Implementation of the Six PDE model

2022 ◽  
pp. 41-82
Author(s):  
William E. Schiesser
Keyword(s):  
Pde Model

Comparison of Two Models for Prediction of Seismic Streamer State Using the Ensemble Kalman Filter

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Jan Vidar Grindheim ◽  
Inge Revhaug ◽  
Egil Pedersen ◽  
Peder Solheim
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Petroleum Exploration ◽  
Drift Angle ◽  
Pde Model ◽  
Survey Line ◽  
Position Data ◽  
Position Prediction ◽  
Increasing Demand ◽  
Marine Seismic

Towed marine seismic streamers are extensively utilized for petroleum exploration. With the increasing demand for efficiency, leading to longer and more densely spaced streamers, as well as four-dimensional (4D) surveys and more complicated survey configurations, the demand for optimal streamer steering has increased significantly. Accurate streamer state prediction is one important aspect of efficient streamer steering. In the present study, the ensemble Kalman filter (EnKF) has been used with two different models for data assimilation including parameter estimation followed by position prediction. The data used are processed position data for a seismic streamer at the very start of a survey line with particularly large cable movements due to currents. The first model is a partial differential equation (PDE) model reduced to two-dimensional (2D), solved using a finite difference method (FDM). The second model is based on a path-in-the-water (PIW) model and includes a drift angle. Prediction results using various settings are presented for both models. A variant of the PIW method gives the overall best results for the present data.

PDE Model with External Transfer

2020 ◽  
pp. 49-70
Author(s):  
William E. Schiesser
Keyword(s):  
Pde Model

scholarly journals Analysis of an HTLV/HIV dual infection model with diffusion

2021 ◽  
Vol 18 (6) ◽  
pp. 9430-9473
Author(s):  
A. M. Elaiw ◽  
◽  
N. H. AlShamrani ◽  
◽  
Keyword(s):  
Lyapunov Functions ◽  
Global Solutions ◽  
Dual Infection ◽  
Steady States ◽  
Infection Model ◽  
Well Posedness ◽  
Pde Model ◽  
Existence And Stability ◽  
Infected Cells ◽  
Theoretical Results

<abstract><p>In the literature, several HTLV-I and HIV single infections models with spatial dependence have been developed and analyzed. However, modeling HTLV/HIV dual infection with diffusion has not been studied. In this work we derive and investigate a PDE model that describes the dynamics of HTLV/HIV dual infection taking into account the mobility of viruses and cells. The model includes the effect of Cytotoxic T lymphocytes (CTLs) immunity. Although HTLV-I and HIV primarily target the same host, CD$ 4^{+} $T cells, via infected-to-cell (ITC) contact, however the HIV can also be transmitted through free-to-cell (FTC) contact. Moreover, HTLV-I has a vertical transmission through mitosis of active HTLV-infected cells. The well-posedness of solutions, including the existence of global solutions and the boundedness, is justified. We derive eight threshold parameters which govern the existence and stability of the eight steady states of the model. We study the global stability of all steady states based on the construction of suitable Lyapunov functions and usage of Lyapunov-LaSalle asymptotic stability theorem. Lastly, numerical simulations are carried out in order to verify the validity of our theoretical results.</p></abstract>

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