Showing papers on "Bernoulli's principle published in 1977"
TL;DR: In this paper, the existence of at least one trajectory corresponding to each binary Bernoulli sequence is shown. But the relation between the two trajectories is not investigated, only trajectories in two dimensions with a negative energy (bound states).
Abstract: The anisotropic Kepler problem is investigated in order to establish the one‐to‐one relation between its trajectories and the binary Bernoulli sequences. The Hamiltonian has a quadratic kinetic energy with an anisotropic mass tensor and a spherically symmetric Coulomb energy. Only trajectories in two dimensions with a negative energy (bound states) are discussed. The previous study of this system was based on extensive numerical computations, but the present work uses only analytical arguments. After a review of the earlier results, their relevance to the understanding of the relation between classical and quantum mechanics is emphasized. The main new result is to show the existence of at least one trajectory corresponding to each binary Bernoulli sequence. The proof employs a number of unusual mathematical tools, although they are all elementary. In particular, the virial as a function of the momenta (rather than the action as a function of the position coordinates) plays a crucial role. Also, different ...
94 citations
TL;DR: In this article, the ergodic properties of expanding piecewise C2 maps of the interval are studied and it is shown that such a map is Bernoulli if it is weak mixing.
Abstract: The ergodic properties of expanding piecewiseC2 maps of the interval are studied. It is shown that such a map is Bernoulli if it is weak-mixing. Conditions are given that imply weak-mixing (and hence Bernoulliness).
62 citations
TL;DR: In this article, the definitions of weak and very weak Bernoulli are reformulated to allow conditioning with respect to the entire past, and for skew products which are measurable by an independent generator of the base, the reformulation allows one to state simple necessary and sufficient conditions for weak or very weakBernoulli, and they use these ideas to give a simple example of a partition which is very weak but not weak.
Abstract: The definitions of weak and very weak Bernoulli are reformulated to allow conditioning with respect to the entire past. For skew products which are measurable with respect to an independent generator of the base this reformulation allows one to state simple necessary and sufficient conditions for weak and very weak Bernoulli. We use these ideas to give a simple example of a partition which is very weak but not weak Bernoulli.
16 citations
9 citations
01 Jan 1977
TL;DR: In this paper, the effects of flow separation and improvements in Bernoulli's equations and the surface boundary condition on transonic flow were discussed. But the results for two-dimensional, steady and unsteady flow were not discussed.
Abstract: Significant old and new results are presented to show to what extent a simplified theory for transonic flow may be used. Solutions are obtained by classical techniques and compared with experiment. Results are given for two-dimensional, steady and unsteady flow and three-dimensional, steady flow. The effects of flow separation and improvements in Bernoulli's equations and the surface boundary condition are also briefly discussed.
6 citations
TL;DR: In this paper, the steady isentropic flow of a fluid which satisfies an arbitrary equation of state is treated, with emphasis on the prediction of pressure, density, velocity, and massflow at the sonic state.
Abstract: The steady isentropic flow of a fluid which satisfies an arbitrary equation of state is treated, with emphasis on the prediction of pressure, density, velocity, and massflow at the sonic state. The isentrope P(v) is described by a limited number of thermodynamic parameters, the most important ones being the soundspeed c and fundamental derivative Γ. Using this description, an application of the Bernoulli equation and appropriate thermodynamic relations yields simple closed-form predictions for the sonic state. These predictions are recognizable as generalizations of well-known ideal gas formulas, but are applicable to fluids very far removed from the ideal gas state, even including liquids. Comparisons in several cases for which precise independent solutions are available suggest that the methods found here are accurate. A derived similarity principle allows the accurate prediction of sonic properties from any single given sonic property.
6 citations
TL;DR: There is a difference between accelerating a fluid by means of a piston in a uniform pipe and accelerating it by a constriction, and the explanation of a variety of simple phenomena by merely quoting Bernoulli's equation may well lead to serious misunderstanding as discussed by the authors.
Abstract: There is a difference between accelerating a fluid by means of a piston in a uniform pipe (or by a change of reference frame) and accelerating it by means of a constriction, and the explanation of a variety of simple phenomena by merely quoting Bernoulli's equation may well lead to serious misunderstanding.
5 citations
TL;DR: In this paper, simple asymptotic estimates for both the Euler and Bernoulli numbers were derived from known results, but I am unable to find them elsewhere in the literature.
