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

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

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

Decision-Making Frameworks For Using Sensor Data And Evolutionary Algorithms To Flush A Contaminated Water Distribution System

In the event that a contaminant enters a water distribution system, opening hydrants to flush contaminated water can protect consumers from becoming exposed. Strategies for operating hydrants can be developed to specify the selection of hydrants and the timing of operations to maximize the amount of contaminant that is removed from the system. As an event unfolds, however, sensor data may be the only information that is available to indicate the location and timing of the contaminant source, and ultimately, hydrant strategies must be selected in a highly uncertain environment. The decision-making framework for making real-time decisions to select hydrant strategies relies on computational and sensor technologies, including the accuracy and precision of sensor data; the timeliness of data availability (e.g., streaming data or data that is collected manually); and computational capabilities to execute search simulation-optimization frameworks in real-time. This research will explore and compare two decision-making frameworks. The first framework integrates real-time algorithms to identify potential source locations and develop hydrant strategies, using precise water quality data and high performance computation. The source identification problem is solved using a multi-population evolution strategies approach, and a genetic algorithm approach is applied to identify hydrant strategies for specified source locations. The second decision-making framework provides a library of response options that can be selected based on sensor data as an event unfolds. The library of hydrant strategies is developed a priori using a simulation-optimization framework. Potential sources are classified based on the order of sensors that are activated, and hydrant strategies are identified to maximize average performance for events within each class through the application of a genetic algorithm framework. The two decision-making frameworks are applied and compared for a set of events that are simulated for a virtual city, Mesopolis

Causes of Stillbirth and Time of Death in Swedish Holstein Calves Examined Post Mortem

This study was initiated due to the observation of increasing and rather high levels of stillbirths, especially in first-calving Swedish Holstein cows (10.3%, 2002). Seventy-six Swedish Holstein calves born to heifers at 41 different farms were post mortem examined in order to investigate possible reasons for stillbirth and at what time in relation to full-term gestation they had occurred. The definition of a stillborn calf was dead at birth or within 24 h after birth after at least 260 days of gestation. Eight calves were considered as having died already in uterus. Slightly less than half of the examined calves (46.1%) were classified as having died due to a difficult calving. Four calves (5.3%) had different kinds of malformations (heart defects, enlarged thymus, urine bladder defect). Approximately one third of the calves (31.6%) were clinically normal at full-term with no signs of malformation and born with no indication of difficulties at parturition or any other reason that could explain the stillbirth. The numbers of male and female calves were rather equally distributed within the groups. A wide variation in post mortem weights was seen in all groups, although a number of the calves in the group of clinically normal calves with unexplained reason of death were rather small and, compared with e.g. those calves categorised as having died due to a difficult calving, their average birth weight was 6 kg lower (39.9 ± 1.7 kg vs. 45.9 ± 1.5 kg, p ≤ 0.01). It was concluded that the cause of stillbirth with a non-infectious aetiology is likely to be multifactorial and difficult calving may explain only about half of the stillbirths. As much as one third of the calves seemed clinically normal with no obvious reason for death. This is a target group of calves that warrants a more thorough investigation in further studies

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