Analytic expressions for electron-ion temperature equilibration rates from the Lenard-Balescu equation.

In this work, we elucidate the mathematical structure of the integral that arises when computing the electron-ion temperature equilibration time for a homogeneous weakly coupled plasma from the Lenard-Balescu equation. With some minor approximations, we derive an analytic formula, requiring no input Coulomb logarithm, for the equilibration rate that is valid for moderate electron-ion temperature ratios and arbitrary electron degeneracy. For large temperature ratios, we derive the necessary correction to account for the coupled-mode effect, which can be evaluated very efficiently using ordinary Gaussian quadrature.

Analysis of unstable behavior in a mathematical model for erythropoiesis.

We consider an age-structured model that describes the regulation of erythropoiesis through the negative feedback loop between erythropoietin and hemoglobin. This model is reduced to a system of two ordinary differential equations with two constant delays for which we show existence of a unique steady state. We determine all instances at which this steady state loses stability via a Hopf bifurcation through a theoretical bifurcation analysis establishing analytical expressions for the scenarios in which they arise.

Diffusion and reaction in the cell glycocalyx and the extracellular matrix.

Many biologically important macromolecular reactions are assembled and catalyzed at the cell lipid-surface and thus, the extracellular matrix and the glycocalyx layer mediate transfer and exchange of reactants and products between the flowing blood and the catalytic lipid-surface. This paper presents a mathematical model of reaction-diffusion equations that simply describes the transfer process and explores its influence on surface reactivity for a prototypical pathway, the tissue factor (Tf) pathway of blood coagulation. The progressively increasing friction offered by the matrix and glycocalyx to reactants and to the product (coagulation factors X, VIIa and Xa) approaching the reactive surface is simulated and tested by solving the equations numerically with both, monotonically decreasing and constant diffusion profiles.

A local spectral inversion of a linearized TV model for denoising and deblurring.

In this paper, we propose a model for denoising and deblurring consisting of a system of linear partial differential equations with locally constant coefficients, obtained as a local linearization of the total variation models. The keypoint of our model is to get the local inversion of the Laplacian operator, which will be done via the Fast Fourier Transform (FFT). Two local schemes will be developed: a pointwise and a piecewise one.