On the noise-induced passage through an unstable periodic orbit II: General case

Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the system's first exit from the interior of the unstable orbit occurs, typically displays the phenomenon of cycling: The distribution of first-exit locations is translated along the unstable periodic orbit proportionally to the logarithm of the noise intensity as the noise intensity goes to zero. We show that for a large class of such systems, the cycling profile is given, up to a model-dependent change of coordinates, by a universal function given by a periodicised Gumbel distribution. Our techniques combine action-functional or large-deviation results with properties of random Poincar\'e maps described by continuous-space discrete-time Markov chains.Comment: 44 pages, 4 figure

Supersymmetric approximations to the 3D supersymmetric O(N) model

We develop several non-perturbative approximations for studying the dynamics of a supersymmetric O(N) model which preserve supersymmetry. We study the phase structure of the vacuum in both the leading order in large-N approximation as well as in the Hartree approximation, and derive the finite temperature renormalized effective potential. We derive the exact Schwinger-Dyson equations for the superfield Green functions and develop the machinery for going beyond the next to leading order in large-N approximation using a truncation of these equations which can also be derived from a two-particle irreducible effective action.Comment: 16 pages, 3 figure

The GAINS Model for Greenhouse Gases - Version 1.0: Carbon Dioxide (CO2)

Many of the traditional air pollutants and greenhouse gases have common sources, offering a cost-effective potential for simultaneous improvements of traditional air pollution problems and climate change. A methodology has been developed to extend the RAINS integrated assessment model to explore synergies and trade-offs between the control of greenhouse gases and air pollution. With this extension, the GAINS (GHG-Air pollution INteraction and Synergies) model will allow the assessment of emission control costs for the six greenhouse gases covered under the Kyoto Protocol (CO2, CH4, N2O and the three F-gases) together with the emissions of air pollutants SO2, NOx, VOC, NH3 and PM. This report describes the first implementation (Version 1.0) of the model extension model to incorporate CO2 emissions. GAINS Version 1.0 assesses 230 options for reducing CO2 emissions from the various source categories, both through structural changes in the energy system (fuel substitution, energy efficiency improvements) and through end-of-pipe measures (e.g., carbon capture). GAINS quantifies for 43 countries/regions in Europe country-specific application potentials of the various options in the different sectors of the economy, and estimates the societal resource costs of these measures. Mitigation potentials are estimated in relation to an exogenous baseline projection that is considered to reflect current planning, and are derived from a comparison of scenario results for a range of carbon prices obtained from energy models. A critical element of the GAINS assessment refers to the assumptions on CO2 mitigation measures for which negative life cycle costs are calculated. There are a number of options for which the accumulated (and discounted over time) cost savings from reduced energy consumption outweigh their investments, even if private interest rates are used. If the construction of the baseline projection assumes a cost-effectiveness rationale, such measures would be autonomously adopted by the economic actors, even in the absence of any CO2 mitigation interest. In practice, however, it can be observed that various market imperfections impede the autonomous penetration. Due to the substantial CO2 mitigation potential that is associated with such negative cost options, projections of future CO2 emissions and even more of the available CO2 mitigation potentials are highly sensitive towards assumptions on their autonomous penetration rates occurring in the baseline projection. Assuming that all negative cost measures would form an integral part of the Energy Outlook developed in 2003 by the Directorate General for Energy and Transport of the European Commission that has been developed with a cost-minimizing energy model, CO2 emissions in Europe would approach 1990 levels in 2020, even in absence of any specific climate policy. Beyond that, GAINS estimates for 2020 an additional reduction potential of 20 percent. With full application of all mitigation measures contained in the GAINS database, the power sector could reduce its CO2 emissions by 550 Mt, the transport sector by 400 Mt, industry by 190 Mt, and the residential and commercial sector by 50 Mt below the baseline projection. Total costs of all these measures would amount to approximately 90 billion Euro/year

