Search results for "algebra"
showing 10 items of 4129 documents
Some Theoretical Results About Stability for IMEX Schemes Applied to Hyperbolic Equations with Stiff Reaction Terms
2010
In this work we are concerned with certain numerical difficulties associated to the use of high order Implicit–Explicit Runge–Kutta (IMEX-RK) schemes in a direct discretization of balance laws with stiff source terms. We consider a simple model problem, introduced by LeVeque and Yee in [J. Comput. Phys 86 (1990)], as the basic test case to explore the ability of IMEX-RK schemes to produce and maintain non-oscillatory reaction fronts.
Beyond ideal two-dimensional metals: Edges, vacancies, and polarizabilities
2018
Recent experimental discoveries of graphene-stabilized patches of two-dimensional (2D) metals have motivated also their computational studies. However, so far the studies have been restricted to ideal and infinite 2D metallic monolayers, which is insufficient because in reality the properties of such metallic patches are governed by microstructures pervaded by edges, defects, and several types of perturbations. Here we use density-functional theory to calculate edge and vacancy formation energies of hexagonal and square lattices of 45 elemental 2D metals. We find that the edge and vacancy formation energies are strongly correlated and decrease with increasing Wigner-Seitz radii, analogously…
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…
A high-resolution layer-wise discontinuous Galerkin formulation for multilayered composite plates
2020
Abstract In this work, a novel high-resolution formulation for multilayered composite plates is presented. The formulations is referred to as high-resolution since it combines (i) Layer-Wise plate theories, which are based on a per-layer, high-order expansion of the primary variables throughout the plate’s thickness, providing a detailed layer-level description of the sought solution; (ii) The discontinuous Galerkin method, a numerical approach based on a discontinuous representation of the unknown fields over the mesh elements and on the introduction of boundary integral operators enforcing inter-element continuity, which allow the natural treatment of high-order mesh elements and provide …
SIMULATION OF THE HEAT TRANSPORT PROBLEMS WITH RADIATION IN PLATE
2001
In the literature [1 -5 ] simple and effective algorithms for mathematical modelling processes of distribution of heat in multilayered spaces are created. In the given work the way of improvement o f accuracy of algorithms is considered at approximation of integrals derivatives more the supreme orders are used.
Chain Connectivity and Conformational Variability of Polymers: Clues to an Adequate Thermodynamic Description of Their Solutions, 1
2003
This is the first of two parts investigating the Flory-Huggins interaction parameter, χ, as a function of composition and chain length. Part 1 encompasses experimental and theorical work. The former comprise the synthesis of poly(dimethylsiloxane)s with different molar mass and the measurements of their second second osmotic virial coefficients, A 2 , in solvents of diverse quality as a function of M via light scattering and osmotic pressures. The theorical analysis is performed by subdividing the dilution process into two clearly separable steps. It yields the following expression for χ ο , the χ value in range of pair interaction : χ ο = α - ζ λ. The parameter α measures the effect of con…
Kramers potential study of the Rouse-like dynamics of short alkane chains.
1999
In this work we present a Kramers potential study of the orientational dynamics and shear viscosity of short chain alkanes. In this approach the determination of the orientational relaxation time is reduced to the calculation of static moments of single chain conformations. We study a chemically realistic alkane model that asymptotically produces Gaussian chain conformations by means of a Monte Carlo simulation. Our results are applicable to single chain descriptions of polymer melt dynamics and to the intrinsic viscosity of molecules in a Theta solvent. When we map the unknown time unit of our relaxation time result for one particular chain length and temperature to the value obtained for …
The F-pure threshold of quasi-homogeneous polynomials
2018
Abstract Inspired by the work of Bhatt and Singh [3] we compute the F-pure threshold of quasi-homogeneous polynomials. We first consider the case of a curve given by a quasi-homogeneous polynomial f in three variables x , y , z of degree equal to the degree of xyz and then we proceed with the general case of a Calabi–Yau hypersurface, i.e. a hypersurface given by a quasi-homogeneous polynomial f in n + 1 variables x 0 , … , x n of degree equal to the degree of x 0 ⋯ x n .
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…