Showing papers on "Bernoulli's principle published in 1999"

"Log-domain state-space": a systematic transistor-level approach for log-domain filtering

Abstract: In this paper the properties of a low-level nonlinear continuous-time circuit element-termed a Bernoulli Cell (or Operator)-are described in a systematic way. This cell is composed of an n-p-n BJT and an emitter-connected grounded capacitor, and is governed by a differential equation of the Bernoulli form. Although this cell has the potential for application in both linear and nonlinear analog signal processing, this paper focuses on the field of input-output linear log-domain filtering. The Bernoulli Cell can be utilized in both the analysis and synthesis of log-domain circuits. The Bernoulli Cell approach leads to the creation of a system of linear differential equations with time dependent coefficients and state variables nonlinearly related to currents internal to the circuit; this set of equations is termed "log-domain state-space", and can be used for the synthesis of linear log-domain filters. Four design examples-including a bandpass biquad-are presented.

Fully Chaotic Maps and Broken Time Symmetry

Abstract: 1. Chaos and Irreversibility. 2. Statistical Mechanics of Maps. 3. The Bernoulli Map. 4. Other One-Dimensional Maps. 5. Intrinsic Irreversibility. 6. Deterministic Diffusion. 7. Afterword. Appendices.

Formalism for multi-fluid equilibria with flow

Abstract: A formalism is developed for flowing multifluid equilibria. In the standard reduced case (massless electrons, quasineutrality) this system simplifies to a pair of second-order partial differential equations for the magnetic and ion flow stream functions plus a Bernoulli equation giving the density. Each species has its own characteristic surfaces, which are the drift surfaces, and three arbitrary surface functions associated with each species. In the case of minimum energy equilibria, the surface functions are no longer arbitrary. The flowing equilibrium system is a generalization of the familiar Grad–Shafranov system for magnetostatic equilibria.

Log-domain filtering and the Bernoulli cell

Abstract: In this paper, the dynamic behavior of a nonlinear circuit element termed a Bernoulli cell is described, which is composed of a suitably biased bipolar junction transistor (BJT) and an emitter connected grounded capacitor. This cell has application in the synthesis of log-domain filters, since it facilitates the development of a low-level design approach in which a frequency-domain transfer function is decomposed into time-domain current product equalities that can be implemented by direct use of the translinear principle (TLP). Furthermore, the dynamic of a log-domain structure can be analyzed and its frequency response can be easily derived when the embedded Bernoulli cells are identified. An analysis and a synthesis example are presented.

Natural extensions for the Rosen fractions

Abstract: The Rosen fractions form an infinite family which generalizes the nearest-integer continued fractions. We find planar natural extensions for the associated interval maps. This allows us to easily prove that the interval maps are weak Bernoulli, as well as to unify and generalize results of Diophantine approximation from the literature.

Control of networks of Euler-Bernoulli beams

Abstract: We consider the exact controllability problem by boundary action of hyperbolic systems of networks of Euler-Bernoulli beams. Using the multiplier method and Ingham's inequality, we give sufficient conditions insuring the exact controllability for all time. These conditions are related to the spectral behaviour of the associated operator and are sufficiently concrete in order to be able to check them on particular networks as illustrated on simple examples.

Applications of dual MRM for determining the natural frequencies and natural modes of an Euler-Bernoulli beam using the singular value decomposition method

Abstract: In this paper, a dual multiple reciprocity method (MRM) is employed to solve the natural frequencies and natural modes for an Euler‐ Bernoulli beam. It is found that the conventional MRM using an essential integral equation results in spurious eigenvalues and modes. By using the natural integral equation of dual MRM, the spurious eigendata can be filtered out. Four numerical examples are given to verify the validity of the present formulation. In one of these four examples, fixed‐fixed supported beam, it is found that the boundary eigenvector cannot be determined by either the essential or natural integral equation alone since the rank of the corresponding leading coefficient matrix is insufficient. The singular value decomposition method is then used to solve the eigenproblem after combining the essential and natural integral equations. This method can avoid the spurious eigenvalue problem and possible indeterminancy of boundary eigenvectors at the same time. q 1999 Elsevier Science Ltd. All rights reserved.

Johann Bernoulli's brachistochrone solution using Fermat's principle of least time

Abstract: Johann Bernoulli's brachistochrone problem is now three hundred years old. Bernoulli's solution to the problem he had proposed used the optical analogy of Fermat's least-time principle. In this analogy a light ray travels between two points in a vertical plane in a medium of continuously varying index of refraction. This solution and connected material are explored in this paper.

