# gst: apropos of avoidance, packing of stiff rods on ellipsoids; the effects of self-avoidance

AA << study the effects of geometry and self-avoidance on the ordering of slender filaments inside nonisotropic containers, considering cortical microtubules in plant cells, and packing of genetic material inside viral capsids as concrete examples. >>

<< Within a mean-field approximation, (AA) show analytically how the shape of the container, together with self-avoidance, affects the ordering of the stiff rods. (They)  find that the strength of the self-avoiding interaction plays a significant role in the preferred packing orientation, leading to a first-order transition for oblate cells, where the preferred orientation changes from azimuthal, along the equator, to a polar one, when self-avoidance is strong enough. >>

<< While for prolate spheroids the ground state is always a polar-like order, strong self-avoidance results with a deep metastable state along the equator. >>

<< the critical behavior of this system is in fact related to the butterfly catastrophe model. >>

Doron Grossman, Eytan Katzav. Effects of self-avoidance on the packing of stiff rods on ellipsoids. Phys. Rev. E 109, 054111. May 9, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.054111

Also: spheroids, self-assembly, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, ellipsoids, spheroids,  oblate- prolate spheroids, avoidance, self-avoidance

# gst: analogy between streamers in sinking spheroids, gyrotactic plumes and chemotactic collapse (when a plume structure blows up when a parm is above a threshold)

<< In a dilute suspension where sinking spheroids or motile gyrotactic microorganisms are modelled as orientable and negatively buoyant particles, (AA) have found analytical solutions to their steady distributions for a given parallel flow profile. The coupling between their distribution and the vertical flow is nonlinear, enabling the uniform base state to bifurcate into a structure reminiscent of the streamers in settling spheroid suspension and gyrotactic plume. This bifurcation depends on a single parameter that is proportional to the average number of particles on a horizontal cross section. In a three-dimensional axisymmetric system, the plume structure blows up when the parameter is above a threshold. (AA) discuss how this singularity is analogous to the chemotactic collapse of a Keller-Segel model, and the significance this analogy entails. >>

Lloyd Fung. Analogy between streamers in sinking spheroids, gyrotactic plumes and chemotactic collapse. arXiv: 2301.07164v1 [physics.flu-dyn]. Jan 17, 2023.

https://arxiv.org/abs/2301.07164

Also

keyword 'collapse' in FonT

https://flashontrack.blogspot.com/search?q=collapse

keyword 'spheroids' in FonT

https://flashontrack.blogspot.com/search?q=spheroids

Keywords: gst, analogy, spheroids, collapse, chemotactic collapse 

# chem: spontaneous reconfiguration of deformable nanoparticles (in response to environmental cues)

<< Deformable nanoparticles (NPs) offer unprecedented opportunities as dynamic building blocks that can spontaneously reconfigure during assembly in response to environmental cues. >>

<< deformable spherical NPs of radius 50 nm whose surface is tailored with octahedrally distributed charged patches and double-cap charged patches adapt their shape differently in response to changes in surface charge coverage and ionic strength. >>

AA << find shape transitions to rounded octahedra, faceted octahedra, faceted bowls, oblate spheroids, spherocylinders, dented beans, and dimpled rounded bowls. >>

AA << demonstrate that similar shape transitions can be achieved in deformable NPs of different sizes. >>️

Fanbo Sun, Nicholas E. Brunk, Vikram Jadhao. Shape control of deformable charge-patterned nanoparticles. Phys. Rev. E 107, 014502. Jan 10, 2023.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.107.014502

Img https://twitter.com/PhysRevE/status/1613183219377086468

Also

keyword 'self-assembly' in FonT

https://flashontrack.blogspot.com/search?q=self-assembly

keyword 'nano' in FonT

https://flashontrack.blogspot.com/search?q=nano

keyword 'nano' in Notes 

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=nano

Keywords: chem, nano, nanoparticles,  NPs, self-assembly, colloids, polymers, vesicle structures.

# gst: apropos of prolate- oblate spheroid transition, the chaotic behavior of a spinless entity around a black hole.

AA << investigate the long-term orbital dynamics of spinless extended bodies in Schwarzschild geometry, and show that periodic deviations from spherical symmetry in the shape of a test body may trigger the onset of chaos. (AA) do this by applying Dixon's formalism at quadrupolar order to a nearly spherical body whose shape oscillates between a prolate and an oblate spheroid. The late-time chaotic behavior is then verified by applying Melnikov's method. >>️

Ricardo A. Mosna, Fernanda F. Rodrigues, Ronaldo S. S. Vieira. Chaotic dynamics of a spinless axisymmetric extended body around a Schwarzschild black hole. arXiv: 2207.04341v1 [gr-qc]. Jul 9, 2022. 

https://arxiv.org/abs/2207.04341

Phys. Rev. D 106, 024016 (2022). 

https://doi.org/10.1103/PhysRevD.106.024016

Also - Oblate and Prolate Spheroid.  

<< The shape of the earth is that of a round ball or sphere slightly flattened at two opposite sides. Such a body is termed a spheroid. There are two kinds of spheroids-oblate and prolate; the former as the shape of an orange, the latter that of a lemon.  >>️

Oblate and Prolate Spheroid.  

https://etc.usf.edu/clipart/30500/30587/spheroid_30587.htm

img    https://etc.usf.edu/clipart/30500/30587/spheroid_30587_sm.gif

Also

keyword 'transition' in FonT: 

https://flashontrack.blogspot.com/search?q=transition

keyword 'transizione' | 'transition' in Notes (quasi-stochastic poetry): 

https://inkpi.blogspot.com/search?q=transizione

https://inkpi.blogspot.com/search?q=transition

Keywords: gst, spheroid, behavior, chaos, transition, black hole

# gst: transitional dynamics among gyrotactic (prolate spheroid) swimmers in turbulence

<< In this study, (AA) consider small, elongated, gyrotactic, swimming particles in homogenous isotropic turbulence (..). Many motile phytoplankton species are gyrotactic, i.e., their swimming direction results from the competition between shear-induced viscous torque and the stabilizing torque due to bottom-heaviness. (..)  Moreover, both single phytoplankton cells and multicellular phytoplankton chains can have elongated shapes, which makes the study of gyrotactic active particles with prolate shapes necessary. >>

AA addressed the following problems:

<< (i) How the clustering is affected by the swimming number Φ and the stability number Ψ? In particular, how to characterize the extent of clustering based on the three-dimensional Voronoi analysis?

(ii) How the clustering is related to the flow structures? This question has two perspectives.  From the space perspective, what are the regions that particles accumulate in? From the time perspective, how long do particles exist in an aggregated state? >>

Zehua Liu, Linfeng Jiang, Chao Sun. Accumulation and alignment of elongated gyrotactic swimmers in turbulence. arXiv:2202.04351v1 [physics.flu-dyn]. Feb 9, 2022.

https://arxiv.org/abs/2202.04351

Also

The effect of noise on the dynamics of microswimmers in externally-driven fluid flows.  

https://flashontrack.blogspot.com/2021/10/gst-effect-of-noise-on-dynamics-of.html

keywords 'turbulence' in FonT   

https://flashontrack.blogspot.com/search?q=turbulence

keywords 'turbolento' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=turbolento

keywords: transition, swimmers,  gyrotactic swimmers, spheroids,  prolate spheroids, stability, turbulence