Theoretical and Numerical Aspect of Fractional Differential Equations with Purely Integral Conditions

In this paper, we are interested in the study of a Caputo time fractional advection–diffusion equation with nonhomogeneous boundary conditions of integral types ∫01vx,tdx and ∫01xnvx,tdx. The existence and uniqueness of the given problem’s solution is proved using the method of the energy inequalities known as the “a priori estimate” method relying on the range density of the operator generated by the considered problem. The approximate solution for this problem with these new kinds of boundary conditions is established by using a combination of the finite difference method and the numerical integration. Finally, we give some numerical tests to illustrate the usefulness of the obtained results.

Influence of graphene nano-platelets dispersion on the thermo-physical properties of sunflower oil

In this article, thermal stability, viscosity, density and surface tension of Graphene nano-platelets dispersed sunflower oil are experimentally determined by varying the Graphene concentration (0.1-1.1wt%) and temperature (40-100?C). The SEM micrograph and the EDS spectra are used to characterize the Graphene. Nanofluids are prepared by ultrasonication technique (two-step method) and the maximum thermal stability of about 280?C is achieved at 1.1wt% Graphene nanofluids. The dynamic viscosity diminished in an exponential shape in acquiescence with Arrhenius equation and the densities of samples are characteristic with linear decrement in the estimated temperature range. Density and surface tension increases with the Graphene concentration, while a reverse trend is observed with temperature rise. The maximum thermal stability, viscosity, density and surface tension is obtained in the nanofluid with 1.1 wt% concentration and the minimum is obtained in the nanofluid with 0.1 wt% concentration.

Chemically Accurate Excitation Energies With Small Basis Sets

<p>By combining extrapolated selected configuration interaction (sCI) energies obtained with the CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively) algorithm with the recently proposed short-range density-functional correction for basis-set incompleteness [Giner et al., J. Chem. Phys. 2018, 149, 194301], we show that one can get chemically accurate vertical and adiabatic excitation energies with, typically, augmented double-ζ basis sets. We illustrate the present approach on various types of excited states (valence, Rydberg, and double excitations) in several small organic molecules (methylene, water, ammonia, carbon dimer and ethylene). The present study clearly evidences that special care has to be taken with very diffuse excited states where the present correction does not catch the radial incompleteness of the one-electron basis set.</p>

Chemically Accurate Excitation Energies With Small Basis Sets

<p>By combining extrapolated selected configuration interaction (sCI) energies obtained with the CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively) algorithm with the recently proposed short-range density-functional correction for basis-set incompleteness [Giner et al., J. Chem. Phys. 2018, 149, 194301], we show that one can get chemically accurate vertical and adiabatic excitation energies with, typically, augmented double-ζ basis sets. We illustrate the present approach on various types of excited states (valence, Rydberg, and double excitations) in several small organic molecules (methylene, water, ammonia, carbon dimer and ethylene). The present study clearly evidences that special care has to be taken with very diffuse excited states where the present correction does not catch the radial incompleteness of the one-electron basis set.</p>