In the polyspheron theory of nuclear structure,' approximate wave functions for the normal state and some excited states of nuclei are constructed of localized is orbitals occupied by one to four nucleons; a nucleus is described in terms of deuterons, tritons, trelions,2 and helions,3 as well as neutrons and protons not included in these clusters (spherons). In the following paragraphs I point ...

We study theoretically the osmotic equilibria for a shell immersed in a suspension of polyions (e.g., colloids, polyelectrolytes, etc.). The shell is treated as impermeable for polyions, but allowing free diffusion of counterions that permeate inside the shell. From the solution of linearized Poisson-Boltzmann equation, we obtain the distribution of a potential and concentration profiles for po...

A number of recently proposed single-reference open-shell perturbation theories based on a spin-restricted open-shell Hartree-Fock reference function are examined, with an emphasis on a consistent formalism within which the theories may be compared. In particular, the effect of unitary transformations among the molecular orbitals on the energy is discussed. Of the seven different perturbation t...

The objective of this paper is to demonstrate how the asymptotic behavior of a shell structure, as the thickness (t) approaches zero, can be evaluated numerically. We consider three representative shell structural problems; the original Scordelis–Lo roof shell problem, a herein proposed modified Scordelis–Lo roof shell problem and the partly clamped hyperbolic paraboloid shell problem. The asym...

We derive the off-shell scattering matrix for a spherical scatterer. The result obtained generalizes the off-on-shell matrix commonly used in the theory of scalar waves propagation in random media.

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 ...

Using Donnell-type shell theory a simple and exact procedure is presented for linear buckling analysis of functionally graded conical shells under axial compressive loads and external pressure. The solution is in the form of a power series in terms of a particularly convenient coordinate system. By analyzing the buckling of a series of conical shells, under various boundary conditions and diffe...

In a recent feature article in this journal, coauthored by Gert van der Heijden, I described the static-dynamic analogy and its role in understanding the localized post-buckling of shell-like structures, looking exclusively at integrable systems. We showed the true significance of the Maxwell energy criterion load in predicting the sudden onset of “shock sensitivity” to lateral disturbances. Th...

The electronic ground states of the recently synthesized stable nonacene derivatives (J. Am. Chem. Soc. 2010, 132, 1261) are open-shell singlets with a polyradical nature instead of closed-shell singlets as originally assumed, according to the unrestricted broken spin-symmetry density functional theory (UBS-DFT) computations (at B3LYP/6-31G*). It is the bulky protecting groups, not the transfer...