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

Interaction of a ring-reinforced shell and a fluid medium

Transient dynamic response of periodically ring- reinforced, infinitely long, circular cylindrical shell to uniform pressure applied through surrounding acoustic mediu

Universality of residence-time distributions in non-adiabatic stochastic resonance

We present mathematically rigorous expressions for the residence-time and first-passage-time distributions of a periodically forced Brownian particle in a bistable potential. For a broad range of forcing frequencies and amplitudes, the distributions are close to periodically modulated exponential ones. Remarkably, the periodic modulations are governed by universal functions, depending on a single parameter related to the forcing period. The behaviour of the distributions and their moments is analysed, in particular in the low- and high-frequency limits.Comment: 8 pages, 1 figure New version includes distinction between first-passage-time and residence-time distribution

Metastability in Interacting Nonlinear Stochastic Differential Equations II: Large-N Behaviour

We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise, in the limit of large N. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent source of white noise. For strong coupling (of the order N^2), the system synchronises, in the sense that all oscillators assume almost the same position in their respective local potential most of the time. In a previous paper, we showed that the transition from strong to weak coupling involves a sequence of symmetry-breaking bifurcations of the system's stationary configurations, and analysed in particular the behaviour for coupling intensities slightly below the synchronisation threshold, for arbitrary N. Here we describe the behaviour for any positive coupling intensity \gamma of order N^2, provided the particle number N is sufficiently large (as a function of \gamma/N^2). In particular, we determine the transition time between synchronised states, as well as the shape of the "critical droplet", to leading order in 1/N. Our techniques involve the control of the exact number of periodic orbits of a near-integrable twist map, allowing us to give a detailed description of the system's potential landscape, in which the metastable behaviour is encoded

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

Patterns of quark mass matrices in a class of Calabi-Yau models

We study a class of superstring models compactified in the 3-generation Calabi-Yau manifold of Tian and Yau. Our analysis includes the complete $E_6$-singlet sector, which has been recently evaluated using techniques of spectral and exact sequences. We use the discrete symmetries of the models to find flat directions of symmetry breaking that leave unbroken a low energy matter parity and make all leptoquarks heavy while preserving light Higgs fields. Then we classify the patterns of ordinary quark mass matrices and show that (without invoking effects due to nonrenormalizable terms) only one structure can accommodate the observed value of fermion masses and mixing angles, with preference for a heavy {\it top} quark ( $m_t\ge 170$ GeV for $V_{13}\le 0.013$ ). The model, which unifies perturbatively and predicts a realistic structure of quark mass matrices with texture zeroes, is one of the many possible string vacua. However, in contrast with what is often assumed in the search for realistic unified scenarios, it is highly nonminimal near the unification scale and the predicted mass matrices have no simple symmetry properties.Comment: 30 (including Tables and Figures), UG-FT-38/9

Reflective STRENGTH-Giving Dialogue Developed to Support Older Adults in Learning to Live with Long-Term Pain: A Method and a Study Design

Background: Long-term musculoskeletal pain is a major health problem that significantly impacts quality of life among older adults. Many lack professional guidance and must learn on their own to live with pain. This calls for a holistic method that addresses older adults’ needs in their situations. The developed method has its foundation in the didactic model: “The challenge – to take control of one’s life with long-term illness. Aim: The aim was to describe the method, Reflective STRENGTH-Giving Dialogue, and present a study design where the method is learned and used by health careprovidersto support older adults in learning to live their lives with long-term pain at home in a way that promotes health, well-being, meaning and strength in life. Methods: The pilot study design consists of an educational program including continuous supervision to health care providers during the accomplishment of dialogues with community dwelling older adults. The key dimensions in Reflective STRENGTH-Giving Dialogue are: Situation: Confront and ascertain the facticity in the current situation; Transition from “one to I” and Take charge in the situation; Reflect upon possibilities and choices; Engagement in fulfilling small and large life projects that gives joy and meaning in life; Get inner strength and courage; Tactful and challenging approach and Holistic perspective. Data will be collected through interviews and questionnaires. Qualitative and quantitative methods (NRS, BPI-SF, GDS, KASAM, MSQ) will be used for analysis. A control-group will be enrolled. Discussion and Relevance of Study: STRENGTH can be used to secure and enhance the quality of personcentered care. The method for dialogues can be a way to holistically and individually guide and support older adults in finding ways to live a meaningful life despite pain and to fulfill their desire to remain at home as long as possible

Relating the Cosmological Constant and Supersymmetry Breaking in Warped Compactifications of IIB String Theory

It has been suggested that the observed value of the cosmological constant is related to the supersymmetry breaking scale M_{susy} through the formula Lambda \sim M_p^4 (M_{susy}/M_p)^8. We point out that a similar relation naturally arises in the codimension two solutions of warped space-time varying compactifications of string theory in which non-isotropic stringy moduli induce a small but positive cosmological constant.Comment: 7 pages, LaTeX, references added and minor changes made, (v3) map between deSitter and global cosmic brane solutions clarified, supersymmetry breaking discussion improved and references adde

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