Showing papers on "Bernoulli's principle published in 2011"

Universality for generalized Wigner matrices with Bernoulli distribution

Abstract: The universality for the eigenvalue spacing statistics of generalized Wigner matrices was established in our previous work [19] under certain conditions on the probability distributions of the matrix elements. A major class of probability measures excluded in [19] are the Bernoulli measures. In this paper, we extend the universality result of [19] to include the Bernoulli measures so that the only restrictions on the probability distributions of the matrix elements are the subexponential decay and the normalization condition that the variances in each row sum up to one. The new ingredient is a strong local semicircle law which improves the error estimate on the Stieltjes transform of the empirical measure of the eigenvalues

Non-linear vibration of Euler-Bernoulli beams

Abstract: In this paper, variational iteration (VIM) and parametrized perturbation (PPM) methods have been used to investigate non-linear vibration of Euler-Bernoulli beams subjected to the axial loads. The proposed methods do not require small parameter in the equation which is difficult to be found for nonlinear problems. Comparison of VIM and PPM with Runge-Kutta 4th leads to highly accurate solutions.

Bernoulli Forward-Backward Smoothing for Joint Target Detection and Tracking

Abstract: In this correspondence, we derive a forward-backward smoother for joint target detection and estimation and propose a sequential Monte Carlo implementation. We model the target by a Bernoulli random finite set since the target can be in one of two “present” or “absent” modes. Finite set statistics is used to derive the smoothing recursion. Our results indicate that smoothing has two distinct advantages over just using filtering: First, we are able to more accurately identify the appearance and disappearance of a target in the scene, and second, we can provide improved state estimates when the target exists.

Three-dimensional extension of Lighthill's large-amplitude elongated-body theory of fish locomotion

Abstract: The goal of this paper is to derive expressions for the pressure forces and moments acting on an elongated body swimming in a quiescent fluid. The body is modelled as an inextensible and unshearable (Kirchhoff) beam, whose cross-sections are elliptic, undergoing prescribed deformations, consisting of yaw and pitch bending. The surrounding fluid is assumed to be inviscid, and irrotational everywhere, except in a thin vortical wake. The Laplace equation and the corresponding Neumann boundary conditions are first written in terms of the body coordinates of a beam treating the body as a fixed surface. They are then simplified according to the slenderness of the body and its kinematics. Because the equations are linear, the velocity potential is sought as a sum of two terms which are linked respectively to the axial movements of the beam and to its lateral movements. The lateral component of the velocity potential is decomposed further into two sub-components, in order to exhibit explicitly the role of the two-dimensional potential flow produced by the lateral motion of the cross-section, and the role played by the curvature effects of the beam on the cross-sectional flow. The pressure, which is given by Bernoulli's equation, is integrated along the body surface, and the expressions for the resultant and the moment are derived analytically. Thereafter, the validity of the force and moment obtained analytically is checked by comparisons with Navier–Stokes simulations (using Reynolds-averaged Navier–Stokes equations), and relatively good agreements are observed.

The facility location problem with Bernoulli demands

Abstract: This paper presents the facility location problem with Bernoulli demands . In this capacitated discrete location stochastic problem the goal is to define an a priori solution for the locations of the facilities and for the allocation of customers to the operating facilities that minimizes the sum of the fixed costs of the open facilities plus the expected value of the recourse function. The problem is formulated as a two-stage stochastic program and two different recourse actions are considered. For each of them, a closed form is presented for the recourse function and a deterministic equivalent formulation is obtained for the case in which the probability of demand is the same for all customers. Numerical results from computational experiments are presented and analyzed.

