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D. Blackmore

Publications and source records attributed to D. Blackmore.

4 recordsLinked to original sources

"Solutocapillary Marangoni flow induced in waterbody by solute source"

The aim of this paper is to experimentally and analytically study the solutocapillary flow induced in a waterbody due to the presence of a solute source on its surface and the mixing induced by this flow of the solutes and gases dissolved at and near the surface into the waterbody. According to the analytic solution, the induced flow is analogous to a doublet flow in the sense that the flow is directed towards the source within a conical region with its vertex at the source, and outside the conical region the flow moves away from the source. The half cone angle for a negative source increases from $\sim$60 degrees with increasing source strength and Schmidt number reaching values greater than 80 degrees. When the cone angle is large, the outflow is restricted to a thin annular boundary layer region. These analytic results are in agreement with our experimental data obtained by the PIV (Particle Image Velocimetry) and PLIF (planar laser-induced fluorescence) techniques. As the solute gradient at the surface gives rise to the force that drives the flow, when the solute diffusion coefficient is reduced the flow becomes stronger and persists longer because the solute gradient is maintained for a longer time and distance. In experiments, the flow changes direction into the waterbody and the surface flow stops when the solute induced surface tension gradient driving the flow becomes comparable to the surface tension gradients that exist on the surface due to temperature gradients.

physics.flu-dyn

The integrable heavenly type equations and their Lie-algebraic structure

There are investigated the Lie algebraic structure and integrability properties of a very interesting class of nonlinear dynamical systems called the heavenly equations, which were initiated by Plebański and later analyzed in a series of articles. Based on the AKS-algebraic and related R-structure schemes there are studied orbits of the corresponding co-adjoint actions, deeply related with the classical Lie-Poisson type structures on them. There is successively demonstrated that their compatibility condition proves to coincide exactly with the corresponding heavenly equation under regard. It is stated that all the heavenly equations allow such an origin and can be equivalently represented as a Lax type compatibility condition for specially built loop vector fields on the torus. The infinite hierarchy of conservations laws, related with the heavenly equations is discussed, its analytical structure, connected with the Casimir invariants is mentioned. In addition, the typical examples of the heavenly equations, demonstrating in details their integrability within the scheme devised in the work, are presented. The Lagrangian representation of the heavenly equations following from their Hamiltonicity with respect to both related commuting to each other evolution flows, as well as their associated bi-Hamiltonian structure are also discussed. The relationship of the heavenly type dynamical ssytems with the classical Lagrange-d'Alambert principle is demonstrated.

nlin.SI

A new exactly solvable spatially one-dimensional quantum superradiance fermi-medium model and its quantum solitonic states

A new exactly solvable spatially one-dimensional quantum superradiance model describing a charged fermionic medium interacting with an external electromagnetic field is proposed. The infinite hierarchy of quantum conservation laws and many-particle Bethe eigenstates that model quantum solitonic impulse structures are constructed. The Hamilton operator renormalization procedure subject to a physically stable vacuum is described, the quantum excitations and quantum solitons, related to the thermodynamical equilibrity of the model, are discussed.

cond-mat.stat-mech