2017/11/16 by Ivan Maryshev, Davide Marenduzzo, Andrew B. Goryachev +1 · 16 citations
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Argument (complex analysis) #Chemistry #Classical mechanics #Closure (psychology) #Computer science #Geometry #Hierarchy #Instability #Kinetic energy #Kinetic theory #Materials science #Mathematics #Mechanics #Micro and Nano Robotics #Microtubule #Molecular motor #Nonlinear Dynamics and Pattern Formation #Orientation (vector space) #Pattern formation #Phase (matter) #Phase diagram #Physics #Quantum mechanics #Similarity (geometry) #Stability (learning theory) #Statistical physics #Theoretical physics #Thermodynamics #Work (physics) #cond-mat.soft
paper · pdf · open access · doi:10.1103/physreve.97.022412
published in Physical review. E 97(2), 022412 (American Physical Society) · 18 pages, 11 figures, Simulation movies can be found at http://dx.doi.org/10.7488/ds/2246
arxiv created 2017/11/16 · openalex publication_date 2018/02/20 · arxiv updated 2018/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this study we formulate a theoretical approach, based on a Boltzmann-like kinetic equation, to describe pattern formation in two-dimensional mixtures of microtubular filaments and molecular motors. Following the previous work by Aranson and Tsimring [Phys. Rev. E 74, 031915 (2006)PLEEE81539-375510.1103/PhysRevE.74.031915] we model the motor-induced reorientation of microtubules as collision rules, and devise a semianalytical method to calculate the corresponding interaction integrals. This procedure yields an infinite hierarchy of kinetic equations that we terminate by employing a well-established closure strategy, developed in the pattern-formation community and based on a power-counting argument. We thus arrive at a closed set of coupled equations for slowly varying local density and orientation of the microtubules, and study its behavior by performing a linear stability analysis and direct numerical simulations. By comparing our method with the work of Aranson and Tsimring, we assess the validity of the assumptions required to derive their and our theories. We demonstrate that our approximation-free evaluation of the interaction integrals and our choice of a systematic closure strategy result in a rather different dynamical behavior than was previously reported. Based on our theory, we discuss the ensuing phase diagram and the patterns observed.