scholarly journals Free Motion of Particles in the Lobachevskii Space in Terms of the Scattering Theory

2019 ◽  
Vol 64 (12) ◽  
pp. 1108
Author(s):  
Yu. A. Kurochkin
Keyword(s):  
Integral Equation ◽  
Scattering Amplitude ◽  
Separation Of Variables ◽  
Free Particle ◽  
Three Dimensional ◽  
Lobachevskii Space ◽  
Analytical Functions ◽  
Axis Of Symmetry ◽  
Cartesian Coordinate ◽  
The Relationship

The problem of the motion of a free particle in the three-dimensional Lobachevskii space are interpreted as scattering by the space. The quantum-mechanical case is considered on the basis of the integral equation derived from the Schr¨odinger equation. After the separation of variables in a quasi-Cartesian coordinate system, the integral equation is derived for the momentum component along the axis of symmetry of a horosphere, which coincides with the z axis. The relationship between the scattering amplitude and analytical functions is established. The methods of iteration and finite differences are used to solve the integral equation.

scholarly journals Description of a free quantum-mechanical particle in the Lobachevsky space based on the integral equation

2019 ◽  
Vol 55 (3) ◽  
pp. 319-324
Author(s):  
Yu. A. Kurochkin
Keyword(s):  
Integral Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Scattering Amplitude ◽  
Separation Of Variables ◽  
Free Particle ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Quantum Mechanical ◽  
Lobachevsky Space

The quantum mechanical problem of the motion of a free particle in the three-dimensional Lobachevsky space is interpreted as space scattering. The quantum case is considered on the basis of the integral equation derived from the Schrödinger equation. The work continues the problem considered in [1] studied within the framework of classical mechanics and on the basis of solving the Schrödinger equation in quasi-Cartesian coordinates. The proposed article also uses a quasi-Cartesian coordinate system; however after the separation of variables, the integral equation is derived for the motion along the axis of symmetry horosphere axis coinciding with the z axis. The relationship between the scattering amplitude and the analytical functions is established. The iteration method and finite differences for solution of the integral equation are proposed.

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

2020 ◽  
Vol 23 (3) ◽  
pp. 306-311
Author(s):  
Yu. Kurochkin ◽  
Dz. Shoukavy ◽  
I. Boyarina
Keyword(s):  
Constant Curvature ◽  
Jacobi Equation ◽  
Separation Of Variables ◽  
Center Of Mass ◽  
Three Dimensional ◽  
Relative Distance ◽  
Dimensional Sphere ◽  
Body System ◽  
Spaces Of Constant Curvature ◽  
Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

scholarly journals Brain capillary structures of schizophrenia cases and controls show a correlation with their neuron structures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Rino Saiga ◽  
Masayuki Uesugi ◽  
Akihisa Takeuchi ◽  
Kentaro Uesugi ◽  
Yoshio Suzuki ◽  
...  
Keyword(s):  
Blood Vessels ◽  
Structural Parameters ◽  
Three Dimensional ◽  
Superior Temporal Gyrus ◽  
Anterior Cingulate ◽  
Dimensional Structure ◽  
Constant Diameter ◽  
The Mean ◽  
Cartesian Coordinate ◽  
Micrometer Scale

AbstractBrain blood vessels constitute a micrometer-scale vascular network responsible for supply of oxygen and nutrition. In this study, we analyzed cerebral tissues of the anterior cingulate cortex and superior temporal gyrus of schizophrenia cases and age/gender-matched controls by using synchrotron radiation microtomography or micro-CT in order to examine the three-dimensional structure of cerebral vessels. Over 1 m of cerebral blood vessels was traced to build Cartesian-coordinate models, which were then used for calculating structural parameters including the diameter and curvature of the vessels. The distribution of vessel outer diameters showed a peak at 7–9 μm, corresponding to the diameter of the capillaries. Mean curvatures of the capillary vessels showed a significant correlation to the mean curvatures of neurites, while the mean capillary diameter was almost constant, independent of the cases. Our previous studies indicated that the neurites of schizophrenia cases are thin and tortuous compared to controls. The curved capillaries with a constant diameter should occupy a nearly constant volume, while neurons suffering from neurite thinning should have reduced volumes, resulting in a volumetric imbalance between the neurons and the vessels. We suggest that the observed structural correlation between neurons and blood vessels is related to neurovascular abnormalities in schizophrenia.

scholarly journals Colourful Poincaré symmetry, gravity and particle actions

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Joaquim Gomis ◽  
Euihun Joung ◽  
Axel Kleinschmidt ◽  
Karapet Mkrtchyan
Keyword(s):  
Field Theory ◽  
Free Particle ◽  
Three Dimensional ◽  
Background Field ◽  
Quantum Field ◽  
Symmetry Factor ◽  
Starting Point ◽  
Poincaré Algebra ◽  
Poincaré Symmetry ◽  
Three Space

