Solution Of Model Research Articles

Activity Calculation and Vacuum Separation Theoretical Research concerning Ag–Cu, Ag–Sb and Cu–Sb Binary Alloys

The Ag–Cu–Sb system is a key component of lead anode slime and boasts an exceptionally high economic recovery value. In this work, six models, including the Molecular Interaction Volume Model (MIVM), Modified Molecular Interaction Volume Model (M-MIVM), Wilson equation, Miedema model, Regular Solution Model (RSE) and Sub-Regular Solution Model (SRSE), are used to calculate the predicted values of the activity and its deviations with experimental data for binary alloys in the Ag–Cu–Sb system for the first time. The result reveals that the overall means of the average relative deviation and average standard deviation of the M-MIVM are 0.01501 and 3.97278%, respectively, which are about two to six times smaller than those of the other five models, indicating the stability and reliability of the M-MIVM. In the meantime, the predicted data of the Cu–Ag binary alloy at 1423 K, Sb–Ag binary alloy at 1250 K and Sb–Cu binary alloy at 1375 K calculated from the M-MIVM are more reliable and pass the Herington test. Then, the separation coefficient–composition (β–x), temperature–composition (T–x–y) and pressure–composition (P–x–y) of the Cu–Ag, Sb–Ag and Sb–Cu binary alloys are plotted based on the M-MIVM and vacuum theories, showing that the Cu–Ag binary alloy is relatively difficult to separate and that high temperatures or high copper contents are detrimental to obtaining high-purity silver. Meanwhile, theoretical data of the T–x–y diagram are consistent with the available experimental data. These results can guide vacuum separation experiments and industrial production concerning Ag–Cu, Ag–Sb and Cu–Sb binary alloys.

A general fractional breast cancer model: Model graph energy, Caputo-Fabrizio derivative existence and uniqueness plus numerical simulation

In the study of epidemiology, mathematical modelling is crucial because it improves understanding of the underlying mechanisms that cause illnesses to spread and offers the possibility of developing preventative interventions. In this paper, we have discussed a fractional mathematical model. A set of fractional differential equations is used to build the model. We have applied a Caputo Fabrizio (CF) to describe the fractional breast cancer model. The model consists of five subpopulations that make up a population. They are disease-free (D), cardiotoxic (E), stages 1 and 2 (A), 3 (B), and 4 (C). We have used a digraph chart to present the breast cancer model. We have used some graph theory concepts to compute the energy of the breast cancer model corresponding digraph. We have demonstrated the existence, uniqueness, and positivity of the model solutions. The fixed point hypothesis demonstrates both the existence of a solution to the suggested fractional breast cancer model as well as the fact that this solution is one of a kind. Numerical simulations are a useful tool for explaining the suggested notion. We have presented a numerical method for simulating the problem. We have used an algorithm modelled after the Adams-Bashforth-Moulton method (ABMM) to solve the model. Numerical simulations of the model in various fractional orders illustrate the theoretical conclusions. We have used the Matlab application to calculate every solution. The results demonstrate the efficacy of the proposed fractional model from an epidemiological standpoint.

On Atangana–Baleanu fractional granular calculus and its applications to fuzzy economic models in market equilibrium

Based on relative-distance-measure fuzzy interval arithmetic (RDM-FIA), this paper presents several new concepts for fuzzy functions in fractional granular calculus with Mittag-Leffler (ML) kernels, such as Atangana–Baleanu (AB) fractional granular integrals, AB fractional granular derivatives, and AB Caputo fractional granular derivatives. Then, we present formulas for the fuzzy granular Laplace transform on Caputo fractional granular derivatives, AB fractional granular derivatives, and AB Caputo fractional granular derivatives. In addition to the relationship between AB fractional granular derivatives and AB Caputo fractional granular derivatives established using the granular Laplace transform, new fractional Newton–Leibniz-type formulas for both derivatives and integrals are proved. As applications, we obtain the fundamental solutions for the fuzzy economic models in the framework of Caputo fractional granular derivatives and AB Caputo fractional granular derivatives by utilizing the fuzzy granular Laplace transform. Several graphical explanations are given to show the dynamic behavior of the fundamental solutions. Moreover, we illustrate the advantages of using RDM-FIA to study the mathematical models of uncertain dynamical systems. The results of this study are illustrated using several numerical examples.

Investigation of soliton solutions for the NWHS model with temperature distribution in an infinitely long and thin rod

This study proposed a modified [Formula: see text]-expansion method to seek the new exact traveling wave solutions of the Newell–White–Head–Segel (NWHS) Model. This is an amplitude equation utilized for distributing temperature within a rod that is infinitely thin and long, or determining the flow velocity of a fluid through a pipe that is infinitely long but has a small diameter. The modified [Formula: see text]-expansion method is used to extract the new exact solutions. The solutions of this model are categorized in hyperbolic, trigonometric, and rational forms. Moreover, we compare our results with the new auxiliary equation method. The 3D, line and corresponding contour representation of these solutions are depicted by choosing the different values of parameters.

Effect of Applying 1% Metformin on Guided Bone Regeneration Processes with Bovine-Derived Xenografts.

