Several problems of current interest involve elastic bottom range-dependent ocean environments with buried or earthquake-type sources, specifically oceanic T-wave propagation studies and interface wave related analyses. Additionally, observed deep shadow-zone arrivals are not predicted by ray theoretic methods, and attempts to model them with fluid-bottom parabolic equation solutions suggest that it may be necessary to account for elastic bottom interactions. In order to study energy conversion between elastic and acoustic waves, current elastic parabolic equation solutions must be modified to allow for seismic starting fields for underwater acoustic propagation environments. Two types of elastic self-starter are presented. An explosive-type source is implemented using a compressional self-starter and the resulting acoustic field is consistent with benchmark solutions. A shear wave self-starter is implemented and shown to generate transmission loss levels consistent with the explosive source. Source fields can be combined to generate starting fields for source types such as explosions, earthquakes, or pile driving. Examples demonstrate the use of source fields for shallow sources or deep ocean-bottom earthquake sources, where down slope conversion, a known T-wave generation mechanism, is modeled. Self-starters are interpreted in the context of the seismic moment tensor.
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http://dx.doi.org/10.1121/1.4790355 | DOI Listing |
BMC Res Notes
January 2025
Department of Mathematics, Jimma University, Jimma, Ethiopia.
Objective: In this work, singularly perturbed time dependent delay parabolic convection-diffusion problem with Dirichlet boundary conditions is considered. The solution of this problem exhibits boundary layer at the right of special domain. In this layer the solution experiences steep gradients or oscillation so that traditional numerical methods may fail to provide smooth solutions.
View Article and Find Full Text PDFHeliyon
January 2025
Department of Mathematics, Dilla University, Dilla, Ethiopia.
This paper deals with the numerical investigation of a singularly perturbed parabolic differential-difference equation with a time lag. The proposed method comprises the method ( ) and the non-standard finite difference methods for temporal and spatial variable discretization, respectively. Besides, the Richardson extrapolation technique is employed to boost the accuracy and order of convergence of the scheme.
View Article and Find Full Text PDFJ Bioenerg Biomembr
December 2024
Mari State University, pl. Lenina 1, Yoshkar-Ola, Mari El, 424001, Russia.
Cholestasis caused by impaired bile secretion in the liver is associated with the accumulation of primary bile acids (BA): cholic acid (CA) and chenodeoxycholic acid (CDCA) in the cells of this organ. The paper studies the uncoupling effect of the CA and CDCA on the succinate-fueled rat liver mitochondria under conditions of ΔpH to Δψ conversion by nigericin. It has been established that without nigericin, the dependence of the resting-state (state 4) respiration rate on the concentrations of these BA is nonlinear and is described by a parabolic equation.
View Article and Find Full Text PDFJ Evol Equ
December 2024
Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849 USA.
Chemotaxis phenomena govern the directed movement of microorganisms in response to chemical stimuli. In this paper, we investigate two Keller-Segel systems of reaction-advection-diffusion equations modeling chemotaxis on thin networks. The distinction between two systems is driven by the rate of diffusion of the chemo-attractant.
View Article and Find Full Text PDFAppl Math Mod Chall
March 2024
Department of Mathematics University of Southern California Los Angeles CA 90089-2532, USA.
The utility of newly developed wearable biosensors for passively, non-invasively, and continuously measuring transdermal alcohol levels in the body in real time has been limited by the fact that raw transdermal alcohol data does not consistently correlate (quantitatively or temporally) with interpretable metrics of breath and blood across individuals, devices, and the environment. A novel method using a population model in the form of a random abstract hybrid system of ordinary and partial differential equations and linear quadratic tracking control in Hilbert space is developed to estimate blood or breath alcohol concentration from the biosensor-produced transdermal alcohol level signal. Using human subject data in the form of 270 drinking episodes, the method is shown to produce estimates of blood or breath alcohol concentration that are highly correlated and thus good predictors of breath analyzer measurements.
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