Sentences with phrase «on ordinary differential equations»

In this study, researchers constructed a mathematical model, based on ordinary differential equations, linking the different molecular processes associated with spine expansion together.

Not exact matches

Ordinary differential equations typically apply when several variables are a function of time, while partial differential equations get used when a variable is dependent on both time and space, says Michael Reed, a professor of mathematics at Duke University who applies mathematics to physiology and medicine.

The framework is based on solving nonlinear coupled ordinary and partial differential equations that model the kinetics of the following phenomena: (1) mass transport in the electrolyte and electrode using the Nernst - Planck equation; (2) electrical potential distribution using the Poisson equation; (3) interfacial reactions that determine the boundary conditions or source terms (using the Butler - Volmer equation or constant - flux conditions); and (4) evolution of the electrode / electrolyte interface using the Allen - Cahn equation within the phase - field modeling (PFM) approach.

We develop systems of ordinary differential equations to address the generic features of the initial phase of spheroid formation and an agent - based three - dimensional computational model to focus on spatial differences in the process.

In a system such as the climate, we can never include enough variables to describe the actual system on all relevant length scales (e.g. the butterfly effect — MICROSCOPIC perturbations grow exponentially in time to drive the system to completely different states over macroscopic time) so the best that we can often do is model it as a complex nonlinear set of ordinary differential equations with stochastic noise terms — a generalized Langevin equation or generalized Master equation, as it were — and average behaviors over what one hopes is a spanning set of butterfly - wing perturbations to assess whether or not the resulting system trajectories fill the available phase space uniformly or perhaps are restricted or constrained in some way.