Minimal Surfaces in Three-Dimensional Riemannian Manifold Associated with a Second-Order ODE

2018 ◽  
Vol 15 (4) ◽  
Author(s):  
T. Bayrakdar ◽  
A. A. Ergin
Keyword(s):  
Riemannian Manifold ◽  
Minimal Surfaces ◽  
Three Dimensional ◽  
Second Order

scholarly journals The Björling problem for minimal surfaces in a Lorentzian three-dimensional Lie group

2014 ◽  
Vol 195 (1) ◽  
pp. 95-110 ◽  
Author(s):  
Adriana A. Cintra ◽  
Francesco Mercuri ◽  
Irene I. Onnis
Keyword(s):  
Lie Group ◽  
Minimal Surfaces ◽  
Three Dimensional ◽  
Björling Problem

scholarly journals ON THE INTEGRABILITY OF A CLASS OF MONGE–AMPÈRE EQUATIONS

2001 ◽  
Vol 13 (04) ◽  
pp. 529-543 ◽  
Author(s):  
J. C. BRUNELLI ◽  
M. GÜRSES ◽  
K. ZHELTUKHIN
Keyword(s):  
Sigma Models ◽  
Minimal Surfaces ◽  
Second Order ◽  
Lax Representation ◽  
Parameter Equation ◽  
Monge Ampere ◽  
Two Parameter

We give the Lax representations for the elliptic, hyperbolic and homogeneous second order Monge–Ampère equations. The connection between these equations and the equations of hydrodynamical type give us a scalar dispersionless Lax representation. A matrix dispersive Lax representation follows from the correspondence between sigma models, a two parameter equation for minimal surfaces and Monge–Ampère equations. Local as well nonlocal conserved densities are obtained.

THREE-DIMENSIONAL STAGNATION-POINT FLOW OVER A PERMEABLE STRETCHING/SHRINKING SHEET WITH A SECOND ORDER SLIP FLOW

2021 ◽  
Vol 10 (9) ◽  
pp. 3273-3282
Author(s):  
M.E.H. Hafidzuddin ◽  
R. Nazar ◽  
N.M. Arifin ◽  
I. Pop
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Flow Model ◽  
Nonlinear Partial Differential Equations ◽  
Slip Flow ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Second Order ◽  
Stagnation Point Flow ◽  
Shrinking Sheet

The problem of steady laminar three-dimensional stagnation-point flow on a permeable stretching/shrinking sheet with second order slip flow model is studied numerically. Similarity transformation has been used to reduce the governing system of nonlinear partial differential equations into the system of ordinary (similarity) differential equations. The transformed equations are then solved numerically using the \texttt{bvp4c} function in MATLAB. Multiple solutions are found for a certain range of the governing parameters. The effects of the governing parameters on the skin friction coefficients and the velocity profiles are presented and discussed. It is found that the second order slip flow model is necessary to predict the flow characteristics accurately.

scholarly journals Implicit Euler Method for Three-Dimensional Turbomachinery Flow Calculation

1993 ◽  
Author(s):  
Shih H. Chen ◽  
Anthony H. Eastland
Keyword(s):  
Three Dimensional ◽  
Prediction Method ◽  
Minimum Cost ◽  
Inviscid Flow ◽  
Turnaround Time ◽  
Euler Method ◽  
Second Order ◽  
Approximate Factorization ◽  
Implicit Euler Method ◽  
Numerical Instabilities

A compressible three-dimensional implicit Euler solution method for turbomachinery flows has been developed. The goal of the present study is to develop an efficient and reliable method that can be used to replace the semi-empirical, semi-analytical quasi-three-dimensional turbomachinery flow prediction method currently being used for multi-stage turbomachinery design at early design stages. Currently, a methodology has been developed based on an inviscid flow model (Euler solver) and tested on single blade rows for validation. The method presented here is derived from the Beam and Warming implicit approximate factorization (AF) finite difference algorithm. To avoid high frequency numerical instabilities associated with the use of central differencing schemes to obtain a spatial second order accuracy, a combined explicit and implicit artificial dissipation model is adopted. This model consists of a second order implicit dissipation and mixed second/fourth order explicit dissipation terms. A Cartesian coordinate H-grid generated by a three-dimensional interactive grid generator developed by Beach is used. Results for SSME High Pressure Fuel Turbine are presented and the comparison with experimental data is discussed. The use of the present implicit Euler method and the three-dimensional turbomachinery interactive grid generator shows that turnaround time could be as short as one day using a workstation. This allows the designers to explore optimal design configurations at minimum cost.

scholarly journals Second-order renormalization group flow of three-dimensional homogeneous geometries

2013 ◽  
Vol 21 (2) ◽  
pp. 435-467 ◽  
Author(s):  
Karsten Gimre ◽  
Christine Guenther ◽  
James Isenberg
Keyword(s):  
Renormalization Group ◽  
Three Dimensional ◽  
Second Order ◽  
Renormalization Group Flow ◽  
Group Flow

scholarly journals GROUP PROPERTIES OF A ONE-DIMENSIONAL NONLINEAR POROELASTICITY EQUATION

2019 ◽  
Vol 4 (1) ◽  
pp. 149-155
Author(s):  
Kholmatzhon Imomnazarov ◽  
Ravshanbek Yusupov ◽  
Ilham Iskandarov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Lie Algebra ◽  
Three Dimensional ◽  
Group Classification ◽  
Second Order ◽  
Partial Differential ◽  
One Dimensional ◽  
Preliminary Group

This paper studies a class of partial differential equations of second order , with arbitrary functions and , with the help of the group classification. The main Lie algebra of infinitely infinitesimal symmetries is three-dimensional. We use the method of preliminary group classification for obtaining the classifications of these equations for a one-dimensional extension of the main Lie algebra.

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