Journal of Mathematical Chemistry最新文献

Approximate analytical solutions to a degenerate reaction–diffusion model pertinent to population dynamics and chemical kinetics have been developed. Both the degenerate diffusivity and the growth function have been formulated as power-law functions. The integral-balance method applied to a preliminary transformed model (via the Danckwerts transformation) and by a direct integration approach has provided physically reasonable results. The model equation scaling has revealed the Fourier number as controlling dimensionless group.

Derivation of exact explicit Einstein-Smolukhowski (ES) relations for non-ideal real gases is purpose of this paper. The ES method of the derivation was modified for this purpose. The new method is based on the rule of differentiation of inverse functions known in mathematics. The modified method turned out to be more effective than the traditional one: the fact is that the modified method always works, while the traditional method is effective only for a small number of simple equations of state (EoS). The method has been tested for four popular EoS: the Lorentz EoS, the Van der Waals EoS, the Peng-Robinson EoS, and the Dieterici EoS. As a result, exact explicit ES formulas for gases obeying these EoS were derived. It was found that the ratio of the diffusion coefficient to the particle mobility coefficient depends not only on the gas temperature, but also on its concentration for all examples of gases. The derived exact formulas can be used to debug codes that simulate molecular dynamics.

We address the demanding J-spectroscopy part of nuclear magnetic resonance (NMR) for encoded time signals. In the fast Fourier transform (FFT), the J-coupled multiplets are mostly unresolved even with strong magnetic fields (e.g. 600 MHz, 14.1T). The problem is further exacerbated by minuscule chemical shift bands hosting such multiplets. Derivative estimations might be tried as an alternative strategy. However, too tightly overlapped resonances require higher-order derivative estimations. These, in turn, uncontrollably enhance the reconstruction instabilities. Hence, a robust optimizing stabilizer is needed. It is provided by the optimized derivative fast Fourier transform, which simultaneously increases resolution and reduces noise. We presently demonstrate that higher-orders (up to 15) of this processor can accurately resolve the J-coupled multiplets into their genuine components hidden within the singlet-appearing resonances in the FFT spectra. This is exemplified with the challenging two triplets (taurine, myo-inositol lying within only 0.02 ppm) for time signals encoded by ovarian NMR spectroscopy from a patient’s excised cancerous cyst fluid specimen.

In combustion simulation, the Arrhenius equation is a key tool for modeling multi-step reactions such as propane and methane reactions. It describes a relationship between the reaction rate, temperature, the pre-exponential factor, and activation energy. Applying these parameters outside their validated temperature and pressure ranges, or for unverified reactions, can result in important errors. The present study optimizes the coefficients of the Arrhenius model for multi-step combustion reactions, by utilizing experimental data and advanced optimization techniques. Our methodology incorporates metaheuristics techniques such as least squares minimization, particle swarm optimization, ant colony optimization, the slime mold algorithm, and the whale optimization algorithm. The results indicate that the optimized coefficients significantly improve the predictions while reducing computational time and associated costs. Furthermore, this paper presents a comprehensive comparative analysis of the various optimization techniques utilized and clarifies the advantages and limitations of each technique in the context of Arrhenius equation optimization.

This paper proposes a uniformly convergent numerical method for a class of singularly perturbed turning point problems with a time-lag defined on a rectangular domain. We consider an interior repulsive turning point with odd multiplicity (geqslant 1). Twin boundary layers arise in the proximity of endpoints of the spatial domain due to the presence of the perturbation parameter. Preliminary results such as minimum principle, stability estimate, and solution derivative bounds for the continuous problem applicable in the convergence analysis are presented. First, we employ the Crank–Nicolson scheme to semi-discretize the continuous problem in the time direction, and then the cubic (mathscr {B})-spline functions on an appropriate Shishkin mesh are used to get a full discretization. The convergence analysis uses the maximum norm to obtain parameter-uniform error estimates. Three test problems are solved numerically to validate the theoretical results and confirm the scheme’s effectiveness.

We present combinatorial cum group theoretical generating function methods for vertex and face colorings of a dodecahedron for all irreducible representations of the icosahedral group. We demonstrate the usefulness of the Mȍbius inversion method. We consider several types of distortions arising from the highly symmetric dodecahedron, in particular, to an elongated dodecahedron and a pyrithohedron (T_h). Elaborate combinatorial enumerations and tables of combinatorial numbers are explicitly constructed for all irreducible representations of both the distorted and the parent undistorted structures. It is shown that the combinatorial cum computational techniques provide new insights into the dynamic chirality arising from such distortions which include the pentagonal distortions, elongated distortions and so forth. We point out applications to the dynamic NMR and ESR spectroscopies as well to the dynamic stereochemistry of topological metamorphosis through a combination of combinatorics and group theory.

By using a strategy that accounts for fading phase-lag, phase-lag and all of its derivatives up to order six can be eliminated. The cost-efficient approach is a new strategy whose aims are to boost algebraic order (AOR) and reduce function evaluations (FEVs). The symbolic representation of the one-of-a-kind approach is PF6DPHFITN142SPS. This method is infinitely periodic since it is P-Stable. The proposed method is general enough to address a large class of periodic and oscillatory problems. This new method was used to solve the difficult problem of Schrödinger-type coupled differential equations in quantum chemistry. Given that each stage only requires (5 , FEVs), the new method could be seen as a cost-effective strategy. With a AOR of 14, we can greatly enhance our current situation.

Extensive studies have investigated second-order singular differential equations to model various phenomena in astrophysics, reaction-diffusion processes, and electrohydrodynamics. However, finding numerical and analytical solutions for these problems with appropriate boundary conditions is challenging due to their inherent nonlinearity. Our current study explores singular second-order differential equations (SSODEs) with boundary conditions, specifically those modelling the distribution of heat sources in the human head and the steady-state temperature distribution in a vessel before a thermal explosion. The fundamental idea behind our approach is initially transforming the differential equation into an equivalent integral form, thereby circumventing the singular behaviour. Subsequently, the optimal homotopy analysis method is employed to scrutinize two distinct models, i.e., the heat conduction model, the thermal explosion model and the spherical catalyst equation. Further, a detailed convergence analysis is conducted in a Banach space framework to ensure the method’s reliability. The accuracy of the new approach is checked by considering various numerical examples with different values of thermogenesis heat production, the Biot number, and metabolic thermogenesis slope. It has been shown that the proposed approach qualitatively and quantitatively approximates the solutions with higher precision than the existing Adomian decomposition method.

We give a simple proof of the well known fact that the approximate eigenvalues provided by the Rayleigh-Ritz method are increasingly accurate upper bounds to the exact ones. To this end, we resort to the variational principle and to a set of suitable projection operators.

This paper presents a qualitative study of a reversible biochemical reaction model with cross-diffusion and Michalis saturation. For the system without diffusion, the existence, stability and Hopf bifurcation of the positive equilibrium have been clearly determined. For the cross-diffusive system, the stability and Turing instability driven by cross-diffusion are studied according to the relationship between the self-diffusion and the cross-diffusion coefficients. Stability and cross-diffusion instability regions are theoretically determined in the plane of the cross-diffusion coefficients. The amplitude equation is derived by using the technique of multiple time scale. With the help of numerical simulation, we verify the analysis results.