On the parabolic Stefan problem for Ostwald ripening with kinetic undercooling and inhomogeneous driving force

AbstractOstwald ripening is the coarsening phenomenon caused by the diffusion and solidification process which occurs in the last stage of a first-order phase transformation. The force that drives the system towards equilibrium is the gradient of the chemical potential that, according to the Gibbs–Thomson condition, on the interface, is proportional to its mean curvature. A quantitative description of Ostwald ripening has been developed by the Lifschitz–Slyozov–Wagner (LSW) theory. We extend the work of Niethammer (2000) [15] which deals with kinetic undercooling in the quasi-static case to the parabolic setting with temporally inhomogeneous driving forces on the solid–liquid interfaces. By means of a priori estimates, local and global existence results for the parabolic Stefan problem, we derive a first order approximation for the dynamical equations for the heat distribution and particle radii and then prove the convergence to a limiting description using a mean-field equation

Narrowband Searches for Continuous and Long-duration Transient Gravitational Waves from Known Pulsars in the LIGO-Virgo Third Observing Run

Isolated neutron stars that are asymmetric with respect to their spin axis are possible sources of detectable continuous gravitational waves. This paper presents a fully coherent search for such signals from eighteen pulsars in data from LIGO and Virgo's third observing run (O3). For known pulsars, efficient and sensitive matched-filter searches can be carried out if one assumes the gravitational radiation is phase-locked to the electromagnetic emission. In the search presented here, we relax this assumption and allow both the frequency and the time derivative of the frequency of the gravitational waves to vary in a small range around those inferred from electromagnetic observations. We find no evidence for continuous gravitational waves, and set upper limits on the strain amplitude for each target. These limits are more constraining for seven of the targets than the spin-down limit defined by ascribing all rotational energy loss to gravitational radiation. In an additional search, we look in O3 data for long-duration (hours-months) transient gravitational waves in the aftermath of pulsar glitches for six targets with a total of nine glitches. We report two marginal outliers from this search, but find no clear evidence for such emission either. The resulting duration-dependent strain upper limits do not surpass indirect energy constraints for any of these targets. © 2022. The Author(s). Published by the American Astronomical Society

A finite difference method for the wide-angle "parabolic" equation in a waveguide with downsloping bottom

We consider the third-order wide-angle "parabolic" equation of underwater acoustics in a cylindrically symmetric fluid medium over a bottom of range-dependent bathymetry. It is known that the initial-boundary-value problem for this equation may not be well posed in the case of (smooth) bottom profiles of arbitrary shape, if it is just posed e.g. with a homogeneous Dirichlet bottom boundary condition. In this article, we concentrate on downsloping bottom profiles and propose an additional boundary condition that yields a well-posed problem, in fact making it L2 -conservative in the case of appropriate real parameters. We solve the problem numerically by a Crank-Nicolson-type finite difference scheme, which is proved to be unconditionally stable and second-order accurate and simulates accurately realistic underwater acoustic problems. © 2012 Wiley Periodicals, Inc

Effect of fast-food Mediterranean-type diet on human plasma oxidation

Oxidation of lipoproteins, particularly of low-density lipoprotein (LDL), is of prime importance in the initiation and progression of atherosclerosis. The Mediterranean diet has been associated with an unexpectedly low rate of cardiovascular events. Type 2 diabetic patients are at high risk of developing atherosclerosis. Functional alterations in the endothelium, which lead to atherosclerosis, are stimulated by oxidized lipoproteins, particularly oxidized LDL. The present study investigated the effect of Greek quick casual Mediterranean-type diet (fast food Mediterranean-type diet) consumption on the resistance to oxidation in plasma from type 2 diabetic patients and healthy human subjects. Lipids from fast food Mediterranean-type foodstuffs were extracted and tested in vitro for their ability to inhibit copper (Cu 2+)-induced LDL oxidation. Foodstuffs that exerted the most potent in vitro antioxidative activity were chosen for the diet of study groups. Eighteen type 2 diabetic patients (group A) and 10 healthy subjects (group B) were fed a 4-week diet contained the chosen foodstuffs, while 17 type 2 diabetic patients (group C) were kept on their regular diet that they were following before the study. Type 2 diabetic patients were treated with sulfonylureas or metformin and were under good glycemic control (hemoglobin A1C <7%). Serum lipoproteins, triglycerides, glucose, body mass index (BMI), and plasma resistance to Cu2+-induced oxidation before and after the 4-week diet were monitored. At the beginning of the study, no statistical difference was detected in plasma resistance to Cu2+-induced oxidation between type 2 diabetic patients (groups A and C) and healthy human subjects (group B), as this was detected at a time before the oxidation products become detectable, namely, lag time. After the 4-week period on the chosen diet the lag time in groups A and B significantly increased, while it was not changed in group C. In type 2 diabetic patients lag time was increased from 57.3 ± 13.3 minutes (mean ± SD) to 103.8 ± 21.8 minutes (mean ± SD) (P < .000), while in healthy human subjects there was an increase from 58.0 ± 8.5 minutes (mean ± SD) to 85.7 ± 21.8 minutes (mean ± SD) (P < .004). In all groups, total cholesterol, high-density lipoprotein-cholesterol, LDL-cholesterol, triglycerides, glucose, and BMI were not changed. Fast food Mediterranean foodstuffs exerted antioxidant activities both in vitro and in vivo after consumption in type 2 diabetic patients and healthy human subjects. Therefore consumption of a fast food Mediterranean-type diet should contribute to prevention against cardiovascular diseases. © Mary Ann Liebert, Inc. and Korean Society of Food Science and Nutrition

A finite element discretization of the standard parabolic equation in generalized boundary fitting coordinates

Summarization: A simplified, but quantitatively reliable approximation of atmospheric sound propagation is given by the standard parabolic equation. The waveguide is a cylindrically symmetric, unbounded, domain with an irregular lower boundary. The associated initial-boundary value problem uses a mixed-type boundary condition along the lower boundary and a nonlocal, absorbing boundary condition of the DtN (or NtD) type, applied on an artificial upper boundary. Exterior wave fields of a constant index of refraction and a linear, when squared (as function of height) one, are considered. The physical, complex waveguide reduces to an orthogonal computational domain by the means of a numerical transformation to generalized coordinates, fitting the lower, irregular boundary. The technique presented is of practical interest for its proper handling of complex ground topographies; it is interfaced with a mesh generator and processes the topographic data retrieved from a geographic information system, hence the transformation of coordinates is computed numerically. The transformed initial-boundary value problem (on the orthogonal computational domain) is discretized by the Crank–Nicolson in time and a continuous, piecewise linear finite element method in space. The propagation of cylindrically symmetric sound waves over a complex terrain, emitted to the atmosphere by a harmonic source, has been studied. The effectiveness of the numerical method introduced, is exploited on several test cases.Presented on: Applied Numerical Mathematic