scholarly journals Volvox barberi flocks, forming near-optimal, two-dimensional, polydisperse lattice packings

2018 ◽  
Author(s):  
Ravi Nicholas Balasubramanian
Keyword(s):  
Germ Cells ◽  
Close Packing ◽  
Two Dimensional ◽  
Optimal Packing ◽  
Normal Distributions ◽  
Dye Tracer ◽  
Dynamical Simulation ◽  
Soft Spheres ◽  
Log Normal ◽  
Lattice Packings

AbstractVolvox barberi is a multicellular green alga forming spherical colonies of 10000-50000 differentiated somatic and germ cells. Here, I show that these colonies actively self-organize over minutes into “flocks” that can contain more than 100 colonies moving and rotating collectively for hours. The colonies in flocks form two-dimensional, irregular, “active crystals”, with lattice angles and colony diameters both following log-normal distributions. Comparison with a dynamical simulation of soft spheres with diameters matched to the Volvox samples, and a weak long-range attractive force, show that the Volvox flocks achieve optimal random close-packing. A dye tracer in the Volvox medium revealed large hydrodynamic vortices generated by colony and flock rotations, providing a likely source of the forces leading to flocking and optimal packing.

Log-normal distributions in parasitology

1984 ◽  
Vol 93 (6) ◽  
pp. 591-598 ◽  
Author(s):  
Sandeep K Malhotra
Keyword(s):  
Normal Distributions ◽  
Log Normal

scholarly journals Two-dimensional metal–organic network with an unusual 36 topology and a cubic close packing pattern

CrystEngComm ◽  
2008 ◽  
Vol 10 (8) ◽  
pp. 954 ◽  
Author(s):  
Hyunuk Kim ◽  
Gyungse Park ◽  
Kimoon Kim
Keyword(s):  
Close Packing ◽  
Two Dimensional ◽  
Metal Organic

scholarly journals Characteristics of Hazard Rate Functions of Log-Normal Distributions

2019 ◽  
Vol 1338 ◽  
pp. 012036
Author(s):  
D Kurniasari ◽  
R Widyarini ◽  
Warsono ◽  
Y Antonio
Keyword(s):  
Hazard Rate ◽  
Normal Distributions ◽  
Rate Functions ◽  
Log Normal

scholarly journals Normal Distribution on the Rotation Group So(3)

1997 ◽  
Vol 29 (3-4) ◽  
pp. 201-233 ◽  
Author(s):  
Dmitry I. Nikolayev ◽  
Tatjana I. Savyolov
Keyword(s):  
Normal Distribution ◽  
Orientation Distribution ◽  
Rotation Group ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Normal Distributions ◽  
The Central Limit Theorem ◽  
Special Cases ◽  
Wrapped Normal ◽  
Circular Normal Distribution

We study the normal distribution on the rotation group SO(3). If we take as the normal distribution on the rotation group the distribution defined by the central limit theorem in Parthasarathy (1964) rather than the distribution with density analogous to the normal distribution in Eucledian space, then its density will be different from the usual (1/2πσ) exp⁡(−(x−m)2/2σ2) one. Nevertheless, many properties of this distribution will be analogous to the normal distribution in the Eucledian space. It is possible to obtain explicit expressions for density of normal distribution only for special cases. One of these cases is the circular normal distribution.The connection of the circular normal distribution SO(3) group with the fundamental solution of the corresponding diffusion equation is shown. It is proved that convolution of two circular normal distributions is again a distribution of the same type. Some projections of the normal distribution are obtained. These projections coincide with a wrapped normal distribution on the unit circle and with the Perrin distribution on the two-dimensional sphere. In the general case, the normal distribution on SO(3) can be found numerically. Some algorithms for numerical computations are given. These investigations were motivated by the orientation distribution function reproduction problem described in the Appendix.

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