The growth of horizontal nanowires (NWs) guided by epitaxial and graphoepitaxial relations with the substrate is becoming increasingly attractive owing to the possibility of controlling their position, direction, and crystallographic orientation. In guided NWs, as opposed to the extensively characterized vertically grown NWs, there is an increasing need for understanding the relation between st...

We implement two recently developed fast Coulomb solvers, HSMA3D (Zhao et al. (2018) [49]) and HSMA2D (Liang (2020) [50]), into a new user package HSMA for the molecular dynamics simulation engine LAMMPS. The is designed efficient accurate modeling of electrostatic interactions in 3D 2D periodic systems with dielectric effects at O(N) cost. implementation hybrid MPI OpenMP parallelized compatib...

In this paper, we study and analyze seven state-of-the-art volumetric illumination methods, in order to determine their differences with respect to the underlying theoretical mathematical models and numerical problems potentially arising during implementation. The chosen models are half angle slicing, directional occlusion shading, multidirectional occlusion shading, shadow volume propagation, ...

Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the boundary of a 3D model (which is a surface). Volumetric parameterization is typically helpful in solving complicated geometric problems pertaining to shape mat...

We show that the full symbol of the Dirichlet to Neumann map of the k-form Laplace’s equation on a Riemannian manifold (of dimension greater than 2) with boundary determines the full Taylor series of the metric at the boundary. This extends the result of Lee and Uhlmann for the case k = 0. The proof avoids the computation of the full symbol by using the calculus of pseudo-differential operators...

Let fβ = hβ + gβ and Fa = Ha +Ga be harmonic mappings obtained by shearing of analytic mappings hβ + gβ = 1/(2isinβ) log ( (1 + ze)/(1 + ze) ) , 0 < β < π and Ha+Ga = z/(1 − z), respectively. Kumar et al. [7] conjectured that if ω(z) = ez(θ ∈ R, n ∈ N) and ωa(z) = (a − z)/(1 − az), a ∈ (−1, 1) are dilatations of fβ and Fa, respectively, then Fa∗̃fβ ∈ S 0 H and is convex in the direction of the r...

In recent years, the CMRC filter has been an attractive candidate for use in mixer and frequency multiplier circuits to improve the performance due to its low-insertion loss, sharp rejection, shorter size and wider stop-band. However, complex structures, too much variables and inefficient design method hindered its widespread use. In this study, we report on the application of the implicit spac...

Hodge theory is a fundamental tool of Kähler geometry. It represents cohomology classes by harmonic forms, and deriving properties of these harmonic forms then in turn yields information about the cohomology. Homology or cohomology groups, however, contain only partial information about the topology of a manifold. The most important topological invariant of a manifold X is the fundamental group...