Topological invariants of rotationally symmetric crystals

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.

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

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100179762 ◽

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.

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

Canadian Journal of Physics ◽

10.1139/cjp-2019-0494 ◽

2020 ◽

Vol 98 (11) ◽

pp. 1015-1022 ◽

Cited By ~ 1

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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Base polynomials for degree and distance based topological invariants of n-bilinear straight pentachain

Journal of Information and Optimization Sciences ◽

10.1080/02522667.2021.1903202 ◽

2021 ◽

pp. 1-17

Author(s):

Abdul Rauf Nizami ◽

Khurram Shabbir ◽

Muhammad Shoaib Sardar ◽

Muhammad Qasim ◽

Murat Cancan ◽

...

Keyword(s):

Topological Invariants

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Rotationally symmetric flow of Reiner-Rivlin fluid over a heated porous wall using numerical approach

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/09544062211034204 ◽

2021 ◽

pp. 095440622110342

Author(s):

Talat Rafiq ◽

M Mustafa ◽

Junaid Ahmad Khan

Keyword(s):

Boundary Layer ◽

Layer Structure ◽

Full Range ◽

Porous Wall ◽

Symmetric Flow ◽

Axial Velocity Component ◽

Suction Velocity ◽

Rotationally Symmetric ◽

Non Linear System ◽

Rotationally Symmetric Flow

This research features one parameter family of solutions representing rotationally symmetric flow of non-Newtonian fluid obeying Reiner-Rivlin model. Such flows take place over a revolving plane permeable surface through origin such that fluid at infinity also undergoes uniform rotation about the vertical axis. Heat transfer accompanied with viscous heating effect is also analyzed. A similarity solution is proposed that results into a coupled non-linear system with four unknowns. Boundary layer structure is characterized by a parameter [Formula: see text] that compares angular velocity of external flow with that of the rotating surface. Solutions are developed by a well-known package bvp4c of MATLAB for full range of [Formula: see text]. Flow pattern for different choices of [Formula: see text] is scrutinized by computing both 2 D and 3 D streamlines. It is further noted that value of suction velocity is important with regards to the sign of axial velocity component. Boundary layer suppresses considerably whenever the surface is permeable. For sufficiently high suction velocity with [Formula: see text], entire fluid undergoes rigid body rotation. In no suction case, axially upward flow accelerates for increasing values of parameter [Formula: see text] in the range [Formula: see text], whereas opposite trend is apparent in the case [Formula: see text]. Results for normalized wall shear and Nusselt number are scrutinized for various choices of embedded parameters.

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Unification of topological invariants in Dirac models

Physical Review B ◽

10.1103/physrevb.103.245146 ◽

2021 ◽

Vol 103 (24) ◽

Author(s):

Gero von Gersdorff ◽

Shahram Panahiyan ◽

Wei Chen

Keyword(s):

Topological Invariants

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Machine learning topological invariants of non-Hermitian systems

Physical Review A ◽

10.1103/physreva.103.012419 ◽

2021 ◽

Vol 103 (1) ◽

Author(s):

Ling-Feng Zhang ◽

Ling-Zhi Tang ◽

Zhi-Hao Huang ◽

Guo-Qing Zhang ◽

Wei Huang ◽

...

Keyword(s):

Machine Learning ◽

Topological Invariants

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Measuring Topological Invariants in a Polaritonic Analog of Graphene

Physical Review Letters ◽

10.1103/physrevlett.126.127403 ◽

2021 ◽

Vol 126 (12) ◽

Author(s):

P. St-Jean ◽

A. Dauphin ◽

P. Massignan ◽

B. Real ◽

O. Jamadi ◽

...

Keyword(s):

Topological Invariants

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Topological invariants for the line graphs of some classes of graphs

Open Chemistry ◽

10.1515/chem-2019-0154 ◽

2019 ◽

Vol 17 (1) ◽

pp. 1483-1490

Author(s):

Xiaoqing Zhou ◽

Mustafa Habib ◽

Tariq Javeed Zia ◽

Asim Naseem ◽

Anila Hanif ◽

...

Keyword(s):

Communication Theory ◽

Chemical Reactivity ◽

Line Graph ◽

Chemical Properties ◽

Topological Invariants ◽

Line Graphs ◽

Physical And Chemical Properties ◽

Physical And Chemical ◽

Ladder Graphs ◽

And Chemical Properties

AbstractGraph theory plays important roles in the fields of electronic and electrical engineering. For example, it is critical in signal processing, networking, communication theory, and many other important topics. A topological index (TI) is a real number attached to graph networks and correlates the chemical networks with physical and chemical properties, as well as with chemical reactivity. In this paper, our aim is to compute degree-dependent TIs for the line graph of the Wheel and Ladder graphs. To perform these computations, we first computed M-polynomials and then from the M-polynomials we recovered nine degree-dependent TIs for the line graph of the Wheel and Ladder graphs.

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Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe

Physical Review D ◽

10.1103/physrevd.104.024006 ◽

2021 ◽

Vol 104 (2) ◽

Author(s):

Ana Alonso-Serrano ◽

David Brizuela ◽

Sara F. Uria

Keyword(s):

Locally Rotationally Symmetric ◽

Rotationally Symmetric

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