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From Obscurity to Enigma

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In 1892 Heaviside wrote the following comment in accompaniment to the publication of his Electrical Papers: But in the year 1887 I came, for a time. to a dead stop, exactly when I came to making practical applications in detail of my theory, with novel conclusions of considerable practical significance relating to long-distance telephony (previsously partly published), in opposition to the views at that time officially advocated.

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... During the last years of the nineteenth century, after having received Gibbs's booklet, Heaviside elaborated a generalisation both of the Divergence theorem and of the Stokes's theorem, an issue already partially discussed by Yavetz (1995). In Sect. ...
... Did Heaviside already know the expressions he translated? As Ido Yavetz pointed out (Yavetz 1995), in the first volume of his Electromagnetic Theory, Heaviside presented a generalisation of the Divergence theorem. Gibbs's equations (44) and (46) can also be regarded as generalisations of the Divergence theorem. ...
... In the case of non-regular surfaces or in the case of a cubic surface, we would need the generalised version for distributions. In the following, first, we will not use any formulation of the Divergence theorem, but we briefly repeat Yavetz's (1995) argument in order to emphasise how to avoid the use of distributions. Second, we show how Heaviside's specific formula for the cube follows from Gibbs's generalisation of the Divergence theorem, with the help of Heaviside's additional hypothesis, by defining the derivatives in the distribution sense. ...
Article
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In June 1888, Oliver Heaviside received by mail an officially unpublished pamphlet, which was written and printed by the American author Willard J. Gibbs around 1881–1884. This original document is preserved in the Dibner Library of the History of Science and Technology at the Smithsonian Institute in Washington DC. Heaviside studied Gibbs’s work very carefully and wrote some annotations in the margins of the booklet. He was a strong defender of Gibbs’s work on vector analysis against quaternionists, even if he criticised Gibbs’s notation system. The aim of our paper is to analyse Heaviside’s annotations and to investigate the role played by the American physicist in the development of Heaviside’s work.
... During the last years of the nineteenth century, after having received Gibbs's booklet, Heaviside elaborated a generalisation both of the Divergence theorem and of the Stokes's theorem, an issue already partially discussed by Ido Yavetz [Yavetz 1995]. In section 5, we shall present a formula for transforming surface-integrals into line-integrals that Heaviside published in his Electromagnetic Theory in 1893. ...
... Did Heaviside already know the expressions he translated? Like Ido Yavetz pointed out ( [Yavetz 1995]), in the first volume of his Electromagnetic Theory, Heaviside presented a generalisation of the Divergence theorem. Gibbs's equations (44) and (46) can also be regarded as generalisations of the Divergence theorem. ...
... In the case of non-regular surfaces or in the case of a cubic surface, we would need the generalised version for distributions. In the following, first, we will not use any formulation of the Divergence theorem, but we briefly repeat Yavetz's argument [Yavetz 1995] in order to emphasise how to avoid the use of distributions. Second, we show how Heaviside's specific formula for the cube follows from Gibbs's generalisation of the Divergence theorem, with the help of Heaviside's additional hypothesis, by defining the derivatives in the distribution sense. ...
Preprint
In June 1888, Oliver Heaviside received by mail an officially unpublished pamphlet, which was written and printed by the American author Willard J. Gibbs around 1881-1884. This original document is preserved in the Dibner Library of the History of Science and Technology at the Smithsonian Institute in Washington DC. Heaviside studied Gibbs's work very carefully and wrote some annotations in the margins of the booklet. He was a strong defender of Gibbs's work on vector analysis against quaternionists, even if he criticized Gibbs's notation system. The aim of our paper is to analyse Heaviside's annotations and to investigate the role played by the American physicist in the development of Heaviside's work.
... The significance of this parameter will become evident later in the paper. Once we have obtained a solution to (15) for J z , we will be able to determine the internal impedance per unit length of the wire from (4) with L = z: ...
... We will construct a solution to (15) by the method of successive approximations, which basically consists of making an educated guess for J z and then substituting this guess into the integral on the right-hand side of (15) to obtain a better estimate for J z . This process is continuously repeated, each time substituting the current estimate to obtain the new, better estimate. ...
... The integral on the right-hand side of (15), which is proportional to (ρ/δ) 2 , can then be viewed as a small correction. However, as we will show, our final result for J z will be a solution to (15) for all values of ρ/δ. ...
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The skin effect in a round wire is an important electromagnetic phenomenon with practical consequences; however, it is usually not presented in any detail at the undergraduate level but reserved for graduate study. The purpose of this paper is to remedy this situation by providing a simple derivation for the skin effect in a round wire that only requires background usually familiar to these students: Maxwell’s equations in integral form, integral calculus (specifically integration of a power) and some elementary properties of series. Graphical results are used to clearly show the current concentrating near the surface as the frequency increases and the accompanying increase in the resistance and decrease in the inductance of the wire. A brief review of the history of the subject shows that several of the scientists familiar to students made contributions to our understanding of the skin effect in a round wire; they include J. C. Maxwell, Lord Rayleigh, Lord Kelvin, O. Heaviside and J. J. Thomson. The validity of the theory is demonstrated by comparing results from the theory with resistances and inductances measured by some of the early pioneers of wireless communication.
