Theoretical Framework for Microscopic Osmotic Phenomena

The basic ingredients of osmotic pressure are a solvent fluid with a soluble molecular species which is restricted to a chamber by a boundary which is permeable to the solvent fluid but impermeable to the solute molecules. For macroscopic systems at equilibrium, the osmotic pressure is given by the classical van't Hoff Law, which states that the pressure is proportional to the product of the temperature and the difference of the solute concentrations inside and outside the chamber. For microscopic systems the diameter of the chamber may be comparable to the length-scale associated with the solute-wall interactions or solute molecular interactions. In each of these cases, the assumptions underlying the classical van't Hoff Law may no longer hold. In this paper we develop a general theoretical framework which captures corrections to the classical theory for the osmotic pressure under more general relationships between the size of the chamber and the interaction length scales. We also show that notions of osmotic pressure based on the hydrostatic pressure of the fluid and the mechanical pressure on the bounding walls of the chamber must be distinguished for microscopic systems. To demonstrate how the theoretical framework can be applied, numerical results are presented for the osmotic pressure associated with a polymer of N monomers confined in a spherical chamber as the bond strength is varied

Spherical Orbifolds for Cosmic Topology

Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the specific point symmetry of the Platonic manifolds with their deck transformations. This analysis in topology leads from manifolds to orbifolds. We discuss the deck transformations of the orbifolds and give eigenmodes for the harmonic analysis as linear combinations of Wigner polynomials on the 3-sphere. These provide new tools for detecting cosmic topology from the CMB radiation.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1011.427

A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales

In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with stiffness in the system of equations by handling systematically the statistical contributions of the fastest dynamics of the fluid and immersed structures over long time steps. An important feature of the numerical method is that time steps can be taken in which the degrees of freedom of the fluid are completely underresolved, partially resolved, or fully resolved while retaining a good level of accuracy. Error estimates in each of these regimes are given for the method. A number of theoretical and numerical checks are furthermore performed to assess its physical fidelity. For a conservative force, the method is found to simulate particles with the correct Boltzmann equilibrium statistics. It is shown in three dimensions that the diffusion of immersed particles simulated with the method has the correct scaling in the physical parameters. The method is also shown to reproduce a well-known hydrodynamic effect of a Brownian particle in which the velocity autocorrelation function exhibits an algebraic tau^(-3/2) decay for long times. A few preliminary results are presented for more complex systems which demonstrate some potential application areas of the method.Comment: 52 pages, 11 figures, published in journal of computational physic

Pulsar-black hole binaries: prospects for new gravity tests with future radio telescopes

The anticipated discovery of a pulsar in orbit with a black hole is expected to provide a unique laboratory for black hole physics and gravity. In this context, the next generation of radio telescopes, like the Five-hundred-metre Aperture Spherical radio Telescope (FAST) and the Square Kilometre Array (SKA), with their unprecedented sensitivity, will play a key role. In this paper, we investigate the capability of future radio telescopes to probe the spacetime of a black hole and test gravity theories, by timing a pulsar orbiting a stellar-mass-black-hole (SBH). Based on mock data simulations, we show that a few years of timing observations of a sufficiently compact pulsar-SBH (PSR-SBH) system with future radio telescopes would allow precise measurements of the black hole mass and spin. A measurement precision of one per cent can be expected for the spin. Measuring the quadrupole moment of the black hole, needed to test GR's no-hair theorem, requires extreme system configurations with compact orbits and a large SBH mass. Additionally, we show that a PSR-SBH system can lead to greatly improved constraints on alternative gravity theories even if they predict black holes (practically) identical to GR's. This is demonstrated for a specific class of scalar-tensor theories. Finally, we investigate the requirements for searching for PSR-SBH systems. It is shown that the high sensitivity of the next generation of radio telescopes is key for discovering compact PSR-SBH systems, as it will allow for sufficiently short survey integration times.Comment: 20 pages, 11 figures, 1 table, accepted for publication in MNRA

Random polarization dynamics in a resonant optical medium

Random optical-pulse polarization switching along an active optical medium in the $\Lambda$-configuration with spatially disordered occupation numbers of its lower energy sub-level pair is described using the idealized integrable Maxwell-Bloch model. Analytical results describing the light polarization-switching statistics for the single self-induced transparency pulse are compared with statistics obtained from direct Monte-Carlo numerical simulations.Comment: 7 pages, 3 figure

Electron propagation in crossed magnetic and electric fields

Laser-atom interaction can be an efficient mechanism for the production of coherent electrons. We analyze the dynamics of monoenergetic electrons in the presence of uniform, perpendicular magnetic and electric fields. The Green function technique is used to derive analytic results for the field--induced quantum mechanical drift motion of i) single electrons and ii) a dilute Fermi gas of electrons. The method yields the drift current and, at the same time it allows us to quantitatively establish the broadening of the (magnetic) Landau levels due to the electric field: Level number k is split into k+1 sublevels that render the $k$th oscillator eigenstate in energy space. Adjacent Landau levels will overlap if the electric field exceeds a critical strength. Our observations are relevant for quantum Hall configurations whenever electric field effects should be taken into account.Comment: 11 pages, 2 figures, submitte

Can we see pulsars around Sgr A*? - The latest searches with the Effelsberg telescope

Radio pulsars in relativistic binary systems are unique tools to study the curved space-time around massive compact objects. The discovery of a pulsar closely orbiting the super-massive black hole at the centre of our Galaxy, Sgr A*, would provide a superb test-bed for gravitational physics. To date, the absence of any radio pulsar discoveries within a few arc minutes of Sgr A* has been explained by one principal factor: extreme scattering of radio waves caused by inhomogeneities in the ionized component of the interstellar medium in the central 100 pc around Sgr A*. Scattering, which causes temporal broadening of pulses, can only be mitigated by observing at higher frequencies. Here we describe recent searches of the Galactic centre region performed at a frequency of 18.95 GHz with the Effelsberg radio telescope.Comment: 3 pages, 2 figures, Proceedings of IAUS 291 "Neutron Stars and Pulsars: Challenges and Opportunities after 80 years", 201