A model for the packing of irregularly shaped grains

In this paper we will attempt to address the problem of the packing properties of granular materials composed of irregularly shaped grains (using configurational statistical mechanics). In particular, we will develop a model for a system of irregular grains based upon perturbing a packing of mono- or poly-disperse spheres. In the mono-disperse case we will show that the system packs less densely than a packing of perfect spheres, except when local correlations between configurations of grains are taken into account. The opposite is found to be true for a perturbation expansion based upon poly-disperse spheres. Finally we will show that for a bi-disperse packing of spheres phase segregation occurs for any size ratio and discuss whether this is to be expected.     

The statistical mechanics of granular systems composed of elongated grains

In this paper we will suggest a model for the packing properties and phase behaviour of a granular material whose constituents are elongated in nature, using the concepts of configurational statistical mechanics. We will show that, depending upon the shape of the grains, the systems need not necessarily undergo a discontinuous first-order phase transition (even at minimum close packing). We will also briefly discuss the relationship between this model and more conventional models, such as Onsager's hard rod model.     

New high-energy luminescence bands from Co2+ in ZnSe

Three sharp absorption features in the energy range 2.36–2.55 eV have been detected in the transmission spectrum of Co-diffused ZnSe, and a number of luminescence transitions originating from the lowest of these states at 2.361 eV have been observed. Photoluminescence excitation spectra prove that these are high energy excited states of the Co²⁺_Zn impurity, a conclusion confirmed by comparison of measured and predicted luminescence energies. This represents the first identification of luminescence branching from a higher excited state of a transition metal ion in any semiconductor. The sharp, weakly phonon-coupled transitions involve either intra-impurity excitation or transitions from the impurity to localised states split off from a minimum in the conduction band. The implications of these observations for the mechanism of host-impurity energy transfer and for the nature of the excited state wavefunctions are discussed.     

Lower bounds for the clique and the chromatic numbers of a graph

G is any simple graph with m edges and n vertices where these vertices have vertex degrees d(1)≥d(2)≥?≥d(n), respectively. General algorithms for the exact calculation of χ(G), the chromatic number of G, are almost always of ‘branch and bound’ type; this type of algorithm requires an easily constructed lower bound for χ(G). In this paper it is shown that, for a number of such bounds (many of which are described here for the first time), the bound does not exceed cl(G) where cl(G) is the clique number of G.In 1972 Myers and Liu showed that cl(G)≥n?(n?2m?n). Here we show that cl(G)≥ n?[n?(2m?n)(1+c²_v)^{$\text{1}\text{2}$}], where c_v is the vertex degree coefficient of variation in G, that cl(G)≥ Bondy's constructive lower bound for χ(G), and that cl(G)≥n?(n?W(G)), where W(G) is the largest positive integer such that W(G)≤d(W(G)+1) [W(G)+1 is the Welsh and Powell upper bound for χ(G)]. It is also shown that cl(G)+$\text{1}\text{3}$>n?(n?L(G))≥n?(n?λ₁) and that χ(G)≥ n?(n?λ₁); λ₁ is the largest eigenvalue of A, the adjacency matrix of G, and L(G) is a newly defined single-valued function of G similar to W(G) in its construction from the vertex degree sequence of G [L(G)≥W(G)].Finally, a ‘greedy’ lower bound for cl(G) is constructed from A and it is shown that this lower bound is never less than Bondy's bound; thereafter, for 150 random graphs with varying numbers of vertices and edge densities, the values of lower bounds given in this paper are listed, thereby illustrating that this last greedily obtained lower bound is almost always better than each of the other bounds.     

ESR spectra of V4+ ions in the semiconductor V3O7

ESR studies on the semiconductor V₃O₇ reveal the existence of intrinsic paramagnetic V⁴⁺ ions. Computer simulations of spectra suggest that the unpaired electron wavefunction extends over ca. 12–14 lattice sites. This partial delocalization of the wavefunction is assumed to arise from minor crystallographic distortions at low temperatures.     

Alpha-particle inelastic scattering form factors in the Coulomb-nuclear interference region

Alpha-particle scattering cross sections have been measured at 15, 18 and 19 MeV from the ground state and first excited state of ⁵²Cr, ⁵⁶Fe, ⁶⁰Ni and ⁶⁴Zn. Excitation functions have also been measured for inelastic α-scattering from ⁵²Cr and ⁶⁰Ni. The data extends into the forwardangle Coulomb-nuclear interference region. The results are analysed with the optical model and DWBA, using the deformed potential model. The relative and absolute magnitudes of the nuclear and Coulomb deformation parameters and the shapes of the form factors have been deduced from the data. The importance of data in the Coulomb-nuclear interference region in determining these quantities is demonstrated.