Aharonov-Bohm effect in monolayer black phosphorus (phosphorene) nanorings

This work presents theoretical demonstration of Aharonov-Bohm (AB) effect in monolayer phosphorene nanorings (PNR). Atomistic quantum transport simulations of PNR are employed to investigate the impact of multiple modulation sources on the sample conductance. In presence of a perpendicular magnetic field, we find that the conductance of both armchair and zigzag PNR oscillate periodically in a low-energy window as a manifestation of the AB effect. Our numerical results have revealed a giant magnetoresistance (MR) in zigzag PNR (with a maximum magnitude approaching two thousand percent). It is attributed to the AB effect induced destructive interference phase in a wide energy range below the bottom of the second subband. We also demonstrate that PNR conductance is highly anisotropic, offering an additional way to modulate MR. The giant MR in PNR is maintained at room temperature in the presence of thermal broadening effect.Comment: 7 pages, 7 figure

A simulation study of confidence intervals for the transition matrix of a reversible Markov chain

Master of ScienceDepartment of StatisticsJames W. Neil

On the Sample Size of Random Convex Programs with Structured Dependence on the Uncertainty (Extended Version)

The "scenario approach" provides an intuitive method to address chance constrained problems arising in control design for uncertain systems. It addresses these problems by replacing the chance constraint with a finite number of sampled constraints (scenarios). The sample size critically depends on Helly's dimension, a quantity always upper bounded by the number of decision variables. However, this standard bound can lead to computationally expensive programs whose solutions are conservative in terms of cost and violation probability. We derive improved bounds of Helly's dimension for problems where the chance constraint has certain structural properties. The improved bounds lower the number of scenarios required for these problems, leading both to improved objective value and reduced computational complexity. Our results are generally applicable to Randomized Model Predictive Control of chance constrained linear systems with additive uncertainty and affine disturbance feedback. The efficacy of the proposed bound is demonstrated on an inventory management example.Comment: Accepted for publication at Automatic

A scenario approach for non-convex control design

Randomized optimization is an established tool for control design with modulated robustness. While for uncertain convex programs there exist randomized approaches with efficient sampling, this is not the case for non-convex problems. Approaches based on statistical learning theory are applicable to non-convex problems, but they usually are conservative in terms of performance and require high sample complexity to achieve the desired probabilistic guarantees. In this paper, we derive a novel scenario approach for a wide class of random non-convex programs, with a sample complexity similar to that of uncertain convex programs and with probabilistic guarantees that hold not only for the optimal solution of the scenario program, but for all feasible solutions inside a set of a-priori chosen complexity. We also address measure-theoretic issues for uncertain convex and non-convex programs. Among the family of non-convex control- design problems that can be addressed via randomization, we apply our scenario approach to randomized Model Predictive Control for chance-constrained nonlinear control-affine systems.Comment: Submitted to IEEE Transactions on Automatic Contro