Eigenvalue Problem in Two Dimension for An Irregular Boundary

An analytical perturbative method is suggested for solving the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0 in two dimensions where {\psi} vanishes on an irregular closed curve. We can thus find the energy levels of a quantum mechanical particle confined in an infinitely deep potential well in two dimensions having an irregular boundary or the vibration frequencies of a membrane whose edge is an irregular closed curve. The method is tested by calculating the energy levels for an elliptical and a supercircular boundary and comparing with the results obtained numerically. Further, the phenomenon of level crossing due to shape variation is also discussed.Comment: 16 pages, 4 figures, v2 matches the journal versio

A Meta-Analysis of the Existing Knowledge of Immunoreactivity against Hepatitis C Virus (HCV)

Approximately 3% of the world population is infected by HCV, which represents a major global health challenge. Almost 400 different scientific reports present immunological data related to T cell and antibody epitopes derived from HCV literature. Analysis of all HCV-related epitope hosted in the Immune Epitope Database (IEDB), a repository of freely accessible immune epitope data, revealed more than 1500 and 1900 distinct T cell and antibody epitopes, respectively. The inventory of all data revealed specific trends in terms of the host and the HCV genotypes from which sequences were derived. Upon further analysis we found that this large number of epitopes reflects overlapping structures, and homologous sequences derived from different HCV isolates. To access and visualize this information we developed a novel strategy that assembles large sets of epitope data, maps them onto reference genomes and displays the frequency of positive responses. Compilation of the HCV immune reactivity from hundreds of different studies, revealed a complex and thorough picture of HCV immune epitope data to date. The results pinpoint areas of more intense reactivity or research activities at the level of antibody, CD4 and CD8 responses for each of the individual HCV proteins. In general, the areas targeted by the different effector immune functions were distinct and antibody reactivity was positively correlated with hydrophilicity, while T cell reactivity correlated with hydrophobicity. At the sequence level, epitopes frequently recognized by both T cell and B cell correlated with low variability, and our analysis thus highlighted areas of potential interest for practical applications. The human reactivity was further analyzed to pinpoint differential patterns of reactivity associated with acute versus chronic infection, to reveal the apparent impact of glycosylation on T cell, but not antibody responses, and to highlight a paucity of studies involved antibody epitopes associated with virus neutralization

Effect of Supplementation with Zinc and Other Micronutrients on Malaria in Tanzanian Children: A Randomised Trial

Hans Verhoef and colleagues report findings from a randomized trial conducted among Tanzanian children at high risk for malaria. Children in the trial received either daily oral supplementation with either zinc alone, multi-nutrients without zinc, multi-nutrients with zinc, or placebo. The investigators did not find evidence from this study that zinc or multi-nutrients protected against malaria episodes

Genetic variability of hepatitis C virus before and after combined therapy of interferon plus ribavirin

We present an analysis of the selective forces acting on two hepatitis C virus genome regions previously postulated to be involved in the viral response to combined antiviral therapy. One includes the three hypervariable regions in the envelope E2 glycoprotein, and the other encompasses the PKR binding domain and the V3 domain in the NS5A region. We used a cohort of 22 non-responder patients to combined therapy (interferon alpha-2a plus ribavirin) for which samples were obtained before initiation of therapy and after 6 or/and 12 months of treatment. A range of 25-100 clones per patient, genome region and time sample were sequenced. These were used to detect general patterns of adaptation, to identify particular adaptation mechanisms and to analyze the patterns of evolutionary change in both genome regions. These analyses failed to detect a common adaptive mechanism for the lack of response to antiviral treatment in these patients. On the contrary, a wide range of situations were observed, from patients showing no positively selected sites to others with many, and with completely different topologies in the reconstructed phylogenetic trees. Altogether, these results suggest that viral strategies to evade selection pressure from the immune system and antiviral therapies do not result from a single mechanism and they are likely based on a range of different alternatives, in which several different changes, or their combination, along the HCV genome confer viruses the ability to overcome strong selective [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]

INTER-ACT: prevention of pregnancy complications through an e-health driven interpregnancy lifestyle intervention – study protocol of a multicentre randomised controlled trial

