Self-intersection local time of planar Brownian motion based on a strong approximation by random walks

The main purpose of this work is to define planar self-intersection local time by an alternative approach which is based on an almost sure pathwise approximation of planar Brownian motion by simple, symmetric random walks. As a result, Brownian self-intersection local time is obtained as an almost sure limit of local averages of simple random walk self-intersection local times. An important tool is a discrete version of the Tanaka--Rosen--Yor formula; the continuous version of the formula is obtained as an almost sure limit of the discrete version. The author hopes that this approach to self-intersection local time is more transparent and elementary than other existing ones.Comment: 36 pages. A new part on renormalized self-intersection local time has been added and several inaccuracies have been corrected. To appear in Journal of Theoretical Probabilit

Surface Instability of Icicles

Quantitatively-unexplained stationary waves or ridges often encircle icicles. Such waves form when roughly 0.1 mm-thick layers of water flow down the icicle. These waves typically have a wavelength of 1cm approximately independent of external temperature, icicle thickness, and the volumetric rate of water flow. In this paper we show that these waves can not be obtained by naive Mullins-Sekerka instability, but are caused by a quite new surface instability related to the thermal diffusion and hydrodynamic effect of thin water flow.Comment: 11 pages, 5 figures, Late

A microscopic 2D lattice model of dimer granular compaction with friction

We study by Monte Carlo simulation the compaction dynamics of hard dimers in 2D under the action of gravity, subjected to vertical and horizontal shaking, considering also the case in which a friction force acts for horizontal displacements of the dimers. These forces are modeled by introducing effective probabilities for all kinds of moves of the particles. We analyze the dynamics for different values of the time $\tau$ during which the shaking is applied to the system and for different intensities of the forces. It turns out that the density evolution in time follows a stretched exponential behavior if $\tau$ is not very large, while a power law tail develops for larger values of $\tau$. Moreover, in the absence of friction, a critical value $\tau^*$ exists which signals the crossover between two different regimes: for $\tau < \tau^*$ the asymptotic density scales with a power law of $\tau$, while for $\tau > \tau^*$ it reaches logarithmically a maximal saturation value. Such behavior smears out when a finite friction force is present. In this situation the dynamics is slower and lower asymptotic densities are attained. In particular, for significant friction forces, the final density decreases linearly with the friction coefficient. We also compare the frictionless single tap dynamics to the sequential tapping dynamics, observing in the latter case an inverse logarithmic behavior of the density evolution, as found in the experiments.Comment: 10 pages, 15 figures, to be published in Phys. Rev.

Phenomenological glass model for vibratory granular compaction

A model for weakly excited granular media is derived by combining the free volume argument of Nowak et al. [Phys. Rev. E 57, 1971 (1998)] and the phenomenological model for supercooled liquids of Adam and Gibbs [J. Chem. Phys. 43, 139 (1965)]. This is made possible by relating the granular excitation parameter \Gamma, defined as the peak acceleration of the driving pulse scaled by gravity, to a temperature-like parameter \eta(\Gamma). The resulting master equation is formally identical to that of Bouchaud's trap model for glasses [J. Phys. I 2, 1705 (1992)]. Analytic and simulation results are shown to compare favourably with a range of known experimental behaviour. This includes the logarithmic densification and power spectrum of fluctuations under constant \eta, the annealing curve when \eta is varied cyclically in time, and memory effects observed for a discontinuous shift in \eta. Finally, we discuss the physical interpretation of the model parameters and suggest further experiments for this class of systems.Comment: 2 references added; some figure labels tweaked. To appear in PR

Compaction of Rods: Relaxation and Ordering in Vibrated, Anisotropic Granular Material

We report on experiments to measure the temporal and spatial evolution of packing arrangements of anisotropic, cylindrical granular material, using high-resolution capacitive monitoring. In these experiments, the particle configurations start from an initially disordered, low-packing-fraction state and under vertical vibrations evolve to a dense, highly ordered, nematic state in which the long particle axes align with the vertical tube walls. We find that the orientational ordering process is reflected in a characteristic, steep rise in the local packing fraction. At any given height inside the packing, the ordering is initiated at the container walls and proceeds inward. We explore the evolution of the local as well as the height-averaged packing fraction as a function of vibration parameters and compare our results to relaxation experiments conducted on spherically shaped granular materials.Comment: 9 pages incl. 7 figure

Cost effectiveness of thrombolytic therapy with tissue plasminogen activator as compared with streptokinase for acute myocardial infarction

BACKGROUND. Patients with acute myocardial infarction who were treated with accelerated tissue plasminogen activator (t-PA) (given over a period of 1 1/2 hours rather than the conventional 3 hours, and with two thirds of the dose given in the first 30 minutes) had a 30-day mortality that was 15 percent lower than that of pati

Assessment of an antibody-in-lymphocyte supernatant assay for the etiological diagnosis of pneumococcal pneumonia in children

