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The rapidly growing online food delivery (OFD) market presents substantial logistical challenges for last-mile delivery operations. Sidewalk delivery robots (SDRs) have emerged as a promising alternative to on-demand workers, as these compact, box-sized robots efficiently deliver food or groceries over short distances via sidewalks. We propose a two-stage stochastic optimization model for a single-depot SDR system with integrated battery-swapping operations. In the first stage, a continuous approximation (CA) method determines the optimal fleet size and the required number of additional swappable batteries. The second-stage solutions are critical to facilitate the first-stage method. These involve solving a routing problem that incorporates battery-swapping decisions and penalties for late arrivals. To address this, we develop a customized heuristic based on adaptive large neighborhood search (ALNS) to generate high-quality solutions for the second stage. The fitted CA model integrates key factors, including time windows, battery swapping, and pickup-delivery orders. Numerical examples highlight the proposed approach’s efficiency in reducing computational time while maintaining solution accuracy. A case study and sensitivity analysis conducted on Purdue University’s campus illustrate the practical impacts of fleet size and the number of swappable batteries. 

We used relaxation-assisted two-dimensional spectroscopy (RA 2DIR) to interrogate the energy transport within oligo(p-phenylene) chains and discovered a way to funnel high-frequency vibrational quanta rapidly (8.6 km/s) and unidirectionally over large distances. The study opens avenues for developing materials with controllable energy transport properties, and devices photonic or electrical properties. 

Abstract Tetradecaphenyl‐p‐terphenyl (2) was synthesized from 2,3,5,6‐tetraphenyl‐1,4‐diiodobenzene (11) by two methods. Ullmann coupling of11with pentaphenyliodobenzene (9) gave compound2in 1.7 % yield, and Sonogashira coupling of11with phenylacetylene, followed by a double Diels‐Alder reaction of the product diyne12with tetracyclone (6), gave2in 1.5 % overall yield. The latter reaction also gave the monoaddition product 4‐(phenylethynyl)‐2,2′,3,3′,4′,5,5′,6,6′‐nonaphenylbiphenyl (13) in 4 % overall yield. The X‐ray structures of compounds2and13show them to possess core aromatic rings distorted into shallow boat conformations. Density functional calculations indicate that these unusual structures are not the lowest energy conformations in the gas phase and may be the result of packing forces in the crystal. In addition, while uncorrected DFT calculations indicate that the strain energy in compound2is approximately 50 kcal/mol, dispersion‐corrected DFT calculations suggest that it is essentially unstrained, due to compensating, favorable, intramolecular interactions of its many phenyl rings. An attempted synthesis of tetradecaphenyl‐o‐terphenyl (4) by reaction of diphenylhexatriyne (14) with three equivalents of tetracyclone at 350 °C gave only the diadduct 2‐(phenylethynyl)‐2′,3,3′,4,4′,5,5′,6,6′‐nonaphenylbiphenyl (15) in 17 % yield. Even higher temperatures failed to produce4and lowered the yield of15, perhaps due to rapid decomposition of the starting materials. Ullmann coupling of 3,4,5,6‐tetraphenyl‐1,2‐diiodobenzene (16) and compound9also failed to give compound4. 

Abstract Highly congested derivatives of biphenyl were prepared by double Diels‐Alder reactions of cyclopentadienones with substituted butadiynes. The reaction of 2,3,5‐tri(tert‐butyl)cyclopentadienone (5) and diphenylbutadiyne (3) gave only the single adduct, 1‐(phenylethynyl)‐2‐phenyl‐3,5,6‐tri‐tert‐butylbenzene (6), and even extreme conditions gave no second addition. When tetracyclone (4) was added to bis(trimethylsilyl)butadiyne (8), two additions were achieved, but one silyl group was lost either during, or immediately following, the second addition to give 2‐(trimethylsilyl)‐2′,3,3′,4,4′,5,5′,6‐octaphenylbiphenyl (11). However, when 3,4‐diphenyl‐2,5‐dimethylcyclopentadienone (12) was added to8, the fully substituted 2,2′‐bis(trimethylsilyl)‐4,4′,5,5′‐tetraphenyl‐3,3′,6,6′‐tetramethylbiphenyl (14) was formed. The X‐ray structures of compounds11and14show them to be quite crowded, but the central biphenyl rings do not exhibit the distortions previously observed in decaphenylbiphenyl. In an alternative approach, arynes were added to 5,5′‐bis(4‐chlorophenyl)‐3,3′,4,4′‐tetraphenyl‐2,2′‐bis(cyclopentadienone) (18). Simple benzyne added twice to give 4,4′‐bis(4‐chlorophenyl)‐2,2′,3,3′‐tetraphenyl‐1,1′‐binaphthyl (19) in low yield, but tetraphenylbenzyne, generated from tetraphenylanthranilic acid, added only once.