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Paul S. Epstein

Bio: Paul S. Epstein is an academic researcher from California Institute of Technology. The author has contributed to research in topics: Cosmic ray & Theory of relativity. The author has an hindex of 17, co-authored 58 publications receiving 3645 citations.


Papers
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Journal ArticleDOI
TL;DR: In this article, approximate solutions for the rate of solution by diffusion of a gas bubble in an undersaturated liquid-gas solution are presented, with the neglect of the translational motion of the bubble.
Abstract: With the neglect of the translational motion of the bubble, approximate solutions may be found for the rate of solution by diffusion of a gas bubble in an undersaturated liquid‐gas solution; approximate solutions are also presented for the rate of growth of a bubble in an oversaturated liquid‐gas solution. The effect of surface tension on the diffusion process is also considered.

1,343 citations

Journal ArticleDOI
TL;DR: In this article, the authors derived the force exerted by the impinging molecules leaving the surface depending on how they leave, assuming the usual Maxwellian distribution of velocities in the gas, the force was found to be M where M=(4π/3) Nma2cmV, N, m, a, and V being the number per unit volume, mass, radius, and mean speed of the molecules and V the speed of a droplet.
Abstract: Kinetic theory of the resistance to a sphere moving through a gas.— (1) Droplets small in comparison with the mean free path. The high degree of accuracy achieved in the experimental determination of the law of motions of droplets through gases, makes a careful theoretical examination of the problem desirable. Assuming the usual Maxwellian distribution of velocities in the gas, the force exerted by the impinging molecules is found to be M where M=(4π/3) Nma2cmV, N, m, a, and cm being the number per unit volume, mass, radius, and mean speed of the molecules and V the speed of the droplet. The force exerted by the molecules leaving the surface depends on how they leave. (1) For uniform evaporation from the whole surface, the force is -M; (2) for specular reflection of all the impinging molecules, -M; (3) for diffuse reflection with unchanged distribution of velocities, -(13/9)M; (4) for diffuse reflection with the Maxwell distribution corresponding to the effective temperature of the part of the surface they come from, -(1+9π/64)M, for a non-conducting droplet (4a), and -(1+π/8)M, for a perfectly conducting droplet (4b). Cases (1) and (2) can not be distinguished experimentally, but (2) is more probable physically. The experimental values agree with 1/10 specular reflection, case (2), and 9/10 diffuse reflection, case (4a) or (4b). For large values of l/a, the droplet behaves like a perfect conductor, case (4b). (2) Comparatively large spheres. The distribution of velocities is no longer Maxwellian because of the hydrodynamic stresses which can not now be neglected. The new law is derived (Eq. 47). The conditions at the surface of the sphere are discussed and it is shown that the diffusely reflected molecules have a Maxwellian distribution corresponding to the temperature and density of the gas, just as though they were reflected with conservation of velocity (specularly). The assumptions of Bassett are theoretically justified and a complete confirmation is obtained for the correction factor for Stokes' law [1+0.7004 (2/s-1) (l/a)] on which Millikan's conclusions are based, especially as to the percentage of specular reflection. (3) Rotating spheres are also considered in an appendix, and the values of the resistance are derived for various cases.

912 citations

Journal ArticleDOI
TL;DR: In this paper, a theory of the Stark effect based on Schroedinger's ideas is presented, where positions of lines practically coincide with those obtained in the writer's old theory which gave an excellent agreement with experiment.
Abstract: A theory of the Stark effect based on Schroedinger's ideas is presented. (1) Positions of lines practically coincide with those obtained in the writer's old theory which gave an excellent agreement with experiment. (2) Intensity expressions are obtained in a simple closed form: (a) Components which, in the old theory, had to be ruled out by a special postulate now drop out automatically. (b) The computed intensities of the remaining components check the observed within the limits of experimental error.

399 citations

Journal ArticleDOI
TL;DR: In this article, a Radiometerkraft auf eine Kreisscheibe von elliptischem Profil wird streng berechnet, and eine etwas ausfuhrlichere Zusammenfassung findet sich am Schlus.
Abstract: Die Radiometerkraft auf eine Kreisscheibe von elliptischem Profil wird streng berechnet. Die Losung ergibt die Einsteinsche Formel als charakteristischen Grenzfall fur schlecht, leitende Scheiben. Eine etwas ausfuhrlichere Zusammenfassung findet sich am Schlus.

