共查询到20条相似文献，搜索用时 671 毫秒
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J.L. Finck 《Journal of The Franklin Institute》1947,243(2):117-129
Based on theory of a previous paper, the writer has developed an equation of state for a system with a single type of transformation. This equation is of the form where h = ε + pv is the total heat, p the pressure, v the specific volume, T the temperature, and p, v, T are considered independent variables. A, B, C, etc., are constants for the system. The latent eat at constant (p, T) is given by . These equations are checked with data on saturated and superheated ammonia, and the agreement is good to within a few tenths of a per cent. Also, checks with data on saturated and superheated steam show agreement within several per cent. 相似文献
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W.F.G. Swann 《Journal of The Franklin Institute》1934,217(1):59-71
It is well known that the wave mechanical ψ equation leads to the conclusion that the centroid of the wave mechanical electron should move according to the classical electrodynamic equation of motion in which, however, the terms representing what is commonly called radiation reaction are absent. If v is the velocity of the electron, the classical rate of change of momentum is . The equation of motion including radiation reaction terms may be regarded as obtainable by replacing this quantity by one obtained by operating upon it with the operator P?1 where α1, α2, etc., are constants and . The main purpose of the paper is to show that if there be any relativistically invariant ψ equation which leads to the classical equation of motion without radiation reaction terms, then by replacing the vector and scalar potentials U and ? in that equation by P(U) and P(?), a relativistically invariant equation of motion will be obtained including the radiation reaction terms, provided that the in P be now regarded as + u · grad, where u is the velocity of the wave mechanical density distribution at a point. The purpose is to use the power to produce the equation of motion as a criterion for suggesting the proper modification of the ψ equation to apply in those cases where, on the classical theory, the electron would suffer great acceleration, as in ionization by rapidly moving corpuscles. 相似文献
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Israel Maizlish 《Journal of The Franklin Institute》1924,197(5):667-690
Present Status of the Problem.—The scattering of X-rays is one of the outstanding problems of electromagnetic radiation which has not been solved satisfactorily. All theories (based on classical electrodynamics) presented thus far do not explain either the diminution in the scattering coefficient, or the observed asymmetry in the scattering, or both. Among such theories we may mention:J. J. Thompson's Theory.—Assuming that the scattering is done by a point electron, and making use of certain additional hypotheses, Thomson showed that the scattering coefficient of any substance is given by and that the intensity of the scattered radiation is given by where N is the number of atoms per c.c., p the number of electrons per atom, e the electronic charge, m the electronic mass, c the velocity of light, Iθ the intensity of the scattered radiation at an angle θ between the incident beam and the radius vector joining the centre of the electron and the point P distant r from the electron, and I is the intensity of the incident beam. This theory explains neither the asymmetry nor the decrease in the coefficient of scattering.Schott's Theory.—Among other things, the assumption is here made that the atom consists of coaxal rings of electron. The electrons in each ring are spaced at equal intervals and revolve with a uniform angular velocity, which, however, may be different for different rings. This theory fails to explain the observed diminution in the scattering coefficient.Debye's Theory.—In its essentials, Debye's theory has the same merits and demerits as that of Schott. Debye assumes that all the electrons in an atom are arranged in a single ring, and that they are spaced at equal intervals. This theory (and also Schott's theory) explains the asymmetry and the “excess scattering,” but is altogether unable to explain the diminution in the scattering coefficient.Modification of the Classical Theory.—The present paper presents a discussion of the possibility of modifying the classical theory (that of J. J. Thomson) so as to account for the decrease in the scattering coefficient as well as the dissymmetry. By assuming that the electron is made up of a number of parts—for simplicity, of two parts—it has been found possible to account for the diminution in the scattering coefficient without, at the same time, explaining the observed asymmetry. To accomplish both objects is what was aimed at in the combination of the present work with that of Debye. In this research the goal has not been perfection between predicted and observed results, but rather to discuss some possible modifications of the classical theory and their consequences. 相似文献
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F.M. Reza 《Journal of The Franklin Institute》1982,314(3):191-202
