Quasipatterns versus superlattices resulting from the superposition of two hexagonal patterns

We present a short review of the experimental observations and mechanisms related to the generation of quasipatterns and superlattices by the Faraday instability with two-frequency forcing. We show how two-frequency forcing makes possible triad interactions that generate hexagonal patterns, twelvefold quasipatterns or superlattices that consist of two hexagonal patterns rotated by an angle α relative to each other. We then consider which patterns could be observed when α does not belong to the set of prescribed values that give rise to periodic superlattices. Using the Swift–Hohenberg equation as a model, we find that quasipattern solutions exist for nearly all values of α. However, these quasipatterns have not been observed in experiments with the Faraday instability for $\alpha \ne \mathrm{\pi }/6$. We discuss possible reasons and mention a simpler framework that could give some hint about this problem.     

On the Motion of Substance in a Channel of a Network: Extended Model and New Classes of Probability Distributions

We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network. This leads to an extension of the model of motion of substance and the extended model contains previous models as particular cases. We use a discrete-time model of motion of substance and consider a stationary regime of motion of substance in a channel containing a finite number of nodes. As results of the study, we obtain a class of probability distributions connected to the amount of substance in nodes of the channel. We prove that the obtained class of distributions contains all truncated discrete probability distributions of discrete random variable ω which can take values 0,1,⋯,N. Theory for the case of a channel containing infinite number of nodes is presented in Appendix A. The continuous version of the discussed discrete probability distributions is described in Appendix B. The discussed extended model and obtained results can be used for the study of phenomena that can be modeled by flows in networks: motion of resources, traffic flows, motion of migrants, etc.     

Correlation functions from a unified variational principle: Trial Lie groups

Time-dependent expectation values and correlation functions for many-body quantum systems are evaluated by means of a unified variational principle. It optimizes a generating functional depending on sources associated with the observables of interest. It is built by imposing through Lagrange multipliers constraints that account for the initial state (at equilibrium or off equilibrium) and for the backward Heisenberg evolution of the observables. The trial objects are respectively akin to a density operator and to an operator involving the observables of interest and the sources. We work out here the case where trial spaces constitute Lie groups. This choice reduces the original degrees of freedom to those of the underlying Lie algebra, consisting of simple observables; the resulting objects are labeled by the indices of a basis of this algebra. Explicit results are obtained by expanding in powers of the sources. Zeroth and first orders provide thermodynamic quantities and expectation values in the form of mean-field approximations, with dynamical equations having a classical Lie–Poisson structure. At second order, the variational expression for two-time correlation functions separates–as does its exact counterpart–the approximate dynamics of the observables from the approximate correlations in the initial state. Two building blocks are involved: (i) a commutation matrix which stems from the structure constants of the Lie algebra; and (ii) the second-derivative matrix of a free-energy function. The diagonalization of both matrices, required for practical calculations, is worked out, in a way analogous to the standard RPA. The ensuing structure of the variational formulae is the same as for a system of non-interacting bosons (or of harmonic oscillators) plus, at non-zero temperature, classical Gaussian variables. This property is explained by mapping the original Lie algebra onto a simpler Lie algebra. The results, valid for any trial Lie group, fulfill consistency properties and encompass several special cases: linear responses, static and time-dependent fluctuations, zero- and high-temperature limits, static and dynamic stability of small deviations.     

Spontaneous excitation of a circularly accelerated atom coupled with vacuum Dirac field fluctuations

We study the spontaneous excitation of a circularly accelerated atom coupled with vacuum Dirac field fluctuations by separately calculating the contribution to the excitation rate of vacuum fluctuations and a cross term which involves both vacuum fluctuations and radiation reaction, and demonstrate that although the spontaneous excitation for the atom in its ground state would occur in vacuum, such atoms in circular motion do not perceive a pure thermal radiation as their counterparts in linear acceleration do since the transition rates of the atom do not contain the Planckian factor characterizing a thermal bath. We also find that the contribution of the cross term that plays the same role as that of radiation reaction in the scalar and electromagnetic fields cases differs for atoms in circular motion from those in linear acceleration. This suggests that the conclusion drawn for atoms coupled with the scalar and electromagnetic fields that the contribution of radiation reaction to the mean rate of change of atomic energy does not vary as the trajectory of the atom changes from linear acceleration to circular motion is not a general trait that applies to the Dirac field where the role of radiation reaction is played by the cross term.     

Prins Cyclization of Styrenes or Acetophenone Catalyzed by DBSA in Water

Dodecylbenzenesulfonic acid (DBSA) was proved to be an efficient catalyst for Prins cyclization of styrenes and formaldehyde or acetaldehyde in water. A tandem dehydration/Prins cyclization reaction using a tertiary alcohol and formaldehyde as substrates proceeded very well by using DBSA as catalyst. Acetophenone, which is less reactive compared with styrene, can also react with formaldehyde when catalyzed by DBSA in water to afford 1,3-dioxan-5-ylphenylmethanone in good yield.     

MICELLE FORMATION BY ANIONIC AND CATIONIC SURFACTANTS IN AQUEOUS 18-CROWN-6 ETHER,P-CYCLODEXTRIN,AND 1,10-PHENANTHROLINE SOLUTIONS AT DIFFERENT TEMPERATURES

The conductances of sodium perfluorooctanoate (SPFO), sodium dodecylsulphate (SDS), dodecyltrimethylammonium bromide (DTAB), and tetradecyltrimethylammonium bromide (TTAB) in 18-crown-6 ether + water (CR+W), p-cyclodextrin + water (CY+W), and 1,10-phenanthroIine + water (Phen+W) mixtures with fixed 4 mM of each additive were determined over the temperature range of 5-55 °C. The conductivity plots for all the surfactants showed single break from which the critical micellization concentration (cmc) and degree of micelle ionization (x) were computed. From the pre and the post micellar slopes of the conductivity curves, the equivalent conductivities of the monomeric (Aass) and the micellar states (Amjc), respectively, were calculated and discussed with respect to the surfactant-additive complexation. It was observed that the micelle formation of all the ionic surfactants irrespective of the nature of their head groups were delayed in CYC+W in comparison to that in CR+W and Phen+W systems over the temperature range studied. The micelle formation of SPFO and SDS in CR+W and Phen+W systems showed stabilization of the respective micelles due to the adsorption of Na⁺-CR and Na+-Phen complexes at the micelle solution interface in comparison to that of DTAB and TTAB.     

Development and Optimization of Twenty-Four Hour Manual Methods for the Collection and Colorimetric Analysis of Atmospheric NO2

Abstract

Manual twenty-four hour colorimetric procedures for the determination of atmospheric NO₂ are described. The methods are based on collecting NO₂ by bubbling ambient air for twenty-four hours through reagents that form stable nitrite solutions. The reagents described have a 93 % collection efficiency over the range of 20 to 750 μg/m³ NO₂ with no apparent interferences. The inadequacies' of the former reference or alkaline method¹ are also described.