Progress in front propagation research

Abstract

We review the progress in the field of front propagation in recent years. We survey many physical, biophysical and cross-disciplinary applications, including reduced-variable models of combustion flames, Reid's paradox of rapid forest range expansions, the European colonization of North America during the 19th century, the Neolithic transition in Europe from 13 000 to 5000 years ago, the description of subsistence boundaries, the formation of cultural boundaries, the spread of genetic mutations, theory and experiments on virus infections, models of cancer tumors, etc. Recent theoretical advances are unified in a single framework, encompassing very diverse systems such as those with biased random walks, distributed delays, sequential reaction and dispersion, cohabitation models, age structure and systems with several interacting species. Directions for future progress are outlined.

Front Speed of Language Replacement

“…Thus, if for some value of (x; y; t + T ) the result for p(x; y; t + T ) computed from Eq. (4) is larger than p max ; then it is simply replaced by p max [18] (more complex models are sometimes used [17], but they are not necessary here).…”

“…and applying linear analysis for = 1 [18,34] (as in Appendix B above), the front speed is found to be c = 2…”

Effects of punishment in a mobile population playing the prisoner's dilemma game

“…In spite of the number of recent models that take into account migration processes in networks [16,20,[22][23][24], Meloni et al noted that the continuous motion of individuals (in contrast to the discontinuous jump of individuals bound to lattice sites of a grid) was an unexplored situation of practical relevance. It could also be important in several applications, e.g., in designing cooperation-based protocols for wireless devices such as robots [25] and in modeling the dynamics of interacting human populations with different cultural traits, e.g., in prehistoric transitions [26]. Therefore, in this paper we will deal with systems with continuous mobility, as proposed in Ref.…”

Vertical cultural transmission effects on demic front propagation: Theory and application to the Neolithic transition in Europe

“…[13] and [21], respectively (for some recent reviews on these and other models, see Refs. [9,11]). Such models are typically based on the assumption that the Neolithic transition was caused by an invasion of farmers, i.e., by demic diffusion.…”

“…Front propagation models have been applied to many physical, biological, and cross-disciplinary systems, including combustion flames [1], Taylor-Couette and Rayleigh-Bénard experiments [2], superconductors [3], viral infections [4], tumor growth [5], and human invasions [6][7][8][9][10][11][12]. The latter application is considered in this paper, going beyond previous models by taking the role of cultural diffusion into account.…”