Abstract: We derive here simple asymptotic estimates for both the Euler and Bernoulli numbers. The derivations follow easily from known results, but I am unable to find them elsewhere in the literature. C. Jordan [1, p. 245 and p. 303] gives some related inequalities. Other properties of these two classical sets of numbers may be found in [1], [3] and [4].
3 citations
TL;DR: In this article, a collection of examples of the application of the L'Hopital-Bernoulli rule in chemical situations is presented. But they do not discuss the use of this rule in the chemical field.
Abstract: Provides a collection of examples of the application of the L'Hopital-Bernoulli rule in chemical situations to illustrate and emphasize its use.
3 citations
01 Jan 1977
TL;DR: In this article, Bernoulli's Equations, Boundary Conditions, Simple Potential Flows, Stream Function, The Complex Potential, ConformaI Mapping, Separation of Variables, Fixed Bodies and Moving Bodies, Green's Theorem and Distributions of Singularities, Hydrodynamic Pressure Forces, Force on a Moving Body in an Unbounded Fluid, General Properties of the Added-Mass Coefficients, The Added Mass of Simple Forms, The Body-Mass Force, force on a Body in a Nonuniform Stream, The Method of Images
Abstract: This chapter contains sections titled: Irrotational Flows, The Velocity Potential, Bernoulli's Equations, Boundary Conditions, Simple Potential Flows, The Stream Function, The Complex Potential, ConformaI Mapping, Separation of Variables, Fixed Bodies and Moving Bodies, Green's Theorem and Distributions of Singularities, Hydrodynamic Pressure Forces, Force on a Moving Body in an Unbounded Fluid, General Properties of the Added-Mass Coefficients, The Added Mass of Simple Forms, The Body-Mass Force, Force on a Body in a Nonuniform Stream, The Method of Images, Problems, References
3 citations
TL;DR: In this paper, the HP-65 programmable pocket calculator was used for computing frequencies of free vibrations of uniform beams with all 10 combinations of homogeneous end-conditions, two-span Bernoulli beams on hinged supports, and Timoshenko beams with 9 of the 10 combinations.
TL;DR: Some methods are proposed for employing a stochastic learning automaton in selecting M largest numbers out of N numbers which are given via realizations of Bernoulli random variables.
Abstract: Some methods are proposed for employing a stochastic learning automaton in selectingM largest numbers out ofN numbers which are given via realizations of Bernoulli random variables. The different methods are compared by simulation.
TL;DR: The Gauss-Hertz principle when coupled with an accessory condition based on the assumption that fluid pressure is always positive is used to derive both well known flows such as Couette and Poiseuille, and the velocity and force fields of a magnetically confined plasma as discussed by the authors.
Abstract: The Gauss–Hertz principle when coupled with an accessory condition based on the assumption that fluid pressure is always positive is used to derive both well known flows such as Couette and Poiseuille, and the velocity and force fields of a magnetically confined plasma.
TL;DR: In this paper, the authors construct automorphisms of Bernoulli processes where the mapping in one direction is causal with bounded memory and the inverse mapping is finite w.p.l.
Abstract: Using an idea of Adler and Weiss, automorphisms of Bernoulli processes are constructed where the mapping in one direction is causal with bounded memory and the inverse mapping is causal with memory which is finite w.p.l. Nontrivial such automorphisms exist only when the letter probability distribution has nontrivial symmetry, e.g., the 2-shift.
01 Jan 1977
TL;DR: In this article, the authors present the principles of the pressure-tube anemometer and describe the principle of dimensional homogeneity and discuss Bernoulli's theorem and its application to the measurement of fluid velocity.
Abstract: This chapter presents the principles of the pressure-tube anemometer. A pressure-tube anemometer measures a pressure difference from which the speed of flow can be deduced. To understand the action of such an instrument, it is necessary to have some knowledge of the pressures that occur in a moving fluid. No anemometer has yet been devised whose calibration can be predicted by theory alone: every type has to be calibrated, and it is of prime importance to know the precise conditions in which the calibration obtained for one particular instrument can be used for other geometrically similar instruments of the same type. The chapter describes the principle of dimensional homogeneity and discusses Bernoulli's theorem and its application to the measurement of fluid velocity. Bernoulli's theorem has importance in the measurement of flow by pressure-tube anemometers and may be simply deduced, that is, by assuming that no frictional forces occur between adjacent particles of the fluid or between the fluid and any solid boundaries with which it is in contact.