The Evolution of Dynamics: Vibration Theory from 1687 to 1742

Abstract: 1 Introduction- 2 Newton (1687)- 21 Pressure Wave- 22 Remarks- 3 Taylor (1713)- 31 Vibrating String- 32 Absolute Frequency- 33 Remarks- 4 Sauveur (1713)- 41 Vibrating String- 42 Remarks- 5 Hermann (1716)- 51 Pressure Wave- 52 Vibrating String- 53 Remarks- 6 Cramer (1722)- 61 Sound- 62 Remarks- 7 Euler (1727)- 71 Vibrating Ring- 72 Sound- 8 Johann Bernoulli (1728)- 81 Vibrating String (Continuous and Discrete)- 82 Remark on the Energy Method- 9 Daniel Bernoulli (1733 1734) Euler (1736) - 91 Linked Pendulum and Hanging Chain- 92 Laguerre Polynomials and J0- 93 Double and Triple Pendula- 94 Roots of Polynomials- 95 Zeros of J0- 96 Other Boundary Conditions- 97 The Bessel Functions Jv- 10 Euler (1735)- 101 Pendulum Condition- 102 Vibrating Rod- 103 Remarks- 11 Johann II Bernoulli (1736)- 111 Pressure Wave- 112 Remarks- 12 Daniel Bernoulli (1739 1740)- 121 Floating Body- 122 Remarks- 123 Dangling Rod- 124 Remarks on Superposition- 13 Daniel Bernoulli (1742)- 131 Vibrating Rod- 132 Absolute Frequency and Experiments- 133 Superposition- 14 Euler (1742)- 141 Linked Compound Pendulum- 142 Dangling Rod and Weighted Chain- 15 Johann Bernoulli (1742) no- 151 One Degree of Freedom- 152 Dangling Rod- 153 Linked Pendulum I- 154 Linked Pendulum II- Appendix: Daniel Bernoulli's Papers on the Hanging Chain and the Linked Pendulum- Theoremata de Oscillationibus Corporum- De Oscillationibus Filo Flexili Connexorum- Theorems on the Oscillations of Bodies- On the Oscillations of Bodies Connected by a Flexible Thread

Global Steady Subsonic Flows through Infinitely Long Nozzles for the Full Euler Equations

Abstract: We are concerned with global steady subsonic flows through general infinitely long nozzles for the full Euler equations. The problem is formulated as a boundary value problem in the unbounded domain for a nonlinear elliptic equation of second order in terms of the stream function. It is established that, when the oscillation of the entropy and Bernoulli functions at the upstream is sufficiently small in $C^{1,1}$ and the mass flux is in a suitable regime, there exists a unique global subsonic solution in a suitable class of general nozzles. The assumptions are required to prevent from the occurrence of supersonic bubbles inside the nozzles. The asymptotic behavior of subsonic flows at the downstream and upstream, as well as the critical mass flux, have been clarified.

Algorithmic tests and randomness with respect to a class of measures

Abstract: This paper offers some new results on randomness with respect to classes of measures, along with a didactical exposition of their context based on results that appeared elsewhere. We start with the reformulation of the Martin-L¨ of definition of randomness (with respect to computable measures) in terms of randomness deficiency functions. A formula that expresses the randomness deficiency in terms of prefix complexity is given (in two forms). Some approaches that go in another direction (from deficiency to complexity) are considered. The notion of Bernoulli randomness (independent coin tosses for an asymmetric coin with some probability p of head) is defined. It is shown that a sequence is Bernoulli if it is random with respect to some Bernoulli

Dynamic response of axially loaded euler-bernoulli beams

Abstract: The current research deals with application of a new analytical technique called Energy Balance Method (EBM) for a nonlinear problem. Energy Balance Method is used to obtain the analytical solution for nonlinear vibra tion behavior of Euler-Bernoulli beams subjected to axial loads. Analytical expressions for geometrically nonlinear vibration of beams are provided. The effect of vibration amplitude on the nonlinear frequency is discussed. Com parison between Energy Balance Method results and those available in literature demonstrates the accuracy of this method. In Energy Balance Method contrary to the con ventional methods, only one iteration leads to high accu racy of the solutions which are valid for a wide range of vibration amplitudes. http://dx.doi.org/10.5755/j01.mech.17.2.335

Closed-form solutions for Euler–Bernoulli arbitrary discontinuous beams

Abstract: Euler–Bernoulli arbitrary discontinuous beams acted upon by static loads are addressed. Based on appropriate Green’s functions here derived in a closed form, the response variables are obtained: (a) for stepped beams with internal springs, as closed-form functions of the beam discontinuity parameters, without enforcing neither internal nor boundary conditions; (b) for stepped beams with internal springs and along-axis supports, as closed-form functions of the unknown reactions of the along-axis supports only, to be computed by enforcing pertinent conditions. A remarkable reduction in computational effort is achieved, in this manner, compared to competing methods in the literature.

