Group Invariant Solutions of the Two-Dimensional Elastodynamics Problem in the Polar Coordinate System

2012 ◽  
Vol 29 (8) ◽  
pp. 084601
Author(s):  
Hou-Guo Li ◽  
Ke-Fu Huang
Keyword(s):  
Coordinate System ◽  
Polar Coordinate System ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Polar Coordinate ◽  
Group Invariant Solutions

scholarly journals Group-Invariant Solutions for Two-Dimensional Free, Wall, and Liquid Jets Having Finite Fluid Velocity at Orifice

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
R. Naz
Keyword(s):  
Fluid Velocity ◽  
Invariant Solution ◽  
Jet Flows ◽  
Order Partial Differential Equation ◽  
Free Wall ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
Third Order ◽  
Group Invariant ◽  
Group Invariant Solutions

The group-invariant solutions for nonlinear third-order partial differential equation (PDE) governing flow in two-dimensional jets (free, wall, and liquid) having finite fluid velocity at orifice are constructed. The symmetry associated with the conserved vector that was used to derive the conserved quantity for the jets (free, wall, and liquid) generated the group invariant solution for the nonlinear third-order PDE for the stream function. The comparison between results for two-dimensional jet flows having finite and infinite fluid velocity at orifice is presented. The general form of the group invariant solution for two-dimensional jets is given explicitly.

Investigating the Polar Qualification System

1998 ◽  
Vol 6 (A) ◽  
pp. A191-A200 ◽  
Author(s):  
Károly J. Kaffka ◽  
László S. Gyarmati
Keyword(s):  
Infrared Spectroscopy ◽  
Coordinate System ◽  
Near Infrared Spectroscopy ◽  
Near Infrared ◽  
Polar Coordinate System ◽  
Base Line ◽  
Two Dimensional ◽  
International Conference ◽  
Polar Coordinate ◽  
Characteristic Features

A new, rapid qualification method was introduced at the 3rd International Conference on Near Infrared Spectroscopy according to which a “quality point” was defined on a two-dimensional “quality plane”. The quality point of the investigated material was given by the center of its spectrum represented in a polar coordinate system. The method was further developed, three interpretations were given for the “center” of the polar spectrum, resulting in three different formulas for determining the x and y coordinates of the quality point. The effect of the change in the amplitude of the absorption peaks, the effect of the noise of the spectrum, the effect of the shifting and tilting the base-line of the spectrum on the location of the quality point were investigated using the three formulas. The results of the investigation and the characteristic features of the three formulas are introduced.

Symmetry Reductions and Exact Solutions of the Two-Layer Model in Atmosphere

2011 ◽  
Vol 66 (1-2) ◽  
pp. 75-86 ◽  
Author(s):  
Zhongzhou Dong ◽  
Fei Huang ◽  
Yong Chen
Keyword(s):  
Vector Fields ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
Layer Model ◽  
Horizontal Structure ◽  
One Dimensional ◽  
Group Invariant ◽  
Group Invariant Solutions ◽  
Two Layer Model ◽  
Model Equations

By means of the classical symmetry method, we investigate the two-layer model in atmosphere. The symmetry group of two-layer model equations is studied and its corresponding group invariant solutions are constructed. Ignoring the discussion of the infinite-dimensional subalgebra, we construct the optimal system of one-dimensional and two-dimensional group invariant solutions. Furthermore, using the associated vector fields of the obtained symmetry, we give out the reductions by one-dimensional and two-dimensional subalgebras, and some explicit solutions of two-layer model equations are obtained. For some interesting solutions, the figures are given out to show their properties. Some solutions can describe the horizontal structure of tropical cyclones (TC). Especially, a new solution of double-eyewall structure of TCs is firstly found in this two-layer model.

Rapid and precise method to convert a two dimensional image from Cartesian to polar coordinate system

1997 ◽  
Vol 68 (9) ◽  
pp. 3490-3493 ◽  
Author(s):  
Weimin Wu ◽  
Yoshihiro Kato ◽  
K. Yamazaki ◽  
M. Yoshino ◽  
A. Danjo ◽  
...  
Keyword(s):  
Coordinate System ◽  
Polar Coordinate System ◽  
Two Dimensional ◽  
Precise Method ◽  
Dimensional Image ◽  
Two Dimensional Image ◽  
Polar Coordinate

scholarly journals Symmetry Reduction of the Two-Dimensional Ricci Flow Equation

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mehdi Nadjafikhah ◽  
Mehdi Jafari
Keyword(s):  
Ricci Flow ◽  
Adjoint Representation ◽  
Flow Equation ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
Similarity Reduction ◽  
One Dimensional ◽  
Group Invariant ◽  
Dimensional Group ◽  
Group Invariant Solutions

This paper is devoted to obtain the one-dimensional group invariant solutions of the two-dimensional Ricci flow ((2D) Rf) equation. By classifying the orbits of the adjoint representation of the symmetry group on its Lie algebra, the optimal system of one-dimensional subalgebras of the ((2D) Rf) equation is obtained. For each class, we will find the reduced equation by the method of similarity reduction. By solving these reduced equations, we will obtain new sets of group invariant solutions for the ((2D) Rf) equation.

Sign in / Sign up

Export Citation Format

Share Document