Modelling train delays with q-exponential functions

We demonstrate that the distribution of train delays on the British railway network is accurately described by q-exponential functions. We explain this by constructing an underlying superstatistical model.Comment: 12 pages, 5 figure

Superstatistical generalization of the work fluctuation theorem

We derive a generalized version of the work fluctuation theorem for nonequilibrium systems with spatio-temporal temperature fluctuations. For chi-square distributed inverse temperature we obtain a generalized fluctuation theorem based on q-exponentials, whereas for other temperature distributions more complicated formulae arise. Since q-exponentials have a power law decay, the decay rate in this generalized fluctuation theorem is much slower than the conventional exponential decay. This implies that work fluctuations can be of relevance for the design of micro and nano structures, since the work done on the system is relatively much larger than in the conventional fluctuation theorem.Comment: 13 pages. Contribution to the Proceedings of `Trends and Perspectives in Extensive and Nonextensive Statistical Mechanics', in honour of Constantino Tsallis' 60th birthday (to appear in Physica A

Speaking of Music and the Counterpoint of Copyright: Addressing Legal Concerns in Making Oral History Available to the Public

Oral history provides society with voices and memories of people and communities experiencing events of the past first-hand. Such history is created through interviews; an interview, however, like any other type of intellectual property—once in a fixed form—is subject to copyright law. In order to make oral history available to the public, it is critically important that individuals generating and acquiring oral history materials clearly understand relevant aspects of copyright law. The varied nature of how one may create, use, and acquire oral history materials can present new, surprising, and sometimes baffling legal scenarios that challenge the experience of even the most skilled curators. This iBrief presents and discusses two real-world scenarios that raise various issues related to oral history and copyright law. These scenarios were encountered by curators at Yale University’s Oral History of American Music archive (OHAM), the preeminent organization dedicated to the collection and preservation of recorded memoirs of the creative musicians of our time. The legal concerns raised and discussed throughout this iBrief may be familiar to other stewards of oral history materials and will be worthwhile for all archivists and their counsel to consider when reviewing their practices and policies

Dynamical modelling of superstatistical complex systems

We show how to construct the optimum superstatistical dynamical model for a given experimentally measured time series. For this purpose we generalise the superstatistics concept and study a Langevin equation with a memory kernel whose parameters fluctuate on a large time scale. It is shown how to construct a synthetic dynamical model with the same invariant density and correlation function as the experimental data. As a main example we apply our method to velocity time series measured in high-Reynolds number turbulent Taylor-Couette flow, but the method can be applied to many other complex systems in a similar way.Comment: 11 pages, 4 figure

Skewed superstatistical distributions from a Langevin and Fokker-Planck approach

The superstatistics concept is a useful statistical method to describe inhomogeneous complex systems for which a system parameter $\beta$ fluctuates on a large spatio-temporal scale. In this paper we analyze a measured time series of wind speed fluctuations and extract the superstatistical distribution function $f(\beta)$ directly from the data. We construct suitable Langevin and Fokker-Planck models with a position dependent $\beta$-field and show that they reduce to standard type of superstatistics in the overdamped limit.Comment: 7 pages, 6 figure

Statistics of 3-dimensional Lagrangian turbulence

We consider a superstatistical dynamical model for the 3-d movement of a Lagrangian tracer particle embedded in a high-Reynolds number turbulent flow. The analytical model predictions are in excellent agreement with recent experimental data for flow between counter-rotating disks. In particular, we calculate the Lagrangian scaling exponents zeta_j for our system, and show that they agree well with the measured exponents reported in [X. Hu et al., PRL 96, 114503 (2006)]. Moreover, the model correctly predicts the shape of velocity difference and acceleration probability densities, the fast decay of component correlation functions and the slow decay of the modulus, as well as the statistical dependence between acceleration components. Finally, the model explains the numerically [P.K. Yeung and S.B. Pope, J. Fluid Mech. 207, 531 (1989)] and experimentally observed fact [B.W. Zeff et al., Nature 421, 146 (2003)] that enstrophy lags behind dissipation.Comment: 5 pages, 3 figures. Replaced by final version accepted by Phys. Rev. Let

Toward nonlinear stability of sources via a modified Burgers equation

Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources which are coherent structures for which the group velocities in the far field point away from the core. Sources actively select wave numbers and therefore often organize the overall dynamics in a spatially extended system. Determining their nonlinear stability properties is challenging as localized perturbations may lead to a non-localized response even on the linear level due to the outward transport. Using a modified Burgers equation as a model problem that captures some of the essential features of coherent structures, we show how this phenomenon can be analysed and nonlinear stability be established in this simpler context.Comment: revised version with some typos fixe

Surface energetics and structure of the Ge wetting layer on Si(100)

Ge deposited on Si(100) initially forms heteroepitaxial layers, which grow to a critical thickness of ~3 MLs before the appearance of three-dimensional strain relieving structures. Experimental observations reveal that the surface structure of this Ge wetting layer is a dimer vacancy line (DVL) superstructure of the unstrained Ge(100) dimer reconstruction. In the following, the results of first-principles calculations of the thickness dependence of the wetting layer surface excess energy for the c(4×2) and 4×6 DVL surface reconstructions are reported. These results predict a wetting layer critical thickness of ~3 MLs, which is largely unaffected by the presence of dimer vacancy lines. The 4×6 DVL reconstruction is found to be thermodynamically stable with respect to the c(4×2) structure for wetting layers at least 2 ML thick. A strong correlation between the fraction of total surface induced deformation present in the substrate and the thickness dependence of wetting layer surface energy is also shown

Are rotation curves in NGC 6946 and the Milky Way magnetically supported?

Following the model of magnetically supported rotation of spiral galaxies, the inner disk rotation is dominated by gravity but magnetism is not negligible at radii where the rotation curve becomes flat, and indeed becomes dominant at very large radii. Values of the order of 1 $\mu$G, or even less, produce a centripetal force when the absolute value of the slope of the curve [$B_\phi$, R] (azimuthal field strength versus radius) is less than $R^{-1}$. The $R^{-1}$-profile is called the critical profile. From this hypothesis, the following is to be expected: at large radii, a ``subcritical'' profile (slope flatter than $R^{-1}$); at still larger radii a $B_\phi$-profile becoming asymptotically critical as the density becomes asymptotically vanishing. Recent observations of magnetic fields in NGC 6946 and the Milky Way are in very good agreement with these predictions. This magnetic alternative requires neither galactic dark matter (DM) nor modification of fundamental laws of physics, but it is not in conflict with these hypotheses, especially with the existence of cosmological cold dark matter (CDM).Comment: 11 pages, 2 figures, accepted for publication in Astron. Astrophy