Ivan Sadovskyy

Stable large-scale solver for Ginzburg-Landau equations for superconductors

Understanding the interaction of vortices with inclusions in type-II superconductors is a major outstanding challenge both for fundamental science and energy applications. At application-relevant scales, the long-range interactions between a dense configuration of vortices and the dependence of their behavior on external parameters, such as temperature and an applied magnetic field, are all important to the net response of the superconductor. Capturing these features, in general, precludes analytical description of vortex dynamics and has also made numerical simulation prohibitively expensive. Here we report on a highly optimized iterative implicit solver for the time-dependent Ginzburg-Landau equations suitable for investigations of type-II superconductors on massively parallel architectures. Its main purpose is to study vortex dynamics in disordered or geometrically confined mesoscopic systems. In this work, we present the discretization and time integration scheme in detail for two types of boundary conditions. We describe the necessary conditions for a stable and physically accurate integration of the equations of motion. Using an inclusion pattern generator, we can simulate complex pinning landscapes and the effect of geometric confinement. We show that our algorithm, implemented on a GPU, can provide static and dynamic solutions of the Ginzburg-Landau equations for mesoscopically large systems over thousands of time steps in a matter of hours. Using our formulation, studying scientifically-relevant problems is a computationally reasonable task.

Optimization of vortex pinning by nanoparticles using simulations of the time-dependent Ginzburg-Landau model

Introducing nanoparticles into superconducting materials has emerged as an efficient route to enhance their current-carrying capability. We address the problem of optimizing vortex pinning landscape for randomly distributed metallic spherical inclusions using large-scale numerical simulations of time- dependent Ginzburg-Landau equations. We found the size and density of particles for which the highest critical current is realized in a fixed magnetic field. For each particle size and magnetic field, the critical current reaches a maximum value at a certain particle density, which typically corresponds to 15{23% of the total volume being replaced by nonsuperconducting material. For fixed diameter, this optimal particle density increases with the magnetic field. Moreover, we found that the optimal particle diameter slowly decreases with the magnetic field from 4.5 to 2.5 coherence lengths at a given temperature. This result shows that pinning landscapes have to be designed for specific applications taking into account relevant magnetic field scales.

Toward Superconducting Critical Current by Design

A new critical-current-by-design paradigm is presented. It aims at predicting the optimal defect landscape in superconductors for targeted applications by elucidating the vortex dynamics responsible for the bulk critical current. To this end, critical current measurements on commercial high-temperature superconductors are combined with large-scale time-dependent Ginzburg-Landau simulations of vortex dynamics.

Effect of hexagonal patterned arrays and defect geometry on the critical current of superconducting films

Understanding the effect of pinning on the vortex dynamics in superconductors is a key factor towards controlling critical current values. Large-scale simulations of vortex dynamics can provide a rational approach to achieve this goal. Here, we use the time-dependent Ginzburg-Landau equations to study thin superconducting films with artificially created pinning centers arranged periodically in hexagonal lattices. We calculate the critical current density for various geometries of the pinning centers --- varying their size, strength, and density. Furthermore, we shed light upon the influence of pattern distortion on the magnetic-field-dependent critical current. We compare our result directly with available experimental measurements on patterned molybdenum-germanium films, obtaining good agreement. Our results give important systematic insights into the mechanisms of pinning in these artificial pinning landscapes and open a path for tailoring superconducting films with desired critical current behavior.

In silico optimization of critical currents in superconductors

For many technological applications of superconductors the performance of a material is determined by the highest current it can carry losslessly-the critical current. In turn, the critical current can be controlled by adding nonsuperconducting defects in the superconductor matrix. Here we report on systematic comparison of different local and global optimization strategies to predict optimal structures of pinning centers leading to the highest possible critical currents. We demonstrate performance of these methods for a superconductor with randomly placed spherical, elliptical, and columnar defects.

Laser-induced micropore formation and modification of cartilage structure in osteoarthritis healing

Abstract. Pores are vital for functioning of avascular tissues. Laser-induced pores play an important role in the process of cartilage regeneration. The aim of any treatment for osteoarthritis is to repair hyaline-type cartilage. The aims of this study are to answer two questions: (1) How do laser-assisted pores affect the cartilaginous cells to synthesize hyaline cartilage (HC)? and (2) How can the size distribution of pores arising in the course of laser radiation be controlled? We have shown that in cartilage, the pores arise predominately near chondrocytes, which promote nutrition of cells and signal molecular transfer that activates regeneration of cartilage. In vivo laser treatment of damaged cartilage of miniature pig joints provides cellular transformation and formation of HC. We propose a simple model of pore formation in biopolymers that paves the way for going beyond the trial-and-error approach when choosing an optimal laser treatment regime. Our findings support the approach toward laser healing of osteoarthritis.