scholarly journals Rotational symmetry of classical orbits, arbitrary quantization of angular momentum and the role of the gauge field in two-dimensional space

2012 ◽  
Vol 21 (4) ◽  
pp. 040303 ◽  
Author(s):  
Jun-Li Xin ◽  
Jiu-Qing Liang
Keyword(s):  
Angular Momentum ◽  
Gauge Field ◽  
Dimensional Space ◽  
Rotational Symmetry ◽  
Two Dimensional ◽  
Classical Orbits

Plane groups – from basic to advanced crystallographic concepts

2003 ◽  
Vol 218 (9) ◽  
Author(s):  
K. Stróż
Keyword(s):  
Packing Density ◽  
Circle Packing ◽  
Dimensional Space ◽  
Two Dimensional ◽  
Plane Symmetry ◽  
Contour Map ◽  
3 Dimensional ◽  
Complex Approach ◽  
Diffraction Patterns

AbstractThe plane groups are rarely discussed in the crystallography courses and the didactic role of the plane groups for teaching symmetry is rather underestimated. Most crystallographic concepts known from 3-dimensional space group descriptions concern also these 2-dimensional groups and can be easier illustrated. Symmetry of atomic layers as well as symmetry of mosaics, lattice designs, symmetry of electron diffraction patterns or any pattern with two-dimensional periodicity can be characterised on a unique basis. Such a pattern can be generated by decorating the points of a crystallographic orbit by different graphical objects. The orbits are visualised as “crystallographic mosaics” (by connection of the closest points of the orbit), they can be characterised by Shubnikov or Laves nets and there always exists a number (circle packing density) that is related to a given orbit. The paper and a didactic computer program presented in it give some ideas and framework for the plane symmetry experiments: from finding the isometries on the generated patterns to identifying the non-characteristic orbits. It is also shown that the contour map of a circle packing density is a good frame for locating symmetry elements, asymmetric units or points with higher plane symmetry into a unit cell. The applied complex approach to the orbit characterisation will narrow the gap existing between concepts used by practising and theoretical crystallographers and mathematicians interested in tessellations.

scholarly journals D = (0|2) DIRAC–MAXWELL–EINSTEIN THEORY AS A WAY FOR DESCRIBING SUPERSYMMETRIC QUARTIONS

1994 ◽  
Vol 09 (09) ◽  
pp. 1555-1568 ◽  
Author(s):  
DMITRIJ P. SOROKIN ◽  
DMITRIJ V. VOLKOV
Keyword(s):  
Gravitational Field ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Dirac Theory ◽  
Einstein Theory ◽  
Abelian Gauge ◽  
Dimensional Space Time

Drawing an analogy with the Dirac theory of fermions interacting with electromagnetic and gravitational field we write down supersymmetric equations of motion and construct a superfield action for particles with spin [Formula: see text] and [Formula: see text] (quartions), where the role of quartion momentum in effective (2+1)-dimensional space–time is played by an Abelian gauge superfield propagating in a basic two-dimensional Grassmann-odd space with a cosmological constant showing itself as the quartion mass. So, the (0|2) (0 even and 2 odd) dimensional model of quartions interacting with the gauge and gravitational field manifests itself as an effective (2 + 1)-dimensional supersymmetric theory.

scholarly journals Encoding and Multiplexing of 2D Images with Orbital Angular Momentum Beams and the Use for Multiview Color Displays

Research ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
J. Chu ◽  
D. Chu ◽  
Q. Smithwick
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Data Communication ◽  
Two Dimensional ◽  
Color Displays ◽  
Future Data ◽  
Communication Scheme ◽  
Communication Needs

The orthogonal nature of different orbital angular momentum modes enables information transmission in optical communications with increased bandwidth through mode division multiplexing. So far the related works have been focused on using orbital angular momentum modes to encode/decode and multiplex point-based on-axis signals for maximum data channel numbers and capacity. Whether orbital angular momentum modes can be utilized to encode/decode off-axis signals for multiplexing in two-dimensional space is of significant importance both fundamentally and practically for its enormous potential in increasing the channel information capacity. In this work, a direct use of orbital angular momentum modes to encode/decode and multiplex two-dimensional images is realized in a scalable multiview display architecture, which can be utilized for viewing three-dimensional images from different angles. The effect of off-axis encoding/decoding and the resultant crosstalk between multiplexed different two-dimensional views are studied. Based on which, a color display of good image quality with four independent views is demonstrated. The resolution of the decoded images is analyzed and the limitation of this approach discussed. Moreover, a spatially multiplexed data communication scheme is also proposed with such a two-dimensional encoding/decoding approach to significantly enhance the data transmission capacity in free space for future data communication needs.

