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Raman spectroscopy and transmission electron microscopy are used to investigate the temperature effects on the stability of metastable silicon phases (Si–III and Si–XII) produced by nanoindentation. It is found that the thickness of the specimen beneath the residual imprint plays an important role in the phase transformation sequence during heating up to 200 °C. Amorphization is preferred in nanoindents located in thin and loosely constrained areas; formation of Si–IV from Si–III/Si–XII is observed in the residual imprints located in the areas with an intermediate thickness; and the formation of an unidentified “Si–XIII” structure, which precedes the formation of Si–IV, is observed in nanoindents constrained by the bulk wafer. The phase transformation sequence in the indented samples under annealing is established as follows: Si–XII→Si–III→Si–XIII (thick sample only)→a-Si or Si–IV→nanocrystalline Si–I→Si–I.

The Multi-Depot Vehicle Routing Problem (MDVRP) is a generalization of the Single-Depot Vehicle Routing Problem (SDVRP) in which vehicle(s) start from multiple depots and return to their depots of origin at the end of their assigned tours. The traditional objective in MDVRP is to minimize the sum of all tour lengths, and existing literature handles this problem with a variety of assumptions and constraints. In this paper, we explore the notion of minimizing the maximal length of a tour in MDVRP ("min-max MDVRP"). We present two heuristics in the paper. The first heuristic is a linear programming-based approach with global improvement. The second one, the region partition heuristic, is proved to be asymptotically optimal and is potentially useful for general network applications. A comparison of the computational implementations for different heuristics is presented.

Plan-view transmission electron microscopy (TEM) and Raman microspectroscopy were used to identify metastable silicon phases in nanoindentation. A mixture of metastable Si-III and Si-XII phases was observed by both selected area diffraction in TEM and Raman analysis. High resolution TEM observations provided detailed structural information about the metastable phases of silicon and the interfaces between different silicon structures. A mechanism of dislocation-induced lattice rotation that leads to a phase transition and distortion-induced amorphization in nanoindentation is proposed.

Various optimization problems in engineering and management are formulated as nonlinear programming problems. Because of the nonconvexity nature of this kind of problems, no efficient approach is available to derive the global optimum of the problems. How to locate a global optimal solution of a nonlinear programming problem is an important issue in optimization theory. In the last few decades, piecewise linearization methods have been widely applied to convert a nonlinear programming problem into a linear programming problem or a mixed-integer convex programming problem for obtaining an approximated global optimal solution. In the transformation process, extra binary variables, continuous variables, and constraints are introduced to reformulate the original problem. These extra variables and constraints mainly determine the solution efficiency of the converted problem. This study therefore provides a review of piecewise linearization methods and analyzes the computational efficiency of various piecewise linearization methods.