2 results
Motor-Mediated Microtubule Self-Organization in Dilute and Semi-Dilute Filament Solutions
- S. Swaminathan, F. Ziebert, I. S. Aranson, D. Karpeev
-
- Journal:
- Mathematical Modelling of Natural Phenomena / Volume 6 / Issue 1 / 2011
- Published online by Cambridge University Press:
- 09 June 2010, pp. 119-137
- Print publication:
- 2011
-
- Article
- Export citation
-
We study molecular motor-induced microtubule self-organization in dilute and semi-dilute filament solutions. In the dilute case, we use a probabilistic model of microtubule interaction via molecular motors to investigate microtubule bundle dynamics. Microtubules are modeled as polar rods interacting through fully inelastic, binary collisions. Our model indicates that initially disordered systems of interacting rods exhibit an orientational instability resulting in spontaneous ordering. We study the existence and dynamic interaction of microtubule bundles analytically and numerically. Our results reveal a long term attraction and coalescing of bundles indicating a clear coarsening in the system; microtubule bundles concentrate into fewer orientations on a slow logarithmic time scale. In semi-dilute filament solutions, multiple motors can bind a filament to several others and, for a critical motor density, induce a transition to an ordered phase with a nonzero mean orientation. Motors attach to a pair of filaments and walk along the pair bringing them into closer alignment. We develop a spatially homogenous, mean-field theory that explicitly accounts for a force-dependent detachment rate of motors, which in turn affects the mean and the fluctuations of the net force acting on a filament. We show that the transition to the oriented state can be both continuous and discontinuous when the force-dependent detachment of motors is important.
5 - Complex fluids
-
- By I. Aranson, D. Blair, P. Vorobieff, G. Metcalfe, T. Shinbrot, J. J. McCarthy, J. M. Ottino, J. S. Olafsen, J. S. Urbach, R. Mikkelsen, M. Versluis, E. Koene, G.-W. van der Bruggert, D. Lohse, M. Tirumkudulu, A. Tripathi, A. Acrivos, J. H. Walther, S.-S. Lee, P. Koumoutsakos, I. Eames, S. B. Dalziel, S. L. Anna, H. Spiegelberg, G. H. McKinley
- M. Samimy, Ohio State University, K. S. Breuer, Brown University, Rhode Island, L. G. Leal, University of California, Santa Barbara, P. H. Steen, Cornell University, New York
-
- Book:
- A Gallery of Fluid Motion
- Published online:
- 25 January 2010
- Print publication:
- 12 January 2004, pp 54-62
-
- Chapter
- Export citation
-
Summary
Interface motion in a vibrated granular layer
Granular materials are now recognized as a distinct state of matter, and studies of their behavior form a fascinating interdisciplinary branch of science. The intrinsic dissipative nature of the interactions between the constituent macroscopic particles gives rise to several basic properties specific to granular substances, setting granular matter apart from the conventional gaseous, liquid, or solid states.
Thin layers of granular materials subjected to vertical vibration exhibit a diversity of patterns. The particular pattern is determined by the interplay between driving frequency f and the acceleration amplitude Γ. Interfaces in vibrated granular layers, existing for large enough amplitude of vibration, separate large domains of flat layers oscillating with opposite phase. These two phases are related to the period-doubling character of the flat layer motion at large plate acceleration. Interfaces are either smooth or “decorated” by periodic undulations depending on parameters of vibration. An additional subharmonic driving results in a controlled displacement of the interface with respect to the center of the experimental cell. The speed and the direction of the interface motion are sensitive to the phase and amplitude of the subharmonic driving.
The image sequence above shows interface nucleation and propagation towards the center of the cell, with dimensionless time tf labeled in each image. The interface forms at the right side wall of the cell due to small-amplitude phase-shifted subharmonic driving. After the additional driving stops, the interface moves towards the center, creating small-scale localized structures in the process.