Showing papers on "Bernoulli's principle published in 2000"

Stabilization of Bernoulli--Euler Beams by Means of a Pointwise Feedback Force

Abstract: We study the energy decay of a Bernoulli--Euler beam which is subject to a pointwise feedback force. We show that both uniform and nonuniform energy decay may occur. The uniform or nonuniform decay depends on the boundary conditions. In the case of nonuniform decay in the energy space we give explicit polynomial decay estimates valid for regular initial data. Our method consists of deducing the decay estimates from observability inequalities for the associated undamped problem via sharp trace regularity results.

Practical Identifiability of Finite Mixtures of Multivariate Bernoulli Distributions

Abstract: The class of finite mixtures of multivariate Bernoulli distributions is known to be nonidentifiable; that is, different values of the mixture parameters can correspond to exactly the same probability distribution. In principle, this would mean that sample estimates using this model would give rise to different interpretations. We give empirical support to the fact that estimation of this class of mixtures can still produce meaningful results in practice, thus lessening the importance of the identifiability problem. We also show that the expectation-maximization algorithm is guaranteed to converge to a proper maximum likelihood estimate, owing to a property of the log-likelihood surface. Experiments with synthetic data sets show that an original generating distribution can be estimated from a sample. Experiments with an electropalatography data set show important structure in the data.

Localization for One Dimensional, Continuum, Bernoulli-Anderson Models

Abstract: We use scattering theoretic methods to prove strong dynamical and exponential localization for one dimensional, continuum, Anderson-type models with singular distributions; in particular the case of a Bernoulli distribution is covered. The operators we consider model alloys composed of at least two distinct types of randomly dispersed atoms. Our main tools are the reflection and transmission coefficients for compactly supported single site perturbations of a periodic background which we use to verify the necessary hypotheses of multi-scale analysis. We show that non-reflectionless single sites lead to a discrete set of exceptional energies away from which localization occurs.

Diffraction of Random Tilings: Some Rigorous Results

Abstract: The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of stochastic product tilings built from cuboids, and of planar random tilings based on solvable dimer models, augmented by a brief outline of the diffraction from the classical 2D Ising lattice gas. We also give a summary of the measure theoretic approach to mathematical diffraction theory which underlies the unique decomposition of the diffraction spectrum into its pure point, singular continuous, and absolutely continuous parts.

Numerical studies of two-dimensional Faraday oscillations of inviscid fluids

Abstract: The dynamics of two-dimensional standing periodic waves at the interface between two inviscid fluids with different densities, subject to monochromatic oscillations normal to the unperturbed interface, is studied under normal- and low-gravity conditions. The motion is simulated over an extended period of time, or up to the point where the interface intersects itself or the curvature becomes very large, using two numerical methods: a boundary-integral method that is applicable when the density of one fluid is negligible compared to that of the other, and a vortex-sheet method that is applicable to the more general case of arbitrary densities. The numerical procedure for the boundary-integral formulation uses a global isoparametric parametrization based on cubic splines, whereas the numerical method for the vortex-sheet formulation uses a local boundary-element parametrization based on circular arcs. Viscous dissipation is simulated by means of a phenomenological damping coefficient added to the Bernoulli equation or to the evolution equation for the strength of the vortex sheet. A comparative study reveals that the boundary-integral method is generally more accurate for simulating the motion over an extended period of time, but the vortex-sheet formulation is significantly more efficient. In the limit of small deformations, the numerical results are in excellent agreement with those predicted by the linear model expressed by Mathieu's equation, and are consistent with the predictions of the Floquet stability analysis. Nonlinear effects for non-infinitesimal amplitudes are manifested in several ways: deviation from the predictions of Mathieu's equation, especially at the extremes of the interfacial oscillation; growth of harmonic waves with wavenumbers in the unstable regimes of the Mathieu stability diagram; formation of complex interfacial structures including paired travelling waves; entrainment and mixing by ejection of droplets from one fluid into the other; and the temporal period tripling observed recently by Jiang et al. (1998). Case studies show that the surface tension, density ratio, and magnitude of forcing play a significant role in determining the dynamics of the developing interfacial patterns.

