Search results for "Linear Algebra"
showing 10 items of 552 documents
Accurate molecular geometries of the protonated water dimer
2000
The equilibrium geometry of the protonated water dimer, H5O2+, was studied using Moller–Plesset perturbation theory and coupled-cluster theory. Constrained geometry optimizations were carried out for the C2 and Cs symmetric structures within the counterpoise framework and near the limit of a complete basis set. In the constrained optimization, the degrees of freedom of the complex are reduced to an intrafragmental distortion and an interfragmental coordinate, making the procedure tractable for large basis sets and explicitly correlated linear r12 methods. The energy of the stationary point of C2 symmetry was found to be 1.2 kJ mol−1 below the energy of the Cs structure.
New-stage discharge relationship for weirs of finite crest lenght
2014
AbstractThe flow process of weirs of finite crest length is analyzed on the basis of the dimensional analysis and incomplete self-similarity theory. The crest length is incorporated in the functional stage-discharge relationship for weirs of finite crest length. The theoretically deduced stage-discharge formula was then calibrated using the experimental data compiled in this research. According to the current experimental data it is also concluded that the performance of the proposed stage-discharge formula is better than the previous dimensional stage-discharge formulae. Also, the proposed stage-discharge formula is applicable for all types of the weirs, i.e., long-crested, broad-crested, …
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…
Relations between multi-resolution analysis and quantum mechanics
2005
We discuss a procedure to construct multiresolution analyses (MRA) of L2 (R) starting from a given seed function h (s) which should satisfy some conditions. Our method, originally related to the quantum mechanical Hamiltonian of the fractional quantum Hall effect, is shown to be model independent. The role of a canonical map between certain canonically conjugate operators is discussed. This clarifies our previous procedure and makes much easier most of the original formulas, producing a convenient framework to produce examples of MRA. © 2005 American Institute of Physics.
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…
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…
Extending CSG with projections: Towards formally certified geometric modeling
2015
We extend traditional Constructive Solid Geometry (CSG) trees to support the projection operator. Existing algorithms in the literature prove various topological properties of CSG sets. Our extension readily allows these algorithms to work on a greater variety of sets, in particular parametric sets, which are extensively used in CAD/CAM systems. Constructive Solid Geometry allows for algebraic representation which makes it easy for certification tools to apply. A geometric primitive may be defined in terms of a characteristic function, which can be seen as the zero-set of a corresponding system along with inequality constraints. To handle projections, we exploit the Disjunctive Normal Form,…
OPTIMIZATIONS FOR TENSORIAL BERNSTEIN–BASED SOLVERS BY USING POLYHEDRAL BOUNDS
2010
The tensorial Bernstein basis for multivariate polynomials in n variables has a number 3n of functions for degree 2. Consequently, computing the representation of a multivariate polynomial in the tensorial Bernstein basis is an exponential time algorithm, which makes tensorial Bernstein-based solvers impractical for systems with more than n = 6 or 7 variables. This article describes a polytope (Bernstein polytope) with a number of faces, which allows to bound a sparse, multivariate polynomial expressed in the canonical basis by solving several linear programming problems. We compare the performance of a subdivision solver using domain reductions by linear programming with a solver using a c…