Two-dimensional coordination polymers in rubidium and caesium complexes with orthanilic acid

The crystal structures of the rubidium and caesium complexes with 2-aminobenzenesulfonic acid (orthanilic acid), [Rb4(C6H6NO3S)4(H2O)]n (1) and [Cs(C6H6NO3S)]n (2) and have been determined at 200 K. Complex 1 has a repeating unit comprising four independent and different Rb coordination centres, (RbO8), (RbO7), (RbN2O4) and (RbO10), each having irregular stereochemistry and involving a number of bidentate chelate sulfonate-O,O’-metal and bridging interactions, giving a two-dimensional polymeric layered structure. Anhydrous complex 2 is also polymeric with the irregular (CsO7) coordination polyhedron comprising six sulfonate oxygen donors from three separate bidentate chelate sulfonate ligands and one monodentate bridging sulfonate oxygen, giving a two-dimensional layered structure.

The persistence of phase-separation in LiFePO4 with two-dimensional Li+ transport : the Cahn-Hilliard-reaction equation and the role of defects

We examine the solution of the two-dimensional Cahn-Hilliard-reaction (CHR) equation in the xy plane as a model of Li+ intercalation into LiFePO4 material. We validate our numerical solution against the solution of the depth-averaged equation, which has been used to model intercalation in the limit of highly orthotropic diffusivity and gradient penalty tensors. We then examine the phase-change behaviour in the full CHR system as these parameters become more isotropic, and find that as the Li+ diffusivity is increased in the x direction, phase separation persists at high currents, even in small crystals with averaged coherency strain included. The resulting voltage curves decrease monotonically, which has previously been considered a hallmark of crystals that fill homogeneously.

A preconditioned Lanczos method for space-fractional reaction-diffusion equations on two-dimensional unstructured meshes

We consider a two-dimensional space-fractional reaction diffusion equation with a fractional Laplacian operator and homogeneous Neumann boundary conditions. The finite volume method is used with the matrix transfer technique of Ilić et al. (2006) to discretise in space, yielding a system of equations that requires the action of a matrix function to solve at each timestep. Rather than form this matrix function explicitly, we use Krylov subspace techniques to approximate the action of this matrix function. Specifically, we apply the Lanczos method, after a suitable transformation of the problem to recover symmetry. To improve the convergence of this method, we utilise a preconditioner that deflates the smallest eigenvalues from the spectrum. We demonstrate the efficiency of our approach for a fractional Fisher’s equation on the unit disk.

Two novel numerical methods for solving the two-dimensional fractional Fitzhugh-Nagumo-monodomain model

Fractional mathematical models represent a new approach to modelling complex spatial problems in which there is heterogeneity at many spatial and temporal scales. In this paper, a two-dimensional fractional Fitzhugh-Nagumo-monodomain model with zero Dirichlet boundary conditions is considered. The model consists of a coupled space fractional diffusion equation (SFDE) and an ordinary differential equation. For the SFDE, we first consider the numerical solution of the Riesz fractional nonlinear reaction-diffusion model and compare it to the solution of a fractional in space nonlinear reaction-diffusion model. We present two novel numerical methods for the two-dimensional fractional Fitzhugh-Nagumo-monodomain model using the shifted Grunwald-Letnikov method and the matrix transform method, respectively. Finally, some numerical examples are given to exhibit the consistency of our computational solution methodologies. The numerical results demonstrate the effectiveness of the methods.

Computational analysis of laminated glass panels under blast loads: A comparison of two dimensional and three dimensional modelling approaches

This paper illustrates the use of finite element (FE) technique to investigate the behaviour of laminated glass (LG) panels under blast loads. Two and three dimensional (2D and 3D) modelling approaches available in LS-DYNA FE code to model LG panels are presented. Results from the FE analysis for mid-span deflection and principal stresses compared well with those from large deflection plate theory. The FE models are further validated using the results from a free field blast test on a LG panel. It is evident that both 2D and 3D LG models predict the experimental results with reasonable accuracy. The 3D LG models give slightly more accurate results but require considerably more computational time compared to the 2D LG models.

Two-dimensional graphene heterojunctions: The tunable mechanical properties

We report the mechanical properties of different two-dimensional carbon heterojunctions (HJs) made from graphene and various stable graphene allotropes, including α-, β-, γ- and 6612-graphyne (GY), and graphdiyne (GDY). It is found that all HJs exhibit a brittle behaviour except the one with α-GY, which however shows a hardening process due to the formation of triple carbon rings. Such hardening process has greatly deferred the failure of the structure. The yielding of the HJs is usually initiated at the interface between graphene and graphene allotropes, and monoatomic carbon rings are normally formed after yielding. By varying the locations of graphene (either in the middle or at the two ends of the HJs), similar mechanical properties have been obtained, suggesting insignificant impacts from location of graphene allotropes. Whereas, changing the types and percentages of the graphene allotropes, the HJs exhibit vastly different mechanical properties. In general, with the increasing graphene percentage, the yield strain decreases and the effective Young’s modulus increases. Meanwhile, the yield stress appears irrelevant with the graphene percentage. This study provides a fundamental understanding of the tensile properties of the heterojunctions that are crucial for the design and engineering of their mechanical properties, in order to facilitate their emerging future applications in nanoscale devices, such as flexible/stretchable electronics.

