The Fano resonance for Anderson impurity systems

We present a general theory for the Fano resonance in Anderson impurity systems. It is shown that the broadening of the impurity level leads to an additional and important contribution to the Fano resonance around the Fermi surface, especially in the mixed valence regime. This contribution results from the interference between the Kondo resonance and the broadened impurity level. Being applied to the scanning tunnelling microscopic experiments, we find that our theory gives a consistent and quantitative account for the Fano resonance lineshapes for both Co and Ti impurities on Au or Ag surfaces. The Ti systems are found to be in the mixed valence regime.Comment: 4 pages, 5 figures, published versio

Effect of turbulence on collisional growth of cloud droplets

We investigate the effect of turbulence on the collisional growth of um-sized droplets through high- resolution numerical simulations with well resolved Kolmogorov scales, assuming a collision and coalescence efficiency of unity. The droplet dynamics and collisions are approximated using a superparticle approach. In the absence of gravity, we show that the time evolution of the shape of the droplet-size distribution due to turbulence-induced collisions depends strongly on the turbulent energy-dissipation rate, but only weakly on the Reynolds number. This can be explained through the energy dissipation rate dependence of the mean collision rate described by the Saffman-Turner collision model. Consistent with the Saffman-Turner collision model and its extensions, the collision rate increases as the square root of the energy dissipation rate even when coalescence is invoked. The size distribution exhibits power law behavior with a slope of -3.7 between a maximum at approximately 10 um up to about 40 um. When gravity is invoked, turbulence is found to dominate the time evolution of an initially monodisperse droplet distribution at early times. At later times, however, gravity takes over and dominates the collisional growth. We find that the formation of large droplets is very sensitive to the turbulent energy dissipation rate. This is due to the fact that turbulence enhances the collisional growth between similar sized droplets at the early stage of raindrop formation. The mean collision rate grows exponentially, which is consistent with the theoretical prediction of the continuous collisional growth even when turbulence-generated collisions are invoked. This consistency only reflects the mean effect of turbulence on collisional growth

Quantitative Central Limit Theorems for Discrete Stochastic Processes

In this paper, we establish a generalization of the classical Central Limit Theorem for a family of stochastic processes that includes stochastic gradient descent and related gradient-based algorithms. Under certain regularity assumptions, we show that the iterates of these stochastic processes converge to an invariant distribution at a rate of O\lrp{1/\sqrt{k}} where $k$ is the number of steps; this rate is provably tight

Thermodynamics of the bilinear-biquadratic spin one Heisenberg chain

The magnetic susceptibility and specific heat of the one-dimensional S=1 bilinear-biquadratic Heisenberg model are calculated using the transfer matrix renormalization group. By comparing the results with the experimental data of ${\rm LiVGe_2O_6}$ measured by Millet et al. (Phys. Rev. Lett. {\bf 83}, 4176 (1999)), we find that the susceptibility data of this material, after subtracting the impurity contribution, can be quantitatively explained with this model. The biquadratic exchange interaction in this material is found to be ferromagnetic, i.e. with a positive coupling constant.Comment: 4 pages, 4 postscript figure

An experimental study of concrete resistivity and the effects of electrode configuration and current frequency on measurement

Electrical resistivity, a measurable parameter of the state of concrete, plays an important role in the assessment of reinforced concrete structures. An experimental study using two-electrode method has been conducted to evaluate the resistivity of Portland cement concrete. Internal and external electrodes were varied in order to understand effect of the electrodes configuration, where carbon fibre (CF) sheets were employed as the internal electrodes and CF and copper sheets were used as external electrodes. Furthermore, frequency of applied current was varied from low to high, to identify the most suitable frequency that can be utilized for stable and reliable results. Optimised internal electrodes configuration and the current frequency of 10,000 Hz were used to measure the resistivity on a series of concrete cubes, which were made using three different water to cement ratios and four different chloride contents