Modelling of Motion of a Volvox Colony using Many-Body System and Its Qualitative Comparison with Observation
Septian Ulan Dini(a*), Sevi Nurafni(b), Achmad Zacky Fairuza(c), Intan Taufik(d), Sparisoma Viridi(a), (b)

(a)Master Program in Physics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia
*septianulandini[at]gmail.com
(b)Master Program in Computational Science, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia
(c)Master Program in Nanotechnology, Graduate School, Institut Teknologi Bandung, Bandung 40132, Indonesia
(d)School of Life Science and Technology, Institut Teknologi Bandung 40132, Indonesia

Abstract

Approximately 500-60,000 volvox cells constructed a colony with a spherical or elliptical hollow form. Each cell can use its flagella to move. In order for a colony of hundred cells to perform a direct motion, there must be a coordination of the flagella. In this work, we assume that the cells already form the spherical colony and can perform some simple motion types, i.e., translational (TRAN), roll (ROLL), spin (SPIN), and superposition of the motions, and neglect detail of each flagellum. It is possible to map each cell in the colony using angular positions with a constant radius R and different \(\theta_i\) and \(\phi_i\), where i = 1, 2, ..., N with N is the number of cells constructing a colony. The canter of the colony is \(r = (x, y, z)\). The TRAN mode can be obtained, where \(x(t) = x(0)+ v_x t\), \(y(t) = y(0)+ v_y t\), \(z(t) = z(0) + v_z t\), ROLL mode with \(\theta(t) = \omega(0) + \omega_\theta t\), and SPIN with \(\phi(t) = \phi(0) + \omega_\phi t\). Through the available observation video,\(v_x\), \(v_y\), \(v_z\), \(\omega_\theta\), and \(\omega_\phi\), are also shown to have a qualitative agreement.

Keywords: Volvox colony, mechanics, many-body system, qualitative model.

Topic: Modelling and Computational Physics