scholarly journals Encoding and Multiplexing of 2D Images with Orbital Angular Momentum Beams and the Use for Multiview Color Displays

Research ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
J. Chu ◽  
D. Chu ◽  
Q. Smithwick
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Data Communication ◽  
Two Dimensional ◽  
Color Displays ◽  
Future Data ◽  
Communication Scheme ◽  
Communication Needs

The orthogonal nature of different orbital angular momentum modes enables information transmission in optical communications with increased bandwidth through mode division multiplexing. So far the related works have been focused on using orbital angular momentum modes to encode/decode and multiplex point-based on-axis signals for maximum data channel numbers and capacity. Whether orbital angular momentum modes can be utilized to encode/decode off-axis signals for multiplexing in two-dimensional space is of significant importance both fundamentally and practically for its enormous potential in increasing the channel information capacity. In this work, a direct use of orbital angular momentum modes to encode/decode and multiplex two-dimensional images is realized in a scalable multiview display architecture, which can be utilized for viewing three-dimensional images from different angles. The effect of off-axis encoding/decoding and the resultant crosstalk between multiplexed different two-dimensional views are studied. Based on which, a color display of good image quality with four independent views is demonstrated. The resolution of the decoded images is analyzed and the limitation of this approach discussed. Moreover, a spatially multiplexed data communication scheme is also proposed with such a two-dimensional encoding/decoding approach to significantly enhance the data transmission capacity in free space for future data communication needs.

The Place of Painting in the Problem of Cinema Frame Composition

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Gergana Tabakova ◽  
Keyword(s):  
Visual Arts ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Formal Theory ◽  
Building Blocks ◽  
Two Dimensional ◽  
Sergei Eisenstein ◽  
Analysis And Synthesis ◽  
Unifying Principles

I offer a glimpse at the essence of the visual arts, which is related to the conceptual and the visual constructions through which the image is constructed. Although very different from painting, cinema, as a visual art, is influenced by it at a depth that is hard to imagine. I am taking into account the views of Sergei Eisenstein – one of the proponents of the formal theory of cinema, displayed in his theoretical works, as well as several of his films. Changes in the visual arts that result from the advent of photography give new meaning and role of painting. Artists occupied in painting are beginning to look for new ways to solve the problem of three-dimensional space in a two-dimensional surface. In the time that cinema develops own language, it sets to itself similar tasks. At that moment, cinema turns to the familiar visual-artistic experience and its forms in order to construct its own imaginative language. Cinema, like painting, gives us the joy of looking at the form in which the correlation of the elements is sensed. Accordingly, in order to bring pleasure and meaning, this form is created in constructions that we know from the field of painting. Editing, the basis of cinematic language, is built by putting together frames that serve as building blocks of the film. In this capacity they are of utmost importance. It is frame’s compositional organization, which at first takes place in a two-dimensional space as in picture that plays a major role in the approach to the editing. The composition of the frame which is the core of the editing process is built in the parameters of the main points through which the composition in painting can be built – rhythm, dynamics, statics, symmetry, asymmetry, analysis and synthesis of form, and at a later stage of the development of cinema – even color. The visual arts are based on similar structures and ways of building the form though they do it through different languages. There are unifying principles that define the world of images. Whether they are moving or static, their construction is often done on the basis of similar intentions and through similar instruments. Knowing them, understanding them, is a tool for creating quality images.

scholarly journals The role of sleep in forming a memory representation of a two-dimensional space

Hippocampus ◽  
2013 ◽  
Vol 23 (12) ◽  
pp. 1189-1197 ◽  
Author(s):  
Marc N. Coutanche ◽  
Carol A. Gianessi ◽  
Avi J.H. Chanales ◽  
Kate W. Willison ◽  
Sharon L. Thompson-Schill
Keyword(s):  
Dimensional Space ◽  
Memory Representation ◽  
Two Dimensional

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

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