An instability criterion for a finite amplitude localized disturbance in a shear flow of electrically conducting fluids

The stability of shear flows of electrically conducting fluids, with respect to finite amplitude three-dimensional localized disturbances is considered. The time evolution of the fluid impulse integral, characterizing such disturbances, for the case of low magnetic Reynolds number is obtained by integrating analytically the vorticity equation. Analysis of the resulted equation reveals a new instability criterion.Comment: 10 pages in LaTex, no figures, accepted in Phys. Fluid

The SQUID Handbook

This two-volume handbook offers a comprehensive and well coordinated presentation of SQUIDs (Superconducting Quantum Interference Devices), including device fundamentals, design, technology, system construction and multiple applications. It is intended to bridge the gap between fundamentals and applications, and will be a valuable textbook reference for graduate students and for professionals engaged in SQUID research and engineering. It will also be of use to specialists in multiple fields of practical SQUID applications, from human brain research and heart diagnostics to airplane and nuclea

Propagation of Light in the Field of Stationary and Radiative Gravitational Multipoles

Extremely high precision of near-future radio/optical interferometric observatories like SKA, Gaia, SIM and the unparalleled sensitivity of LIGO/LISA gravitational-wave detectors demands more deep theoretical treatment of relativistic effects in the propagation of electromagnetic signals through variable gravitational fields of the solar system, oscillating and precessing neutron stars, coalescing binary systems, exploding supernova, and colliding galaxies. Especially important for future gravitational-wave observatories is the problem of propagation of light rays in the field of multipolar gravitational waves emitted by a localized source of gravitational radiation. Present paper suggests physically-adequate and consistent mathematical solution of this problem in the first post-Minkowskian approximation of General Relativity which accounts for all time-dependent multipole moments of an isolated astronomical system.Comment: 36 pages, no figure

Cooling of a mirror by radiation pressure

We describe an experiment in which a mirror is cooled by the radiation pressure of light. A high-finesse optical cavity with a mirror coated on a mechanical resonator is used as an optomechanical sensor of the Brownian motion of the mirror. A feedback mechanism controls this motion via the radiation pressure of a laser beam reflected on the mirror. We have observed either a cooling or a heating of the mirror, depending on the gain of the feedback loop.Comment: 4 pages, 6 figures, RevTe

Nonlinear Electron Oscillations in a Viscous and Resistive Plasma

New non-linear, spatially periodic, long wavelength electrostatic modes of an electron fluid oscillating against a motionless ion fluid (Langmuir waves) are given, with viscous and resistive effects included. The cold plasma approximation is adopted, which requires the wavelength to be sufficiently large. The pertinent requirement valid for large amplitude waves is determined. The general non-linear solution of the continuity and momentum transfer equations for the electron fluid along with Poisson's equation is obtained in simple parametric form. It is shown that in all typical hydrogen plasmas, the influence of plasma resistivity on the modes in question is negligible. Within the limitations of the solution found, the non-linear time evolution of any (periodic) initial electron number density profile n_e(x, t=0) can be determined (examples). For the modes in question, an idealized model of a strictly cold and collisionless plasma is shown to be applicable to any real plasma, provided that the wavelength lambda >> lambda_{min}(n_0,T_e), where n_0 = const and T_e are the equilibrium values of the electron number density and electron temperature. Within this idealized model, the minimum of the initial electron density n_e(x_{min}, t=0) must be larger than half its equilibrium value, n_0/2. Otherwise, the corresponding maximum n_e(x_{max},t=tau_p/2), obtained after half a period of the plasma oscillation blows up. Relaxation of this restriction on n_e(x, t=0) as one decreases lambda, due to the increase of the electron viscosity effects, is examined in detail. Strong plasma viscosity is shown to change considerably the density profile during the time evolution, e.g., by splitting the largest maximum in two.Comment: 16 one column pages, 11 figures, Abstract and Sec. I, extended, Sec. VIII modified, Phys. Rev. E in pres

Stochastic Flux-Freezing and Magnetic Dynamo

We argue that magnetic flux-conservation in turbulent plasmas at high magnetic Reynolds numbers neither holds in the conventional sense nor is entirely broken, but instead is valid in a novel statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle tra jectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. We discuss empirical evidence for spontaneous stochasticity, including our own new numerical results. We then use a Lagrangian path-integral approach to establish stochastic flux-freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux-conservation must remain stochastic at infinite magnetic Reynolds number. As an important application of these results we consider the kinematic, fluctuation dynamo in non-helical, incompressible turbulence at unit magnetic Prandtl number. We present results on the Lagrangian dynamo mechanisms by a stochastic particle method which demonstrate a strong similarity between the Pr = 1 and Pr = 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. We finally consider briefly some consequences for nonlinear MHD turbulence, dynamo and reconnectionComment: 29 pages, 10 figure

Ultrasensitive inertial and force sensors with diamagnetically levitated magnets

We theoretically show that a magnet can be stably levitated on top of a punctured superconductor sheet in the Meissner state without applying any external field. The trapping potential created by such induced-only superconducting currents is characterized for magnetic spheres ranging from tens of nanometers to tens of millimeters. Such a diamagnetically levitated magnet is predicted to be extremely well isolated from the environment. We propose to use it as an ultrasensitive force and inertial sensor. A magnetomechanical readout of its displacement can be performed by using superconducting quantum interference devices. An analysis using current technology shows that force and acceleration sensitivities on the order of 10−23  N/√Hz (for a 100-nm magnet) and 10−14  g/√Hz (for a 10-mm magnet) might be within reach in a cryogenic environment. Such remarkable sensitivities, both in force and acceleration, can be used for a variety of purposes, from designing ultrasensitive inertial sensors for technological applications (e.g., gravimetry, avionics, and space industry), to scientific investigations on measuring Casimir forces of magnetic origin and gravitational physics