Fabrication of Asymmetric Electrode Pairs with Nanometer Separation Made of Two Distinct Metals

We report a simple and reproducible method to fabricate two metallic electrodes made of different metals with a nanometer-sized gap. These electrodes are fabricated by defining a pair of gold electrodes lithographically and electrodepositing a second metal onto one of them. The method enables the fabrication of pairs of metallic electrodes that exhibit distinct magnetic properties or work functions. The utility of this technique is demonstrated by making single-electron tunneling devices incorporating 2-nm gold nanocrystals.Comment: 3 figures, 1 colo

Relative Entropy: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations

Using a one-dimensional macromolecule in aqueous solution as an illustration, we demonstrate that the relative entropy from information theory, $\sum_k p_k\ln(p_k/p_k^*)$, has a natural role in the energetics of equilibrium and nonequilibrium conformational fluctuations of the single molecule. It is identified as the free energy difference associated with a fluctuating density in equilibrium, and is associated with the distribution deviate from the equilibrium in nonequilibrium relaxation. This result can be generalized to any other isothermal macromolecular systems using the mathematical theories of large deviations and Markov processes, and at the same time provides the well-known mathematical results with an interesting physical interpretations.Comment: 5 page

Generalized Haldane Equation and Fluctuation Theorem in the Steady State Cycle Kinetics of Single Enzymes

Enyzme kinetics are cyclic. We study a Markov renewal process model of single-enzyme turnover in nonequilibrium steady-state (NESS) with sustained concentrations for substrates and products. We show that the forward and backward cycle times have idential non-exponential distributions: \QQ_+(t)=\QQ_-(t). This equation generalizes the Haldane relation in reversible enzyme kinetics. In terms of the probabilities for the forward ($p_+$) and backward ($p_-$) cycles, $k_BT\ln(p_+/p_-)$ is shown to be the chemical driving force of the NESS, $\Delta\mu$. More interestingly, the moment generating function of the stochastic number of substrate cycle $\nu(t)$, follows the fluctuation theorem in the form of Kurchan-Lebowitz-Spohn-type symmetry. When $\lambda$ = $\Delta\mu/k_BT$, we obtain the Jarzynski-Hatano-Sasa-type equality: $\equiv$ 1 for all $t$, where $\nu\Delta\mu$ is the fluctuating chemical work done for sustaining the NESS. This theory suggests possible methods to experimentally determine the nonequilibrium driving force {\it in situ} from turnover data via single-molecule enzymology.Comment: 4 pages, 3 figure

Simulation of Parallel Blade-Vortex Interaction using a Discrete Vortex Method. G.U. Aero Report no. 9832

Numerical results are presented for two-dimensional vortex-aerofoil interaction using a grid-free discrete vortex method. The effects of the passing vortex on the surface pressure distribution and hence the aerodynamic force and moment of the aerofoil are examined in detail for a variety of interaction geometries. For some head-on interaction cases, vortex-induced local flow separation is also predicted on the aft part of the aerofoil surfaces. Extensive comparisons are made with other numerical results and the results from the Glasgow University BVI windtunnel test, which show good agreement

The 3-D Vortex Particle Method and the Fast Summation Algorithm. G.U. Aero Report 9620

In this report the vortex particle method developed by G.S. Winckelmans and A. Leonard for the computation of 3-D unsteady viscous flows is briefly reviewed. Numerical results are given for the interesting phenomenon of the fusion of two vortex rings, which shows that the method works well for long time computation. To reduce the high computational cost of the direct summation, a fast hierarchical algorithm for 3-D vortex particle interactions is being implemented

The 3-D Vortex Particle Method and the Fast Summation Algorithm. G.U. Aero Report 9620

In this report the vortex particle method developed by G.S. Winckelmans and A. Leonard for the computation of 3-D unsteady viscous flows is briefly reviewed. Numerical results are given for the interesting phenomenon of the fusion of two vortex rings, which shows that the method works well for long time computation. To reduce the high computational cost of the direct summation, a fast hierarchical algorithm for 3-D vortex particle interactions is being implemented

Properties of solutions of stochastic differential equations driven by the G-Brownian motion

In this paper, we study the differentiability of solutions of stochastic differential equations driven by the $G$-Brownian motion with respect to the initial data and the parameter. In addition, the stability of solutions of stochastic differential equations driven by the $G$-Brownian motion is obtained