We show how the nature of the the phase transition in the two-dimensional bimodal Ising spin glass model can be understood in terms of elementary excitations. Although the energy gap with the ground state is expected to be 4J in the ferromagnetic phase, a gap 2J is in fact found if the finite lattice is wound around a cylinder of odd circumference L. This 2J gap is really a finite size effect that should not occur in the thermodynamic limit of the ferromagnet. The spatial influence of the frustration must be limited and not wrap around the system if L is large enough. In essence, the absence of 2J excitations defines the ferromagnetic phase without recourse to calculating magnetisation or investigating the system response to domain wall defects. This study directly investigates the response to temperature. We also estimate the defect concentration where the phase transition to the spin glass glass state occurs. The value pc = 0.1045(11) is in reasonable agreement with the literature.

New mathematical models are formulated and analytical solutions are presented for the diffusional release of a solute from both non-erodible and biodegradable multi-layered slab matrices in which the initial drug loading c0 is greater than the solubility limit cs. A Stefan problem with moving boundaries results from this formulation. An inward moving diffusional front separates the reservoir (unextracted region) containing the undissolved drug from the partially extracted region. The cumulative mass released is determined as a function of time. The ultimate goal of such an investigation is to provide a reliable design tool for the fabrication of specialized implantable capsule/drug combinations to deliver prespecified and reproducible dosages over a wide spectrum of conditions and required durations of therapeutic treatment. Such a mathematical/computational tool may also prove effective in the prediction of suitable dosages for other drugs of differing chemical or molecular properties without additional elaborate animal testing.

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Abstract.Recently, the National Bureau of Agricultural Commodity and Food Standards (ACFS) have drafted a manual of Thai colour rice standards. However, there are no quantitative descriptions of rice colour and its measurement method. These drawbacks might lead to misunderstanding for people who use the manual. In this work, we proposed an inexpensive method, using flatbed scanning together with image analysis, to quantitatively measure rice colour and colour uniformity. To demonstrate its general applicability for colour differentiation of rice, we applied it to different kinds of pigmented rice, including Riceberry rice with and without uniform colour and Chinese black rice.