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1 – 10 of 361
Article
Publication date: 1 February 2006

Jing‐li Fu, Li‐qun Chen and Xiang‐wei Chen

In this letter, based on the infinitesimal transformations with respect to the generalized coordinates and generalized momentums, we obtain the definition, determining equations…

121

Abstract

In this letter, based on the infinitesimal transformations with respect to the generalized coordinates and generalized momentums, we obtain the definition, determining equations and structure equation of the momentum‐dependent symmetry for the systems. This study directly leads to the non‐ Noether type conserved quantity for the systems. Further we also give the inverse issue of the momentum‐dependent symmetries of the systems. However, a theory of momentum‐dependent symmetries of the nonconservative Hamiltonian systems is established. Finally, an example is discussed to illustrate the results.

Details

Multidiscipline Modeling in Materials and Structures, vol. 2 no. 2
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 1 August 2006

Fakhar Kamran, Chen Zu‐Chi, Ji Xiaoda and Yi Cheng

Providing a much easier (direct) approach to calculate the Lie point symmetries of (3 + 1) unsteady Navier‐Stokes equations for viscous, incompressible flow in cylindrical polar…

Abstract

Purpose

Providing a much easier (direct) approach to calculate the Lie point symmetries of (3 + 1) unsteady Navier‐Stokes equations for viscous, incompressible flow in cylindrical polar coordinates.

Design/methodology/approach

Lie group theory, is applied to the equations of motion. Symmetries obtained through a direct approach are then used to reduce (3 + 1) Navier‐Stokes system to a system of ordinary differential equations.

Findings

We observed that the approach applied here to calculate the symmetries of the group is entirely straightforward and involves less calculation as compared to the computer programs such as LIE, Symmgrp.max (MACSYMA) or other symbolic manipulation systems. Further, results obtained here will be practical and useful in comprehending the fluid flow behavior.

Research limitations/implications

We only obtained the exact solution through basic transformations (translation and scaling). The similarity reduction through other subalgebras (finite and infinite dimensions) can be used to explore more facts about the Navier‐Stokes equations.

Originality/value

Direct approach provided in this paper can be utilized to achieve symmetries of other physically important PDEs.

Details

Engineering Computations, vol. 23 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 23 October 2023

Gorakh Nath and Abhay Maurya

The purpose of the present article is to obtain the similarity solution for the shock wave generated by a piston propagating in a self-gravitating nonideal gas under the impact of…

Abstract

Purpose

The purpose of the present article is to obtain the similarity solution for the shock wave generated by a piston propagating in a self-gravitating nonideal gas under the impact of azimuthal magnetic field for adiabatic and isothermal flows.

Design/methodology/approach

The Lie group theoretic method given by Sophus Lie is used to obtain the similarity solution in the present article.

Findings

Similarity solution with exponential law shock path is obtained for both ideal and nonideal gas cases. The effects on the flow variables, density ratio at the shock front and shock strength by the variation of the shock Cowling number, adiabatic index of the gas, gravitational parameter and nonidealness parameter are investigated. The shock strength decreases with an increase in the shock Cowling number, nonidealness parameter and adiabatic index, whereas the strength of the shock wave increases with an increase in gravitational parameter.

Originality/value

Propagation of shock wave with spherical geometry in a self-gravitating nonideal gas under the impact of azimuthal magnetic field for adiabatic and isothermal flows has not been studied by any author using the Lie group theoretic method.

Details

Engineering Computations, vol. 40 no. 9/10
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 5 June 2017

Ram Jiwari, Vikas Kumar, Ram Karan and Ali Saleh Alshomrani

This paper aims to deal with two-dimensional magneto-hydrodynamic (MHD) Falkner–Skan boundary layer flow of an incompressible viscous electrically conducting fluid over a…

Abstract

Purpose

This paper aims to deal with two-dimensional magneto-hydrodynamic (MHD) Falkner–Skan boundary layer flow of an incompressible viscous electrically conducting fluid over a permeable wall in the presence of a magnetic field.

Design/methodology/approach

Using the Lie group approach, the Lie algebra of infinitesimal generators of equivalence transformations is constructed for the equation under consideration. Using these suitable similarity transformations, the governing partial differential equations are reduced to linear and nonlinear ordinary differential equations (ODEs). Further, Haar wavelet approach is applied to the reduced ODE under the subalgebra 4.1 for constructing numerical solutions of the flow problem.

Findings

A new type of solutions was obtained of the MHD Falkner–Skan boundary layer flow problem using the Haar wavelet quasilinearization approach via Lie symmetric analysis.

Originality/value

To find a solution for the MHD Falkner–Skan boundary layer flow problem using the Haar wavelet quasilinearization approach via Lie symmetric analysis is a new approach for fluid problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Book part
Publication date: 23 June 2016

Amos Golan and Robin L. Lumsdaine

Although in principle prior information can significantly improve inference, incorporating incorrect prior information will bias the estimates of any inferential analysis. This…

Abstract

Although in principle prior information can significantly improve inference, incorporating incorrect prior information will bias the estimates of any inferential analysis. This fact deters many scientists from incorporating prior information into their inferential analyses. In the natural sciences, where experiments are more regularly conducted, and can be combined with other relevant information, prior information is often used in inferential analysis, despite it being sometimes nontrivial to specify what that information is and how to quantify that information. In the social sciences, however, prior information is often hard to come by and very hard to justify or validate. We review a number of ways to construct such information. This information emerges naturally, either from fundamental properties and characteristics of the systems studied or from logical reasoning about the problems being analyzed. Borrowing from concepts and philosophical reasoning used in the natural sciences, and within an info-metrics framework, we discuss three different, yet complimentary, approaches for constructing prior information, with an application to the social sciences.

