New results for molecular formation under pairwise potential minimization

We establish new lower bounds on the distance between two points of a minimum energy configuration of N points in ℝ³ interacting according to a pairwise potential function. For the Lennard-Jones case, this bound is 0.67985 (and 0.7633 in the planar case). A similar argument yields an estimate for the minimal distance in Morse clusters, which improves previously known lower bounds. Moreover, we prove that the optimal configuration cannot be two-dimensional, and establish an upper bound for the distance to the nearest neighbour of every particle, which depends on the position of this particle. On the boundary of the optimal configuration polytope, this is unity while in the interior, this bound depends on the potential function. In the Lennard-Jones case, we get the value . Also, denoting by V _N the global minimum in an N point minimum energy configuration, we prove in Lennard-Jones clusters for all N≥2, while asymptotically holds (as opposed to in the planar case, confirming non-planarity for large N).     

Second-harmonic generation and the influence of flexoelectricity in the nematic phases of bent-core oxadiazoles

Second-harmonic generation (SHG) in the nematic phase of bent-core oxadiazole-based liquid crystals (LCs) was studied and compared to that for the rod-like compound 4-cyano-4?-n-octylbiphenyl (8CB). Weak, isotropically scattered second-harmonic (SH) light was observed for all materials, consistent with SHG by nematic director fluctuations. The SH intensity produced by the bent-core materials was found to be up to ~ 3.4 times that of 8CB. We discuss this result in terms of the dependence of SH intensity on temperature, elastic constants and flexoelectric coefficients. We have calculated the latter by using a molecular field approach with atomistic modelling, thus demonstrating how molecular parameters contribute to the flexoelectric coefficients and illustrating the potential of this method for predicting the flexoelectric behaviour of bent-core LCs. We show that the increased SH signal in the bent-core compounds is partly due to their nematic phases being at a much higher temperature, and also potentially due to them having greater flexoelectric coefficients, up to ~1.5 times those of 8CB. These estimates are consistent with reports of increased flexoelectric coefficients in bent-core compounds in comparison to rod-like compounds.     

Multilevel multi-leader multiple-follower games with nonseparable objectives and shared constraints

Computational Management Science - Multi-leader multi-follower (MLMF) games are hierarchical games in which a collection of players in the upper-level, called leaders, compete in a Nash game...     

Omnidirectional and tunable symmetrical confined states in photonic quantum-well structures with single-negative materials

The symmetrical confined states are found in photonic quantum-well structures with single-negative materials, in which the photonic barrier is based on the zero-effective-phase gap. The number and frequencies of the symmetrical confined states can be tuned by varying the period number and thicknesses of the well photonic crystal, respectively. Furthermore, the symmetrical confined states of the structures are less sensitive to the incident angle and polarization, compared with previous confined states of photonic quantum-well structures based on the Bragg or zero-average-index gap. The structures open a promising way to fabricate symmetrically tunable and omnidirectional multichannel filters for future dense wavelength division multiplexing applications.     

Development of composite inorganic building blocks for MOFs

A general direction for diversifying metal-organic frameworks (MOFs) is demonstrated by the synthesis of composite inorganic clusters between indium and s-, d-, and f-block elements. These previously unknown heterometallic clusters, with various nuclearity, geometry, charge, and metal-to-metal ratios, significantly expand the pool of inorganic building blocks that are highly effective for the construction of porous MOFs with high gas uptake capacity.     

Orientation control in nanoparticle filled block copolymer cold zone annealed films

Nanoparticles provide an attractive route to modifying polymer thin film properties, yet controlling the dispersion and morphology of functionalized nanoparticle filled films is often difficult. Block copolymers can provide an ideal template for directed assembly of nanoparticles under controlled nanoparticle‐polymer interactions. Previously we observed that neat films of cylinder forming poly(styrene‐b‐methyl methacrylate) PS‐b‐PMMA block copolymer (c‐BCP) orient vertically with dynamic sharp thermal cold zone annealing (CZA‐S) over wide range of CZA‐S speed (0.1–10) μm/s. Here, we introduce a low concentration (1–5 wt %) of nanoparticles of phenolic group functionalized CdS (fCdS‐NP), to PMMA cylinder forming polystyrene‐b‐poly (methyl methacrylate) block copolymer (c‐BCP) films. Addition of the fCdS‐NP induces a vertical to horizontal orientation transition at low CZA‐S speed, V = 5 μm/s. The orientation flip studies were analyzed using AFM and GISAXS. These results confirm generality of our previously observed orientation transition in c‐BCP under low speed CZA‐S with other nanoparticles (gold [Au‐NP], fulleropyrrolidine [NCPF‐NP]) in the same concentration range, but reveal new aspects not previously examined: (1) A novel observation of significant vertical order recovery from 5–10% vertical cylindrical fraction at V = 5 μm/s to 46–63% vertical cylindrical fraction occurring at high CZA‐S speed, V = 10 μm/s for the fCdS nanoparticle filled films. (2) We rule out the possibility that a nanoparticle wetting layer on the substrate is responsible for the vertical to horizontal flipping transition. (3) We demonstrate that the orientation flipping results can be achieved in a nanoparticle block copolymer system where the nanoparticles are apparently better‐dispersed within only one (matrix PS) domain unlike our previous nanoparticle system studied. We consider facile processing conditions to fabricate functionalized nanoparticles filled PS‐PMMA block copolymer films with controlled anisotropy, a useful strategy in the design of next generation electronic and photonic materials. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 604–614     

A Trust-Region Algorithm for Global Optimization

We consider the global minimization of a bound-constrained function with a so-called funnel structure. We develop a two-phase procedure that uses sampling, local optimization, and Gaussian smoothing to construct a smooth model of the underlying funnel. The procedure is embedded in a trust-region framework that avoids the pitfalls of a fixed sampling radius. We present a numerical comparison to three popular methods and show that the new algorithm is robust and uses up to 20 times fewer local minimizations steps.     

Efficiently packing unequal disks in a circle

Placing non-overlapping circles in a smallest container is a hard task. In this paper we present our strategy for optimally placing circles in a smallest circle which led us to win an international competition by properly mixing local and global optimization strategies with random search and local moves.