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

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

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

Exact Solutions of Exceptional Gauge Theories from Toric Geometry

We derive four dimensional gauge theories with exceptional groups $F_4$, $E_8$, $E_7$, and $E_7$ with matter, by starting from the duality between the heterotic string on $K3$ and F-theory on a elliptically fibered Calabi-Yau 3-fold. This configuration is compactified to four dimensions on a torus, and by employing toric geometry, we compute the type IIB mirrors of the Calabi-Yaus of the type IIA string theory. We identify the Seiberg-Witten curves describing the gauge theories as ALE spaces fibered over a $P^1$ base.Comment: 18 pages, 5 figures, uses harvmac and eps

Narrow-line magneto-optical cooling and trapping of strongly magnetic atoms

Laser cooling on weak transitions is a useful technique for reaching ultracold temperatures in atoms with multiple valence electrons. However, for strongly magnetic atoms a conventional narrow-line magneto-optical trap (MOT) is destabilized by competition between optical and magnetic forces. We overcome this difficulty in Er by developing an unusual narrow-line MOT that balances optical and magnetic forces using laser light tuned to the blue side of a narrow (8 kHz) transition. The trap population is spin-polarized with temperatures reaching below 2 microkelvin. Our results constitute an alternative method for laser cooling on weak transitions, applicable to rare-earth-metal and metastable alkaline earth elements.Comment: To appear in Phys. Rev. Lett. 4 pages, 5 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

Langevin dynamics with a tilted periodic potential

We study a Langevin equation for a particle moving in a periodic potential in the presence of viscosity $\gamma$ and subject to a further external field $\alpha$. For a suitable choice of the parameters $\alpha$ and $\gamma$ the related deterministic dynamics yields heteroclinic orbits. In such a regime, in absence of stochastic noise both confined and unbounded orbits coexist. We prove that, with the inclusion of an arbitrarly small noise only the confined orbits survive in a sub-exponential time scale.Comment: 38 pages, 6 figure

Liquid-jet target for laser-plasma soft x-ray generation

We describe a new liquid-target system for low-debris laser-plasma soft x-ray sources. The system is based on a microscopic liquid jet and is experimentally evaluated for 0.7-1 keV proximity lithography and water-window x-ray microscopy applications. Compared to an existing liquid-droplet target, this target system has the same low debris emission, high x-ray photon flux, and narrow spectral bandwidth. The advantages of the liquid-jet target include improved x-ray flux stability, increased range of suitable target liquids, and elimination of the need for temporal synchronization, thereby allowing less complex laser systems to be used. (C) 1996 American Institute of Physics