Abstract. We show that any collection of n-dimensional orbifolds with sectional curvature and volume uniformly bounded below, diameter bounded above, and with only isolated singular points contains orbifolds of only finitely many orbifold homeomorphism types. This is a generalization to the orbifold category of a similar result for manifolds proven by Grove, Petersen, and Wu. It follows that any Laplace isospectral collection of orbifolds with sectional curvature uniformly bounded below and having only isolated singular points also contains only finitely many orbifold homeomorphism types. The main steps of the argument are to show that any sequence from the collection has subsequence that converges to an orbifold, and then to show that the homeomorphism between the underlying spaces of the limit orbifold and an orbifold from the subsequence that is guaranteed by Perelman's stability theorem must preserve orbifold structure.

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Abstract. We construct a Laplace isospectral deformation of metrics on an orbifold quotient of a nilmanifold. Each orbifold in the deformation contains singular points with order two isotropy. Isospectrality is obtained by modifying a generalization of Sunada's theorem due to DeTurck and Gordon.

We show that a Laplace isospectral family of two dimensional Riemannian orbifolds, sharing a lower bound on sectional curvature, contains orbifolds of only a finite number of orbifold category diffeomorphism types. We also show that orbifolds of only finitely many orbifold diffeomorphism types may arise in any collection of 2-orbifolds satisfying lower bounds on sectional curvature and volume, and an upper bound on diameter. An argument converting spectral data to geometric bounds shows that the first result is a consequence of the second.

The use of nonaqueous solvents for conversion of biomass molecules into platform chemicals and fuels is hindered by a lack of solubility data and models. Accordingly, the solubility of the model carbohydrate, cellobiose, was measured at 20 °C in 18 organic liquids and water. Solubility ranged from <0.001 g L–1 in hydrocarbon solvents to >100 g L–1 in hydrogen bond acceptor solvents. Three models were analyzed to evaluate accuracy and to understand factors that affect cellobiose solubility: Hansen’s solubility theory (HST), linear free energy relationship (LFER), and several versions of the UNIQUAC functional-group activity coefficients (UNIFAC) model. Cellobiose Hansen solubility parameters (HSPs) were estimated using experimental solubility measurements, but the model was unable to correctly distinguish several of the good solvents from the poor ones. A regressed LFER containing contributions from solvent excess molar refraction, polarizability/dipolarity, acidity, basicity, and molar volume was able to match measured solubilities to within ±2 log units (AAD of 66% and ARD of 27%). The LFER model indicated that good solvents were highly polarizable and had low molar volume, consistent with the good cellobiose solubility observed for water. A modified version of UNIFAC, including an additional association term (A-UNIFAC), predicted the solubility of cellobiose and several other carbohydrates in water and alcohols to within ±0.65 log units (AAD of 25% and ARD of 6.7%), indicating that the A-UNIFAC framework can be used in a predictive manner. This work provides guidance for future studies on the use of nonaqueous solvents for biomass conversion.