Fast protonic conductivity in crystalline benzenehexasulfonic acid hydrates

We report on the crystal structures of two hydrates of benzenehexasulfonic acid, its water sorption isotherm, temperature- and humidity-dependent conductivity, along with ¹H NMR studies. At comparable humidities and temperatures, this crystalline material shows conductivity similar to Nafion, which conducts protons via liquid water channels. We believe that the presented discovery of fast protonic conductivity in benzenehexasulfonic acid at low humidities is encouraging for further efforts in developing highly sulfonated polymers as membranes for fuel cells.     

Observations of surface modifications induced by the multiple pulse irradiation using a soft picosecond x-ray laser beam

To study the interactions between picosecond soft x-ray laser (SXRL) beams and material surfaces, gold (Au), copper (Cu), and silicon (Si) surfaces were irradiated with SXRL pulses having a wavelength of 13.9 nm and a duration of ～7 ps. Following irradiation, the surfaces of the substrates were observed using a scanning electron microscope and an atomic force microscope. With single pulse irradiation, ripple-like structures were formed on the Au and Cu surfaces. These structures were different from previously investigated conical structures formed on an Al surface. In addition, it was confirmed that the development of modified structures, i.e., growth of hillocks on the Au and Cu surfaces, was observed after multiple SXRL pulse exposures. However, on the Si surface, deep holes that seemed to be melted structures induced by the accumulation of multiple pulses of irradiations were found. Therefore, it was concluded that SXRL beam irradiation of various material surfaces causes different types of surface modifications, and the changes in the surface behaviors are attributed to the differences in the elemental properties, such as the attenuation length of x-ray photons.     

NMR-Based Approaches in the Study of Foods

In this review, the three different NMR-based approaches usually used to study foodstuffs are described, reporting specific examples. The first approach starts with the food of interest that can be investigated using different complementary NMR methodologies to obtain a comprehensive picture of food composition and structure; another approach starts with the specific problem related to a given food (frauds, safety, traceability, geographical and botanical origin, farming methods, food processing, maturation and ageing, etc.) that can be addressed by choosing the most suitable NMR methodology; finally, it is possible to start from a single NMR methodology, developing a broad range of applications to tackle common food-related challenges and different aspects related to foods.     

Equilibrium programming using proximal-like algorithms

We compute constrained equilibria satisfying an optimality condition. Important examples include convex programming, saddle problems, noncooperative games, and variational inequalities. Under a monotonicity hypothesis we show that equilibrium solutions can be found via iterative convex minimization. In the main algorithm each stage of computation requires two proximal steps, possibly using Bregman functions. One step serves to predict the next point; the other helps to correct the new prediction. To enhance practical applicability we tolerate numerical errors. Research supported partly by the Norwegian Research Council, project: Quantec 111039/401.     

Asymptotic behaviour of a family of gradient algorithms in ℝ d and Hilbert spaces

The asymptotic behaviour of a family of gradient algorithms (including the methods of steepest descent and minimum residues) for the optimisation of bounded quadratic operators in ℝ^d and Hilbert spaces is analyzed. The results obtained generalize those of Akaike (1959) in several directions. First, all algorithms in the family are shown to have the same asymptotic behaviour (convergence to a two-point attractor), which implies in particular that they have similar asymptotic convergence rates. Second, the analysis also covers the Hilbert space case. A detailed analysis of the stability property of the attractor is provided.     

Effect of Detachments in Asymmetric Simple Exclusion Processes

Asymmetric simple exclusion processes are important for understanding low-dimensional multi-particle dynamic phenomena. The effect of irreversible detachments of particles on dynamics of asymmetric simple exclusion processes is studied using analytical and computer simulation techniques. In the simplest model, where particles can only detach from a single site in the bulk of the system, a theory is presented and used to calculate explicitly phase diagrams and particle density profiles. The complexity of the phase behavior is discussed in terms of a recent domain-wall theory for driven lattice systems. The theoretical results qualitatively and quantitatively agree with computer Monte Carlo simulations.     

Generalizations of the odd degree theorem and applications

LetV ⊂ ℙℝ ⁿ be an algebraic variety, such that its complexificationV _ℂ ⊂ ℙ ⁿ is irreducible of codimensionm ≥ 1. We use a sufficient condition on a linear spaceL ⊂ ℙℝ ⁿ of dimensionm + 2r to have a nonempty intersection withV, to show that any six dimensional subspace of 5 × 5 real symmetric matrices contains a nonzero matrix of rank at most 3.     

Modulation of Gravity Waves with Shear in Water

The effect of water shear on the stability of infinitesimal perturbations (in the form of side bands) to a finite-amplitude gravity wave is investigated both numerically and analytically. The shear is modeled by a piecewise-linear velocity profile. Nonlinear cubic Schrödinger equation for the wave envelope of a slowly varying wave train is derived. It is shown that depending on the direction of propagation (along or against the shear) of the finite-amplitude waves, the effect of shear on the stability is substantially different. In most cases, however, the shear strength increase first enhances, but later suppresses, the instability.