Exponential convergence for one dimensional contact processes

The complete convergence theorem implies that starting from any initial distribution the one dimensional contact process converges to a limit ast. In this paper we give a necessary and sufficient condition on the initial distribution for the convergence to occur with exponential rapidity.This work was discussed while the authors were visiting the Nankai Mathematics Institute in Tianjin.Partially supported by the National Science Foundation, the Army Research Office through the Mathematical Sciences Institute at Cornell University, and a Guggenheim fellowship.Research supported by the National Science Foundation of China.     

Critical behavior of the two-dimensional first passage time

We study the two-dimensional first passage problem in which bonds have zero and unit passage times with probabilityp and 1–p, respectively. We prove that as the zero-time bonds approach the percolation thresholdp _c, the first passage time exhibits the same critical behavior as the correlation function of the underlying percolation problem. In particular, if the correlation length obeys(p) ¦p–p _c¦^–v, then the first passage time constant satisfies(p)¦p–p _c¦^v. At p_c, where it has been asserted that the first passage time from 0 tox scales as ¦x¦ to a power with 0<<1, we show that the passage times grow like log ¦x¦, i.e., the fluid spreads exponentially rapidly.     

Multidimensional random walks in random environments with subclassical limiting behavior

In this paper we will describe and analyze a class of multidimensional random walks in random environments which contain the one dimensional nearest neighbor situation as a special case and have the pleasant feature that quite a lot can be said about them. Our results make rigorous a heuristic argument of Marinari et al. (1983), and show that in anyd< we can have (a)X _n is recurrent and (b)X _n (logn)².AMS Mid Career Fellowship 1984–1986. Research also partially supported by NSF Grant MCS 83-00836     

Physically based molecular device model in a transient circuit simulator

Two efficient, physically based models for the real-time simulation of molecular device characteristics of single molecules are developed. These models assume that through-molecule tunnelling creates a steady-state Lorentzian distribution of excess electron density on the molecule and provides for smooth transitions for the electronic degrees of freedom between the tunnelling, molecular-excitation, and charge-hopping transport regimes. They are implemented in the fREEDA™ transient circuit simulator to allow for the full integration of nanoscopic molecular devices in standard packages that simulate entire devices including CMOS circuitry. Methods are presented to estimate the parameters used in the models via either direct experimental measurement or density-functional calculations. The models require 6–8 orders of magnitude less computer time than do full a priori simulations of the properties of molecular components. Consequently, molecular components can be efficiently implemented in circuit simulators. The molecular-component models are tested by comparison with experimental results reported for 1,4-benzenedithiol.     

Validation of a simple, sensitive method for the determination of beta-estradiol in bovine urine using gas-chromatography negative-ion chemical ionization mass spectrometry

A new method is presented for the analysis of 17[small beta]-estradiol in bovine urine. After deconjugation, the sample is cleaned up using an OASIS[trade mark sign] HLB disposable cartridge and extracted into 1-chlorobutane. The hormone is derivatized using pentafluorobenzoyl chloride. The derivatized estradiol is quantitated using gas-chromatography negative-ion chemical ionization mass spectrometry. Calibrations, obtained using spiked blank urine, are linear in the range of 100-1000 pg mL(-1) with CC[small alpha] approximately 170 pg mL(-1) and CC[small beta] of 287 pg mL(-1). Recoveries are in the range of 80 to 130%. The method is rugged, rapid and sensitive when compared to other hormone methods.     

Ring expansion-annulation strategy for the synthesis of substituted azulenes and oligoazulenes. 2. Synthesis of azulenyl halides, sulfonates, and azulenylmetal compounds and their application in transition-metal-mediated coupling reactions

A "ring expansion-annulation strategy" for the synthesis of substituted azulenes is described based on the reaction of beta'-bromo-alpha-diazo ketones with rhodium carboxylates. The key transformation involves an intramolecular Buchner reaction followed by beta-elimination of bromide, tautomerization, and in situ trapping of the resulting 1-hydroxyazulene as a carboxylate or triflate ester. Further synthetic elaboration of the azulenyl halide and sulfonate annulation products can be achieved by employing Heck, Negishi, Stille, and Suzuki coupling reactions. Reaction of the azulenyl triflate 84 with pinacolborane provides access to the azulenylboronate 91, which participates in Suzuki coupling reactions with alkenyl and aryl iodides. The application of these coupling reactions to the synthesis of biazulenes, terazulene 101, and related oligoazulenes is described, as well as the preparation of the azulenyl amino acid derivative 110.     

The reaction of allenylsilanes with α,β-unsaturated acylsilanes: new annulation approaches to five and six-membered carbocyclic compounds

The reaction of α,β-unsaturated acylsilanes with allenylsilanes can be directed to produce either five or six-membered carbocyclic compounds.     

Some general results concerning the critical exponents of percolation processes

Summary In this paper we will give some results concerning the critical exponents of percolation processes which are valid for any model. These results show that in several respects the behavior which occurs for percolation on the binary tree provides bounds on one side for what happens in general. These results and their proofs are closely related to their analogues for the Ising model.Alfred P. Sloan Fellow. This work partially supported by NSF grant MCS 80-02732.     

A pseudoreceptor docking study of 4,5-α-epoxymorphinans with a range of dielectric constants

Summary Thirteen 4,5-epoxymorphinan agonists with established analgesic action were docked into an Asp-Lys-His-Phe pseudoreceptor complex under a range of distance-dependent dielectric conditions. The number of compounds with potential energies of the docked complexes that agreed in rank order with corresponding analgesic potencies was determined for each condition. Two dielectric conditions, n-decane (1.991) and ethanol (24.3), enabled the greatest number of compounds to relate to their pseudoreceptors with each having 9 and 8 successes respectively. Both of these conditions demonstrated unique influences on the types of structures that were successfully docked. For example, the morphine stereoisomer -isomorphine, the geometric isomer B/C trans-morphine, and the 8-position-substituted -isomorphine were successes in the n-decane condition, whereas the ethanol condition produced the substituted codeine derivatives dihydroco-deinone and dihydroxycodeinone. These findings emphasize the importance of dielectric influence when developing force-field modeled quantitative structure-activity relationships for a closely related homologous series.