Details

Essays in Honor of Aman Ullah
Type: Book
ISBN: 978-1-78560-786-8

Keywords

Article
Publication date: 5 January 2015

Ghodrat Ebadi, Aida Mojaver, Sachin Kumar and Anjan Biswas

The purpose of this paper is to discuss the integrability studies to the long-short wave equation that is studied in the context of shallow water waves. There are several…

Abstract

Purpose

The purpose of this paper is to discuss the integrability studies to the long-short wave equation that is studied in the context of shallow water waves. There are several integration tools that are applied to obtain the soliton and other solutions to the equation. The integration techniques are traveling waves, exp-function method, G′/G-expansion method and several others.

Design/methodology/approach

The design of the paper is structured with an introduction to the model. First the traveling wave hypothesis approach leads to the waves of permanent form. This eventually leads to the formulation of other approaches that conforms to the expected results.

Findings

The findings are a spectrum of solutions that lead to the clearer understanding of the physical phenomena of long-short waves. There are several constraint conditions that fall out naturally from the solutions. These poses the restrictions for the existence of the soliton solutions.

Originality/value

The results are new and are sharp with Lie symmetry analysis and other advanced integration techniques in place. These lead to the connection between these integration approaches.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 February 1998

Norbert Wiener

Reviews the proceedings of the Norbert Wiener Centenary Congress and includes the paper “The history and prehistory of cybernetics”, which is not included in the collected works.

310

Abstract

Reviews the proceedings of the Norbert Wiener Centenary Congress and includes the paper “The history and prehistory of cybernetics”, which is not included in the collected works.

Details

Kybernetes, vol. 27 no. 1
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 7 December 2015

Julie Rust

This paper aims to delve deeply into the sometimes clashing interplays in English classrooms to explore the ways in which new media makes visible long-existing discourses and…

Abstract

Purpose

This paper aims to delve deeply into the sometimes clashing interplays in English classrooms to explore the ways in which new media makes visible long-existing discourses and assumptions about the purpose of schools and the roles of teachers and students.

Design/methodology/approach

This piece draws upon discourse analysis and utilizes the frame of strategies versus tactics (de Certeau, 1984) to trace the complex classroom interplays between a high school English teacher, a partnering researcher and a high school junior during the process of a month-long digital photography project.

Findings

Data reveal that, at times, both teachers and students made moves to preserve the status quo of the school space (through strategies), and at other times, worked to reshape the space for more relevant purposes (through tactics.) Strategies that emerge from teacher moves include the formalization of requirements and the controlling of bodies; the student strategy described is the perpetuation of stereotypes. Teacher tactics reported include repositioning identities, reframing “the work” and opening up space for inquiry. Student tactics include resistance, shifting to the personal, subverting a given task and self-positioning. The author argues that generative potential exists at the intersection of teacher tactics and student tactics, and calls for furthering the co-construction of classroom spaces.

Originality/value

By zooming in on the process, rather than the product, that ensued as the focal student created and defended her photographs representing school as jail, this paper emphasizes the agency that both teachers and students can enact in sometimes limiting classroom spaces.

Details

English Teaching: Practice & Critique, vol. 14 no. 3
Type: Research Article
ISSN: 1175-8708

Keywords

Article
Publication date: 15 May 2023

Li Li and Xican Li

In order to make full use of the generalized greyness of interval grey number, this paper analyzes the properties and its applications of generalized greyness.

Abstract

Purpose

In order to make full use of the generalized greyness of interval grey number, this paper analyzes the properties and its applications of generalized greyness.

Design/methodology/approach

Firstly, the static properties of generalized greyness in bounded background domain, infinite background domain and infinitesimal background domain are analyzed. Then, this paper gives the dynamic properties of generalized greyness in bounded background domain, infinite background domain and infinitesimal background domain and explains the dialectical principle contained in it. Finally, the generalized greyness is used to judge the effectiveness of interval grey number transformation.

Findings

The results show that the generalized greyness of interval grey number has relativity, normativity, unity, eternity and conservation. The static and dynamic properties of generalized greyness are the same in the infinite and infinitesimal background domain, while they are different in the bounded background domain. The generalized greyness can be used as an index to judge whether the grey number transformation is greyness or information preservation.

Practical implications

The research shows that the generalized greyness can be used as an index to judge the validity of the grey number transformation and also can be applied in grey evaluation, grey decision-making and grey prediction and so on.

Originality/value

The paper succeeds in realizing the mathematical principle of “white is black”, the “greyness clock-slow effect” of the value domain of interval grey number and the generalized greyness conservation principle, which provides a theoretical basis for the rational use of generalized greyness of interval grey number.

Details

Grey Systems: Theory and Application, vol. 13 no. 3
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 1 April 1995

Panayiotis Papadopoulos and Robert L. Taylor

This paper addresses the loading/unloading conditions of thediscrete initial—value problem of plastic flow at infinitesimal deformations. As in the continuum problem, it is…

Abstract

This paper addresses the loading/unloading conditions of thediscrete initial—value problem of plastic flow at infinitesimal deformations. As in the continuum problem, it is established that the strain—space formulation of the loading conditions is primary. Generalized trapezoidal and mid‐point rules are discussed. The loading conditions established for the general non‐associated flow problem are shown to naturally reduce to well‐known inequalities for flow rules obeying normality.

Details

Engineering Computations, vol. 12 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

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