Search results for " Mathematics"
showing 10 items of 10797 documents
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.
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…
On numerical broadening of particle size spectra: a condensational growth study using PyMPDATA 1.0
2021
Abstract. The work discusses the diffusional growth in particulate systems such as atmospheric clouds. It focuses on the Eulerian modeling approach in which the evolution of the probability density function describing the particle size spectrum is carried out using a fixed-bin discretization. The numerical diffusion problem inherent to the employment of the fixed-bin discretization is scrutinized. The work focuses on the applications of MPDATA family of numerical schemes. Several MPDATA variants are explored including: infinite-gauge, non-oscillatory, third-order-terms and recursive antidiffusive correction (double pass donor cell, DPDC) options. Methodology for handling coordinate transfor…
HF radar for wind waves measurements in the Malta-Sicily Channel
2018
Abstract The CALYPSO HF radar network is a permanent and fully operational observing system currently composed of four CODAR SeaSonde stations. The system is providing real-time hourly maps of sea surface currents and waves data in the Malta-Sicily Channel. The present work aims to compare significant wave height measurements by HF Radar to wave data from numerical models and satellite altimeter. This is the first time that this set of wave data are analysed since the four HF radars were installed between 2012 and 2015. Results suggest that CODAR HF Radar wave data are a reliable source of wave information even in the case of extreme events, providing an avenue to improve and complete the o…
Evidence of active fluid seepage (AFS) in the southern region of the central Mediterranean Sea
2018
Abstract Active fluid seepage (AFS) at the seafloor is a global phenomenon associated with seafloor morphologies in different geodynamic contexts. Advanced geophysical techniques have allowed geoscientists to characterise pockmarks, mounds and flares associated with AFS. We present a range of new marine geological data acquired in the southern region of the central Mediterranean Sea (northern Sicily continental margin, northwestern Sicily Channel and offshore of the Maltese Islands), which allow us to identify AFSs. AFSs are spatially distributed as clusters, aligned or isolated at different depths, ranging from few decametres offshore of the Maltese Islands; up to 400 m offshore of norther…
Nitrogen broadening of SF6 transitions in the nu3 band
2001
Abstract Nitrogen induced pressure-broadened halfwidths of a number of ν3 transitions of SF6 are calculated using the complex Robert–Bonamy (CRB) formalism. The calculations are made at 200, 250, 296 and 350 K and the temperature dependence of the halfwidths are determined. The intermolecular potential is taken as a sum of the leading electrostatic and Lennard-Jones [6] , [7] , [8] , [9] , [10] , [11] , [12] atom–atom components. The dynamics of the collision process are correct to second order in time. The calculated halfwidths are used to simulate the ν3 spectrum, which is compared to a simulation made using the HITRAN96 halfwidths and measurements made at the Universite Pierre et Marie C…