Order parameter equations for front transitions: Planar and circular fronts

Abstract

Near a parity breaking front bifurcation, small perturbations may reverse the propagation direction of fronts. Often this results in nonsteady asymptotic motion such as breathing and domain breakup. Exploiting the time scale differences of an activator-inhibitor model and the proximity to the front bifurcation, we derive equations of motion for planar and circular fronts. The equations involve a translational degree of freedom and an order parameter describing transitions between left and right propagating fronts. Perturbations, such as a space dependent advective field or uniform curvature (axisymmetric spots), couple these two degrees of freedom. In both cases this leads to a transition from stationary to oscillating fronts as the parity breaking bifurcation is approached. For axisymmetric spots, two additional dynamic behaviors are found: rebound and collapse.

Dissipative solitons

“…A natural generalization of the one-component r-d equation in one spatial dimension is the extension to two or three spatial dimensions [496,497,546,554]. The corresponding equation is given by…”

“…We also mention the works [26,30,76,363,502,506,509,[544][545][546][547]. For further insight into the behaviour of front solutions of (37) we make the ansatz u ¼ u() with ¼ x À ct and c as a constant.…”

Order parameter equations for front transitions: Nonuniformly curved fronts

“…We are interested in solutions of Eqns (19) at long times where they become independent of the fast time scale t: ∂v (n) /∂t → 0 as t → ∞. For n = 1, the stationary solution of (19) with the asymptotic condition (24) is [28] v (1)…”

The β[sup +] decay of [sup 37]K as a multi-faceted probe of fundamental physics

“…Although the calculation of the phase space factor depends on Q 5 and so is very sensitive to uncertainties in the Q value, this is known to ±0.003% [20] in 37 Ka nd so does not limit the calculation of its ft value. The ground state branching ratio -t he one of interest in this work -i s known to ±0.14% [21] which is still small compared to the precision with which the half-life is currently known: ±0.6% [22]; it is the half-life which currently limits the precision of the ft-value of this decay.…”