Ultrasmall volume Plasmons - yet with complete retardation effects

Nano particle-plasmons are attributed to quasi-static oscillation with no wave propagation due to their subwavelength size. However, when located within a band-gap medium (even in air if the particle is small enough), the particle interfaces are acting as wave-mirrors, incurring small negative retardation. The latter when compensated by a respective (short) propagation within the particle substantiates a full-fledged resonator based on constructive interference. This unusual wave interference in the deep subwavelength regime (modal-volume<0.001lambda^3) significantly enhances the Q-factor, e.g. 50 compared to the quasi-static limit of 5.5.Comment: 16 pages, 6 figure

Stochastics theory of log-periodic patterns

We introduce an analytical model based on birth-death clustering processes to help understanding the empirical log-periodic corrections to power-law scaling and the finite-time singularity as reported in several domains including rupture, earthquakes, world population and financial systems. In our stochastics theory log-periodicities are a consequence of transient clusters induced by an entropy-like term that may reflect the amount of cooperative information carried by the state of a large system of different species. The clustering completion rates for the system are assumed to be given by a simple linear death process. The singularity at t_{o} is derived in terms of birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge

Regulating Highly Automated Robot Ecologies: Insights from Three User Studies

Highly automated robot ecologies (HARE), or societies of independent autonomous robots or agents, are rapidly becoming an important part of much of the world's critical infrastructure. As with human societies, regulation, wherein a governing body designs rules and processes for the society, plays an important role in ensuring that HARE meet societal objectives. However, to date, a careful study of interactions between a regulator and HARE is lacking. In this paper, we report on three user studies which give insights into how to design systems that allow people, acting as the regulatory authority, to effectively interact with HARE. As in the study of political systems in which governments regulate human societies, our studies analyze how interactions between HARE and regulators are impacted by regulatory power and individual (robot or agent) autonomy. Our results show that regulator power, decision support, and adaptive autonomy can each diminish the social welfare of HARE, and hint at how these seemingly desirable mechanisms can be designed so that they become part of successful HARE.Comment: 10 pages, 7 figures, to appear in the 5th International Conference on Human Agent Interaction (HAI-2017), Bielefeld, German

Log-periodic corrections to scaling: exact results for aperiodic Ising quantum chains

Log-periodic amplitudes of the surface magnetization are calculated analytically for two Ising quantum chains with aperiodic modulations of the couplings. The oscillating behaviour is linked to the discrete scale invariance of the perturbations. For the Fredholm sequence, the aperiodic modulation is marginal and the amplitudes are obtained as functions of the deviation from the critical point. For the other sequence, the perturbation is relevant and the critical surface magnetization is studied.Comment: 12 pages, TeX file, epsf, iopppt.tex, xref.tex which are joined. 4 postcript figure

Resonant guided wave networks

A resonant guided wave network (RGWN) is an approach to optical materials design in which power propagation in guided wave circuits enables material dispersion. The RGWN design, which consists of power-splitting elements arranged at the nodes of a waveguide network, results in wave dispersion which depends on network layout due to localized resonances at several length scales in the network. These structures exhibit both localized resonances with Q ~ 80 at 1550 nm wavelength as well as photonic bands and band-gaps in large periodic networks at infrared wavelengths.Comment: 9 pages, 5 figure

Are Financial Crashes Predictable?

We critically review recent claims that financial crashes can be predicted using the idea of log-periodic oscillations or by other methods inspired by the physics of critical phenomena. In particular, the October 1997 `correction' does not appear to be the accumulation point of a geometric series of local minima.Comment: LaTeX, 5 pages + 1 postscript figur

Binary Tree Approach to Scaling in Unimodal Maps

Ge, Rusjan, and Zweifel (J. Stat. Phys. 59, 1265 (1990)) introduced a binary tree which represents all the periodic windows in the chaotic regime of iterated one-dimensional unimodal maps. We consider the scaling behavior in a modified tree which takes into account the self-similarity of the window structure. A non-universal geometric convergence of the associated superstable parameter values towards a Misiurewicz point is observed for almost all binary sequences with periodic tails. There are an infinite number of exceptional sequences, however, which lead to superexponential scaling. The origin of such sequences is explained.Comment: 25 pages, plain Te

Multifractality in Time Series

We apply the concepts of multifractal physics to financial time series in order to characterize the onset of crash for the Standard & Poor's 500 stock index x(t). It is found that within the framework of multifractality, the "analogous" specific heat of the S&P500 discrete price index displays a shoulder to the right of the main peak for low values of time lags. On decreasing T, the presence of the shoulder is a consequence of the peaked, temporal x(t+T)-x(t) fluctuations in this regime. For large time lags (T>80), we have found that C_{q} displays typical features of a classical phase transition at a critical point. An example of such dynamic phase transition in a simple economic model system, based on a mapping with multifractality phenomena in random multiplicative processes, is also presented by applying former results obtained with a continuous probability theory for describing scaling measures.Comment: 22 pages, Revtex, 4 ps figures - To appear J. Phys. A (2000

Singular measures in circle dynamics

Critical circle homeomorphisms have an invariant measure totally singular with respect to the Lebesgue measure. We prove that singularities of the invariant measure are of Holder type. The Hausdorff dimension of the invariant measure is less than 1 but greater than 0