... The laws of electrodynamics are the Maxwell equations. The Maxwell equations (as written by Heaviside [42][43][44][45][46] and others [47][48][49][50]) are universal laws valid over an enormous range of times and distances. They are used to compute electrical forces within atoms and between stars. ...
... The laws of electrodynamics are the Maxwell equations. The Maxwell equations (as written by Heaviside [42][43][44][45][46] and others [47][48][49][50]) are universal laws valid over an enormous range of times and distances. They are used to compute electrical forces within atoms and between stars. ...
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Statistical mechanics has grown without bounds in space. Statistical mechanics of noninteracting point particles in an unbounded perfect gas is widely used to describe liquids like concentrated salt solutions of life and electrochemical technology, including batteries. Liquids are filled with interacting molecules. A perfect gas is a poor model of a liquid. Statistical mechanics without spatial bounds is impossible as well as imperfect, if molecules interact as charged particles, as nearly all atoms do. The behavior of charged particles is not defined until boundary structures and values are defined because charges are governed by Maxwell’s partial differential equations. Partial differential equations require boundary structures and conditions. Boundary conditions cannot be defined uniquely ‘at infinity’ because the limiting process that defines ‘infinity’ includes such a wide variety of structures and behaviors, from elongated ellipses to circles, from light waves that never decay, to dipolar fields that decay steeply, to Coulomb fields that hardly decay at all. Boundaries and boundary conditions needed to describe matter are not prominent in classical statistical mechanics. Statistical mechanics of bounded systems is described in the EnVarA system of variational mechanics developed by Chun Liu, more than anyone else. EnVarA treatment does not yet include Maxwell equations.
... Na verdade, meu objetivo é estender a aplicação de tais funções ao estudo de sistemas hiperestáticos, propondo um método elegante e consistente para auxílio ao mapeamento de rupturas em vigas prismáticas. [11]. No século XX, essas funções foram aplicadas em uma variedade de situações, incluindo análise de programação de produtividade. ...
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p>Present treatise deals with applications of singularity functions from a broad perspective in civil engineering, extending its use to hyperstatics, and deepening mathematical questions little explored before. The content is presented through examples discussed in detail, giving to the reader a clear and objective reading. Original mathematical formulations are developed, such as the Macaulay-Serpa series. The treatise is extended to the calculation of hyperstatic porticoes and to the modeling of triangular loads. In this context, the theory appears as an important instrument for the analysis of ruptures in reinforced concrete beams. For the accomplishment of this treatise, an exhaustive search of bibliographical references was made, showing that the existent literature on the subject, mostly of foreign origin, is quite limited. Key words: Singularity functions, reinforced concrete, hyperstatics, discontinuous loading, elastic curve. ==================================================================================== O presente tratado versa sobre aplicações das funções de singularidade numa ampla perspectiva da engenharia civil, estendendo seu uso à hiperestática e aprofundando questões matemáticas pouco exploradas anteriormente. O conteúdo é apresentado através de exemplos discutidos em detalhes, proporcionando ao leitor uma leitura clara e objetiva. Formulações matemáticas originais são desenvolvidas, como a série Macaulay-Serpa. O tratado é estendido ao cálculo de pórticos hiperestáticos e à modelagem de cargas triangulares. Nesse contexto, a teoria aparece como um instrumento importante para a análise de rupturas em vigas de concreto armado. Para a realização deste tratado, foi feita uma busca exaustiva das referências bibliográficas, mostrando que a literatura existente sobre o assunto, principalmente de origem estrangeira, é bastante limitada. Palavras-Chave: Funções de singularidade, concreto armado, hiperestática, carga descontínua, curva elástica. </p
... has to travel the space in between, and cannot simply disappear and reappear (Yavetz, 1995). Together with the first principle of thermodynamics, i.e., the energy of an isolated system is constant, it implies that if a system is broken into parts the system can be decomposed energetically in subsystems that exchange energy. ...
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This paper proposes a unified energy-based modeling and energy-aware control paradigm for robotic systems. The paradigm is inspired by the layered and distributed control system of organisms, and uses the fundamental notion of energy in a system and the energy exchange between systems during interaction. A universal framework that models actuated and interacting robotic systems is proposed, which is used as the basis for energy-based and energy-limited control. The proposed controllers act on certain energy budgets to accomplish a desired task, and decrease performance if a budget has been depleted. These budgets ensure that a maximum amount of energy can be used, to ensure passivity and stability of the system. Experiments show the validity of the approach.
... A apărut astfel tubul electronic cu cinci electrozi, pentoda. Invenția acesteia, în 1926, îi aparține lui Bernard Tellegen 22 . ...
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This short presentation is an overview of the main facts and historical moments that have marked the development of theoretical and practical knowledge on vacuum tubes, as well as those who contributed with ideas, theories and experiments in the development of these devices that have dominated for nearly a century the electronics and telecommunications. There are mentioned here the essential moments preceding the making of the first vacuum tube, those representing its actual invention and, further, those that led to their improvement. Also, are highlighted some moments on the development of some of the most important applications of these devices.
... This scientific basis was developed by the brilliant and eccentric British physicist Oliver Heaviside in a series of papers published between 1887 and 1890 [Heaviside 1892;Nahin 1988;Yavetz 1995]. A devoted Maxwellian, Heaviside based his theoretical analysis of the propagation of telephone currents on Maxwell's theory of electromagnetism, which still around 1890 was considered an arcane and academic theory in the world of practical engineers. ...
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