Sentence examples for by a diffusion equation from inspiring English sources

We approximate commodity flows in these networks by a diffusion equation, with nonlinearities introduced to model capacity limits.

It is shown that the mixing in the longitudinal direction can be described by a diffusion equation.

The dynamics of the magnetization are described by the Landau Lifshitz Gilbert equation, while the dynamics of the spin are described by a diffusion equation with discontinuous coefficients.

In this theory, fluid flow is described by a diffusion equation that can be derived from Eqs. (11), (12) and (30) in their paper: (1) where ϕ, Ks, Kf, pf, t, K, and η denote the porosity, bulk moduli of the solid and fluid phases, respectively, fluid pressure, time, permeability and fluid-phase viscosity, respectively (Suzuki and Yamashita, 2006).

Morphogen gradient formation can be modelled by a diffusion equation where C x) is morphogen concentration at distance x from the production zone, v is effective morphogen secretion rate, w is width of the production zone, a is cell diameter, k is degradation rate and D is effective morphogen diffusion coefficient (Kicheva et al, 2007; Lander, 2007).

This restoring force is akin to a harmonic potential centered around x − 0 and the stochastic dynamics is equivalently described by a diffusion equation for the probability distribution P x0, τ), ∂ ∂ τ P (z, τ ) = 1 2 N s ∂ 2 ∂ z 2 z P (z, τ ) − α ∂ ∂ z (1 − z / z − ) z P (z, τ ), (18 where we have denoted x0 by z for simplicity.

The key idea is to steepen the interface, independently of the underlying volume-fraction transport equation, by solving a diffusion equation with reverse time, i.e. an anti-diffusion equation, after each advection time step of the volume fraction.

By treating light as particles and with sufficient scatter, optical diffusion tomography (ODT) allows for deep-tissue imaging by using a diffusion equation to describe the spatially dependent optical properties [ 11– 13].

The complex skin depth is related to the surface impedance by p= Z/iωμ 0. A diffusion equation for E y can be derived from Maxwell's equations (Hermance and Peltier 1970), in Cartesian coordinates: nabla^{2} E_{y} = {text{i}}omega mu_{o} sigma E_{y}, (3)where (nabla^{2} = frac{{partial^{2} }}{{partial x^{2} }} + frac{{partial^{2} }}{{partial z^{2} }}).

In a theoretical section, we show that the assumption that soil particles follow parabolic trajectories when splashed by raindrop impacts leads to a diffusion equation.

This gradient is represented not by an explicit diffusion equation, but parametrically, by a function that decreases nonlinearly from a maximal value at the distal tip and in which the tip value itself decreases nonlinearly with time (see File S2).