A unified theory of conjugate flows

1971 ◽  
Vol 269 (1201) ◽  
pp. 587-643 ◽  
Keyword(s):  
Common Ground ◽  
Ad Hoc ◽  
Nonlinear Operator ◽  
Index Theory ◽  
Nonlinear Operator Equation ◽  
Infinite Dimensions ◽  
Scalar Property ◽  
Wave Phenomena ◽  
Conjugate Flows

Various examples of flow systems are known in which the study of conjugate flows (i.e. flows uniform in the direction of streaming which separately satisfy the hydrodynamical equations) is crucial to the understanding of observed wave phenomena. Open-channel flows are the best-known example, with which remarkable qualitative similarities have been revealed in studies of other systems: for instance, it has appeared in general that any pair of conjugate flows is transcritical (i.e. if one flow is supercritical according to a generalized definition, then the other is subcritical). So far the common ground among theoretical treatments has been defined only by intuitive analogies, and the aim of this paper is to give unity to the whole subject by identifying the elements that are intrinsically responsible for universal properties. The problem is accordingly considered in the form of an abstract (nonlinear) operator equation, whose solution representing a conjugate flow is a vector in a linear space of finite or infinite dimensions: all known examples are reducible to this form and other applications may be anticipated. The generalized treatment on these lines must have recourse to new methods, however, of a more powerful kind than would suffice for the ad hoc treatment of particular examples. A resume of the required mathematical material is presented in §2. The main substance of the paper is in § 3. In § 3.1 the supercritical and subcritical classification of flows is explained generally, being shown to depend on the eigenvalues of the Frechet derivative of the nonlinear operator presented by the hydrodynamical problem. In §3.3 fixed-point principles are used to define general conditions under which the existence of conjugate flows in a proposed category is guaranteed, and also in this subsection a special argument is given to exemplify the transcritical property of conjugate flows. Several aspects are covered in §3.4 by means of index theory, in particular the problem of classifying a multiplicity of conjugate flows possible in a given system and the question of what conditions ensure uniqueness. In §3.5 variational methods are used to account for the differences in flow force that appear to be an essential attribute of frictionless conjugate flows (flow force is a scalar property which is generally stationary to small variations about a solution of the hydrodynamical equations). The last three sections of the paper present treatments of specific examples illustrating the unified viewpoint given by the theory. Proofs of two topological theorems used in §3.4 are presented in appendix 1, and in appendix 2 the reasons for the variational significance of flow force are examined.

Classification of Attacks Against the Mobile AD Hoc Networks

2012 ◽  
Vol 2 (3) ◽  
pp. 77-80
Author(s):  
V. Karamchand Gandhi ◽  
◽  
D.P.Jeyabalan D.P.Jeyabalan
Keyword(s):  
Ad Hoc Networks ◽  
Mobile Ad Hoc Networks ◽  
Ad Hoc ◽  
Mobile Ad Hoc ◽  
Hoc Networks

The stand-up comedian as an egocentric communicator

2021 ◽  
Vol 18 (1) ◽  
pp. 1-23
Author(s):  
Ibukun Filani
Keyword(s):  
Concept Formation ◽  
Common Ground ◽  
Ad Hoc ◽  
Propositional Content ◽  
Communicative Behavior ◽  
Stand Up Comedy ◽  
General Perspective

Abstract The general perspective in pragmatics research on stand-up comedy is that the comedian co-produces humor with the audience. In this paper, I argue that the stand-up comedian’s communicative behavior is also partly rooted in egocentrism. To achieve this, I adopted a sociocognitive approach to intention and egocentrism in analyzing a routine that was performed in Chicago by Okey Bakassi, a Nigerian stand-up comedian. I operationalize egocentrism as one of the humor strategies of the comedian. While focusing on the propositional content of the comedian’s utterances, the analysis revealed strategies like privatization, ad hoc concept formation and ad hoc coherence, which the comedian used in individualizing the prior common ground to generate the needed incongruity for humor in the performance sphere.

scholarly journals Rhetorical questions as aggressive, friendly or sarcastic/ironical questions with imposed answers

ExELL ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 68-82
Author(s):  
Džemal Špago
Keyword(s):  
Common Ground ◽  
Peer To Peer ◽  
The Other ◽  
Communication Style ◽  
Communication Styles ◽  
Social Standing ◽  
Frequency Of Use ◽  
Different Types ◽  
Rhetorical Questions

