Model Equations Research Articles

Estimation of Radon Flux Density Changes in Temporal Vicinity of the Shipunskoe Earthquake with Mw = 7.0, 17 August 2024 with the Use of the Hereditary Mathematical Model

Using the data of radon accumulation in a chamber with excess volume at one of the points of the Kamchatka subsurface gas-monitoring network, the change in radon flux density due to seismic waves and post-seismic relaxation of the medium is shown. A linear fractional equation is considered to be a model equation. The change of radon-transport intensity due to changes in the state of the geo-environment is described by a fractional Gerasimov–Caputo derivative of constant order. Presumably, the order of the fractional derivative is related to the radon-transport intensity in the geosphere. Using the Levenberg–Marquardt method, the optimal values of the model parameters were determined based on experimental data: air exchange coefficient and order of fractional derivative, which allowed the solving of the problems of radon flux density determination. Data in the temporal neighborhood of a strong earthquake with Mw=7.0, which occurred in the northern part of Avacha Bay on 17 August 2024, were used. As a result of the modeling, it is shown that the strong seismic impact and subsequent processes led to changes in the radon flux in the accumulation chamber. The obtained model curves agree well with the real data, and the obtained estimates of radon flux density agree with the theory.

Photokinetics of Photothermal Reactions

Photothermal reactions, involving both photochemical and thermal reaction steps, are the most abundant sequences in photochemistry. The derivation of their rate laws is standardized, but the integration of these rate laws has not yet been achieved. Indeed, the field still lacks integrated rate laws for the description of these reactions’ behavior and/or identification of their reaction order. This made difficult a comprehensive account of the photokinetics of photothermal reactions, which created a gap in knowledge. This gap is addressed in the present paper by introducing an unprecedented general model equation capable of mapping out the kinetic traces of such reactions when exposed to light or in the dark. The integrated rate law model equation also applies when the reactive medium is exposed to either monochromatic or polychromatic light irradiation. The validity of the model equation was established against simulated data obtained by a fourth-order Runge–Kutta method. It was then used to describe and quantify several situations of photothermal reactions, such as the effects of initial concentration, spectator molecules, and incident radiation intensity, and the impact of the latter on the photonic yield. The model equation facilitated a general elucidation method to determine the intrinsic reaction parameters (quantum yields and absorptivities of the reactive species) for any photothermal mechanism whose number of species is known. This paper contributes to rationalizing photokinetics along the same general guidelines adopted in chemical kinetics.

Comment on: ‘Modulation instability and extraction of fractional optical solitons in the presence of generalized Kudryashov’s law and dual form of non-local nonlinearity’

Abstract The present comment points out all the shortcomings that occurred during the modulational instability analysis in the recent work published by Chahlaoui et al [Phys. Scr. 99 075226] and then methodically presents the investigation of the modulational instability of the steady-state solution of their model equation in the special case of time derivatives in the ordinary sense.

External Validation of Two 10-Year Stroke Risk Prediction Models Using Korean Genome and Epidemiology Study Data.

This study aimed to externally validate two 10-year stroke risk prediction models: one developed in Korea (Model 1) and the other in China (Model 2), using community-based cohort data. Data from 8432 participants in Model 1 and 8915 participants in Model 2 were analyzed. Stroke risk was calculated based on each model's equations, and model performance was assessed using the area under the receiver operating characteristic curve (AUC). Age, blood pressure, and diabetes mellitus were significant common risk factors for stroke in both men and women. The AUCs of Model 1 were 0.72 for men and 0.68 for women, while those of Model 2 were 0.70 for men and 0.66 for women. When simplified to include 3-5 significant factors, the AUCs of Model 1 remained almost unchanged for both sexes, while those of Model 2 were 0.68 for men and 0.63 for women. In conclusion, the performance of both models was insufficient for the participants in this study. Therefore, it is suggested that stroke prediction models be developed using the most significant risk factors of each target population.

Dynamics of One-Directional Functionally Graded Plates with Different Sizes of Microstructure: Theoretical Tolerance Modelling

The dynamics of thin elastic one-directional non-periodic plates are considered in this paper. The structure of these plates is, at a macro level, functionally graded along the x1-axis, but at the micro level it is non-periodic (tolerance-periodic). In the plates, the effect of a microstructure size on their behaviour can play a crucial role. The tolerance modelling method allows for this effect to be taken into account. This paper mainly proposes that tolerance modelling leads to model equations of two different tolerance models for one-directional functionally graded plates with two kinds of tolerance-periodic microstructures, i.e., (a) those having a microstructure size that is an order of the plate thickness, d~l, and (b) those having the plate thickness that is smaller than a microstructure size, d << l. Derived model equations are characterised by slowly varying coefficients. A subset of these coefficients is contingent on the microstructure size. The models presented herein determine formulas for both fundamental lower-order vibration frequencies and higher-order vibration frequencies, which are related to the microstructure. These models of such plates are implemented in a rudimentary example of free vibrations. Using the Ritz method, formulas of frequencies are obtained.

