Topic

# Steady state

About: Steady state is a research topic. Over the lifetime, 5059 publications have been published within this topic receiving 86216 citations. The topic is also known as: steady.

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TL;DR: Gardner as mentioned in this paper describes some STEADY-state solutions of the UNSATURATED MOISTURE FLOW EQUATION with application to EVAPORATION from a WATER TABLE.

Abstract: SOME STEADY-STATE SOLUTIONS OF THE UNSATURATED MOISTURE FLOW EQUATION WITH APPLICATION TO EVAPORATION FROM A WATER TABLE W. GARDNER; Soil Science

2,346 citations

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TL;DR: In this paper, the authors generalized the chemical mechanism of Field, Koros, and Noyes for the oscillatory Belousov reaction by a model composed of five steps involving three independent chemical intermediates.

Abstract: The chemical mechanism of Field, Koros, and Noyes for the oscillatory Belousov reaction has been generalized by a model composed of five steps involving three independent chemical intermediates. The behavior of the resulting differential equations has been examined numerically, and it has been shown that the system traces a stable closed trajectory in three dimensional phase space. The same trajectory is attained from other phase points and even from the point corresponding to steady state solution of the differential equations. The model appears to exhibit limit cycle behavior. By stiffly coupling the concentrations of two of the intermediates, the limit cycle model can be simplified to a system described by two independent variables; this coupled system is amenable to analysis by theoretical techniques already developed for such systems.

1,172 citations

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TL;DR: In this article, a theoretical analysis of the flow of added current carriers in homogeneous semiconductors is given, and a general formulation of differential equations and boundary condition relationships in suitable reduced variables and parameters are derived from fundamental equations which take into account the phenomena of drift, diffusion, and recombination.

Abstract: A theoretical analysis of the flow of added current carriers in homogeneous semiconductors is given. The simplifying assumption is made at the outset that trapping effects may be neglected, and the subsequent treatment is intended particularly for application to germanium. In a general formulation, differential equations and boundary-condition relationships in suitable reduced variables and parameters are derived from fundamental equations which take into account the phenomena of drift, diffusion, and recombination. This formulation is specialized so as to apply to the steady state of constant total current in a single cartesian distance coordinate, and properties of solutions which give the electrostatic field and the concentrations and flow densities of the added carriers are discussed. The ratio of hole to electron concentration at thermal equilibrium occurs as parameter. General solutions are given analytically in closed form for the intrinsic semiconductor, for which the ratio is unity, and for some limiting cases as well. Families of numerically obtained solutions dependent on a parameter proportional to total current are given for n-type germanium for the ratio equal to zero. The solutions are utilized in a consideration of simple boundary-value problems concerning a single plane source in an infinite filament.

622 citations

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Brown University

^{1}TL;DR: In this article, a steady-state technique for measuring heat capacity using ac heating is described, where heat is applied sinusoidally in time to a sample coupled thermally to a reservoir; the resultant equilibrium temperature of the sample contains a term that is both inversely proportional to the heat capacity and measurable with high precision.

Abstract: A steady-state technique for measuring heat capacity using ac heating is described. Heat is applied sinusoidally in time to a sample coupled thermally to a reservoir; the resultant equilibrium temperature of the sample contains a term that is both inversely proportional to the heat capacity and measurable with high precision. The effects of various corrections that must be applied to the data are considered in detail. Measurements of the absolute magnitude of the heat capacity of indium and the field dependence of the heat capacity of beryllium have been made and are used to illustrate the power of the method. The observed quantum oscillations in the heat capacity of beryllium are in agreement with predictions based on other measurements.

573 citations

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TL;DR: In this article, the authors investigate the instability of a surface of discontinuity when the displacements and velocities are no longer small, and the assumption of small motions cannot be applied to the case under consideration and the equations of motion, in their approximate form, no longer give a picture of the flow.

Abstract: Helmholtz was the first to remark on the instability of those “liquid surfaces” which separate portions of fluid moving with different velocities, and Kelvin, in investigating the influence of wind on waves in water, supposed frictionless, has discussed the conditions under which a plane surface of water becomes unstable. Adopting Kelvin’s method, Rayleigh investigated the instability of a surface of discontinuity. A clear and easily accessible rendering of the discussion is given by Lamb. The above investigations are conducted upon the well-known principle of “small oscillations”—there is a basic steady motion, upon which is superposed a flow, the squares of whose components of velocity can be neglected. This method has the advantage of making the equations of motion linear. If by this method the flow is found to be stable, the equations of motion give the subsequent history of the system, for the small oscillations about the steady state always remain “small.” If, however, the method indicates that the system is unstable, that is, if the deviations from the steady state increase exponentially with the time, the assumption of small motions cannot, after an appropriate interval of time, be applied to the case under consideration, and the equations of motion, in their approximate form, no longer give a picture of the flow. For this reason, which is well known, the investigations of Rayleigh only prove the existence of instability during the initial stages of the motion. It is the object of this note to investigate the form assumed by the surface of discontinuity when the displacements and velocities are no longer small.

464 citations