11,467 research outputs found
Influence of the absorber dimensions on wavefront shaping based on volumetric optoacoustic feedback
The recently demonstrated control over light distribution through turbid
media based on real-time three-dimensional optoacoustic feedback has offered
promising prospects to interferometrically focus light within scattering
objects. Nevertheless, the focusing capacity of the feedback-based approach is
strongly conditioned by the number of effectively resolvable optical modes
(speckles). In this letter, we experimentally tested the light intensity
enhancement achieved with optoacoustic feedback measurements from different
sizes of absorbing microparticles. The importance of the obtained results is
discussed in the context of potential signal enhancement at deep locations
within a scattering medium where the effective speckle sizes approach the
minimum values dictated by optical diffraction
Hadamard Regularization
Motivated by the problem of the dynamics of point-particles in high
post-Newtonian (e.g. 3PN) approximations of general relativity, we consider a
certain class of functions which are smooth except at some isolated points
around which they admit a power-like singular expansion. We review the concepts
of (i) Hadamard ``partie finie'' of such functions at the location of singular
points, (ii) the partie finie of their divergent integral. We present and
investigate different expressions, useful in applications, for the latter
partie finie. To each singular function, we associate a partie-finie (Pf)
pseudo-function. The multiplication of pseudo-functions is defined by the
ordinary (pointwise) product. We construct a delta-pseudo-function on the class
of singular functions, which reduces to the usual notion of Dirac distribution
when applied on smooth functions with compact support. We introduce and analyse
a new derivative operator acting on pseudo-functions, and generalizing, in this
context, the Schwartz distributional derivative. This operator is uniquely
defined up to an arbitrary numerical constant. Time derivatives and partial
derivatives with respect to the singular points are also investigated. In the
course of the paper, all the formulas needed in the application to the physical
problem are derived.Comment: 50 pages, to appear in Journal of Mathematical Physic
Common adversaries form alliances: modelling complex networks via anti-transitivity
Anti-transitivity captures the notion that enemies of enemies are friends,
and arises naturally in the study of adversaries in social networks and in the
study of conflicting nation states or organizations. We present a simplified,
evolutionary model for anti-transitivity influencing link formation in complex
networks, and analyze the model's network dynamics. The Iterated Local
Anti-Transitivity (or ILAT) model creates anti-clone nodes in each time-step,
and joins anti-clones to the parent node's non-neighbor set. The graphs
generated by ILAT exhibit familiar properties of complex networks such as
densification, short distances (bounded by absolute constants), and bad
spectral expansion. We determine the cop and domination number for graphs
generated by ILAT, and finish with an analysis of their clustering
coefficients. We interpret these results within the context of real-world
complex networks and present open problems
Lorentzian regularization and the problem of point-like particles in general relativity
The two purposes of the paper are (1) to present a regularization of the
self-field of point-like particles, based on Hadamard's concept of ``partie
finie'', that permits in principle to maintain the Lorentz covariance of a
relativistic field theory, (2) to use this regularization for defining a model
of stress-energy tensor that describes point-particles in post-Newtonian
expansions (e.g. 3PN) of general relativity. We consider specifically the case
of a system of two point-particles. We first perform a Lorentz transformation
of the system's variables which carries one of the particles to its rest frame,
next implement the Hadamard regularization within that frame, and finally come
back to the original variables with the help of the inverse Lorentz
transformation. The Lorentzian regularization is defined in this way up to any
order in the relativistic parameter 1/c^2. Following a previous work of ours,
we then construct the delta-pseudo-functions associated with this
regularization. Using an action principle, we derive the stress-energy tensor,
made of delta-pseudo-functions, of point-like particles. The equations of
motion take the same form as the geodesic equations of test particles on a
fixed background, but the role of the background is now played by the
regularized metric.Comment: 34 pages, to appear in J. Math. Phy
Distributional versions of Littlewood's Tauberian theorem
We provide several general versions of Littlewood's Tauberian theorem. These
versions are applicable to Laplace transforms of Schwartz distributions. We
apply these Tauberian results to deduce a number of Tauberian theorems for
power series where Ces\`{a}ro summability follows from Abel summability. We
also use our general results to give a new simple proof of the classical
Littlewood one-sided Tauberian theorem for power series.Comment: 15 page
Minimum of and the phase transition of the Linear Sigma Model in the large-N limit
We reexamine the possibility of employing the viscosity over entropy density
ratio as a diagnostic tool to identify a phase transition in hadron physics to
the strongly coupled quark-gluon plasma and other circumstances where direct
measurement of the order parameter or the free energy may be difficult.
