Simulation of the Gravitational Collapse and Fragmentation of Rotating Molecular Clouds

In this paper we study the process of the subsequent (runaway) fragmentation of the rotating isothermal Giant Molecular Cloud (GMC) complex. Our own developed Smoothed Particle Hydrodynamics (SPH) gas-dynamical model successfully reproduce the observed Cloud Mass-distribution Function (CMF) in our Galaxy (even the differences between the inner and outer parts of our Galaxy). The steady state CMF is established during the collapse within a free-fall timescale of the GMC. We show that one of the key parameters, which defines the observed slope of the present day CMF, is the initial ratio of the rotational (turbulent) and gravitational energy inside the fragmented GMC.Comment: 8 pages, 9 EPS figures, special forma.cls class file is use

Acoustic Radiation Force and Torque on Small Particles as Measures of the Canonical Momentum and Spin Densities

We examine acoustic radiation force and torque on a small (subwavelength) absorbing isotropic particle immersed in a monochromatic (but generally inhomogeneous) sound-wave field. We show that by introducing the monopole and dipole polarizabilities of the particle, the problem can be treated in a way similar to the well-studied optical forces and torques on dipole Rayleigh particles. We derive simple analytical expressions for the acoustic force (including both the gradient and scattering forces) and torque. Importantly, these expressions reveal intimate relations to the fundamental field properties introduced recently for acoustic fields: the canonical momentum and spin angular momentum densities. We compare our analytical results with previous calculations and exact numerical simulations. We also consider an important example of a particle in an evanescent acoustic wave, which exhibits the mutually-orthogonal scattering (radiation-pressure) force, gradient force, and torque from the transverse spin of the field.Comment: 7 pages, 3 figures, Supplemental Material, to appear in Phys. Rev. Let

A cesium gas strongly confined in one dimension : sideband cooling and collisional properties

We study one-dimensional sideband cooling of Cesium atoms strongly confined in a far-detuned optical lattice. The Lamb-Dicke regime is achieved in the lattice direction whereas the transverse confinement is much weaker. The employed sideband cooling method, first studied by Vuletic et al.\cite{Vule98}, uses Raman transitions between Zeeman levels and produces a spin-polarized sample. We present a detailed study of this cooling method and investigate the role of elastic collisions in the system. We accumulate $83(5)$ of the atoms in the vibrational ground state of the strongly confined motion, and elastic collisions cool the transverse motion to a temperature of $2.8 \mu$K=$0.7 \hbar\omega_{\rm osc}/k_{\rm B}$, where $\omega_{\rm osc}$ is the oscillation frequency in the strongly confined direction. The sample then approaches the regime of a quasi-2D cold gas. We analyze the limits of this cooling method and propose a dynamical change of the trapping potential as a mean of cooling the atomic sample to still lower temperatures. Measurements of the rate of thermalization between the weakly and strongly confined degrees of freedom are compatible with the zero energy scattering resonance observed previously in weak 3D traps. For the explored temperature range the measurements agree with recent calculations of quasi-2D collisions\cite{Petr01}. Transparent analytical models reproduce the expected behavior for $k_{\rm B}T \gg \hbar \omega_{\rm osc}$ and also for $k_{\rm B}T \ll \hbar \omega_{\rm osc}$ where the 2D features are prominent.Comment: 18 pages, 12 figure

A rigorous derivation of the stationary compressible Reynolds equation via the Navier-Stokes equations

We provide a rigorous derivation of the compressible Reynolds system as a singular limit of the compressible (barotropic) Navier-Stokes system on a thin domain. In particular, the existence of solutions to the Navier-Stokes system with non-homogeneous boundary conditions is shown that may be of independent interest. Our approach is based on new a priori bounds available for the pressure law of hard sphere type. Finally, uniqueness for the limit problem is established in the 1D case