We investigate the influence of the thermal properties of the boundaries in turbulent Rayleigh-Bénard convection on analytical bounds on convective heat transport. Using the Doering-Constantin background flow method, we systematically formulate a bounding principle on the Nusselt-Rayleigh number relationship for general mixed thermal boundary conditions of constant Biot number η which continuou...

Rayleigh scattering generates intensity noise close to an optical carrier that propagates in a single-mode optical fiber. This noise degrades the performance of optoelectronic oscillators and RF-photonic links. When using a broad linewidth laser, we previously found that the intensity noise power scales linearly with optical power and fiber length, which is consistent with guided entropy mode R...

Light scattering and absorption by particles suspended in the atmosphere modifies the transfer of solar energy in the atmosphere, thereby influencing global and regional climate change and atmospheric visibility. Of particular interest are the optical properties of particles in the Rayleigh regime, where particles are small compared with the wavelength of the scattered or absorbed light, becaus...

In this paper we describe a novel method for delivering a precise, known amount of electric charge to a micron-sized solid target. Aerosolised microparticles passed through a plasma discharge will acquire significant electric charge. The fluid stability under evaporative stress is a key aspect that is core to the research. Initially stable charged aerosols subject to evaporation (i.e. a continu...

By methods of modern spectral analysis, we rigorously find distributions of eigenvalues of linearized operators associated with an ideal hydromagnetic Couette-Taylor flow. The transition to instability in the limit of a vanishing magnetic field has a discontinuous change compared to the Rayleigh stability criterion for hydrodynamical flows, which is known as the Velikhov-Chandrasekhar paradox.

We derive Kramers' formula as singular limit of the Fokker-Planck equation with double-well potential. The convergence proof is based on the Rayleigh principle of the underlying Wasser-stein gradient structure and complements a recent result by Peletier, Savaré and Veneroni.

We investigate the near-field inverse scattering problem with evanescent waves. An analytic solution to this problem within the weak-scattering approximation is used to show that the usual Rayleigh limit may be overcome even when measurements are made without phase information. Applications to a novel form of three-dimensional microscopy with subwavelength resolution are described.