Showing papers on "Bernoulli's principle published in 1982"

An Approximate Zero-One Law

Abstract: We prove an approximate zero-one law, which holds for finite Bernoulli schemes. An application to percolation theory is given.

T, T-1 transformation is not loosely Bernoulli*

Abstract: The T, T-' problem, open since 1971, is to demonstrate that the T, T` transformation, a naturally arising K transformation, is not Bernoulli. It is shown here not even to be loosely Bernoulli.

Examples of conservative diffeomorphisms of the two-dimensional torus with coexistence of elliptic and stochastic behaviour

Abstract: We find very simple examples of C∞-arcs of diffeomorphisms of the two-dimensional torus, preserving the Lebesgue measure and having the following properties: (1) the beginning of an arc is inside the set of Anosov diffeomorphisms; (2) after the bifurcation parameter every diffeomorphism has an elliptic fixed point with the first Birkhoff invariant non-zero (the KAM situation) and an invariant open area with almost everywhere non-zero Lyapunov characteristic exponents, moreover where the diffeomorphism has Bernoulli property; (3) the arc is real-analytic except on two circles (for each value of parameter) which are inside the Bernoulli property area.

A composite velocity procedure for the compressible Navier-Stokes equations

Abstract: A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.

Thermodynamic principle of virtual dissipation and the dynamics of physical-chemical fluid mixtures including radiation pressure

Abstract: Equations of motion are obtained for a viscous fluid mixture including thermal and intermolecular diffusion as well as chemical reactions and radiation pressure. They are derived by applying the thermodynamic principle of virtual dissipation. The method also incorporates a new approach to the chemical thermodynamics of open systems which leads to new concepts and formulas for the heat of reaction and the affinity. They are simpler and more general than classical values. Instead of chemical potentials, new “convective potentials” are used which involve physical properties restricted to the system. They do not require extrapolations to absolute zero or the use of undetermined constants. No statistical theory is involved. A noncalorimetric evaluation of the heat of mixing is obtained from the concept of injection pressure of each substance in the mixture. Field equations are derived and a coupling between viscous stress gradients and diffusion is brought out. The convective potentials lead to a new evaluation of the thermodynamic functions of mixtures as well as a new generalized formulation of the Gibbs-Duhem theorem. Translational invariance of the dissipation is discussed and related to total momentum balance. Lagrangian equations of motion with generalized collective coordinates are derived directly from the variational principle and should provide a powerful approach to problems of stellar dynamics with radiation pressure.

A direct proof that vwb processes are closed in the\(\bar d\)-metric

Abstract: As defined in the literature, a process is very weak Bernoulli if a certain propertyP(e) is satisfied for everye>0. By means of an easy proof, it is shown that givene>0, there existsδ>0 such that given any two stationary processes whose\(\bar d\)-distance is less thanδ, if one of the processes is very weak Bernoulli then the other process is “almost” very weak Bernoulli in the sense that the propertyP(e) is satisfied. Using this result a direct proof can be given that the very weak Bernoulli processes are closed under the\(\bar d\)-distance, and also that a finitely determined process is very weak Bernoulli. Relativized versions of these results are also considered.

A note on structural properties of the Bernoulli two-armed bandit problem

Abstract: A certain monotonicity property is proved for the optimal expected cumulative discounted reward associated with a dynamic programming model with finite horizon, describing the Bernoulli: two-armed bandit problem. This property leads to a positive answer to the conjecture formulated in [3, p. 473]. For two special cases a stay-on-a-winner rule is obtained as a by-product.

Integrals and symmetries: the Bernoulli-Laplace-Lenz vector

Abstract: The notions of 'independent constants of motion' are clarified emphasising the role of precise definition of the background space. Using a well defined algorithm that relates symmetries of equations of motion of a classical system (Newtonian, Lagrangian or Hamiltonian) to a conserved object in one-to-one fashion, the symmetries of the Coulomb and linear force problems are determined.

A special family of ergodic flows and their\(\bar d - limits\)

Abstract: A flow built under a step function with a multi-step Markov partition on the base is a direct product of a Bernoulli flow with a finite rotation. A $$\bar d - limit$$ of the flows in this family cannot have two irrationally related rotation factors. $$\bar d - closure$$ of this family is shown to consist of all direct products of Bernoulli flows and flows of rational pure point spectrum with respect to some number.

On a Class of Generalized $K$-Entropies and Bernoulli Shifts

Abstract: Die Arbeit bringt die Konstruktion cines für die Diskussion urn die Verailgemeinerung der K-Entropie wichtigen Beispicis. Fur den Fall, daI3 der ProzeB dürch einen Bernoulli-shift und cine nur aus Zylindermengen bestehende Verteilung beschrieben werden kann, wird eine Formel zur Berechnung der verallgemeinerten Entropie angegeben. In Vorbindung damit wird auf ncuurtige Weise ein Optimierungsproblem fiber der Menge aller Wahrscheinliehkeitsvektoren gleicher Entropie behandelt.

The Intrinsic Geometrical and Physical Properties of Plane Steady Gas Flow

Abstract: The main purpose of the present paper is to establish a relation between the intrinsic geometrical and physical properties of plane steady gas flow, i.e., between the geometry of the flow pattern on one side and the flow variables on the other. This is accomplished by complete integration of the governing fluid dynamics equations in an a priori unknown system of curvilinear coordinates. The complete solution is presented by explicit expressions for the metric tensor components associated with the curvilinear system in terms of the flow Mach number and the Bernoulli constant along the streamlines. The curvilinear system relative to a Cartesian reference frame is a posteriors determined by quadratures. Several examples including subsonic, sonic, supersonic, rotational, and irrotational flow are discussed to illuminate the special technique and its potential for determining flow patterns that result from particular geometrical and/or physical specifications.

Chapter 8 – statistics

Abstract: Publisher Summary This chapter describes the basic principles of statistics. A random variable is a rule that assigns a numerical value to each outcome of an experiment. A random variable is called (1) finite discrete if it can take on only finitely many possible values; (2) infinite discrete if it can take on infinitely many values that can be arranged in a sequence; and (3) continuous if its possible values form an entire interval of numbers. If X is a random variable and x is a number, then P(X = x) is the probability that X will take on the value x. The chapter also discusses the arithmetic average or mean of the numbers, the standard deviation, and Chebyshev's theorem. It highlights that eExperiments for which there are only two possible outcomes are called Bernoulli experiments or Bernoulli trials. It is traditional to label arbitrarily one of the two outcomes success and the other failure.

Finitely fixed implies loosely Bernoulli, a direct proof

Abstract: As defined in the literature, a process is loosely Bernoulli if a certain propertyP(ɛ) is satisfied for every ɛ>0. Using only facts about stationary joinings of processes, it is shown that given ɛ>0 there exists δ>0 such that whenever two processes are separated by less than δ in the\(\bar f\)-metric and one of them is loosely Bernoulli, the other is “almost” loosely Bernoulli in the sense thatP(ɛ) is satisfied. As easy corollaries, one has that loosely Bernoulli processes are closed in the\(\bar f\)and that finitely fixed processes are loosely Bernoulli.

Calculation of the interaction of planar jets of ideal gas with different Bernoulli constants

Abstract: A numerical method is proposed for calculating stationary planar jet flows with unequal total heads in different jets in the case when the medium is ideal and compressible and the flow is subsonic, adiabatic, and irrotational in each individual jet. Features of the method are considered in the example of the calculation of the interaction of two free jets flowing along the sides of a wedge. The line separating the jets is the line of a shear discontinuity. The results of the calculations are given.