Abstract We construct a generalisation of the three-dimensional Poincaré algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincaré gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincaré symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory.

scholarly journals A Field Measurement Based Wind Characteristics Analysis of a Typhoon in Near-Ground Boundary Layer

Atmosphere ◽  
2021 ◽  
Vol 12 (7) ◽  
pp. 873
Author(s):  
Dandan Xia ◽  
Liming Dai ◽  
Li Lin ◽  
Huaifeng Wang ◽  
Haitao Hu
Keyword(s):  
Turbulence Intensity ◽  
Field Measurement ◽  
Three Dimensional ◽  
Wind Data ◽  
Statistical Characteristics ◽  
Gust Factor ◽  
Characteristics Analysis ◽  
Wind Characteristics ◽  
The Mean ◽  
The Relationship

The field measurement was conducted to observe the wind field data of West Pacific typhoon “Maria” in this research. With the application of ultrasonic anemometers installed in different heights (10 m, 80 m, 100 m) of the tower, the three dimensional wind speed data of typhoon “Maria” was acquired. In addition, vane-type anemometers were installed to validate the accuracy of the wind data from ultrasonic anemometers. Wind characteristics such as the mean wind profile, turbulence intensity, integral length scale, and wind spectrum are studied in detail using the collected wind data. The relationship between the gust factor and turbulence intensity was also studied and compared with the existing literature to demonstrate the characteristics of Maria. The statistical characteristics of the turbulence intensity and gust factor are presented. The corresponding conclusion remarks are expected to provide a useful reference for designing wind-resistant buildings and structures.

scholarly journals Three-dimensional relationships between tumor cells and microcirculation with double cyanine immunolabeling, laser scanning confocal microscopy, and computer-assisted reconstruction: an alternative to cast corrosion preparations.

1994 ◽  
Vol 42 (5) ◽  
pp. 681-686 ◽  
Author(s):  
V Rummelt ◽  
L M Gardner ◽  
R Folberg ◽  
S Beck ◽  
B Knosp ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Blood Vessels ◽  
Tumor Cells ◽  
Laser Scanning ◽  
Three Dimensional ◽  
Melanoma Cells ◽  
Tumor Blood Vessels ◽  
The Relationship ◽  
Scanning Electron

The morphology of the microcirculation of uveal melanomas is a reliable market of tumor progression. Scanning electron microscopy of cast corrosion preparations can generate three-dimensional views of these vascular patterns, but this technique sacrifices the tumor parenchyma. Formalin-fixed wet tissue sections 100-150 microns thick from uveal melanomas were stained with the lectin Ulex europaeus agglutinin I (UEAI) and proliferating cell nuclear antigen (PCNA) to demonstrate simultaneously the tumor blood vessels and proliferating tumor cells. Indocarbocyanine (Cy3) was used as a fluorophore for UEAI and indodicarbocyanine (Cy5) was used for PCNA. Double labeled sections were examined with a laser scanning confocal microscope. Images of both stains were digitized at the same 5-microns intervals and each of the two images per interval was combined digitally to form one image. These combined images were visualized through voxel processing to study the relationship between melanoma cells expressing PCNA and various microcirculatory patterns. This technique produces images comparable to scanning electron microscopy of cast corrosion preparations while permitting simultaneous localization of melanoma cells expressing PCNA. The microcirculatory tree can be viewed from any perspective and the relationship between tumor cells and the tumor blood vessels can be studied concurrently in three dimensions. This technique is an alternative to cast corrosion preparations.

On the Flexural-Torsional Behavior of a Straight Elastic Beam Subject to Terminal Moments

1993 ◽  
Vol 60 (2) ◽  
pp. 498-505 ◽  
Author(s):  
Z. Tan ◽  
J. A. Witz
Keyword(s):  
Coordinate System ◽  
Cross Section ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Beam ◽  
Cartesian Coordinate System ◽  
Kinematic Constraints ◽  
Torsional Behavior ◽  
Cartesian Coordinate

This paper discusses the large-displacement flexural-torsional behavior of a straight elastic beam with uniform circular cross-section subject to arbitrary terminal bending and twisting moments. The beam is assumed to be free from any kinematic constraints at both ends. The equilibrium equation is solved analytically with the full expression for curvature to obtain the deformed configuration in a three-dimensional Cartesian coordinate system. The results show the influence of the terminal moments on the beam’s deflected configuration.

Sign in / Sign up

Export Citation Format

Share Document