Sentences with phrase «of ordinary differential equations»

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.

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.

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.

With respect to solvers, in 1993, he developed the world's fastest ordinary differential equation solver in a three - dimensional model for a given level of accuracy and applied it to atmospheric chemistry.

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.

They implemented ordinary differential equations — a process for describing how things change over time — to improve their ability to infer what these gene relationships might look like and to allow more dynamic simulation of these biological processes over time.

We have built a linear ordinary differential equation (ODE) based model for the kinetics of β - selection in the presence or absence of Itpkb.

Complex nonlinear multivariate systems often exhibit «strange attractors» — local fixed points in a set of coupled nonlinear ordinary differential equations — that function as foci for Poincare cycles in the multivariate phase space.

Such systems occur in numerous domains of physics and can be described by both ordinary and partial differential equations.