11,558 research outputs found
Levy--Brownian motion on finite intervals: Mean first passage time analysis
We present the analysis of the first passage time problem on a finite
interval for the generalized Wiener process that is driven by L\'evy stable
noises. The complexity of the first passage time statistics (mean first passage
time, cumulative first passage time distribution) is elucidated together with a
discussion of the proper setup of corresponding boundary conditions that
correctly yield the statistics of first passages for these non-Gaussian noises.
The validity of the method is tested numerically and compared against
analytical formulae when the stability index approaches 2, recovering
in this limit the standard results for the Fokker-Planck dynamics driven by
Gaussian white noise.Comment: 9 pages, 13 figure
Transfer molding of PMR-15 polyimide resin
Transfer molding is an economically viable method of producing small shapes of PMR-15 polyimide. It is shown that with regard to flexural, compressive, and tribological properties transfer-molded PMR-15 polyimide is essentially equivalent to PMR-15 polyimide produced by the more common method of compression molding. Minor variations in anisotropy are predictable effects of molding design and secondary finishing operations
Invariant expectations and vanishing of bounded cohomology for exact groups
We study exactness of groups and establish a characterization of exact groups
in terms of the existence of a continuous linear operator, called an invariant
expectation, whose properties make it a weak counterpart of an invariant mean
on a group. We apply this operator to show that exactness of a finitely
generated group implies the vanishing of the bounded cohomology of with
coefficients in a new class of modules, which are defined using the Hopf
algebra structure of .Comment: Final version, to appear in the Journal of Topology and Analysi
Anomalous diffusion and generalized Sparre-Andersen scaling
We are discussing long-time, scaling limit for the anomalous diffusion
composed of the subordinated L\'evy-Wiener process. The limiting anomalous
diffusion is in general non-Markov, even in the regime, where ensemble averages
of a mean-square displacement or quantiles representing the group spread of the
distribution follow the scaling characteristic for an ordinary stochastic
diffusion. To discriminate between truly memory-less process and the non-Markov
one, we are analyzing deviation of the survival probability from the (standard)
Sparre-Andersen scaling.Comment: 5 pages, 3 figure
Transport in a Levy ratchet: Group velocity and distribution spread
We consider the motion of an overdamped particle in a periodic potential
lacking spatial symmetry under the influence of symmetric L\'evy noise, being a
minimal setup for a ``L\'evy ratchet.'' Due to the non-thermal character of the
L\'evy noise, the particle exhibits a motion with a preferred direction even in
the absence of whatever additional time-dependent forces. The examination of
the L\'evy ratchet has to be based on the characteristics of directionality
which are different from typically used measures like mean current and the
dispersion of particles' positions, since these get inappropriate when the
moments of the noise diverge. To overcome this problem, we discuss robust
measures of directionality of transport like the position of the median of the
particles displacements' distribution characterizing the group velocity, and
the interquantile distance giving the measure of the distributions' width.
Moreover, we analyze the behavior of splitting probabilities for leaving an
interval of a given length unveiling qualitative differences between the noises
with L\'evy indices below and above unity. Finally, we inspect the problem of
the first escape from an interval of given length revealing independence of
exit times on the structure of the potential.Comment: 9 pages, 12 figure
Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything
Zero Determinant (ZD) strategies are a new class of probabilistic and
conditional strategies that are able to unilaterally set the expected payoff of
an opponent in iterated plays of the Prisoner's Dilemma irrespective of the
opponent's strategy, or else to set the ratio between a ZD player's and their
opponent's expected payoff. Here we show that while ZD strategies are weakly
dominant, they are not evolutionarily stable and will instead evolve into less
coercive strategies. We show that ZD strategies with an informational advantage
over other players that allows them to recognize other ZD strategies can be
evolutionarily stable (and able to exploit other players). However, such an
advantage is bound to be short-lived as opposing strategies evolve to
counteract the recognition.Comment: 14 pages, 4 figures. Change in title (again!) to comply with Nature
Communications requirements. To appear in Nature Communication
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