Nanostructured materials are a new class of materials which provide one of the greatest potentials for improving performance and extended capabilities of products in a number of industrial sectors, including the aerospace, tooling, automotive, electronic, recording, cosmetics, electric motor, duplication, and refrigeration industries. Encompassed by this class of materials are multilayers, nano...

The nonrelativistic problem of a particle immersed in a triangular potential well, set forth by N. A. Rao and B. A. Kagali, is revised. It is shown that these researchers misunderstood the full meaning of the potential and obtained a wrong quantization condition. By exploring the space inversion symmetry, this work presents the correct solution to this problem with potential applications in ele...

We study the bound state spectrum and the conditions for entering a supercritical regime in graphene with strong intrinsic and Rashba spin-orbit interactions within the topological insulator phase. Explicit results are provided for a disk-shaped potential well and for the Coulomb center problem.

In this paper, the equations of motion for geodesics in the neutral rotating Black Ring metric are derived and the separability of these equations is considered. The bulk of the paper is concerned with sets of solutions where the geodesic equations can be examined analytically specifically geodesics confined to the axis of rotation, geodesics restricted to the equatorial plane, and geodesics th...

We describe a simple numerical simulation, suitable for an undergraduate project (or graduate problem set), of the Brownian motion of a particle in a Hooke-law potential well. Understanding this physical situation is a practical necessity in many experimental contexts, for instance in single molecule biophysics; and its simulation helps the student to appreciate the dynamical character of therm...

The amount and nature of the evolution of the X-ray properties of clusters of galaxies provides information on the formation of structure in the universe and on the properties of the universe itself. The cluster luminosity temperature relation does not evolve strongly, suggesting that the hot X-ray gas had a more complicated thermodynamic history than simply collapsing into the cluster potentia...

New redshift surveys of galaxies in the field of compact groups have discovered a population of faint galaxies which act as satellites orbiting in the potential well of the bright group. Here we analyze the mass distribution of the groups by comparing the mass derived from the bright members and the mass obtained from the satellite galaxies. Our analysis indicates the presence of a dark halo ar...

For a class of semilinear parabolic equations, we prove both global existence and finite-time blow-up depending on the initial datum. The proofs involve tools from the potential-well theory, from the criticalpoint theory, and from classical comparison principles.