scholarly journals A Lattice Boltzmann Scheme for Diffusion Equation in Spherical Coordinate

2018 ◽  
Vol 1 (4) ◽  
Author(s):  
Debabrata Datta ◽  
T K Pal
Keyword(s):  
Diffusion Equation ◽  
Coordinate System ◽  
Lattice Boltzmann ◽  
Spherical Coordinate System ◽  
Cartesian Coordinate System ◽  
Spherical Coordinate ◽  
Cartesian Coordinate ◽  
Lattice Boltzmann Models ◽  
Boltzmann Method ◽  
Good Agreement

Lattice Boltzmann models for diffusion equation are generally in Cartesian coordinate system. Very few researchers have attempted to solve diffusion equation in spherical coordinate system. In the lattice Boltzmann based diffusion model in spherical coordinate system extra term, which is due to variation of surface area along radial direction, is modeled as source term. In this study diffusion equation in spherical coordinate system is first converted to diffusion equation which is similar to that in Cartesian coordinate system by using proper variable. The diffusion equation is then solved using standard lattice Boltzmann method. The results obtained for the new variable are again converted to the actual variable. The numerical scheme is verified by comparing the results of the simulation study with analytical solution. A good agreement between the two results is established.

scholarly journals GAUSS QUADRATURES – THE KEYSTONE OF LATTICE BOLTZMANN MODELS

2013 ◽  
Vol 25 (01) ◽  
pp. 1340016 ◽  
Author(s):  
BENJAMIN PIAUD ◽  
STÉPHANE BLANCO ◽  
RICHARD FOURNIER ◽  
VICTOR EUGEN AMBRUŞ ◽  
VICTOR SOFONEA
Keyword(s):  
Coordinate System ◽  
Lattice Boltzmann ◽  
Equilibrium Distribution ◽  
Temperature Jump ◽  
Equilibrium Distribution Function ◽  
Maximum Order ◽  
Spherical Coordinate ◽  
Gauss Hermite Quadrature ◽  
Cartesian Coordinate ◽  
Lattice Boltzmann Models

In this paper, we compare two families of Lattice Boltzmann (LB) models derived by means of Gauss quadratures in the momentum space. The first one is the HLB (N;Qx,Qy,Qz) family, derived by using the Cartesian coordinate system and the Gauss–Hermite quadrature. The second one is the SLB (N;K,L,M) family, derived by using the spherical coordinate system and the Gauss–Laguerre, as well as the Gauss–Legendre quadratures. These models order themselves according to the maximum order N of the moments of the equilibrium distribution function that are exactly recovered. Microfluidics effects (slip velocity, temperature jump, as well as the longitudinal heat flux that is not driven by a temperature gradient) are accurately captured during the simulation of Couette flow for Knudsen number (kn) up to 0.25.

Three-dimensional quantum mechanics in a curved space based on the q-addition

2019 ◽  
Vol 34 (29) ◽  
pp. 1950177
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Coordinate System ◽  
Three Dimensional ◽  
One Dimension ◽  
Cartesian Coordinate System ◽  
Spherical Coordinate ◽  
Curved Space ◽  
Dimension Formula ◽  
Cartesian Coordinate

In this paper, we extend the theory of the [Formula: see text]-deformed quantum mechanics in one dimension[Formula: see text] into three-dimensional case. We relate the [Formula: see text]-deformed quantum theory to the quantum theory in a curved space. We discuss the diagonal metric based on [Formula: see text]-addition in the Cartesian coordinate system and core radius of neutron star. We also discuss the diagonal metric based on [Formula: see text]-addition in the spherical coordinate system and [Formula: see text]-deformed Heisenberg atom model.

Study on the Diffusion Equations of Water Pollutants in Various Water Areas with Different Waterflow States

2011 ◽  
Vol 183-185 ◽  
pp. 1030-1034
Author(s):  
Xiao Ling Lei ◽  
Bo Tao
Keyword(s):  
Coordinate System ◽  
Diffusion Equations ◽  
Cylindrical Coordinate System ◽  
Cartesian Coordinate System ◽  
Coordinate Systems ◽  
Spherical Coordinate ◽  
Water Pollutants ◽  
Cylindrical Coordinate ◽  
Cartesian Coordinate ◽  
Further Development

The development and application of the diffusion equations of water pollutants are synthetically discussed. Depending on Cartesian Coordinate system, the water pollutants diffusion equations in different waterflow states are reviewed. And further development of the water pollutants diffusion equations in different waterflow states is extended to Cylindrical Coordinate system and Spherical Coordinate system respectively. This makes the simulating and modeling of water pollutants diffusion much more accurate and convenient in various water areas with different waterflow states by using different coordinate systems.