Numerical solution of a nonlinear model of chromatography considering different isotherms and gradient profiles

In gradient chromatography, the mobile phase composition is progressively altered to regulate the propagation rates of the injected mixture components. Resultantly, improved separation of mixture components can be attained, the recycling time that must pass between two consecutive injections can be reduced, and, hence, the column’s efficiency and selectivity can be enhanced. A coupled modeling framework, integrating a lumped kinetic model and the convection–diffusion equation for solvent volume fraction, is employed to approximate the process. The influence of different isotherm models on the process dynamics is examined through numerical simulations. A semi-discrete second-order finite volume scheme is suggested to approximate the model equations. Impacts of positive and negative gradients, gradient shapes, gradient starting and ending times, axial dispersion, Henry’s constants, nonlinearity coefficients, mass transfer coefficients, and different adsorption isotherms are investigated. The theoretical findings presented in this study may facilitate further advancements in the field of gradient elution chromatography.

Vibration-Based Damage Prediction in Composite Concrete–Steel Structures Using Finite Elements

The prediction of structural damage through vibrational analysis is a critical task in the field of composite structures. Structural defects and damage can negatively influence the load-carrying capacity of the beam. Therefore, detecting structural damage early is essential to preventing catastrophic failures. This study addresses the challenge of predicting damage in composite concrete–steel beams using a vibration-based finite element approach. To tackle this complex task, a finite element model to a quasi-static analysis emulating a four-point pure bending experimental test was performed. Notably, the numerical model equations were carefully modified using the Newton–Raphson method to account for the stiffness degradation resulting from material strains. These modified equations were subsequently employed in a modal analysis to compute modal shapes and natural frequencies corresponding to the stressed state. The difference between initial and damaged modal shape curvatures served as the foundation for predicting a damage index. The approach effectively captured stiffness degradation in the model, leading to observable changes in modal responses, including a reduction in natural frequencies and variations in modal shapes. This enabled the accurate prediction of damage instances during construction, service, or accidental load scenarios, thereby enhancing the structural and operational safety of composite system designs. This research contributes to the advancement of vibration-based methods for damage detection, emphasizing the complexities in characterizing damage in composite structural geometries. Further exploration and refinement of this approach are essential for the precise classification of damage types.

Separation Process for Methanol–Methylal–Methyl Formate Multicomponent System in Polyformaldehyde Production Waste Liquid: Modeling and Techno-Economic Analysis

The vapor–liquid equilibrium (VLE) data of the ternary system methanol–methyl formate–methylal was measured at atmospheric pressure using a modified Rose equilibrium kettle with vapor–liquid double circulation method. The experiment data were correlated with the NRTL, UNIQUAC, and Wilson activity coefficient model equations. The results shown that the root mean square deviation (RMSD) between the calculated and simulated values of the three models followed the order: UNIQUAC ≈ NRTL < Wilson, and except for the RMSD (T) in the range of 0.4–0.5, the others are less than 0.01. In addition, the NRTL model was selected to link with Aspen Plus software to simulate the separation process of polyformaldehyde (POM) waste liquid. The simulation results show that the methyl formate in POM waste stream can be purified by simple distillation, while the methylal separated from the POM waste liquid, which was affected by factors like the azeotropic behavior of binary components, necessitates a complex distillation process. Under optimal operating conditions, the recovery yield of methyl formate through direct distillation can reach 99.7%, with an economic benefit of 6960.1 CNY per ton of waste liquid. Although the economic benefit of the multi-component distillation reach 7281.2 CNY, the increase in the number of equipment and the complexity of the process have negative impacts.

Structural Equation Modelling of Retinopathy of Prematurity Treatment Integrating Both Physical and Clinical Effects

Background: We sought to develop a structural equation model (SEM) identifying physical and clinical risk factors associated with treatment for retinopathy of prematurity (ROP). Methods: This retrospective, observational, case–control study included 314 infants screened for ROP between April 2004 and July 2024. A bivariate binary logistic regression model, decision tree, and structural equation model (SEM) were employed to develop a more general model for ROP requiring treatment. Results: In the SEM, the factors significantly associated with ROP treatment included the retinal avascular area according to disk diameter (DD) (p < 0.001), weekly vascularisation rate (DD/w) (p < 0.001), and duration of intubation (days) (p < 0.001). In addition, the following significant associations were identified in both the bivariate analysis and the SEM: lower gestational age (p < 0.001) and birth weight (p <0.001) were associated with greater retinal avascular area; low postnatal weight gain (p < 0.027) was associated with a slow rate of retinal vascularisation; sepsis (p < 0.001), ductus arteriosus (p < 0.001), and the need for transfusion (p < 0.001) were associated with longer intubation mechanical ventilation (IMV). Conclusions: Lower gestational age, lower birth weight, sepsis, ductus arteriosus, transfusion, and lower weight gain increase the risk of requiring ROP treatment. In the SEM, this association is represented through three intermediate physical endogenous variables, namely, the greater temporal avascular area of the retina, the lower postnatal vascularisation rate, and the greater duration of IMV.

Digitalization of the Algerian Transportation Sector

This research endeavors to shed light on the pivotal significance of advancing the public transport sector in Algeria, emphasizing the urgent need for a thorough examination of the factors influencing the integration of electronic payment systems. This research scrutinizes the determinants influencing the adoption of the Hafilati application-an electronic payment and bus tracking system introduced by the Urban and Semi-Urban Transport public institution in Tiaret. Employing the Technology Acceptance Model and structural equation modelling, the study investigates the attitudes and behaviors of 296 customers regarding the adoption of these services. The results highlight a robust correlation between perceived benefits and the intention of customers to use the services. Conversely, perceived risks exhibit a negative impact on both perceived benefits and the ease of use. This examination significantly advances our understanding of the pivotal factors shaping the adoption of digital technologies within the transport sector. It sheds light on crucial considerations for stakeholders and policymakers, providing valuable insights into enhancing the acceptance and utilization of such technological innovations in urban and semi-urban transportation settings.

Interaction of mixed localized waves in optical media with higher-order dispersion

This work focuses on the interaction of mixed localized waves in optical media with higher-order dispersions whose dynamics are governed by a modified cubic–quintic nonlinear Schrödinger equation. For proving the integrability of this model equation, we start by building a Lax pair and an infinitely many conservation laws. Applying the linear stability analysis method, the baseband modulational instability of a stationary continuous wave solution is investigated. Studying the baseband modulational instability phenomenon, we show that the optical loss influences the instability gain spectrum: the stationary continuous wave solution under consideration satisfies the condition of the baseband modulational instability only when the optical loss is neglected. According to the generalized perturbation (n,p−n)–fold Darboux transformation, the existence and properties of the parametric first-, second-, and third-order mixed localized wave solutions for the model equation are constructed when the loss term is neglected. The built solutions helping, we engineer in optical media with higher-order dispersions new nonlinear structures showing interactions between various kinds of nonlinear waves such as multi-peak bright/dark solitons, bright/dark breathers, bright/dark rogue waves, as well as periodic waves. Graphical illustrations are then used for investigating main characteristics of the mixed localized waves propagating on vanishing/nonvanishing continuous wave background. Interestingly, our study produces nonlocal breathers in which the entire optical field oscillates periodically in conjunction with the central local oscillation during transmission. Investigating the effects of various parameters on the nonlinear structures resulting from built mixed localized wave solutions of the model equation, we show that parameter of the fourth-order dispersion can be used to describe wave compression. Also, we show that the model parameters are useful for controlling the optical waves in lossless optical media with both higher-order dispersion whose dynamics are governed by the model equation under consideration. Our results are useful for investigating mixed localized waves in nonlinear metamaterials with cubic–quintic nonlinearity, detuning intermodal dispersion, self steepening and self-frequency effects, and nonlinear third- and fourth-order dispersions.

OPTIMIZATION OF CONCRETE CONTAINING LIMESTONE DUST AND LOCUST BEAN POD ASH BY CENTRAL COMPOSITE DESIGN.

The over-reliance on concrete produced from cement had kept the cost of construction high and also prevented people from building modern and cost-effective houses most especially by rural dwellers in the developing nations. Emission of carbon footprint during cement production depletes the ozone layer which is a major concern to researchers all over the world. This investigation focused on the partial replacement of cement with Locust Bean Pod Ash (LBPA) and Limestone Dust (LSD) with a characteristic strength of 20 N/mm2 . Tests were conducted on slump, compressive, and flexural strength. The results of the physical properties showed that cement had a specific gravity of 3.14, LSD and LBPA had 2.72 and 2.61 respectively. The result of the slump test for the admixed concrete containing LSD/LBPA showed that they were workable and the higher the replacement of cement with LBPA/LSD, the higher the slump value. Optimization of the admixed concrete properties was done by numerical method. Limestone dust was kept at 5% for all the runs, and LBPA ranged from 5% to 25% at curing ages of 28, 60, and 90 days. The analysis of variance showed that the model developed was significant. The optimal value obtained was 5% LSD and 5.4% LBPA at 90 days with compressive strength of 26.9 N/mm2 and flexural strength of 3.5 N/mm2 . Model equations were developed for both compressive and flexural strengths. This research recommends 5% LSD and 5.4% LBPA as cement replacements in the production of concrete.

OPTIMIZATION OF USED ENGINE OIL AS ADMIXTURE IN CONCRETE USING RESPONSE SURFACE METHODOLOGY

Maintenance of industrial machinery and automobile engines produces a large amount of Used Engine Oil (UEO) as waste. This waste oil is harmful to the environment, pollutes the land and kills the aquatic habitats. Used engine oil poured into household drains or directly onto the field will pollute fresh water by entering rivers and groundwater. Efforts are shifted to conversion of Used Engine Oil into useful material for concrete production as a replacement for SP430 superplasticizer. This research deals with optimizing Used Engine Oil in M20 grade concrete using response surface methodology. The oxide composition of UEO revealed 37% of SO3, 15.5% of CaO, 17.7% OF ZnO, 9% of P2O5. The research revealed that the workability of the concrete mixes were between medium and high. The control mix slump value was 50mm but when UEO and superplasticizer were used, the slump obtained were 54mm and 52mm respectively. Concrete samples were produced and strength properties were tested at 7, 14 and 28 days of curing by water immersion. The test result showed that water absorption decreased with increase in UEO. Compressive strength increased with increase in dosage and curing days. Also, there was gradual increase in flexural and splitting tensile tests with the increase in UEO. Model equations and optimal values of UEO concrete were generated by numerical optimization. The optimal value was 11.4ml of UEO at 28 days which gave compressive strength result of 26.7 N/mm2 , flexural strength 8.3N/mm2 , tensile strength 18.9 N/mm2 and water absorption of 0.7%. Therefore, 11.4ml of UEO is recommended for use as superplasticizer in M20 grade concrete.

An Integrated Framework for Infectious Disease Control Using Mathematical Modeling and Deep Learning.

Infectious diseases are a major global public health concern. Precise modeling and prediction methods are essential to develop effective strategies for disease control. However, data imbalance and the presence of noise and intensity inhomogeneity make disease detection more challenging. Goal: In this article, a novel infectious disease pattern prediction system is proposed by integrating deterministic and stochastic model benefits with the benefits of the deep learning model. Results: The combined benefits yield improvement in the performance of solution prediction. Moreover, the objective is also to investigate the influence of time delay on infection rates and rates associated with vaccination. Conclusions: In this proposed framework, at first, the global stability at disease free equilibrium is effectively analysed using Routh-Haurwitz criteria and Lyapunov method, and the endemic equilibrium is analysed using non-linear Volterra integral equations in the infectious disease model. Unlike the existing model, emphasis is given to suggesting a model that is capable of investigating stability while considering the effect of vaccination and migration rate. Next, the influence of vaccination on the rate of infection is effectively predicted using an efficient deep learning model by employing the long-term dependencies in sequential data. Thus making the prediction more accurate.

Non-Newtonian dynamics modelled with non-linear transport coefficients at the mesoscale by using dissipative particle dynamics.

We derive the algorithms for the dynamics of the standard dissipative particle dynamics model (DPD) for a velocity-dependent friction coefficient. By introducing simple estimators of the local rate of strain we propose an interparticle friction coefficient that decreases for high deformation rates, eventually leading to the macroscopic shear-thinning behaviour. We have derived the appropriate fluctuation-dissipation theorems that include the correction of the spurious behaviour due to the coupling of the non-linear friction and the fluctuations. The consistency of the model has been numerically investigated, including the Maxwell-Boltzmann distribution for the particle velocities as well as the comparison with the standard linear model for various stresses. The shear-thinning behaviour is clearly reported. Finally, along with the important methodological aspects related to the derivation of the algorithms for non-linear interparticle friction, we introduce a novel two-step algorithm that permits us the integration of the dynamic equations of the DPD model without the explicit derivation of the corrective terms due to the spurious behaviour.

Quasi-3D model to simulate flow in straight channels within vegetation patches

Understanding the interaction between flow dynamics and riparian vegetation is essential for effective river management and conservation of the river environment, including the river ecosystem. Numerical simulations have emerged as a valuable tool for this purpose, offering cost-effective and scalable approach. In this paper, we conducted a comparative analysis between the Bottom Velocity Computation (BVC) method for quasi-three-dimensional models, which is the enhanced depth-integrated model with sub-grid three-dimensional model, conventional two-dimensional model, and three-dimensional model to explore the three-dimensional (3D) flow effects induced by the presence of vegetation patches. The vegetation resistance evaluation method for non-equilibrium open channel flows was extended to two dimensions and incorporated into the equations for the BVC models to evaluate the interaction of the vegetation, three-dimensional eddy motion, and turbulence in a depth-integrated model. Our simulations focused on straight channels containing patches of vegetation. The results showed that the velocities within the vegetated areas were observed to decrease, while velocities in non-vegetated areas increased. Moreover, the BVC model showed consistency with experimental data compared to 2DC model. Specifically, the 2DC model tended to overestimate velocities in non-vegetated areas due to its inability to capture momentum transport from non-vegetated areas. This discrepancy highlights the importance of considering 3D flow effects for simulating flows in vegetated areas.

A time-domain finite element formulation of the equivalent fluid model for the acoustic wave equation

Sound-absorptive materials such as foam can be described by the equivalent fluid (EF) model. The homogenized fluid’s acoustic behavior is thereby described by complex-valued, frequency-dependent acoustic material parameters. When transforming the acoustic wave equation for the EF model from the frequency domain to the time domain, convolution integrals arise. The auxiliary differential equation (ADE) method is used to circumvent the direct calculation of these convolution integrals. The wave equation and the coupled set of ordinary ADEs are solved in the time domain using the finite element (FE) method. The approach relies on approximating the complex-valued frequency response functions of the inverse equivalent bulk modulus and density by a sum of rational functions consisting of real and complex poles. The order of the rational function approximation defines the number of additionally introduced auxiliary variables per nodal degree of freedom. The presented FE formulation includes a narrow-band non-reflecting boundary condition (NRBC) for normal incidence. The implementation in openCFS shows optimal temporal and spatial convergence for a semi-infinite duct based on the analytic plane wave solution for harmonic excitation. The simulation of a pressure pulse propagating in an infinite EF domain with a scatterer demonstrates the capability for multidimensional, actual transient problems.

Observational constraints on a generalized equation of state model

Observational constraints on a generalized equation of state model

ESG Practices and Corporate Dividend Decision: A Moderated Mediating Analysis

The study examines the direct and indirect roles of CEO efficiency and firm reputation respectively, in order to investigate the relationship between ESG practices and corporate dividend decisions of the Indian companies. The data is collected from NSE Nifty 500 and S&P BSE 500 index of the Indian listed firms during the period 2013 to 2022. The study also aims in addressing the drawbacks of the previous literature who assumes the direct relationships of the ESG disclosure on corporate dividend decisions which are inconclusive. Using the fixed effect model and structural equation model, the study demonstrates favourable and substantial correlations between ESG practices and dividend decisions that are conveyed through the corporate reputation. Further, through the application of the Instrument Variable Two Stage Least Square (2SLS IV) regression approach, CEO’s efficiency amplifies the insignificant impact of ESG disclosure on the company’s reputation. The results report that company reputation is a matter of stakeholders’ perceptions and reputation is distinct from the actual character and behaviour of the companies with the longitudinal data. The outcome of the study offers insights into how lack of consideration of factors results in inconsistent findings as reported in the previous literature.

Thermodynamic and Kinetic Assessment of Cobalt II Adsorption Using Green Synthesized NiO/γ-Al2O3 Nanoparticles

Introduction: Disposal of heavy metals into the water as a result of industrial development might cause a threat Health and the environment. aim of this study was to assess the uptake of Co2+ from aqueous solutions via NiO/ γ-Al2O3 nano catalysts. Methods: The main variables that affect the percentage of metal removal were assessed. It took about 50 minutes to attain equilibrium for the elimination of Co+2 ions. It was discovered that raising the adsorbate concentration and increasing the surface weight somewhat lowered the removal of cobalt ions. Results: The removal of cobalt ions was shown to depend on temperature,due to ecothermic natural of this prosess increasing temperature associated with decrease the elemination . Conclusions: The adsorption seems to be spontaneous, exothermic, and less random according to calculated values of the thermodynamic functions (∆G, ∆H, and ∆S) of the adsorption. After the data were fitted into a number of kinetic models, including the Elovich model, pseudo-first order, pseudo-second order, and intraparticle diffusion equations, it was discovered that the pseudo-second-order model performed the best at describing the adsorption, with a high correlation factor (R2).