Existence of liouvillian solutions in the problem of motion of a rotationally symmetric body on a sphere

2018 ◽  
Author(s):  
Alexander S. Kuleshov ◽  
Vera A. Katasonova
Keyword(s):  
Symmetric Body ◽  
Liouvillian Solutions ◽  
Rotationally Symmetric

On the Potential Theory of the Interaction of an Actuator Disk and a Body

1972 ◽  
Vol 16 (04) ◽  
pp. 271-277
Author(s):  
J. A. Sparenberg
Keyword(s):  
Potential Theory ◽  
The Body ◽  
Symmetric Body ◽  
Actuator Disk ◽  
Rotationally Symmetric

Actuator disks in the neighborhood of a rotationally symmetric body have been considered. The fluid is assumed to be incompressible and inviscid. The finite disturbances of the fluid by the body have been taken into account, and the theory is linearized with respect to the velocities induced by the actuator disk. The vorticity shed by the disk, its efficiency, and the force induced on the hull are discussed.

Practical Correction of Three Fold Astigmatism in the Philips CM TEM

1996 ◽  
Vol 54 ◽  
pp. 418-419
Author(s):  
Arno J. Bleeker ◽  
Mark H.F. Overwijk ◽  
Max T. Otten
Keyword(s):  
Optical Properties ◽  
Phase Contrast ◽  
The Other ◽  
Objective Lens ◽  
Symmetric Part ◽  
A Posteriori ◽  
Contrast Transfer Function ◽  
High Brightness ◽  
Rotationally Symmetric ◽  
Brightness Field

With the improvement of the optical properties of the modern TEM objective lenses the point resolution is pushed beyond 0.2 nm. The objective lens of the CM300 UltraTwin combines a Cs of 0. 65 mm with a Cc of 1.4 mm. At 300 kV this results in a point resolution of 0.17 nm. Together with a high-brightness field-emission gun with an energy spread of 0.8 eV the information limit is pushed down to 0.1 nm. The rotationally symmetric part of the phase contrast transfer function (pctf), whose first zero at Scherzer focus determines the point resolution, is mainly determined by the Cs and defocus. Apart from the rotationally symmetric part there is also the non-rotationally symmetric part of the pctf. Here the main contributors are not only two-fold astigmatism and beam tilt but also three-fold astigmatism. The two-fold astigmatism together with the beam tilt can be corrected in a straight-forward way using the coma-free alignment and the objective stigmator. However, this only works well when the coefficient of three-fold astigmatism is negligible compared to the other aberration coefficients. Unfortunately this is not generally the case with the modern high-resolution objective lenses. Measurements done at a CM300 SuperTwin FEG showed a three fold-astigmatism of 1100 nm which is consistent with measurements done by others. A three-fold astigmatism of 1000 nm already sinificantly influences the image at a spatial frequency corresponding to 0.2 nm which is even above the point resolution of the objective lens. In principle it is possible to correct for the three-fold astigmatism a posteriori when through-focus series are taken or when off-axis holography is employed. This is, however not possible for single images. The only possibility is then to correct for the three-fold astigmatism in the microscope by the addition of a hexapole corrector near the objective lens.

New Feasible Concepts of Aberration Correction for Realizing High-Resolution Electron Microscopes

1990 ◽  
Vol 48 (1) ◽  
pp. 202-203
Author(s):  
H. Rose
Keyword(s):  
Spherical Aberration ◽  
Wave Length ◽  
Electron Wave ◽  
Optical Lens ◽  
Resolution Electron ◽  
Rotationally Symmetric ◽  
Electron Microscopes ◽  
The Cost ◽  
Imaging Performance ◽  
Acceleration Voltage

The imaging performance of the light optical lens systems has reached such a degree of perfection that nowadays numerical apertures of about 1 can be utilized. Compared to this state of development the objective lenses of electron microscopes are rather poor allowing at most usable apertures somewhat smaller than 10-2 . This severe shortcoming is due to the unavoidable axial chromatic and spherical aberration of rotationally symmetric electron lenses employed so far in all electron microscopes.The resolution of such electron microscopes can only be improved by increasing the accelerating voltage which shortens the electron wave length. Unfortunately, this procedure is rather ineffective because the achievable gain in resolution is only proportional to λ1/4 for a fixed magnetic field strength determined by the magnetic saturation of the pole pieces. Moreover, increasing the acceleration voltage results in deleterious knock-on processes and in extreme difficulties to stabilize the high voltage. Last not least the cost increase exponentially with voltage.

scholarly journals Mixed fluid cosmological model in f(R, T) gravity

2020 ◽  
Vol 98 (11) ◽  
pp. 1015-1022 ◽  
Author(s):  
Parbati Sahoo ◽  
Barkha Taori ◽  
K.L. Mahanta
Keyword(s):  
Cosmological Model ◽  
Bianchi Type ◽  
Type I ◽  
Time Varying ◽  
Eos Parameter ◽  
Barotropic Fluid ◽  
Rotationally Symmetric ◽  
Expansion Of The Universe ◽  
The Universe ◽  
Mixed Fluid

We construct a locally rotationally symmetric (LRS) Bianchi type-I cosmological model in f(R, T) theory of gravity when the source of gravitation is a mixture of barotropic fluid and dark energy (DE) by employing a time-varying deceleration parameter. We observe through the behavior of the state finder parameters (r, s) that our model begins from the Einstein static era and goes to ΛCDM era. The equation of state (EOS) parameter (ωd) for DE varies from the phantom (ω < –1) phase to quintessence (ω > –1) phase, which is consistent with observational results. It is found that the discussed model can reproduce the current accelerating phase of the expansion of the universe.

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