1,437 research outputs found
Disruption of the three-body gravitational systems: Lifetime statistics
We investigate statistics of the decay process in the equal-mass three-body
problem with randomized initial conditions. Contrary to earlier expectations of
similarity with "radioactive decay", the lifetime distributions obtained in our
numerical experiments turn out to be heavy-tailed, i.e. the tails are not
exponential, but algebraic. The computed power-law index for the differential
distribution is within the narrow range, approximately from -1.7 to -1.4,
depending on the virial coefficient. Possible applications of our results to
studies of the dynamics of triple stars known to be at the edge of disruption
are considered.Comment: 13 pages, 2 tables, 3 figure
Coherent interaction of laser pulses in a resonant optically dense extended medium under the regime of strong field-matter coupling
Nonstationary pump-probe interaction between short laser pulses propagating
in a resonant optically dense coherent medium is considered. A special
attention is paid to the case, where the density of two-level particles is high
enough that a considerable part of the energy of relatively weak external
laser-fields can be coherently absorbed and reemitted by the medium. Thus, the
field of medium reaction plays a key role in the interaction processes, which
leads to the collective behavior of an atomic ensemble in the strongly coupled
light-matter system. Such behavior results in the fast excitation interchanges
between the field and a medium in the form of the optical ringing, which is
analogous to polariton beating in the solid-state optics. This collective
oscillating response, which can be treated as successive beats between light
wave-packets of different group velocities, is shown to significantly affect
propagation and amplification of the probe field under its nonlinear
interaction with a nearly copropagating pump pulse. Depending on the probe-pump
time delay, the probe transmission spectra show the appearance of either
specific doublet or coherent dip. The widths of these features are determined
by the density-dependent field-matter coupling coefficient and increase during
the propagation. Besides that, the widths of the coherent features, which
appear close to the resonance in the broadband probe-spectrum, exceed the
absorption-line width, since, under the strong-coupling regime, the frequency
of the optical ringing exceeds the rate of incoherent relaxation. Contrary to
the stationary strong-field effects, the density- and coordinate-dependent
transmission spectra of the probe manifest the importance of the collective
oscillations and cannot be obtained in the framework of the single-atom model.Comment: 10 pages, 8 figures, to be published in Phys. Rev.
Reflexive Cones
Reflexive cones in Banach spaces are cones with weakly compact intersection
with the unit ball. In this paper we study the structure of this class of
cones. We investigate the relations between the notion of reflexive cones and
the properties of their bases. This allows us to prove a characterization of
reflexive cones in term of the absence of a subcone isomorphic to the positive
cone of \ell_{1}. Moreover, the properties of some specific classes of
reflexive cones are investigated. Namely, we consider the reflexive cones such
that the intersection with the unit ball is norm compact, those generated by a
Schauder basis and the reflexive cones regarded as ordering cones in a Banach
spaces. Finally, it is worth to point out that a characterization of reflexive
spaces and also of the Schur spaces by the properties of reflexive cones is
given.Comment: 23 page
Evaluating 35 Methods to Generate Structural Connectomes Using Pairwise Classification
There is no consensus on how to construct structural brain networks from
diffusion MRI. How variations in pre-processing steps affect network
reliability and its ability to distinguish subjects remains opaque. In this
work, we address this issue by comparing 35 structural connectome-building
pipelines. We vary diffusion reconstruction models, tractography algorithms and
parcellations. Next, we classify structural connectome pairs as either
belonging to the same individual or not. Connectome weights and eight
topological derivative measures form our feature set. For experiments, we use
three test-retest datasets from the Consortium for Reliability and
Reproducibility (CoRR) comprised of a total of 105 individuals. We also compare
pairwise classification results to a commonly used parametric test-retest
measure, Intraclass Correlation Coefficient (ICC).Comment: Accepted for MICCAI 2017, 8 pages, 3 figure
Total Absorption Dual Readout Calorimetry R&D
Abstract This calorimetry R&D focuses on establishing a proof of concept for totally active hadron calorimetry. The research program involves evaluating the performance of the different crystal and glass samples in combination with different light collection and readout alternatives to optimize simultaneous collection of Cerenkov and scintillation light components for application of the Dual Readout technique to total absorption calorimetry. We performed initial studies in two short test beam phases in April and November 2010 at Fermilab. Here we present first measurements from these two beam tests
Best approximation by downward sets with applications
We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs (W,x), where x E X and W is a closed downward subset of X.C
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