240 citations

Journal ArticleDOI
TL;DR: The purpose of it was to answer the question whether it is permissible to apply the ordinary rules for constructing the path of a ray to problems of radio-telegraphy, since certain layers of the atmosphere possess a considerable conductivity.
Abstract: The problem of wave propagation in a conducting and absorbing medium was approached from the point of view of geometrical optics in a preceding paper.(1) The purpose of it was to answer the question whether it is permissible to apply the ordinary rules for constructing the path of a ray to problems of radio-telegraphy, since certain layers of the atmosphere possess a considerable conductivity.

197 citations


Cited by
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Journal ArticleDOI
TL;DR: In der Anwendung der Quantentheorie auf die Molekeln kann man folgende Entwicklungsstufen unterscheiden: Das erste Stadium1) ersetzt die zweiatomige Molekel durch das Hantelmodell, das als einfacher „Rotator“ behandelt wird as discussed by the authors.
Abstract: In der Anwendung der Quantentheorie auf die Molekeln kann man folgende Entwicklungsstufen unterscheiden: Das erste Stadium1) ersetzt die zweiatomige Molekel durch das Hantelmodell, das als einfacher „Rotator“ behandelt wird. Mehratomige Molekeln werden in entsprechender Weise als starre „Kreisel“ angesehen.2) Dieser Standpunkt erlaubt es, die einfachsten Gesetze der Bandenspektren und der spezifischen Warme mehratomiger Gase zu erklaren. Das nachste Stadium1) last die Annahme starrer Verbindungen zwischen den Atomen fallen und berucksichtigt die Kernschwingungen, zunachst als harmonische Schwingungen; dabie ergenben sich nach Sponer3) und Kratzer4) Zusammenhange zwischen den einzelnen Banden eines Bandensystems.

4,131 citations

Book ChapterDOI
01 Jan 1960

3,018 citations

Book
01 Oct 2013
TL;DR: In this paper, the fundamental physical processes involved in bubble dynamics and the phenomenon of cavitation are described and explained, and a review of the free streamline methods used to treat separated cavity flows with large attached cavities is provided.
Abstract: This book describes and explains the fundamental physical processes involved in bubble dynamics and the phenomenon of cavitation. It is intended as a combination of a reference book for those scientists and engineers who work with cavitation or bubble dynamics and as a monograph for advanced students interested in some of the basic problems associated with this category of multiphase flows. A basic knowledge of fluid flow and heat transfer is assumed but otherwise the analytical methods presented are developed from basic principles. The book begins with a chapter on nucleation and describes both the theory and observations of nucleation in flowing and non-flowing systems. The following three chapters provide a systematic treatment of the dynamics of the growth, collapse or oscillation of individual bubbles in otherwise quiescent liquids. Chapter 4 summarizes the state of knowledge of the motion of bubbles in liquids. Chapter 5 describes some of the phenomena which occur in homogeneous bubbly flows with particular emphasis on cloud cavitation and this is followed by a chapter summarizing some of the experiemntal observations of cavitating flows. The last chapter provides a review of the free streamline methods used to treat separated cavity flows with large attached cavities.

2,994 citations

Journal ArticleDOI
TL;DR: In this paper, a laser-Doppler velocimeter (LDV) study of velocity profiles in the laminar boundary layer adjacent to a heated flat plate revealed that the seed particles used for the LDV measurements were driven away from the plate surface by thermophoretic forces, causing a particle free region within the boundary layer of approximately one half the boundary-layer thickness.
Abstract: A laser-Doppler velocimeter (LDV) study of velocity profiles in the laminar boundary layer adjacent to a heated flat plate revealed that the seed particles used for the LDV measurements were driven away from the plate surface by thermophoretic forces, causing a particle-free region within the boundary layer of approximately one half the boundary-layer thickness. Measurements of the thickness of this region were compared with particle trajectories calculated according to several theories for the thermophoretic force. It was found that the theory of Brock, with an improved value for the thermal slip coefficient, gave the best agreement with experiment for low Knudsen numbers, λ/R = O(10−1), where λ is the mean free path and R the particle radius.Data obtained by other experimenters over a wider range of Knudsen numbers are compared, and a fitting formula for the thermophoretic force useful over the entire range 0 [les ] λ/R [les ] ∞ is proposed which agrees within 20% or less with the majority of the available data.

1,372 citations