The study of the relativistic dynamics of thin shells of matter is a current subject of investigation when the framework of general relativity is adopted [1, 2, 3, 4]. Here, we will explore how the framework of special relativity can produce a law of motion which can be compared with expansion data of a supernova remnant (SNR). From a classical point of view, the temporal evolution of the SNR i...

Abstract We investigate norms of spectral projectors on thin spherical shells for the Laplacian generic tori, including rectangular tori. state a conjecture and partially prove it, improving previous results concerning arbitrary

Through acoustic scattering theory we derive the mass density and bulk modulus of a spherical shell that can eliminate scattering from an arbitrary object in the interior of the shell--in other words, a 3D acoustic cloaking shell. Calculations confirm that the pressure and velocity fields are smoothly bent and excluded from the central region as for previously reported electromagnetic cloaking ...

In 1947, Lehmer conjectured that the Ramanujan τ -function τ(m) never vanishes for all positive integers m, where the τ(m) are the Fourier coefficients of the cusp form ∆24 of weight 12. Lehmer verified the conjecture in 1947 for m < 214928639999. In 1973, Serre verified up to m < 10, and in 1999, Jordan and Kelly for m < 22689242781695999. The theory of spherical t-design, and in particular th...

The linear force-free field of a plasma in between spherical shells is found allowing for inhomogeneous boundary conditions. A three-dimensional solution is found by analysis and used as a benchmark to test a solution in terms of an expansion of eigenfunctions where the coefficients are determined by a new method. Alternative methods are also applied in the context of the spherical shell exampl...

We theoretically and numerically analyze thermal invisibility based on the concept of scattering cancellation and mantle cloaking. We show that a small object can be made completely invisible to heat diffusion waves, by tailoring the heat conductivity of the spherical shell enclosing the object. This means that the thermal scattering from the object is suppressed, and the heat flow outside the ...

Spherical PbSe@SiO2 nanoparticles have been successfully synthesized within reverse micelles via metal alkoxide hydrolysis and condensation within a microemulsion system. These core-shell nanoparticles were characterized by transmission electron microscopy (TEM), NIR absorption spectroscopy, energy-dispersive X-ray analysis, and TEM electron diffractions. It shows that the obtained core-shell s...

New experimental results on 43S and 44S reveal that these nuclei are located in a transitional region of prolate-spherical shape coexistence between the spherical 48Ca and the oblate 42Si. The origin of the deformation is discussed in terms of the evolution of the single particle energy levels leading to the compression of the orbitals in the sd and p f shells for protons and neutrons, respecti...

We investigate the localization of charged particles by the image potential of spherical shells, such as fullerene buckyballs. These spherical image states exist within surface potentials formed by the competition between the attractive image potential and the repulsive centripetal force arising from the angular motion. The image potential has a power law rather than a logarithmic behavior. Thi...