On the long time behavior of free stochastic Schrödinger evolutions

We discuss the time evolution of the wave function which is the solution of a stochastic Schrödinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and uniqueness of solutions. We observe that there exist three time regimes: the collapse regime, the classical regime and the diffusive regime. Concerning the latter, we assert that the general solution converges almost surely to a diffusing Gaussian wave function having a finite spread both in position as well as in momentum. This paper corrects and completes earlier works on this issue.

Small- and waiting-time behaviour of the thin-film-equation

We consider the small-time behavior of interfaces of zero contact angle solutions to the thin-film equation. For a certain class of initial data, through asymptotic analyses, we deduce a wide variety of behavior for the free boundary point. These are supported by extensive numerical simulations. © 2007 Society for Industrial and Applied Mathematics

Impact properties of glass/plant fibre hybrid laminates

The use of plants fibre reinforced composites has continuously increased during recent years. Their low density, higher environmental friendliness, and reduced cost proved particularly attractive for low-tech applications e.g., in building, automotive and leisure time industry. However, a major limitation to the use of these materials in structural components is unsatisfactory impact performance. An intermediate approach, the production of glass/ plant fibre hybrid laminates, has also been explored, trying to obtain materials with sufficient impact properties, whilst retaining a reduced cost and a substantial environmental gain. A survey is given on some aspects, crucial for the use of glass/plant fibre hybrid laminates in structural components: performance of hybrids when subjected to impact testing; the effect of laminate configuration, manufacturing procedure and fibre treatment on impact properties of the composite. Finally, indications are provided for a suitable selection of plant fibres with minimal extraction damage and sufficient toughness, for introduction in an impact-resistant glass/plant fibre hybrid laminate.

Disentangling multi-level systems: averaging, correlations and memory

We consider two weakly coupled systems and adopt a perturbative approach based on the Ruelle response theory to study their interaction. We propose a systematic way of parameterizing the effect of the coupling as a function of only the variables of a system of interest. Our focus is on describing the impacts of the coupling on the long term statistics rather than on the finite-time behavior. By direct calculation, we find that, at first order, the coupling can be surrogated by adding a deterministic perturbation to the autonomous dynamics of the system of interest. At second order, there are additionally two separate and very different contributions. One is a term taking into account the second-order contributions of the fluctuations in the coupling, which can be parameterized as a stochastic forcing with given spectral properties. The other one is a memory term, coupling the system of interest to its previous history, through the correlations of the second system. If these correlations are known, this effect can be implemented as a perturbation with memory on the single system. In order to treat this case, we present an extension to Ruelle's response theory able to deal with integral operators. We discuss our results in the context of other methods previously proposed for disentangling the dynamics of two coupled systems. We emphasize that our results do not rely on assuming a time scale separation, and, if such a separation exists, can be used equally well to study the statistics of the slow variables and that of the fast variables. By recursively applying the technique proposed here, we can treat the general case of multi-level systems.

Law of large numbers for super-brownian motions with a single point source

We investigate the super-Brownian motion with a single point source in dimensions 2 and 3 as constructed by Fleischmann and Mueller in 2004. Using analytic facts we derive the long time behavior of the mean in dimension 2 and 3 thereby complementing previous work of Fleischmann, Mueller and Vogt. Using spectral theory and martingale arguments we prove a version of the strong law of large numbers for the two dimensional superprocess with a single point source and finite variance.

(Non-)ergodicity of a degenerate diffusion modeling the fiber lay down process

We analyze the large time behavior of a stochastic model for the lay down of fibers on a moving conveyor belt in the production process of nonwovens. It is shown that under weak conditions this degenerate diffusion process has a unique invariant distribution and is even geometrically ergodic. This generalizes results from previous works [M. Grothaus and A. Klar, SIAM J. Math. Anal., 40 (2008), pp. 968–983; J. Dolbeault et al., arXiv:1201.2156] concerning the case of a stationary conveyor belt, in which the situation of a moving conveyor belt has been left open.

