Characterization of the mechanical properties of the cortex region of human hair fibers by multiparametric atomic force microscopy mapping

We show the benefit of the use of atomic force microscopy (AFM) in spectroscopy force mode (FV: force volume) for evaluation of the cosmetic active effectiveness in improving the mechanical properties of human hair fibers cortex region. For this, we characterized human hair fibers without and with chemical damage caused by bleaching process. Fiber and resin (embedding material) data were obtained simultaneously in the mapping in order to have the resin data as a reference to ensure a coherent comparison between data from the different fiber groups. Our AFM results, which were evaluated using statistical tests, demonstrated the degradation of fibers after bleaching, corroborating the findings of transmission electron microscopy analysis and the effectiveness of a cosmetic active ingredient in improving the Young's modulus (elastic modulus) (E) of the damaged fibers. We also found a radial decrease in the natural logarithm of Young's modulus ln(E) along the cross-section of the active group fiber, which is compatible with confocal Raman spectroscopy analysis by other authors, demonstrating variation of the active permeation with depth. We note that Young's modulus was also determined by a tensile tester (macro-scale technique), in which it was not possible to obtain statistically significant differences between the groups, evidencing the advantage of the FV-AFM analysis. We also found an increase in ln(E) accompanied by a decrease in maximum adhesion force between tip and sample (negative Pearson correlation coefficient). This result can be explained by the fact that structures composed of hydrophobic components have a higher Young's modulus than structures composed of hydrophilic components.

Tangential velocity constraint for orbital maneuvers with Theory of Functional Connections

Maneuvering a spacecraft in the cislunar space is a complex problem, since it is highly perturbed by the gravitational influence of both the Earth and the Moon, and possibly also the Sun. Trajectories minimizing the needed fuel are generally preferred in order to decrease the mass of the payload. A classical method to constrain maneuvers is mathematically modeling them using the Two Point Boundary Value Problem (TPBVP), defining spacecraft positions at the start and end of the trajectory. Solutions to this problem can then be obtained with optimization techniques like the nonlinear least squares conjugated with the Theory of Functional Connections (TFC) to embed the constraints, which recently became an effective method for deducing orbit transfers. In this paper, we propose a tangential velocity (TV) type of constraints to design orbital maneuvers. We show that the technique presented in this paper can be used to transfer a spacecraft (e.g. from the Earth to the Moon) and perform gravity assist maneuvers (e.g. a swing-by with the Moon). In comparison with the TPBVP, solving the TV constraints via TFC offers several advantages, leading to a significant reduction in computational time. Hence, it proves to be an efficient technique to design these maneuvers.