![]() ![]() The scaling is controlled by the stagnation point of the flow. That near the critical value of the Stokes number, Stc, the amount of deposition has the unusual scaling law ofĮxp(-1/(St-Stc)1/2). ![]() Particle inertia is measured by the Stokes number, St. Inertia, below which no point particles deposit. ![]() It is known that particle inertia can drive this deposition, and that there is a critical value of this Instead the particles in the air may deviate from the path of the air and so collide with the surface of When air flows over an obstacle suchĪs an aircraft wing or tree branch, these particles may not follow the same paths as the air flowing around the The Earth’s atmosphere is an aerosol, it contains suspended particles. While results are presented for pulse interaction in the QCGLE, the numerical scheme can also be applied to a wider class of parabolic PDEs. For the case of three pulse interaction a range of dynamics, including chaotic pulse interaction, are found. For the two-pulse problem, cells of periodic behaviour, separated by an infinite set of heteroclinic orbits, are shown to 'split' under perturbation creating complex spiral behaviour. Results are presented here for two-and three-pulse interactions. This fast-slow system is integrated numerically using adaptive time-stepping. With small parameter ϵ = e −λr d 0 where λr is a constant and d0 > 0 is the minimal pulse separation distance, we write the fast-slow system in terms of first-order and second-order correction terms only, a formulation which is solved more efficiently than the full system. This centre-manifold projection overcomes the difficulties of other, more orthodox, numerical schemes, by yielding a fast-slow system describing 'slow' ordinary differential equations for the locations and phases of the individual pulses, and a 'fast' partial differential equation for the remainder function. The scheme is based on a global centre-manifold reduction where one considers the solution of the QCGLE as the composition of individual pulses plus a remainder function, which is orthogonal to the adjoint eigenfunctions of the linearised operator about a single pulse. We formulate an effective numerical scheme that can readily, and accurately, calculate the dynamics of weakly interacting multi-pulse solutions of the quintic complex Ginzburg-Landau equation (QCGLE) in one space dimension. ![]()
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