Acoustically induced oscillation and rotation of a large drop in space

A 2.5 cm diameter water drop was successfully deployed and manipulated in a triaxial acoustic resonance chamber during a 240 sec low-gravity SPAR rocket flight. Oscillation and rotation were induced by modulating and phase shifting the signals to the speakers. Portions of the film record were digitized and analyzed. Spectral analysis brought out the n = 2, 3, 4 free oscillation modes of the drop, its very low-frequency center-of-mass motion in the acoustic potential well, and the forced oscillation frequency. The drop boundaries were least-square fitted to general ellipses, providing eccentricities of the distorted drop. The normalized equatorial area of the rotating drop was plotted vs a rotational parameter, and was in excellent agreement with values derived from the theory of equilibrium shapes of rotating liquid drops

A critical layer model for turbulent pipe flow

A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale motions. The model is derived by treating the nonlinearity in the perturbation equation (involving the Reynolds stress) as an unknown forcing, yielding a linear relationship between the velocity field response and this nonlinearity. We do not assume small perturbations. We examine propagating modes, permitting comparison of our results to experimental data, and identify the steady component of the velocity field that varies only in the wall-normal direction as the turbulent mean profile. The "optimal" forcing shape, that gives the largest velocity response, is assumed to lead to modes that will be dominant and hence observed in turbulent pipe flow. An investigation of the most amplified velocity response at a given wavenumber-frequency combination reveals critical layer-like behaviour reminiscent of the neutrally stable solutions of the Orr-Sommerfeld equation in linearly unstable flow. Two distinct regions in the flow where the influence of viscosity becomes important can be identified, namely a wall layer that scales with $R^{+1/2}$ and a critical layer, where the propagation velocity is equal to the local mean velocity, that scales with $R^{+2/3}$ in pipe flow. This framework appears to be consistent with several scaling results in wall turbulence and reveals a mechanism by which the effects of viscosity can extend well beyond the immediate vicinity of the wall.Comment: Submitted to the Journal of Fluid Mechanics and currently under revie

Jacobi multipliers, non-local symmetries and nonlinear oscillators

Constants of motion, Lagrangians and Hamiltonians admitted by a family of relevant nonlinear oscillators are derived using a geometric formalism. The theory of the Jacobi last multiplier allows us to find Lagrangian descriptions and constants of the motion. An application of the jet bundle formulation of symmetries of differential equations is presented in the second part of the paper. After a short review of the general formalism, the particular case of non-local symmetries is studied in detail by making use of an extended formalism. The theory is related to some results previously obtained by Krasil'shchi, Vinogradov and coworkers. Finally the existence of non-local symmetries for such two nonlinear oscillators is proved.Comment: 20 page

Modular Solutions to Equations of Generalized Halphen Type

Solutions to a class of differential systems that generalize the Halphen system are determined in terms of automorphic functions whose groups are commensurable with the modular group. These functions all uniformize Riemann surfaces of genus zero and have $q$--series with integral coefficients. Rational maps relating these functions are derived, implying subgroup relations between their automorphism groups, as well as symmetrization maps relating the associated differential systems.Comment: PlainTeX 36gs. (Formula for Hecke operator corrected.

Novel self-assembled morphologies from isotropic interactions

We present results from particle simulations with isotropic medium range interactions in two dimensions. At low temperature novel types of aggregated structures appear. We show that these structures can be explained by spontaneous symmetry breaking in analytic solutions to an adaptation of the spherical spin model. We predict the critical particle number where the symmetry breaking occurs and show that the resulting phase diagram agrees well with results from particle simulations.Comment: 4 pages, 4 figure

The Adsorption of Atomic Nitrogen on Ru(0001): Geometry and Energetics

The local adsorption geometries of the (2x2)-N and the (sqrt(3)x sqrt(3))R30^o -N phases on the Ru(0001) surface are determined by analyzing low-energy electron diffraction (LEED) intensity data. For both phases, nitrogen occupies the threefold hcp site. The nitrogen sinks deeply into the top Ru layer resulting in a N-Ru interlayer distance of 1.05 AA and 1.10 AA in the (2x2) and the (sqrt(3)x sqrt(3))R30^o unit cell, respectively. This result is attributed to a strong N binding to the Ru surface (Ru--N bond length = 1.93 AA) in both phases as also evidenced by ab-initio calculations which revealed binding energies of 5.82 eV and 5.59 eV, respectively.Comment: 17 pages, 5 figures. Submitted to Chem. Phys. Lett. (October 10, 1996

Quasi-doubly periodic solutions to a generalized Lame equation

We consider the algebraic form of a generalized Lame equation with five free parameters. By introducing a generalization of Jacobi's elliptic functions we transform this equation to a 1-dim time-independent Schroedinger equation with (quasi-doubly) periodic potential. We show that only for a finite set of integral values for the five parameters quasi-doubly periodic eigenfunctions expressible in terms of generalized Jacobi functions exist. For this purpose we also establish a relation to the generalized Ince equation.Comment: 15 pages,1 table, accepted for publication in Journal of Physics

General relativistic gravitational field of a rigidly rotating disk of dust: Solution in terms of ultraelliptic functions

In a recent paper we presented analytic expressions for the axis potential, the disk metric, and the surface mass density of the global solution to Einstein's field equations describing a rigidly rotating disk of dust. Here we add the complete solution in terms of ultraelliptic functions and quadratures.Comment: 5 pages, published in 1995 [Phys. Rev. Lett. 75 (1995) 3046