Michael I. Tribelsky

Anomalous light absorption by small particles

Light absorption by a spatially uniform spherical nanoparticle in the vicinity of surface plasmon (polariton) resonances is studied in detail based on the exact Mie solution. It is shown that the maximal absorption is achieved for a particle from weakly dissipating materials and may have very unusual properties. A simple universal formula describing the resonant absorption lineshape as a function of the particle size and its complex dielectric permittivity is obtained. Possible comparison with experiment is discussed.

Giant in-particle field concentration and Fano resonances at light scattering by high-refractive-index particles

The work of AEM was supported by the Australian Research Council via Future Fellowship program (Grant No. FT110100037).

Laser Pulse Heating of Spherical Metal Particles

We consider the general problem of laser pulse heating of spherical metal particles with the sizes ranging from nanometers to millimeters. We employ the exact Mie solution of the diffraction problem and solve the heat-transfer equation to determine the maximum temperature rise at the particle surface as a function of optical and thermometric parameters of the problem. Primary attention is paid to the case when the thermal diffusivity of the particle is much larger than that of the environment, as it is in the case of metal particles in fluids. We show that, in this case, for any given duration of the laser pulse, the maximum temperature rise as a function of the particle size reaches a maximum at a certain finite size of the particle. We suggest simple approximate analytical expressions for this dependence, which cover the entire parameter range of the problem and agree well with direct numerical simulations.

Fano Resonances: A Discovery that Was Not Made 100 Years Ago

Scattering: We have missed the presence of resonant scattering behavior in the Rayleigh region for years, but a clue was lurking in quantum theory.

The ultimate absorption at light scattering by a single obstacle

Based on fundamental properties of the light scattering by a particle under a plane, linearly polarized wave illumination, we rigorously prove the existence of the ultimate upper limit for the light absorption by any partial mode and calculate this limit explicitly. The limit is a certain simple universal function of the incident light wave number, and the multipolarity of the corresponding partial mode solely. It does not depend on the optical constants of the scatterer, its size, or even its shape. First, we obtain this result for the scattering by a spherical particle. Then, we generalize it to an arbitrary finite obstacle. The results are valid for any polarization of the incident wave, any angle of its incidence, and any type of the scatterer (homogeneous, stratified, or with smoothly variable refractive index). We also prove that the maximal partial absorption cross section for any finite scatterer cannot exceed the corresponding value for a homogeneous sphere in 3D and circular cylinder in 2D. As an example, the results are applied to maximize the absorption cross section of a spherical core-shell structure.

Predictability of Market Prices

The dynamics of actual market prices is analyzed based upon the theory of dynamical chaos. It is shown that the dynamics is typical for that of chaotic dynamical systems. A number of particular examples (exchange rates USD vs. JPY, XAU vs. USD, oil, etc.) is considered in detail. The topological structure of the corresponding strange attractors is reconstructed. It allows predicting the price dynamics in future with high accuracy. The main advantage of the approach is that, as long as the forecast period lies below the so-called prediction horizon, the prediction error does not increase in the course of time.

Hydrodynamic Waves in Regions with Smooth Loss of Convexity of Isentropes: General Phenomenological Theory

A general phenomenological theory of hydrodynamic waves in regions with smooth loss of convexity of isentropes is developed, based on the fact that for most media these regions in the p-V plane are anomalously small. Accordingly the waves are usually weak and can be described in the manner analogous to that for weak shock waves of compression. The corresponding generalized Burgers equation is derived and analyzed. The exact solution of the equation for steady shock waves of rarefaction is obtained and discussed.

New type of turbulence, or how symmetry results in chaos

Pattern formation and transition to chaos in a macroscopic dissipative system is discussed. It is supposed that the system has a continuous family of spatially uniform states, which can be transformed into each other by a certain symmetry transformation. If such a system undergoes instability against spatially periodic perturbations with a finite wavenumber, interplay of short-wavelength modes associated with the instability and long-wavelengths modes generated by the symmetry transformation affects the dynamics of the system dramatically. In particular, it may result in direct transition from a spatially uniform state to spatiotemporal chaos, analogous to second order phase transition in equilibrium systems. The obtained results may be applied to kinetic of polymerization, to reaction-diffusion problems, to flame propagation, to some hydrodynamic problems, etc.

Universal Defect Dynamics in Two-Dimensional Convective Roll Patterns.

The process of annihilation of two point defects with opposite topological charges in a roll pattern is discussed for electrohydrodynamic convection in a nematic layer. It is shown that at the final stage of the process the distance between the centers of defects which are being annihilated varies as the square root of the time, down-counted from the annihilation moment. Such a scaling is associated with topological properties of the slowly varying complex amplitude of the order parameter and is suggested as a generic law for annihilation or spontaneous, barrierless nucleation of pairs of defects in extended systems. Experimental evidence of the scaling in the case of electrohydrodynamic convection in MBBA is obtained.