Applications of Haar Wavelet-Finite Difference Hybrid Method and Its Convergence for Hyperbolic Nonlinear Schrödinger Equation with Energy and Mass Conversion

This article is concerned with the numerical solution of nonlinear hyperbolic Schro¨dinger equations (NHSEs) via an efficient Haar wavelet collocation method (HWCM). The time derivative is approximated in the governing equations by the central difference scheme, while the space derivatives are replaced by finite Haar series, which transform it to full algebraic form. The experimental rate of convergence follows the theoretical statements of convergence and the conservation laws of energy and mass are also presented, which strengthens the proposed method to be convergent and conservative. The Haar wavelets based on numerical results for solitary wave shape of |φ| are discussed in detail. The proposed approach provides a fast convergent approximation to the NHSEs. The reliability and efficiency of the method are illustrated by computing the maximum error norm and the experimental rate of convergence for different problems. Comparisons are performed with various existing methods in recent literature and better performance of the proposed method is shown in various tables and figures.

Predictive modeling of virus inactivation by UV

Disinfection strategies are commonly applied to inactivate pathogenic viruses in water, food, air, and on surfaces to prevent the spread of infectious diseases. Determining how quickly viruses are inactivated to mitigate health risks is not always feasible due to biosafety restrictions or difficulties with virus culturability. Therefore, methods that would rapidly predict kinetics of virus inactivation by UV254 would be valuable, particularly for emerging and difficult-to-culture viruses. We conducted a rapid systematic literature review to collect high-quality inactivation rate constants for a wide range of viruses. Using these data and basic virus information (e.g., genome sequence attributes), we developed and evaluated four different model classes, including linear and non-linear approaches, to find the top performing prediction model. For both the (+) ssRNA and dsDNA virus types, multiple linear regressions were the top performing model classes. In both cases, the cross-validated root mean squared relative prediction errors were similar to those associated with experimental rate constants. We tested the models by predicting and measuring inactivation rate constants for two viruses that were not identified in our systematic review, including a (+) ssRNA mouse coronavirus and a dsDNA marine bacteriophage; the predicted rate constants were within 7% and 71% of the experimental rate constants, respectively. Finally, we applied our models to predict the UV254 rate constants of several viruses for which high-quality UV254 inactivation data are not available. Our models will be valuable for predicting inactivation kinetics of emerging or difficult-to-culture viruses.

Exact and numerical solutions of the fractional Sturm–Liouville problem

In the paper, we discuss the regular fractional Sturm-Liouville problem in a bounded domain, subjected to the homogeneous mixed boundary conditions. The results on exact and numerical solutions are based on transformation of the differential fractional Sturm-Liouville problem into the integral one. First, we prove the existence of a purely discrete, countable spectrum and the orthogonal system of eigenfunctions by using the tools of Hilbert-Schmidt operators theory. Then, we construct a new variant of the numerical method which produces eigenvalues and approximate eigenfunctions. The convergence of the procedure is controlled by using the experimental rate of convergence approach and the orthogonality of eigenfunctions is preserved at each step of approximation. In the final part, the illustrative examples of calculations and estimation of the experimental rate of convergence are presented.

Rate coefficients for the reaction of OH radicals with cis-3-hexene: an experimental and theoretical study

Microcanonical variational rate coefficients and experimental rate coefficients for the OH addition to cis-3-hexene have been determined. Theoretical results showed a non-Arrhenius profile and good agreement with the experimental data.

Abnormal salt effects on a cation/anion reaction. An interpretation based on the analysis of the components of the experimental rate constant

Salt effects (NaNO3) on the kinetics of the reactions [Fe(CN)6]3– + [Ru(NH3)5(pyz)]2+ = [Fe(CN)6]4– + [Ru(NH3)5(pyz)]3+ (pyz = pyrazine) were studied through T-jump measurements. An abnormal (positive) salt effect on the forward reaction was observed and a normal (negative) effect on the reverse one. These facts imply an asymmetric behavior of anion/cation reactions depending on the charge sign of the oxidant and reductant. The results can be rationalized by using the Marcus–Hush treatment for electron-transfer reactions after decomposition of the experimental rate constants into their components.