The natural modes of an underdamped dynamical system are given by the characteristic numbers of the quadratic operator pencil where the operator A depends on the dissipative and reactive elements of the system, while B depends solely on the reactive elements. The operator P(s) for every applied stimulus vector signal x must satisfy: A measure of underdamped behaviour is suggested by predetermining an angular region |φ| containing all natural modes of the system, When a comparison between positive operators A and B is available, say B2=KA, then The paper is motivated by Duffin-Krein-Gohberg's earlier mathematical contributions. 相似文献
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Marcelo Menezes Morato Manh Quan Nguyen Olivier Sename Luc Dugard 《Journal of The Franklin Institute》2019,356(3):1196-1224
This article is concerned with the control of a Semi-Active suspension system of a 7DOF Full Vehicle model, equipped with four Electro Rheological (ER) dampers, taking into account their incipient dissipativity constraints. Herein, a real-time, fast, advanced control structure is presented within the Model Predictive Control framework for Linear Parameter Varying (LPV) systems. The control algorithm is developed to provide a suitable trade-off between comfort and handling performances of the vehicle in a very limited sampling period (), in view of a possible realtime implementation on a real vehicle. The control structure is tested and compared to other standard fast control approaches. Full nonlinear realistic simulation results illustrate the overall good operation and behaviour of the proposed control approach. 相似文献
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This paper mainly considers the consensus for first-order discrete-time multi-agent systems w.r.t. two key parameters, the step size T and the delay τ. First, the consensus is recast into the concurrent stability for a series of trinomials. Then, for each associated trinomial, we derive a necessary and sufficient stability condition, based on proving the two invariance properties for the asymptotic behavior of the critical unitary roots. As a result, the exhaustive consensus region in the parameter space (i.e., the parameter set such that the multi-agent system reaches a consensus iff T and τ belong to that set) is determined. Furthermore, we show that the obtained result also applies to systems with diverse input delays, through an extra sufficient consensus condition. Finally, two illustrative examples are presented. 相似文献
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A procedure is described for determining the characteristics of adiabatic flow through a rocket nozzle with and without composition change. The method of calculation is illustrated for the expansion of pure hydrogen gas from a chamber temperature of 306° K. and a pressure of 20.42 atm. to atmospheric pressure.The study indicates that the exhaust velocity and temperature are highest for flow where complete equilibrium is reached at each temperature with respect to the reaction Flow with composition change requires a nozzle exit to nozzle throat area ratio somewhat greater than that determined for adiabatic flow without composition change for the same ratio of chamber pressure to exit pressure.The residence time in a given temperature range is computed as a function of gas temperature for the two types of flow. The results of this calculation may be used to determine the minimum required reaction rates which allow composition changes during flow through the nozzle. 相似文献
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C.C.H. Tang 《Journal of The Franklin Institute》1973,296(2):137-149
In this paper we attempt to obtain approximate solutions of improved accuracy for a class of differential equations of the form , where ε is a real parameter less than unity, ωc is a positive real constant of order unity and μ(x) is a singular function of x in the region of interest. It does not appear to be possible to find a general analytic expression for the error estimate of the approximate solution. For the case μ(x) = x?2, however, it is shown that the approximate solution is accurate to 0(ε2), as x → 0? from negative values, by comparing it with the numerically integrated solution. For the same case, the approximate solution is orders of magnitude more accurate than Poincaré's first-order perturbation solution, which is accurate to as x → 0?. This work arose in search of analytic solutions to a linearized form of the restricted three-body problem. 相似文献
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J.C. Dunn 《Journal of The Franklin Institute》1973,295(2):117-133
If T maps a convex domain DT into itself, and if {ωn} is a real sequence with range in (0, 1] then the recursive averaging process, generates a sequence {x?n}; with range in DT. Under suitable conditions on DT, T and {ωn} the sequence {x?n} will converge in some sense to a fixed point of T. We prove that if DT is a closed convex subset of a complex Hilbert space H, if Tω = (1 ? ω) I + ωT is a strict contraction for some ω ? (0, 1], and if {ωn} satisfies the conditions, and then, for arbitrary ξ ? DT, {x?n} converges strongly to (the unique) fixed point of T. We also prove that if DT and {ωn} satisfy the foregoing conditions, if T has at least one fixed point, and if Tω is non-expansive for some ω ? (0, 1], then for all ξ ? DT, {x?n} converges at least weakly to some fixed point of T. Finally, we apply these results to linear equations involving bounded normal operators and obtain an extension of the classical Neumann operator series. 相似文献
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