~!T7T€p KaL TO lcupeVEW Kat T6 vyu.f~ew of! TO Ttj-tvew ~ j-t~ TSj-tV€W ~ cpapj-taKdmv ~ j-t~ cpapj-taKeVm • trJ"Tlv, d.A.A.a T?! woi. J OHN Dewey, "the most profound and understanding thinker on education that the world has yet known" (Ernest C. Moore), has said repeatedly that mankind so far has been ruled by things and by words, not by thought. Humanity has not been in possession of the cond...

Naturally, deformed rocks commonly contain crack arrays (joints) forming patterns with systematic relationships to the large-scale deformation. Kinematically, joints can be mode-1, -2 or -3 or combinations of these, but there is no overarching theory for the development of the patterns. We develop a model motivated by dislocation pattern formation in metals. The problem is formulated in one dim...

We extend the mechanism for noise-induced phase transitions proposed by Ibañes et al. [Phys. Rev. Lett. 87, 020601 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this mechanism is not driven by a short-time instability amplified by collective effects. The phenomenon is analyzed by means of a modulated mean field approximation ...

We analyze pattern formation in doubly resonant intracavity second-harmonic generation in the presence of competing nondegenerate parametric downconversion. We show that for positive cavity detuning of the fundamental frequency the threshold for parametric oscillation is lower than that of transverse, pattern forming instabilities. The parametric oscillation strongly modifies the pattern dynami...

There has been an apparent increase in the frequency and duration of El Niño–Southern Oscillation events in the last two decades relative to the prior period of record. Furthermore, 1990–95 was the longest period of sustained high Darwin sea level pressure in the instrumental record. Variations in the frequency and duration of such events are of considerable interest because of their implicatio...

We investigate the impact of cyclic competition on pattern formation in the rock-paper-scissors game. By separately considering random and prepared initial conditions, we observe a critical influence of the competition rate p on the stability of spiral waves and on the emergence of biodiversity. In particular, while increasing values of p promote biodiversity, they may act detrimentally on spat...

We present a comprehensive study of pattern formation in single-field relaxational systems with field-dependent coefficients. A modulated mean-field theory leads to a form amenable to analysis via the geometric architecture developed in our earlier work for systems that exhibit phase transitions between global steady states [Phys. Rev. E 69, 011102 (2004)]. We demonstrate that the phase diagram...