AbstractRhetorical questions (RQs), as a cross-breed of questions and statements, represent an effective tool in putting forward the Speaker’s ideas, as well as influencing the ideas and opinions of other people. Because of their communicative effectiveness and multifunctionality, they are frequently used in different contexts and for different purposes, and, as such, they represent an interesting topic for further research. The aim of this paper is threefold: (i) to explore the nature of the implied answer to RQs, (ii) to offer a classification of RQs based on the Speaker’s communication style, and (iii) to examine whether (or to what extent) the Speaker-Addressee relationship (peer-to-peer, superior-to-inferior, inferior-to-superior) influences the selection and frequency of use of different types of RQs. Using Stalnaker’s (2002) model of Common Ground and Caponigro and Sprouse’s (2007) concepts of Speaker’s and Addressee’s Beliefs, the author redefines the nature of the answers implied by RQs, claiming that they are imposed on the Addressee rather than mutually recognized as obvious. Based on the model of communication styles as defined by Yuan et al. (2018), RQs are classified into aggressive, friendly and sarcastic/ironical questions with imposed answers. The analysis of the corpus, which consisted of 275 RQs taken from ten American movie scripts, showed that friendly RQs are more common than the other two types, and that, in instances where one of the interlocutors is in a superior position, superior-to-inferior RQs are by far more common than vice versa. The finding that RQs asked by inferiors make up less than a third of RQs occurring between interlocutors with different social standing is in line with the view that answers to RQs are imposed on Addressees.

Group Equivariant Singularity Theory in the Bifurcation of Interfacial Wilton Ripples

2015 ◽  
Vol 25 (11) ◽  
pp. 1550147
Author(s):  
Mark Jones
Keyword(s):  
Nonlinear Operator ◽  
Singularity Theory ◽  
Nonlinear Operator Equation ◽  
Infinite Dimensional ◽  
Two Fluids ◽  
Near Resonance ◽  
Classical Procedure ◽  
Symmetry Properties ◽  
System Of Polynomial Equations ◽  
Secondary Bifurcations

An investigation is made into the capillary-gravity waves which arise on the interface of two fluids and which are formed by the interaction of the first two harmonics of the motion. The problem is transformed into a nonlinear operator equation between suitable function spaces which is shown to be invariant under certain group actions. The infinite dimensional problem is reduced, by the classical procedure of Lyapunov–Schmidt, to a finite system of polynomial equations, known as the bifurcation equations. Because these equations inherit the symmetry properties of the original operator, it is possible to make quite specific statements concerning their structure, thus rendering their analysis easier. Solutions to the equations are sought, both in the cases of exact and of near-resonance. A wide variety of solutions is found depending on the values of the parameters: both simple, multiple and secondary bifurcations may occur, and in addition, there may exist isolated solution curves.

The Existence of Solutions for Nonlinear Operator Equations

2008 ◽  
Vol 15 (1) ◽  
pp. 45-52
Author(s):  
Marek Galewski
Keyword(s):  
Nonlinear Operator ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Nonlinear Operator Equation ◽  
Global Minima ◽  
Operator Equations ◽  
Nonlinear Operator Equations ◽  
Dual Variational Method ◽  
Dual Action ◽  
Primal And Dual

Abstract We provide the existence results for a nonlinear operator equation Λ*Φ′ (Λ𝑥) = 𝐹′(𝑥), in case 𝐹 – Φ is not necessarily convex. We introduce the dual variational method which is based on finding global minima of primal and dual action functionals on certain nonlinear subsets of their domains and on investigating relations between the minima obtained. The solution is a limit of a minimizng sequence whose existence and convergence are proved. The application for the non-convex Dirichlet problem with P.D.E. is given.

Bifurcations, symmetries and the notion of fixed subspace

2021 ◽  
pp. 2130006
Author(s):  
Giampaolo Cicogna
Keyword(s):  
Topological Index ◽  
Ad Hoc ◽  
Index Theory ◽  
Typical Case ◽  
One Dimensional ◽  
Dimension Formula ◽  
Symmetry Properties ◽  
Equivariant Bifurcation ◽  
Stationary Bifurcation ◽  
Bifurcation Problems

In the context of stationary bifurcation problems admitting a symmetry, this paper is focused on the key notion of Fixed Subspace (FS), and provides a review of some applications aimed at detecting bifurcating solutions in various situations. We start recalling, in its commonly used simplified version, the old Equivariant Bifurcation Lemma (EBL), where the FS is one-dimensional; then we provide a first generalization in a typical case of non-semisimple critical eigenvalues, where the presence of the symmetry produces a non-trivial situation. Next, we consider the case of FSs of dimension [Formula: see text] in very different contexts. First, relying on the topological index theory and in particular on the Krasnosel’skii theorem, we provide a largely applicable statement of an extension of the EBL. Second, we propose a completely different and new application which combines symmetry properties with the notion of stability of bifurcating solutions. We also provide some simple examples, constructed ad hoc to illustrate the various situations.