Spectral analysis and stabilization of a chain of serially connected Euler-Bernoulli beams and strings

Abstract: We consider N Euler-Bernoulli beams and N strings alternatively connected to one another and forming a particular network which is a chain beginning with a string. We study two stabilization problems on the same network and the spectrum of the corresponding conservative system: the characteristic equation as well as its asymptotic behavior are given. We prove that the energy of the solution of the rst dissipative system tends to zero when the time tends to in nity under some irrationality assumptions on the length of the strings and beams. On another hand we prove a polynomial decay result of the energy of the second system, independently of the length of the strings and beams, for all regular initial data. Our technique is based on a frequency domain method and combines a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent.

Weak isomorphisms between Bernoulli shifts

Abstract: In this note, we prove that if G is a countable group that contains a nonabelian free subgroup then every pair of nontrivial Bernoulli shifts over G are weakly isomorphic.

Static Analysis of Functionally Graded Piezoelectric Beams under Thermo-Electro-Mechanical Loads

Abstract: This paper presents the analysis of static bending of beams made of functionally graded piezoelectric materials (FGPMs) under a combined thermo-electro-mechanical load. The Euler Bernoulli theory (...

Electromechanical Modeling and Normal Form Analysis of an Aeroelastic Micro-Power Generator

Abstract: Combining theories in continuous-systems vibrations, piezoelectricity, and fluid dynamics, we develop and experimentally validate an analytical electromechanical model to predict the response behavior of a self-excited micro-power generator. Similar to music- playing harmonica that create tones via oscillations of reeds when subjected to air blow, the proposed device uses flow-induced self-excited oscillations of a piezoelectric beam embedded within a cavity to generate electric power. To obtain the desired model, we adopt the non- linear EulerBernoulli beam's theory and linear constitutive relationships. We use Hamilton's principle in conjunction with electric circuits theory and the inextensibility condition to derive the partial differential equation that captures the transversal dynamics of the beam and the ordinary differential equation governing the dynamics of the harvesting circuit. Using the steady Bernoulli equation and the continuity equation, we further relate the exciting pressure at the surface of the beam to the beam's deflection, and the inflow rate of air. Subsequently, we employ a Galerkin's descritization to reduce the order of the model and show that a single- mode reduced-order model of the infinite-dimensional system is sufficient to predict the response behavior. Using the method of multiple scales, we develop an approximate analytical solution of the resulting reduced-order model near the stability boundary and study the normal form of the resulting bifurcation. We observe that a Hopf bifurcation of the super- critical nature is responsible for the onset of limit-cycle oscillations.

a modified logvinovich model for hydrodynamic loads on an asymmetric wedge entering water with a roll motion

Abstract: The water entry problem of an asymmetric wedge with roll motion was analyzed by the method of a modified Logvinovich model (MLM). The MLM is a kind of analytical model based on the Wagner method, which linearizes the free surface condition and body boundary condition. The difference is that the MLM applies a nonlinear Bernoulli equation to obtain pressure distribution, which has been proven to be helpful to enhance the accuracy of hydrodynamic loads. The Wagner condition in this paper was generalized to solve the problem of the water entry of a wedge body with rotational velocity. The comparison of wet width between the MLM and a fully nonlinear numerical approach was given, and they agree well with each other. The effect of angular velocity on the hydrodynamic loads of a wedge body was investigated.

A new bernoulli sub-ode method for constructing traveling wave solutions for two nonlinear equations with any order

Abstract: In this paper, a new generalized Bernoulli sub-ODE method is proposed to construct exact solutions of nonlinear equations. The validity of the method is testied by nding new exact traveling wave solutions of the BBM equation with any order and general Gardner equation.

A generalized Isserlis theorem for location mixtures of Gaussian random vectors

Abstract: In a recent paper, Michalowicz et al. provide an extension of Isserlis theorem to the case of a Bernoulli location mixture of a Gaussian vector. We extend here this result to the case of any location mixture of Gaussian vector; we also provide an example of the Isserlis theorem for a "scale location" mixture of Gaussian, namely the d-dimensional generalized hyperbolic distribution.

