8,544 research outputs found
Bubble Raft Model for a Paraboloidal Crystal
We investigate crystalline order on a two-dimensional paraboloid of
revolution by assembling a single layer of millimeter-sized soap bubbles on the
surface of a rotating liquid, thus extending the classic work of Bragg and Nye
on planar soap bubble rafts. Topological constraints require crystalline
configurations to contain a certain minimum number of topological defects such
as disclinations or grain boundary scars whose structure is analyzed as a
function of the aspect ratio of the paraboloid. We find the defect structure to
agree with theoretical predictions and propose a mechanism for scar nucleation
in the presence of large Gaussian curvature.Comment: 4 pages, 4 figure
Evaluating the capabilities and uncertainties of droplet measurements for the fog droplet spectrometer (FM-100)
Droplet size spectra measurements are crucial to obtain a quantitative microphysical description of clouds and fog. However, cloud droplet size measurements are subject to various uncertainties. This work focuses on the error analysis of two key measurement uncertainties arising during cloud droplet size measurements with a conventional droplet size spectrometer (FM-100): first, we addressed the precision with which droplets can be sized with the FM-100 on the basis of the Mie theory. We deduced error assumptions and proposed a new method on how to correct measured size distributions for these errors by redistributing the measured droplet size distribution using a stochastic approach. Second, based on a literature study, we summarized corrections for particle losses during sampling with the FM-100. We applied both corrections to cloud droplet size spectra measured at the high alpine site Jungfraujoch for a temperature range from 0 °C to 11 °C. We showed that Mie scattering led to spikes in the droplet size distributions using the default sizing procedure, while the new stochastic approach reproduced the ambient size distribution adequately. A detailed analysis of the FM-100 sampling efficiency revealed that particle losses were typically below 10% for droplet diameters up to 10 μm. For larger droplets, particle losses can increase up to 90% for the largest droplets of 50 μm at ambient wind speeds below 4.4 m s<sup>−1</sup> and even to >90% for larger angles between the instrument orientation and the wind vector (sampling angle) at higher wind speeds. Comparisons of the FM-100 to other reference instruments revealed that the total liquid water content (LWC) measured by the FM-100 was more sensitive to particle losses than to re-sizing based on Mie scattering, while the total number concentration was only marginally influenced by particle losses. Consequently, for further LWC measurements with the FM-100 we strongly recommend to consider (1) the error arising due to Mie scattering, and (2) the particle losses, especially for larger droplets depending on the set-up and wind conditions
Diffusive transport in networks built of containers and tubes
We developed analytical and numerical methods to study a transport of
non-interacting particles in large networks consisting of M d-dimensional
containers C_1,...,C_M with radii R_i linked together by tubes of length l_{ij}
and radii a_{ij} where i,j=1,2,...,M. Tubes may join directly with each other
forming junctions. It is possible that some links are absent. Instead of
solving the diffusion equation for the full problem we formulated an approach
that is computationally more efficient. We derived a set of rate equations that
govern the time dependence of the number of particles in each container
N_1(t),N_2(t),...,N_M(t). In such a way the complicated transport problem is
reduced to a set of M first order integro-differential equations in time, which
can be solved efficiently by the algorithm presented here. The workings of the
method have been demonstrated on a couple of examples: networks involving
three, four and seven containers, and one network with a three-point junction.
Already simple networks with relatively few containers exhibit interesting
transport behavior. For example, we showed that it is possible to adjust the
geometry of the networks so that the particle concentration varies in time in a
wave-like manner. Such behavior deviates from simple exponential growth and
decay occurring in the two container system.Comment: 21 pages, 18 figures, REVTEX4; new figure added, reduced emphasis on
graph theory, additional discussion added (computational cost, one
dimensional tubes
Astrophysical Fluid Dynamics via Direct Statistical Simulation
In this paper we introduce the concept of Direct Statistical Simulation (DSS)
for astrophysical flows. This technique may be appropriate for problems in
astrophysical fluids where the instantaneous dynamics of the flows are of
secondary importance to their statistical properties. We give examples of such
problems including mixing and transport in planets, stars and disks. The method
is described for a general set of evolution equations, before we consider the
specific case of a spectral method optimised for problems on a spherical
surface. The method is illustrated for the simplest non-trivial example of
hydrodynamics and MHD on a rotating spherical surface. We then discuss possible
extensions of the method both in terms of computational methods and the range
of astrophysical problems that are of interest.Comment: 26 pages, 11 figures, added clarifying remarks and references, and
corrected typos. This version is accepted for publication in The
Astrophysical Journa
Wavy stripes and squares in zero P number convection
A simple model to explain numerically observed behaviour of chaotically
varying stripes and square patterns in zero Prandtl number convection in
Boussinesq fluid is presented. The nonlinear interaction of mutually
perpendicular sets of wavy rolls, via higher mode, may lead to a competition
between the two sets of wavy rolls. The appearance of square patterns is due to
the secondary forward Hopf bifurcation of a set of wavy rolls.Comment: 8 pages and 3 figures, late
Search for Short-Term Periodicities in the Sun's Surface Rotation: A Revisit
The power spectral analyses of the Sun's surface equatorial rotation rate
determined from the Mt. Wilson daily Doppler velocity measurements during the
period 3 December 1985 to 5 March 2007 suggests the existence of 7.6 year, 2.8
year, 1.47 year, 245 day, 182 day and 158 day periodicities in the surface
equatorial rotation rate during the period before 1996.
