Sentence examples for travelling front from inspiring English sources
The phrase "travelling front" is not standard in written English and may cause confusion.
It could be used in contexts discussing the forefront of travel or advancements in travel technology, but it is not commonly recognized. Example: "The travelling front of the tourism industry is constantly evolving with new technologies and experiences."
In [8], Gourley considered the existence of travelling front solutions and their qualitative form for equation (1.2).
To test the generalized multi-symplectic scheme, several numerical experiments on the travelling front solution are carried out, the results of which imply that the generalized multi-symplectic scheme can simulate the travelling front solution accurately and satisfy the modified conservation laws well when step sizes and the damping parameter satisfy the inequality (41).
For travelling front solutions, in a system with exponentially decaying spatial interactions, we make use of an interface approach to calculate the instantaneous wave speed analytically as a series expansion in the noise strength.
For a symmetric choice of synaptic kernel (w(x)=w vert xvert )), which decays exponentially, the one-dimensional model (3) with a constant threshold is known to support a travelling front solution [22, 23] that connects a high activity state to a low activity state.
Instance of a travelling front (blue) for the bump distribution.
As regards travelling fronts the work of Bressloff and Webber [9] has shown that this can result in 'fast' perturbations of the front shape as well as a 'slow' horizontal displacement of the wave profile from its uniformly translating position.
Moreover, by working with the Heaviside choice, as in (1), we will be able to build on the interface approach of Amari [21] to obtain explicit results for travelling fronts and bumps, and their dependence on the threshold noise structure.
It is shown that, when the spectrum of oscillations contains a pronounced second subharmonic (nonlinear response of the photochemical system to diurnal variations of solar radiation), reaction-diffusion waves in the form of travelling fronts and pulses of the phase of two-day oscillations may be excited in this region of the atmosphere.
In [3], the authors established the existence of positive travelling fronts for N-dimensional delayed reaction diffusion systems.
In this paper we have explored the role of threshold noise on travelling fronts and bumps in a simple neural field model with a Heaviside nonlinearity.
