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

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

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

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

On the Geometric Interpretation of N = 2 Superconformal Theories

We clarify certain important issues relevant for the geometric interpretation of a large class of N = 2 superconformal theories. By fully exploiting the phase structure of these theories (discovered in earlier works) we are able to clearly identify their geometric content. One application is to present a simple and natural resolution to the question of what constitutes the mirror of a rigid Calabi-Yau manifold. We also discuss some other models with unusual phase diagrams that highlight some subtle features regarding the geometric content of conformal theories.Comment: 25 pages, note adde

Lemon Factory Extension

Martin works for Urban Future Organization (UFO), an internationally networked architectural practice involved in advanced digital design and fabrication. This new administrative wing is being added to an existing factory outside Messina in Sicily, sitting adjacent to a production building which is actually Italy’s largest producer of lemon juice and lemon extracts / essences. The brief was for a sequence of flexible spaces to house the reception area, staff offices, meeting spaces and canteen, along with a swimming pool and a fitness centre. The interior of the building reacts to the requirement to keep the spaces fluid and able to change their use over time. The project is currently on site and scheduled for completion in Spring 2008. In terms of research questions investigated, the key ones were how to develop new techniques of modulation design and structural design in what is a highly active earthquake zone, and then – given this crucial demand – how to create a new kind of flexible spatial organisation for a rapidly evolving company. In its design processes, the Lemon Factory has to be understood as part of a line of projects being carried out by the UFO practice and by similar entities – such as Ocean or Foreign Office Architects – into free-form, fluid and linear architectural forms, allying to this the pursuit of new forms of digital design and manufacturing in architecture. This project has been exhibited like other UFO project in important events such as the 2004 Venice Biennale, 2006 Beijing Biennale, and also in books like the press through articles such as in Building Design (7 March 2003, pp. 12-15). Urban Future Organization is a collaborative practice in which Martin and Yau are senior design figures, both being equally responsible for designing major projects such as the Lemon Factory near Messina

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

Severe asphyxia due to delivery-related malpractice in Sweden 1990–2005

Aim The objective of the thesis was to describe the most common causes of substandard care during labour contributing to severe asphyxia or neonatal death, to study risk factors related to asphyxia associated with substandard care and to explore the occurrence of substandard care during labour. Background There are about 100 000 infants born every year in Sweden. Most infants are born healthy after uncomplicated deliveries. However, 20-50 claims for financial compensation are made annually to the Patients Advisory Committee (PA C) on suspicion that substandard care during labour has contributed to severe asphyxia causing cerebral palsy or death. Even if this group of patients is notably small, asphyxia causes life-long impairment and immeasurable suffering to the patients and their families. In addition, the insurance costs are substantial and amount to 25% of all costs related to substandard care in Sweden. With the exception of this group of patients, and claims to the Health Services Disciplinary Board, the frequency of substandard care in relation to childbirth is fairly unknown. Material and methods Inclusion criteria were pregnancies with a gestational length ≥ 33 weeks, a spontaneous or induced start of labour, a normal CTG at admission for labour, and Apgar score < 7 at 5 minutes of age (Papers I-IV). 472 case records of deliveries from 1990-2005, filed at the PAC were scrutinised. In Paper I and II the deliveries and acts of neonatal resuscitation procedures are described. In Paper III, maternal characteristics, factors related to care and infant characteristics for patients receiving lifelong financial compensation from PAC are compared with all infants with full Apgar score at 5 minutes of age born after a vaginal start during the same time period in Sweden (n=1.141 059). In Paper IV deliveries and risk factors from 313 infants with Apgar score < 7at 5 minutes of age, born in the Stockholm County are compared with 313 infants with full Apgar score at five minutes of age, matched for year of birth. Results One-hundred and seventy-seven infants were considered to have been severely asphyxiated due to substandard care during labour (Paper I-III). The most common occurrences of malpractice in conjunction with labour were neglecting to supervise fetal well-being (98%), neglecting signs of fetal asphyxia (71%), including incautious use of oxytocin (71%) and choosing a non-optimal mode of delivery (52%) (Paper I). Resuscitation of the 177 severely asphyxiated infants was unsatisfactory in 47%. The most important flaw was the defective compliance with the guidelines concerning ventilation and prompt paging for skilled personnel in cases of imminent asphyxia (Paper II). Risk factors associated with asphyxia included maternal age ≥ 30 years, short maternal stature (< 159 cm), previous caesarean delivery, insulin-dependent diabetes, induced deliveries and night deliveries, where the increases in risk were doubled to a four-fold. In addition, dystocia of labour was associated with a five-fold increase in risk, which was further increased if epidural anaesthesia or opioids were used. Small- and large-for-gestational age infants, post-term (> 42 weeks) births, twins and breech deliveries had a three to eight-fold increase in risk of asphyxia when there was substandard care during labour (Paper III). Two thirds of infants born in the Stockholm region 2004-2006, with Apgar score < 7 at 5 minutes but also one third of the healthy controls were subjected to some kind of substandard care during labour (Paper IV). The main causes of substandard care during labour were related to misinterpretation of CTG, not acting timely on abnormal CTG, and incautious use of oxytocin. The risk of asphyxia increased with duration of abnormal CTG and was increased fifteen-fold when this was abnormal for ≥ 90 minutes. Oxytocin was provided without sign of inertia in 20% of cases and controls and the risk of asphyxia was increased more than fivefold in cases of tachysystole. Infants born after a spontaneous vaginal delivery with abnormal CTG for more than 45 minutes had a more than sevenfold risk of low Apgar score. In instrumental deliveries that were considered complex, there was a more than seventeen-fold risk of an Apgar score < 7 at 5 minutes of age. Assuming that substandard care is causative for low Apgar score, we estimate that 42% of the cases could be prevented by avoiding substandard care (Paper IV). Conclusion It is possible to improve patient safety during labour by applying educational efforts on fetal surveillance and increasing awareness of risk factors associated with asphyxia. The main causes of substandard care during labour are related to misinterpretation of CTG, not acting timely on abnormal CTG, misinterpretation of guidelines and misuse of oxytocin. Low Apgar score at 5 minutes of age can substantially, be prevented by avoiding substandard care