On the Stability and the Approximation of Branching Distribution Flows, with Applications to Nonlinear Multiple Target Filtering

Abstract: We analyze the exponential stability properties of a class of measure-valued equations arising in nonlinear multi-target filtering problems. We also prove the uniform convergence properties w.r.t. the time parameter of a rather general class of stochastic filtering algorithms, including sequential Monte Carlo type models and mean field particle interpretation models. We illustrate these results in the context of the Bernoulli and the Probability Hypothesis Density filter, yielding what seems to be the first results of this kind in this subject.

Bernoulli actions and infinite entropy

Abstract: We show that, for countable sofic groups, a Bernoulli action with infinite entropy base has infinite entropy with respect to every sofic approximation sequence. This builds on the work of Lewis Bowen in the case of finite entropy base and completes the computation of measure entropy for Bernoulli actions over countable sofic groups. One consequence is that such a Bernoulli action fails to have a generating countable partition with finite entropy if the base has infinite entropy, which in the amenable case is well known and in the case that the acting group contains the free group on two generators was established by Bowen.

On an Efficient Finite Element Method for Navier-Stokes-ω with Strong Mass Conservation

Abstract: We study an efficient finite element method for the NS-ω model, that uses van Cittert approximate deconvolution to improve accuracy and Scott-Vogelius elements to provide pointwise mass conservative solutions and remove the dependence of the (often large) Bernoulli pressure error on the velocity error. We provide a complete numerical analysis of the method, including well-posedness, unconditional stability, and optimal convergence. Additionally, an improved choice of filtering radius (versus the usual choice of the average mesh width) for the scheme is found, by identifying a connection with a scheme for the velocity-vorticity-helicity NSE formulation. Several numerical experiments are given that demonstrate the performance of the scheme, and the improvement offered by the new choice of the filtering radius. 2010 Mathematical subject classification: 76D05; 76F99; 65M60.

Bernoulli equilibrium states for surface diffeomorphisms

Abstract: Suppose $f\colon M\to M$ is a $C^{1+\alpha}$ $(\alpha>0)$ diffeomorphism on a compact smooth orientable manifold $M$ of dimension 2, and let $\mu_\Psi$ be an equilibrium measure for a Holder-continuous potential $\Psi\colon M\to \mathbb R$. We show that if $\mu_\Psi$ has positive measure-theoretic entropy, then $f$ is measure-theoretically isomorphic mod $\mu_\Psi$ to the product of a Bernoulli scheme and a finite rotation.

Understanding Bernoulli’s principle through simulations

Abstract: Computer simulations are used to develop a deeper understanding of Bernoulli’s principle. Hard disks undergoing elastic collisions are injected into a Venturi nozzle and the pressure in the narrow throat of the nozzle is compared to the pressure in the wider section of the pipe. This model system is an ideal student project because the theory and programming are straightforward, and the computational cost is low.

Stable orbit equivalence of Bernoulli shifts over free groups

Abstract: Previous work showed that every pair of nontrivial Bernoulli shifts over a fixed free group are orbit equivalent. In this paper, we prove that if $G_1,G_2$ are nonabelian free groups of finite rank then every nontrivial Bernoulli shift over $G_1$ is stably orbit equivalent to every nontrivial Bernoulli shift over $G_2$. This answers a question of S. Popa.

Fast computation of Bernoulli, Tangent and Secant numbers

Abstract: We consider the computation of Bernoulli, Tangent (zag), and Secant (zig or Euler) numbers. In particular, we give asymptotically fast algorithms for computing the first n such numbers in O(n^2.(log n)^(2+o(1))) bit-operations. We also give very short in-place algorithms for computing the first n Tangent or Secant numbers in O(n^2) integer operations. These algorithms are extremely simple, and fast for moderate values of n. They are faster and use less space than the algorithms of Atkinson (for Tangent and Secant numbers) and Akiyama and Tanigawa (for Bernoulli numbers).

On the convolution of heterogeneous Bernoulli random variables

Abstract: In this paper, some ordering properties of convolutions of heterogeneous Bernoulli random variables are discussed. It is shown that, under some suitable conditions, the likelihood ratio order and the reversed hazard rate order hold between convolutions of two heterogeneous Bernoulli sequences. The results established here extend and strengthen the previous results of Pledger and Proschan (1971) and Boland, Singh and Cukic (2002).