T he goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered in this paper have the characteristic that only a subset of the binary variables have non-zero objective function coefficients if modeled as an MILP. This class of problems is formulated as a hybrid MILP/CP model that involves some of the MILP constraints, a reduced set of the CP constraints, and equivalence relations between the MILP and the CP variables. An MILP/CP based decomposition method and an LP/CP-based branch-and-bound algorithm are proposed to solve these hybrid models. Both these algorithms rely on the same relaxed MILP and feasibility CP problems. An application example is considered in which the least-cost schedule has to be derived for processing a set of orders with release and due dates using a set of dissimilar parallel machines. It is shown that this problem can be modeled as an MILP, a CP, a combined MILP-CP OPL model (Van Hentenryck 1999), and a hybrid MILP/CP model. The computational performance of these models for several sets shows that the hybrid MILP/CP model can achieve two to three orders of magnitude reduction in CPU time.

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Nanoscale contacts between metals and semiconductors are critical for further downscaling of electronic and optoelectronic devices. However, realizing nanocontacts poses significant challenges since conventional approaches to achieve ohmic contacts through Schottky barrier suppression are often inadequate. Here we report the realization and characterization of low n-type Schottky barriers (B0.35 eV) formed at epitaxial contacts between Au-In alloy catalytic particles and GaAs-nanowires. In comparison to previous studies, our detailed characterization, employing selective electrical contacts defined by high-precision electron beam lithography, reveals the barrier to occur directly and solely at the abrupt interface between the catalyst and nanowire. We attribute this lowest-to-date-reported Schottky barrier to a reduced density of pinning states (B10 17 m À 2 ) and the formation of an electric dipole layer at the epitaxial contacts. The insight into the physical mechanisms behind the observed lowenergy Schottky barrier may guide future efforts to engineer abrupt nanoscale electrical contacts with tailored electrical properties.

Human experience informs us of the two extreme consequences of crowding: random behavior of the individuals, in which each takes a singular path; and cooperative behavior, in which the individuals in the crowd act in a predictable uniform manner, such as in a military organization These extremes find parallels in the crowded situations encountered at the molecular level, exemplified for the former by glassy states, such as often encountered in polymeric materials,1 or for the latter, in the uniform archetypal arrangements of crystals or liquid crystals. Here we review the cooperative characteristics of uniform arrangements that take a chiral form and explore how these characteristics lead to left‐ and right‐handedness. These studies lead us to understand the basis of amplification of chirality in regular arrays, in which small influences have large consequences, and how chiral cooperativity acts in the resolution of conflict between influences favoring left‐ and right‐handedness.2