Dependence of small-scale atomic clock performance on frequency modulation parameters used in the frequency control loop

We demonstrate a direct correspondence between FM parameters used in a frequency-locked loop that is based on multifield FM spectroscopy and the stability of a small-scale coherent population trapping atomic clock. Optimized FM parameters lead to an Allan deviation of 2.8 x 10(-11)/square root tau, while the clock stability deteriorates in a predictable manner for the other FM parameters.     

Asymptotic revenue equivalence of asymmetric auctions with interdependent values

We prove an asymptotic revenue equivalence among weakly asymmetric auctions with interdependent values, in which bidders have either asymmetric utility functions or asymmetric distributions of signals.     

Large auctions with risk-averse bidders

We study private-value auctions with n risk-averse bidders, where n is large. We first use asymptotic analysis techniques to calculate explicit approximations of the equilibrium bids and of the seller’s revenue in any k-price auction (k = 1, 2, . . .). These explicit approximations show that in all large k-price auctions the effect of risk-aversion is O(1/n ²) small. Hence, all large k-price auctions with risk-averse bidders are O(1/n ²) revenue equivalent. The generalization, that all large auctions are O(1/n ²) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as ${n\longrightarrow \infty }We study private-value auctions with n risk-averse bidders, where n is large. We first use asymptotic analysis techniques to calculate explicit approximations of the equilibrium bids and of the seller’s revenue in any k-price auction (k = 1, 2, . . .). These explicit approximations show that in all large k-price auctions the effect of risk-aversion is O(1/n ²) small. Hence, all large k-price auctions with risk-averse bidders are O(1/n ²) revenue equivalent. The generalization, that all large auctions are O(1/n ²) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as n? ￥{n\longrightarrow \infty } with risk-averse bidders is strictly below the risk-neutral limit. Therefore, these auction mechanisms are not revenue equivalent to large k-price auctions even to leading-order as n? ￥{n\longrightarrow \infty }.     

Existence of nondetermined sets for some two person games over reals

Various two person games with perfect information over reals are shown to have a nondetermined set. A game formulated by Mycielski is solved. This is a part of the author’s Ph.D. thesis, prepared at the Hebrew University under the supervision of Professor Azriel Levy, to whom the author wishes to express his warm thanks.     

Tracking chemical kinetics in high-throughput systems

Combinatorial chemistry and high‐throughput experimentation (HTE) have revolutionized the pharmaceutical industry—but can chemists truly repeat this success in the fields of catalysis and materials science? We propose to bridge the traditional “discovery” and “optimization” stages in HTE by enabling parallel kinetic analysis of an array of chemical reactions. We present here the theoretical basis to extract concentration profiles from reaction arrays and derive the optimal criteria to follow (pseudo)first‐order reactions in time in parallel systems. We use the information vector f and introduce in this context the information gain ratio, χ_r, to quantify the amount of useful information that can be obtained by measuring the extent of a specified reaction r in the array at any given time. Our method is general and independent of the analysis technique, but it is more effective if the analysis is performed on‐line. The feasibility of this new approach is demonstrated in the fast kinetic analysis of the carbon–sulfur coupling between 3‐chlorophenylhydrazonopropane dinitrile and β‐mercaptoethanol. The theory agrees well with the results obtained from 31 repeated C? S coupling experiments.     

Copper-catalyzed Suzuki cross-coupling using mixed nanocluster catalysts

A small library of copper and noble metal nanoclusters is designed and synthesized. These clusters are tested as catalysts in the Suzuki cross-coupling of various aryl halides with phenylboronic acid. It is found that copper and copper/noble metal combination nanoclusters are active catalysts for this reaction, the most active being the combined copper/palladium clusters. Iodo-, bromo-, and chloroarenes can be used. In the case of p-nitrobromobenzene, a one-pot cross-coupling and selective hydrogenation is achieved.     

Self-assembly of a hexagonal phase of wormlike micelles containing metal nanoclusters

Stable nanoclusters (approximately 2 nm in diameter) of copper, silver, gold, palladium, and ruthenium coated with hydrophobic coronas are easily trapped in self-assembled "soft crystal" hexagonal phase gels made of water and surfactants. The system's crystal structure and phase behavior are studied in detail. A partial phase diagram showing the hexagonal phase region for the water/SDS/toluene region is presented. High-energy X-ray scattering and cross-polarized optical microscopy experiments show that the clusters are tightly confined within the tubes. The thermal gel-fluid transitions of the hexagonal phase are investigated, and it is shown that the hexagonal phase can melt and recrystallize repeatedly. The melt/gel cycles enable easy trapping of various metal clusters in pre-prepared hexagonal phases. In contrast to spherical micelles, the hexagonal phase doped with metal clusters can grow without limit, basically up to the container walls (Ru-doped soft crystals grew to 0.5 mm over 2 months, forming wormlike tubes that are more than 50 microm long but only 7-10 nm in diameter).