Preparation and characterization of nanocomposites based on linear medium density polyethylene/cellulose nanofibers from Agave tequilana bagasse waste

In the Mexican state of Jalisco, a significant amount of fibrous agave waste is generated from the tequila industry every year. The objective of this study was to establish the potential of obtaining cellulose nanofibers (CNF) from the bagasse waste of Agave tequilana, and then incorporate them into a linear medium density polyethylene matrix to obtain nanocomposites through the thermocompression process. These nanoparticles were used to prepare nanocomposites of the selected matrix, incorporating 1 to 5 wt% of CNF. All of the prepared composites had a low water absorption. Increases in tensile strength and in modulus and flexural properties occurred when the concentration of the CNF was augmented. However, in the case of nanocomposites with 5 wt%, a decrease in elongation was observed.

Exact solutions of equal-width equation and its conservation laws

In this work we investigate the equal-width equation, which is used for simulation of (1-D) wave propagation in non-linear medium with dispersion process. Firstly, Lie symmetries are determined and then used to establish an optimal system of one-dimensional subalgebras. Thereafter with its aid we perform symmetry reductions and compute new invariant solutions, which are snoidal and cnoidal waves. Additionally, the conservation laws for the aforementioned equation are established by invoking multiplier method and Noether’s theorem.

Локализация возбуждений вблизи тонкого дефектного слоя с нелинейными свойствами, разделяющего линейный и нелинейный кристаллы

It is shown that the localized and quasi-local stationary states exist near a thin defect layer with nonlinear properties separating a linear medium from a non-linear medium of Kerr type. Localized states are characterized by a monotonically decreasing field amplitude on both sides of the interface. Quasi-local states are described by a field in the form of a standing wave in a linear medium and monotonously decreasing in a nonlinear medium. The contacts with nonlinear self-focusing and defocusing media are analyzed. The mathematical formulation of the proposed model is a system of linear and nonlinear Schrödinger equations with a potential that is nonlinear with respect to the field and which simulates a thin defect layer with nonlinear properties. Dispersion relations determining the energy of local and quasi-local states are obtained. The expressions for energies were obtained explicitly in limiting cases and the conditions for their existence were indicated.

Квазиоптическое уравнение в средах со слабым поглощением

The form of a quasi-optical equation for a beam of monochromatic radiation propagating through a layer of a weakly absorbing linear medium is analyzed. It is concluded that the standard form of this equation should be modified using an “effective diffusion coefficient.”