scholarly journals Helical Hypersurfaces in Minkowski Geometry E 1 4

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1206
Author(s):  
Erhan Güler
Keyword(s):  
Minkowski Geometry ◽  
Axis Of Rotation

We define helical (i.e., helicoidal) hypersurfaces depending on the axis of rotation in Minkowski four-space E 1 4 . There are three types of helicoidal hypersurfaces. We derive equations for the curvatures (i.e., Gaussian and mean) and give some examples of these hypersurfaces. Finally, we obtain a theorem classifying the helicoidal hypersurface with timelike axes satisfying Δ I H = A H .

On Variations in the Chandler Frequency

1972 ◽  
Vol 1 ◽  
pp. 77-85
Author(s):  
H.J.M. Abraham ◽  
J.N. Boots
Keyword(s):  
Axis Of Rotation ◽  
The Earth ◽  
Actual Motion ◽  
Chandler Frequency

This paper suggests that some of the reported changes in the Chandler frequency are associated with inelastic changes in the Earth. There has been controversy as to how much of the apparent secular polar drift is due to actual motion of the axis of rotation within the Earth, and how much it is merely the reflection of movements by certain observatories. Therefore, when more southern data are available it will be interesting to see whether similar results are obtained.

Reference Coordinate System Requirements for Geophysics

1975 ◽  
Vol 26 ◽  
pp. 87-92
Author(s):  
P. L. Bender
Keyword(s):  
Coordinate System ◽  
Polar Motion ◽  
Main Part ◽  
Measurement Techniques ◽  
Reference Points ◽  
Angular Motion ◽  
Coordinate Systems ◽  
Axis Of Rotation ◽  
The Earth ◽  
Fixed System

AbstractFive important geodynamical quantities which are closely linked are: 1) motions of points on the Earth’s surface; 2)polar motion; 3) changes in UT1-UTC; 4) nutation; and 5) motion of the geocenter. For each of these we expect to achieve measurements in the near future which have an accuracy of 1 to 3 cm or 0.3 to 1 milliarcsec.From a metrological point of view, one can say simply: “Measure each quantity against whichever coordinate system you can make the most accurate measurements with respect to”. I believe that this statement should serve as a guiding principle for the recommendations of the colloquium. However, it also is important that the coordinate systems help to provide a clear separation between the different phenomena of interest, and correspond closely to the conceptual definitions in terms of which geophysicists think about the phenomena.In any discussion of angular motion in space, both a “body-fixed” system and a “space-fixed” system are used. Some relevant types of coordinate systems, reference directions, or reference points which have been considered are: 1) celestial systems based on optical star catalogs, distant galaxies, radio source catalogs, or the Moon and inner planets; 2) the Earth’s axis of rotation, which defines a line through the Earth as well as a celestial reference direction; 3) the geocenter; and 4) “quasi-Earth-fixed” coordinate systems.When a geophysicists discusses UT1 and polar motion, he usually is thinking of the angular motion of the main part of the mantle with respect to an inertial frame and to the direction of the spin axis. Since the velocities of relative motion in most of the mantle are expectd to be extremely small, even if “substantial” deep convection is occurring, the conceptual “quasi-Earth-fixed” reference frame seems well defined. Methods for realizing a close approximation to this frame fortunately exist. Hopefully, this colloquium will recommend procedures for establishing and maintaining such a system for use in geodynamics. Motion of points on the Earth’s surface and of the geocenter can be measured against such a system with the full accuracy of the new techniques.The situation with respect to celestial reference frames is different. The various measurement techniques give changes in the orientation of the Earth, relative to different systems, so that we would like to know the relative motions of the systems in order to compare the results. However, there does not appear to be a need for defining any new system. Subjective figures of merit for the various system dependon both the accuracy with which measurements can be made against them and the degree to which they can be related to inertial systems.The main coordinate system requirement related to the 5 geodynamic quantities discussed in this talk is thus for the establishment and maintenance of a “quasi-Earth-fixed” coordinate system which closely approximates the motion of the main part of the mantle. Changes in the orientation of this system with respect to the various celestial systems can be determined by both the new and the conventional techniques, provided that some knowledge of changes in the local vertical is available. Changes in the axis of rotation and in the geocenter with respect to this system also can be obtained, as well as measurements of nutation.

The spindle stage: A powerful optical tool

1988 ◽  
Vol 46 ◽  
pp. 52-53
Author(s):  
Mickey E. Gunter ◽  
F. Donald Bloss
Keyword(s):  
Significant Error ◽  
Optical Data ◽  
Refractive Indices ◽  
Axis Of Rotation ◽  
Polarizing Microscope ◽  
Microscope Stage

A single, reasonably homogeneous, nonopaque 30-to-300 μm crystal, mounted on a spindle stage and studied by immersion methods under a polarizing microscope, yields optical data frequently sufficient to identify and characterize a substance unequivocally. The data obtainable include (1) the orientation of the crystal's principal vibration axes and (2) its principal refractive indices, to within 0.0002 if desired, for light vibrating along these principal vibration axes. Spindle stages tend to be simple and relatively inexpensive, some costing less than $50. They permit rotation of the crystal about a single axis which is parallel to the microscope stage. This spindle or S-axis is thus perpendicular to the M-axis, namely the microscope stage's axis of rotation.A spindle stage excels when studying anisotropic crystals. It orients uniaxial crystals within minutes and biaxial crystals almost as quickly so that their principal refractive indices - ɛ and ω (uniaxial); α, β and γ (biaxial) - can be determined without significant error from crystal misorientation.

