Theoretical investigation of the dangling bond defects in hydrogenated amorphous silicon (a-Si:H) by the self-consistent-field X-alpha scattered-wave cluster molecular-orbital method

We have performed molecular-orbital investigations of the local electronic nature of the dangling bond defect centers in hydrogenated amorphous silicon (a-Si:H) using the self-consistent-field X-alpha scattered-wave (SCF-Xα-SW) cluster molecular-orbital method. The results are able to provide a theoretical explanation for the existence of a negative effective correlation energy U_eff for these defect centers in terms of thir local chemical character. Implications of these results are discussed.     

Metal insulator transition due to surface roughness scattering in a quantum well

We calculate the critical width a_c for a quantum well structure as function of the two-dimensional electron density. For a > a_c the electron gas has a finite dc conductivity at temperature zero, and for a < a_c the dc conductivity is zero. Homogeneous background doping, remote doping, and surface roughness scattering are considered. Due to surface roughness we find a strong increase of a_c at high electron concentration, in novel contrast to heterostructures. Explicit results are presented for GaAs and InAs quantum wells and compared with experimental results. Experiments are suggested to test the predictions of the localization theory.     

Free vibration of an elliptic ring membrane clamped along two confocal ellipses

Free vibration of an elliptical ring membrane clamped along two confocal ellipses is studied analytically, and the natural frequencies are tabulated for the first four modes of vibration.     

Estimates for the probability of ruin starting with a large initial reserve

Using the strong approximation of the risk reserve process, the accuracy of the diffusion approximation of the ruin probabilities is studied.     

An (s,S) random lifetime inventory model with a positive lead time

Positive lead times substantially complicate the modeling and analysis of inventory systems with finite shelf lifetimes and they have not been sufficiently addressed in the existing literature. In this paper, we analyze an (s, S) continuous review model with a positive lead time. We assume an exponential lifetime and an exponential lead time. Matrix-geometric solutions can be obtained for the steady state probability distribution of the inventory level. We then derive the total expected cost function. We carry out numerical studies and gain insights to the selection of system parameters. The findings on the impact of a positive lead time on the optimal reorder point and reorder batch size will be useful in developing strategies in handling inventory problems with finite lifetimes and positive lead times.     

Phase Transitions and Spatio-Temporal Fluctuations in Stochastic Lattice Lotka–Volterra Models

We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka–Volterra type interactions defined on a d-dimensional lattice. Introducing spatial degrees of freedom and allowing for stochastic fluctuations generically invalidates the classical, deterministic mean-field picture. Already within mean-field theory, however, spatial constraints, modeling locally limited resources, lead to the emergence of a continuous active-to-absorbing state phase transition. Field-theoretic arguments, supported by Monte Carlo simulation results, indicate that this transition, which represents an extinction threshold for the predator population, is governed by the directed percolation universality class. In the active state, where predators and prey coexist, the classical center singularities with associated population cycles are replaced by either nodes or foci. In the vicinity of the stable nodes, the system is characterized by essentially stationary localized clusters of predators in a sea of prey. Near the stable foci, however, the stochastic lattice Lotka–Volterra system displays complex, correlated spatio-temporal patterns of competing activity fronts. Correspondingly, the population densities in our numerical simulations turn out to oscillate irregularly in time, with amplitudes that tend to zero in the thermodynamic limit. Yet in finite systems these oscillatory fluctuations are quite persistent, and their features are determined by the intrinsic interaction rates rather than the initial conditions. We emphasize the robustness of this scenario with respect to various model perturbations.