From the cell cycle to circadian rhythms, oscillatory processes are fundamental to biology. Emerging from nonlinear dynamical interactions, oscillatory mechanisms are best understood through mathematical modeling. Ordinary differential equations (ODEs) are one framework in which the complex interactions giving rise to biological oscillations may be modeled. Key to ODE models are the model param...

We consider the integration of one-dimensional highly oscillatory functions. Based on analytic continuation, rapidly converging quadrature rules are derived for a fairly general class of oscillatory integrals with an analytic integrand. The accuracy of the quadrature increases both for the case of a fixed number of points and increasing frequency, and for the case of an increasing number of poi...

The purpose of this paper is to present an indirect boundary integral method for the oscillatory Stokes flow provided by the translational oscillations of two rigid spheres in an incompressible Newtonian fluid of infinite expanse. 1. Introduction. The study of oscillatory Stokes flows has a key role in the understanding of the biomechanics of blood flow, the Brownian motion, the motion of swimm...

We discuss efficient solutions to systems of shifted linear systems arising in computations for oscillatory hydraulic tomography (OHT). The reconstruction of hydrogeological parameters such as hydraulic conductivity and specific storage, using limited discrete measurements of pressure (head) obtained from sequential oscillatory pumping tests, leads to a nonlinear inverse problem. We tackle this...

The onset of double diffusive convection in a binary viscoelastic fluid saturated porous layer, which is heated and salted from below in the presence of Soret effect is studied using both linear and nonlinear stability analyses. The linear theory is being related to the normal mode method. The modified Darcy law for the viscoelastic fluid of the Oldroyd type is used to model the momentum equati...

Quantifying similarities and differences between neural response patterns is an important step in understanding neural coding in sensory systems. It is difficult, however, to compare the degree of similarity among transient oscillatory responses. We developed a novel method of wavelet correlation analysis for quantifying similarity between transient oscillatory responses, and tested the method ...