The elastic wave transparency phenomenon of a solid sphere coated with metamaterials is investigated in a solid host medium having nonzero shear modulus. The first three scattering coefficients of the coated sphere are derived in the Rayleigh limit and expressed in terms of the effective parameters of the coated sphere assemblage. It is found that the effective bulk modulus, mass density, and s...

Oakland, MD 21550 The diffraction limit for lensless imaging, defined as the sharpest possible point image obtainable with a pinhole aperture, is analyzed and compared to the corresponding limit for imaging with lenses by means of theoretical considerations and numerical computations using the FresnelLommel diffraction theory for circular apertures. The numerical result (u = p) obtained for the...

We address the stability of multicharged finite systems driven by Coulomb forces beyond the Rayleigh instability limit. Our exploration of the nuclear dynamics of heavily charged Morse clusters enabled us to vary the range of the pair potential and of the fissibility parameter, which results in distinct fragmentation patterns and in the angular distributions of the fragments. The Rayleigh insta...

New types of symmetry for the Rayleigh equation are found. For small Atwood number, an analytic solution is obtained for a smoothly varying density profile. It is shown that a transition layer with a finite width can undergo some kind of stratification. PACS numbers: 47.20.-k, 52.35.Py. e-mail:[email protected] Although Rayleigh had investigated the instability (known now as Rayleigh-Ta...

The Navier-Stokes equation driven by heat conduction is studied. As a prototype we consider Rayleigh-Bénard convection, in the Boussinesq approximation. Under a large aspect ratio assumption, which is the case in Rayleigh-Bénard experiments with Prandtl number close to one, we prove the existence of a global strong solution to the 3D NavierStokes equation coupled with a heat equation, and the e...

High-precision measurements implemented with light are desired in all fields of science. However, light acts as a wave, and the Rayleigh criterion in classical optics yields a diffraction limit that prevents obtaining a resolution smaller than the wavelength. Sub-wavelength interference has potential application in lithography because it beats the classical Rayleigh resolution limit. Here, we c...

We consider a system of hard spheres in thermal equilibrium. Using Lanford's result about the convergence of the solutions of the BBGKY hierarchy to the solutions of the Boltzmann hierarchy, we show that in the low-density limit (Boltzmann-Grad limit): (i) the total time correlation function is governed by the linearized Boltzmann equation (proved to be valid for short times), (ii) the self tim...

In this paper, a gas-kinetic BGK model is constructed for the Rayleigh-Bénard thermal convection in the incompressible flow limit, where the flow field and temperature field are described by two coupled BGK models. Since the collision times and pseudo-temperature in the corresponding BGK models can be different, the Prandtl number can be changed to any value instead of a fixed Pr = 1 in the ori...

We consider the M → 0 limit for tagged particle diffusion in a 1-dimensional Rayleigh-gas, studied originaly by Sinai and Soloveichik [14], respectively by Szász and Tóth [19]. In this limit we derive a new type of model for tagged paricle diffusion, with Calogero-Moser-Sutherland (i.e. inverse quadratic) interaction potential between the two central particles. Computer simulations on this new ...