In a previous paper we introduced various definitions of stability and instability for non-autonomous differential equations, and applied these to investigate the bifurcations in some simple models. In this paper we present a more systematic theory of local bifurcations in scalar non-autonomous equations.

We analyze the influence of choice of boundary condition (no-slip and Navier’s slip boundary conditions) on linear stability of Hagen–Poiseuille flow. Several heuristic arguments based on detailed analysis of spectrum of the Stokes operator are given, and it is concluded that Navier’s slip boundary condition should have a destabilizing effect on the flow. Finally the linear stability problem is...

The spatially inhomogeneous large N solutions to Kazakov–Migdal model are analyzed. The set of nonlinear differential equations is derived in the continuum limit. In one dimensional case these equations has a natural interpretation in terms of the dynamics of a Fermi gas. The multidimensional case seems to be inconsistent because of its instability related to the collapse of eigenvalues of the ...

A reactive fluid dissolving the surrounding rock matrix can trigger an instability in the dissolution front, leading to spontaneous formation of pronounced channels or wormholes. Theoretical investigations of this instability have typically focused on a steadily propagating dissolution front that separates regions of high and low porosity. In this paper we show that this is not the only possibl...

A weakly nonlinear multiple-scales analysis is performed for singly resonant second-harmonic generation. Coupled amplitude equations are derived that describe pattern formation above the transverse instability threshold. The amplitude equations explain the absence of roll patterns and are in good agreement with numerical results. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 42.65.Sf;...

The stability of the TAP mean field equations is reanalyzed with the conclusion that the exclusive reason for the breakdown at the spin glass instability is an inconsistency for the value of the local susceptibility. The natural requirement of self-consistency leads to modified equations which are in complete agreement with the original ones above the instability. Essentially altered results be...

In this paper a quantum mechanical description of the assembly/disassembly process for microtubules is proposed. We introduce creation and annihilation operators that raise or lower the microtubule length by a tubulin layer. Following that, the Hamiltonian and corresponding equations of motion are derived that describe the dynamics of microtubules. These Heisenberg-type equations are then trans...

The Cross-Newell equations for hexagons and triangles are derived for general real gradient systems, and are found to be in fluxdivergence form. Specific examples of complex governing equations that give rise to hexagons and triangles and which have Lyapunov functionals are also considered, and explicit forms of the Cross-Newell equations are found in these cases. The general nongradient case i...

A combined experimental and numerical study of a Rayleigh-Bénard-Poiseuille air flow in a rectangular channel is presented. The aim of the present paper is to characterize a secondary instability, referred to as wavy instability and known to be a convective instability, with the objective to identify the best situation for an optimal homogenization of heat transfers in the system. A periodic me...