Optical properties of two-electron quantum dots in low lying para- and ortho-states

Two low lying energy levels of 3D two-electron quantum dot with rigid confinement (the wave functions vanish at the surface of the quantum dot) are obtained by the variational and perturbation methods. There are two kind of quantum dots: para- and ortho-dots with antiparallel and parallel electron spins, respectively. An ensemble of the two-electron quantum dots contains para-dots in the ground state and ortho-dots in the lowest metastable state at low enough temperatures. The optical parameters of GaAs two-electron quantum dot are calculated with the help of obtained energy levels and compared with the optical parameters known for the one electron GaAs quantum dot. The Coulomb interaction between electrons is responsible for the blue shift of maxima of the absorption coefficient and refractive index of two-electron quantum dots.     

Results on Nonlocal Boundary Value Problems

In this article, we provide a variational theory for nonlocal problems where nonlocality arises due to the interaction in a given horizon. With this theory, we prove well-posedness results for the weak formulation of nonlocal boundary value problems with Dirichlet, Neumann, and mixed boundary conditions for a class of kernel functions. The motivating application for nonlocal boundary value problems is the scalar stationary peridynamics equation of motion. The well-posedness results support practical kernel functions used in the peridynamics setting.

We also prove a spectral equivalence estimate which leads to a mesh size independent upper bound for the condition number of an underlying discretized operator. This is a fundamental conditioning result that would guide preconditioner construction for nonlocal problems. The estimate is a consequence of a nonlocal Poincaré-type inequality that reveals a horizon size quantification. We provide an example that establishes the sharpness of the upper bound in the spectral equivalence.     

Quantitative characterization of shear force regulation for scanning electrochemical microscopy

The quest for higher spatial resolution in scanning electrochemical microscopy (SECM) calls for the application of smaller probe electrodes. When electrodes are to be used in the feedback mode, smaller electrodes require higher intrinsic kinetics at the sample. The fabrication of nanoelectrodes, as well as their use as SECM probes at constant distance, are reported. The properties of shear force regulation system are characterized quantitatively. Simultaneous topography and reactivity imaging were demonstrated using gold microstructures on a glass substrate.     

Weighted and regularity estimates for nonlinear equations on Reifenberg flat domains

Global weighted Lp estimates are obtained for the gradient of solutions to nonlinear elliptic Dirichlet boundary value problems over a bounded nonsmooth domain. Morrey and Hölder regularity of solutions are also established, as a consequence. These results generalize various existing estimates for nonlinear equations. The nonlinearities are of at most linear growth and assumed to have a uniform small mean oscillation. The boundary of the domain, on the other hand, may exhibit roughness but assumed to be sufficiently flat in the sense of Reifenberg. Our approach uses maximal function estimates and Vitali covering lemma, and also known regularity results of solutions to nonlinear homogeneous equations.     

Direct approach to the problem of strong local minima in calculus of variations

Let (M,g) be a two-dimensional compact Riemannian manifold. In this paper, we use the method of blowing up analysis to prove several Moser–Trudinger type inequalities for vector bundle over (M,g). We also derive an upper bound of such inequalities under the assumption that blowing up occurs. The research of the second author was partially supported by NSFC grant and the Foundation of Shanghai for Priority Academic Discipline.     

Nonlocal Constrained Value Problems for a Linear Peridynamic Navier Equation

In this paper, we carry out further mathematical studies of nonlocal constrained value problems for a peridynamic Navier equation derived from linear state-based peridynamic models. Given the nonlocal interactions effected in the model, constraints on the solution over a volume of nonzero measure are natural conditions to impose. We generalize previous well-posedness results that were formulated for very special kernels of nonlocal interactions. We also give a more rigorous treatment to the convergence of solutions to nonlocal peridynamic models to the solution of the conventional Navier equation of linear elasticity as the horizon parameter goes to zero. The results are valid for arbitrary Poisson ratio, which is a characteristic of the state-based peridynamic model.     

Photovoltaic characteristics and dye regeneration kinetics in D149-sensitized ZnO with varied dye loading and film thickness

Porous ZnO electrodes on fluorine-doped tin oxide (FTO) were prepared by electrochemical deposition from an O(2)-saturated ZnCl(2) solution in the presence of eosin Y as a structure directing agent (SDA). Sensitization was reached by desorption of the SDA and subsequent adsorption of the indoline dye D149. The influence of film thickness and dye concentration in the films on their photovoltaic characteristics, recombination, and dye regeneration kinetics was investigated. The recombination kinetics was analyzed by time-resolved photovoltage measurements. The dye regeneration by iodide ions in the electrolyte was investigated using scanning electrochemical microscopy (SECM) feedback mode approach curves. Analysis of a SECM kinetic model shows strongly different effective D149 regeneration rate constants k'(ox) for D149-ZnO electrodes of systematically varied film thickness and dye loading. It was found that the short-circuit current density J(sc) and k'(ox) correlated directly with the adsorbed dye concentration. k'(ox) was found to be independent of the dye loading but correlated strongly with the dye concentration in the film or inversely with the film thickness. Furthermore, we discussed the perspective of correlating macroscopic cell characteristics with SECM kinetics data.