Regular and Irregular Packing Problems

The idea behind hyper-heuristics is to discover some combination of straightforward heuristics to solve a wide range of problems. To be worthwhile, such a combination should outperform the single heuristics. This article presents a GA-based method that produces general hyper-heuristics that solve two-dimensional regular (rectangular) and irregular (convex polygonal) bin-packing problems. A hyper-heuristic is used to define a high-level heuristic that controls low-level heuristics. The hyper-heuristic should decide when and where to apply each single low-level heuristic, depending on the given problem state. In this investigation two kinds of heuristics were considered: for selecting the figures (pieces) and objects (bins), and for placing the figures into the objects. Some of the heuristics were taken from the literature, others were adapted, and some other variations developed by us. We chose the most representative heuristics of their type, considering their individual performance in various studies and also in an initial experimentation on a collection of benchmark problems. The GA included in the proposed model uses a variable-length representation, which evolves combinations of condition-action rules producing hyper-heuristics after going through a learning process which includes training and testing phases. Such hyper-heuristics, when tested with a large set of benchmark problems, produce outstanding results for most of the cases. The testbed is composed of problems used in other similar studies in the literature. Some additional instances for the testbed were randomly generated.     

Hydrodynamic Fluctuations in Laminar Fluid Flow. II. Fluctuating Squire Equation

We use fluctuating hydrodynamics to evaluate the enhancement of thermally excited fluctuations in laminar fluid flow using plane Couette flow as a representative example. In a previous publication (J. Stat. Phys. 144:774, 2011) we derived the energy amplification arising from thermally excited wall-normal fluctuations by solving a fluctuating Orr-Sommerfeld equation. In the present paper we derive the energy amplification arising from wall-normal vorticity fluctuation by solving a fluctuating Squire equation. The thermally excited wall-normal vorticity fluctuations turn out to yield the dominant contribution to the energy amplification. In addition, we show that thermally excited streaks, even in the absence of any externally imposed perturbations, are present in laminar fluid flow.     

Asymptotic Formulae and Divisor Problems

We investigate the asymptotic behaviour of the summatory functions of _z(n, ), _k(n, ) z ⁽ⁿ⁾ and _k(n, ) z ⁽ⁿ⁾.     

A Higher-Order Internal Wave Model Accounting for Large Bathymetric Variations

A higher-order strongly nonlinear model is derived to describe the evolution of large amplitude internal waves over arbitrary bathymetric variations in a two-layer system where the upper layer is shallow while the lower layer is comparable to the characteristic wavelength. The new system of nonlinear evolution equations with variable coefficients is a generalization of the deep configuration model proposed by Choi and Camassa [ 1 ] and accounts for both a higher-order approximation to pressure coupling between the two layers and the effects of rapidly varying bottom variation. Motivated by the work of Rosales and Papanicolaou [ 2 ], an averaging technique is applied to the system for weakly nonlinear long internal waves propagating over periodic bottom topography. It is shown that the system reduces to an effective Intermediate Long Wave (ILW) equation, in contrast to the Korteweg-de Vries (KdV) equation derived for the surface wave case.     

Quantum dynamics in ultracold atomic physics

We review recent developments in the theory of quantum dynamics in ultracold atomic physics, including exact techniques and methods based on phase-space mappings that are applicable when the complexity becomes exponentially large. Phase-space representations include the truncated Wigner, positive-P and general Gaussian operator representations which can treat both bosons and fermions. These phase-space methods include both traditional approaches using a phase-space of classical dimension, and more recent methods that use a non-classical phase-space of increased dimensionality. Examples used include quantum Einstein-Podolsky-Rosen (EPR) entanglement of a four-mode BEC, time-reversal tests of dephasing in single-mode traps, BEC quantum collisions with up to 106 modes and 105 interacting particles, quantum interferometry in a multi-mode trap with nonlinear absorption, and the theory of quantum entropy in phase-space. We also treat the approach of variational optimization of the sampling error, giving an elementary example of a nonlinear oscillator.     

Measurement of the phase behaviour of the binary systems {carbon dioxide (CO2) + non-ionic surfactants (CiEOj)}

Solubility experiments of ethoxylates surfactants denoted as C_iEO_j (where C_i = hydrocarbon tail, EO_j = oxyethylene groups, i = 6 to 8 and j = 3 to 5) in sub- and supercritical carbon dioxide were carried out at different temperatures, pressures, and concentrations in a Cailletet apparatus as a representative model for dry cleaning system. For a variety of compositions, results are reported for binary systems within temperature and pressure ranges of (260 to 310) K and (2.0 to 10) MPa respectively. In each experiment, the surfactants reach equilibrium with carbon dioxide at different concentrations. The data show that with all the surfactants upon increasing concentration, the liquid–liquid (L–L) curve shifts to lower temperatures. Therefore, the one-phase solution gap is reduced in pressure and temperature at higher concentrations. When the length of the hydrocarbon tail remains constant and the ethoxylated chain is increased from three to five groups, the L–L curve once again shifts to lower temperatures and the two phases start earlier. This effect can be attributed to the higher surfactant’s polarity due to the increase in j. On the other hand, when the number of ethoxylated groups j remains constant and the length of the hydrocarbon tail is increased from six to eight carbon atoms, no significant shift in the L–L curve is observed. That signals the fact that the appearance of two phases is directly related to the number of ethoxylated group which determine the polarity of the molecule.     

Laser flash photolysis in a O3/Cl2 mixture at 266 nm in a very low-pressure flow system

The laser flash photolysis in a very low-pressure flow system with mass spectrometry detection technique was developed for the study of oxidation reactions of chlorofluorocarbons. In this work, we have studied the UV photolysis of O3 in the presence of Cl2 at room temperature, which presents two catalytic cycles of O3 depletion with efficiencies dependent on the partial pressures in the photoreactor. The ozone dissociation was initiated with fourth harmonic pulses of a Nd:YAG laser. The detection of the reactants and the final and intermediate reaction products was performed with real-time mass spectrometry. The variations of the O3, Cl2 and ClO concentration were measured. The equations system associated to a proposed kinetic scheme was solved numerically and excellent agreement with the experimental results was obtained. The results from this work allowed the determination of the wall loss rates of the O(1D), Cl and ClO radicals.