Related papers: Analytically Solvable Asymptotic Model of Atrial E…
Excitable membranes are an important type of nonlinear dynamical system and their study can be used to provide a connection between physical and biological circuits. We discuss two models of excitable membranes important in cardiac and…
We extend a non-Tikhonov asymptotic embedding, proposed earlier, for calculation of conduction velocity restitution curves in ionic models of cardiac excitability. Conduction velocity restitution is the simplest nontrivial spatially…
A recent method called Asymptotic Taylor expansion (ATEM) is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrodinger equation for the bistable potentials. Optimal…
We consider a free interface problem which stems from a solid-gas model in combustion with pattern formation. We derive a third-order, fully nonlinear, self-consistent equation for the flame front. Asymptotic methods reveal that the…
In this study, we investigate the dynamics of moving fronts in three-dimensional spaces, which form as a result of in-situ combustion during oil production. This phenomenon is also observed in other contexts, such as various autowave models…
An accurate closed-form solution is obtained to the SIR Epidemic Model through the use of Asymptotic Approximants (Barlow et. al, 2017, Q. Jl Mech. Appl. Math, 70 (1), 21-48). The solution is created by analytically continuing the divergent…
For a particular case of three-body scattering in two dimensions, and matching analytical expressions at a transition point, we obtain accurate solutions for the hyperspherical adiabatic basis and potential. We find analytical expressions…
We present a new approach for physics-based computational modeling of diseased human lungs. Our main object is the development of a model that takes the novel step of incorporating the dynamics of airway recruitment/de-recruitment into an…
Atrial fibrillation is a heart rhythm disorder that affects tens of millions people worldwide. The most effective treatment is catheter ablation. This involves irreversible heating of abnormal cardiac tissue facilitated by electroanatomical…
Our evolving understanding of the heterocellular cardiac environment demands innovative tools for its study. While murine models are lauded for their versatility and accessibility, they are constrained by scale; tools designed for larger…
In [8], asymptotic expansion of the martingale with mixed normal limit was provided. The expansion formula is expressed by the adjoint of a random symbol with coefficients described by the Malliavin calculus, differently from the standard…
This review focuses on the computerized modeling of the electrophysiology of the human atria, emphasizing the simulation of common arrhythmias such as atrial flutter (AFlut) and atrial fibrillation (AFib). Which components of the model are…
Mathematical models of cardiac electrical excitation are increasingly complex, with multiscale models seeking to represent and bridge physiological behaviours across temporal and spatial scales. The increasing complexity of these models…
The mechanism of atrial fibrillation (AF) is poorly understood, resulting in disappointing success rates of ablative treatment. Different mechanisms defined largely by different atrial activation patterns have been proposed and, arguably,…
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
The field of analytic combinatorics, which studies the asymptotic behaviour of sequences through analytic properties of their generating functions, has led to the development of deep and powerful tools with applications across mathematics…
We explore the feasibility of using fast-slow asymptotic to eliminate the computational stiffness of the discrete-state, continuous-time deterministic Markov chain models of ionic channels underlying cardiac excitability. We focus on a…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…
A new variational basis with well-behaved local approximation properties and multiple output is proposed for Coulomb systems. The trial function has proper behaviour at all Coulomb centres. Nonlinear asymptotic parameters are introduced…
Recent research is revealing how cognitive processes are supported by a complex interplay between the brain and the rest of the body, which can be investigated by the analysis of physiological features such as breathing rhythms, heart rate,…