All organic host-guest crystals based on a dumb-bell-shaped conjugated host for light harvesting through resonant energy transfer

Together we glow: Fully organic host-guest crystals with two dyes inserted in their parallel nanochannels display broad emission in the visible range thanks to resonant energy transfer. The conjugated host crystal provides light harvesting in the UV region.     

Conformity and precision of CO2 densimetry in CO2 inclusions: microthermometry versus Raman microspectroscopic densimetry

To assess the ability of densimetry for CO₂ fluid in CO₂ inclusions, we compare two methods, microthermometry and Raman microspectroscopic densimetry for CO₂. The comparative experiment was performed for nine CO₂ inclusions in three mantle xenoliths. The results are as follows: (1) microthermometry precisely determines CO₂ density with the range of 0.65 to 1.18 g/cm³ compared with Raman microspectroscopic densimetry; (2) CO₂ density obtained by Raman microspectroscopic densimetry is fairly consistent with that by microthermometry; (3) it is hard to determine CO₂ density in CO₂ inclusion with diameter of less than around 3 µm using microthermometry; and (4) microthermometry can be applied only to the CO₂ inclusion whose CO₂ density ranges from around 0.65 to 1.18 g/cm³, whereas the Raman microspectroscopic densimetry is applicable to CO₂ density ranging from 0.1 to 1.24 g/cm³. The above features carry the potential for estimation of depth origin of mantle‐derived rocks. The depth where the rocks were trapped by host magma can be estimated using both geothermometric data and CO₂ fluid density in CO₂ inclusions in the rocks. Typical precisions of density of CO₂ in CO₂ inclusions obtained by the Raman microspectroscopic densimetry (~0.01 g/cm³) and by the microthermometry (< 0.001 g/cm³) correspond to uncertainties in the depth origin of 2.4 km and < 1.7 km, respectively, at 1000 ± 50 °C. In case of the mantle under 750–1250 °C and 1 GPa, the CO₂ fluid has a density ranging from 1.06 g/cm³ to 1.21 g/cm³, which are well measured by the Raman microspectroscopic densimetry. Combination of both densimetries for CO₂ in mantle minerals elucidates the deep structure of the Earth. Copyright © 2012 John Wiley & Sons, Ltd.     

Disordered elastic systems and one-dimensional interfaces

We briefly introduce the generic framework of disordered elastic systems (DES), giving a short ‘recipe’ of a DES modeling and presenting the quantities of interest in order to probe the static and dynamical disorder-induced properties of such systems. We then focus on a particular low-dimensional DES, namely the one-dimensional interface in short-ranged elasticity and short-ranged quenched disorder. Illustrating different elements given in the introductory sections, we discuss specifically the consequences of the interplay between a finite temperature T>0$T>0$ and a finite interface width ξ>0$\xi >0$ on the static geometrical fluctuations at different lengthscales, and the implications on the quasistatic dynamics.     

On the Elastic Modulus of Powders

For the design of silos and similar equipment for storage, handling and processing of particulate materials, a thorough understanding of the mechanical behaviour of powders is of great importance. Whereas strength properties of powders have been investigated by many workers, the elastic behaviour at small deformations has been much less in focus. In that respect, a simple preliminary theory of uniaxial elasticity has been derived for particles, based on a simple system of spherical and monosized particles of a homogenous and elastically isotropic material. The equation σ = E_p?_el² gives the relationship between stress, elastic modulus and elastic deformation for the unloading of a given powder at a specific consolidation stress/ compression level. Comparisons with experimental results of real powders in a uniaxial tester show surprisingly good agreement in many cases. The equation seems to describe the elasticity of powders fairly well, although it is only a preliminary derivation based on simple considerations.     

Approximating a Zero of Sum of Two Monotone Operators Which Solves a Fixed Point Problem in Reflexive Banach Spaces

Abstract

The purpose of this paper is to introduce an iterative method for approximating a point in the set of zeros of the sum of two monotone mappings, which is also a solution of a fixed point problem for a Bregman strongly nonexpansive mapping in a real reflexive Banach space. With our iterative technique, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a variational inclusion problem for sum of two monotone mappings and the set of solutions of a fixed point problem for Bregman strongly nonexpansive mapping. We give applications of our result to convex minimization problem, convex feasibility problem, variational inequality problem, and equilibrium problem. Our result complements and extends some recent results in literature.     

A differential inclusion-based approach for solving nonsmooth convex optimization problems

This article presents a differential inclusion-based neural network for solving nonsmooth convex programming problems with inequality constraints. The proposed neural network, which is modelled with a differential inclusion, is a generalization of the steepest descent neural network. It is proved that the set of the equilibrium points of the proposed differential inclusion is equal to that of the optimal solutions of the considered optimization problem. Moreover, it is shown that the trajectory of the solution converges to an element of the optimal solution set and the convergence point is a globally asymptotically stable point of the proposed differential inclusion. After establishing the theoretical results, an algorithm is also designed for solving such problems. Typical examples are given which confirm the effectiveness of the theoretical results and the performance of the proposed neural network.     

New algorithms for the split variational inclusion problems and application to split feasibility problems

ABSTRACT

In this paper, we suggest two new iterative methods for finding an element of the solution set of split variational inclusion problem in real Hilbert spaces. Under suitable conditions, we present weak and strong convergence theorems for these methods. We also apply the proposed algorithms to study the split feasibility problem. Finally, we give some numerical results which show that our proposed algorithms are efficient and implementable from the numerical point of view.