A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction–diffusion equations

Fractional differential equations have been increasingly used as a powerful tool to model the non-locality and spatial heterogeneity inherent in many real-world problems. However, a constant challenge faced by researchers in this area is the high computational expense of obtaining numerical solutions of these fractional models, owing to the non-local nature of fractional derivatives. In this paper, we introduce a finite volume scheme with preconditioned Lanczos method as an attractive and high-efficiency approach for solving two-dimensional space-fractional reaction–diffusion equations. The computational heart of this approach is the efficient computation of a matrix-function-vector product f(A)bf(A)b, where A A is the matrix representation of the Laplacian obtained from the finite volume method and is non-symmetric. A key aspect of our proposed approach is that the popular Lanczos method for symmetric matrices is applied to this non-symmetric problem, after a suitable transformation. Furthermore, the convergence of the Lanczos method is greatly improved by incorporating a preconditioner. Our approach is show-cased by solving the fractional Fisher equation including a validation of the solution and an analysis of the behaviour of the model.

Diagnostics and two-dimensional simulation of low-frequency inductively coupled plasmas with neutral gas heating and electron heat fluxes

This article presents the results on the diagnostics and numerical modeling of low-frequency (∼460 KHz) inductively coupled plasmas generated in a cylindrical metal chamber by an external flat spiral coil. Experimental data on the electron number densities and temperatures, electron energy distribution functions, and optical emission intensities of the abundant plasma species in low/intermediate pressure argon discharges are included. The spatial profiles of the plasma density, electron temperature, and excited argon species are computed, for different rf powers and working gas pressures, using the two-dimensional fluid approach. The model allows one to achieve a reasonable agreement between the computed and experimental data. The effect of the neutral gas temperature on the plasma parameters is also investigated. It is shown that neutral gas heating (at rf powers≥0.55kW) is one of the key factors that control the electron number density and temperature. The dependence of the average rf power loss, per electron-ion pair created, on the working gas pressure shows that the electron heat flux to the walls appears to be a critical factor in the total power loss in the discharge.

Reactive species in Ar+H2 plasma-aided nanofabrication : two-dimensional discharge modelling

Understanding the generation of reactive species in a plasma is an important step towards creating reliable and robust plasma-aided nanofabrication processes. A two-dimensional fluid simulation of the number densities of surface preparation species in a low-temperature, low-pressure, non-equilibrium Ar+H2 plasma is conducted. The operating pressure and H2 partial pressure have been varied between 70-200 mTorr and 0.1-50%, respectively. An emphasis is placed on the application of these results to nanofabrication. A reasonable balance between operating pressures and H 2 partial pressures that would optimize the number densities of the two working units largely responsible for activation and passivation of surface dangling bonds (Ar+ and H respectively) in order to achieve acceptable rates of surface activation and passivation is obtained. It is found that higher operating pressures (150-200 mTorr) and lower H2 partial pressures (∼5%) are required in order to ensure high number densities of Ar+ and H species. This paper contributes to the improvement of the controllability and predictability of plasma-based nanoassembly processes.

Two-dimensional simulation of nanoassembly precursor species in Ar+H2+C2H2 reactive plasmas

The results of two-dimensional fluid simulation of number densities and fluxes of the main building blocks and surface preparation species involved in nanoassembly of carbon-based nanopatterns in Ar+H2+C2H2 reactive plasmas are reported. It is shown that the process parameters and non-uniformity of surface fluxes of each particular species may affect the targeted nanopattern quality. The results can be used to improve predictability of plasma-aided nanofabrication processes and optimize the parameters of plasma nanotools.KGaA, Weinheim.

Two-dimensional simulation of nanoparticle deposition from high-density plasmas on microstructured surfaces

Selective and controlled deposition of plasma-grown nanoparticles is one of the pressing problems of plasma-aided nanofabrication. The results of advanced numerical simulations of motion of charge-variable nanoparticles in the plasma presheath and sheath areas and in localized microscopic electric fields created by surface microstructures are reported. Conditions for site-selective deposition of such nanoparticles onto individual microstructures and open surface areas within a periodic micropattern are formulated. The effects of plasma parameters, surface potential, and micropattern features on nanoparticle deposition are investigated and explained using particle charging and plasma force arguments. The results are generic and applicable to a broad range of nanoparticle-generating plasmas and practical problems ranging from management of nanoparticle contamination in microelectronics to site-selective nanoparticle deposition into specified device locations, and synthesis of advanced microporous materials and nanoparticle superlattices. © 2007 American Institute of Physics.