3,280 research outputs found
Detecting independence of random vectors: generalized distance covariance and Gaussian covariance
Distance covariance is a quantity to measure the dependence of two random
vectors. We show that the original concept introduced and developed by
Sz\'{e}kely, Rizzo and Bakirov can be embedded into a more general framework
based on symmetric L\'{e}vy measures and the corresponding real-valued
continuous negative definite functions. The L\'{e}vy measures replace the
weight functions used in the original definition of distance covariance. All
essential properties of distance covariance are preserved in this new
framework. From a practical point of view this allows less restrictive moment
conditions on the underlying random variables and one can use other distance
functions than Euclidean distance, e.g. Minkowski distance. Most importantly,
it serves as the basic building block for distance multivariance, a quantity to
measure and estimate dependence of multiple random vectors, which is introduced
in a follow-up paper [Distance Multivariance: New dependence measures for
random vectors (submitted). Revised version of arXiv: 1711.07775v1] to the
present article.Comment: Published at https://doi.org/10.15559/18-VMSTA116 in the Modern
Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA)
by VTeX (http://www.vtex.lt/
Strong Effect of Weak Charging in Suspensions of Anisotropic Colloids
Suspensions of hard colloidal particles frequently serve as model systems in
studies on fundamental aspects of phase transitions. But often colloidal
particles that are considered as ``hard'' are in fact weakly charged. If the
colloids are spherical, weak charging has a only a weak effect on the
structural properties of the suspension, which can be easily corrected for.
However, this does not hold for anisotropic particles.
We introduce a model for the interaction potential between charged ellipsoids
of revolution (spheroids) based on the Derjaguin approximation of
Debye--H\"uckel Theory and present a computer simulation study on aspects of
the system's structural properties and phase behaviour. In line with previous
experimental observations, we find that even a weak surface charge has a strong
impact on the correlation functions. A likewise strong impact is seen on the
phase behaviour, in particular, we find stable cubatic order in suspensions of
oblate ellipsoids
Emergency physicians are more accurate in detecting pulmonary embolism at the emergency department then internal medicine physicians
Cutting costs – the impact of price-lists on the cost development in the emergency department
Connectivity percolation in suspensions of hard platelets
We present a study on connectivity percolation in suspensions of hard
platelets by means of Monte Carlo simulation. We interpret our results using a
contact-volume argument based on an effective single--particle cell model. It
is commonly assumed that the percolation threshold of anisotropic objects
scales as their inverse aspect ratio. While this rule has been shown to hold
for rod-like particles, we find that for hard plate-like particles the
percolation threshold is non-monotonic in the aspect ratio. It exhibits a
shallow minimum at intermediate aspect ratios and then saturates to a constant
value. This effect is caused by the isotropic-nematic transition pre-empting
the percolation transition. Hence the common strategy to use highly
anisotropic, conductive particles as fillers in composite materials in order to
produce conduction at low filler concentration is expected to fail for
plate-like fillers such as graphene and graphite nanoplatelets
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