Sentences with phrase «nonlinear differential»

You don't really know whether the process is this or that nonlinear differential equation, and you aren't really sure what the distribution of forcing should be, etc..

This, plus the fact that remarkable close simulations of the time series are obtained with a model consisting of a few nonlinear differential equations suggest the intriguing possibility that there are simple rules governing the complex behavior of global paleoclimate.»

They converted those relationships into a coupled pair of nonlinear differential equations.

Not exact matches

Demetrios Christodoulou of ETH Zurich in Switzerland and Richard Hamilton of Columbia University in New York City won the mathematics prize for their work on nonlinear partial differential equations in Lorentzian and Riemannian geometry and their applications to general relativity and topology.

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.

The mathematical methods used by Willi Jaeger are notedly manifold and range from nonlinear partial differential equations to bifurcation theory and optimization to visualization and multi-scale methods.

If one tried to actually write «the» partial differential equation for the global climate system, it would be a set of coupled Navier - Stokes equations with unbelievably nasty nonlinear coupling terms — if one can actually include the physics of the water and carbon cycles in the N - S equations at all.

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.

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.

The equations that describe it are the Navier - Stokes equations, which are nonlinear partial differential equations so complex that mathematicians haven't even been able to prove that a solution exists in the general case, let alone solve it.