Kinematic Performance Evaluation for Heavy Duty Industrial Robot

2014 ◽  
Vol 940 ◽  
pp. 148-152
Author(s):  
S.Q. Li ◽  
Y.Y. Zou ◽  
Y.J. Li ◽  
Yan Jie Li
Keyword(s):  
Performance Evaluation ◽  
Coordinate System ◽  
Traditional Method ◽  
Industrial Robot ◽  
Experimental Results ◽  
Cartesian Coordinate System ◽  
Heavy Duty ◽  
Spherical Coordinate ◽  
Kinematic Performance ◽  
Cartesian Coordinate

Serial industrial robot has been widely used in assembly, welding, painting and other fields in which high kinematic performance is required. In this study, an non-contact approach for accuracy measuring is presented. Comparing with the traditional method based on spherical coordinate system, the approach presented in this study is based on the Cartesian coordinate system which has higher measuring accuracy. Furthermore, kinematic performance evaluation experiments for two types of industrial robot prototypes are proceeded. Experimental results testified that the accuracy of the target robot and proved the efficiency of the approach.

scholarly journals Half-a-century Burial of ρ, θ and φ in PDB

2021 ◽  
Author(s):  
Wei Li
Keyword(s):  
Deep Learning ◽  
Coordinate System ◽  
Structure Prediction ◽  
Data Bank ◽  
Learning Technology ◽  
Cartesian Coordinate System ◽  
Short Article ◽  
Spherical Coordinate ◽  
Cartesian Coordinate ◽  
Two Sides

Since the launch of Protein Data Bank (PDB) in 1971, Cartesian coordinate system (CCS) has been the default approach to specify atomic positions in biomolecular experimental structures with X, Y and Z. In 2020, a local spherical coordinate system (LSCS) approach was proposed as an alternative to CCS, i.e., ρ, θ and φ. Recently, the continued application of deep learning technology in protein structure prediction (PSP) saw a leap forward in the accuracy of PSP, as evidenced by AlphaFold of Google’s DeepMind. However, there still is room for the improvement of the performances of PSP algorithms to date. Given that geometrically, CCS and LSCS are like the two sides of a coin, this short article puts forward a hypothesis that the time is now ripe to end the half-a-century burial of ρ, θ and φ in PDB, and use them as LSCS features for the design of novel PSP algorithms in future.

Comparison Considerations Toward Investigating the Factors of Load and Age Group on the Maximum Reach Envelope

2020 ◽  
pp. 001872082096501
Author(s):  
Heather Johnston ◽  
Colleen Dewis ◽  
John Kozey
Keyword(s):  
Coordinate System ◽  
Three Dimensional ◽  
Spherical Coordinate System ◽  
Upper Body ◽  
Group Differences ◽  
Anthropometric Measures ◽  
Younger Adults ◽  
Present Measurement ◽  
Spherical Coordinate ◽  
Cylindrical Coordinate

Objective The objectives were to compare cylindrical and spherical coordinate representations of the maximum reach envelope (MRE) and apply these to a comparison of age and load on the MRE. Background The MRE is a useful measurement in the design of workstations and quantifying functional capability of the upper body. As a dynamic measure, there are human factors that impact the size, shape, and boundaries of the MRE. Method Three-dimensional reach measures were recorded using a computerized potentiometric system for anthropometric measures (CPSAM) on two adult groups (aged 18–25 years and 35–70 years). Reach trials were performed holding .0, .5, and 1 kg. Results Three-dimensional Cartesian coordinates were transformed into cylindrical ( r, θ , Z) and spherical ( r, θ, ϕ) coordinates. Median reach distance vectors were calculated for 54 panels within the MRE as created by incremented banding of the respective coordinate systems. Reach distance and reach area were compared between the two groups and the loaded conditions using a spherical coordinate system. Both younger adults and unloaded condition produced greater reach distances and reach areas. Conclusions Where a cylindrical coordinate system may reflect absolute reference for design, a normalized spherical coordinate system may better reflect functional range of motion and better compare individual and group differences. Age and load are both factors that impact the MRE. Application These findings present measurement considerations for use in human reach investigation and design.

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.

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