Abstract Background Excessive maternal pre-pregnancy and gestational weight gain are related to pregnancy- and birth outcomes. The interpregnancy time window offers a unique opportunity to intervene in order to acquire a healthy lifestyle before the start of a new pregnancy. Methods INTER-ACT is an e-health driven multicentre randomised controlled intervention trial targeting women at high risk of pregnancy- and birth related complications. Eligible women are recruited for the study at day 2 or 3 postpartum. At week 6 postpartum, participants are randomised into the intervention or control arm of the study. The intervention focuses on weight, diet, physical activity and mental well-being, and comprises face-to-face coaching, in which behavioural change techniques are central, and use of a mobile application, which is Bluetooth-connected to a weighing scale and activity tracker. The intervention is rolled out postpartum (4 coaching sessions between week 6 and month 6) and in a new pregnancy (3 coaching sessions, one in each trimester of pregnancy); the mobile app is used throughout the two intervention phases. Data collection includes data from the medical record of the participants (pregnancy outcomes and medical history), anthropometric data (height, weight, waist- and hip circumferences, skinfold thickness and body composition by bio-electrical impedance analysis), data from the mobile app (physical activity and weight; intervention group only) and questionnaires (socio-demographics, breastfeeding, food intake, physical activity, lifestyle, psychosocial factors and process evaluation). Medical record data are collected at inclusion and at delivery of the subsequent pregnancy. All other data are collected at week 6 and month 6 postpartum and every subsequent 6 months until a new pregnancy, and in every trimester in the new pregnancy. Primary outcome is the composite endpoint score of pregnancy-induced hypertension, gestational diabetes mellitus, caesarean section, and large-for-gestational-age infant in the subsequent pregnancy. Discussion INTER-ACT is a unique randomised controlled lifestyle intervention trial in its implementation between pregnancies and during the subsequent pregnancy, with an e-health driven approach. Trial registration ClinicalTrials.gov Identifier: NCT02989142 . Registered August 2016

MILES • Numbers in brackets indicate References at end of paper. Presented at the Tenth International Congress of Applied Me-chanics

