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     

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.     

Special pair dance and partner selection: elementary steps in proton transport in liquid water

Conditional and time-dependent radial distribution functions reveal the details of the water structure surrounding the hydronium during the proton mobility process. Using this methodology for classical multistate empirical valence bond (MS-EVB) and ab initio molecular dynamics trajectories, as well as quantal MS-EVB trajectories, we supply statistical proof that proton hops in liquid water occur by a transition from the H3O+[3H2O] Eigen-complex, via the H5O2+ Zundel-complex, to a H3O+[3H2O] centered on a neighboring water molecule. In the "resting period" before a transition, there is a distorted hydronium with one of its water ligands at a shorter distance and another at a longer distance than average. The identity of this "special partner" interchanges rapidly within the three first-shell water ligands. This is coupled to cleavage of an acceptor-type hydrogen bond. Just before the transition, a partner is selected by an additional translation of the H3O+ moiety in its direction, possibly enabled by loosening of donor-type hydrogen bonds on the opposite side. We monitor the transition in real time, showing how the average structure is converted to a distorted H5O2+ cation constituting the transitional complex for proton hopping between water molecules.     

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.     

A novel homogeneous immunoassay for anthrax detection based on the AlphaLISA method: detection of B. anthracis spores and protective antigen (PA) in complex samples

Amplified Luminescent Proximity Homogeneous Assay (AlphaLISA) technology is an energy-transfer-based assay, utilizing singlet oxygen as an energy donor to a fluorescent acceptor. The long singlet oxygen migration distance allows the energy transfer mechanism to go up to ～200 nm, facilitating flexible and sensitive homogeneous immunoassays. While soluble protein detection using AlphaLISA was previously described, the detection of particles such as bacteria and viruses was not reported. In this work, we show for the first time the implementation of the AlphaLISA technology for the detection of a particulate antigen, i.e., Bacillus anthracis spores. Here, we show that an efficient particle immunoassay requires a high acceptor-to-donor ratio (>4:1). The results suggested that the high acceptor/donor ratio is required to avoid donor aggregation (“islands”) on the spore surface, hence facilitating donor/acceptor interaction. The developed assay enabled the detection of 10⁶ spores/mL spiked in PBS. We also demonstrate the development of a highly sensitive AlphaLISA assay for the detection of the main toxin component of anthrax, protective antigen (PA). The assay enabled the detection of 10 and 100 pg/mL PA in buffer and spiked naïve rabbit sera, respectively, and was successfully implemented in sera of anthrax-infected rabbits. To summarize, this study demonstrates that AlphaLISA enables detection of anthrax spores and toxin, utilizing short homogeneous assays. Moreover, it is shown for the first time that this technology facilitates the detection of particulate entities and might be suitable for the detection of other bacteria or viruses.     

Longitudinal Relaxation Enhancement in 1H NMR Spectroscopy of Tissue Metabolites via Spectrally Selective Excitation

Nuclear magnetic resonance spectroscopy is governed by longitudinal (T₁) relaxation. For protein and nucleic acid experiments in solutions, it is well established that apparent T₁ values can be enhanced by selective excitation of targeted resonances. The present study explores such longitudinal relaxation enhancement (LRE) effects for molecules residing in biological tissues. The longitudinal relaxation recovery of tissue resonances positioned both down‐ and upfield of the water peak were measured by spectrally selective excitation/refocusing pulses, and compared with conventional water‐suppressed, broadband‐excited counterparts at 9.4 T. Marked LRE effects with up to threefold reductions in apparent T₁ values were observed as expected for resonances in the 6–9 ppm region; remarkably, statistically significant LRE effects were also found for several non‐exchanging metabolite resonances in the 1–4 ppm region, encompassing 30–50 % decreases in apparent T₁ values. These LRE effects suggest a novel means of increasing the sensitivity of tissue‐oriented experiments, and open new vistas to investigate the nature of interactions among metabolites, water and macromolecules at a molecular level.