1,286 research outputs found

    Some exact solutions to the Lighthill Whitham Richards Payne traffic flow equations II: moderate congestion

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    We find a further class of exact solutions to the Lighthill Whitham Richards Payne (LWRP) traffic flow equations. As before, using two consecutive Lagrangian transformations, a linearization is achieved. Next, depending on the initial density, we either obtain exact formulae for the dependence of the car density and velocity on x, t, or else, failing that, the same result in a parametric representation. The calculation always involves two possible factorizations of a consistency condition. Both must be considered. In physical terms, the lineup usually separates into two offshoots at different velocities. Each velocity soon becomes uniform. This outcome in many ways resembles not only Rowlands, Infeld and Skorupski J. Phys. A: Math. Theor. 46 (2013) 365202 (part I) but also the two soliton solution to the Korteweg-de Vries equation. This paper can be read independently of part I. This explains unavoidable repetitions. Possible uses of both papers in checking numerical codes are indicated at the end. Since LWRP, numerous more elaborate models, including multiple lanes, traffic jams, tollgates etc. abound in the literature. However, we present an exact solution. These are few and far between, other then found by inverse scattering. The literature for various models, including ours, is given. The methods used here and in part I may be useful in solving other problems, such as shallow water flow.Comment: 15 pages, 7 figure

    Electromagnetic Oscillations in a Spherical Conducting Cavity with Dielectric Layers. Application to Linear Accelerators

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    We present an analysis of electromagnetic oscillations in a spherical conducting cavity filled concentrically with either dielectric or vacuum layers. The fields are given analytically, and the resonant frequency is determined numerically. An important special case of a spherical conducting cavity with a smaller dielectric sphere at its center is treated in more detail. By numerically integrating the equations of motion we demonstrate that the transverse electric oscillations in such cavity can be used to accelerate strongly relativistic electrons. The electron's trajectory is assumed to be nearly tangential to the dielectric sphere. We demonstrate that the interaction of such electrons with the oscillating magnetic field deflects their trajectory from a straight line only slightly. The Q factor of such a resonator only depends on losses in the dielectric. For existing ultra low loss dielectrics, Q can be three orders of magnitude better than obtained in existing cylindrical cavities.Comment: Extended version with one new section, modified title and new abstract, 10 pages, 13 figure

    Mill on logic

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    Working within the broad lines of general consensus that mark out the core features of John Stuart Mill’s (1806–1873) logic, as set forth in his A System of Logic (1843–1872), this chapter provides an introduction to Mill’s logical theory by reviewing his position on the relationship between induction and deduction, and the role of general premises and principles in reasoning. Locating induction, understood as a kind of analogical reasoning from particulars to particulars, as the basic form of inference that is both free-standing and the sole load-bearing structure in Mill’s logic, the foundations of Mill’s logical system are briefly inspected. Several naturalistic features are identified, including its subject matter, human reasoning, its empiricism, which requires that only particular, experiential claims can function as basic reasons, and its ultimate foundations in ‘spontaneous’ inference. The chapter concludes by comparing Mill’s naturalized logic to Russell’s (1907) regressive method for identifying the premises of mathematics

    ,,BIERZESZ CZTERY LUB PIĘĆ NUT, JEDNĄ WYRZUCASZ, JEDNĄ PRZESUWASZ…”, czyli temat główny z Gwiezdnych wojen i Marsz imperialny jako standardy muzyki filmowej oraz ich wpływ na kulturę popularną

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    Każdy ma swoje zapachy, smaki, zdjęcia, które są związane z nami w konkretnych sytuacjach. Podobnie jest z muzyką i melodiami. Większość z nas może nucić „Ode to Joy”, „Für Elise” lub… „Imperial March” z „Gwiezdnych wojen”. Jaka jest najsilniejsza jakość muzyki z tej sagi? Dynamizm? Prostota? A może ton instrumentów? Spróbuję znaleźć powód.Zdjęcia z tego zdjęcia są i są z nim związane. Wies jest z muzyką i melodiami. Większość z nas może nucić „Oda do radości”, „Für Elise” lub… „Imperial March” z „Gwiezdnych wojen”. Jaka jest najsilniejsza jakość muzyki z tej sagi? Dynamizm? Prostota? A może ton instrumentów? Spróbuję znaleźć powód
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