High‐order ADER‐WENO ALE schemes on unstructured triangular meshes—application of several node solvers to hydrodynamics and magnetohydrodynamics

In this paper, we present a class of high‐order accurate cell‐centered arbitrary Lagrangian–Eulerian (ALE) one‐step ADER weighted essentially non‐oscillatory (WENO) finite volume schemes for the solution of nonlinear hyperbolic conservation laws on two‐dimensional unstructured triangular meshes. High order of accuracy in space is achieved by a WENO reconstruction algorithm, while a local space–time Galerkin predictor allows the schemes to be high order accurate also in time by using an element‐local weak formulation of the governing PDE on moving meshes. The mesh motion can be computed by choosing among three different node solvers, which are for the first time compared with each other in this article: the node velocity may be obtained either (i) as an arithmetic average among the states surrounding the node, as suggested by Cheng and Shu, or (ii) as a solution of multiple one‐dimensional half‐Riemann problems around a vertex, as suggested by Maire, or (iii) by solving approximately a multidimensional Riemann problem around each vertex of the mesh using the genuinely multidimensional Harten–Lax–van Leer Riemann solver recently proposed by Balsara et al. Once the vertex velocity and thus the new node location have been determined by the node solver, the local mesh motion is then constructed by straight edges connecting the vertex positions at the old time level tⁿ with the new ones at the next time level t^{n + 1}. If necessary, a rezoning step can be introduced here to overcome mesh tangling or highly deformed elements. The final ALE finite volume scheme is based directly on a space–time conservation formulation of the governing PDE system, which therefore makes an additional remapping stage unnecessary, as the ALE fluxes already properly take into account the rezoned geometry. In this sense, our scheme falls into the category of direct ALE methods. Furthermore, the geometric conservation law is satisfied by the scheme by construction. We apply the high‐order algorithm presented in this paper to the Euler equations of compressible gas dynamics as well as to the ideal classical and relativistic magnetohydrodynamic equations. We show numerical convergence results up to fifth order of accuracy in space and time together with some classical numerical test problems for each hyperbolic system under consideration. Copyright © 2014 John Wiley & Sons, Ltd.     

How Does Solvation Affect the Binding of Hydrophilic Amino Saccharides to Cucurbit[7]uril with Exceptional Anomeric Selectivity?

Cucurbit[7]uril (CB[7]) is known to bind strongly to hydrophilic amino saccharide guests with exceptional α‐anomer selectivities under aqueous conditions. Single‐crystal X‐ray crystallography and computational methods were used to elucidate the reason behind this interesting phenomenon. The crystal structures of protonated galactosamine (GalN) and glucosamine (GluN) complexes confirm the inclusion of α anomers inside CB[7] and disclose the details of the host–guest binding. Whereas computed gas‐phase structures agree with these crystal structures, gas‐phase binding free energies show preferences for the β‐anomer complexes over their α counterparts, in striking contrast to the experimental results under aqueous conditions. However, when the solvation effect is considered, the binding structures drastically change and the preference for the α anomers is recovered. The α anomers also tend to bind more tightly and leave less space in the CB[7] cavity toward inclusion of only one water molecule, whereas loosely bound β anomers leave more space toward accommodating two water molecules, with markedly different hydrogen‐bonding natures. Surprisingly, entropy seems to contribute significantly to both anomeric discrimination and binding. This suggests that of all the driving factors for the strong complexation of the hydrophilic amino saccharide guests, water mediation plays a crucial role in the anomer discrimination.     

Molecular dynamics simulation of poly(3‐hexylthiophene) helical structure In Vacuo and in amorphous polymer surrounding

The stability of poly(3‐hexylthiophene) (P3HT) helical structure has been investigated in vacuo and in amorphous polymer surrounding via molecular dynamics‐based simulations at temperatures below and above the P3HT melting point. The results show that the helical chain remains stable at room temperature both in vacuo and in amorphous surrounding, and promptly loses its structure at elevated temperatures. However, the amorphous surrounding inhibits the destruction of the helix at higher temperatures. In addition, it is shown that the electrostatic interactions do not significantly affect the stability of the helical structure. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2448–2456     

Capturing Transient Endoperoxide in the Singlet Oxygen Oxidation of Guanine

The chemistry of singlet O₂ toward the guanine base of DNA is highly relevant to DNA lesion, mutation, cell death, and pathological conditions. This oxidative damage is initiated by the formation of a transient endoperoxide through the Diels–Alder cycloaddition of singlet O₂ to the guanine imidazole ring. However, no endoperoxide formation was directly detected in native guanine or guanosine, even at ?100 °C. Herein, gas‐phase ion–molecule scattering mass spectrometry was utilized to capture unstable endoperoxides in the collisions of hydrated guanine ions (protonated or deprotonated) with singlet O₂ at ambient temperature. Corroborated by results from potential energy surface exploration, kinetic modeling, and dynamics simulations, various aspects of endoperoxide formation and transformation (including its dependence on guanine ionization and hydration states, as well as on collision energy) were determined. This work has pieced together reaction mechanisms, kinetics, and dynamics data concerning the early stage of singlet O₂ induced guanine oxidation, which is missing from conventional condensed‐phase studies.     