Oscillation analysis of numerical solution of Nonlinear Operator Equation

2021 ◽  
Vol 7 (5) ◽  
pp. 2111-2126
Author(s):  
Yang Zhou ◽  
Cuimei Li
Keyword(s):  
Numerical Solution ◽  
Operator Equation ◽  
Vibration Analysis ◽  
Nonlinear Operator ◽  
Vibration Spectrum ◽  
Nonlinear Operator Equation ◽  
Analysis Method ◽  
Analysis Model ◽  
Oscillation Analysis ◽  
Analysis Equation

There is a problem of low accuracy in the analysis of the vibration of the numerical solution of the nonlinear operator equation. In this work, the vibration analysis equation is constructed by the step-by-step search method, and the vibration quadrant of the equation is divided by the dichotomy method. The vibration spectrum is determined by the iteration method, and the vibration analysis model of the numerical solution of the nonlinear operator equation is constructed. The vibration analysis of the numerical solution of the nonlinear operator equation is completed based on the solution of the model and the numerical calculation and display of the step-by-step Fourier. The experimental results show that the proposed method has higher accuracy than the traditional vibration analysis method, which meets the requirements of the vibration analysis of the numerical solution of nonlinear operator equation.

Towards Smarter Cities and Roads

2014 ◽  
pp. 16-50 ◽  
Author(s):  
Irina Tal ◽  
Gabriel-Miro Muntean
Keyword(s):  
Architectural Design ◽  
Vehicular Ad Hoc Networks ◽  
Ad Hoc ◽  
Clustering Algorithms ◽  
Research Area ◽  
General Classification ◽  
Comprehensive Survey ◽  
Hoc Networks ◽  
Promising Avenue

This chapter highlights the importance of Vehicular Ad-Hoc Networks (VANETs) in the context of smarter cities and roads, a topic that currently attracts significant academic, industrial, and governmental planning, research, and development efforts. In order for VANETs to become reality, a very promising avenue is to bring together multiple wireless technologies in the architectural design. Clustering can be employed in designing such a VANET architecture that successfully uses different technologies. Moreover, as clustering addresses some of VANETs' major challenges, such as scalability and stability, it seems clustering will have an important role in the desired vehicular connectivity in the cities and roads of the future. This chapter presents a comprehensive survey of clustering schemes in the VANET research area, covering aspects that have never been addressed before in a structured manner. The survey presented in this chapter provides a general classification of the clustering algorithms, presents some of the most advanced and latest algorithms in VANETs, and in addition, constitutes the only work in the literature to the best of authors' knowledge that also reviews the performance assessment of clustering algorithms.

Geometric Interoperability With Epsilon Solidity

2005 ◽  
Vol 6 (3) ◽  
pp. 213-220 ◽  
Author(s):  
Jianchang Qi ◽  
Vadim Shapiro
Keyword(s):  
Data Sharing ◽  
Ad Hoc ◽  
Industrial Applications ◽  
Data Interoperability ◽  
Systematic Classification ◽  
Geometric Data ◽  
Modeling Systems ◽  
Data Translation ◽  
Lost Time

Geometric data interoperability is critical in industrial applications where geometric data are transferred (translated) among multiple modeling systems for data sharing and reuse. A big obstacle in data translation lies in that geometric data are usually imprecise and geometric algorithm precisions vary from system to system. In the absence of common formal principles, both industry and academia embraced ad hoc solutions, costing billions of dollars in lost time and productivity. This paper explains how the problem of interoperability, and data translation in particular, may be formulated and studied in terms of a recently developed theory of ε-solidity. Furthermore, a systematic classification of problems in data translation shows that in most cases ε-solids can be maintained without expensive and arbitrary geometric repairs.

Sign in / Sign up

Export Citation Format

Share Document