On the growth and decay of acceleration waves in random media

Abstract: We study the effects of material spatial randomness on the growth to shock or decay of acceleration waves. In the deterministic formulation, such waves are governed by a Bernoulli equation d α /d x = −μ ( x ) α + β ( x ) α 2 in which the material coefficients μ and β represent the dissipation and elastic nonlinearity, respectively. In the case of a random microstructure, the wavefront sees the local details: it is a mesoscale window travelling through a random continuum. Upon a stochastic generalization of the Bernoulli equation, both coefficients become stationary random processes, and the critical amplitude α c as well as the distance to form a shock x ∞ become random variables. We study the character of these variables, especially as compared to the deterministic setting, for various cases of the random process: (i) one white noise; (ii) two independent white noises; (iii) two correlated Gaussian noises; and (iv) an Ornstein–Uhlenbeck process. Situations of fully positively, negatively or zero correlated noises in μ and β are investigated in detail. Particular attention is given to the determination of the average critical amplitude〈 α c〉, equations for the evolution of the moments of α , the probability of formation of a shock wave within a given distance x , and the average distance to form a shock wave. Specific comparisons of these quantities are made with reference to a homogeneous medium defined by the mean values of the μ , β x process.

Ergodicity of hard spheres in a box

Abstract: We prove that the system of two hard balls in a ) rectangular box is ergodic and, therefore, actually it is a Bernoulli flow.

System for isotropically measuring fluid movement in three-dimensions

Abstract: A system for measuring wind direction and velocity utilizing a sphere which is capable of making differential orthogonal pressure measurements, using pressure sensors located inside the sphere along apertures forming orthogonal axes of the sphere. The preferred embodiment applies the Bernoulli principle to the sphere which has the apertures disposed along the orthogonal axes, and which measures the wind velocity and direction, whereas an alternative embodiment applies the Reynold's principle by using a sphere having no apertures therein, and resulting in a more robust meteorological measurement device which can also measure other meteorological data which is combined with the wind data to produce forecasting of air and weather patterns in a localized area.

Solutions to the Bernoulli Integral of the Funnel Flow

Abstract: The most significant feature of a magnetized accretion system is perhaps the formation of a funnel or a curtain flow. In the standard model, which is axisymmetric and steady, the Bernoulli integral for the funnel can be obtained. The existence of a solution to the Bernoulli integral has largely been taken for granted, but no single consistent solution has ever been provided. All evidence indicates that a steady and axisymmetrical magnetically funneled accretion could be rather difficult. We explored the topology of the Bernoulli integral and have found solutions only when the funnel flow velocity is close to (poloidal) Alfven velocity. Such solutions are associated with strong toroidal magnetic fields at the funnel base, in which the toroidal magnetic pressure causes magnetic levitation of materials. Interestingly, they are the same toroidal magnetic fields that carry away the angular momentum from the accreting matter. The angular velocity of the funnel base can then be larger than the stellar rotation rate, contrary to the common wisdom that the funnel must be in corotation with the star. Our results put stringent constrains on the disk truncation radius.

Sufficient conditions for the regularity of the solutions of the Navier-Stokes equations

Abstract: In this paper we find sufficient conditions, involving only the pressure, that ensure the regularity of weak solutions to the Navier–Stokes equations. Conditions involving only the pressure were previously obtained in [7,4]. Following a remark in this last reference we improve, in particular, Kaniel's result [7]. Our condition can be seen at the light of the heuristic idea that the pressure behaves similarly to the modulus squared of the velocity. Copyright © 1999 John Wiley & Sons, Ltd.

An iterative method for the computation of the solutions of nonlinear equations

Abstract: In this paper, we present new iterative methods for the computation of zeros of C 1 functions. The idea is mainly based on a new asymptotic expansion (the Bernoulli expansion) for regular functions. Just as the Newton method is derived from the linear part of the Taylor polynomial, the new methods are analogously derived from the quadratic part of the Bernoulli expansion. We prove that the proposed procedures combine the assured convergence of bisection-like algorithms with a superlinear convergence speed which characterizes Newton-like methods. We show that the order of this new procedure is p= 2 and that the cost per iteration is completely equivalent to that of the Newton method. Finally some numerical experiments are performed. The related results seem to indicate that at least one of the proposed techniques works better than the Newton method. Moreover, the given method used in connection with an enclosing-interval procedure [2], is competitive with the ones recently proposed by Alefeld and Potra [2].

Exact Solution of the Wave‐Resistance Problem for a Submerged Cylinder. II. The Non‐linear Problem

Abstract: . We study the problem of wave resistance for a “slender” cylinder submerged in a heavy fluid of finite depth with the cylinder moving at uniform supercritical speed in the direction orthogonal to its generators. We look for a divergence‐free, irrotational flow; the boundary of the region occupied by the fluid (consisting of the free surface, the bottom and the obstacle profile) is assumed to belong to streamlines and the Bernoulli condition is taken on the free surface. The problem is transformed, via the hodograph map, into a problem set in a strip with a cut. By using a “hard” version of the inverse function theorem and by taking account of the results obtained in Part I (which we recall here), we prove the existence of a complex velocity function satisfying all the requirements of the problem. In particular, this function is continuous up to the surface of the obstacle, and the only possible singularities appear at the end‐points where the boundary is not smooth. Moreover, two stagnation points appear near to the extremities of the submerged body.

Poisson Broken Lines Process and its Application to Bernoulli First Passage Percolation

Abstract: In this note we introduce a process, which we call 'the Poisson broken lines process", and we compute the intensity of a point process which is obtained by intersecting the Poisson broken lines process with an abscissa axis. In the second part we apply this result to compute an explicit lower bound for the time constant of a planar Bernoulli first passage percolation model with the parameter p < pc.