Molecular dynamics simulations of monodisperse/bidisperse polymer melt crystallization

We use large scale coarse‐grained molecular dynamics simulations to study the kinetics of polymer melt crystallization. For monodisperse polymer melts of several chain lengths under various cooling protocols, we show that short chains have a higher terminal crystallinity value compared to longer ones. They align at the early stages and then cease evolving. Long chains, however, align, fold into lamella structures and then slowly optimize their dangling ends for the remaining simulation time. We then identify the mechanism behind bidisperse blend crystallization. To this end, we introduce a new algorithm (called Individual Chain Crystallinity) that allows the calculation of the crystallinity separately for short and long chains in the blend. We find that, in general, bidispersity hinders crystallization significantly. At first the crystallinity of the long chain components exceeds that of the monodisperse melt, but subsequently falls below the corresponding monodisperse melt curve after a certain “crossover time.” The time of the crossover can be attributed to the time required for the full crystallization of the short chains. This indicates that at the early stages the short chains are helping long chains to crystallize. However, after all short chains have crystallized they start to hinder the crystallization of the long chains by obstructing their motion. Lastly, polymer crystallization upon various thermodynamic protocols is studied. Slower cooling is found to increase the crystallinity value. Upon an instantaneous deep quench and subsequent isothermal relaxation, the crystallinity grows rapidly with time at early stages and subsequently saturates. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2318–2326     

Mechanical properties and thermal conductivity of the twisted graphene nanoribbons

Molecular dynamics method was used to simulate the twists of four GNRs (graphene nanoribbons), two AGNRs (armchair GNRs), and two ZGNRs (zigzag GNRs). Thermal conductivity of the length-fixing GNRs under torsion and at high temperature was calculated. It is found that the ZGNRs have better torsional rigidity than the AGNRs; under the torsional deformation of 34.2°/nm local buckling occurs in the length-fixing GNRs, and under the deformation of 22.8°/nm overall buckling occurs in the ones with free-length. In the range of investigated twist-angle and temperature, the thermal conductivity of the length-fixing GNRs decreases with the increase of torsional deformation and temperature. The wider GNRs have better anti-torsion capability and thermal conductivity.     

Modification of hydrophilic channels in Nafion membranes by DMBA: Mechanism and effects on proton conductivity

Modification of proton conductive channels (PCCs) in Nafion has been achieved with the assistance of 3, 4‐dimethylbenzaldehyde (DMBA). During annealing, ionic clusters develop from small isolated spheres (1.72 nm) to wide continuous channels (5.15 nm), and the crystallinity of Nafion/DMBA membranes is also improved from 17% to 32% as shown by X‐ray diffraction. Molecular dynamic simulation reveals that hydrogen bonding and hydrophobic interaction between DMBA and Nafion work synergistically to achieve better phase separation. The morphology–property relationship shows that, versus various PCCs width, the corresponding proton conductivities vary greatly from 0.079 to 0.139 S/cm at 80 °C. By carefully tuning the width of PCCs, the proton conductivity shows an improvement of 22–34% as compared with pristine Nafion. A significant enhancement on the maximum power density is achieved for the membrane electrode assembly on Nafion/DMBA‐8h (as high as 1018 mW/cm^?2), yielding an enhancement of 39% on pristine Nafion‐8h (730 mW/cm^?2). © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 52, 1107–1117     

A superconvergent universality induced by non-associativity

The star products in symbolic dynamics, as effective algebraic operations for describing self-similar bifurcation structure in classical dynamical systems, are found to have either associativity or non-associativity. In this Letter, non-associative star products in trimodal iterative dynamical systems are considered. As the left and right operations have different effects, right-associative star products break the conventional Feigenbaum's metric universality. Through high precision parallel computation, it is found that period-p-tupling bifurcation processes described by right-associative star products exhibit a superconvergent universality of double exponential form.     

Global dynamics of a reaction–diffusion system with mass conservation

We study global dynamics of a mass conserved reaction–diffusion system. First, we show the global-in-time existence of the solution with compact orbit. Then the dynamical stability of local minima associated with a variational function is proven.     

Highly Selective Zeolite Topologies for Flue Gas Separation

The separation of carbon dioxide from flue gas is essential for the reduction of greenhouse gas emissions. In adsorptive methods, the challenge lies in the choice of suitable porous materials. Among all zeolite topologies, a number of adsorbents with pore dimensions in the range of the guest molecules were identified to allow an excellent separation by diffusion, and MRE and AFO zeolite topologies appear to be the best candidates based on equilibrium adsorption. Also, it was found that the behavior of this gas mixture in DFT and APD zeolites differed from the normal behavior.