WE CONSIDER here the free oscillations of an annular cylinder of an inviscid liquid contained in a rotating (about its axis) cylindrical tank of radius a and height h and having an inner, free surface of (equilibrium) radius b. We shall assume that the gravitational acceleration (if any) is negligible compared with the centripetal acceleration and that the equilibrium configuration of the liquid is a rigid-body rotation. The problem described here arises in connection with the motion of fuel in a spinning rocket. Related problems are presented by a liquid-filled top The Eigenvalue Problem Let (r, 6, z) be a set of cylindrical polar co-ordinates rotating with the angular velocity co about the z-axis, (u, v, w) the corresponding components of relative velocity, p the perturbation pressure, and p the density of the liquid. The equations of small motion then are « is an acceleration potential that satisfies We seek solutions for (u, v, w, p) Journal of Applied Mechanics at the tank walls and that correspond to an oscillatory displacement of the free surface, say r = 6 + i?(0, z, t). The kinematic and dynamic boundary conditions at this free surface are u = JJ, and p = 0. (6a, 6) We may assume an oscillatory solution to (l)- where <r denotes the angular frequency (in the rotating co-ordinate system; the angular frequency for a fixed observer is a -rrua), m and n are integers, f(r) must satisfy the (modified) Bessel equation and It then remains to satisfy the boundary conditions (4a) and (6a, 6). Letting r = 6 + t) in (7d), assuming |?)| b, and invoking Differentiating (11) with respect to t, eliminating ??, through (6a) and (7a), and multiplying the result by 4/<j 2 yields The investigation of the free oscillations is now reduced to the following eigenvalue problem: find those values of the parameter DECEMBER 1 9 6 1 / 491 Copyright © 1961 by ASME H for which the differential equation Two-Dimensional Oscillations The simplest of all special cases is two-dimensional motion, for which n -0. A solution to (8) then is given by Substituting Three-Dimensional Oscillations The more general, three-dimensional, solution can be expressed in terms of Bessel functions (cf. Given preassigned values of m, a, (3, and an assumed (i.e., guessed) value of fx, say fi", we integrate the ordinary first-order = 0 (20a) differential equation and proceed by iteration until y n agrees with n" to the required accuracy. The selection of the initial guess, /Ko, is based on the results of the two-dimensional motion [see where The result (27) is derived in Appendix 1 and displayed in Discussion of the Results A given tank is characterized by its inner radius 6, outer radius a, and depth h or, more conveniently, by the dimensionless ratios b/a and A/26; a given mode is characterized by the integers m (number of 0-nodes), n (number of z-nodes), and p (number of r-nodes). The motions between any two z-nodes are, however, essentially identical and depend only on the effective depth ratio h/2nh, rather than on /i/26 and n independently. We therefore may describe our results in terms of the four dimensionless parameters b/a, h/2nb, m, and p. We may prescribe b/a and h/2nb arbitrarily (except that 0 < b/a < 1) and choose any integral value for in, say m = 0, ±1, ±2, . . . (the restriction to integral values of m is a consequence of the requirement that the motion be periodic in 6); there then exist two infinite sets of eigenvalues u and corresponding frequencies a for each triplet of b/a, h/2nb, and m-namely, two eigenvalues for each p = 0, 1, 2, ... . The reader might find it interesting to compare this state of affairs with that for a nonrotating cylindrical tank under the influence of gravity. The fact that radial nodes (at which the radial velocity vanishes) are possible for free surface oscillations on a rotating liquid and that the two frequencies for a given nodal pattern differ in magnitude as well as sign are both consequences of the Coriolis force. Neither of these phenomena would be possible under the influence of centrifugal force alone. If we were to ignore the Coriolis accelerations 2wv and 2un in the equations of motion (la, b) we would have to replace (96) by The solutions of (8) then would involve only the nonoscillatory Bessel functions /", and K m , radial nodes would be impossible, and the two eigenvalues for given b/a, h/2nb, and m would differ only in sign. The distributions of velocity for typical modes without and with radial nodes with h/2nb = 1, b/a = 0.6, and m = 1 are illustrated in Let us now consider the behavior of the eigenvalue n as a function of the geometric and modal parameters, bearing in mind that the corresponding natural frequency a is inversely proportional to p. We shall restrict our discussion to m = ±1 (changing the sign of m only interchanges the positive and negative values of p), but we remark that increasing m does not necessarily increase the natural frequency. We also emphasize that |?re| = 1 is by far the most important case in practice, since only such modes are excited by rigid-body, transverse motions of the tank, all modes with \m\ T* 1 being orthogonal to the mode \m\ = 1. The dependence of p on n, the number of z-nodes is especially simple: the eigenvalue p decreases monotonically, and hence the frequency increases monotonically with n. Journal of Applied Mechanic

The longitudinal static stability of an aerodynamically alleviated marine vehicle, a mathematical model

An assessment of the relative speeds and payload capacities of airborne and waterborne vehicles highlights a gap that can be usefully filled by a new vehicle concept, utilizing both hydrodynamic and aerodynamic forces. A high- speed marine vehicle equipped with aerodynamic surfaces is one such concept. In 1904, Bryan & Williams (Bryan & Williams 1904 Proc. R. Soc. Lond. 73, 100-116 (doi: 10.1098/rspl.1904.0017)) published an article on the longitudinal dynamics of aerial gliders, and this approach remains the foundation of all the mathematical models studying the dynamics of airborne vehicles. In 1932, Perring & Glauert (Perring & Glauert 1932 Reports and Memoranda no. 1493) presented a mathematical approach to study the dynamics of seaplanes experiencing the planing effect. From this work, planing theory has developed. The authors propose a unified mathematical model to study the longitudinal stability of a high-speed planing marine vehicle with aerodynamic surfaces. A kinematics framework is developed. Then, taking into account the aerodynamic, hydrostatic and hydrodynamic forces, the full equations of motion, using a small perturbation assumption, are derived and solved specifically for this concept. This technique reveals a new static stability criterion that can be used to characterize the longitudinal stability of high-speed planing vehicles with aerodynamic surfaces