Search results for "Function"

Modified Gaussian models applied to the description and deconvolution of peaks in chiral liquid chromatography.

2020

Abstract The description of the profiles of chromatographic peaks has been studied extensively, with a large number of proposed mathematical functions. Among them, the accuracy achieved with modified Gaussian models that describe the deviation of an ideal Gaussian peak as a change in the peak variance or standard deviation over time, has been highlighted. These models are, in fact, a family of functions of different complexity with great flexibility to adjust chromatographic peaks over a wide range of asymmetries and shapes. However, an uncontrolled behaviour of the signal may occur outside the region being fitted, forcing the use of different strategies to overcome this problem. In this wo…

Theoretical study of oligomeric alumatranes present in the chemistry of materials from micro to mesoporous molecular sieves and alumina composites

2008

Quantum chemical calculations using density functional theory have been carried out to investigate molecular precursors based on alumatranes which are one of the components with silatranes for the preparation of mesoporous aluminosilicate materials. In the same way, some oligomeric alumatranes of this study take part in chemical syntheses related to materials such as zeolites and alumina composite. Gas phase and solution equilibrium geometries of the alumatrane precursors were fully optimized at B3LYP level, modeling solvent effects using a self-consistent reaction field (SCRF). From these optimized geometries, calculations of the 1 H, 13 C and 27 Al NMR chemical shifts at GIAO/B3LYP/6-31G(…

2019

Abstract The aim of this work is to present a formulation to solve the one-dimensional Ising model using the elementary technique of mathematical induction. This formulation is physically clear and leads to the same partition function form as the transfer matrix method, which is a common subject in the introductory courses of statistical mechanics. In this way our formulation is a useful tool to complement the traditional more abstract transfer matrix method. The method can be straightforwardly generalised to other short-range chains, coupled chains and is also computationally friendly. These two approaches provide a more complete understanding of the system, and therefore our work can be o…

A tangent formula derived from Patterson-function arguments. VII. Solution of inorganic structures from powder data with accidental overlap

2000

Accidental overlap constitutes one of the principal limitations for the solution of crystal structures from powder diffraction data, since it reduces the number of available intensities for direct-methods application. In this work, the field of application of the direct-methods sum function is extended to cope with powder patterns with relatively large amounts of accidental overlap. This is achieved by refining not only the phases of the structure factors but also the estimated intensities of the severely overlapped peaks during the structure solution process. This procedure has been specifically devised for inorganic compounds with uncertain cell contents and with probable severe atomic di…

Nonexistence Results for Higher Order Fractional Differential Inequalities with Nonlinearities Involving Caputo Fractional Derivative

2021

Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis …

Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry

2017

This work deals with free transport equations with partly diffuse stochastic boundary operators in slab geometry. Such equations are governed by stochastic semigroups in $L^{1}$ spaces$.\ $We prove convergence to equilibrium at the rate $O\left( t^{-\frac{k}{2(k+1)+1}}\right) \ (t\rightarrow +\infty )$ for $L^{1}$ initial data $g$ in a suitable subspace of the domain of the generator $T$ where $k\in \mathbb{N}$ depends on the properties of the boundary operators near the tangential velocities to the slab. This result is derived from a quantified version of Ingham's tauberian theorem by showing that $F_{g}(s):=\lim_{\varepsilon \rightarrow 0_{+}}\left( is+\varepsilon -T\right) ^{-1}g$ exists…

Application of cohesive-zone models to delamination behaviour of composite material

2012

International audience; The parameters of cohesive elements have to be chosen correctly in the simulation of composite delamination by finite element method: such as interface strength, interface stiffness and shape of cohesive law. The purpose of this work is to investigate their influence on the accuracy of the results obtained. A three-dimensional cohesive-zone model has been established using Ls-dyna to simulate Double-Cantilever-Beam mode I (DCB) and Edge-Notched-Flexure mode II (ENF) tests. The influence of these parameters of cohesive element on the maximum load and the slope of load-displacement curve have been discussed by comparing experimental and numerical results. Four traction…

Metallic subnanometer porous silicon: A theoretical prediction

2021

In the present work, T-Si, a silicon-based counterpart of T-carbon, has been designed with the aid of density functional theory (DFT) calculations. Its stability has been fully confirmed from energetic, mechanical, lattice dynamic, and thermodynamic aspects. Due to the space extrusion, the delocalized electrons on the ${\mathrm{Si}}_{4}$ tetrahedrons are squeezed onto the inter-tetrahedron $\mathrm{Si}\ensuremath{-}\mathrm{Si}$ bonds, which therefore leads T-Si to be metallic. Furthermore, the electronic conductivity of this new material has also been predicted and discussed in this work. This new silicon allotrope with a low density of $0.869\mathrm{g}/{\mathrm{cm}}^{3}$ can even floats on…

Grand-canonical approach to density functional theory of electrocatalytic systems: Thermodynamics of solid-liquid interfaces at constant ion and elec…

2018

Properties of solid-liquid interfaces are of immense importance for electrocatalytic and electrochemical systems, but modeling such interfaces at the atomic level presents a serious challenge and approaches beyond standard methodologies are needed. An atomistic computational scheme needs to treat at least part of the system quantum mechanically to describe adsorption and reactions, while the entire system is in thermal equilibrium. The experimentally relevant macroscopic control variables are temperature, electrode potential, and the choice of the solvent and ions, and these need to be explicitly included in the computational model as well; this calls for a thermodynamic ensemble with fixed…

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…