Analysis of the phenomenon of speculative trading in one of its basic manifestations: postage stamp bubbles

We document and analyze the empirical facts concerning one of the clearest evidence of speculation in financial trading as observed in the postage collection stamp market. We unravel some of the mechanisms of speculative behavior which emphasize the role of fancy and collective behavior. In our conclusion, we propose a classification of speculative markets based on two parameters, namely the amplitude of the price peak and a second parameter that measures its ``sharpness''. This study is offered to anchor modeling efforts to realistic market constraints and observations.Comment: 9 pages, 5 figures and 2 tables, in press in Int. J. Mod. Phys.

Long-term stability of the HR 8799 planetary system without resonant lock

HR 8799 is a star accompanied by four massive planets on wide orbits. The observed planetary configuration has been shown to be unstable on a timescale much shorter than the estimated age of the system (~ 30 Myr) unless the planets are locked into mean motion resonances. This condition is characterised by small-amplitude libration of one or more resonant angles that stabilise the system by preventing close encounters. We simulate planetary systems similar to the HR 8799 planetary system, exploring the parameter space in separation between the orbits, planetary masses and distance from the Sun to the star. We find systems that look like HR 8799 and remain stable for longer than the estimated age of HR 8799. None of our systems are forced into resonances. We find, with nominal masses and in a narrow range of orbit separations, that 5 of 100 systems match the observations and lifetime. Considering a broad range of orbit separations, we find 12 of 900 similar systems. The systems survive significantly longer because of their slightly increased initial orbit separations compared to assuming circular orbits from the observed positions. A small increase in separation leads to a significant increase in survival time. The low eccentricity the orbits develop from gravitational interaction is enough for the planets to match the observations. With lower masses, but still comfortably within the estimated planet mass uncertainty, we find 18 of 100 matching and long-lived systems in a narrow orbital separation range. In the broad separation range, we find 82 of 900 matching systems. Our results imply that the planets in the HR 8799 system do not have to be in strong mean motion resonances.Comment: Accepted for publication in A&

Products of Random Matrices

We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the norm of the matrix and a parameter characterizing its skewness. The distribution may have importance as an uncommitted prior in statistical image analysis.Comment: 9 pages, 1 figur

Scaling Behavior of Quasi-One-Dimensional Vortex Avalanches in Superconducting Films

Scaling behaviour of dynamically driven vortex avalanches in superconducting YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ films deposited on tilted crystalline substrates has been observed using quantitative magneto-optical imaging. Two films with different tilt angles are characterized by the probability distributions of avalanche size in terms of the number of moving vortices. It is found in both samples that these distributions follow power-laws over up to three decades, and have exponents ranging between 1.0 and 1.4. The distributions also show clear finite-size scaling, when the system size is defined by the depth of the flux penetration front -- a signature of self-organized criticality. A scaling relation between the avalanche size exponent and the fractal dimension, previously derived theoretically from conservation of the number of magnetic vortices in the stationary state and shown in numerical simulations, is here shown to be satisfied also experimentally.Comment: 7 pages, 5 figure

Decay dynamics of quantum dots influenced by the local density of optical states of two-dimensional photonic crystal membranes

We have performed time-resolved spectroscopy on InAs quantum dot ensembles in photonic crystal membranes. The influence of the photonic crystal is investigated by varying the lattice constant systematically. We observe a strong slow down of the quantum dots' spontaneous emission rates as the two-dimensional bandgap is tuned through their emission frequencies. The measured band edges are in full agreement with theoretical predictions. We characterize the multi-exponential decay curves by their mean decay time and find enhancement of the spontaneous emission at the bandgap edges and strong inhibition inside the bandgap in good agreement with local density of states calculations.Comment: 9 pages (preprint), 3 figure

Synchronization and Coarsening (without SOC) in a Forest-Fire Model

We study the long-time dynamics of a forest-fire model with deterministic tree growth and instantaneous burning of entire forests by stochastic lightning strikes. Asymptotically the system organizes into a coarsening self-similar mosaic of synchronized patches within which trees regrow and burn simultaneously. We show that the average patch length grows linearly with time as t-->oo. The number density of patches of length L, N(L,t), scales as ^{-2}M(L/), and within a mean-field rate equation description we find that this scaling function decays as e^{-1/x} for x-->0, and as e^{-x} for x-->oo. In one dimension, we develop an event-driven cluster algorithm to study the asymptotic behavior of large systems. Our numerical results are consistent with mean-field predictions for patch coarsening.Comment: 5 pages, 4 figures, 2-column revtex format. To be submitted to PR

