Journal of Mathematical Chemistry最新文献

Differential cross sections for simultaneous capture of both electrons by alpha particles from helium targets are computed. Employed are several quantum-mechanical distorted wave four-body methods of first- and second-orders. The main focus is on the cross section sensitivity as a function of different perturbation interactions and scattering states. Two aspects are considered. One is for theories with the same perturbation interactions and different scattering states. The other is for theories with the same scattering states and different perturbation interactions. In this context, the interference effect on two levels is examined. One compares the yields from the internuclear potential and the interactions between nuclei and two electrons. The other contrasts the contributions from the channel states with and without the distorted waves generated by the relative motions of nuclei. Depending on the employed theory, differential cross sections can be strongly or mildly influenced by the variability in all the mentioned frameworks. The salient illustrations are reported at intermediate energies 180-900 keV for which the experimental data are available. It is found that the second-order theories are in much better agreement with the measured cross sections than the first-order theories.

We simplify some proposed formulas for hydrostatic pressure on a molecule by G. Subramanian, N. Mathew and J. Leiding, J. Chem. Phys. 143, 134109 (2015). We apply the formulas to an artificial triatom ABC whose potential energy surface is formed by a combination of Morse curves.

Let (G=(V(G),E(G))) be a simple graph and denote by (d_{u}) the degree of the vertex (uin V(G)). Using a geometric approach, Gutman introduced a new vertex-degree-based topological index, defined as

and named Sombor index. It is a molecular descriptor with an impressive research activity in recent years. In this paper we propose and initiate the study of a family of topological indices, also conceived from a geometric point of view, called irregularity integral Sombor indices, that generalize the Sombor index. Also, we study the application of these indices in QSPR/QSAR research.

As is known that many existing numerical methods for time fractional nonlinear subdiffusion equations (TFNSEs) often suffer from the phenomenon of order reduction, because the solution of TFNSEs usually has the initial singularity. To overcome this order reduction problem, in this paper, an improved Euler method is proposed for solving TFNSEs based on the technique of variable transformation in time. Then, it is proved that the temporal convergence order of the proposed method is the first order for any fractional order (alpha in (0,1)), which achieves the optimal convergence order of the Euler method. Finally, numerical experiments are given to verify the correctness of our theoretical results.

A parameter-uniform solution is presented for singularly perturbed turning point problems with twin boundary layers. A fitted mesh is created in order to resolve the layers, and the provided equation is discretized using the cubic B-spline basis functions on this mesh. For the analytic solution and its derivatives, asymptotic bounds are provided. A brief analysis shows that the method is first-order precise in time and second-order accurate (up to a logarithm factor) in space, and that it is uniformly convergent regardless of the minuscule parameter. Two test problems are offered in order to verify the theoretical results.

In this paper, we discuss an efficient numerical method to obtain all solutions of fractional Gelfand equation with Dirichlet boundary condition. More precisely, we derive a good initial value motivated by the bifurcation curve of fractional Gelfand equation. It is obvious to see that the number of solutions depends on the value of parameter in fractional Gelfand equation. By collocation technique and finite difference method, numerical solutions can be found very quickly based on Newton iteration method with the aid of such initial guess. Numerical simulation for one-dimensional fractional Gelfand equation are provided, which demonstrates the accuracy and easy-to-implement of our algorithm.

The dual phosphorylation network provides an essential component of intracellular signaling, affecting the expression of phenotypes and cell metabolism. For particular choices of kinetic parameters, this system exhibits multistationarity, a property that is relevant in the decision-making of cells. Determining which reaction rate constants correspond to monostationarity and which produce multistationarity is an open problem. The system’s monostationarity is linked to the nonnegativity of a specific polynomial. A previous study by Feliu et al. provides a sufficient condition for monostationarity via a decomposition of this polynomial into nonnegative circuit polynomials. However, this decomposition is not unique. We extend their work by a systematic approach to classifying such decompositions in the dual phosphorylation network. Using this classification, we provide a qualitative comparison of the decompositions into nonnegative circuit polynomials via empirical experiments and improve on previous conditions for the region of monostationarity.

This paper investigates a higher-order numerical technique for solving an inhomogeneous time fractional reaction-advection-diffusion equation with a nonlocal condition. The time-fractional operator involved here is the Caputo derivative. We discretize the Caputo derivative by an L1–2 formula, while the compact finite difference scheme approximates the spatial derivatives. The numerical approach is based on Taylor’s expansion combined with modified Gauss elimination. A thorough study demonstrates that the suggested approach is unconditionally stable. Tabular results show that the proposed scheme has fourth-order accuracy in space and ((3-beta ))-th-order accuracy in time. The numerical results of two test problems demonstrate the effectiveness and reliability of the theoretical estimates.

This study focuses on crafting and examining the high-order numerical technique for the two-dimensional time-fractional Burgers equation(2D-TFBE) arising in modelling of polymer solution. The time derivative of order ({alpha }) in the equation (where (alpha in (0,1))) is approximated using the fast scheme, while space derivatives are discretized via a tailored finite point formula (TFPF) which relies on exponential basis. This method uses exponential functions to simultaneously fit the local solution’s properties in time and space, serving as basis functions within the TFPF framework. The analysis of convergence and stability of the method are rigorously examined theoretically and these are supported by the numerical examples showcasing its applicability and accuracy. It is proven that the method is unconditionally stable and maintains an accuracy of order ({mathcal {O}}(tau ^2+h_{varkappa }+h_y+epsilon + varepsilon ^{-2}e^{-frac{beta _{n,m}^{k+1}}{2varepsilon ^2}}+e^{-gamma _0frac{h}{varepsilon }} )), where (tau ) represents the temporal step size, and (h_{varkappa }) and (h_y) are spatial step sizes. Computational outcomes align well with the theoretical analysis. Furthermore, when compared to the standard scheme, our method attains the same level of accuracy with significantly lowering computational demands and minimizing storage requirements. This proposed numerical scheme has higher convergence rate and significantly minimizes consumed CPU time compared to other methods.

A family of new exponentially fitted two-derivative Runge–Kutta (TDRK) methods with exponential order up to two for solving the Schrödinger equation is obtained in this paper. Error analysis is conducted in terms of the asymptotic expressions of the energy. Linear stability and phase properties are analyzed. Numerical results are reported to show the efficiency and robustness of the new methods in comparison with some RK type methods specially tuned to the integration of the radial time-independent Schrödinger equation with the Woods-Saxon potential.