E. I. Tanskanen | Searcharxiv

arXiv2016

One year in the Earth's magnetosphere: A global MHD simulation and spacecraft measurements

The response of the Earth's magnetosphere to changing solar wind conditions are studied with a 3D Magnetohydrodynamic (MHD) model. One full year (155 Cluster orbits) of the Earth's magnetosphere is simulated using Grand Unified Magnetosphere Ionosphere Coupling simulation (GUMICS-4) magnetohydrodynamic code. Real solar wind measurements are given to the code as input to create the longest lasting global magnetohydrodynamics simulation to date. The applicability of the results of the simulation depends critically on the input parameters used in the model. Therefore, the validity and the variance of the OMNIWeb data is first investigated thoroughly using Cluster measurement close to the bow shock. The OMNIWeb and the Cluster data were found to correlate very well before the bow shock. The solar wind magnetic field and plasma parameters are not changed significantly from the $L_1$ Lagrange point to the foreshock, therefore the OMNIWeb data is appropriate input to the GUMICS-4. The Cluster SC3 footprints are determined by magnetic field mapping from the simulation results and the Tsyganenko (T96) model in order to compare two methods. The determined footprints are in rather good agreement with the T96. However, it was found that the footprints agree better in the northern hemisphere than the southern one during quiet conditions. If the By is not zero, the agreement of the GUMICS-4 and T96 footprint is worse in longitude in the southern hemisphere. Overall, the study implies that a 3D MHD model can increase our insight of the response of the magnetosphere to solar wind conditions.

physics.space-ph↗

arXiv2005

How to formulate membrane potential in a spatially homogeneous myocyte model?

Membrane potential in a mathematical model of a cardiac myocyte can be formulated in different ways. Assuming a spatially homogeneous myocyte that is strictly charge-conservative and electroneutral as a whole, two methods will be compared: (1) the differential formulation dV/dt=-I/C_m of membrane potential used traditionally; and (2) the capacitor formulation, where membrane potential is defined algebraically by the capacitor equation V=Q/C_m. We examine the relationship between the formulations, assumptions under which each formulation is consistent, and show that the capacitor formulation provides a transparent, physically realistic formulation of membrane potential, whereas use of the differential formulation may introduce unintended and undesirable behavior, such as monotonic drift of concentrations. We prove that the drift of concentrations in the differential formulation arises as a compensation for failure to assign all currents in concentrations. As an example of these considerations, we present an electroneutral, explicitly charge-conservative formulation of Winslow et al. model (1999), and extend it to describe membrane potentials between intracellular compartments.

q-bio.CB↗