However, there is no variation of any kind in the more accurately measured
data during the period after 1995. That is, the aforementioned periodicities in
the data during the period before the year 1996 may be artifacts of the
uncertainties of those data due to the frequent changes in the instrumentation
of the Mt. Wilson spectrograph. On the other hand, the temporal behavior of
most of the activity phenomena during cycles 22 (1986-1996) and 23 (after 1997)
is considerably different. Therefore, the presence of the aforementioned
short-term periodicities during the last cycle and absence of them in the
current cycle may, in principle, be real temporal behavior of the solar
rotation during these cycles.Comment: 11 pages, 6 figures, accepted for publication in Solar Physic
Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum Transformations
Simple derivation is presented of the four families of infinitely many shape
invariant Hamiltonians corresponding to the exceptional Laguerre and Jacobi
polynomials. Darboux-Crum transformations are applied to connect the well-known
shape invariant Hamiltonians of the radial oscillator and the
Darboux-P\"oschl-Teller potential to the shape invariant potentials of
Odake-Sasaki. Dutta and Roy derived the two lowest members of the exceptional
Laguerre polynomials by this method. The method is expanded to its full
generality and many other ramifications, including the aspects of generalised
Bochner problem and the bispectral property of the exceptional orthogonal
polynomials, are discussed.Comment: LaTeX2e with amsmath, amssymb, amscd 26 pages, no figure
Instabilities in the Envelopes and Winds of Very Massive Stars
The high luminosity of Very Massive Stars (VMS) means that radiative forces
play an important, dynamical role both in the structure and stability of their
stellar envelope, and in driving strong stellar-wind mass loss. Focusing on the
interplay of radiative flux and opacity, with emphasis on key distinctions
between continuum vs. line opacity, this chapter reviews instabilities in the
envelopes and winds of VMS. Specifically, we discuss how: 1) the iron opacity
bump can induce an extensive inflation of the stellar envelope; 2) the density
dependence of mean opacity leads to strange mode instabilities in the outer
envelope; 3) desaturation of line-opacity by acceleration of near-surface
layers initiates and sustains a line-driven stellar wind outflow; 4) an
associated line-deshadowing instability leads to extensive small-scale
structure in the outer regions of such line-driven winds; 5) a star with
super-Eddington luminosity can develop extensive atmospheric structure from
photon bubble instabilities, or from stagnation of flow that exceeds the
"photon tiring" limit; 6) the associated porosity leads to a reduction in
opacity that can regulate the extreme mass loss of such continuum-driven winds.
Two overall themes are the potential links of such instabilities to Luminous
Blue Variable (LBV) stars, and the potential role of radiation forces in
establishing the upper mass limit of VMS.Comment: 44 pages, 13 figures. Chapter to appear in the book "Very Massive
Stars in the Local Universe", Springer, J.S. Vink, e
Coarse-grained model of entropic allostery
Many signaling functions in molecular biology require proteins to bind to substrates such as DNA in response to environmental signals such as the simultaneous binding to a small molecule. Examples are repressor proteins which may transmit information via a conformational change in response to the ligand binding. An alternative entropic mechanism of "allostery" suggests that the inducer ligand changes the intramolecular vibrational entropy, not just the mean static structure. We present a quantitative, coarse-grained model of entropic allostery, which suggests design rules for internal cohesive potentials in proteins employing this effect. It also addresses the issue of how the signal information to bind or unbind is transmitted through the protein. The model may be applicable to a wide range of repressors and also to signaling in trans-membrane proteins
Phase transitions in self-gravitating systems and bacterial populations with a screened attractive potential
We consider a system of particles interacting via a screened Newtonian
potential and study phase transitions between homogeneous and inhomogeneous
states in the microcanonical and canonical ensembles. Like for other systems
with long-range interactions, we obtain a great diversity of microcanonical and
canonical phase transitions depending on the dimension of space and on the
importance of the screening length. We also consider a system of particles in
Newtonian interaction in the presence of a ``neutralizing background''. By a
proper interpretation of the parameters, our study describes (i)
self-gravitating systems in a cosmological setting, and (ii) chemotaxis of
bacterial populations in the original Keller-Segel model
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