Minimum-weight springs

Load deflection curves for minimum weight spring

Castaing's instability in a trapped ultra-cold gas

We consider a trapped ultra-cold gas of (non-condensed) bosons with two internal states (described by a pseudo spin) and study the stability of a longitudinal pseudo spin polarization gradient. For this purpose, we numerically solve a kinetic equation corresponding to a situation close to an experiment at JILA. It shows the presence of Castaing's instability of transverse spin polarization fluctuations at long wavelengths. This phenomenon could be used to create spontaneous transverse spin waves.Comment: 5 pages, 3 figures; equation (8) corrected; submitted to EPJ

Jeans instability of a galactic disk embedded in a live dark halo

We investigate the Jeans instability of a galactic disk embedded in a dynamically responsive dark halo. It is shown that the disk-halo system becomes nominally Jeans unstable. On small scales the instability is suppressed, if the Toomre stability index Q_T is higher than a certain threshold, but on large scales the Jeans instability sets invariably in. However, using a simple self-consistent disk-halo model it is demonstrated that this occurs on scales which are much larger than the system so that this is indeed only a nominal effect. From a practical point of view the Jeans instability of galactic disks is not affected by a live dark halo.Comment: 3 pages, 1 figure, accepted by Astron. Astrophy

Hard discs under steady shear: comparison of Brownian dynamics simulations and mode coupling theory

Brownian dynamics simulations of bidisperse hard discs moving in two dimensions in a given steady and homogeneous shear flow are presented close to and above the glasstransition density. The stationary structure functions and stresses of shear-melted glass are compared quantitatively to parameter-free numerical calculations of monodisperse hard discs using mode coupling theory within the integration through transients framework. Theory qualitatively explains the properties of the yielding glass but quantitatively overestimatesthe shear-driven stresses and structural anisotropies.Comment: 1. The original Phil. Trans. R. Soc. contains an error in the caption of the y-axes of the upper left panel in figure 9: There's a factor \dot{\gamma} missing in the denominato

Dynamical friction force exerted on spherical bodies

We present a rigorous calculation of the dynamical friction force exerted on a spherical massive perturber moving through an infinite homogenous system of field stars. By calculating the shape and mass of the polarization cloud induced by the perturber in the background system, which decelerates the motion of the perturber, we recover Chandrasekhar's drag force law with a modified Coulomb logarithm. As concrete examples we calculate the drag force exerted on a Plummer sphere or a sphere with the density distribution of a Hernquist profile. It is shown that the shape of the perturber affects only the exact form of the Coulomb logarithm. The latter converges on small scales, because encounters of the test and field stars with impact parameters less than the size of the massive perturber become inefficient. We confirm this way earlier results based on the impulse approximation of small angle scatterings.Comment: 5 pages, 2 figures, accepted in MNRA

Bond formation and slow heterogeneous dynamics in adhesive spheres with long--ranged repulsion: Quantitative test of Mode Coupling Theory

A colloidal system of spheres interacting with both a deep and narrow attractive potential and a shallow long-ranged barrier exhibits a prepeak in the static structure factor. This peak can be related to an additional mesoscopic length scale of clusters and/or voids in the system. Simulation studies of this system have revealed that it vitrifies upon increasing the attraction into a gel-like solid at intermediate densities. The dynamics at the mesoscopic length scale corresponding to the prepeak represents the slowest mode in the system. Using mode coupling theory with all input directly taken from simulations, we reveal the mechanism for glassy arrest in the system at 40% packing fraction. The effects of the low-q peak and of polydispersity are considered in detail. We demonstrate that the local formation of physical bonds is the process whose slowing down causes arrest. It remains largely unaffected by the large-scale heterogeneities, and sets the clock for the slow cluster mode. Results from mode-coupling theory without adjustable parameters agree semi-quantitatively with the local density correlators but overestimate the lifetime of the mesoscopic structure (voids).Comment: 10 pages, 8 figure

Mathematical theory of the Goddard trajectory determination system

Basic mathematical formulations depict coordinate and time systems, perturbation models, orbital estimation techniques, observation models, and numerical integration methods