Change Of Total Potential Energy Research Articles

Fast electrostatic solvers for kinetic Monte Carlo simulations

Kinetic Monte Carlo (KMC) is an important computational tool in theoretical physics and chemistry. In contrast to standard Monte Carlo, KMC permits the description of time dependent dynamical processes and is not restricted to systems in equilibrium. Compared to Molecular Dynamics, it allows simulations over significantly longer timescales. Recently KMC has been applied successfully in modelling of novel energy materials such as Lithium-ion batteries and organic/perovskite solar cells. Motivated by this, we consider general solid state systems which contain free, interacting particles which can hop between localised sites in the material. The KMC transition rates for those hops depend on the change in total potential energy of the system. For charged particles this requires the frequent calculation of electrostatic interactions, which is usually the bottleneck of the simulation. To avoid this issue and obtain results in reasonable times, many studies replace the long-range potential by a phenomenological short range approximation. This, however, leads to systematic errors and unphysical results. On the other hand standard electrostatic solvers such as Ewald summation or fast Poisson solvers are highly inefficient in the KMC setup or introduce uncontrollable systematic errors at high resolution.In this paper we describe how the Fast Multipole Method by Greengard and Rokhlin can be adapted to overcome this issue by dramatically reducing computational costs. We exploit the fact that each update in the transition rate calculation corresponds to a single particle move and changes the configuration only by a small amount. This allows us to construct an algorithm which scales linearly in the number of charges for each KMC step, something which had not been deemed to be possible before.We demonstrate the performance and parallel scalability of the method by implementing it in a performance portable software library, which was recently developed in our group. We describe the high-level Python interface of the code which makes it easy to adapt to specific use cases.

Asymptotic analysis of notch induced crack nucleation

AbstractIn the present study, a semi‐analytical asymptotic approach is used in order to analyse the change of total potential energy due to the initiation of a crack at a sharp re‐entrant corner. The semi‐analytical solution nature allows for reducing the numerical effort compared to a purely numerical treatment and provides a deeper physical insight into the fracture mechanics problem. Finally, the obtained asymptotic solutions are compared to numerical reference solutions. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Crack initiation: A non-local energy approach

A crack initiation criterion is proposed for brittle material where nucleation is treated as a sudden and discrete rupture event at the macroscopic level. At the heart of the criterion is the finite difference form of the energy release rate; an expression for the characteristic length is derived and the change in total potential energy is obtained from an asymptotic argument. The criterion can predict crack onset at a sharp or blunt notch. Fracture toughness and material strength are the only input requirements. The effectiveness of the criterion is demonstrated through predictions that are compared to experimental data.

Effects of Vacancy Defects on the Interfacial Shear Strength of Carbon Nanotube Reinforced Polymer Composite

We investigate the effects of the vacancy defects (i.e., missing atoms) in carbon nanotubes (CNTs) on the interfacial shear strength (ISS) of the CNT-polyethylene composite with the molecular dynamics simulation. In the simulation, the crystalline polyethylene matrix is set up in a hexagonal array with the polymer chains parallel to the CNT axis. Vacancy defects in the CNT are introduced by removing the corresponding atoms from the pristine CNT (i.e., CNT without any defect). Three patterns of vacancy defects with three different sizes are considered. Two types of interfaces, with and without cross-links between the CNT and the matrix are also considered here. Polyethylene chains are used as cross-links between the CNT and the matrix. The Brenner potential is used for the carbon-carbon interaction in the CNT, while the polymer is modeled by a united-atom potential. The nonbonded van der Waals interaction between the CNT and the polymer matrix and within the polymer matrix itself is modeled with the Lennard-Jones potential. To determine the ISS, we conduct the CNT pull-out from the polymer matrix and the ISS has been estimated with the change of total potential energy of the CNT-polymer system. The simulation results reveal that the vacancy defects significantly influence the ISS. Moreover, the simulation clarifies that CNT breakage occurs during the pull-out process for large size vacancy defect which ultimately reduces the reinforcement.

MHD Equilibrium and Kink Stability in Damavand Tokamak

Magnetohydrodynamic (MHD) equilibrium is vulnerable to numerous destabilizing mechanisms. Instabilities introduce distortions to the plasma magnetic surfaces and its boundaries, their driving force being the radial gradient of plasma toroidal current density. For certain modal numbers, internal kink modes may develop, and their study is feasible according to the energy principle, in which the change in total potential energy due to the disturbance is evaluated. In this article, we present a totally new analysis of MHD equilibrium and stability, and apply it to Damavand tokamak which has a large aspect ratio. For this purpose, we combine perturbation and Green’s function methods to solve for the equilibrium configuration. At this stage, plasma profiles are found explicitly in terms of Bessel functions, and we present a simple expression for estimation of total toroidal plasma current. Then the rest of plasma profiles, including poloidal magnetic flux, safety factor, and toroidal current density, are obtained and plotted. In the next step, we turn to the stability calculations and show that Damavand plasma is resistant to most of the disturbances.

Computer simulation of carbon nanotube pull-out from polymer by the molecular dynamics method

Abstract The influence of the polymer matrix density, chemical cross-links in the interface, and geometrical defect in the carbon nanotubes (CNTs) on the CNT pull-out from polymer has been analyzed by the molecular dynamics simulation. The interfacial shear strength (ISS) has also been estimated with the change of total potential energy. In the simulation, the crystalline polyethylene matrix is set up in a hexagonal array with the polymer chains parallel to the CNT axis. First, we investigate the effect of the polymer matrix density on the ISS by changing the distance between the chains. Simulated results show that the ISS increases with the increase of matrix density. Next, we examine the cross-link effect on the ISS by adding polyethylene cross-links in the interface. Here, an energy based switching criterion addressing cross-links traveling on the CNT has been proposed. It is found that the presence of cross-links and the cross-link positions affect the ISS. Finally, pentagon–heptagon defect, which reduces the tensile strength of the CNT and has been experimentally observed by Hashimoto et al. [Hashimoto A, Suenaga K, Gloter A, Urita K, Iijima S. Direct evidence for atomic defects in graphene layers. Nature 2004;430:870–3], has been addressed as a geometrical defect in the CNT. When cross-links are present between the CNT and the polymer, this defect reduces the ISS due to the improper connections of cross-links around this defective region.