Equilibrium properties of disordered spin models with two-scale interactions

Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely connected structure, have become well understood. Many features generalize to sparse Erdös- Rényi graph structures above the percolation threshold and to Bethe lattices when appropriate boundary conditions apply. In this paper, we consider spin states subject to a combination of sparse strong interactions with weak dense interactions, which we term a composite model. The equilibrium properties are examined through the replica method, with exact analysis of the high-temperature paramagnetic, spin-glass, and ferromagnetic phases by perturbative schemes. We present results of replica symmetric variational approximations, where perturbative approaches fail at lower temperature. Results demonstrate re-entrant behaviors from spin glass to ferromagnetic phases as temperature is lowered, including transitions from replica symmetry broken to replica symmetric phases. The nature of high-temperature transitions is found to be sensitive to the connectivity profile in the sparse subgraph, with regular connectivity a discontinuous transition from the paramagnetic to ferromagnetic phases is apparent.

Molecular architecture influences on material properties of pharmaceutical compounds

Salt formation has extensively been studied as a strategy to improve drug solubility but it has not been explored as a strategy to improve mechanical properties. A better understanding of which factors of the solid state can have an influence in the mechanical properties of pharmaceutical powders can help to optimise and reduce cost of tablet manufacturing. The aim of this study was to form different series of amine salts of flurbiprofen, gemfibrozil and diclofenac and to establish predictive relationships between architectural characteristics and physicochemical and mechanical properties of the salts. For this purpose, three different carboxylic acid drugs were selected: flurbiprofen, gemfibrozil and diclofenac, similar in size but varying in flexibility and shape and three different series of counterions were also chosen: one with increasing bulk and no hydroxyl groups to limit the hydrogen bonding potential; a second one with increasing number of hydroxyl groups and finally a third series, related to the latter in number of hydroxyl groups but with different molecular shape and flexibility. Physico-chemical characterization was performed (DSC, TGA, solubility, intrinsic dissolution rate, particle size, true density) and mechanical properties measured using a compaction replicator. Strained molecular conformations produce weaker compacts as they have higher energy than preferred conformations that usually lie close to energy minimums and oppose plastic deformation. It was observed that slip planes, which correspond to regions of weakest interaction between the planes, were associated with improved plasticity and stronger compacts. Apart from hydrogen bonds, profuse van der Waals forces can result in ineffective slip planes. Salts displaying two-dimensional densely hydrogen bonded layers produced stronger compacts than salts showing one-dimensional networks of non-bonded columns, probably by reducing the attachment energy between layers. When hydrogen bonds are created intramolecularly, it is possible that the mechanical properties are compromised as they do not contribute so much to create twodimensional densely bonded layers and they can force molecules into strained conformations. Some types of hydrogen bonding network may be associated with improved mechanical properties, such as type II, or R (10) 3 4 using graph-set notation, versus type III, or R (12) 4 8 , columns. This work clearly demonstrates the potential of investigating crystal structure-mechanical property relationship in pharmaceutical materials.

Typical case behaviour of spin systems in random graph and composite ensembles

This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm. The algorithm can be formulated in the large system limit as a branching process, for which critical properties can be analysed. Far from the critical point a set of differential equations may be used to model the process, and these are solved by numerical integration and exact bounding methods. The multi-access channel problem is formulated as an equilibrium statistical physics problem for the case of bit transmission on a channel with power control and synchronisation. A sparse code division multiple access method is considered and the optimal detection properties are examined in typical case by use of the replica method, and compared to detection performance achieved by interactive decoding methods. These codes are found to have phenomena closely resembling the well-understood dense codes. The composite model is introduced as an abstraction of canonical sparse and dense disordered spin models. The model includes couplings due to both dense and sparse topologies simultaneously. The new type of codes are shown to outperform sparse and dense codes in some regimes both in optimal performance, and in performance achieved by iterative detection methods in finite systems.