Dynamics of the Transition from a Thin Accretion Disk to an Advection-dominated Accretion Flow

Abstract: We consider an optically thin advection-dominated accretion flow (ADAF) that is connected at a finite transition radius to an outer optically thick, geometrically thin disk. We include turbulent energy transport and examine ADAF models that satisfy the following boundary conditions at the transition radius: (1) the temperature of the gas is much lower than the virial temperature, (2) the rotation is super-Keplerian, and (3) the net radial flux of energy is outward. We numerically solve the height-integrated viscous hydrodynamic equations with these boundary conditions. We find that the Bernoulli parameter is positive for a wide range of radius, indicating that outflows may be possible from ADAFs. Turbulent energy transport enhances the Bernoulli parameter. We compare our numerical global solutions with two published analytical solutions. We find that the solution of Honma represents the transition region well, while the self-similar solution of Narayan & Yi works better away from the transition. However, neither analytical solution is able to represent the density or angular momentum profile in the inner region of the ADAF, where the flow makes a sonic transition.

Non-linear simulations of wave-induced motions of a floating body by means of the mixed Eulerian-Lagrangian method

Abstract: A non-linear calculation method based on the mixed Eulerian-Lagrangian (MEL) method is presented for wave-induced motions of a two-dimensional floating body Attention is focused on an effe

Azimuthally symmetric MHD and two-fluid equilibria with arbitrary flows

Abstract: Magnetohydrodynamic (MHD) and two-fluid quasi-neutral equilibria with azimuthal symmetry, gravity and arbitrary ratios of (nonrelativistic) flow speed to acoustic and Alfven speeds are investigated. In the two-fluid case, the mass ratio of the two species is arbitrary, and the analysis is therefore applicable to electron-positron plasmas. The methods of derivation can be extended in an obvious manner to several charged species. Generalized Grad-Shafranov equations, describing the equilibrium magnetic field, are derived. Flux function equations and Bernoulli relations for each species, together with Poisson's equation for the gravitational potential, complete the set of equations required to determine the equilibrium. These are straightforward to solve numerically. The two-fluid system, unlike the MHD system, is shown to be free of singularities. It is demonstrated analytically that there exists a class of incompressible MHD equilibria with magnetic field-aligned flow. A special sub--class first identified by S. Chandrasekhar, in which the flow speed is everywhere equal to the local Alfven speed, is compatible with virtually any azimuthally symmetric magnetic configuration. Potential applications of this analysis include extragalactic and stellar jets, and accretion disks.

A Bernoulli Cell-Based Investigation of the Non-Linear Dynamics in Log-Domain Structures

Abstract: This paper presents a low-level treatment of the non-linear dynamics encountered in log-domain structures, by means of a non-linear circuit element termed a Bernoulli Cell. This cell comprises an npn BJT and an emitter-connected grounded capacitor, and its dynamic behavior is determined by a differential equation of the Bernoulli form. The identification of the Bernoulli Cell leads to the creation of a system of linear differential equations which describe the dynamics of the derived log-domain state-variables. Furthermore, it is shown that the Bernoulli Cell has a memristive type dynamic behavior. The approach aids the analysis of log-domain circuits, and allows the internal non-linear currents to be conveniently expressed in closed analytical form. A worked example for a specific topology with confirming simulation results in both frequency and time-domain is presented. The celebrated Hodgkin-Huxley nerve axon membrane dynamics are also successfully simulated as a characteristic example of memristive behavior.

A Lagrangian Model for Baroclinic Genesis of Mesoscale Vortices. Part I: Theory

Abstract: The problem of weakly stratified, weakly sheared flow over (or under) obstacles is solved approximately by using a Lagrangian approach that obtains solutions on isentropic or Bernoulli surfaces and hence reveals the vortex lines immediately. The new method is based on a decomposition of the vorticity in dry, inviscid, isentropic flow into baroclinic and barotropic components. The formulas for both baroclinic and barotropic vorticity are exact formal solutions of the vorticity equation. A nonhydrostatic Lagrangian model approximates these solutions based on a primary-flow–secondary-flow approach. The assumed primary flow is a three-dimensional steady potential flow so that it is a solution of the governing inviscid equations only in the absence of stratification and preexisting vorticity. It is chosen to be irrotational in order to eliminate the primary flow as the origin of rotation. Three particular potential flows are chosen for their simplicity and because pieces of them approximate mesoscale ...

Carleman Estimates for the Euler-Bernoulli Plate Operator

Abstract: We present some a{priori estimates of Carleman type for the Euler{ Bernoulli plate operator. As an application, we consider a problem of boundary observability for the Euler{Bernoulli plate coupled with the heat equation.