Profile of European adults interested in internet-based personalized nutrition: The Food4Me Study

Purpose Personalised intervention may have greater potential for reducing the global burden of non-communicable diseases and for promoting better health and wellbeing across the life-span than the conventional “one size fits all” approach. However, the characteristics of individuals interested in personalised nutrition (PN) are unclear. Therefore, the aim of this study was to describe the characteristics of European adults interested in taking part in an internet-based PN study. Methods Individuals from seven European countries (UK, Ireland, Germany, the Netherlands, Spain, Greece and Poland) were invited to participate in the study via the Food4Me website (http://www.food4me.org). Two screening questionnaires were used to collect data on socio-demographic, anthropometric and health characteristics as well as dietary intakes. Results A total of 5662 individuals expressed an interest in the study (mean age 40 ± 12.7; range 15-87 years). Of these 64.6% were female and 96.9% were Caucasian. Overall, 12.9% were smokers and 46.8% reported the presence of a clinically diagnosed disease. Furthermore, 46.9% were overweight or obese and 34.9% were sedentary during leisure time. Assessment of dietary intakes showed that 54.3% of individuals reported consuming at least 5 portions of fruit and vegetables per day, 45.9% consumed more than 3 servings of wholegrains and 37.2% limited their salt intake to less than 5.75g per day. Conclusions Our data indicate that individuals volunteering to participate in an internet-based PN study are broadly representative of the European adult population, most of whom had adequate nutrient intakes but who could benefit from improved dietary choices and greater physical activity. Future use of internet-based PN approaches is thus relevant to a wide target audience.

Higher education as a portfolio investment: students’ choices about studying, term time employment, leisure, and loans

Recent UK changes in the number of students entering higher education, and in the nature of financial support, highlight the complexity of students’ choices about human capital investments. Today’s students have to focus not on the relatively narrow issue of how much academic effort to invest, but instead on the more complicated issue of how to invest effort in pursuit of ‘employability skills’, and how to signal such acquisitions in the context of a highly competitive graduate jobs market. We propose a framework aimed specifically at students’ investment decisions, which encompasses corner solutions for both borrowing and employment while studying.

Small time two-sided LIL behavior for Lévy processes at zero

We wish to characterize when a Lévy process X t crosses boundaries b(t), in a two-sided sense, for small times t, where b(t) satisfies very mild conditions. An integral test is furnished for computing the value of sup t→0|X t |/b(t) = c. In some cases, we also specify a function b(t) in terms of the Lévy triplet, such that sup t→0 |X t |/b(t) = 1.

Functional disconnection of a prefrontal cortical-dorsal striatal system disrupts choice reaction time performance: implications for attentional function

This series of experiments investigated the role of a prefrontal cortical-dorsal striatal circuit in attention, using a continuous performance task of sustained and spatially divided visual attention. A unilateral excitotoxic lesion of the medial prefrontal cortex and a contralateral lesion of the medial caudate-putamen were used to "disconnect" the circuit. Control groups of rats with unilateral lesions of either structure were tested in the same task. Behavioral controls included testing the effects of the disconnection lesion on Pavlovian discriminated approach behavior. The disconnection lesion produced a significant reduction in the accuracy of performance in the attentional task but did not impair Pavlovian approach behavior or affect locomotor or motivational variables, providing evidence for the involvement of this medial prefrontal corticostriatal system in aspects of visual attentional function.

