Kinetic Monte Carlo simulation of faceted islands in heteroepitaxy using multi-state lattice model

A solid-on-solid model is generalized to study the formation of Ge pyramid islands bounded by (105) facets on Si(100) substrates in two dimensions. Each atomic column is not only characterized by the local surface height but also by two deformation state variables dictating the local surface tilt and vertical extension. These deformations phenomenologically model surface reconstructions in (105) facets and enable the formation of islands which better resemble faceted pyramids. We demonstrate the model by application to a kinetic limited growth regime. We observe significantly reduced growth rates after faceting and a continuous nucleation of new islands until overcrowding occurs.Comment: 7 pages, 5 figure

Prediction of Atomization Energy Using Graph Kernel and Active Learning

Data-driven prediction of molecular properties presents unique challenges to the design of machine learning methods concerning data structure/dimensionality, symmetry adaption, and confidence management. In this paper, we present a kernel-based pipeline that can learn and predict the atomization energy of molecules with high accuracy. The framework employs Gaussian process regression to perform predictions based on the similarity between molecules, which is computed using the marginalized graph kernel. To apply the marginalized graph kernel, a spatial adjacency rule is first employed to convert molecules into graphs whose vertices and edges are labeled by elements and interatomic distances, respectively. We then derive formulas for the efficient evaluation of the kernel. Specific functional components for the marginalized graph kernel are proposed, while the effect of the associated hyperparameters on accuracy and predictive confidence are examined. We show that the graph kernel is particularly suitable for predicting extensive properties because its convolutional structure coincides with that of the covariance formula between sums of random variables. Using an active learning procedure, we demonstrate that the proposed method can achieve a mean absolute error of 0.62 +- 0.01 kcal/mol using as few as 2000 training samples on the QM7 data set

Surplus Angle and Sign-flipped Coulomb Force in Projectable Horava-Lifshitz Gravity

We obtain the static spherically symmetric vacuum solutions of Horava-Lifshitz gravity theory, imposing the detailed balance condition only in the UV limit. We find the solutions in two different coordinate systems, the Painlev\'e-Gullstrand coordinates and the Poincare coordinates, to examine the consequences of imposing the projectability condition. The solutions in two coordinate systems are distinct due to the non-relativistic nature of the HL gravity. In the Painleve-Gullstrand coordinates complying with the projectability condition, the solution involves an additional integration constant which yields surplus angle and implies attractive Coulomb force between same charges.Comment: 13 page

Tunable nonlinear PT-symmetric defect modes with an atomic cell

We propose a scheme of creating a tunable highly nonlinear defect in a one-dimensional photonic crystal. The defect consists of an atomic cell filled in with two isotopes of three-level atoms. The probe-field refractive index of the defect can be made parity-time (PT) symmetric, which is achieved by proper combination of a control field and of Stark shifts induced by a far-off-resonance field. In the PT-symmetric system families of stable nonlinear defect modes can be formed by the probe field.Comment: 4 pages, 2 figures, to be appeared in Opt. Let