arXiv subjects

Radostin D. Simitev

Publications and source records attributed to Radostin D. Simitev.

25 records · Page 2Linked to original sources

arXiv2015

Mathematical Modelling of Heart Rate Changes in the Mouse

The CVS is composed of numerous interacting and dynamically regulated physiological subsystems which each generate measurable periodic components such that the CVS can itself be presented as a system of weakly coupled oscillators. The interactions between these oscillators generate a chaotic blood pressure waveform signal, where periods of apparent rhythmicity are punctuated by asynchronous behaviour. It is this variability which seems to characterise the normal state. We used a standard experimental data set for the purposes of analysis and modelling. Arterial blood pressure waveform data was collected from conscious mice instrumented with radiotelemetry devices over $24$ hours, at a $100$ Hz and $1$ kHz time base. During a $24$ hour period, these mice display diurnal variation leading to changes in the cardiovascular waveform. We undertook preliminary analysis of our data using Fourier transforms and subsequently applied a series of both linear and nonlinear mathematical approaches in parallel. We provide a minimalistic linear and nonlinear coupled oscillator model and employed spectral and Hilbert analysis as well as a phase plane analysis. This provides a route to a three way synergistic investigation of the original blood pressure data by a combination of physiological experiments, data analysis viz. Fourier and Hilbert transforms and attractor reconstructions, and numerical solutions of linear and nonlinear coupled oscillator models. We believe that a minimal model of coupled oscillator models that quantitatively describes the complex physiological data could be developed via such a method. Further investigations of each of these techniques will be explored in separate publications.

q-bio.TO↗

arXiv2015

Dynamo Effects Near The Transition from Solar to Anti-Solar Differential Rotation

Numerical MHD simulations play increasingly important role for understanding mechanisms of stellar magnetism. We present simulations of convection and dynamos in density-stratified rotating spherical fluid shells. We employ a new 3D simulation code for the solution of a physically consistent anelastic model of the process with a minimum number of parameters. The reported dynamo simulations extend into a "buoyancy-dominated" regime where the buoyancy forcing is dominant while the Coriolis force is no longer balanced by pressure gradients and strong anti-solar differential rotation develops as a result. We find that the self-generated magnetic fields, despite being relatively weak, are able to reverse the direction of differential rotation from anti-solar to solar-like. We also find that convection flows in this regime are significantly stronger in the polar regions than in the equatorial region, leading to non-oscillatory dipole-dominated dynamo solutions, and to concentration of magnetic field in the polar regions. We observe that convection has different morphology in the inner and at the outer part of the convection zone simultaneously such that organized geostrophic convection columns are hidden below a near-surface layer of well-mixed highly-chaotic convection. While we focus the attention on the buoyancy-dominated regime, we also demonstrate that conical differential rotation profiles and persistent regular dynamo oscillations can be obtained in the parameter space of the rotation-dominated regime even within this minimal model.

astro-ph.SR↗

arXiv2014

Quasi-geostrophic approximation of anelastic convection

The onset of convection in a rotating cylindrical annulus with parallel ends filled with a compressible fluid is studied in the anelastic approximation. Thermal Rossby waves propagating in the azimuthal direction are found as solutions. The analogy to the case of Boussinesq convection in the presence of conical end surfaces of the annular region is emphasized. As in the latter case the results can be applied as an approximation for the description of the onset of anelastic convection in rotating spherical fluid shells. Reasonable agreement with three-dimensional numerical results published by Jones et al. (J. Fluid Mech., vol. 634, 2009, pp. 291-319) for the latter problem is found. As in those results the location of the onset of convection shifts outward from the tangent cylinder with increasing number $N_ρ$ of density scale heights until it reaches the equatorial boundary. A new result is that at a much higher number $N_ρ$ the onset location returns to the interior of the fluid shell.

physics.flu-dyn↗

arXiv2013

Proceedings of the 2013 UK National Conference on Geophysical, Astrophysical and Industrial Magnetohydrodynamics at Glasgow

This document presents an accurate record of the scientific programme of the 2013 UK National Conference on Geophysical, Astrophysical and Industrial Magnetohydrodynamics held on 23rd and 24th of May 2013 at the School of Mathematics and Statistics of the University of Glasgow. The abstracts of presented contributions are listed in chronological order and a full list of participants and their affiliations is included.

physics.flu-dyn↗

arXiv2011

Solar cycle properties described by simple convection-driven dynamos

Simple models of magnetic field generation by convection in rotating spherical shells exhibit properties resembling those observed on the sun. The {assumption of the Boussinesq approximation made in these models} prevents a realistic description of the solar cycle, but through a physically motivated change in the boundary condition for the differential rotation the propagation of dynamo waves towards higher latitudes can be reversed at least at low latitudes.

astro-ph.SR↗

arXiv2007

Asymptotic analysis and analytical solutions of a model of cardiac excitation

We describe an asymptotic approach to gated ionic models of single-cell cardiac excitability. It has a form essentially different from the Tikhonov fast-slow form assumed in standard asymptotic reductions of excitable systems. This is of interest since the standard approaches have been previously found inadequate to describe phenomena such as the dissipation of cardiac wave fronts and the shape of action potential at repolarization. The proposed asymptotic description overcomes these deficiencies by allowing, among other non-Tikhonov features, that a dynamical variable may change its character from fast to slow within a single solution. The general asymptotic approach is best demonstrated on an example which should be both simple and generic. The classical model of Purkinje fibers (Noble, 1962) has the simplest functional form of all cardiac models but according to the current understanding it assigns a physiologically incorrect role to the Na current. This leads us to suggest an ``Archetypal Model'' with the simplicity of the Noble model but with a structure more typical to contemporary cardiac models. We demonstrate that the Archetypal Model admits a complete asymptotic solution in quadratures. To validate our asymptotic approach, we proceed to consider an exactly solvable ``caricature'' of the Archetypal Model and demonstrate that the asymptotic of its exact solution coincides with the solutions obtained by substituting the ``caricature'' right-hand sides into the asymptotic solution of the generic Archetypal Model. This is necessary, because, unlike in standard asymptotic descriptions, no general results exist which can guarantee the proximity of the non-Tikhonov asymptotic solutions to the solutions of the corresponding detailed ionic model.

q-bio.TO↗

arXiv2005

Conditions for propagation and block of excitation in an asymptotic model of atrial tissue

Detailed ionic models of cardiac cells are difficult for numerical simulations because they consist of a large number of equations and contain small parameters. The presence of small parameters, however, may be used for asymptotic reduction of the models. Earlier results have shown that the asymptotics of cardiac equations are non-standard. Here we apply such a novel asymptotic method to an ionic model of human atrial tissue in order to obtain a reduced but accurate model for the description of excitation fronts. Numerical simulations of spiral waves in atrial tissue show that wave fronts of propagating action potentials break-up and self-terminate. Our model, in particular, yields a simple analytical criterion of propagation block, which is similar in purpose but completely different in nature to the `Maxwell rule' in the FitzHugh-Nagumo type models. Our new criterion agrees with direct numerical simulations of break-up of re-entrant waves.

physics.bio-ph↗