Fractional powers of the noncommutative Fourier's law by the S‐spectrum approach

Let e_?, for ? = 1,2,3, be orthogonal unit vectors in and let be a bounded open set with smooth boundary ?Ω. Denoting by a point in Ω, the heat equation, for nonhomogeneous materials, is obtained replacing the Fourier law, given by the following: into the conservation of energy law, here a, b, are given functions. With the S‐spectrum approach to fractional diffusion processes we determine, in a suitable way, the fractional powers of T. Then, roughly speaking, we replace the fractional powers of T into the conservation of energy law to obtain the fractional evolution equation. This method is important for nonhomogeneous materials where the Fourier law is not simply the negative gradient. In this paper, we determine under which conditions on the coefficients a, b, the fractional powers of T exist in the sense of the S‐spectrum approach. More in general, this theory allows to compute the fractional powers of vector operators that arise in different fields of science and technology. This paper is devoted to researchers working in fractional diffusion and fractional evolution problems, partial differential equations, and noncommutative operator theory.     

Well-posedness of an evolution problem with nonlocal diffusion

We prove the well-posedness of a general evolution reaction–nonlocal diffusion problem under two sets of assumptions. In the first set, the main hypothesis is the Lipschitz continuity of the range kernel and the bounded variation of the spatial kernel and the initial datum. In the second set of assumptions, we relax the Lipschitz continuity of the range kernel to Hölder continuity, and assume monotonic behavior. In this case, the spatial kernel and the initial data can be just integrable functions. The main applications of this model are related to the fields of Image Processing and Population Dynamics.     

On uniform propagation of chaos

In this paper we obtain a time-uniform propagation estimate for a system of interacting diffusion processes. Using a well defined metric function h , our result guarantees a time-uniform estimate for the convergence of a class of interacting stochastic differential equations towards their mean field limit, under conditions that ensure that the decay associated to the internal dynamics term dominates the interaction and noise terms. Our result should have diverse applications, particularly in neuroscience, and allows for models more elaborate than the one of Wilson and Cowan. In particular, the internal dynamics need not be that of linear decay.     

Generic applications of 13C‐detected NMR diffusion to formulated systems with suppression of thermal convection induced by proton decoupling

Fast and effective structural/compositional analysis on formulated systems represents one of the major challenges encountered in analytical science. ¹³C‐detected diffusion represents a promising tool to tackle the aforementioned challenges, particularly in industry. Toward exploring the generic applications of ¹³C‐detected diffusion, thermal convection induced by ¹H decoupling has been identified as a key factor that resulted in significantly reduced resolution in the diffusion dimension. Optimization of experimental parameters and utilization of double‐stimulated echo‐based pulse sequence both can effectively suppress the thermal convection caused by the ¹H decoupling, the success of which allows robust and generic applications of ¹³C‐detected diffusion to systems from mixtures of small molecules, polymer blends, and copolymers to actual complex formulated systems. The method is particularly powerful in differentiating small molecules from polymers, polymer blends from copolymers, and end‐group analysis. Copyright © 2016 John Wiley & Sons, Ltd.     

氦气提纯技术发展现状与应用分析

为实现氦气资源的循环利用,有必要对氦气进行回收纯化。文中对目前国内外氦气的提纯技术发展现状进行了分析介绍,并综合分析比较了这些方法的应用原理、优缺点及发展趋势,针对各自的使用特点,给出了几种详细的提纯工艺实现方法,为促进我国氦气提纯技术的发展提供了新的思路。     

Studium der Abbaugeschwindigkeit der Oberfläche von markierten festen Stoffen zwecks reaktionskinetischer Untersuchungen, 2. Mitt.: Anwendung von mittels Diffusionstechnik hergestellten Trägern

Eine der oft angewandten Möglichkeiten der Markierung fester Träger mit gasförmigen Tracern ist die Diffusionstechnik. Die mit dieser Technik hergestellten Träger wurden zu reaktionskinetischen und analytischen Bestimmungen herangezogen. Im vorliegenden Artikel werden die Grenzen und die Möglichkeiten der Anwendung dieser Träger anhand der in der früheren Mitteilung abgeleiteten allgemeinen Erwägungen theoretisch begründet.