New diagnostic tests for the etiology of childhood pneumonia are needed. We evaluated the antibody-in-lymphocyte supernatant (ALS) assay to detect immunoglobulin (Ig) G secretion from ex vivo peripheral blood mononuclear cell (PBMC) culture, as a potential diagnostic test for pneumococcal pneumonia. We enrolled 348 children with pneumonia admitted to Patan Hospital, Kathmandu, Nepal between December 2015 and September 2016. PBMCs sampled from participants were incubated for 48 h before harvesting of cell culture supernatant (ALS). We used a fluorescence-based multiplexed immunoassay to measure the concentration of IgG in ALS against five conserved pneumococcal protein antigens. Of children with pneumonia, 68 had a confirmed etiological diagnosis: 12 children had pneumococcal pneumonia (defined as blood or pleural fluid culture-confirmed; or plasma CRP concentration ≥60 mg/l and nasopharyngeal carriage of serotype 1 pneumococci), and 56 children had non-pneumococcal pneumonia. Children with non-pneumococcal pneumonia had either a bacterial pathogen isolated from blood (six children); or C-reactive protein <60 mg/l, absence of radiographic consolidation and detection of a pathogenic virus by multiplex PCR (respiratory syncytial virus, influenza viruses, or parainfluenza viruses; 23 children). Concentrations of ALS IgG to all five pneumococcal proteins were significantly higher in children with pneumococcal pneumonia than in children with non-pneumococcal pneumonia. The concentration of IgG in ALS to the best-performing antigen discriminated between children with pneumococcal and non-pneumococcal pneumonia with a sensitivity of 1.0 (95% CI 0.73–1.0), specificity of 0.66 (95% CI 0.52–0.78) and area under the receiver-operating characteristic curve (AUROCC) 0.85 (95% CI 0.75–0.94). Children with pneumococcal pneumonia were older than children with non-pneumococcal pneumonia (median 5.6 and 2.0 years, respectively, p < 0.001). When the analysis was limited to children ≥2 years of age, assay of IgG ALS to pneumococcal proteins was unable to discriminate between children with pneumococcal pneumonia and non-pneumococcal pneumonia (AUROCC 0.67, 95% CI 0.47–0.88). This method detected spontaneous secretion of IgG to pneumococcal protein antigens from cultured PBMCs. However, when stratified by age group, assay of IgG in ALS to pneumococcal proteins showed limited utility as a test to discriminate between pneumococcal and non-pneumococcal pneumonia in children

Spatial linear dark field control and holographic modal wavefront sensing with a vAPP coronagraph on MagAO-X

The Magellan Extreme Adaptive Optics (MagAO-X) Instrument is an extreme AO system coming online at the end of 2019 that will be operating within the visible and near-IR. With state-of-the-art wavefront sensing and coronagraphy, MagAO-X will be optimized for high-contrast direct exoplanet imaging at challenging visible wavelengths, particularly Hα. To enable high-contrast imaging, the instrument hosts a vector apodizing phase plate (vAPP) coronagraph. The vAPP creates a static region of high contrast next to the star that is referred to as a dark hole; on MagAO-X, the expected dark hole raw contrast is ∼4  ×  10  −  6. The ability to maintain this contrast during observations, however, is limited by the presence of non-common path aberrations (NCPA) and the resulting quasi-static speckles that remain unsensed and uncorrected by the primary AO system. These quasi-static speckles within the dark hole degrade the high contrast achieved by the vAPP and dominate the light from an exoplanet. The aim of our efforts here is to demonstrate two focal plane wavefront sensing (FPWFS) techniques for sensing NCPA and suppressing quasi-static speckles in the final focal plane. To sense NCPA to which the primary AO system is blind, the science image is used as a secondary wavefront sensor. With the vAPP, a static high-contrast dark hole is created on one side of the PSF, leaving the opposite side of the PSF unocculted. In this unobscured region, referred to as the bright field, the relationship between modulations in intensity and low-amplitude pupil plane phase aberrations can be approximated as linear. The bright field can therefore be used as a linear wavefront sensor to detect small NCPA and suppress quasi-static speckles. This technique, known as spatial linear dark field control (LDFC), can monitor the bright field for aberrations that will degrade the high-contrast dark hole. A second form of FPWFS, known as holographic modal wavefront sensing (hMWFS), is also employed with the vAPP. This technique uses hologram-generated PSFs in the science image to monitor the presence of low-order aberrations. With LDFC and the hMWFS, high contrast across the dark hole can be maintained over long observations, thereby allowing planet light to remain visible above the stellar noise over the course of observations on MagAO-X. Here, we present simulations and laboratory demonstrations of both spatial LDFC and the hMWFS with a vAPP coronagraph at the University of Arizona Extreme Wavefront Control Laboratory. We show both in simulation and in the lab that the hMWFS can be used to sense low-order aberrations and reduce the wavefront error (WFE) by a factor of 3  −  4  ×  . We also show in simulation that, in the presence of a temporally evolving pupil plane phase aberration with 27-nm root-mean-square (RMS) WFE, LDFC can reduce the WFE to 18-nm RMS, resulting in factor of 6 to 10 gain in contrast that is kept stable over time. This performance is also verified in the lab, showing that LDFC is capable of returning the dark hole to the average contrast expected under ideal lab conditions. These results demonstrate the power of the hMWFS and spatial LDFC to improve MagAO-X’s high-contrast imaging capabilities for direct exoplanet imaging.Instrumentatio

Patterns in random walks and Brownian motion

We ask if it is possible to find some particular continuous paths of unit length in linear Brownian motion. Beginning with a discrete version of the problem, we derive the asymptotics of the expected waiting time for several interesting patterns. These suggest corresponding results on the existence/non-existence of continuous paths embedded in Brownian motion. With further effort we are able to prove some of these existence and non-existence results by various stochastic analysis arguments. A list of open problems is presented.Comment: 31 pages, 4 figures. This paper is published at http://link.springer.com/chapter/10.1007/978-3-319-18585-9_