921 research outputs found
Reconnections of Vortex Loops in the Superfluid Turbulent HeII. Rates of the Breakdown and Fusion processes
Kinetics of merging and breaking down vortex loops is the important part of
the whole vortex tangle dynamics. Another part is the motion of individual
lines, which obeys the Biot-Savart law in presence of friction force and of
applied external velocity fields if any. In the present work we evaluate the
coefficients of the reconnection rates and
. Quantity is a number (per unit of time and per unit of
volume) of events, when two loops with lengths and collide and
form the single loop of length . Quantity
describes the rate of events, when the single loop of the length breaks
down into two the daughter loops of lengths and . These
quantities ave evaluated as the averaged numbers of zeroes of vector
connecting two points on the loops of
and at moment of time . Statistics of the individual
loops is taken from the Gaussian model of vortex tangle. PACS-number 67.40Comment: 9 pages, 5 figures, To be submitted to JLT
Evolution of a Network of Vortex Loops in the Turbulent Superfluid Helium; Derivation of the Vinen Equation
The evolution a network of vortex loops due to the fusion and breakdown in
the turbulent superfluid helium is studied. We perform investigation on the
base of the "rate equation" for the distribution function of number of
loops in space of their length . There are two mechanisms for change of
quantity . Firstly, the function changes due to deterministic process of
mutual friction, when the length grows or decreases depending on orientation.
Secondly, the change of occurs due to random events when the loop
crosses itself breaking down into two daughter or two loops collide merging
into one larger loop. Accordingly the "rate equation" includes the "collision"
term collecting random processes of fusion and breakdown and the deterministic
term. Assuming, further, that processes of random colliding are fastest we are
in position to study more slow processes related to deterministic term. In this
way we study the evolution of full length of vortex loops per unit volume-so
called vortex line density . It is shown this evolution to obey
the famous Vinen equation. In conclusion we discuss properties of the Vinen
equation from the point of view of the developed approach.Comment: Presentation at QFS2006, submitted to JLT
Large-scale structure of time evolving citation networks
In this paper we examine a number of methods for probing and understanding
the large-scale structure of networks that evolve over time. We focus in
particular on citation networks, networks of references between documents such
as papers, patents, or court cases. We describe three different methods of
analysis, one based on an expectation-maximization algorithm, one based on
modularity optimization, and one based on eigenvector centrality. Using the
network of citations between opinions of the United States Supreme Court as an
example, we demonstrate how each of these methods can reveal significant
structural divisions in the network, and how, ultimately, the combination of
all three can help us develop a coherent overall picture of the network's
shape.Comment: 10 pages, 6 figures; journal names for 4 references fixe
Low thrust propulsion in a coplanar circular restricted four body problem
This paper formulates a circular restricted four body problem (CRFBP), where the three primaries are set in the stable Lagrangian equilateral triangle configuration and the fourth body is massless. The analysis of this autonomous coplanar CRFBP is undertaken, which identies eight natural equilibria; four of which are close to the smaller body, two stable and two unstable, when considering the primaries to be the Sun and two smaller bodies of the solar system. Following this, the model incorporates `near term' low-thrust propulsion capabilities to generate surfaces of articial equilibrium points close to the smaller primary, both in and out of the plane containing the celestial bodies. A stability analysis of these points is carried out and a stable subset of them is identied. Throughout the analysis the Sun-Jupiter-Asteroid-Spacecraft system is used, for conceivable masses of a hypothetical asteroid set at the libration point L4. It is shown that eight bounded orbits exist, which can be maintained with a constant thrust less than 1:5 10􀀀4N for a 1000kg spacecraft. This illustrates that, by exploiting low-thrust technologies, it would be possible to maintain an observation point more than 66% closer to the asteroid than that of a stable natural equilibrium point. The analysis then focusses on a major Jupiter Trojan: the 624-Hektor asteroid. The thrust required to enable close asteroid observation is determined in the simplied CRFBP model. Finally, a numerical simulation of the real Sun-Jupiter-624 Hektor-Spacecraft is undertaken, which tests the validity of the stability analysis of the simplied model
