Quantitative assessment of moisture damage for cacao bean quality using two-dimensional gas chromatography combined with time-of-flight mass spectrometry and chemometrics

Quality control of cacao beans is a significant issue in the chocolate industry. In this report, we describe how moisture damage to cacao beans alters the volatile chemical signature of the beans in a way that can be tracked quantitatively over time. The chemical signature of the beans is monitored via sampling the headspace of the vapor above a given bean sample. Headspace vapor sampled with solid-phase micro-extraction (SPME) was detected and analyzed with comprehensive two-dimensional gas chromatography combined with time-of-flight mass spectrometry (GC × GC–TOFMS). Cacao beans from six geographical origins (Costa Rica, Ghana, Ivory Coast, Venezuela, Ecuador, and Panama) were analyzed. Twenty-nine analytes that change in concentration levels via the time-dependent moisture damage process were measured using chemometric software. Biomarker analytes that were independent of geographical origin were found. Furthermore, prediction algorithms were used to demonstrate that moisture damage could be verified before there were visible signs of mold by analyzing subsets of the 29 analytes. Thus, a quantitative approach to quality screening related to the identification of moisture damage in the absence of visible mold is presented.     

Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model

We consider Hermitian and symmetric random band matrices H in d ≥ 1 dimensions. The matrix elements H _xy , indexed by \({x,y \in \Lambda \subset \mathbb{Z}^d}\), are independent, uniformly distributed random variables if \({\lvert{x-y}\rvert}\) is less than the band width W, and zero otherwise. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales \({t\ll W^{d/3}}\). We also show that the localization length of the eigenvectors of H is larger than a factor W ^d/6 times the band width. All results are uniform in the size \({\lvert{\Lambda}\rvert}\) of the matrix.     

Eigenvalue confinement and spectral gap for random simplicial complexes

We consider the adjacency operator of the Linial‐Meshulam model for random simplicial complexes on n vertices, where each d‐cell is added independently with probability p to the complete ‐skeleton. Under the assumption , we prove that the spectral gap between the smallest eigenvalues and the remaining eigenvalues is with high probability. This estimate follows from a more general result on eigenvalue confinement. In addition, we prove that the global distribution of the eigenvalues is asymptotically given by the semicircle law. The main ingredient of the proof is a Füredi‐Komlós‐type argument for random simplicial complexes, which may be regarded as sparse random matrix models with dependent entries. © 2017 Wiley Periodicals, Inc. Random Struct. Alg., 51, 506–537, 2017     

Conductivity variations in composites of α-zirconium phosphate and fumed silica

Composite proton-conducting solid electrolytes have been formed from α-zirconium phosphate (α-Zr(HPO₄)₂·H₂O, α-ZrP) and high surface area non-porous fumed silica in varying mole ratios. Conductivity variations as a function of temperature and relative humidity have been characterised and compared to that for a similarly prepared delaminated ZrP (no silica). Conductivities increase with relative humidity and E_a decreases at high silica mole fractions. Conduction is via exposed lamellar surfaces and other microstructural imperfections in the composites.     

A thermoelastic model for an experiment involving a solid-solid phase transition

An experiment was carried out by Sammis and Dein [1974] to support the notion that large creep strains could be generated in the earth's mantle by solid-solid phase transitions. The predictions of the thermoelastic model given here are in qualitative agreement with the results of their experiment.     

Local Semicircle Law for Random Regular Graphs

We consider random d‐regular graphs on N vertices, with degree d at least (log N)⁴. We prove that the Green's function of the adjacency matrix and the Stieltjes transform of its empirical spectral measure are well approximated by Wigner's semicircle law, down to the optimal scale given by the typical eigenvalue spacing (up to a logarithmic correction). Aside from well‐known consequences for the local eigenvalue distribution, this result implies the complete (isotropic) delocalization of all eigenvectors and a probabilistic version of quantum unique ergodicity.© 2017 Wiley Periodicals, Inc.     

On Saint-Venant's principle in the two-dimensional linear theory of elasticity

Archive for Rational Mechanics and Analysis -     

Sudden tensile loading of a rubberlike bar

In uniaxial tension, the stress–strain curve for rubber changes curvature from concave to convex as the strain increases. For sudden tensile loading of a bar, a one-dimensional model that reflects this behavior leads to an under-determined problem reminiscent of that arising in materials capable of undergoing phase transitions. In the latter setting, adding the kinetic relation underlying the phase change to the conventional statement of the problem removes the indeterminacy; the same is true when such a relation is used in a formal way in the problem for rubber. This presents a physical question: What is the evolutionary process at the microscale whose kinetics are needed in the dynamics of rubber?     

Surface-amplified ligand disorder in CdSe quantum dots determined by electron and coherent vibrational spectroscopies

This Article reports measurements of the intra- and intermolecular ordering of tight-binding octylphosphonate ligands on the surface of colloidal CdSe quantum dots (QDs) within solid state films, and the dependence of this order on the size of the QDs. The order of the organic ligands, as probed by vibrational sum frequency generation (SFG) spectroscopy, decreases as the radius of the QDs decreases; this decrease is correlated with a decrease in the order of underlying Cd(2+), as detected by X-ray photoelectron spectroscopy (XPS) line width measurements, for radii of the QDs, R > 2.4 nm, and is independent of the disorder of the Cd(2+) for R < 2.4 nm. We believe that, for R < 2.4, the decreasing order of the ligands with decreasing size is due to an increase in the curvature of the QD surfaces. Disorder in the Cd(2+) results from the presence of a shell of Cd(2+)-surfactant complexes that form during synthesis, so this work demonstrates the possibility for chemical control over molecular order within films of colloidal QDs by changing the surfactant mixture.