q\bar q pair creation in a flux tube with confinement

We calculate the effect of radial confinement on the Schwinger pair production rate by solving the Dirac equation in a flux-tube cylinder containing a constant chromoelectric field in the longitudinal direction. We show how the Dirac equation separates into radial and longitudinal equations for a mass term which has an arbitrary radial dependence and introduce radial confinement by having a finite mass inside the cylinder and an infinitely large mass outside. The resulting boundary conditions are equivalent to the MIT boundary condition. The equations are solved analytically for a constant quark mass inside the flux-tube, which acts like a waveguide. The discretization of the transverse wave vector which has a continuous spectrum in the non-confined case leads to a large suppression of the Schwinger pair-production rate for small radii. The minimal radius where pairs are created decreases with increasing field strength. The suppression turns out to be larger for heavier quarks than for light quarks.     

Mössbauer study of spin-glass Fe x Zn1−x F2 system

⁵⁷Fe Mössbauer effect measurements in the diluted Ising antiferromagnet Fe _x Zn_1?x F₂ withx=0.25 andx=0.57 at temperatures between 4.2 and 55 K, are reported. DC suceptibility measurements show a spin-glass (SG) phase at low temperatures forx≤0.31. Our Mössbauer spectra show a phase transition to a SG state with antiferromagnetic order (AFSG) forx=0.25 and only antiferromagnetic order forx=0.57.     

Book Reviews

Unsigned book reviews are by the Book Review Editor.     

A Tabu Search Approach for Delivering Pet Food and Flour in Switzerland

In this paper, we consider a real-life vehicle routeing problem that occurs in a major Swiss company producing pet food and flour. In contrast with usual hypothetical problems, a large variety of restrictions has to be considered. The main constraints are relative to the accessibility and the time windows at customers, the carrying capacities of vehicles, the total duration of routes and the drivers' breaks. To find good solutions to this problem, we propose two heuristic methods: a fast straightforward insertion procedure and a method based on tabu search techniques. Next, the produced solutions are compared with the routes actually covered by the company. Our outcomes indicate that the total distance travelled can be reduced significantly when such methods are used.     

Scanning tunnelling microscopic images of the surface ordering of the liquid crystal 4-n-octyl-4'-cyanobiphenyl

Images of the surface ordering of 4-n-octyl-4'-cyanobiphenyl, a room temperature smectic liquid crystal deposited upon graphite, have been obtained by scanning tunnelling microscopy. The microscope was operated in air using the constant-current mode. Under certain tunnelling conditions it has been possible to resolve both the aliphatic and aromatic parts of the molecule, and to observe individual benzene rings. Two previously unreported conformations have been observed: an overlapping bilayer structure with spacing 3.7 nm, and a monolayer structure with spacing 2.4 nm. The latter structure may represent the first visual evidence for a surface polar ordered structure.     

On a Conjecture of Bannai and Ito: There are Finitely Many Distance-regular Graphs with Degree 5, 6 or 7

Bannai and Ito conjectured in a 1987 paper that there are finitely many distance-regular graphs with fixed degree that is greater than two. In a series of papers they showed that their conjecture held for distance-regular graphs with degrees 3 or 4. In this paper we prove that the Bannai–Ito conjecture holds for degrees 5–7.