Search

The relaxation time of several second generation molecular motors is analysed by calculating the minimum energy path between the metastable and stable states and evaluating the transition rate within harmonic transition state theory based on energetics obtained from density functional theory. Comparison with published experimental data shows remarkably good agreement and demonstrates the predictive capability of the theoretical approach. While previous measurements by Feringa and coworkers [Chem.\,Eur.\,J.\,(2017) 23, 6643] have shown that a replacement of the stereogenic hydrogen by a fluorine atom increases the relaxation time because of destabilization of the transition state for the thermal helix inversion, we find that a replacement of CH$_3$ by a CF$_3$ group at the same site shortens the relaxation time because of elevated energy of the metastable state without a significant shift in the transition state energy. Since these two fluorine substitutions have an opposite effect on the relaxation time, the two combined can provide a way to fine tune the rotational speed of a molecular motor.

We develop a Lagrangian quantization formalism for a class of theories obtained by the restriction of the configuration space of gauge fields from a wider (parental) gauge theory. This formalism is based on application of the Batalin-Vilkovisky technique for quantization of theories with linearly dependent generators, their linear dependence originating from a special type of projection from the originally irreducible gauge generators of the parental theory. The algebra of these projected generators is shown to be closed for parental gauge algebras closed off shell. We demonstrate that new physics of the restricted theory, as compared to its parental theory, is associated with the rank deficiency of a special gauge-restriction operator reflecting the gauge transformations of the restriction constraints functions -- this distinguishes the restricted theory from its partial gauge fixing. As a byproduct of this technique a workable algorithm for the one-loop effective action in generic first-stage reducible theory was constructed, along with the explicit set of tree-level Ward identities for gauge field, ghost, and ghosts-for-ghosts propagators. The formalism is applied to unimodular gravity theory, and its one-loop effective action is obtained in terms of functional determinants of minimal second-order operators, calculable on generic backgrounds by Schwinger-DeWitt technique of local curvature expansion. The result is shown to be equivalent to Einstein gravity theory with a cosmological term up to a special contribution of the global degree of freedom associated with the variable value of the cosmological constant. The role of this degree of freedom in a special duality relation between Einstein theory and unimodular gravity is briefly discussed., Comment: 30 pages (two-column revtex), updated to journal version (including the title), misprints corrected, references and minor discussions added

Present study is dedicated to the problem of electrochemical analysis of multicomponent mixtures such as milk. A combination of cyclic voltammetry facilities and machine learning technique made it possible to create a pattern recognition system for antibiotic residues in skimmed milk. A multielectrode sensor including copper, nickel and carbon fiber was fabricated for the collection of electrochemical data. Chemical aspects of processes occurring at the electrode surface were discussed and simulated with the help of molecular docking and density functional theory modelling. It was assumed that the antibiotic fingerprint reveals as potential drift of electrodes owing to redox degradation of antibiotic molecules followed by pH change or complexation with ions present in milk. Gradient boosting algorithm showed the best efficiency towards training the machine learning model. High accuracy was achieved for recognition of antibiotics in milk. The elaborated method may be incorporated into existing milking systems at dairy farms for monitoring the residue concentrations of antibiotics., Comment: 38 pages

We analyze the spatial structure of asymptotics of a solution to a singularly perturbed system of mass transfer equations. The leading term of the asymptotics is described by a parabolic equation with possibly degenerate spatial part. We prove a theorem that establishes a relationship between the degree of degeneracy and the numbers of equations in the system and spatial variables in some particular cases. The work hardly depends on the calculation of the eigenvalues of matrices that determine the spatial structure of the asymptotics by the means of computer algebra system Wolfram Mathematica. We put forward a hypothesis on the existence of the found connection for an arbitrary number of equations and spatial variables., Comment: 5 pages

We investigate properties of bound and resonance states in the $_{\Lambda}^{9}$Be nucleus. To reveal the nature of these states, we use a three-cluster $2\alpha+\Lambda$ microscopic model. The model incorporates Gaussian and oscillator basis functions and reduces a three-cluster Schr\"{o}dinger equation to a two-body like many-channel problem with the two-cluster subsystems ($_{\Lambda}^{5}$He and $^8$Be) being in a bound or a pseudo-bound state. Influence of the cluster polarization on the energy and widths of resonance states in $_{\Lambda}^{9}$Be and on elastic and inelastic $_{\Lambda}^{5}$He+$\alpha$ scattering is analyzed., Comment: 42 pages, 5 figures, extended version of the paper, submitted to Nucl. Phys. A

We study the one-loop covariant effective action of Lifshitz theories using the heat kernel technique. The characteristic feature of Lifshitz theories is an anisotropic scaling between space and time. This is enforced by the existence of a preferred foliation of space-time, which breaks Lorentz invariance. In contrast to the relativistic case, covariant Lifshitz theories are only invariant under diffeomorphisms preserving the foliation structure. We develop a systematic method to reduce the calculation of the effective action for a generic Lifshitz operator to an algorithm acting on known results for relativistic operators. In addition, we present techniques that drastically simplify the calculation for operators with special properties. We demonstrate the efficiency of these methods by explicit applications., Comment: 36 pages, matches journal version