The effect of additive noise on dynamical hysteresis

We investigate the properties of hysteresis cycles produced by a one-dimensional, periodically forced Langevin equation. We show that depending on amplitude and frequency of the forcing and on noise intensity, there are three qualitatively different types of hysteresis cycles. Below a critical noise intensity, the random area enclosed by hysteresis cycles is concentrated near the deterministic area, which is different for small and large driving amplitude. Above this threshold, the area of typical hysteresis cycles depends, to leading order, only on the noise intensity. In all three regimes, we derive mathematically rigorous estimates for expectation, variance, and the probability of deviations of the hysteresis area from its typical value.Comment: 30 pages, 5 figure

Spacetime structure of the global vortex

We analyse the spacetime structure of the global vortex and its maximal analytic extension in an arbitrary number of spacetime dimensions. We find that the vortex compactifies space on the scale of the Hubble expansion of its worldvolume, in a manner reminiscent of that of the domain wall. We calculate the effective volume of this compactification and remark on its relevance to hierarchy resolution with extra dimensions. We also consider strongly gravitating vortices and derive bounds on the existence of a global vortex solution.Comment: 19 pages revtex, 2 figures, minor changes, references adde

Memory Effects and Scaling Laws in Slowly Driven Systems

This article deals with dynamical systems depending on a slowly varying parameter. We present several physical examples illustrating memory effects, such as metastability and hysteresis, which frequently appear in these systems. A mathematical theory is outlined, which allows to show existence of hysteresis cycles, and determine related scaling laws.Comment: 28 pages (AMS-LaTeX), 18 PS figure

On the Rational Type 0f Moment Angle Complexes

In this note it is shown that the moment angle complexes Z(K;(D^2,,S^1)) which are rationally elliptic are a product of odd spheres and a diskComment: This version avoids the use of an incorrect result from the literature in the proof of Theorem 1.3. There is some text overlap with arXiv:1410.645

Beyond the Fokker-Planck equation: Pathwise control of noisy bistable systems

We introduce a new method, allowing to describe slowly time-dependent Langevin equations through the behaviour of individual paths. This approach yields considerably more information than the computation of the probability density. The main idea is to show that for sufficiently small noise intensity and slow time dependence, the vast majority of paths remain in small space-time sets, typically in the neighbourhood of potential wells. The size of these sets often has a power-law dependence on the small parameters, with universal exponents. The overall probability of exceptional paths is exponentially small, with an exponent also showing power-law behaviour. The results cover time spans up to the maximal Kramers time of the system. We apply our method to three phenomena characteristic for bistable systems: stochastic resonance, dynamical hysteresis and bifurcation delay, where it yields precise bounds on transition probabilities, and the distribution of hysteresis areas and first-exit times. We also discuss the effect of coloured noise.Comment: 37 pages, 11 figure

Criminal Law: Customer’s Permanent Exclusion From Retail Store Due to Prior Shoplifting Arrests Held Enforceable Under Criminal Trespass Statute

In interpretive research, trustworthiness has developed to become an important alternative for measuring the value of research and its effects, as well as leading the way of providing for rigour in the research process. The article develops the argument that trustworthiness plays an important role in not only effecting change in a research project’s original setting, but also that trustworthy research contributes toward building a body of knowledge that can play an important role in societal change. An essential aspect in the development of this trustworthiness is its relationship to context. To deal with the multiplicity of meanings of context, we distinguish between contexts at different levels of the research project: the domains of the researcher, the collective, and the individual participant. Furthermore, we argue that depending on the primary purpose associated with the collective learning potential, critical potential, or performative potential of phenomenographic research, developing trustworthiness may take different forms and is related to aspects of pedagogical legitimacy, social legitimacy, and epistemological legitimacy. Trustworthiness in phenomenographic research is further analysed by distinguishing between the internal horizon – the constitution of trustworthiness as it takes place within the research project – and the external horizon, which points to the impact of the phenomenographic project in the world mediated by trustworthiness