Diet digestibility, rate of passage, and eating and rumination behavior of Jersey and Holstein cows

Diet digestibility and rate of passage, eating and rumination behavior, dry matter intake (DMI), and lactation performance were compared in 6 Jersey and 6 Holstein multiparous cows. Cows were fed gestation diets according to body weight (BW) beginning 7 wk before expected calving and ad libitum amounts of a lactation diet postpartum. Diet digestibility and rate of passage were measured in 5-d periods at wk 5 prepartum and wk 6 and 14 of lactation. Eating and ruminating behavior was measured over 5-d periods at wk 5 and 2 prepartum and wk 2, 6, 10, and 14 of lactation. Milk yield and DMI were higher in Holsteins, but milk energy output per kilogram of metabolic BW (BW0.75) and intake capacity (DMI/kg of BW) did not differ between breeds. Holsteins spent longer ruminating per day compared with Jerseys, but daily eating time did not differ between breeds. Jerseys spent more time eating and ruminating per unit of ingested feed. The duration and number of meals consumed did not differ between breeds, but the meals consumed by Jerseys were distributed more evenly throughout each 24-h period, providing a more regular supply of feed to the rumen. Feed passed through the digestive tract more quickly in Jerseys compared with Holsteins, suggesting particle breakdown and rumen outflow were faster in Jerseys, but this may also reflect the relative size of their digestive tract. Neutral detergent fiber digestibility was greater in Jerseys, despite the shorter rumen retention time, but digestibility of dry matter, organic matter, starch, and N did not differ between breeds. Utilization of digested N for tissue retention was higher at wk 5 prepartum and lower at wk 14 of lactation in Jerseys. In contrast to numerous published studies, intake capacity of Jerseys was not higher than that of Holsteins, but in the present study, cows were selected on the basis of equal expected milk energy yield per kilogram of metabolic BW. Digestibility of neutral detergent fiber and rate of digesta passage were higher in Jerseys, probably as a consequence of increased mastication per unit of feed consumed in Jerseys and their smaller size.

An evaluation of different growth functions for describing the profile of live weight with time (age) in meat and egg strains of chicken

A total of 86 profiles from meat and egg strains of chickens (male and female) were used in this study. Different flexible growth functions were evaluated with regard to their ability to describe the relationship between live weight and age and were compared with the Gompertz and logistic equations, which have a fixed point of inflection. Six growth functions were used: Gompertz, logistic, Lopez, Richards, France, and von Bertalanffy. A comparative analysis was carried out based on model behavior and statistical performance. The results of this study confirmed the initial concern about the limitation of a fixed point of inflection, such as in the Gompertz equation. Therefore, consideration of flexible growth functions as an alternatives to the simpler equations (with a fixed point of inflection) for describing the relationship between live weight and age are recommended for the following reasons: they are easy to fit, they very often give a closer fit to data points because of their flexibility and therefore a smaller RSS value, than the simpler models, and they encompasses simpler models for the addition of an extra parameter, which is especially important when the behavior of a particular data set is not defined previously.

Effects of UV-blocking films on the dispersal behavior of Encarsia formosa (Hymenoptera : Aphelinidae)

The parasitoid Encarsia formosa Gahan (Hymenoptera: Aphelinidae) has been used successfully for the control of Trialeurodes vaporariorum (Westwood) (Homoptera: Aleyrodidae). The development of UV-blocking plastic films has added a new component to future integrated pest management systems by disrupting insect pest infestation when UV light is excluded. Because both T. vaporariorum and E. formosa are reported to have similar spectral efficiency, there was a need to identify the impact of UV-blocking films on the dispersal behavior of both the pest and the natural enemy. In field studies, using choice-chamber experiments, E. formosa showed some preference to disperse into compartments where less UV light was blocked. However, further studies indicated that the effect was primarily attributable to the different light diffusion properties of the films tested. Thus, unlike its whitefly host, when the UV-absorbing properties of the films were similar, but the light diffusion properties differed, E.formosa adults preferred to disperse into compartments clad with films that had high light diffusion properties. When the plastic films differed most in their UV-absorbing capacity and had no light-diffusion capability, the initial dispersal of E. formosa between treatments was similar, although a small preference toward the environment with UV light was observed over time. When parasitoid dispersal was measured 3 h after release, more parasitoids were found on plants, suggesting that the parasitoids would search plants for whitefly hosts, even in a UV-blocked light environment. The potential for the integration of UV-blocking films with E. formosa in an advanced whitefly management system is discussed.