Quantum electrodynamics of resonance energy transfer in nanowire systems

Nonradiative resonance energy transfer (RET) provides the ability to transfer excitation energy between contiguous nanowires (NWs) with high efficiency under certain conditions. Nevertheless, the well-established Forster formalism commonly used to represent RET was developed for energy transfer primarily between molecular blocks (i.e., from one molecule, or part of a molecule, to another). Although deviations from Forster theory for functional blocks such as NWs have been studied previously, the role of the relative distance, the orientation of transition dipole moment pairs, and the passively interacting matter on electronic energy transfer are to a large extent unknown. Thus, a comprehensive theory that models RET in NWs is required. In this context, analytical insights to give a deeper and more intuitive understanding of the distance and orientation dependence of RET in NWs is presented within the framework of quantum electrodynamics. Additionally, the influence of an included intermediary on the rate of excitation energy transfer is illustrated, embracing indirect energy transfer rate and quantum interference. The results deliver equations that afford new intuitions into the behavior of virtual photons. In particular, results indicate that RET efficiency in a NW system can be explicitly expedited or inhibited by a neighboring mediator, depending on the relative spacing and orientation of NWs

A Distributed Approach for the Optimal Power Flow Problem Based on ADMM and Sequential Convex Approximations

The optimal power flow (OPF) problem, which plays a central role in operating electrical networks is considered. The problem is nonconvex and is in fact NP hard. Therefore, designing efficient algorithms of practical relevance is crucial, though their global optimality is not guaranteed. Existing semi-definite programming relaxation based approaches are restricted to OPF problems where zero duality holds. In this paper, an efficient novel method to address the general nonconvex OPF problem is investigated. The proposed method is based on alternating direction method of multipliers combined with sequential convex approximations. The global OPF problem is decomposed into smaller problems associated to each bus of the network, the solutions of which are coordinated via a light communication protocol. Therefore, the proposed method is highly scalable. The convergence properties of the proposed algorithm are mathematically substantiated. Finally, the proposed algorithm is evaluated on a number of test examples, where the convergence properties of the proposed algorithm are numerically substantiated and the performance is compared with a global optimal method.Comment: 14 page

On the Convergence of Alternating Direction Lagrangian Methods for Nonconvex Structured Optimization Problems

Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods. The study of the convergence properties of these methods is in general difficult due to the nonconvexity of the problem. In this paper, two distributed solution methods that combine the fast convergence properties of augmented Lagrangian-based methods with the separability properties of alternating optimization are investigated. The first method is adapted from the classic quadratic penalty function method and is called the Alternating Direction Penalty Method (ADPM). Unlike the original quadratic penalty function method, in which single-step optimizations are adopted, ADPM uses an alternating optimization, which in turn makes it scalable. The second method is the well-known Alternating Direction Method of Multipliers (ADMM). It is shown that ADPM for nonconvex problems asymptotically converges to a primal feasible point under mild conditions and an additional condition ensuring that it asymptotically reaches the standard first order necessary conditions for local optimality are introduced. In the case of the ADMM, novel sufficient conditions under which the algorithm asymptotically reaches the standard first order necessary conditions are established. Based on this, complete convergence of ADMM for a class of low dimensional problems are characterized. Finally, the results are illustrated by applying ADPM and ADMM to a nonconvex localization problem in wireless sensor networks.Comment: 13 pages, 6 figure

Optical control of resonance energy transfer in quantum dot systems

We demonstrate that the rate of resonance energy transfer can be extensively controlled through an applied off-resonant radiation field under favourable physical configurations of the quantum dots