Local data assimilation in the estimation of barotropic and baroclinic open boundary conditions

Abstract: The problem of data assimilation in the specification of open boundary conditions for limited area models is addressed in this paper. Optimization approaches are detailed, which are based on combining available data on an open boundary with the physics of the hydrodynamical model. In our case the physics is in terms of the flux of energy through the open boundary. These optimized boundary conditions, for both barotropic and baroclinic situations, interpreted physically as special linearizations of the Bernoulli equation for each normal mode. Because of the complexity of decomposing variables into normal modes for open boundaries with varying bathymetry, we present two alternative approaches. The first is a simplification of the optimized baroclinic boundary condition based on normal modes. The second makes use of empirical orthogonal functions instead of normal modes. The results of testing and comparisons of these approaches are presented for coupling coarse- and fine-resolution models. In this case our approach is in assimilating values and variables from a large-scale model (along the open boundaries of a limited area model). In the proposed coupling schemes the energy fluxes are estimated either from coarse or from fine-grid model results. With the progress of oceanographic observing systems we would like to explore ways of combining model outputs with the oceanographic measurements in order to estimate energy fluxes used in optimized open boundary conditions.

On axisymmetric double adiabatic MHD equilibria with plasma flow

Abstract: The stationary equilibrium of an axisymmetric plasma characterized by toroidal and poloidal flows is considered within the framework of ideal double adiabatic magnetohydrodynamic equations. The problem is reduced to a nonlinear partial differential equation for the poloidal magnetic flux function, containing six surface functions, plus a nonlinear algebraic Bernoulli equation defining the plasma density. Ellipticity conditions and bifurcations of its solutions are discussed in the limit of small beta, appropriated for tokamak-like equilibria. Possible connections with the L-H transition are suggested.

Slug-plug flow analyses of stratified flows in a horizontal duct by means of MARS

Abstract: The objectives of this study are to perform the slug-plug flow analyses of stratified flows in a horizontal duct by means of the MARS (Multi-interfaces Advection and Reconstruction Solver) developed by the author which based on the piece-wise linear calculation as a volume tracking procedure and the continuum surface force model (CSF) for the surface tension, and to investigate the effect of the Bernoulli term for slug-plug flows, i.e., so-called the topological law, on the competition between inertial forces and gravitation forces. Some discussion on the primary jump condition at the interface in the MARS is described in the paper. The results of the direct numerical simulation (DNS) by the MARS are compared with the experimental one. The slugging positions obtained by the DNS are in good agreement with the experimental one. Since the mass conservation between before the plugging and after slugging can be shown by the DNS here, the authors may conclude that this physical/numerical model based on the MARS is reliable.

The origins of hydraulics and hydrodynamics in the work of the Petersburg academicians of the 18th century

Abstract: The first fruitful theoretical studies of the motion of fluids were begun in Petersburg during the period of establishment of the Academy of Sciences there in the latter half of the 1720's. These studies were carried out by those leading representatives of 18th-century physico-mathematical sciences, the Petersburg Academicians Daniel Bernoulli and Leonhard Euler. While working in Petersburg, Bernoulli and Euler simultaneously set out to develop the science of fluid motion on the basis of the law of conservation of living forces (kinetic energy). When their first results turned out to be identical, Euler conceded the right to pursue further studies in this field to his older colleague. As a result, at the beginning of the 1730's, Bernoulli laid the foundations of theoretical hydraulics on the basis of the law of living forces balance, which in his treatment approximated the law of energy conservation. Bernoulli published his theory of hydraulics in his famous Hydrodynamics (1738), the most significant treatise on physical mechanics to appear in the 18th century. Hydrodynamics proper (of an ideal fluid), as currently understood, was created 20 or so years later by Euler, who gave it something closely resembling its present form in the papers he produced during the 1750's

The behavior of Bernoulli shifts relative to their factors

Abstract: We present numerous examples of ways that a Bernoulli shift can behave relative to a family of factors. This shows the similarities between the properties which collections of ergodic transformations can have and the behavior of a Bernoulli shift relative to a collection of its factors. For example, we construct a family of factors of a Bernoulli shift which have the same entropy, and any extension of one of these factors has more entropy, yet no two of these factors sit the same. This is the relative analog of Ornstein and Shields uncountable collection of nonisomorphic $K$ transformations of the same entropy. We are able to construct relative analogs of almost all the zero entropy counter-examples constructed by Rudolph (1979), as well as the $K$ counterexamples constructed by Hoffman (1997). This paper provides a solution to a problem posed by Ornstein (1975).

Instances of exact prediction and a new type of inequalities obtained by anchoring

Abstract: Prediction in Bernoulli sources is considered. Instead of looking at approximate or asymptotic results, we determine exactly certain optimal predictors. The results are still sporadic, and call for future extension. The technique depends on a new theoretical framework for certain optimization problems, and a new type of information inequalities, characterized by so-called anchoring.