Bernoulli’s equation

Abstract: In a forthcoming article we will look at some examples of the application of Bernoulli’s equation. From this article I hope the reader has developed a feel for some aspects of fluid motion: the concept of a fluid particle, the two types of fluid acceleration and how motion in one part of the fluid causes motion in other parts of the fluid. Bernoulli’s equation can be viewed in two ways. One as Newton’s second law applied to a line of fluid particles in a stream-tube. The second as a statement of energy conservation: the change in gravitational potential energy plus the change in kinetic energy is equal to the work done by the pressure forces.

An analog of the Bernoulli and Cauchy-Lagrange integrals for a time-dependent vortex flow of an ideal incompressible fluid

Abstract: An expression with a constant value over all space (including multiply connected domains) relating the pressure function to the square of the velocity and the characteristics of the traveling vortices is derived for a time-dependent ideal incompressible fluid flow with nonzero vorticity. When there are bodies in the flow, they must also be represented in the form of traveling vortices. For steady-state flow the formula obtained goes over into the Bernoulli integral and for time-dependent irrotational flow into the Cauchy-Lagrange integral.

Pressure Effects in Line Accretion

Abstract: Some previous results concerning pressure effects in line accretion should be ignored, as they are based on an inadequate Bernoulli equation. The behavior of velocity (density) is studied in the vicinity of the stagnation, singular and asymptotic points, also collecting together the results spread throughout the literature for isothermal and pressure-free flows. The cut-off distance of the accretion column and the resulting gravitational drag on the velocity of the accretor are found from a unified condition on the boundary pressure.

Simple model of the plasma torch developed for application to an arc-plasma waste-treatment system

Abstract: A simple theoretical model describing physics of the plasma torch plume is developed in connection with its applications to the arc-plasma waste-treatment system. The theoretical analysis is carried out by making use of Bernoulli's pressure-balance equation, which provides a stable equilibrium solution of the gas density in the plume ejected from the torch into a high-pressure reactor chamber with 4e 1, there is no stable equilibrium solution satisfying Bernoulli's equation. Therefore, it is expected that the observable plasma data may change abruptly as the chamber pressure crosses the borderline defined by 4e = 1. Indeed, most of the plasma data measured in an experiment change abruptly at the pressure borderline of 4e = 1. The oxygen torch plume is theoretically analyzed for the arc-plasma waste-treatment system...

Estimation of a Bernoulli parameter p from imperfect trials

Abstract: Imperfect Bernoulli trials arise when the outcome of a Bernoulli experiment is not known with certainty. In signal processing, we often need to estimate a probability of occurrence p of an event from imperfect Bernoulli trials. A typical example is the estimation of the probability of a signal being present in noisy data. In his famous essay, Bayes solved the same problem but for perfect trials. In this letter, a solution is provided for imperfect trials. It is shown that it includes Bayes' solution as a special case.

Simultaneous Doppler/catheter measurements of pressure gradients in aortic valve disease: a correction to the Bernoulli equation based on velocity decay in the stenotic jet.

Abstract: Background and aim of the study Characterization of the severity of a stenotic aortic valve relies on accurate measurement of the pressure drop across the valve. A simplified form of the Bernoulli equation has been used to estimate pressure drops using Doppler ultrasound, but these measurements often overestimate gold standard measurements performed during cardiac catheterization. Sources of discrepancy between the Doppler and catheter measurements have been identified, but no method has been developed to fully reconcile the two techniques. Methods In this study we developed a correction to the clinical form of the Bernoulli equation based on receiving chamber geometry and turbulent jet profiles. The theoretical treatment of the mechanical energy balance, assuming a shape to the stenotic jet profile is described, and the assumptions in our model are discussed. The use of the model was then demonstrated in an in vivo clinical study in which simultaneous Doppler and catheter data were obtained. Results Discrepancies between Doppler and catheter are shown to be a function of the predicted pressure recovery location based on our assumed profile. There exists a distance of about 8.67 valve radii downstream where agreement in peak pressure gradients is theoretically achieved. Conclusion The results demonstrate the ability to characterize pressure recovery distal to the valve. Our approach, to substitute a more appropriate velocity profile into the mechanical energy balance, unifies geometric parameters and the physics of turbulent jet flow in an equation involving quantities already routinely measured in an echocardiographic examination of aortic stenosis. This allows for both the maximal and recovered pressure gradient to be obtained from the Doppler data. These results have implications for optimal pressure sensor placement for the assessment of aortic stenosis and also for the evaluation of prosthetic heart valves in vitro.

A first course in fluid mechanics for civil engineers.

Abstract: Book review / Critiques de livres Dr. Gray is presently an Associate Professo in the Department of Civil and Environmental Engineering at West Virginia University at Morgantown in West Virginia. He has considerable experience in teaching fluid mechanics, has published over 100 papers and reports in fluid mechanics, and also has industrial experience. He wrote this text in fluid mechanics for a one-semester course for civil, environmental, and agricultural engineers to provide a narrower focus rather than attempt to cover the whole range of fluid mechanics. Dr. Gray believes that such a narrow focus might motivate the students more readily. This book uses both the US Customary and SI systems of units. This book has 15 chapters and two appendices that deal with Tables of Fluid Properties and Answers to Selected Problems; it also has a Subject Index. The first chapter presents the scope of engineering fluid mechanics — a brief description of many books dealing with fluid mechanics along with a discussion of units. The second chapter treats fluid properties with the discussion of viscosity left to a later chapter. Chapters 3 and 4 present a thorough discussion of the principles of hydrostatics, covering pressure distribution in liquids, manometers, idea of piezometric head, stratified layers, and force exerted on plane surfaces. Discussion of force exerted on curved surfaces and buoyancy is delayed until chapter 14. Chapter 5 presents a discussion of fluid dynamics, starting with the development of the Euler equation along the streamline and its integration to obtain the Bernoulli equation. The author then uses the Bernoulli equation to present and discuss a number of elementary problems like water jets in air, pitot and pitot-static tubes, venturimeter, and sharpcrested weirs. Chapter 5 closes with the development of the Euler equations in the Cartesian system with the Z axis in the vertical direction. Chapter 6 is a rather lengthy presentation of the mass conservation equation. Chapter 7 presents a discussion of viscosity and a detailed derivation of fully developed laminar flor in a circular pipe and ends with a partially complete derivation of the NavierStokes equation in the Cartesian system. Chapter 8 presents a good derivation of the energy equation, which is correctly identified as different from the Bernoulli equation. The idea of the piezometric and total heads is discussed along with some standard problems. Chapter 9 is entitled Pipe Flow 1 and develops the Poiseuille equation using the energy equation and the results derived from chapter 7. It also presents a short discussion of turbulent flow. Chapter 10 presents a brief discussion on dimensional analysis. Pipe Flow 2 constitutes chapter 11, which deals with head loss for turbulent flow in circular pipes, discusses the Moody Diagram, minor losses, and standard pipe flow problems with some comments on turbulent flow in non-circular pipes. The momentum equation is developed in Chapter 12 along with a thorough discussion of a number of problems. Chapter 13 deals with open channel flow. It discusses uniform flow using the Manning equation as well as the friction factor method and nonuniform flow using the idea of the specific head. It also deals with gravity waves including the hydraulic jump. Chapter 15 deals with physical models and similarity. It discusses geometrically similar Reynolds and Froude models as well as some distorted models and ends with brief comments on river models. The treatment of the Euler and Navier-Stokes equations in the Cartesian system could have been made more general by tilting the axes and combining the pressure and body force terms into piezometric gradients. This set of Euler equations could have been integrated to obtain the Bernoulli equation, which would have required the author to present at least a brief treatment of vorticity and potential flow. Further, using the Navier-Stokes equations, the author could have shown how these equations could be simplified to solve a few simple flows, including the Poiseuille equation, in an elegant manner. On the whole, this book is written clearly; it emphasizes engineering relevance, presents numerous worked-out examples, and provides a number of problems for the reader to solve. I think that this book provides a pragmatic introduction to engineering fluid mechanics for students in civil engineering, including environmental and agricultural engineering, and I would recommend this book to them.

One-sided Lebesgue Bernoulli maps of the sphere of degree n2 and 2n2

Abstract: We prove that there are families of rational maps of the sphere of degree n2(n=2,3,4,…) and 2n2(n=1,2,3,…) which, with respect to a finite invariant measure equivalent to the surface area measure, are isomorphic to one-sided Bernoulli shifts of maximal entropy. The maps in question were constructed by Boettcher (1903--1904) and independently by Lattes (1919). They were the first examples of maps with Julia set equal to the whole sphere.

One-sided lebesgue bernoulli maps of the sphere

Abstract: We prove that there are families of rational maps of the sphere of degree n2 (n = 2, 3, 4 ,...) and 2n 2 (n = 1, 2, 3 ,...) which, with respect to a finite invariant measure equivalent to the surface area measure, are isomorphic to one-sided Bernoulli shifts of maximal entropy. The maps in question were constructed by Boettcher (1903-1904) and independently by Lattes (1919). They were the first examples of maps with Julia set equal to the whole sphere.

q-probability: I. Basic discrete distributions

Abstract: For basic discrete probability distributions, $-$ Bernoulli, Pascal, Poisson, hypergeometric, contagious, and uniform, $-$ $q$-analogs are proposed.

Extension of Bernoulli's theorem on steady flows of inviscid fluids to steady flows of plastic solids

Abstract: A differential equation is derived which is valid along any streamline in a steady flow of a general continuum where the streamline is also a trajectory of principal stress For special materials and flow conditions this equation can be integrated to give algebraic relations between variables along the streamline For inviscid fluids this leads to Bernoulli's famous theorem relating pressure and velocity along any streamline For three-dimensional ideal flows of Tresca plastic solids and planar ideal flows of general rigid/perfectly plastic solids, it also leads to known results along any streamline For other special constitutive materials in rigid/plastic solids additional streamline relations are obtained

Toward a canonical-Hamiltonian and microscopic field theory of classical liquids

Abstract: The old problem of describing the classical dynamics of simple liquids, modeled by standard many-particle Hamiltonians with two-body interactions, in terms of canonically conjugated collective variables, which are field variables, is taken up in this paper where both periodic and free boundary conditions are considered. Particle densities or their Fourier components are well known to be the natural collective coordinates of the problem but what about their conjugate variables? An original application of the method of generating functions of the type of Hamilton's principal function is developed to construct their conjugated momenta which turn out to be momentum potentials. The many-particle Hamiltonians are then written in terms of these two fields. The kinetic part turns out to be exactly that of a compressible, irrotational and inviscid fluid modulo the minor change of the variables, i.e., particle density and momentum potential instead of mass density and velocity potential. The potential energy is non-local in density since it expresses the mutual interactions of the particles in the initial Hamiltonian. This property is absent from any theory of classical fluids. The resulting equations of motions are (1) the continuity equation for the time derivative of the density and (2) a generalized Bernoulli equation for the time derivative of the momentum potential, generalized in the sense that it is non-local in density. To our knowledge this is a new equation in this field. Several applications and generalizations of this equation are also discussed in the text as well as the question of the thermodynamic versus the continuum limits.

Flow-rate measurement method and differential- pressure-type flowmeter utilizing it

Abstract: PROBLEM TO BE SOLVED: To accurately measure the flow rate of a fluid with large viscosity and that with a low speed. SOLUTION: A differential-pressure-type flowmeter for obtaining the amount of pressure change and the flow rate of fluid by utilizing a constriction mechanism and calculating the flow rate of the fluid is provided with an operation means 6 for calculating the amount of correction pressure change from the first differential pressure and the second differential pressure between the inlet of a constriction mechanism 1 and a constriction part only by the change in the sectional area of a pipeline based on the Bernoulli's theorem, obtaining a flow rate by utilizing the amount of correction pressure change, and calculating the flow rate of the fluid according to the flow rate and the sectional area in the pipeline.

An Extension of the Sum-the-Odds Theorem to the Stopping Problems on the Bernoulli Trials of Random Length

Abstract: The optimal stopping problem of choosing the best item from the population of unknown size has been studied by Presman and Sonin [4], Irle [2] and Petruccelli [3]. As an extension of this problem, we consider the problem of maximizing the probability of stopping on the last success on the independent Bernoulli trials of random length and give a sucient condition for the optimal rule to be of threshold type. This result can be considered as a generalization of the Sum-the-Odds Theorem by Bruss [1]. Bruss theorem is also extended to the problem of stopping on one of the last m successes on the independent Bernoulli trials and the problem of stopping on the last success when the Bernoulli random variables are Markov dependent. Moreover we consider the stopping problem with refusal.