Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—theory

This paper is concerned with the development of an improved second-order homogenization method incorporating field fluctuations for nonlinear composite materials. The idea is to combine the desirable features of two different, earlier methods making use of “linear comparison composites”, the properties of which are chosen optimally from suitably designed variational principles. The first method (Ponte Castañeda, J. Mech. Phys. Solids 39 (1991) 45) makes use of the “secant” moduli of the phases, evaluated at the second moments of the strain field over the phases, and delivers bounds, but these bounds are only exact to first-order in the heterogeneity contrast. The second method (Ponte Castañeda, J. Mech. Phys. Solids 44 (1996) 827) makes use of the “tangent” moduli, evaluated at the phase averages (or first moments) of the strain field, and yields estimates that are exact to second-order in the contrast, but that can violate the bounds in some special cases. These special cases turn out to correspond to situations, such as percolation phenomena, where field fluctuations, which are captured less accurately by the second-order method than by the bounds, become important. The new method delivers estimates that are exact to second-order in the contrast, making use of generalized secant moduli incorporating both first- and second-moment information, in such a way that the bounds are never violated. Some simple applications of the new theory are given in Part II of this work.     

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.     

Asymptotic behavior of the conducting properties of high-contrast media

The asymptotic-shielding effect and the asymptotic behavior of the conductivity of a medium containing closely spaced, perfectly conducting inclusions. It is proved that in the presence of asymptotic shielding for pairs of adjacent particles, the original continuous problem can be approximated by a finite-dimensional problem. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 128–140, May–June, 2005.     

On the Shape of the Eshelby Inclusions

It is shown, based on properties of analytic functions, that for inclusions of constant eigenstrain and eigenstress that the shape of the inclusion is restricted and any part of a plane (i.e. polyhedral inclusion) is prohibited. This revised version was published online in August 2006 with corrections to the Cover Date.     

Stability of shells of revolution made of a particulate composite with nonlinear elastic inclusions and damageable matrix

The bifurcation instability problem for shells of revolution made of particulate composites with nonlinear elastic inclusions and damageable matrix is formulated and solved __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 55–65, November 2007.     

Multiple Solutions for a Differential Inclusion Problem with Nonhomogeneous Boundary Conditions

In this paper, we use a mountain pass theorem with Cerami type conditions for locally Lipschitz functions to investigate the existence of at least one nontrivial solution for a differential inclusion problem involving the p-Laplacian and with nonlinear and nonsmooth boundary conditions. Moreover, by a symmetric version of the mountain pass theorem, we prove the existence of infinitely many solutions.     

Discretizations of Linear Elliptic Partial Differential Inclusions

Differential inclusions provide a suitable framework for modelling choice and uncertainty. In finite dimensions, the theory of ordinary differential inclusions and their numerical approximations is well-developed, whereas little is known for partial differential inclusions, which are the deterministic counterparts of stochastic partial differential equations.

The aim of this article is to analyze strategies for the numerical approximation of the solution set of a linear elliptic partial differential inclusion. The geometry of its solution set is studied, numerical methods are proposed, and error estimates are provided.     

原位低温拉曼光谱技术在储层流体包裹体分析中的应用

准确获取流体包裹体中盐的类型一直是包裹体研究的重要问题。采用原位低温拉曼光谱技术对民丰洼陷深部天然气储层流体包裹体进行了分析。常温拉曼光谱综合分析表明,包裹体中流体为含甲烷的盐水溶液。在—180℃下对包裹体进行了原位低温拉曼光谱分析,结果显示包裹体中含有NaCl,CaCl_2,MgCl_2等盐类,其中以NaCl为主,CaCl_2含量很少,MgCl_2含量极少。根据沉积成岩过程分析了包裹体中流体的成因,解释了储层成岩作用的机理。研究结果表明,原位低温拉曼光谱是获取储层包裹体中流体性质的一种有效方法。在包裹体原位低温拉曼光谱分析技术基础上,结合沉积成岩过程,可以给储层的成岩作用类型和成岩反应机理给出重要证据。     

Controllability Results for Semilinear Evolution Inclusions with Nonlocal Conditions

In this paper, we prove controllabillity results for mild solutions defined on a compact real interval for first-order semilinear differential and integrodifferential evolution inclusions in Banach spaces with nonlocal conditions. By using suitable fixed-point theorems, we study the cases when the multivalued map has convex values as well as nonconvex values.