Dataset Information

On the reaction-diffusion type modelling of the self-propelled object motion.

ABSTRACT: In this study, we propose a mathematical model of self-propelled objects based on the Allen-Cahn type phase-field equation. We combine it with the equation for the concentration of surfactant used in previous studies to construct a model that can handle self-propelled object motion with shape change. A distinctive feature of our mathematical model is that it can represent both deformable self-propelled objects, such as droplets, and solid objects, such as camphor disks, by controlling a single parameter. Furthermore, we demonstrate that, by taking the singular limit, this phase-field based model can be reduced to a free boundary model, which is equivalent to the [Formula: see text]-gradient flow model of self-propelled objects derived by the variational principle from the interfacial energy, which gives a physical interpretation to the phase-field model.

SUBMITTER: Nagayama M

PROVIDER: S-EPMC10400585 | biostudies-literature | 2023 Aug

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

On the reaction-diffusion type modelling of the self-propelled object motion.

Nagayama Masaharu M Monobe Harunori H Sakakibara Koya K Nakamura Ken-Ichi KI Kobayashi Yasuaki Y Kitahata Hiroyuki H

Scientific reports 20230803 1

In this study, we propose a mathematical model of self-propelled objects based on the Allen-Cahn type phase-field equation. We combine it with the equation for the concentration of surfactant used in previous studies to construct a model that can handle self-propelled object motion with shape change. A distinctive feature of our mathematical model is that it can represent both deformable self-propelled objects, such as droplets, and solid objects, such as camphor disks, by controlling a single p ...[more]

PMID: 37537247

Similar Datasets

Project description:Taxic behavior as a response to an external stimulus is a fundamental function of living organisms. Some bacteria successfully implement chemotaxis without directly controlling the direction of movement. They periodically alternate between run and tumble, i.e., straight movement and change in direction, respectively. They tune their running period depending on the concentration gradient of attractants around them. Consequently, they respond to a gentle concentration gradient stochastically, which is called "bacterial chemotaxis." In this study, such a stochastic response was reproduced by a non-living self-propelled object. We used a phenanthroline disk floating on an aqueous solution of Fe[Formula: see text]. The disk spontaneously alternated between rapid motion and rest, similar to the run-and-tumble motion of bacteria. The movement direction of the disk was isotropic independent of the concentration gradient. However, the existing probability of the self-propelled object was higher at the low-concentration region, where the run length was longer. To explain the mechanism underlying this phenomenon, we proposed a simple mathematical model that considers random walkers whose run length depends on the local concentration and direction of movement against the gradient. Our model adopts deterministic functions to reproduce the both effects, which is instead of stochastic tuning the period of operation used in the previous reports. This allows us to analyze the proposed model mathematically, which indicated that our model reproduces both positive and negative chemotaxis depending on the competition between the local concentration effect and it's gradient effect. Owing to the newly introduced directional bias, the experimental observations were reproduced numerically and analytically. The results indicate that the directional bias response to the concentration gradient is an essential parameter for determining bacterial chemotaxis. This rule might be universal for the stochastic response of self-propelled particles in living and non-living systems.

Project description:To interact successfully with moving objects in our environment we need to be able to predict their behavior. Predicting the position of a moving object requires an estimate of its velocity. When flow parsing during self-motion is incomplete–that is, when some of the retinal motion created by self-motion is incorrectly attributed to object motion–object velocity estimates become biased. Further, the process of flow parsing should add noise and lead to object velocity judgements being more variable during self-motion. Biases and lowered precision in velocity estimation should then translate to biases and lowered precision in motion extrapolation. We investigate this relationship between self-motion, velocity estimation and motion extrapolation with two tasks performed in a realistic virtual reality (VR) environment: first, participants are shown a ball moving laterally which disappears after a certain time. They then indicate by button press when they think the ball would have hit a target rectangle positioned in the environment. While the ball is visible, participants sometimes experience simultaneous visual lateral self-motion in either the same or in the opposite direction of the ball. The second task is a two-interval forced choice task in which participants judge which of two motions is faster: in one interval they see the same ball they observed in the first task while in the other they see a ball cloud whose speed is controlled by a PEST staircase. While observing the single ball, they are again moved visually either in the same or opposite direction as the ball or they remain static. We expect participants to overestimate the speed of a ball that moves opposite to their simulated self-motion (speed estimation task), which should then lead them to underestimate the time it takes the ball to reach the target rectangle (prediction task). Seeing the ball during visually simulated self-motion should increase variability in both tasks. We expect to find performance in both tasks to be correlated, both in accuracy and precision.

Dataset Information

On the reaction-diffusion type modelling of the self-propelled object motion.

Publications

On the reaction-diffusion type modelling of the self-propelled object motion.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets