Journal of Mathematical Chemistry最新文献

In this paper, we formulate a classical stochastic delayed chemostat model and verify that this model has a unique global positive solution. Furthermore, we investigate the dynamical behavior of this solution. We find that the solution of stochastic delayed system will oscillate around the equilibriums of the corresponding deterministic delayed model, moreover, analytical findings reveal that time delay has very significant effects on the extinction and persistence of the microorganism, that is to say, when the time delay is smaller, microorganism will be persistent; when the time delay is larger, microorganism will be extinct. Finally, computer simulations are carried out to illustrate the obtained results. In addition, we can also find by the computer simulation that larger noise may lead to microorganism become extinct, although microorganism is persistent in the deterministic delayed system when the time delay is smaller.

We present a parameter-robust finite difference method for solving a system of weakly coupled singularly perturbed convection-diffusion equations. The diffusion coefficient of each equation is a small distinct positive parameter. Due to this, the solution to the system has, in general, overlapping boundary layers. The problem is discretized using a particular combination of a compact second-order difference scheme and a central difference scheme on a piecewise-uniform Shishkin mesh. The convergence analysis is given, and the method is shown to have almost second-order uniform convergence in the maximum norm with respect to the perturbation parameters. The results of numerical experiments are in agreement with the theoretical outcomes.

Applying a phase-fitting method might potentially vanish the phase-lag and its first derivative. Improving algebraic order (AOR) and decreasing function evaluations (FEvs) are the goals of the new strategy called the cost-efficient approach. Equation PF2DPHFITN142SPS demonstrates the unique method. The suggested approach is P-Stable, meaning it is indefinitely periodic. The proposed method is applicable to a wide variety of periodic and/or oscillatory issues. The challenging problem of Schrödinger-type coupled differential equations was solved in quantum chemistry by using this novel approach. Since the new method only needs 5FEvs to run each stage, it may be considered a cost-efficient approach. With an AOR of 14, we can significantly improve our present predicament.

This paper focuses on an efficient computational method for solving the singularly perturbed Burger-Huxley equations. The difficulties encountered in solving this problem come from the nonlinearity term. The quasilinearization technique linearizes the nonlinear term in the differential equation. The finite difference approximation is formulated to approximate the derivatives in the differential equations and then accelerate its rate of convergence to improve the accuracy of the solution. The stability and consistency analysis were investigated to guarantee the convergence analysis of the formulated method. Numerical examples are considered for numerical illustrations. Numerical experiments were conducted to sustain the theoretical results and to show that the proposed method produces a more correct solution than some surviving methods in the literature.

In the present paper, we mainly consider the direct solution of cyclic tridiagonal linear systems. By using the specific low-rank and Toeplitz-like structure, we derive a structure-preserving factorization of the coefficient matrix. Based on the combination of such matrix factorization and Sherman–Morrison–Woodbury formula, we then propose a cost-efficient algorithm for numerically solving cyclic tridiagonal linear systems, which requires less memory storage and data transmission. Furthermore, we show that the structure-preserving matrix factorization can provide us with an explicit formula for n-th order cyclic tridiagonal determinants. Numerical examples are given to demonstrate the performance and efficiency of our algorithm. All of the experiments are performed on a computer with the aid of programs written in MATLAB.

Applying a phase-fitting method might potentially vanish the phase-lag and its first derivative. Improving algebraic order (AOR) and decreasing function evaluations (FEvs) are the goals of the new strategy called the cost-efficient approach. Equation PF1DPHFITN142SPS demonstrates the unique method. The suggested approach is P-Stable, meaning it is indefinitely periodic. The proposed method is applicable to a wide variety of periodic and/or oscillatory issues. The challenging problem of Schrödinger-type coupled differential equations was solved in quantum chemistry by using this novel approach. Since the new method only needs 5FEvs to run each stage, it may be considered a cost-efficient approach. With an AOR of 14, we can significantly improve our present predicament.

In the realm of renewable energy, platinum (Pt) nanoparticles are crucial components in fuel cells. They particularly excel in hydrogen fuel cells, where their role as catalysts significantly boosts the efficiency of electrochemical reactions. Cerium oxide nanoparticles are highly prized in engineering and industry for their exceptional catalytic abilities. They are particularly notable for their role in reducing vehicle emissions and facilitating the oxidation of carbon monoxide and hydrocarbons. Their oxygen storage capacity, crucial in regulating oxygen levels during catalytic reactions, is vital in automotive exhaust systems. Such an appealing area has led us to explore the dynamic behaviours of a specialized hybrid nanofluid- a mixture of radioactive platinum, cerium oxide, and water within a vertically extended vibrating Riga channel. This model is set under the cumulative consequences of sudden pressure gradient onset, electromagnetic forces, electromagnetic radiation, and chemical reactions. This physical model consists of a static right wall and a left wall that undergoes transverse vibrations. This flow scenario is mathematically described using time-dependent partial differential equations. A closed-form solution for the flow-regulating equations is obtained by harnessing the Laplace transform (LT) method. The study meticulously details the ascendancy of various critical parameters on the functions and quantities of the model, particularly for hybrid nanofluid (HNF) and nanofluid (NF), using graphical and tabular representations. Our findings manifest an expansion in the modified Hartmann number notably boosts the fluid velocity across the Riga channel. The fluid temperature in HNF is consistently lower in HNF compared to NF. The species concentration levels in HNF and NF lower with rising Schmidt numbers and chemical reaction parameters. A widened width of magnets and electrodes results in lowered shear stresses at the Riga wall in both HNF and NF. Furthermore, the rate of heat transfer (RHT) at the vibrating wall for HNF consistently shows higher values than for NF. These novel insights have far-reaching implications in various industrial and engineering applications, including the development of catalytic converters, the optimization of hydrogen fuel cells, the efficient oxidation of carbon monoxide and hydrocarbons, and advancements in materials processing techniques.

Piezoelectric nanostructures have attracted significant attention owing to their capacity for converting mechanical energy into electrical energy, enabling applications in biomedical fields, actuators, and energy harvesting devices. Boron nitride nanotubes (BNNTs) exhibit unique properties that make them attractive candidates for piezoelectric applications. However, the influence of BNNT chiralities on their piezoelectric behavior has not been thoroughly explored. In this study, we investigated the piezoelectric effect of zigzag and armchair chiralities of BNNT structures, aiming to elucidate the relationship between chirality and piezoelectric response by discovering a novel protocol for simulating the electrical behavior of BNNTs at the nanoscale level. We employed a computational method to examine the piezoelectric potential of BNNT structures. First, we established an equivalent-sized three-dimensional (3D) model of zigzag and armchair BNNT structures using nanotube modeler software. The obtained models were then subjected to mesh analysis to generate finite element method simulations. The simulations were finally performed to analyze the electrical response of the BNNT structures under external mechanical forces. We observed that the electrical responses of zigzag BNNT were 1.6 times greater than armchair one. In conclusion, our study sheds light on the piezoelectric potential of zigzag and armchair chiralities of BNNT structures. Furthermore, our findings contribute to the understanding of the electrical properties of BNNTs and their potential for various medical and industrial applications. The knowledge gained from this study provides a foundation for further research and development in the field of piezoelectric nanostructures, paving the way for innovative advancements in nanotechnology.

For Brusselator diffusion–reaction model involving complex forming reaction with the activator species, an amplitude equation has been derived in the framework of a weakly nonlinear theory. Complexing reaction with the activator species strongly influences the time-dependent amplitudes such as in Hopf-wave bifurcations, whereas time-independent amplitudes such as in Turing—bifurcations, are independent of complexing reaction with the activator species. Complexing reaction arrests the arrival of Hopf—bifurcations and the domain of excitable non-oscillations such created may be used effectively for Turing-structure generation by inducing inhomogeneous perturbations of nonzero wavenumber mode. Any major complexing interaction with the activator species in a biological oscillatory network is bound to alter the domains of Hopf/Turing bifurcations affecting the course of physiological self-organization processes.

SARS CoV-2 virus (COVID-19) emerged as a highly infectious human pathogen in late 2019. Started in China but rapidly started spreading all over the world and soon became a pandemic. More than seven million deaths have been reported so far that devasted millions of families worldwide. Several drugs, such as hydroxychloroquine, chloroquine, remdesivir, favipiravir and arbidol have undergone some clinical studies since early 2020, but their safety concerns remained a serious issue. However, within an year from late 2019, several successful vaccines were invented to prevent people from the infection. Almost at the same time, two drugs were discovered. These are PAXLOVID™ (nirmatrelvir, ritonavir) from Pfizer and molnupiravir from Merck which were soon approved by the US-FDA, for emergency use in the treatment of COVID-19. But several challenges were soon reported in treatments with these drugs, particularly for those who are immunocompromised or have vaccine immunity and suffering for a long time from the infection (known as long-COVID). Complex issues for treatments of long-COVID patients continue to remain unresolved. Thus, discovery of new drugs to assist treatment for emerging COVID-19 problems is urgently needed. But it is important to note that discovery of new COVID-19 therapeutics, particularly small molecules is not a simple task. However, there are several excellent reviews on attempts for COVID-19 drug discovery including a handful of articles on theoretical approaches towards the goal. This review summarizes the theoretical attempts for discovery of COVID-19 drugs, their challenges and future opportunities along with efforts from the author’s lab.