23,284 research outputs found
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 -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 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
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