Normal modes of carbon nanotubes: similarities and differences with their continuum counterpart

Carbon nanotubes (CNTs) possess a range of unusually interesting and useful physicochemical properties. In this paper, the mechanical properties of single wall CNTs are investigated via free vibration normal modes using molecular mechanics models. The forcefield used is empirical and the usual assumptions of potential energy contributions coming from bondstretching, bond angle bending, and bond twisting for two, three, and four atom interactions respectively, are made. The validity of continuum behaviour is examined by comparing the modal spacing obtained from the molecular mechanics models and that obtained from classical continuum elastodynamics. The breakdown of continuum behaviour is systematically characterised for various combinations of length to diameter ratio as well as for the number of atoms per circumference

Computational modelling of the vortex state in high-temperature superconductors

The vortex state in high temperature superconductors is investigated using computer simulations. Vortices are represented as particles and we employ Langevin dynamics to study the statics and dynamics of the system.We show that the long-range nature of the vortex-vortex interaction can result in numerical artefacts, and provide two techniques to overcome these problems: (i) using a ‘smooth’ cut-off which reduces the interaction force near the cut-off smoothly to zero, and (ii) an infinite lattice summation technique applicable for a K0-Bessel function interaction potential.Using these methods, we investigate a two-dimensional vortex system driven over a weak random potential. We observe the moving Bragg glass regime, and study the recently predicted critical transverse force. Our results agree with and extend other theoretical and numerical works, and provide important confirmation for the moving glass theory. We investigate the critical transverse force as a function of system size, temperature, driving force and disorder strength. We provide numerical estimates to assist experimentalists in verifying its existence.We study vortex matter in three-dimensional layered superconductors in the limit of zero Josephson coupling. The long-range nature of the electromagnetic interaction between pancake vortices in the c-direction allows us to employ a meanfield method: all attractive inter-layer interactions are described by a substrate potential, which pancakes experience in addition to the in-layer pancake repulsion. Using an averaged pancake-density, we iteratively re-compute the substrate potential. The self-consistent method converges, depending on temperature, either to a pancake lattice or a pancake liquid. We investigate different methods to perform these simulation efficiently, and compute the instability line for the transition from solid to liquid, the melting line and the entropy jump across the transition

Ubermag - Research Software Engineering

Topics of this contribution: Notebook as user interface. Reproducibility, interactive documentation. Special feature of ubermag: provides domain specific language (for micromagnetic research) how to express problem, which is then translated into configuration files for the simulation engine automatically. Software engineering github actions for CI. Unit tests, system tests. Testing notebooks through nbval. Pre-commit hooks. Software design: connect to existing libraries where possible, such as numpy, scipy, matplotlib, pandas, k3d, recently xarray. Packaging. Pypi, conda-forge, spack

Finite element optimizations for efficient non-linear electrical tomography reconstruction

Electrical Tomography can produce accurate results only if the underlying 2D or 3D volume discretization is chosen suitably for the applied numerical algorithm. We give general indications where and how to optimize a finite element discretization of a volume under investigation to enable efficient computation of potential distributions and the reconstruction of materials. For this, we present an error estimator and material-gradient indicator as a driver for adaptive mesh refinement and show how finite element mesh properties affect the efficiency and accuracy of the solutions

A systematic approach to multiphysics extensions of finite-element-based micromagnetic simulations: Nmag

Extensions of the basic micromagnetic model that include effects such as spin-current interaction, diffusion of thermal energy or anisotropic magnetoresistance are often studied by performing simulations that use case-specific ad-hoc extensions of widely used software packages such as OOMMF or Magpar. We present the novel software framework 'Nmag' that handles specifications of micromagnetic systems at a sufficiently abstract level to enable users with little programming experience to automatically translate a description of a large class of dynamical multifield equations plus a description of the system's geometry into a working simulation. Conceptually, this is a step towards a higher-level abstract notation for classical multifield mutliphysics simulations, similar to the change from assembly language to a higher level human-and-machine-readable formula notation for mathematical terms (FORTRAN) half a century ago. We demonstrate the capability of this approach through two examples, showing 1) a reduced dimensionality model coupling two copies of the micromagnetic sector and 2) the computation of a spatial current density distribution for anisotropic magnetoresistance (AMR). For cross-wise validation purposes, we also show how Nmag compares to the OOMMF and Magpar packages on a selected micromagnetic toy system. We furthermore, briefly discuss the limiations of our framework and related conceptual questions