It has been conjectured that the minimum of eta/s does indeed occur at the
phase transition. We now make a careful assessment in a controled theoretical
framework, the Linear Sigma Model at large-N, and indeed find that the minimum
of eta/s occurs near the second order phase transition of the model due to the
rapid variation of the order parameter (here the sigma vacuum expectation
value) at a temperature slightly smaller than the critical one.Comment: 22 pages, 19 figures, v2, some references and several figures added,
typos corrected and certain arguments clarified, revised for PR
"Clumpiness" Mixing in Complex Networks
Three measures of clumpiness of complex networks are introduced. The measures
quantify how most central nodes of a network are clumped together. The
assortativity coefficient defined in a previous study measures a similar
characteristic, but accounts only for the clumpiness of the central nodes that
are directly connected to each other. The clumpiness coefficient defined in the
present paper also takes into account the cases where central nodes are
separated by a few links. The definition is based on the node degrees and the
distances between pairs of nodes. The clumpiness coefficient together with the
assortativity coefficient can define four classes of network. Numerical
calculations demonstrate that the classification scheme successfully
categorizes 30 real-world networks into the four classes: clumped assortative,
clumped disassortative, loose assortative and loose disassortative networks.
The clumpiness coefficient also differentiates the Erdos-Renyi model from the
Barabasi-Albert model, which the assortativity coefficient could not
differentiate. In addition, the bounds of the clumpiness coefficient as well as
the relationships between the three measures of clumpiness are discussed.Comment: 47 pages, 11 figure
"Clumpiness" Mixing in Complex Networks
Three measures of clumpiness of complex networks are introduced. The measures
quantify how most central nodes of a network are clumped together. The
assortativity coefficient defined in a previous study measures a similar
characteristic, but accounts only for the clumpiness of the central nodes that
are directly connected to each other. The clumpiness coefficient defined in the
present paper also takes into account the cases where central nodes are
separated by a few links. The definition is based on the node degrees and the
distances between pairs of nodes. The clumpiness coefficient together with the
assortativity coefficient can define four classes of network. Numerical
calculations demonstrate that the classification scheme successfully
categorizes 30 real-world networks into the four classes: clumped assortative,
clumped disassortative, loose assortative and loose disassortative networks.
The clumpiness coefficient also differentiates the Erdos-Renyi model from the
Barabasi-Albert model, which the assortativity coefficient could not
differentiate. In addition, the bounds of the clumpiness coefficient as well as
the relationships between the three measures of clumpiness are discussed.Comment: 47 pages, 11 figure
Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism
Three decades of work on the quantum field equations of pure Yang-Mills
theory have distilled two families of solutions in Landau gauge. Both coincide
for high (Euclidean) momentum with known perturbation theory, and both predict
an infrared suppressed transverse gluon propagator, but whereas the solution
known as "scaling" features an infrared power law for the gluon and ghost
propagators, the "massive" solution rather describes the gluon as a vector
boson that features a finite Debye screening mass.
In this work we examine the gauge dependence of these solutions by adopting
stochastic quantization. What we find, in four dimensions and in a rainbow
approximation, is that stochastic quantization supports both solutions in
Landau gauge but the scaling solution abruptly disappears when the parameter
controlling the drift force is separated from zero (soft gauge-fixing),
recovering only the perturbative propagators; the massive solution seems to
survive the extension outside Landau gauge. These results are consistent with
the scaling solution being related to the existence of a Gribov horizon, with
the massive one being more general.
We also examine the effective action in Faddeev-Popov quantization that
generates the rainbow and we find, for a bare vertex approximation, that the
the massive-type solutions minimise the quantum effective action.Comment: 13 pages, 7 figures. Change of title to reflect version accepted for
publicatio
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