Recovery of a quarkonium system from experimental data

For confining potentials of the form q(r)=r+p(r), where p(r) decays rapidly and is smooth for r>0, it is proved that q(r) can be uniquely recovered from the data {E_j,s_j}, where E_j are the bound states energies and s_j are the values of u'_j(0), and u_j(r) are the normalized eigenfunctions of the problem -u_j" +q(r)u_j=E_ju_j, r>0, u_j(0)=0, ||u_j||=1, where the norm is L^2(0, \infty) norm. An algorithm is given for recovery of p(r) from few experimental data

Whittaker-Hill equation and semifinite-gap Schroedinger operators

A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by applying Darboux transformations to the Whittaker-Hill equation. We give a criterion of the regularity of the corresponding potentials and investigate the spectral properties of the new operators.Comment: Revised versio

Convergence of expansions in Schr\"odinger and Dirac eigenfunctions, with an application to the R-matrix theory

Expansion of a wave function in a basis of eigenfunctions of a differential eigenvalue problem lies at the heart of the R-matrix methods for both the Schr\"odinger and Dirac particles. A central issue that should be carefully analyzed when functional series are applied is their convergence. In the present paper, we study the properties of the eigenfunction expansions appearing in nonrelativistic and relativistic $R$-matrix theories. In particular, we confirm the findings of Rosenthal [J. Phys. G: Nucl. Phys. 13, 491 (1987)] and Szmytkowski and Hinze [J. Phys. B: At. Mol. Opt. Phys. 29, 761 (1996); J. Phys. A: Math. Gen. 29, 6125 (1996)] that in the most popular formulation of the R-matrix theory for Dirac particles, the functional series fails to converge to a claimed limit.Comment: Revised version, accepted for publication in Journal of Mathematical Physics, 21 pages, 1 figur

Nature-Inspired Interconnects for Self-Assembled Large-Scale Network-on-Chip Designs

Future nano-scale electronics built up from an Avogadro number of components needs efficient, highly scalable, and robust means of communication in order to be competitive with traditional silicon approaches. In recent years, the Networks-on-Chip (NoC) paradigm emerged as a promising solution to interconnect challenges in silicon-based electronics. Current NoC architectures are either highly regular or fully customized, both of which represent implausible assumptions for emerging bottom-up self-assembled molecular electronics that are generally assumed to have a high degree of irregularity and imperfection. Here, we pragmatically and experimentally investigate important design trade-offs and properties of an irregular, abstract, yet physically plausible 3D small-world interconnect fabric that is inspired by modern network-on-chip paradigms. We vary the framework's key parameters, such as the connectivity, the number of switch nodes, the distribution of long- versus short-range connections, and measure the network's relevant communication characteristics. We further explore the robustness against link failures and the ability and efficiency to solve a simple toy problem, the synchronization task. The results confirm that (1) computation in irregular assemblies is a promising and disruptive computing paradigm for self-assembled nano-scale electronics and (2) that 3D small-world interconnect fabrics with a power-law decaying distribution of shortcut lengths are physically plausible and have major advantages over local 2D and 3D regular topologies

Photometric variability of candidate white dwarf binary systems from Palomar Transient Factory archival data

We present a sample of 59 periodic variables from the Palomar Transient Factory, selected from published catalogues of white dwarf (WD) candidates. The variability can likely be attributed to ellipsoidal variation of the tidally distorted companion induced by the gravity of the primary (WD or hot subdwarf) or to the reflection of hot emission by a cooler companion. We searched 11311 spectroscopically or photometrically selected WD candidates from three hot star/WD catalogues, using the Lomb-Scargle periodogram to single out promising sources. We present period estimates for the candidates, 45 of which were not previously identified as periodic variables, and find that most have a period shorter than a few days. Additionally, we discuss the eclipsing systems in our sample and present spectroscopic data on selected sources

Vortex structure in exponentially shaped Josephson junctions

We report the numerical calculations of the static vortex structure and critical curves in exponentially shaped long Josephson junctions for in-line and overlap geometries. Each solution of the corresponding boundary value problem is associated with the Sturm-Liouville problem whose minimal eigenvalue allows to make a conclusion about the stability of the vortex. The change in width of the junction leads to the renormalization of the magnetic flux in comparison to the case of a linear one-dimensional model. We study the influence of the model's parameters and, particularly, the shape parameter on the stability of the states of the magnetic flux. We compare the vortex structure and critical curves for the in-line and overlap geometries. Our numerically constructed critical curve of the Josephson junction matches well with the experimental one.Comment: 8 pages, 10 figures, NATO Advanced Research Workshop on "Vortex dynamics in superconductors and other complex systems" Yalta, Crimea, Ukraine, 13-17 September 200