Additive global noise delays Turing bifurcations

We apply a stochastic center manifold method to the calculation of noise-induced phase transitions in the stochastic Swift-Hohenberg equation. This analysis is applied to the reduced mode equations that result from Fourier decomposition of the field variable and of the temporal noise. The method shows a pitchfork bifurcation at lower perturbation order, but reveals a novel additive-noise-induced postponement of the Turing bifurcation at higher order. Good agreement is found between the theory and the numerics for both the reduced and the full system. The results are generalizable to a broad class of nonlinear spatial systems.     

First-order distributed feedback dye laser effect in reflection pumping geometry

Tunable distributed feedback lasing output based on reflection grating configuration instead of the traditional transmission one was realized from rhodamine 6G (R6G)-doped ethanol and 4-dicyanomethylene-2-methyl-6- (p-dimethylaminostyryl)-4H-pyran-(DCM)-doped methanol. Pure gain coupling and additional index coupling were obtained in R6G-doped ethanol and DCM-doped methanol, respectively. The tuning, which was found to be independent of the refractive index of the lasing media, went through the entire stimulated emission band for the two cases. Dual-peak lasing emission indicative of the existence of an index grating was observed in DCM-doped methanol. The interval between the two peaks increased with pump energy.     

Nonlinear behaviour of the instability of steady natural convection in a vertical air layer

In this paper we deal with the flow of natural convection between two vertical planes with horizontal temperature gradient. We show that periodic steady flow occur when Rayleigh number increases. Critical values are obtained numerically and a nonlinear analysis is presented according to Center manifold method.     

3D Study of the Morphology and Dynamics of Zeolite Nucleation

The principle aspects and constraints of the dynamics and kinetics of zeolite nucleation in hydrogel systems are analyzed on the basis of a model Na‐rich aluminosilicate system. A detailed time‐series EMT‐type zeolite crystallization study in the model hydrogel system was performed to elucidate the topological and temporal aspects of zeolite nucleation. A comprehensive set of analytical tools and methods was employed to analyze the gel evolution and complement the primary methods of transmission electron microscopy (TEM) and nuclear magnetic resonance (NMR) spectroscopy. TEM tomography reveals that the initial gel particles exhibit a core–shell structure. Zeolite nucleation is topologically limited to this shell structure and the kinetics of nucleation is controlled by the shell integrity. The induction period extends to the moment when the shell is consumed and the bulk solution can react with the core of the gel particles. These new findings, in particular the importance of the gel particle shell in zeolite nucleation, can be used to control the growth process and properties of zeolites formed in hydrogels.     

Convergence to a Single Wave in the Fisher-KPP Equation

The authors study the large time asymptotics of a solution of the Fisher-KPP reaction-diffusion equation,with an initial condition that is a compact perturbation of a step function.A well-known result of Bramson states that,in the reference frame moving as 2t-(3/2) log t+x∞,the solution of the equation converges as t-→ +o∞ to a translate of the traveling wave corresponding to the minimal speed c* =2.The constant x∞ depends on the initial condition u(0,x).The proof is elaborate,and based on probabilistic arguments.The purpose of this paper is to provide a simple proof based on PDE arguments.     

Hohenberg–Kohn theorems in the presence of magnetic field

In this article, we examine Hohenberg–Kohn theorems for Current Density Functional Theory, that is, generalizations of the classical Hohenberg–Kohn theorem that includes both electric and magnetic fields. In the Vignale and Rasolt formulation (Vignale and Rasolt, Phys. Rev. Lett. 1987, 59, 2360), which uses the paramagnetic current density, we address the issue of degenerate ground states and prove that the ensemble‐representable particle and paramagnetic current density determine the degenerate ground states. For the formulation that uses the total current density, we note that the proof suggested by Diener (Diener, J. Phys.: Condens. Matter. 1991, 3, 9417) is unfortunately not correct. Furthermore, we give a proof that the magnetic field and the ensemble‐representable particle density determine the scalar and vector potentials up to a gauge transformation. This generalizes the result of Grayce and Harris (Grayce and Harris, Phys. Rev. A 1994, 50, 3089) to the case of degenerate ground states. We moreover prove the existence of a positive wavefunction that is the ground state of infinitely many different Hamiltonians. © 2014 Wiley Periodicals, Inc.     

