Interaction of surfactants with poloxamers 338 and its effect on some properties of cream base

The aim. Study of the interaction of surfactants with poloxamer 338 (P338) and the effect of P338 on the properties of cream bases. Materials and methods. Solutions of the surfactants and P338 as well as cream bases were under study. The average hydrodynamic diameter (Dh) and zeta potential (ζ‑potential) were determined by the light scattering intensity and electrophoretic mobility of micelles. The electron paramagnetic resonance (EPR) spectra of spin probes in micelles, solvents and bases were obtained; the type of spectrum, isotropic constant (AN), rotational correlation times (τ) and anisotropy parameter (ε) were determined. Liquids and cream bases were studied by capillary and rotational viscometry; the flow behaviour and yield stress (t0), dynamic and apparent viscosity (η) as well as the hysteresis (thixotropic) area (AH) were determined. The microstructure of the bases was examined by optical microscopy. The strength of adhesion (Sm) was assessed by the pull-off test, and the absorption of water was studied by dialysis. Results. Under the impact of P338 the hydrodynamic diameters of micelles formed by cationic, anionic and nonionic surfactants decreased as well as the absolute values of their ζ‑potential became lower, but the microviscosity of the micelle nuclei increased. There was also a change in the structure of the aggregates of surfactant with fatty alcohols; EPR spectra, which were superpositions characteristic for the lateral phase separation, converted into triplets that indicated the uniform distribution of lipophilic probes in the surfactant phase. When the content of P338 increased to 17 %, the rheological parameters of the bases increased drastically, the flow behaviour and the microstructure changed. The bases had the consistency of cream within temperature range from 25 °C to 70 °C and completely restored their apparent viscosity, which had decreased under shear stress. P338 enhances the adhesive properties of the bases. Due to their microstructure, cream bases have a lower ability to absorb water compared to a solution and gel containing 17 % and 20 % P338, respectively. Conclusions. The structure of surfactant micelles and aggregates of surfactants with fatty alcohols changed under impact of P338 due to the interaction of surfactants with P338. As a result of this interaction, at a sufficiently high concentration of P338, the microstructure and flow behaviour of bases changed, their rheological parameters, which remain high at temperatures from 25 °C to 70 °C, increased significantly, and water absorption parameters decreased. The bases with P338 were more adhesive

Error bounds of block sparse signal recovery based on q-ratio block constrained minimal singular values

In this paper, we introduce the q-ratio block constrained minimal singular values (BCMSV) as a new measure of measurement matrix in compressive sensing of block sparse/compressive signals and present an algorithm for computing this new measure. Both the mixed ℓ2/ℓq and the mixed ℓ2/ℓ1 norms of the reconstruction errors for stable and robust recovery using block basis pursuit (BBP), the block Dantzig selector (BDS), and the group lasso in terms of the q-ratio BCMSV are investigated. We establish a sufficient condition based on the q-ratio block sparsity for the exact recovery from the noise-free BBP and developed a convex-concave procedure to solve the corresponding non-convex problem in the condition. Furthermore, we prove that for sub-Gaussian random matrices, the q-ratio BCMSV is bounded away from zero with high probability when the number of measurements is reasonably large. Numerical experiments are implemented to illustrate the theoretical results. In addition, we demonstrate that the q-ratio BCMSV-based error bounds are tighter than the block-restricted isotropic constant-based bounds.

Elastic reverse time migration using acoustic propagators

Elastic wave imaging has been a significant challenge in the exploration industry due to the complexities in wave physics and numerical implementation. We have separated the governing equations for P- and S-wave propagation without the assumptions of homogeneous Lamé parameters to capture the mode conversion between the two body waves in an isotropic, constant-density medium. The resulting set of two coupled second-order equations for P- and S-potentials clearly demonstrates that mode conversion only occurs at the discontinuities of the shear modulus. Applying the Born approximation to the new equations, we derive the PP, PS, SP, and SS imaging conditions from the first gradients of waveform matching objective functions. The resulting images are consistent with the physical perturbations of the elastic parameters, and, hence, they are automatically free of the polarity reversal artifacts in the converted images. When implementing elastic reverse time migration (RTM), we find that scalar wave equations can be used to back propagate the recorded P-potential, as well as individual components in the vector field of the S-potential. Compared with conventional elastic RTM, the proposed elastic RTM implementation using acoustic propagators not only simplifies the imaging condition, it but also reduces the computational cost and the artifacts in the images. We have determined the accuracy of our method using 2D and 3D numerical examples.

Anisotropic elasticity of silicon and its application to the modelling of X-ray optics

The crystal lattice of single-crystal silicon gives rise to anisotropic elasticity. The stiffness and compliance coefficient matrix depend on crystal orientation and, consequently, Young's modulus, the shear modulus and Poisson's ratio as well. Computer codes (in Matlab and Python) have been developed to calculate these anisotropic elasticity parameters for a silicon crystal in any orientation. These codes facilitate the evaluation of these anisotropy effects in silicon for applications such as microelectronics, microelectromechanical systems and X-ray optics. For mechanically bent X-ray optics, it is shown that the silicon crystal orientation is an important factor which may significantly influence the optics design and manufacturing phase. Choosing the appropriate crystal orientation can both lead to improved performance whilst lowering mechanical bending stresses. The thermal deformation of the crystal depends on Poisson's ratio. For an isotropic constant Poisson's ratio, ν, the thermal deformation (RMS slope) is proportional to (1 + ν). For a cubic anisotropic material, the thermal deformation of the X-ray optics can be approximately simulated by using the average of ν12and ν13as an effective isotropic Poisson's ratio, where the direction 1 is normal to the optic surface, and the directions 2 and 3 are two normal orthogonal directions parallel to the optical surface. This average is independent of the direction in the optical surface (the crystal plane) for Si(100), Si(110) and Si(111). Using the effective isotropic Poisson's ratio for these orientations leads to an error in thermal deformation smaller than 5.5%.