Synchrotron FTIR microscopy of synthetic and natural CO2–H2O fluid inclusions

Fluid inclusions provide a record of the physical and chemical composition of fluids that flow through the Earth's crust. Here, we describe a novel use of synchrotron Fourier Transform Infrared (FTIR) microscopy to map three parameters in individual fluid inclusions: (1) very low concentrations of CO₂, (2) variations of the state of CO₂ and (3) variations in water structure. The intensity of the synchrotron light source allows compositional mapping of individual fluid inclusions, which provides high-resolution images of the distribution of different CO₂ and H₂O species within individual inclusions. High resolution spectra of the CO₂, recorded here for the first time in fluid inclusions, show the rotational lines of CO₂ gas. The results reveal predicted as well as unexpected distributions of CO₂ gas in the inclusions.     

Nonsmooth Lyapunov pairs for infinite-dimensional first-order differential inclusions

The main objective of this paper is to provide new explicit criteria to characterize weak lower semicontinuous Lyapunov pairs or functions associated to first-order differential inclusions in Hilbert spaces. These inclusions are governed by a Lipschitzian perturbation of a maximally monotone operator. The dual criteria we give are expressed by means of the proximal and basic subdifferentials of the nominal functions while primal conditions are described in terms of the contingent directional derivative. We also propose a unifying review of many other criteria given in the literature. Our approach is based on advanced tools of variational analysis and generalized differentiation.     

Stability analysis for periodic solution of BAM neural networks with discontinuous neuron activations and impulses

In this paper, we present a general class of BAM neural networks with discontinuous neuron activations and impulses. By using the fixed point theorem in differential inclusions theory, we investigate the existence of periodic solution for this neural network. By constructing the suitable Lyapunov function, we give a sufficient condition which ensures the uniqueness and global exponential stability of the periodic solution. The results of this paper show that the Forti’s conjecture is true for BAM neural networks with discontinuous neuron activations and impulses. Further, a numerical example is given to demonstrate the effectiveness of the results obtained in this paper.     

System of generalized resolvent equations with corresponding system of variational inclusions

The purpose of this paper is to introduce a new system of generalized resolvent equations with corresponding system of variational inclusions in uniformly smooth Banach spaces. We establish an equivalence relation between system of generalized resolvent equations and system of variational inclusions. The iterative algorithms for finding the approximate solutions of system of generalized resolvent equations are proposed. The convergence of approximate solutions of system of generalized resolvent equations obtained by the proposed iterative algorithm is also studied.      

General implicit variational inclusion problems based on A-maximal (m)-relaxed monotonicity (AMRM) frameworks

A general framework for an algorithmic procedure based on the variational convergence of operator sequences involving A-maximal (m)-relaxed monotone (AMRM) mappings in a Hilbert space setting is developed, and then it is applied to approximating the solution of a general class of nonlinear implicit inclusion problems involving A-maximal (m)-relaxed monotone mappings. Furthermore, some specializations of interest on existence theorems and corresponding approximation solvability theorems on H-maximal monotone mappings are included that may include several other results for general variational inclusion problems on general maximal monotonicity in the literature.     

Micro‐Raman investigations on inclusions of unusual habit in a commercial tanzanite gemstone

The vibrational properties of submillimetre size inclusions of unusual habit in a commercial tanzanite gemstone were investigated by confocal Raman microspectroscopy with the aim of probing both their chemical composition and crystal structure. Highly contrasted Raman spectra were recorded in confocal conditions from several inclusions incorporated at different depths, ranging between a few microns to some tens of microns beneath the gemstone surface. The observed spectral features were identified as specific markers of hematite (α‐Fe₂O₃). Their unambiguous assignment has been inferred by comparing our experimental findings with the literature data recorded either in single crystals of hematite or in other iron oxides and oxyhydroxides. Our results rule out the presence of any pseudomorphic variety of hematite in the investigated gemstone, while confocal micro‐Raman spectroscopy definitively proved itself as a very reliable, relatively costless and noninvasive tool for unambiguous identification of subsurface regions of gemstones. Copyright © 2011 John Wiley & Sons, Ltd.     

Large complete band gap in two-dimensional phononic crystal slabs with elliptic inclusions

Phononic band structure with periodic elliptic inclusions for the square lattice is investigated based on the plane wave expansion method. The numerical results show the systems composed of tungsten (W) elliptic rods embedded in a silicon (Si) matrix can exhibit a larger complete band gap than the conventional circular phononic crystal (PC) slabs. The phononic band structure of the plate-mode waves and the width of the first complete band gap can be tuned by varying the ratio of the minor axis and the major axis, the orientation angle of the elliptic rods and the thickness of the PC slabs. We also study the band structure of plate-mode waves propagating in two-dimensional (2D) slabs with periodic elliptic inclusions coated on uniform substrate.     

Two optical bistability domains in composites of metal nanoparticles with nonlinear dielectric core

It is shown that the local field in metal spherical particles with a dielectric core in an external varying electric field has two maxima at two different frequencies. The second maximum becomes more important with an increment in the metal fraction. Due to the nonlinear dielectric function of the core, the composite of these inclusions may have two optically induced bistability domains at different frequencies. At rather high metal fraction, two bistability domains merge and form one entire bistability domain. The parameters of these domains are studied numerically. The paper focuses on the second bistability domain, which has not been discussed in the literature so far. This domain exists in a comparatively narrow frequency range and its onset fields are lower than those of the first bistability domain. The lowest bistability onset fields are obtained in the entire domain. This peculiarity of the optical induced bistability in the metal composite with small dielectric cores can be attractive for possible applications.     

Detection of small amounts of H2O in CO2‐rich fluid inclusions using Raman spectroscopy

Raman spectroscopic analysis at low (−100 °C) or high (100–200 °C) temperature is shown to be effective for detecting small amounts of H₂O in CO₂‐rich fluid inclusions from the deep lithosphere, which have previously been thought to be water‐free. Copyright © 2009 John Wiley & Sons, Ltd.     

A higher order method for input-affine uncertain systems

Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide several theoretical improvements to the algorithm, including its extension to piecewise constant and sinusoidal approximations of uncertain inputs, updates on the affine approximation bounds and a generalized formula for the analytical error. The approach proposed is able to achieve higher order convergence with respect to the current state-of-the-art. We implemented the methodology in Ariadne, a library for the verification of continuous and hybrid systems. For evaluation purposes, we introduce ten systems from the literature, with varying degrees of nonlinearity, number of variables and uncertain inputs. The results are hereby compared with two state-of-the-art approaches to time-varying uncertainties in nonlinear systems.