Analysis of the effect of inert gas on alveolar/venous blood partial pressure by using the operator splitting method.

This study aims to investigate how inert gas affects the partial pressure of alveolar and venous blood using a fast and accurate operator splitting method (OSM). Unlike previous complex methods, such as the finite element method (FEM), OSM effectively separates governing equations into smaller sub-problems, facilitating a better understanding of inert gas transport and exchange between blood capillaries and surrounding tissue. The governing equations were discretized with a fully implicit finite difference method (FDM), which enables the use of larger time steps. The model employed partial differential equations, considering convection-diffusion in blood and only diffusion in tissue. The study explores the impact of initial arterial pressure, breathing frequency, blood flow velocity, solubility, and diffusivity on the partial pressure of inert gas in blood and tissue. Additionally, the effects of anesthetic inert gas and oxygen on venous blood partial pressure were analyzed. Simulation results demonstrate that the high solubility and diffusivity of anesthetic inert gas lead to its prolonged presence in blood and tissue, resulting in lower partial pressure in venous blood. These findings enhance our understanding of inert gas interaction with alveolar/venous blood, with potential implications for medical diagnostics and therapies.

Taxis-driven complex patterns of a plankton model.

This paper reports an important conclusion that self-diffusion is not a necessary condition for inducing Turing patterns, while taxis could establish complex pattern phenomena. We investigate pattern formation in a zooplankton-phytoplankton model incorporating phytoplankton-taxis, where phytoplankton-taxis describes the zooplankton that tends to move toward the high-densities region of the phytoplankton population. By using the phytoplankton-taxis sensitivity coefficient as the Turing instability threshold, one shows that the model exhibits Turing instability only when repulsive phytoplankton-taxis is added into the system, while the attractive-type phytoplankton-taxis cannot induce Turing instability of the system. In addition, the system does not exhibit Turing instability when the phytoplankton-taxis disappears. Numerically, we display the complex patterns in 1D, 2D domains and on spherical and zebra surfaces, respectively. In summary, our results indicate that the phytoplankton-taxis plays a pivotal role in giving rise to the Turing pattern formation of the model. Additionally, these theoretical and numerical results contribute to our understanding of the complex interaction dynamics between zooplankton and phytoplankton populations.

Estimation and prediction of the multiply exponentially decaying daily case fatality rate of COVID-19.

The spread of the COVID-19 disease has had significant social and economic impacts all over the world. Numerous measures such as school closures, social distancing, and travel restrictions were implemented during the COVID-19 pandemic outbreak. Currently, as we move into the post-COVID-19 world, we must be prepared for another pandemic outbreak in the future. Having experienced the COVID-19 pandemic, it is imperative to ascertain the conclusion of the pandemic to return to normalcy and plan for the future. One of the beneficial features for deciding the termination of the pandemic disease is the small value of the case fatality rate (CFR) of coronavirus disease 2019 (COVID-19). There is a tendency of gradually decreasing CFR after several increases in CFR during the COVID-19 pandemic outbreak. However, it is difficult to capture the time-dependent CFR of a pandemic outbreak using a single exponential coefficient because it contains multiple exponential decays, i.e., fast and slow decays. Therefore, in this study, we develop a mathematical model for estimating and predicting the multiply exponentially decaying CFRs of the COVID-19 pandemic in different nations: the Republic of Korea, the USA, Japan, and the UK. We perform numerical experiments to validate the proposed method with COVID-19 data from the above-mentioned four nations.

An Explicit Adaptive Finite Difference Method for the Cahn-Hilliard Equation.

In this study, we propose an explicit adaptive finite difference method (FDM) for the Cahn-Hilliard (CH) equation which describes the process of phase separation. The CH equation has been successfully utilized to model and simulate diverse field applications such as complex interfacial fluid flows and materials science. To numerically solve the CH equation fast and efficiently, we use the FDM and time-adaptive narrow-band domain. For the adaptive grid, we define a narrow-band domain including the interfacial transition layer of the phase field based on an undivided finite difference and solve the numerical scheme on the narrow-band domain. The proposed numerical scheme is based on an alternating direction explicit (ADE) method. To make the scheme conservative, we apply a mass correction algorithm after each temporal iteration step. To demonstrate the superior performance of the proposed adaptive FDM for the CH equation, we present two- and three-dimensional numerical experiments and compare them with those of other previous methods.