An efficient edge based data structure for the compressible Reynolds-averaged Navier–Stokes equations on hybrid unstructured meshes

An efficient edge based data structure has been developed in order to implement an unstructured vertex based finite volume algorithm for the Reynolds-averaged Navier–Stokes equations on hybrid meshes. In the present approach, the data structure is tailored to meet the requirements of the vertex based algorithm by considering data access patterns and cache efficiency. The required data are packed and allocated in a way that they are close to each other in the physical memory. Therefore, the proposed data structure increases cache performance and improves computation time. As a result, the explicit flow solver indicates a significant speed up compared to other open-source solvers in terms of CPU time. A fully implicit version has also been implemented based on the PETSc library in order to improve the robustness of the algorithm. The resulting algebraic equations due to the compressible Navier–Stokes and the one equation Spalart–Allmaras turbulence equations are solved in a monolithic manner using the restricted additive Schwarz preconditioner combined with the FGMRES Krylov subspace algorithm. In order to further improve the computational accuracy, the multiscale metric based anisotropic mesh refinement library PyAMG is used for mesh adaptation. The numerical algorithm is validated for the classical benchmark problems such as the transonic turbulent flow around a supercritical RAE2822 airfoil and DLR-F6 wing-body-nacelle-pylon configuration. The efficiency of the data structure is demonstrated by achieving up to an order of magnitude speed up in CPU times.     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Maximal Subrings and Covering Numbers of Finite Semisimple Rings

We classify the maximal subrings of the ring of n×n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring.     

A simple three‐wave approximate Riemann solver for the Saint‐Venant‐Exner equations

Erosion and sediments transport processes have a great impact on industrial structures and on water quality. Despite its limitations, the Saint‐Venant‐Exner system is still (and for sure for some years) widely used in industrial codes to model the bedload sediment transport. In practice, its numerical resolution is mostly handled by a splitting technique that allows a weak coupling between hydraulic and morphodynamic distinct softwares but may suffer from important stability issues. In recent works, many authors proposed alternative methods based on a strong coupling that cure this problem but are not so trivial to implement in an industrial context. In this work, we then pursue 2 objectives. First, we propose a very simple scheme based on an approximate Riemann solver, respecting the strong coupling framework, and we demonstrate its stability and accuracy through a number of numerical test cases. However, second, we reinterpret our scheme as a splitting technique and we extend the purpose to propose what should be the minimal coupling that ensures the stability of the global numerical process in industrial codes, at least, when dealing with collocated finite volume method. The resulting splitting method is, up to our knowledge, the only one for which stability properties are fully demonstrated.     

Time-dependent Ginzburg–Landau equations for multi-gap superconductors

We numerically solve the time-dependent Ginzburg–Landau equations for two-gap superconductors using the finite-element technique. The real-time simulation shows that at low magnetic field, the vortices in small-size samples tend to form clusters or other disorder structures. When the sample size is large, stripes appear in the pattern. These results are in good agreement with the previous experimental observations of the intriguing anomalous vortex pattern, providing a reliable theoretical basis for the future applications of multi-gap superconductors.     

Effect of additive length and chemistry on the morphology of blends of conjugated thiophenes and fullerene derivative acceptor molecules

Small molecule additives have been shown to increase the device efficiency of conjugated polymer (donor) and fullerene derivative (acceptor) based organic solar cells by modifying the morphology of the device active layer. In this paper we conduct a systematic study of how additives affect the donor‐acceptor morphology using molecular dynamics simulations of blends of thiophene‐based oligomers, mimicking poly(3‐dodecylthiophene) (P3DDT) or poly(2,2′:5′,2”‐3,3”‐didocyl‐terthiophene) (PTTT), and fullerene derivatives with additives of varying length and chemical functionalization, mimicking experimentally used additives like methyl ester additives, diiodooctane, and alkanedithiols. We find that functionalization of additives with end groups that are attracted to acceptor molecules are necessary to induce increased donor‐acceptor macrophase separation. In blends where acceptors intercalate between oligomer alkyl side chains, functionalized additives decrease acceptor intercalation. Functionalized additives with shorter alkyl segments increase acceptor macrophase separation more than additives with same chemical functionalization but longer alkyl segments. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1046–1057     

Computational Analysis Reveals a Critical Point Mutation in the N-Terminal Region of the Signaling Lymphocytic Activation Molecule Responsible for the Cross-Species Infection with Canine Distemper Virus

Infection of hosts by morbilliviruses is facilitated by the interaction between viral hemagglutinin (H-protein) and the signaling lymphocytic activation molecule (SLAM). Recently, the functional importance of the n-terminal region of human SLAM as a measles virus receptor was demonstrated. However, the functional roles of this region in the infection process by other morbilliviruses and host range determination remain unknown, partly because this region is highly flexible, which has hampered accurate structure determination of this region by X-ray crystallography. In this study, we analyzed the interaction between the H-protein from canine distemper virus (CDV-H) and SLAMs by a computational chemistry approach. Molecular dynamics simulations and fragment molecular orbital analysis demonstrated that the unique His28 in the N-terminal region of SLAM from Macaca is a key determinant that enables the formation of a stable interaction with CDV-H, providing a basis for CDV infection in Macaca. The computational chemistry approach presented should enable the determination of molecular interactions involving regions of proteins that are difficult to predict from crystal structures because of their high flexibility.     

Monte Carlo simulation of electric conductivity for pure and doping fullerene (C60)

In this paper, we have used Monte Carlo (MC) method to simulate and study the temperature and doping effects on the electric conductivity of fullerene (C60). The results show that the band gap has reduced by the doping and the charge carrier transport is facilitated from valence band to conduction band by the temperature where is touched a 300 K. In this case, the conductivity reached a value of $4\times {10}^{-7}\text{S}{\text{cm}}^{-1}$. The electric conductivity of C60 can increase by the triphenylmethane dye crystal violet (CV) alkali metal to reach $4\times {10}^{-3}\text{S}{\text{cm}}^{-1}$ at 303 K. Our results of MC simulation have a good agreement with those extracted from literature [10], [33].     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Periodic Néel skyrmion transport

In this work, we have used the MuMax3 software to simulate devices consisting of a ferromagnetic thin film placed over a heavy metal thin film. The devices are two interconnected partial-disks where a Néel domain wall is formed in the disks junction. In our simulations we investigate devices with disk radius $r=50$ nm and different distance d between the disks centers (from $d=12$ nm to $d=2R=100$ nm). By applying strong sinusoidal external magnetic fields, we find a mechanism able to create, annihilate and even manipulate a skyrmion in each side of the device. This mechanism is discussed in terms of interactions between skyrmion and domain wall. The Néel domain wall formed in the center of the device interacts with the Néel skyrmion, leading to a process of transporting a skyrmion from one disk to the other periodically. Our results have relevance for potential applications in spintronics such as logical devices.