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

Modulated amplitude waves with nonzero phases in Bose-Einstein condensates

In this paper we give a frame for application of the averaging method to Bose-Einstein condensates (BECs) and obtain an abstract result upon the dynamics of BECs. Using aver- aging method, we determine the location where the modulated amplitude waves (periodic or quasi-periodic) exist and we also study the stability and instability of modulated amplitude waves (periodic or quasi-periodic). Compared with the previous work, modulated amplitude waves studied in this paper have nontrivial phases and this makes the problem become more diffcult, since it involves some singularities.Comment: 17 pages, 2 figure

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

Multiscale characterizations of surface anisotropies

Anisotropy can influence surface function and can be an indication of processing. These influences and indications include friction, wetting, and microwear. This article studies two methods for multiscale quantification and visualization of anisotropy. One uses multiscale curvature tensor analysis and shows anisotropy in horizontal coordinates i.e., topocentric. The other uses multiple bandpass filters (also known as sliding bandpass filters) applied prior to calculating anisotropy parameters, texture aspect ratios (Str) and texture directions (Std), showing anisotropy in horizontal directions only. Topographies were studied on two milled steel surfaces, one convex with an evident large scale, cylindrical form anisotropy, the other nominally flat with smaller scale anisotropies; a EDMed surface, an example of an isotropic surface; and an additively manufactured surface with pillar-like features. Curvature tensors contain the two principal curvatures, i.e., maximum and minimum curvatures, which are orthogonal, and their directions, at each location. Principal directions are plotted for each calculated location on each surface, at each scale considered. Histograms in horizontal coordinates show altitude and azimuth angles of principal curvatures, elucidating dominant texture directions at each scale. Str and Std do not show vertical components, i.e., altitudes, of anisotropy. Changes of anisotropy with scale categorically failed to be detected by traditional characterization methods used conventionally. These multiscale methods show clearly in several representations that anisotropy changes with scale on actual surface measurements with markedly different anisotropies

Lysis and Amplifciation of Neonatal Sepsis Causing Pathogens

Neonatal sepsis, resulting from a bloodstream infection within the first few weeks of life, is the leading cause of newborn deaths worldwide. The gold standard of neonatal sepsis diagnosis requires a blood culture to identify the infecting bacteria, however require days of incubation, expensive equipment, and expertise. Any delay in diagnosis is critical, as the condition can be treated easily if appropriate antibiotics are administered promptly. A low-cost, rapid, and sensitive diagnostic test would enable more timely treatment and lead to better patient outcomes with fewer required resources. Point-of-care, nucleic acid amplification assays are a promising alternative to blood culture that quickly deliver sensitive results with minimal sample volume. However, these require isolated and purified template DNA from the pathogenic bacteria, a task that is difficult to achieve in a field setting. This study sought to develop a simple one-step lysis and amplification protocol for three common bacterial causes of neonatal sepsis, Streptococcus agalacitae, Klebsiella pnemoniae, and Staphylococcus aureus. The combined efficacy of enzymes, proteinase K and achromopeptidase (ACP), and heat to lyse each of these bacteria for direct DNA amplification was examined. Results showed that all three strains could be effectively lysed by applying 1 U of ACP and incubating for 10 minutes at 37° C. No adverse effects were seen in amplification reactions containing ACP if the compound was inactivated prior to amplification at 85° C for 2 minutes. The demonstrated effectiveness of ACP in rapid bacterial lysis validates its usefulness in a point-of-care device for neonatal sepsis

Metastability of non-reversible mean-field Potts model with three spins

We examine a non-reversible, mean-field Potts model with three spins on a set with $N\uparrow\infty$ points. Without an external field, there are three critical temperatures and five different metastable regimes. The analysis can be extended by a perturbative argument to the case of small external fields. We illustrate the case of large external fields with some phenomena which are not present in the absence of external field.Comment: 34 pages, 12 figure

Cardiovascular and cancer mortality in relation to dietary polychlorinated biphenyls and marine polyunsaturated fatty acids: A nutritional-toxicological aspect of fish consumption

Background. Co-exposure to environmental contaminants present in fish could mitigate the beneficial effects of fish consumption and possibly explain the lack of association observed for mortality in some geographical regions. Objective. To assess the independent associations of dietary exposure to polychlorinated biphenyls (PCBs) and long-chain omega-3 fish fatty acids intake with cardiovascular and cancer mortality. Methods. We used the prospective population-based Swedish Mammography Cohort and the Cohort of Swedish Men comprising 32 952 women and 36 545 men, free from cancer, cardiovascular disease and diabetes at baseline in 1998. Validated estimates of dietary PCBs and long-chain omega-3 fish fatty acids [i.e. eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA)] intake were obtained via a food frequency questionnaire at baseline. Information on death was ascertained through register linkage. Results. During a mean follow-up of 15.5 years, we ascertained 16 776 deaths. We observed for cardiovascular mortality, comparing extreme quintiles in multivariable models mutually adjusted for PCBs and EPA-DHA, dose-dependent associations for dietary PCB exposure, hazard ratio (HR) 1.31 (CI 95%: 1.08 to 1.57; P-trend 0.005) and for dietary EPA-DHA intake, HR 0.79 (CI 95%: 0.66 to 0.95; P-trend 0.041). For cancer mortality, no clear associations were discerned. Conclusion. The beneficial effect of fish consumption on the cardiovascular system seems compromised by co-exposure to PCBs – one likely explanation for the inconsistent associations observed between fish consumption and mortalityThe Swedish Research Council under the grant no 2017-00822 and 2017-00644 (SIMPLER) supported the stud

Toric Calabi-Yau supermanifolds and mirror symmetry

We study mirror symmetry of supermanifolds constructed as fermionic extensions of compact toric varieties. We mainly discuss the case where the linear sigma A-model contains as many fermionic fields as there are U(1) factors in the gauge group. In the mirror super-Landau-Ginzburg B-model, focus is on the bosonic structure obtained after integrating out all the fermions. Our key observation is that there is a relation between the super-Calabi-Yau conditions of the A-model and quasi-homogeneity of the B-model, and that the degree of the associated superpotential in the B-model is given in terms of the determinant of the fermion charge matrix of the A-model.Comment: 20 pages, v2: references adde