Acceleration scheme for particle transport in kinetic Monte Carlo methods

Abstract

Kinetic Monte Carlo (kMC) simulations are frequently used to study (electro-)chemical processes within science and engineering. kMC methods provide insight into the interplay of stochastic processes and can link atomistic material properties with macroscopic characteristics. Significant problems concerning the computational demand arise if processes with large time disparities are competing. Acceleration algorithms are required to make slow processes accessible. Especially, the accelerated superbasin kMC (AS-kMC) scheme has been frequently applied within chemical reaction networks. For larger systems, the computational overhead of the AS-kMC is significant as the computation of the superbasins is done during runtime and comes with the need for large databases. Here, we propose a novel acceleration scheme for diffusion and transport processes within kMC simulations. Critical superbasins are detected during the system initialization. Scaling factors for the critical rates within the superbasins, as well as a lower bound for the number of sightings, are derived. Our algorithm exceeds the AS-kMC in the required simulation time, which we demonstrate with a 1D-chain example. In addition, we apply the acceleration scheme to study the time-of-flight (TOF) of charge carriers within organic semiconductors. In this material class, time disparities arise due to a significant spread of transition rates. The acceleration scheme allows a significant acceleration up to a factor of 65 while keeping the error of the TOF values negligible. The computational overhead is negligible, as all superbasins only need to be computed once.

Tutorial on the Use of Deep Learning in Diffuse Optical Tomography

“…The MC method has many improvements that incorporate other interaction types such as fluorescence and Raman scattering [25], time and frequency-resolved setups, and extensions to 3D samples [26][27][28]. More recently, MC methods have also found applications in the food industry [29], deep learning [30], to study chemical processes [31], and mainly in biomedicine. Many available Monte-Carlo-based tools are online [11,31,32], customized for light propagation in biological tissues to help the biomedical community access efficient and accurate modeling of light transport.…”

“…More recently, MC methods have also found applications in the food industry [29], deep learning [30], to study chemical processes [31], and mainly in biomedicine. Many available Monte-Carlo-based tools are online [11,31,32], customized for light propagation in biological tissues to help the biomedical community access efficient and accurate modeling of light transport. The human body has four basic types of tissue: connective tissue, epithelial tissue (skin, linings of various passages inside the body), muscle tissue, and nervous tissue, with these containing subcategories, for example, skeletal muscle, smooth muscle, and cardiac muscle.…”

Utilizing Data-Driven Optimization to Automate the Parametrization of Kinetic Monte Carlo Models

“…The insufficient sampling of slow processes is in particular problematic if they represent the critical transition to obtain certain system properties. The most common approach to bridge time-scale disparities is so-called temporal acceleration schemes. − In essence, such algorithms define (heuristic) criteria to artificially scale down the transition rates of fast processes to enable a more frequent sampling of the crucial slow processes.…”

Modeling of Space-Charge Layers in Solid-State Electrolytes: A Kinetic Monte Carlo Approach and Its Validation

“…In general, kMC methods are a special subclass of Monte Carlo algorithms that can simulate the time evolution of nondeterministic systems. kMC models have been developed for numerous different applications such as charge transport in disordered organic semiconductors, − crystal growth, , chemical reaction networks, − vacancy diffusion, , and electrochemical systems. − In the direct context of solid-state electrolytes, kMC also has been applied. For instance, Wolverton and co-workers calculated the room-temperature ion conductivities of cation- and anion-substituted LiBH 4 -based SSEs .…”