Monte Carlo reconstruction of the inflationary potential
We present Monte Carlo reconstruction, a new method for ``inverting''
observational data to constrain the form of the scalar field potential
responsible for inflation. This stochastic technique is based on the flow
equation formalism and has distinct advantages over reconstruction methods
based on a Taylor expansion of the potential. The primary ansatz required for
Monte Carlo reconstruction is simply that inflation is driven by a single
scalar field. We also require a very mild slow roll constraint, which can be
made arbitrarily weak since Monte Carlo reconstruction is implemented at
arbitrary order in the slow roll expansion. While our method cannot evade
fundamental limits on the accuracy of reconstruction, it can be simply and
consistently applied to poor data sets, and it takes advantage of the attractor
properties of single-field inflation models to constrain the potential outside
the small region directly probed by observations. We show examples of Monte
Carlo reconstruction for data sets similar to that expected from the Planck
satellite, and for a hypothetical measurement with a factor of five better
parameter discrimination than Planck.Comment: 10 pages, 5 figures (RevTeX 4) Version submitted to PRD: references
added, minor clarification
Caloric Curves and Nuclear Expansion
Nuclear caloric curves have been analyzed using an expanding Fermi gas
hypothesis to extract average nuclear densities. In this approach the observed
flattening of the caloric curves reflects progressively increasing expansion
with increasing excitation energy. This expansion results in a corresponding
decrease in the density and Fermi energy of the excited system. For nuclei of
medium to heavy mass apparent densities ~ 0.4 rho_0 are reached at the higher
excitation energies.Comment: 4 pages, 3 figure
Bayesian system identification of dynamical systems using highly informative training data
This paper is concerned with the Bayesian system identification of structural dynamical systems using experimentally obtained training data. It is motivated by situations where, from a large quantity of training data, one must select a subset to infer probabilistic models. To that end, using concepts from information theory, expressions are derived which allow one to approximate the effect that a set of training data will have on parameter uncertainty as well as the plausibility of candidate model structures. The usefulness of this concept is then demonstrated through the system identification of several dynamical systems using both physics-based and emulator models. The result is a rigorous scientific framework which can be used to select 'highly informative' subsets from large quantities of training data
Inflation with a constant ratio of scalar and tensor perturbation amplitudes
The single scalar field inflationary models that lead to scalar and tensor
perturbation spectra with amplitudes varying in direct proportion to one
another are reconstructed by solving the Stewart-Lyth inverse problem to
next-to-leading order in the slow-roll approximation.
The potentials asymptote at high energies to an exponential form,
corresponding to power law inflation, but diverge from this model at low
energies, indicating that power law inflation is a repellor in this case. This
feature implies that a fine-tuning of initial conditions is required if such
models are to reproduce the observations. The required initial conditions might
be set through the eternal inflation mechanism.
If this is the case, it will imply that the spectral indices must be nearly
constant, making the underlying model observationally indistinguishable from
power law inflation.Comment: 20 pages, 7 figures. Major changes to the Introduction following
referee's comments. One figure added. Some other minor changes. No conclusion
was modifie
Lemaitre-Tolman-Bondi model and accelerating expansion
I discuss the spherically symmetric but inhomogeneous Lemaitre-Tolman- Bondi
(LTB) metric, which provides an exact toy model for an inhomogeneous universe.
Since we observe light rays from the past light cone, not the expansion of the
universe, spatial variation in matter density and Hubble rate can have the same
effect on redshift as acceleration in a perfectly homogeneous universe. As a
consequence, a simple spatial variation in the Hubble rate can account for the
distant supernova data in a dust universe without any dark energy. I also
review various attempts towards a semirealistic description of the universe
based on the LTB model.Comment: Invited Review for a special Gen. Rel. Grav. issue on Dark Energy. 17
pages, 3 figure
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