Boojum and stripe textures in long-range orientationally ordered monolayers on solid substrates

Long-range organization of molecular tilt azimuth is a striking feature in monolayers at the air-water interface. We show that the boojum and stripe textures of pentadecanoic acid (PDA) with the continuous variations of molecular tilt azimuth formed at the air-water interface at temperatures lower than room temperature can be preserved after being transferred to glass substrates at low dipping speeds. The long-range tilt order in the transferred boojums and stripes is resolved by frictional force microscopy at room temperature, suggesting that the tilt order is "frozen" through the interaction of PDA molecules with the glass surface. The transferred stripe structure can be used as a unique alignment layer to induce a continuously azimuthal orientation of nematic liquid crystals.     

Carbon Dioxide Reforming of Methane Using a Dielectric Barrier Discharge Reactor: Effect of Helium Dilution and Kinetic Model

The carbon dioxide reforming of methane to synthesis gas was investigated in a dielectric barrier discharge reactor at room temperature. The influence of dilution of reactants by helium was studied. We showed that, at a fixed contact time, the conversions of CH₄ and CO₂ increase when the amount of helium in the gas mixture increases. This result is attributed to the “penning ionization” phenomenon, which corresponds to an energy transfer from excited He to molecules in ground state (CH₄, CO₂). The selectivity to products is affected by the dilution factor. As soon as helium is present in a large amount the formation of products resulting from recombination of methyl radicals (such as C₂, C₃ and C₄) is less favourable due to the lowest probability of collisions to proceed. A kinetic model is proposed based on the assumption that the reactant molecules CH₄ or CO₂ are attacked by active species produced by the plasma discharges, and the production of this active species are function of the plasma power. This model which takes into account the dilution by helium fits particularly well the experimental data we obtained.     

Correction factors for boundary diffusion in reaction-diffusion master equations

The reaction-diffusion master equation (RDME) has been widely used to model stochastic chemical kinetics in space and time. In recent years, RDME-based trajectorial approaches have become increasingly popular. They have been shown to capture spatial detail at moderate computational costs, as compared to fully resolved particle-based methods. However, finding an appropriate choice for the discretization length scale is essential for building a reasonable RDME model. Moreover, it has been recently shown [R. Erban and S. J. Chapman, Phys. Biol. 4, 16 (2007); R. Erban and S. J. Chapman, Phys. Biol. 6, 46001 (2009); D. Fange, O. G. Berg, P. Sjo?berg, and J. Elf, Proc. Natl. Acad. Sci. U.S.A. 107, 46 (2010)] that the reaction rates commonly used in RDMEs have to be carefully reassessed when considering reactive boundary conditions or binary reactions, in order to avoid inaccurate--and possibly unphysical--results. In this paper, we present an alternative approach for deriving correction factors in RDME models with reactive or semi-permeable boundaries. Such a correction factor is obtained by solving a closed set of equations based on the moments at steady state, as opposed to modifying probabilities for absorption or reflection. Lastly, we briefly discuss existing correction mechanisms for bimolecular reaction rates both in the limit of fast and slow diffusion, and argue why our method could also be applied for such purpose.     

Development of hybrid elution systems for efficient purification of stilbenoids using centrifugal partition chromatography coupled to mass spectrometry

The phytochemical study of the root extract of the stilbenoid-rich Vitis riparia × Vitis berlandieri grapevine was carried out by centrifugal partition chromatography (CPC). For this reason, we developed a new elution mode we named back-step, which allowed us to obtain cleaner fractions and a more efficient separation process when used in conjunction with a classical elution approach. Three hydroxystilbenes: (E)-resveratrol, (E)-?-viniferin and (E)-vitisin C, with greater than 90% purity were thus obtained through such process, with minimal sample handling and purification steps. Online coupling of CPC to ESI mass spectrometry was used for optimization of the separation parameters and to facilitate the characterization of the stilbenoids. This study details the first phytochemical investigation of stilbenoids from the hybrid species together with a new elution mode able to widen the range of ARIZONA biphasic systems.