Calculation of minor hysteresis loops under metastable to stable transformations in vortex matter

We present a model in which metastable supercooled phase and stable equilibrium phase of vortex matter coexist in different regions of a sample. Minor hysteresis loops are calculated with the simple assumption of the two phases of vortex matter having field-independent critical current densities. We use our earlier published ideas that the free energy barrier separating the metastable and stable phases reduces as the magnetic induction moves farther from the first order phase transition line, and that metastable to stable transformations occur in local regions of the sample when the local energy dissipation exceeds a critical value. Previously reported anomalous features in minor hysteresis loops are reproduced, and calculated field profiles are presented.Comment: 9pages, 7 figure

The formation of the solar system

The solar system started to form about 4.56 Gyr ago and despite the long intervening time span, there still exist several clues about its formation. The three major sources for this information are meteorites, the present solar system structure and the planet-forming systems around young stars. In this introduction we give an overview of the current understanding of the solar system formation from all these different research fields. This includes the question of the lifetime of the solar protoplanetary disc, the different stages of planet formation, their duration, and their relative importance. We consider whether meteorite evidence and observations of protoplanetary discs point in the same direction. This will tell us whether our solar system had a typical formation history or an exceptional one. There are also many indications that the solar system formed as part of a star cluster. Here we examine the types of cluster the Sun could have formed in, especially whether its stellar density was at any stage high enough to influence the properties of today's solar system. The likelihood of identifying siblings of the Sun is discussed. Finally, the possible dynamical evolution of the solar system since its formation and its future are considered.Comment: 36 pages, 7 figures, invited review in Physica Script

Solitons in the one-dimensional forest fire model

Fires in the one-dimensional Bak-Chen-Tang forest fire model propagate as solitons, resembling shocks in Burgers turbulence. The branching of solitons, creating new fires, is balanced by the pair-wise annihilation of oppositely moving solitons. Two distinct, diverging length scales appear in the limit where the growth rate of trees, $p$, vanishes. The width of the solitons, $w$, diverges as a power law, $1/p$, while the average distance between solitons diverges much faster as $d \sim \exp({\pi}^2/12p)$.Comment: 4 pages with 2 figures include

The role of antibiotics in the treatment of chronic prostatitis: A consensus statement

Practical guidelines for the diagnosis and treatment of chronic prostatitis are presented. Chronic prostatitis is classified as chronic bacterial prostatitis (culture-positive) and chronic inflammatory prostatitis (culture-negative). If chronic bacterial prostatitis is suspected, based on relevant symptoms or recurrent UTIs, underlying urological conditions should be excluded by the following tests: rectal examination, midstream urine culture and residual urine. The diagnosis should be confirmed by the Meares and Stamey technique. Antibiotic therapy is recommended for acute exacerbations of chronic prostatitis, chronic bacterial prostatitis and chronic inflammatory prostatitis, if there is clinical, bacteriological or supporting immunological evidence of prostate infection. Unless a patient presents with fever, antibiotic treatment should not be initiated immediately except in cases of acute prostatitis or acute episodes in a patient with chronic bacterial prostatitis. The work-up, with the appropriate investigations should be done first, within a reasonable time period which, preferably, should not be longer than 1 week. During this period, nonspecific treatment, such as appropriate analgesia to relieve symptoms, should be given. The minimum duration of antibiotic treatment should be 2-4 weeks. If there is no improvement in symptoms, treatment should be stopped and reconsidered. However, if there is improvement, it should be continued for at least a further 2-4 weeks to achieve clinical cure and, hopefully, eradication of the causative pathogen. Antibiotic treatment should not be given for 6-8 weeks without an appraisal of its effectiveness. Currently used antibiotics are reviewed. Of these, the fluoroquinolones ofloxacin and ciprofloxacin are recommended because of their favourable antibacterial spectrum and pharmacokinetic profile. A number of clinical trials are recommended and a standard study design is proposed to help resolve some outstanding issues