Spectral degeneracy and escape dynamics for intermittent maps with a hole

We study intermittent maps from the point of view of metastability. Small neighbourhoods of an intermittent fixed point and their complements form pairs of almost-invariant sets. Treating the small neighbourhood as a hole, we first show that the absolutely continuous conditional invariant measures (ACCIMs) converge to the ACIM as the length of the small neighbourhood shrinks to zero. We then quantify how the escape dynamics from these almost-invariant sets are connected with the second eigenfunctions of Perron-Frobenius (transfer) operators when a small perturbation is applied near the intermittent fixed point. In particular, we describe precisely the scaling of the second eigenvalue with the perturbation size, provide upper and lower bounds, and demonstrate $L^1$ convergence of the positive part of the second eigenfunction to the ACIM as the perturbation goes to zero. This perturbation and associated eigenvalue scalings and convergence results are all compatible with Ulam's method and provide a formal explanation for the numerical behaviour of Ulam's method in this nonuniformly hyperbolic setting. The main results of the paper are illustrated with numerical computations.Comment: 34 page

Phase Transition in a One-Dimensional Extended Peierls-Hubbard Model with a Pulse of Oscillating Electric Field: II. Linear Behavior in Neutral-to-Ionic Transition

Dynamics of charge density and lattice displacements after the neutral phase is photoexcited is studied by solving the time-dependent Schr\"odinger equation for a one-dimensional extended Peierls-Hubbard model with alternating potentials. In contrast to the ionic-to-neutral transition studied previously, the neutral-to-ionic transition proceeds in an uncooperative manner as far as the one-dimensional system is concerned. The final ionicity is a linear function of the increment of the total energy. After the electric field is turned off, the electronic state does not significantly change, roughly keeping the ionicity, even if the transition is not completed, because the ionic domains never proliferate. As a consequence, an electric field with frequency just at the linear absorption peak causes the neutral-to-ionic transition the most efficiently. These findings are consistent with the recent experiments on the mixed-stack organic charge-transfer complex, TTF-CA. We artificially modify or remove the electron-lattice coupling to discuss the origin of such differences between the two transitions.Comment: 17 pages, 9 figure

An investigation of thermodynamics, microscopic structure, depolarized Rayleigh scattering, and collision dynamics in Xe-N-2 supercritical mixtures

We would like to dedicate this work to the late Professor W. A. Steele (W.A.S.), Penn State University, USA. NATO Research-Project SA 5-2-05(CRG 950087) JARC (97) 288 is acknowledged for project funding to J.S., H.V. and W.A.S. The Greek State Scholarships Foundation (IKY) is acknowledged for an award based on performance to S. M. This work was supported by computational time granted from the Greek Research & Technology Network (GRNET) in the National HPC facility ARIS. The CPU time of the Computing Centre of the University of Athens (Greece) is gratefully acknowledged. This research utilized Queen Mary’s Mid-Plus computational facilities, supported by QMUL Research-IT and funded by EPSRC grant EP/K000128/1. J.K. acknowledges financial support from the NSF Grant No. CHE-1565872 to Millard Alexander

ERROR PROPAGATION IN EXTENDED CHAOTIC SYSTEMS

A strong analogy is found between the evolution of localized disturbances in extended chaotic systems and the propagation of fronts separating different phases. A condition for the evolution to be controlled by nonlinear mechanisms is derived on the basis of this relationship. An approximate expression for the nonlinear velocity is also determined by extending the concept of Lyapunov exponent to growth rate of finite perturbations.Comment: Tex file without figures- Figures and text in post-script available via anonymous ftp at ftp://wpts0.physik.uni-wuppertal.de/pub/torcini/jpa_le

Evidence for Complex Subleading Exponents from the High-Temperature Expansion of the Hierarchical Ising Model

Using a renormalization group method, we calculate 800 high-temperature coefficients of the magnetic susceptibility of the hierarchical Ising model. The conventional quantities obtained from differences of ratios of coefficients show unexpected smooth oscillations with a period growing logarithmically and can be fitted assuming corrections to the scaling laws with complex exponents.Comment: 10 pages, Latex , uses revtex. 2 figures not included (hard copies available on request

Existence and Stability of Steady Fronts in Bistable CML

We prove the existence and we study the stability of the kink-like fixed points in a simple Coupled Map Lattice for which the local dynamics has two stable fixed points. The condition for the existence allows us to define a critical value of the coupling parameter where a (multi) generalized saddle-node bifurcation occurs and destroys these solutions. An extension of the results to other CML's in the same class is also displayed. Finally, we emphasize the property of spatial chaos for small coupling.Comment: 18 pages, uuencoded PostScript file, J. Stat. Phys. (In press

Analytical model of non-Markovian decoherence in donor-based charge quantum bits

We develop an analytical model for describing the dynamics of a donor-based charge quantum bit (qubit). As a result, the quantum decoherence of the qubit is analytically obtained and shown to reveal non-Markovian features: The decoherence rate varies with time and even attains negative values, generating a non-exponential decay of the electronic coherence and a later recoherence. The resulting coherence time is inversely proportional to the temperature, thus leading to low decoherence below a material dependent characteristic temperature.Comment: 19 pages, 3 figure

Forecasting in the light of Big Data

Predicting the future state of a system has always been a natural motivation for science and practical applications. Such a topic, beyond its obvious technical and societal relevance, is also interesting from a conceptual point of view. This owes to the fact that forecasting lends itself to two equally radical, yet opposite methodologies. A reductionist one, based on the first principles, and the naive inductivist one, based only on data. This latter view has recently gained some attention in response to the availability of unprecedented amounts of data and increasingly sophisticated algorithmic analytic techniques. The purpose of this note is to assess critically the role of big data in reshaping the key aspects of forecasting and in particular the claim that bigger data leads to better predictions. Drawing on the representative example of weather forecasts we argue that this is not generally the case. We conclude by suggesting that a clever and context-dependent compromise between modelling and quantitative analysis stands out as the best forecasting strategy, as anticipated nearly a century ago by Richardson and von Neumann

A First Analysis of the Potential Impact of Climate Change on the Efficiency and Reliability of Solar and Hydro Energy Sources

Climate change impacts our electric power system in several ways, affecting both the load and generation. Here we investigate one part of these impacts, the effect of climate change on the supply of renewable energy. Analyzing 60 years of data, climate change is found to impact both the total supply available and its variability. This impact is found to vary significantly with location. Here we focus on and compare two disparate locations, Palma de Mallorca in the Balearic Islands and Cordova, Alaska. Using novel metrics, this analysis demonstrates the feasibility of a process to evaluate the changing needs for energy storage as well as the ability to evaluate the impact on grid reliability regarding both penetration of the increasing renewable resources and changes in the variability of the resource. This framework can be used to quantify the impact on both transmission grids and microgrids and can guide possible mitigation paths

An Initial Analysis of the Impact of Future Climate Change on the Efficiency and Reliability of Solar, Wind and Hydro Energy Sources

Climate change will impact our electric power system, affecting both the load and generation and thereby the grid reliability. Here we investigate one part of these impacts, the effect of future climate change on the supply of renewable energy. Analyzing model output data through 2100, climate change is found to impact both the total supply available and its variability. This impact is however found to vary significantly with location. Here we focus on and compare a few disparate locations, Palma de Mallorca in the Balearic Islands, Cordova Alaska, McAllen TX and Oroville CA. Using developed metrics, this analysis applies a developed process to evaluate the changing needs for energy storage as well as the ability to evaluate the impact on grid reliability from both penetration of increasing renewable resources and changes in the variability of the resource on both transmission grids and microgrids in order to guide possible mitigation paths