On the other hand, distributing the entire residual by an upwind scheme provides second-order accuracy; however, such an approach is unstable for diffusion dominated problems, since residual distribution schemes are characterized by undamped modes associated with the discretization of the diffusive fluctuation.
(1.21) However, if the unstable nonlinear diffusion operator is of fourth order, as in Delta^{3} u pm u + Delta^{2} bigl(|u|^{p-1}ubigr)=0 quad mbox{in }mathbb{R}^{N}, (1.22) we again arrive at the 'second-order' Sobolev range as in (1.10).
In this paper, we are concerned with the output regulation of an unstable reaction-diffusion PDE with regulator delay and unmatched disturbances, which are generated by an exosystem.
Measurements and numerical simulations considered freely (outwardly -propagating spherical laminar premixed flames at boutwardly -propagatinge preferential-diffusphericalitions with fuelaminaralence ratios in the range 0.45–4.00, premixeds in the range 0.35–4.00 atm, volumetric oxygen concentrations in the nonflamesat in the range 0.125–0.210, and Karlovitz numboth in the range 0.0–0.6.
Application of the method to one-dimensional two-phase flow of falling particles particles confirms that the equations are stable with and unstable without artificial diffusion in the volume fraction equation.
Markstein numbers were in the range −1 to 6, with unstable (stable) preferential-diffusion conditions observed at fuel-equivalence ratios below (above) roughly 0.7.
The occurrence of a Turing instability means that a solution which is stable in the absence of diffusion becomes unstable when diffusion is incorporated in the system.
Chaotic dynamical systems possess the following main characteristics: sensitivity to tiny changes in initial conditions, random-like behavior, ergodicity, unstable periodic orbits, desired diffusion and confusion properties, and one-way property.
One possible rationale for localizing biosynthetic enzymes is to limit diffusion of unstable or harmful reaction intermediates.
Turing instability arises when a spatially homogeneous equilibrium is asymptotically stable in the absence of diffusion and becomes unstable when diffusion is added to the model [ 25].
Or, on contrary, is identity diffusion a manifestation of unstable relationships, and consequently, of unstable inner representations of self- and object relations, which undermine the sense of self-sameness, which BPD patients suffer from?
