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An integro-ODE-PDE model for Covid-19 pandemic with vaccination and loss of immunity:Well-posedness, RBF-FD numerical scheme and simulation
No full textDuring an epidemic, the way individuals spread the infection can vary depending on the number of days they have been infected. Vaccination is a key factor in the control of the transmission of the pathogen. We propose an SIR-like model to simulate the propagation of a virus in a closed population. The model presents a continuous structure in age of infectivity and in age of immunity. By using a fixed point theorem, we then prove the well-posedness of the model and properties of its solution. Then we present the radial basis function-generated finite difference method, which we use to numerically solve our problem. Finally, numerical simulations are explored to witness the impact of the parameter values in the model.</p
Correction:Extraction of Ta and Nb from a Coltan Bearing Ore by Means of Ammonium Bifluoride Fluorination and Sulfuric Acid Leaching (Minerals, (2021), 11, 12, (1392), 10.3390/min11121392)
No full textThe contact details of the author Alidor Shikika have been updated. The original publication [1] contained a typographical error in the XRD data collection description (radiation source wavelength), and a mistake in the XRD data itself (ABF/ore mass ratio of 3/1) due to a copy–paste error. A correction has been made to Section 2. Materials and Methods, Subsection 2.2. Ore Characterization, second paragraph: The mineral-phase analysis of the ore was carried out by an X-ray Bruker D8-ECO diffractometer with CuKα radiation (λ = 1.54 Å). The sample was pulverized before being scanned between 3 and 90°2θ at a rate of 0.02°2θ per second. In the original publication, there was a mistake in Figure 13 as published. The XRD pattern (b) corresponding to the ABF/ore mass ratio of 3/1 was incorrectly plotted when importing data from the XY file, leading to data misrepresentation. The corrected Figure 13 appears below. The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.</p
Linear-Quadratic optimal control for boundary controlled networks of waves
No full textLinear-quadratic (LQ) optimal controls are computed for a class of boundary controlled, boundary observed hyperbolic infinite-dimensional systems, which may be viewed as networks of waves. The main results of this paper consist in converting the infinite-dimensional continuous-time systems into infinite-dimensional discrete-time systems for which the operators' dynamics are matrices, in solving the LQ-optimal control problem in discrete time, and then in interpreting the solution in the continuous-time variables, giving rise to the optimal boundary control input. The results are applied to two examples, a small network of three vibrating strings and a co-currentheat-exchanger, for which boundary sensors and actuators are considered.Linear-quadratic (LQ) optimal controls are computed for a class of boundary controlled, boundary observed hyperbolic infinite-dimensional systems, which may be viewed as networks of waves. The main results of this paper consist in converting the infinite-dimensional continuous-time systems into infinite-dimensional discrete-time systems for which the operators' dynamics are matrices, in solving the LQ-optimal control problem in discrete time, and then in interpreting the solution in the continuous-time variables, giving rise to the optimal boundary control input. The results are applied to two examples, a small network of three vibrating strings and a co-current heat-exchanger, for which boundary sensors and actuators are considered.</p
