6,051 research outputs found
A generalization and short proof of a theorem of Hano on affine vector fields
We prove that a bounded affine vector field on a complete Finsler manifold is
a Killing vector field. This generalizes the analogous result of Hano for
Riemannian manifolds. Even though our result is more general, the proof is
significantly simpler.Comment: 3 page
The contact dynamics method for granular media
In this paper we review the simulation method of the non-smooth contact
dynamics. This technique was designed to solve the unilateral and frictional
contact problem for a large number of rigid bodies and has proved to be
especially valuable in research of dense granular materials during the last
decade. We present here the basic principles compared to other methods and the
detailed description of a 3D algorithm. We point out an artifact manifesting
itself in spurious sound waves and discuss the applicability of the method.Comment: for the proceedings of the 7th Granada Seminar, 23 pages, 8 figure
Random walks on complex networks with inhomogeneous impact
In many complex systems, for the activity f(i) of the constituents or nodes
i, a power-law relationship was discovered between the standard deviation
sigma(i) and the average strength of the activity: sigma(i) ~ ^alpha;
universal values alpha = 1/2 or 1 were found, however, with exceptions. With
the help of an impact variable we introduce a random walk model where the
activity is the product of the number of visitors at a node and their impact.
If the impact depends strongly on the node connectivity and the properties of
the carrying network are broadly distributed (like in a scale free network) we
find both analytically and numerically non-universal alpha values. The exponent
always crosses over to the universal value of 1 if the external drive
dominates.Comment: 4 pages, 3 figures, revised tex
The Epps effect revisited
We analyse the dependence of stock return cross-correlations on the sampling
frequency of the data known as the Epps effect: For high resolution data the
cross-correlations are significantly smaller than their asymptotic value as
observed on daily data. The former description implies that changing trading
frequency should alter the characteristic time of the phenomenon. This is not
true for the empirical data: The Epps curves do not scale with market activity.
The latter result indicates that the time scale of the phenomenon is connected
to the reaction time of market participants (this we denote as human time
scale), independent of market activity. In this paper we give a new description
of the Epps effect through the decomposition of cross-correlations. After
testing our method on a model of generated random walk price changes we justify
our analytical results by fitting the Epps curves of real world data.Comment: 23 pages, 10 figures, 2 tables; added references, added figures and
statistical details, extended overview on literatur
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