On the effectiveness of exponential type orbitals with hyperbolic cosine functions in atomic calculations

Unconventional basis functions, constructed from exponential type orbitals (ETOs) with hyperbolic cosine functions, are applied to Roothaan-Hartree-Fock calculations of atoms within the minimal basis sets framework. The most popular ETOs, Slater type orbitals, B functions and \(\psi ^{(\alpha ^*)}\) functions with \(\alpha ^*=2\), and two types of hyperbolic cosine functions, \(\cosh (\beta r)\) and \(\cosh (\beta r+\gamma )\), are used in this work. The performance of the present basis functions is investigated and compared to the conventional double-zeta Slater-type basis set and numerical Hartree-Fock results. The improvement in the atomic energies clearly demonstrates how the accuracy increases when we move from ETO to ETO with hyperbolic cosine basis functions. The resulting improved minimal basis sets can also be useful in molecular calculations.     

Hydrogenation of diacetyl over composite-supported egg-shell noble metal catalysts

Two composite supports with a mixed inorganic–organic structure were synthesized: BTAl and UTAl. Hydrophilic–hydrophobic dual properties of the supports were suitable for preparing egg-shell-supported metal catalysts for selective hydrogenation reactions. The catalysts were characterized by ICP, XRD, OM, TEM, EPMA, XPS and TGA. Their mechanical resistance was assessed. Activity and selectivity were tested with the hydrogenation of 2,3-butanedione (diacetyl) to 3-hydroxy-2-butanoneacetoin (acetoin). The same order of increasing metal particle size was found for the two tested supports: Pt < Ru < Pd. The XPS analysis showed that the metal/composite catalysts reduced in H2 at 503 K had two kinds of active sites: reduced (Me°) and electron-deficient (Me⁺). It was rationalized that the hydrogen bond cleavage was performed on the Me° active sites, while reactant adsorption occurred on the Me⁺ sites. The differences in activity and selectivity between the composite catalysts were attributed to electronic effects on the different metals and to different adsorptive properties of the different polymers. The high selectivity to acetoin was attributed to the preferential adsorption of diacetyl as compared to the adsorption of acetoin. The BTAl catalysts were slightly more active and selective than the UTAl ones. This was attributed to electronic effects caused by remnant organic groups on the composite supports (urethane or biphenyl on UTAl or BTAl, respectively). Pd-BTAl was the most active and selective catalyst, a fact related to electronic effects of both palladium and the support.     

Optical activity of films based on chitosan of various molecular masses and modifications

The effect of chemical (polysalt → polybase reaction) and physicochemical (heat and vapor processing) modifications of the films of chitosan of various molecular masses and prehistories on the optical activity of the polysaccharide is studied. For both of the chitosan chemical modifications, the following dependence that is nontrivial for high-molecular compounds is established: [α] = f(log\({\bar M_\eta }\)); as the degree of polymerization decreases, the modulus of [α] of the films increases. The X-ray diffraction study shows that the differences in the optical activity of the samples with different \({\bar M_\eta }\) are caused by a restriction in the mobility of the macromolecular sections upon formation of the films of high-molecular chitosan and incompleteness of the relaxation processes of the film systems to the state with energetically favorable conformations. The comparison of humidity and optical and biological activities of the initial and dehydrated chitosan films is performed. The chitosan films in the salt modification feature moderate bactericidal activity, which decreases with an increase in \({\bar M_\eta }\) of the polymer. The thermal processing of the salt modification reduces the antibacterial action; a conversion to the base form is accompanied by the loss of bactericidal activity.     

Study of oriented polyethylene structures using a Raman longwave acoustic mode

This paper concerns the basics of using longwave (low-frequency) Raman spectroscopy in the region of a longitudinal acoustic mode for the study of structural features of polymers. Using ultrahighmolecular- weight polyethylene (UHMW PE)-based reactor powders, gels, and oriented fibers obtained by the gel technology, the length distribution of straight-chain segments and its relation to the morphology of the sample were analyzed. An important role of the low-frequency Raman spectroscopy in creating domestic gel technology for preparing ultrahigh-strength threads from polyethylene was demonstrated.     

On parallel Branch and Bound frameworks for Global Optimization

Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity.     

Stable iterative Lagrange principle in convex programming as a tool for solving unstable problems

A convex programming problem in a Hilbert space with an operator equality constraint and a finite number of functional inequality constraints is considered. All constraints involve parameters. The close relation of the instability of this problem and, hence, the instability of the classical Lagrange principle for it to its regularity properties and the subdifferentiability of the value function in the problem is discussed. An iterative nondifferential Lagrange principle with a stopping rule is proved for the indicated problem. The principle is stable with respect to errors in the initial data and covers the normal, regular, and abnormal cases of the problem and the case where the classical Lagrange principle does not hold. The possibility of using the stable sequential Lagrange principle for directly solving unstable optimization problems is discussed. The capabilities of this principle are illustrated by numerically solving the classical ill-posed problem of finding the normal solution of a Fredholm integral equation of the first kind.     

Application of numerical schemes with singling out the boundary layer for the computation of turbulent flows using eddy-resolving approaches on unstructured grids

The use of eddy-resolving approaches to solving problems on arbitrary unstructured grids is investigated. The applications of such approaches requires the use of low dissipation numerical schemes, which can lead to numerical oscillations of the solution on unstructured grids. Numerical oscillations typically occur in domains with large gradients of velocities, in particular, in the near-wall layer. It is proposed to single out the boundary layer and use a numerical scheme with increased numerical dissipation in it. The algorithm for singling out the boundary layer uses a switching function to change the parameters of the numerical scheme. This algorithm is formulated based on the BCD scheme from the family NVD. Its validity and advantages are investigated using the zonal RANS–LES approach for solving some problems of turbulent flow of incompressible fluids.     

Optimization method in problems of acoustic cloaking of material bodies

Optimization problems for a three-dimensional model of acoustic scattering are formulated and studied. These problems arise in designing tools for cloaking material bodies by applying the wave flow method. The cloaking effect is achieved due to an optimal choice of variable parameters of the inhomogeneous isotropic medium occupying the sought shell. The solvability of direct and optimization problems for the acoustic scattering model is proved, and sufficient conditions ensuring the uniqueness and stability of optimal solutions are established.     

New polymer composites based on keratin and polyethylene

New biodegradable composites based on keratin and polyethylene have been produced under shear deformation. It has been demonstrated that the introduction of keratin leads to an increase in elastic modulus and to a decrease in ultimate tensile strength and elongation at break of the compositions. Elongation at break ε_b depends on the keratin dispersity; the highest ε_b values are observed for the compositions containing the smallest keratin particles. It has been shown that the compositions are susceptible to mold fungi; i.e., they are biodegradable.