Subminiature micropower digital recorder

High-density digital data, collected periodically or randomly from multiplicity of sensors, are recorded by subminiature recorder. Magnetic recording head is energized with suitable pulsatile signals to reverse polarization on magnetically-sensitive tape while tape is immobilized at recording head. Prior to next recording, set tape so new area of tape is at recording head

Eigen-analysis of Inviscid Fluid Structure Interaction (FSI) Systems with Complex Boundary Conditions

A method for extracting the eigenvalues and eigenmodes from complex coupled fluid-structure interaction (FSI) systems is presented. The FSI system under consideration in this case is a one-sided, inviscid flow over a finite-length compliant surface with complex boundary conditions, although the method could be applied to any FSI system. The flow is solved for the inviscid case using a boundary-element method solution of Laplace’s equation, while the finite compliant surface is solved through a finite-difference solution of the one-dimensional beam equation. The crux of the method lies in reducing the coupled fluid and structural equations down to a set of coupled linear differential equations. Standard Krylov subspace projection methods may then be used to determine the eigenvalues of the large system of linear equations. This method is applied to the analysis of hydroelastic FSI systems with complex boundary conditions that would be difficult or otherwise impossible to analyse using standard Galerkin methods. Specifically, the complex cases of inhomogeneous and discontinuous compliant wall properties and arbitrary hinge-joint conditions along the compliant surface are considered

Eigen-analysis of a Fully Viscous Boundary-Layer flow Interacting with a Finite Compliant Surface

A method and preliminary results are presented for the determination of eigenvalues and eigenmodes from fully viscous boundary layer flow interacting with a finite length one-sided compliant wall. This is an extension to the analysis of inviscid flow-structure systems which has been established in previous work. A combination of spectral and finite-difference methods are applied to a linear perturbation form of the full Navier-Stokes equations and one-dimensional beam equation. This yields a system of coupled linear equations that accurately define the spatio-temporal development of linear perturbations to a boundary layer flow over a finite-length compliant surface. Standard Krylov subspace projection methods are used to extract the eigenvalues from this complex system of equations. To date, the analysis of the development of Tollmien-Schlichting (TS) instabilities over a finite compliant surface have relied upon DNS-type results across a narrow (or even singular) spectrum of TS waves. The results from this method have the potential to describe conclusively the role that a finite length compliant surface has in the development of two-dimensional TS instabilities and other FSI instabilities across a broad spectrum

Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with negative constant drift, described by a Fokker-Planck equation with a potential V(x) = - [b \ln(x) + a\, x], for b>0 and a<0. The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process, that has been extensively studied for its applications in physics, biology and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schroedinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a negative constant drift. We conclude with a comparison with other analytical methods and with numerical solutions.Comment: 21 pages, 8 figure

Windings of the 2D free Rouse chain

We study long time dynamical properties of a chain of harmonically bound Brownian particles. This chain is allowed to wander everywhere in the plane. We show that the scaling variables for the occupation times T_j, areas A_j and winding angles \theta_j (j=1,...,n labels the particles) take the same general form as in the usual Brownian motion. We also compute the asymptotic joint laws P({T_j}), P({A_j}), P({\theta_j}) and discuss the correlations occuring in those distributions.Comment: Latex, 17 pages, submitted to J. Phys.

Forces on Bins - The Effect of Random Friction

In this note we re-examine the classic Janssen theory for stresses in bins, including a randomness in the friction coefficient. The Janssen analysis relies on assumptions not met in practice; for this reason, we numerically solve the PDEs expressing balance of momentum in a bin, again including randomness in friction.Comment: 11 pages, LaTeX, with 9 figures encoded, gzippe

Levy-Student Distributions for Halos in Accelerator Beams

We describe the transverse beam distribution in particle accelerators within the controlled, stochastic dynamical scheme of the Stochastic Mechanics (SM) which produces time reversal invariant diffusion processes. This leads to a linearized theory summarized in a Shchr\"odinger--like (\Sl) equation. The space charge effects have been introduced in a recent paper~\cite{prstab} by coupling this \Sl equation with the Maxwell equations. We analyze the space charge effects to understand how the dynamics produces the actual beam distributions, and in particular we show how the stationary, self--consistent solutions are related to the (external, and space--charge) potentials both when we suppose that the external field is harmonic (\emph{constant focusing}), and when we \emph{a priori} prescribe the shape of the stationary solution. We then proceed to discuss a few new ideas~\cite{epac04} by introducing the generalized Student distributions, namely non--Gaussian, L\'evy \emph{infinitely divisible} (but not \emph{stable}) distributions. We will discuss this idea from two different standpoints: (a) first by supposing that the stationary distribution of our (Wiener powered) SM model is a Student distribution; (b) by supposing that our model is based on a (non--Gaussian) L\'evy process whose increments are Student distributed. We show that in the case (a) the longer tails of the power decay of the Student laws, and in the case (b) the discontinuities of the L\'evy--Student process can well account for the rare escape of particles from the beam core, and hence for the formation of a halo in intense beams.Comment: revtex4, 18 pages, 12 figure

Stochastic Gravity

Gravity is treated as a stochastic phenomenon based on fluctuations of the metric tensor of general relativity. By using a (3+1) slicing of spacetime, a Langevin equation for the dynamical conjugate momentum and a Fokker-Planck equation for its probability distribution are derived. The Raychaudhuri equation for a congruence of timelike or null geodesics leads to a stochastic differential equation for the expansion parameter $\theta$ in terms of the proper time $s$. For sufficiently strong metric fluctuations, it is shown that caustic singularities in spacetime can be avoided for converging geodesics. The formalism is applied to the gravitational collapse of a star and the Friedmann-Robertson-Walker cosmological model. It is found that owing to the stochastic behavior of the geometry, the singularity in gravitational collapse and the big-bang have a zero probability of occurring. Moreover, as a star collapses the probability of a distant observer seeing an infinite red shift at the Schwarzschild radius of the star is zero. Therefore, there is a vanishing probability of a Schwarzschild black hole event horizon forming during gravitational collapse.Comment: Revised version. Eq. (108) has been modified. Additional comments have been added to text. Revtex 39 page