Topology of Foliations and Decomposition of Stochastic Flows of Diffeomorphisms

Let M be a compact manifold equipped with a pair of complementary foliations, say horizontal and vertical. In Catuogno et al. (Stoch Dyn 13(4):1350009, 2013) it is shown that, up to a stopping time \(\tau \), a stochastic flow of local diffeomorphisms \(\varphi _t\) in M can be written as a Markovian process in the subgroup of diffeomorphisms which preserve the horizontal foliation composed with a process in the subgroup of diffeomorphisms which preserve the vertical foliation. Here, we discuss topological aspects of this decomposition. The main result guarantees the global decomposition of a flow if it preserves the orientation of a transversely orientable foliation. In the last section, we present an Itô-Liouville formula for subdeterminants of linearised flows. We use this formula to obtain sufficient conditions for the existence of the decomposition for all \(t\ge 0\).     

A Remark on the Decay of Correlations for Mixed-Range Spin Vector Models

In this short note we present some explicit conditions under which the Theorem of Braga et al. (J. Stat. Phys. 129:587–591, 2007) can be extended to spin-spin correlation functions of mixed short-range/long-range ferromagnetic vector spin models in the disordered phase.     

Determination of diclofenac in pharmaceutical preparations by diffuse reflectance photometry

A quantitative analytical method for the determination of diclofenac in pharmaceutical preparations by diffuse reflectance in the visible region of the spectrum is presented. The color reaction is done directly in the measuring cell immediately after mixing, using small volumes of the analyte solution, of the reagent and of the buffer solutions. All reflectance measurements were carried out in a home made reflectometer equipped with a red LED as light source and a LDR as detector. The calibration curves were constructed from 1.0 to 18 mg mL⁻¹ (about 3.0 × 10⁻³ to 5.5 × 10⁻² mol L⁻¹) of sodium diclofenac or of potassium diclofenac in the analytical solution, with typical correlation coefficients equal to 0.999. The detection limit was estimated to be about 0.7 mg mL⁻¹ (2 × 10⁻³ mol L⁻¹). The method was applied to determine diclofenac in solid and liquid pharmaceutical preparations. The R.S.D. varied from 2% to 4% depending of the sample. The results were compared with those obtained with the HPLC procedure recommended by the United States Pharmacopoeia using the statistical Student's t-test procedure.     

Intrinsic acidity of dimethylhalonium ions: evidence for hyperconjugation in dimethylhalonium ylides in the gas phase

The intrinsic acidity of dimethylhalonium ions has been determined, both by theoretical methods and by gas-phase reactions of the isolated ions with pyridine bases. The calculated geometry of the dimethylhalonium ions shows a bent structure with the C-X-C angle decreasing in the order Cl > Br > I. Thermochemical calculations for the reaction of the dimethylhalonium ions with pyridine, 2,6-dimethylpyridine, and 2,6-di-tert-butylpyridine indicate that proton transfer, with the formation of the dimethylhalonium ylide is endothermic, whereas methyl transfer, with formation of methylhalide, is exothermic. The endothermicities for proton transfer are, nevertheless, dependent on the steric hindrance of the base. The bulkier the bases, the less endothermic the proton-transfer reaction is. Experimental gas-phase reactions support the calculations, showing that methyl transfer is the major reaction of dimethylchloronium and dimethyliodonium with pyridine, whereas proton transfer, as well as single electron transfer, is observed for the bulkier bases. The calculations also indicate that acidity increases in the order chloronium > bromonium > iodonium. NBO calculations predict that hyperconjugation with the sigma carbon-halogen orbital plays a role in stabilizing the halonium ylide species in the gas phase.     

Master integrals for double real radiation emission in heavy-to-light quark decay

We evaluate analytically the master integrals for double real radiation emission in the \(b \rightarrow u W^*\) decay, where b and u are a massive and massless quark, respectively, while \(W^{*}\) is an off-shell charged weak boson. Since the W boson can subsequently decay in a lepton anti-neutrino pair, the results of the present paper constitute a further step toward a fully analytic computation of differential distributions for the semileptonic decay of a b quark at NNLO in QCD. The latter partonic process plays a crucial role in the study of inclusive semileptonic charmless decays of B mesons. Our results are expressed in terms of multiple polylogarithms of maximum weight four.     

Shock Fluctuations for the Hammersley Process

We consider the Hammersley interacting particle system starting from a shock initial profile with densities \(\rho ,\lambda \in {\mathbb R}\) (\( \rho < \lambda \)). The microscopic shock is taken as the position of a second-class particle initially at the origin, and the main results are: (i) a central limit theorem for the shock; (ii) the variance of the shock equals \(2[\lambda \rho (\lambda - \rho )]^{-1}t + O(t^{2/3})\). By using the same method of proof, we also prove similar results for first-class particles.     

Introduction to Topological Phases and Electronic Interactions in (2+1) Dimensions

A brief introduction to topological phases is provided, considering several two-band Hamiltonians in one and two dimensions. Relevant concepts of the topological insulator theory, such as: Berry phase, Chern number, and the quantum adiabatic theorem, are reviewed in a basic framework, which is meant to be accessible to non-specialists. We discuss the Kitaev chain, SSH, and BHZ models. The role of the electromagnetic interaction in the topological insulator theory is addressed in the light of the pseudo-quantum electrodynamics (PQED). The well-known parity anomaly for massless Dirac particle is reviewed in terms of the Chern number. Within the continuum limit, a half-quantized Hall conductivity is obtained. Thereafter, by considering the lattice regularization of the Dirac theory, we show how one may obtain the well-known quantum Hall conductivity for a single Dirac cone. The renormalization of the electron energy spectrum, for both small and large coupling regime, is derived. In particular, it is shown that massless Dirac particles may, only in the strong correlated limit, break either chiral or parity symmetries. For graphene, this implies the generation of Landau-like energy levels and the quantum valley Hall effect.     

Measuring void fraction and velocity fields of a stepped spillway for skimming flow using non-intrusive methods

Stepped spillways have higher energy dissipation than smoother hydraulic structures used to divert flood discharges. The inception point related to air entrainment is, however, located further upstream causing an undesired bulking of the flow depth. For large discharge rates and for straight stepped spillways, the skimming flow regime may be assumed two dimensional; this is an attractive feature for the application of non-intrusive flow visualization techniques because these methods measure the flow characteristics in the vicinity of the sidewalls which are likely to correlate with the flow at the centre of the flume. This paper tests the hypothesis that such techniques can be used to measure the flow inside the flume. The hypothesis is tested against measurements taken with an intrusive probe. Void fraction contour lines and velocity fields are obtained in 12 different stepped spillway configurations using the image processing procedure and the bubble image velocimetry, respectively. The void fraction and velocity results are overall consistent with the probe measurements. The velocity fields show a persistent underestimation of the probe measurements which can at least be partially explained by sidewall effects and possible probe’s overestimation.