Mobility of small molecules in membrane materials based on copolyimide P84

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Lattice Boltzmann method for the fractional sub‐diffusion equation

A lattice Boltzmann model for the fractional sub‐diffusion equation is presented. By using the Chapman–Enskog expansion and the multiscale time expansion, several higher‐order moments of equilibrium distribution functions and a series of partial differential equations in different time scales are obtained. Furthermore, the modified partial differential equation of the fractional sub‐diffusion equation with the second‐order truncation error is obtained. In the numerical simulations, comparisons between numerical results of the lattice Boltzmann models and exact solutions are given. The numerical results agree well with the classical ones. Copyright © 2015 John Wiley & Sons, Ltd.     

Localization of temperature sensitive areas on analog circuits

We introduce a novel easy to apply method to detect critical temperature sensitive areas on analog circuits. Our method is based on heat diffusion on a silicon micro-chip: the corners of a temperature sensitive micro-chip are heated up directly by ESD diodes or infrared laser light. This heat stimulus at the corners results in an inhomogeneous temperature distribution. Thus, the temperature is a function in time and space. The elapsed time to change the chip status from “fail” to “pass” as a reaction to the heat stimulus correlates with the distance to the heat source. This correlation is extracted from COMSOL simulations and experimental results. A numerical program based on that correlation succeeded in localization of the temperature sensitive chip module.Micro-chips affected by corner MOSFETs in the subthreshold regime are used to demonstrate our method.     

Robust multilevel methods for quadratic finite element anisotropic elliptic problems

This paper discusses a class of multilevel preconditioners based on approximate block factorization for conforming finite element methods employing quadratic trial and test functions. The main focus is on diffusion problems governed by a scalar elliptic partial differential equation with a strongly anisotropic coefficient tensor. The proposed method provides a high robustness with respect to non‐grid‐aligned anisotropy, which is achieved by the interaction of the following components: (i) an additive Schur complement approximation to construct the coarse‐grid operator; (ii) a global block (Jacobi or Gauss–Seidel) smoother complementing the coarse‐grid correction based on (i); and (iii) utilization of an augmented coarse grid, which enhances the efficiency of the interplay between (i) and (ii). The performed analysis indicates the high robustness of the resulting two‐level method. Moreover, numerical tests with a nonlinear algebraic multilevel iteration method demonstrate that the presented two‐level method can be applied successfully in the recursive construction of uniform multilevel preconditioners of optimal or nearly optimal order of computational complexity. Copyright © 2013 John Wiley & Sons, Ltd.     

Molecule motion at polymer brush interfaces from single‐molecule experimental perspectives

Polymer brushes have been widely used as functional surface coatings for broad applications including antifouling, energy storage, and lubrications. Understanding the molecule dynamics at polymer brush interfaces is important in unraveling the structure–property relationships in these materials and establishing a new materials design paradigm of novel functional polymer thin films with efficient interfacial transport. By applying modern fluorescence‐based single‐molecule spectroscopic and microscopic techniques, molecule dynamics at varied polymer brush interfaces have been experimentally investigated in recent years. New insights are given to the understandings of some unique and unusual materials properties of polymer brush thin films. This review summarizes some recent studies of molecular diffusion at polymer brush interfaces, highlights some new understandings of the interfacial properties of polymer brushes, and discusses future research opportunities in this field. © 2013 Wiley Periodicals, Inc. J. Polym. Sci. Part B: Polym. Phys. 2014 , 52, 85–103     

Compressive advection and multi‐component methods for interface‐capturing

This paper develops methods for interface‐capturing in multiphase flows. The main novelties of these methods are as follows: (a) multi‐component modelling that embeds interface structures into the continuity equation; (b) a new family of triangle/tetrahedron finite elements, in particular, the P₁DG‐P₂(linear discontinuous between elements velocity and quadratic continuous pressure); (c) an interface‐capturing scheme based on compressive control volume advection methods and high‐order finite element interpolation methods; (d) a time stepping method that allows use of relatively large time step sizes; and (e) application of anisotropic mesh adaptivity to focus the numerical resolution around the interfaces and other areas of important dynamics. This modelling approach is applied to a series of pure advection problems with interfaces as well as to the simulation of the standard computational fluid dynamics benchmark test cases of a collapsing water column under gravitational forces (in two and three dimensions) and sloshing water in a tank. Two more test cases are undertaken in order to demonstrate the many‐material and compressibility modelling capabilities of the approach. Numerical simulations are performed on coarse unstructured meshes to demonstrate the potential of the methods described here to capture complex dynamics in multiphase flows. Copyright © 2015 John Wiley & Sons, Ltd.     

Exact Solution of a(2+1)-Dimensional Anisotropic Star in Finch and Skea Spacetime

We provide a new class of interior solution of a(2+1)-dimensional anisotropic star in Finch and Skea spacetime corresponding to the BTZ black hole. We develop the model by considering the MIT bag model EOS and a particular ansatz for the metric function grrproposed by Finch and Skea [M.R. Finch and J.E.F. Skea, Class. Quantum.Grav. 6(1989) 467]. Our model is free from central singularity and satisfies all the physical requirements for the acceptability of the model.     

Facile Fabrication of Well‐Dispersed Pt Nanoparticles in Mesoporous Silica with Large Open Spaces and Their Catalytic Applications

In this paper, a facile strategy is reported for the preparation of well‐dispersed Pt nanoparticles in ordered mesoporous silica (Pt@OMS) by using a hybrid mesoporous phenolic resin‐silica nanocomposite as the parent material. The phenolic resin polymer is proposed herein to be the key in preventing the aggregation of Pt nanoparticles during their formation process and making contributions both to enhance the surface area and enlarge the pore size of the support. The Pt@OMS proves to be a highly active and stable catalyst for both gas‐phase oxidation of CO and liquid‐phase hydrogenation of 4‐nitrophenol. This work might open new avenues for the preparation of noble metal nanoparticles in mesoporous silica with unique structures for catalytic applications.     

Polymer chain diffusion in polymer blends: A theoretical interpretation based on a memory function formalism

The diffusion of polymer chains in miscible polymer blends with large dynamic asymmetry—those where the two blend components display very different segmental mobility—is not well understood yet. In the extreme case of the blend system of poly(ethylene oxide) (PEO) and poly(methyl methacrylate)(PMMA), the diffusion coefficient of PEO chains in the blend can change by more than five orders of magnitude while the segmental time scale hardly changes with respect to that of pure PEO. This behavior is not observed in blend systems with small or moderate dynamic asymmetry as, for instance, polyisoprene/poly(vinyl ethylene) blends. These two very different behaviors can be understood and quantitatively explained in a unified way in the framework of a memory function formalism, which takes into account the effect of the collective dynamics on the chain dynamics of a tagged chain. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1239–1245