Lotka-Volterra particle-based/PDE hybrid simulation

We recently developed a hybrid simulation scheme for reaction-diffusion processes. In this simulation, we focus on the classic Lotka-Volterra (predator-prey) model. We couple particle-based simulations of the predator-prey dynamics with an inhomogeneous reservoir mediated by the Lotka Volterra reaction-diffusion PDE. Here we show only the concentration of preys. The right half of the simulation shows the reservoir represented by the finite difference simulation of the PDE. The left half shows the mean-field behavior of 2080 particle-based simulations. This simulation was implemented by one of my formers master’s student, Margarita Kostré. This work is about to be published.

Brownian motion simulation of ellipsoidal particles

This simulation models the Brownian movement of ellipsoidal particles under an interaction potential called the Gay-Berne potential. This potential is an anisotropic form of the Lennard-Jones 12-6 potential. The interparticle attraction is larger for a preferred orientation, so the system tends to a nematic phase, where most particles are aligned. This is particularly useful to model liquid crystalline systems. This simulation was implemented using the MSM/RD software.

Pentamer formation

Five identical particles, each with two binding sites, are simulated here. The simulation shows how a pentamer can be formed from a relatively simple model. The interaction potential is modeled using a patchy particles potential, which gives rise to both isotropic and anisotropic interactions that generate forces and torques between the particles. The Brownian diffusion is modeled using overdamped Langevin dynamics. The rotational diffusion is also modeled using overdamped Langevin dynamics. Unlike the previous simulation, the rotational motion has three degrees of freedom, so we used quaternions to describe the orientations of the particles. This entails writing the equations of motion in terms of quaternions. This simulation was implemented using the MSM/RD software.

Protein-ligand binding

This simulation emulates the interaction between a macromolecule with several binding sites (spherical particle with patches) and a small ligand (asterisk shaped particle). Similar to the previous example, the interactions are modeled using a patchy particle potential. The diffusion is modeled using overdamped Langevin dynamics, and the orientation is described using quaternions. However, we introduce an additional feature here. The binding site in the ligand (red tip) can be turned on and off through a Markovian switch. This models the conformation change of a ligand between a configuration that can bind or not with the macromolecule. This simulation was implemented using the MSM/RD software.

Fluids and interfaces simulations

Shocktube computational experiments

This computational experiment is to emulate real-world lab experiments done with a shock tube. We show a shock traveling from the left to the right end of the shock tube. The shock first travels through air and then hits a cylindrical container filled with water. The top plot shows a transversal cut of the three-dimensional setup, where the cylindrical container is represented by the small rectangle. It plots the pressure contours obtained by solving the three dimensional Euler equations with an air-solid-water interface by using a Tammann equation of state. The small bottom plot shows the pressure profile along the central horizontal axis. Below we show a three-dimensional visualization of the same simulation. This simulation was implemented using the Clawpack software.

Pipeline integrity

We show here a transversal cut of a pipe, where we plot only part of its circumference. The two black circular lines show the edges of a metal pipe. We model the fluid inside the pipe as a dense fluid and the fluid out the pipe as water. As we are interested in the stress produced within the pipe, we implement this setup using the elasticity equations. We place a device in the origin of the simulation that produces an oscillating pressure signal inside the pipe. As the signal interacts with the pipe and returns to the device, we obtain a rebound signal that can be used to analyze the integrity of the pipe. The plot shows the pressure, which corresponds to the trace of the stress tensor. This simulation was implemented using the Clawpack software