scholarly journals Images of point charges in conducting ellipses and prolate spheroids

2021 ◽  
Vol 62 (9) ◽  
pp. 092902
Author(s):  
Matt Majic
Keyword(s):  
Prolate Spheroids

On the Abramov approach for the approximation of whispering gallery modes in prolate spheroids

2020 ◽  
pp. 125599
Author(s):  
Pierluigi Amodio ◽  
Anton Arnold ◽  
Tatiana Levitina ◽  
Giuseppina Settanni ◽  
Ewa B. Weinmüller
Keyword(s):  
Whispering Gallery Modes ◽  
Whispering Gallery ◽  
Prolate Spheroids

scholarly journals On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 846
Author(s):  
Donya Ohadi ◽  
David S. Corti ◽  
Mark J. Uline
Keyword(s):  
Equation Of State ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Pure Component ◽  
Excluded Volume ◽  
Theory Approach ◽  
Prolate Spheroidal ◽  
Empirical Correction ◽  
Prolate Spheroids ◽  
Onsager Theory

Modifications to the traditional Onsager theory for modeling isotropic–nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee–Parsons resummation term. The Lee–Parsons resummation term uses the Carnahan–Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager’s original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee–Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equation of state.

scholarly journals Accumulation of motile elongated micro-organisms in turbulence

2013 ◽  
Vol 739 ◽  
pp. 22-36 ◽  
Author(s):  
Caijuan Zhan ◽  
Gaetano Sardina ◽  
Enkeleida Lushi ◽  
Luca Brandt
Keyword(s):  
Turbulent Flow ◽  
Three Dimensional ◽  
Laminar Flows ◽  
Marine Life ◽  
Prolate Spheroids ◽  
Linear Shear ◽  
Local Shear ◽  
Micro Organisms ◽  
Hydrodynamic Effects ◽  
Preferential Alignment

AbstractWe study the effect of turbulence on marine life by performing numerical simulations of motile micro-organisms, modelled as prolate spheroids, in isotropic homogeneous turbulence. We show that the clustering and patchiness observed in laminar flows, linear shear and vortex flows, are significantly reduced in a three-dimensional turbulent flow mainly because of the complex topology; elongated micro-organisms show some level of clustering in the case of swimmers without any preferential alignment whereas spherical swimmers remain uniformly distributed. Micro-organisms with one preferential swimming direction (e.g. gyrotaxis) still show significant clustering if spherical in shape, whereas prolate swimmers remain more uniformly distributed. Due to their large sensitivity to the local shear, these elongated swimmers react more slowly to the action of vorticity and gravity and therefore do not have time to accumulate in a turbulent flow. These results show how purely hydrodynamic effects can alter the ecology of micro-organisms that can vary their shape and their preferential orientation.

Pressure Stability of Orthotropic Prolate Spheroids

1968 ◽  
Vol 12 (03) ◽  
pp. 163-164
Author(s):  
Herbert Becker
Keyword(s):  
External Pressure ◽  
Stress Fields ◽  
Membrane Stress ◽  
Doubly Curved Shells ◽  
Instability Theory ◽  
Mathematical Relation ◽  
Prolate Spheroids ◽  
Pressure Stability ◽  
Doubly Curved ◽  
Orthotropic Shells

Through the use of general instability theory for doubly curved orthotropic shells, a mathematical relation was developed to predict external pressure buckling of stiffened prolate spheroids. The procedure was applied to two experiments which were found to be in fair agreement with theory. In general, the method is applicable to doubly curved shells with orthotropic material properties (composites) as well as geometric orthotropicity, and subject to arbitrary membrane stress fields. It is not limited to pressure alone. Furthermore, because of the closed form of the solutions to many problems, the procedure would be particularly useful for optimization purposes.

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