728 research outputs found
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
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
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
Superstring Cosmology
Aspects of superstring cosmology are reviewed with an emphasis on the
cosmological implications of duality symmetries in the theory. The string
effective actions are summarized and toroidal compactification to four
dimensions reviewed. Global symmetries that arise in the compactification are
discussed and the duality relationships between the string effective actions
are then highlighted. Higher-dimensional Kasner cosmologies are presented and
interpreted in both string and Einstein frames, and then given in dimensionally
reduced forms. String cosmologies containing both non-trivial
Neveu-Schwarz/Neveu-Schwarz and Ramond-Ramond fields are derived by employing
the global symmetries of the effective actions. Anisotropic and inhomogeneous
cosmologies in four-dimensions are also developed. The review concludes with a
detailed analysis of the pre-big bang inflationary scenario. The generation of
primordial spectra of cosmological perturbations in such a scenario is
discussed. Possible future directions offered in the Horava-Witten theory are
outlined.Comment: 161 pages, latex with epsf, 15 figures. Minor changes, additional
references and figures. Version to appear in Physics Report
Proposal for the Open String Tachyon Effective Action in the Linear Dilaton Background
In this paper we propose tachyon effective actions for unstable D-branes in
superstring and bosonic string theories in the presence of the linear dilaton
background.Comment: 18 page
- …