scholarly journals On the 3D → 2D Isomerization of Hexaborane(12)

Chemistry ◽  
2021 ◽  
Vol 3 (1) ◽  
pp. 28-38
Author(s):  
Josep M. Oliva-Enrich ◽  
Ibon Alkorta ◽  
José Elguero ◽  
Maxime Ferrer ◽  
José I. Burgos
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Transition States ◽  
Three Dimensional ◽  
Reaction Coordinate ◽  
Intrinsic Reaction Coordinate ◽  
Limiting Factor ◽  
Two Dimensional ◽  
Axis Of Rotation

By following the intrinsic reaction coordinate connecting transition states with energy minima on the potential energy surface, we have determined the reaction steps connecting three-dimensional hexaborane(12) with unknown planar two-dimensional hexaborane(12). In an effort to predict the potential synthesis of finite planar borane molecules, we found that the reaction limiting factor stems from the breaking of the central boron-boron bond perpendicular to the C2 axis of rotation in three-dimensional hexaborane(12).

scholarly journals Dendrogramic Representation of Data: CHSH Violation vs. Nonergodicity

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 971
Author(s):  
Oded Shor ◽  
Felix Benninger ◽  
Andrei Khrennikov
Keyword(s):  
Experimental Data ◽  
Clustering Algorithms ◽  
Realistic Model ◽  
Minkowski Geometry ◽  
Ultrametric Spaces ◽  
Chsh Inequality ◽  
Classical Quantum ◽  
Basic Features ◽  
Totally Disconnected ◽  
Explicate Order

This paper is devoted to the foundational problems of dendrogramic holographic theory (DH theory). We used the ontic–epistemic (implicate–explicate order) methodology. The epistemic counterpart is based on the representation of data by dendrograms constructed with hierarchic clustering algorithms. The ontic universe is described as a p-adic tree; it is zero-dimensional, totally disconnected, disordered, and bounded (in p-adic ultrametric spaces). Classical–quantum interrelations lose their sharpness; generally, simple dendrograms are “more quantum” than complex ones. We used the CHSH inequality as a measure of quantum-likeness. We demonstrate that it can be violated by classical experimental data represented by dendrograms. The seed of this violation is neither nonlocality nor a rejection of realism, but the nonergodicity of dendrogramic time series. Generally, the violation of ergodicity is one of the basic features of DH theory. The dendrogramic representation leads to the local realistic model that violates the CHSH inequality. We also considered DH theory for Minkowski geometry and monitored the dependence of CHSH violation and nonergodicity on geometry, as well as a Lorentz transformation of data.

Formation and dynamics of Saturn and its disk simulated by using a new N-body model

Open Physics ◽  
2003 ◽  
Vol 1 (4) ◽  
Author(s):  
A. Pavlov ◽  
Y. Pavlova
Keyword(s):  
Surface Density ◽  
Electromagnetic Interaction ◽  
The Core ◽  
Body Model ◽  
Magnetic Forces ◽  
Axis Of Rotation ◽  
Gravitational Model ◽  
Minor Part ◽  
Body Self ◽  
A Minor

AbstractThe formation of Saturn and its disk is simulated using a new N-body self-gravitational model. It is demonstrated that the formation of the disk and the planet is the result of gravitational contraction of a slowly rotated particle cloud that have a shape of slightly deformed sphere. The sphere was flattened by a coefficient of 0.8 along the axis of rotation. During the gravitational contraction, the major part of the cloud transformed into a planet and a minor part transformed into a disk. The thin structured disk is a result of the electromagnetic interaction in which the magnetic forces acting on charged particles of the cloud originate in the core of the planet. The simulation program gives such parameters of Saturn as the escape velocity of about 35 km/s at the surface, density, rotational velocities of the rings and temperature distribution.

scholarly journals Triggering avalanches by transverse perturbations in a rotating drum

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Vicente Salinas ◽  
Cristóbal Quiñinao ◽  
Sebastián González ◽  
Gustavo Castillo
Keyword(s):  
Hopf Bifurcation ◽  
Theoretical Model ◽  
Order Parameter ◽  
Small Scale ◽  
Rotating Drum ◽  
Governing Parameter ◽  
Stick Slip ◽  
Slip Regime ◽  
Axis Of Rotation

AbstractWe study the role of small-scale perturbations in the onset of avalanches in a rotating drum in the stick-slip regime. By vibrating the system along the axis of rotation with an amplitude orders of magnitude smaller than the particles’ diameter, we found that the order parameter that properly describes the system is the kinetic energy. We also show that, for high enough frequencies, the onset of the avalanche is determined by the amplitude of the oscillation, contrary to previous studies that showed that either acceleration or velocity was the governing parameter. Finally, we present a theoretical model that explains the transition between the continuous and discrete avalanche regimes as a supercritical Hopf bifurcation.

Cervical Plate Stiffness Affects the Distribution of Loads and the Location of the Instantaneous Axis of Rotation of the Spine In Vitro

2016 ◽  
Vol 16 (10) ◽  
pp. S260-S261 ◽  
Author(s):  
Josh Peterson ◽  
Carolyn Chlebek ◽  
Ashley Clough ◽  
Alexandra Wells ◽  
Eric H. Ledet
Keyword(s):  
Instantaneous Axis Of Rotation ◽  
Axis Of Rotation ◽  
Cervical Plate ◽  
Instantaneous Axis
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