Search results for "basis"
showing 10 items of 760 documents
OpenMolcas: From Source Code to Insight
2019
In this article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multico…
Towards Stable Radial Basis Function Methods for Linear Advection Problems
2021
In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced strongly in RBF methods. By now it is well-known that this can lead to stability problems, however. Here, we follow a different path and propose two novel RBF approaches which are based on a weak enforcement of BCs. By using the concept of flux reconstruction and simultaneous approximation terms (SATs), respectively, we are able to prove that both new RBF schemes are strongly (energy) stable. Numerical results in one and two spatial dimensions for both scalar equations and systems are presented, supporting our theoret…
Gradient design for liquid chromatography using multi-scale optimization.
2017
Abstract In reversed phase-liquid chromatography, the usual solution to the “general elution problem” is the application of gradient elution with programmed changes of organic solvent (or other properties). A correct quantification of chromatographic peaks in liquid chromatography requires well resolved signals in a proper analysis time. When the complexity of the sample is high, the gradient program should be accommodated to the local resolution needs of each analyte. This makes the optimization of such situations rather troublesome, since enhancing the resolution for a given analyte may imply a collateral worsening of the resolution of other analytes. The aim of this work is to design mul…
An atlas- and data-driven approach to initializing reaction-diffusion systems in computer cardiac electrophysiology
2016
The cardiac electrophysiology (EP) problem is governed by a nonlinear anisotropic reaction-diffusion system with a very rapidly varying reaction term associated with the transmembrane cell current. The nonlinearity associated with the cell models requires a stabilization process before any simulation is performed. More importantly, when used in a 3-dimensional (3D) anatomy, it is not sufficient to perform this stabilization on the basis of isolated cells only, since the coupling of the different cells through the tissue greatly modulates the dynamics of the system. Therefore, stabilization of the system must be performed on the entire 3D model. This work develops a novel procedure for the i…
On the impact of side methyl groups on the structure and vibrational properties of β-carotenoids. The case of butadiene and isoprene
2021
Abstract Theoretical consideration about the impact of methyl groups on the structure and vibrational properties of β-carotenoids, using medium size molecules of trans-butadiene and trans-isoprene, are reported. Density functional theory (DFT) calculations with correlation-consistent and polarization-consistent basis sets were applied to trans-1,3-butadiene and trans-isoprene as the smallest building bricks of β-carotenoids. Their structure and harmonic vibrations were estimated in the complete basis set limit (CBS) using the non-linear least square fit. Optimized geometries and harmonic frequencies, obtained with B3LYP and BLYP density functionals and large basis sets, were favorably repro…
Estimating the temperature evolution of foodstuffs during freezing with a 3D meshless numerical method
2015
Abstract Freezing processes are characterised by sharp changes in specific heat capacity and thermal conductivity for temperatures close to the freezing point. This leads to strong nonlinearities in the governing PDE that may be difficult to resolve using traditional numerical methods. In this work we present a meshless numerical method, based on a local Hermite radial basis function collocation approach in finite differencing mode, to allow the solution of freezing problems. By introducing a Kirchhoff transformation and solving the governing equations in Kirchhoff space, the strength of nonlinearity is reduced while preserving the structure of the heat equation. In combination with the hig…
Testing experimental designs in liquid chromatography (I): Development and validation of a method for the comprehensive inspection of experimental de…
2020
The basis of interpretive optimisation in liquid chromatography is the prediction of resolution, from appropriate solute retention models. The reliability of the process depends critically on the quality of the experimental design. This work develops, validates and applies a general methodology aimed to evaluate the quality of any training experimental design, which will be applied in Part II to design optimisation. The methodology is based on the systematic evaluation of the uncertainties associated to the prediction of retention times in comprehensive scans of both isocratic and gradient experimental conditions. It is able to evaluate comprehensively experimental designs of arbitrary comp…
Layer-Wise Discontinuous Galerkin Methods for Piezoelectric Laminates
2020
In this work, a novel high-order formulation for multilayered piezoelectric plates based on the combination of variable-order interior penalty discontinuous Galerkin methods and general layer-wise plate theories is presented, implemented and tested. The key feature of the formulation is the possibility to tune the order of the basis functions in both the in-plane approximation and the through-the-thickness expansion of the primary variables, namely displacements and electric potential. The results obtained from the application to the considered test cases show accuracy and robustness, thus confirming the developed technique as a supplementary computational tool for the analysis and design o…
Pressure-Driven Isostructural Phase Transition in InNbO4: In Situ Experimental and Theoretical Investigations
2017
[EN] The high-pressure behavior of technologically important visible-light photocatalytic semiconductor In.NbO4, adopting a monoclinic wolframite-type structure at ambient conditions, was investigated using synchrotron-based X-ray diffraction, Raman spectroscopic measurements, and first-principles calculations. The experimental results indicate the occurrence of a pressure-induced isostructural phase transition in the studied compound beyond 10.8 GPa. The large volume collapse associated with the phase transition and the coexistence of two phases observed over a wide range of pressure shows the nature of transition to be first-order. There is an increase in the oxygen anion coordination num…
Complete basis set prediction of methanol isotropic nuclear magnetic shieldings and indirect nuclear spin–spin coupling constants (SSCC) using polari…
2009
Efficient B3LYP and BHandH density functionals were used to estimate methanol's nuclear magnetic isotropic shieldings and spin–spin coupling constants in the basis set limit. Polarization‐consistent pcS‐n and pcJ‐n (n = 0, 1, 2, 3 and 4), and segmented contracted XZP, where X = D, T, Q and 5, basis sets were used and the results fitted with simple mathematical formulas. The performance of the methods was assessed from comparison with experiment and higher level calculations. 1J(CH) and 3J(HH) values were determined from very diluted solutions in deuterochloroform and compared with theoretical predictions. The agreement between complete basis set (CBS) density functional theory (DFT) predict…