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1 – 10 of 361Jing‐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…
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.
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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.
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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.
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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.
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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.
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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.
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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.
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.
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.
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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.
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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.
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