Generalized Variational Principle for Compressible S2-Flow in Mixed-Flow Turbomachinery Using Semi-Inverse Method

1998 ◽  
Vol 15 (2) ◽  
Author(s):  
Ji-Huan He
Keyword(s):  
Variational Principle ◽  
Inverse Method ◽  
Generalized Variational Principle ◽  
Mixed Flow

scholarly journals On the semi-inverse method and variational principle

2013 ◽  
Vol 17 (5) ◽  
pp. 1565-1568 ◽  
Author(s):  
Xue-Wei Li ◽  
Ya Li ◽  
Ji-Huan He
Keyword(s):  
Heat Conduction ◽  
Variational Principle ◽  
Inverse Method ◽  
Generalized Variational Principle ◽  
Open Forum ◽  
One Dimensional ◽  
History Of

In this Open Forum, Liu et al. proved the equivalence between He-Lee 2009 variational principle and that by Tao and Chen (Tao, Z. L., Chen, G. H., Thermal Science, 17(2013), pp. 951-952) for one dimensional heat conduction. We confirm the correction of Liu et al.?s proof, and give a short remark on the history of the semi-inverse method for establishment of a generalized variational principle.

scholarly journals Generalized Variational Principle for the Fractal (2 + 1)-Dimensional Zakharov–Kuznetsov Equation in Quantum Magneto-Plasmas

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1022
Author(s):  
Yan-Hong Liang ◽  
Kang-Jia Wang
Keyword(s):  
Variational Principle ◽  
Variational Formulation ◽  
Inverse Method ◽  
Fractal Theory ◽  
Traveling Wave Solutions ◽  
Generalized Variational Principle ◽  
Fractal Derivative ◽  
Fractal Space ◽  
First Time ◽  
Symmetric Theory

In this paper, we propose the fractal (2 + 1)-dimensional Zakharov–Kuznetsov equation based on He’s fractal derivative for the first time. The fractal generalized variational formulation is established by using the semi-inverse method and two-scale fractal theory. The obtained fractal variational principle is important since it not only reveals the structure of the traveling wave solutions but also helps us study the symmetric theory. The finding of this paper will contribute to the study of symmetry in the fractal space.

Lagrange crisis and generalized variational principle for 3D unsteady flow

2019 ◽  
Vol 30 (3) ◽  
pp. 1189-1196 ◽  
Author(s):  
Ji-Huan He
Keyword(s):  
Variational Principle ◽  
Unsteady Flow ◽  
Lagrange Multiplier ◽  
Unknown Function ◽  
Inverse Method ◽  
Variational Principles ◽  
Multiplier Method ◽  
Generalized Variational Principle ◽  
Content Type ◽  
3D Unsteady Flow

Purpose A three-dimensional (3D) unsteady potential flow might admit a variational principle. The purpose of this paper is to adopt a semi-inverse method to search for the variational formulation from the governing equations. Design/methodology/approach A suitable trial functional with a possible unknown function is constructed, and the identification of the unknown function is given in detail. The Lagrange multiplier method is used to establish a generalized variational principle, but in vain. Findings Some new variational principles are obtained, and the semi-inverse method can easily overcome the Lagrange crisis. Practical implications The semi-inverse method sheds a promising light on variational theory, and it can replace the Lagrange multiplier method for the establishment of a generalized variational principle. It can be used for the establishment of a variational principle for fractal and fractional calculus. Originality/value This paper establishes some new variational principles for the 3D unsteady flow and suggests an effective method to eliminate the Lagrange crisis.

scholarly journals Generalized Variational Principle for Long Water-Wave Equation by He's Semi-Inverse Method

2009 ◽  
Vol 2009 ◽  
pp. 1-5 ◽  
Author(s):  
Weimin Zhang
Keyword(s):  
Water Wave ◽  
Inverse Method ◽  
Variational Principles ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Partial Differential Equation ◽  
Variational Formula ◽  
Generalized Variational Principle ◽  
Partial Differential ◽  
Water Wave Problem ◽  
Mathematics And Physics

Variational principles for nonlinear partial differential equations have come to play an important role in mathematics and physics. However, it is well known that not every nonlinear partial differential equation admits a variational formula. In this paper, He's semi-inverse method is used to construct a family of variational principles for the long water-wave problem.

A GENERALIZED VARIATIONAL PRINCIPLE FOR TRANSPORT PHENOMENA

1958 ◽  
Vol 36 (10) ◽  
pp. 1308-1318 ◽  
Author(s):  
G. E. Tauber
Keyword(s):  
Magnetic Field ◽  
Variational Principle ◽  
Ritz Method ◽  
Transport Coefficients ◽  
Distribution Functions ◽  
Generalized Variational Principle ◽  
Lattice Vibrations ◽  
Arbitrary Direction ◽  
Energy Surfaces ◽  
Thermomagnetic Phenomena

A generalized variational principle has been formulated which takes the phonon distribution functions and the external magnetic field into account, is valid for an arbitrary direction of the electric field and polarization of the lattice vibrations, and does not depend on any special form of the energy surfaces. The various transport coefficients, for both thermoelectric and thermomagnetic phenomena, are obtained by the Ritz method in terms of infinite determinants without requiring an explicit solution of the transport equations.

A fractal modification of Chen–Lee–Liu equation and its fractal variational principle

2021 ◽  
pp. 2150214
Author(s):  
Ji-Huan He ◽  
Chun-Hui He ◽  
Tareq Saeed
Keyword(s):  
Variational Principle ◽  
Solitary Wave ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Inverse Method ◽  
Ultrashort Pulses

The Chen–Lee–Liu equation is a modified Schrödinger equation to describe a solitary wave of ultrashort pulses in optics, which lead to a discontinuous time, so a fractal modification is suggested and a fractal variational principle is established by the semi-inverse method.

New Solitary Wave Solution for the Boussinesq Wave Equation Using the Semi-Inverse Method and the Exp-Function Method

2009 ◽  
Vol 64 (11) ◽  
pp. 709-712 ◽  
Author(s):  
Wenjun Liu
Keyword(s):  
Wave Equation ◽  
Variational Principle ◽  
Solitary Wave ◽  
Wave Solution ◽  
Variational Formulation ◽  
Function Method ◽  
Inverse Method ◽  
Solitary Wave Solution ◽  
Solitary Solutions

Using the semi-inverse method, a variational formulation is established for the Boussinesq wave equation. Based on the obtained variational principle, solitary solutions in the sech-function and expfunction forms are obtained

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