The effect of phase-matched third-harmonic generation on the structure and stability of spatial solitary waves is investigated. A power threshold for the existence of two-frequency spatial solitons is found, and the multistability of solitary waves in a Kerr medium owing to a higher-order nonlinear phase shift caused by cascaded third-order processes is revealed.

Infectious disease incidence data are increasingly available at the level of the individual and include high-resolution spatial components. Therefore, we are now better able to challenge models that explicitly represent space. Here, we consider five topics within spatial disease dynamics: the construction of network models; characterising threshold behaviour; modelling long-distance interaction...

The spatial distribution information of clay layer occurrence depth (CLOD), particularly the spatial distribution maps of occurrence of clay layers at depths less than a certain threshold, in alluvial soils is crucial to designing appropriate plans and measures for precision agriculture and environmental management in alluvial plains. Markov chain geostatistics (MCG), which was proposed recentl...

A spatial time series dataset is a collection of time series, each referencing a location in a common spatial framework. Correlation analysis is often used to identify pairs of potentially interacting elements from the cross product of two spatial time series datasets. However, the computational cost of correlation analysis is very high when the dimension of the time series and the number of lo...

We describe a nonlinear optical system that supports spiral pattern solutions in the field intensity. This new spatial structure is found to bifurcate above a secondary instability in the internally pumped optical parametric oscillator. The analytical predictions of threshold and spatial scale for the instability are supplemented by detailed numerical investigations of the formation of spiral p...