Self-organization of Ce adatoms on Ag(111): a kinetic Monte Carlo study

One of the most fascinating experimental results in fabrication of artificial nanostructures is the creation of the macroscopically ordered superlattice of Ce adatoms on Ag111 F. Silly et al., Phys. Rev. Lett. 92, 016101 2004. Here, performing kinetic Monte Carlo simulations, we study the formation of Ce superlattice at the atomic scale. It is demonstrated that the surface-state mediated long-range interaction between Ce adatoms can lead to their self-assembly into a well ordered structure. The temperature of the substrate and the concentration of Ce adatoms are shown to play a key role in this process

Effect of rounded corners on the magnetic properties of pyramidal-shaped shell structures

In recent years, the advance of novel chemical growth techniques has led to the fabrication of complex, three-dimensional magnetic nanostructures. The corners and edges of such realistic geometries are generally not sharp but rounded. In a previous article we have argued that high demagnetization fields in the vicinity of sharp edges lead to the formation of an asymmetric vortex state in pyramidal-shaped magnetic shell structures. The asymmetric vortex state is potentially interesting with respect to future magnetic memory devices. In this work a micromagnetic model is used to investigate the effect of rounded corners and edges on the magnetic reversal process within these pyramidal-shaped magnetic shell structures. In particular, we explore the degree of rounding, which has to be introduced in order to suppress the asymmetric vortex state. Another emphasis is placed on the magnetic reversal of (quasi-)homogeneous states within these structures. We demonstrate that the rounding of corners significantly reduces the coercivity. This complies with former studies on cuboidal structures, which suggest the important effect of corners on the magnetic reversal of homogeneous magnetic states. The present study uses a finite-element discretization for the numerical solution of the micromagnetic equations, which provides flexibility with respect to the modeling of complex shapes. In particular, this method is very accurate with respect to structures with a smooth surface

Magneto-resistance in a lithography defined single constrained domain wall spin valve

We have measured domain wall magnetoresistance in a single lithographically constrained domain wall. An H-shaped Ni nano-bridge was fabricated by e-beam lithography with the two sides being single magnetic do- mains showing independent magnetic switching. The connection between the sides constraining the domain wall when the sides line up anti-parallel. The magneto-resistance curve clearly identifies the magnetic con- figurations that are expected from a spin valve-like structure. The value of the magneto-resistance at room temperature is around 0.1% or 0.4 ­. This value is shown to be in agreement with a theoretical formulation based on spin accumulation. Micromagnetic simulations show it is possible to reduce the size of the domain wall further by shortening the length of the bridge

Magnetic anisotropy terms in [110] MBE grown REFe2 films involving the strain term ???

The magnetic anisotropy parameters in [110] MBE grown films of REFe2 compounds are not the same as those in the bulk. This is due to the presence of a shear strain εxy, frozen in during crystal growth. In this paper, calculated magnetic anisotropy parameters for [110] MBE grown REFe2 films, that directly involve the shear strain εxy, are presented and discussed. In addition to the usual first order Callen and Callen term K˜'2, there are nine second order terms six of which involve cross terms between εxy and the cubic crystal field terms B4 and B6. Two of the second order cross terms are identified as being important: K˜"242(T) and K˜"262(T). Of these, the rank-two term K˜"242(T) dominates over a large temperature range. It has the same angular dependence as the first order term K˜'2, but with a more rapid temperature dependence. The correction at T = 0K for TbFe2, DyFe2, HoFe2, ErFe2, and TmFe2, amounts to ~+9.2%, -13.9%, -11.6%, +22.7%, and 27.1%, respectively. Similar comments are made concerning the rank-four K˜"264(T) term

Jupyter in Computational Science

The articles in this special section discusses the applications supported by the Jupyter Notebook. Before notebooks, a scientist working with Python code, for instance, might have used a mixture of script files and code typed into an interactive shell. The shell is good for rapid experimentation, but the code and results are typically transient, and a linear record of everything that was tried would be long and not very clear. The notebook interface combines the convenience of the shell with some of the benefits of saving and editing code in a file, while also incorporating results, including rich output, such as plots, in a document that can be shared with others. The Jupyter Notebook is used through a web browser. Although it is often run locally, on a desktop or a laptop, this design means that it can also be used remotely, so the computation occurs, and the notebook files are saved, on an institutional server, a high-performance computing facility or in the clo