Volume integrals associated with the inhomegeneous Helmholtz equation. Part 2: Cylindrical region; rectangular region

Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) + alpha(2), for the cases of a finite cylindrical region and a region of rectangular parallelepiped. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r r' and r 4', where r and r' are distances from the origin to the point of observation and source, respectively. When the wave number approaches zero, the results reduce directly to the potentials of variable densities

Quantum Correction in Exact Quantization Rules

An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to $N\pi$, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the quantum correction is an invariant, independent of the number of nodes in the wave function. In those systems, the energy levels of all the bound states can be easily calculated from the exact quantization rule and the solution for the ground state, which can be obtained by solving the Riccati equation. With this new method, we re-calculate the energy levels for the one-dimensional systems with a finite square well, with the Morse potential, with the symmetric and asymmetric Rosen-Morse potentials, and with the first and the second P\"{o}schl-Teller potentials, for the harmonic oscillators both in one dimension and in three dimensions, and for the hydrogen atom.Comment: 10 pages, no figure, Revte

On the momentum-dependence of K−K^{-}-nuclear potentials

The momentum dependent $K^{-}$-nucleus optical potentials are obtained based on the relativistic mean-field theory. By considering the quarks coordinates of $K^-$ meson, we introduced a momentum-dependent "form factor" to modify the coupling vertexes. The parameters in the form factors are determined by fitting the experimental $K^{-}$-nucleus scattering data. It is found that the real part of the optical potentials decrease with increasing $K^-$ momenta, however the imaginary potentials increase at first with increasing momenta up to $P_k=450\sim 550$ MeV and then decrease. By comparing the calculated $K^-$ mean free paths with those from $K^-n$/$K^-p$ scattering data, we suggested that the real potential depth is $V_0\sim 80$ MeV, and the imaginary potential parameter is $W_0\sim 65$ MeV.Comment: 9 pages, 4 figure

Etching-dependent reproducible memory switching in vertical SiO2 structures

Vertical structures of SiO$_{2}$ sandwiched between a top tungsten electrode and conducting non-metal substrate were fabricated by dry and wet etching methods. Both structures exhibit similar voltage-controlled memory behaviors, in which short voltage pulses (1 $\mu$s) can switch the devices between high- and low-impedance states. Through the comparison of current-voltage characteristics in structures made by different methods, filamentary conduction at the etched oxide edges is most consistent with the results, providing insights into similar behaviors in metal/SiO/metal systems. High ON/OFF ratios of over 10$^{4}$ were demonstrated.Comment: 6 pages, 3 figures + 2 suppl. figure

Single Molecule Michaelis-Menten Equation beyond Quasi-Static Disorder

The classic Michaelis-Menten equation describes the catalytic activities for ensembles of enzyme molecules very well. But recent single-molecule experiment showed that the waiting time distribution and other properties of single enzyme molecule are not consistent with the prediction based on the viewpoint of ensemble. It has been contributed to the slow inner conformational changes of single enzyme in the catalytic processes. In this work we study the general dynamics of single enzyme in the presence of dynamic disorder. We find that at two limiting cases, the slow reaction and nondiffusion limits, Michaelis-Menten equation exactly holds although the waiting time distribution has a multiexponential decay behaviors in the nondiffusion limit.Particularly, the classic Michaelis-Menten equation still is an excellent approximation other than the two limits.Comment: 10 pages, 1 figur