The speed of biased random walk on percolation clusters

 We consider biased random walk on supercritical percolation clusters in ℤ². We show that the random walk is transient and that there are two speed regimes: If the bias is large enough, the random walk has speed zero, while if the bias is small enough, the speed of the random walk is positive. Received: 20 November 2002 / Revised version: 17 January 2003 Published online: 15 April 2003 Research supported by Microsoft Research graduate fellowship. Research partially supported by the DFG under grant SPP 1033. Research partially supported by NSF grant #DMS-0104073 and by a Miller Professorship at UC Berkeley. Mathematics Subject Classification (2000): 60K37; 60K35; 60G50 Key words or phrases: Percolation – Random walk     

On the cover time of random walks on graphs

This article deals with random walks on arbitrary graphs. We consider the cover time of finite graphs. That is, we study the expected time needed for a random walk on a finite graph to visit every vertex at least once. We establish an upper bound ofO(n ²) for the expectation of the cover time for regular (or nearly regular) graphs. We prove a lower bound of (n logn) for the expected cover time for trees. We present examples showing all our bounds to be tight.Mike Saks was supported by NSF-DMS87-03541 and by AFOSR-0271. Jeff Kahn was supported by MCS-83-01867 and by AFOSR-0271.     

Electronic determinants of photoacidity in cyanonaphthols

We present semiempirical AM1 calculations for the ground and excited state of 2-naphthol and some of its cyano derivatives in the gas phase. Following photoexcitation, the Mulliken electron density on the oxygen diminishes slightly for the acid and more conspicuously for the anionic conjugated base. This agrees with the measured solvatochromic parameters for 2-naphthol. In both electronic states, we find a nice correlation with the measured pK values in water. The electronic charge distribution on the distal ring of the anion agrees with the experimental acidity order in both S(0) and S(1). Upon excitation, it increases predominantly in positions 3, 5, and 8. The ring system of the anion assumes an alternate quinoidal structure in the ground state of the anion, which becomes more symmetric in the relaxed excited state. This suggests that the enhanced aromatic character of a 4n electron system in the excited state allows for better delocalization of the oxygen charge within the ring.     

Organo tin nucleophiles iii. Palladium catalyzed reductive cleavage of allylic heterosubstituents with tin hydride

Tributyl tin hydride, serving as an efficient hydride transfer agent, allows highly chemoselective palladium catalyzed reductions of allylic heterosubstituents even in presence of aldehydes, benzyl acetate and benzyl chloride.     

Locality,factorizability, and the Maxwell Boltzmann distribution

A classical gas at equilibrium satisfies the locality conditionif the correlations between local fluctuations at a pair of remote small regions diminish in the thermodynamic limit. The gas satisfies a strong locality conditionif the local fluctuations at any number of remote locations have no (pair, triple, quadruple....) correlations among them in the thermodynamic limit. We prove that locality is equivalent to a certain factorizability condition on the distribution function. The analogous quantum condition fails in the case of a freeBose gas. Next we prove that strong locality is equivalent to the total factorizability of the distribution function, and thus (given Liourilles theorem) to the Maxwell Boltzmann distribution for an ideal gas.Dedicated to Professor Max Jammer on the occasion of his eightieth birthday. April 13. 1995.     

The effect of random restrictions on formula size

We consider the formula size complexity of boolean functions over the base consisting of ∧, ∨, and ¬ gates. In 1961 Subbotovskaya proved that, for any boolean function on n variables, setting all but a randomly chosen ?n variables to randomly chosen constants, reduces the expected complexity of the induced function by at least a factor. This fact was used by Subbotovskaya to derive a lower bound of Ω(n^1.5) for the formula size of the parity function, and more recently by Andreev who exhibited at lower bound of ΩC(n^2.5/log^O(1)(n)) for a function in P. We present the first improvement of Subbotovskaya's result, showing that the expected formual complexity of a function restricted as above is at most an O(?^γ) franction of its original complexity, for This allows us to give an improved lower bound of Ω(n^2.556…) for Andreev's function. At the time of discovery, this was the best formula lower bound known for any function in NP. © 1993 John Wiley & Sons, Inc.     

Exact solution of the excited-state geminate A*+B <==> C*+D reaction with two different lifetimes and quenching

The authors obtain, in the Laplace transform space, the exact analytic solution for the Green function and survival probabilities for the excited-state diffusion-influenced reversible geminate reaction, A*+B <==> C*+D, with two different lifetimes and in the presence of an added quenching process. This extends a previous investigation by Popov and Agmon [J. Chem. Phys. 117, 5770 (2002)] of the ground-state reaction without quenching. The long-time asymptotic behavior of the survival probabilities is obtained in the time domain. It is found to be different from the equal-lifetime case. This paper also provides a useful short-time approximation for the kinetics.     

Spatiotemporal model for the progression of transgressive dunes

Transgressive dune fields, which are active sand areas surrounded by vegetation, exist on many coasts. In some regions like in Fraser Island in Australia, small dunes shrink while large ones grow, although both experience the same climatic conditions. We propose a general mathematical model for the spatiotemporal dynamics of vegetation cover on sand dunes and focus on the dynamics of transgressive dunes. Among other possibilities, the model predicts growth parallel to the wind with shrinkage perpendicular to the wind, where, depending on geometry and size, a transgressive dune can initially grow although eventually shrink. The larger is the initial area the slower its stabilization process. The model’s predictions are supported by field observations from Fraser Island in Australia.     

The synthesis and characterization of thiol-based aryl diazonium modified glassy carbon electrode for the voltammetric determination of low levels of Hg(II)

Electrochemical determination of Hg(II) in aquatic solutions on bare and modified glassy carbon electrode (GCE) is reported. Optimizing the parameters used for a bare GCE, such as the electrolyte solution, the potential and time of deposition, resulted in linear response over a large range of Hg(II) concentrations (4–160 ppb) using linear sweep anodic stripping voltammetry. Modification of the electrode with 4,4′-disulfanediyldibenzenediazonium (DSBD) yielded a lowest detection limit of 1 ppb. Two procedures for DSBD synthesis are described for the first time, and the product was characterized by microanalysis, FTIR and ¹H-NMR. The electrochemical attachment of DSBD to the electrode was studied and compared with the electrochemical behaviour of DSBD analogous molecules, i.e. 4-aminophenyl disulfide, p-aminothiophenol and phenyl disulfide.