Search results for " math"

Reversed polarized emission in highly strained a-plane GaN/AlN multiple quantum wells

2010

The polarization of the emission from a set of highly strained $a$-plane GaN/AlN multiple quantum wells of varying well widths has been studied. A single photoluminescence peak is observed that shifts to higher energies as the quantum well thickness decreases due to quantum confinement. The emitted light is linearly polarized. For the thinnest samples the preferential polarization direction is perpendicular to the wurtzite $c$ axis with a degree of polarization that decreases with increasing well width. However, for the thickest well the preferred polarization direction is parallel to the $c$ axis. Raman scattering, x-ray diffraction, and transmission electron microscopy studies have been p…

Multimode time-dependent gyrotron equations for different time scales

2017

The work of H.K. was supported by the European Regional Development Funding of the Project No. 1.1.1.1/ 16/A/004.

Diagrammatic Expansion for Positive Spectral Functions in the Steady-State Limit

2019

Recently, a method was presented for constructing self-energies within many-body perturbation theory that are guaranteed to produce a positive spectral function for equilibrium systems, by representing the self-energy as a product of half-diagrams on the forward and backward branches of the Keldysh contour. We derive an alternative half-diagram representation that is based on products of retarded diagrams. Our approach extends the method to systems out of equilibrium. When a steady-state limit exists, we show that our approach yields a positive definite spectral function in the frequency domain.

Spin-orbit ZORA and four-component Dirac-Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble …

2015

Hartree-Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin-orbit zeroth-order regular approximation Hamiltonian in combination with the large Slater-type basis set QZ4P as well as with the four-component Dirac-Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles …

Approximate treatment of higher excitations in coupled-cluster theory. II. Extension to general single-determinant reference functions and improved a…

2008

The theory and implementation of approximate coupled-cluster (CC), in particular approximate CC singles, doubles, triples, and quadruples methods, are discussed for general single-determinant reference functions. While the extension of iterative approximate models to the non-Hartree-Fock case is straightforward, the generalization of perturbative approaches is not trivial. In contrast to the corresponding perturbative triples methods, there are additional terms required for non-Hartree-Fock reference functions, and there are several possibilities to derive approximations to these terms. As it turns out impossible to develop an approach that is consistent with the canonical Hartree-Fock-base…

Smoothed Spherical Truncation based on Fuzzy Membership Functions: Application to the Molecular Encoding.

2019

A novel spherical truncation method, based on fuzzy membership functions, is introduced to truncate interatomic (or interaminoacid) relations according to smoothing values computed from fuzzy membership degrees. In this method, the molecules are circumscribed into a sphere, so that the geometric centers of the molecules are the centers of the spheres. The fuzzy membership degree of each atom (or aminoacid) is computed from its distance with respect to the geometric center of the molecule, by using a fuzzy membership function. So, the smoothing value to be applied in the truncation of a relation (or interaction) is computed by averaging the fuzzy membership degrees of the atoms (or aminoacid…

Harmonic morphisms in nonlinear potential theory

1992

This article concerns the following problem: given a family of partial differential operators with similar structure and given a continuous mapping f from an open set Ω in Rn into Rn, then when does f pull back the solutions of one equation in the family to solutions of another equation in that family? This problem is typical in the theory of differential equations when one wants to use a coordinate change to study solutions in a different environment.

Viewpoint: Atomic-Scale Design Protocols toward Energy, Electronic, Catalysis, and Sensing Applications

2019

Nanostructured materials are essential building blocks for the fabrication of new devices for energy harvesting/storage, sensing, catalysis, magnetic, and optoelectronic applications. However, because of the increase of technological needs, it is essential to identify new functional materials and improve the properties of existing ones. The objective of this Viewpoint is to examine the state of the art of atomic-scale simulative and experimental protocols aimed to the design of novel functional nanostructured materials, and to present new perspectives in the relative fields. This is the result of the debates of Symposium I "Atomic-scale design protocols towards energy, electronic, catalysis…

Fractals and geography

2007

Stochastic Galerkin method for cloud simulation

2018

AbstractWe develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertainties that arise due to unknown input data, such as model parameters and initial or boundary conditions. The developed stochastic Galerkin method combines the space-time approximation obtained by a suitable finite volume method with a spectral-type approximation based on the generalized polynomial chaos expansion in the stochastic space. The resulting numerical scheme yields a second-order accurate approximation in both space and time and exponential convergence in the stochastic space. Our numerical results…