Background: Although xenografts have shown successful results in GBR procedures due to their osteoconductive properties, many authors have opted to add co-adjuvant drugs to favor osteogenesis and differentiate cells into an osteoblastic lineage. Metformin has been shown to have bone-protective properties, regulating osteoclast differentiation, as well as the ability to promote osteoblast mineralization and differentiation. The present study aimed to evaluate the effect of the local application of a 1% metformin solution on bone neoformation in the treatment of an experimental bone defect in a guided bone regeneration animal model with a particulated bovine hydroxyapatite xenograft with hyaluronate. Methods: With this purpose in mind, two critical defects with 8 mm diameter and 0.5 mm depth were created in eight male New Zealand rabbit calvarias. Titanium cylinders were fixed in each defect and filled with particulate hydroxyapatite of bovine origin and sodium hyaluronate, with sterile injectable saline added to the control group and sterile 1% metformin solution added to the test group. At 6 weeks, the animals were euthanized, and samples were obtained and prepared for histomorphometric analysis. Results: A higher percentage of new bone formation was observed in the metformin samples than in the control samples, both in the region closest to the animal's calvaria and in the most distal region analyzed. A higher average bone-biomaterial contact percentage was observed in the samples, with metformin in both the proximal and distal regions. There was no statistically significant difference in the mean value in either region in both parameters. Conclusion: The local application of a 1% metformin solution in an animal model of guided bone regeneration with particulate bovine hydroxyapatite and hyaluronate resulted in greater bone neoformation and xenograft osseointegration than in the control group.

LDCML: a novel ai-driven approach for privacy-preserving anonymization of quasi-identifiers

Introduction: The exponential growth of data generation has led to an escalating concern for data privacy on a global scale. This work introduces a pioneering approach to address the often overlooked data privacy leakages associated with quasi-identifiers, leveraging artificial intelligence, machine learning and data correlation analysis as foundational tools. Traditional data privacy measures predominantly focus on anonymizing sensitive attributes and exact identifiers, leaving quasi-identifiers in their raw form, potentially exposing privacy vulnerabilities.Objective: The primary objective of the presented work, is to anonymise the quasi-identifiers to enhance the overall data privacy preservation with minimal data utility degradation.Methods: In this study, the authors propose the integration of ℓ-diversity data privacy algorithms with the OPTICS clustering technique and data correlation analysis to anonymize the quasi-identifiers.Results: To assess its efficacy, the proposed approach is rigorously compared against benchmark algorithms. The datasets used are - Adult dataset and Heart Disease Dataset from the UCI machine learning repository. The comparative metrics are - Relative Distance, Information Loss, KL Divergence and Execution Time.Conclusion: The comparative performance evaluation of the proposed methodology demonstrates its superiority over established benchmark techniques, positioning it as a promising solution for the requisite data privacy-preserving model. Moreover, this analysis underscores the imperative of integrating artificial intelligence (AI) methodologies into data privacy paradigms, emphasizing the necessity of such approaches in contemporary research and application domains.

Analytical solutions of virus propagation model in blockchain networks

The main goal of this paper is to find analytical solutions of a system of nonlinear ordinary differential equations arising in the virus propagation in blockchain networks. The presented method reduces the problem to an Abel differential equation of the first kind and solve it directly.

Dynamic Bayesian Game Optimization Method for Multi-Energy Hub Systems with Incomplete Load Information

The interconnection of Energy Hub can enhance the energy efficiency and reliability associated with the independent operation of energy systems. However, the traditional optimal scheduling methods are hard to tackle the situation with the incomplete load information and competitive constraints of a multi-Energy Hub. This paper proposes a dynamic Bayesian game optimization scheduling strategy considering incomplete information on users’ load-side demand. First, a load forecast error coefficient is introduced to handle the conditional probability problem caused by incomplete information through the Bayesian rule. The constraint relationship among multi-Energy Hub under the dynamic price mechanism is analyzed to meet the economic and environmental coordination goals under load uncertainty. Second, extending from Nash equilibrium to Bayes Nash equilibrium proves the existence and uniqueness of Nash equilibrium solutions in Bayesian game models. The decision game algorithm is used to optimize the scheduling of the multi-Energy Hub and subsequently ensure the autonomous scheduling of the system and solve the information barriers. Finally, an Integrated Energy System composed of three Energy Hubs was used to validate the effectiveness and superiority of the proposed optimization method. Results show that under the Bayesian game decision, the multi-Energy Hub game model has reduced the total cost of the Integrated Energy System by 0.78%, which can improve the economic benefit and address the environmental pollution problem.

Bessel Polynomials: Application in Finding Optimal Solution of Fractional COVID-19 Model Using Lagrange Multipliers

Bessel Polynomials: Application in Finding Optimal Solution of Fractional COVID-19 Model Using Lagrange Multipliers

A Sustainable and Cost‐Effective Bioadsorbent for the Removal of Allura Red from Contaminated Water

AbstractFood grade dyes pose severe health hazards when consumed in excessive amounts or enter body via contaminated water. Despite its harmful effects, Allura Red (AR) is very less explored dye for its removal, especially using agricultural/fruit waste. This study presents efficient removal of an important and unsafe food grade dye, AR via adsorption. Waste watermelon peel waste has been used for the first time for treatmenting wastewater contaminated with AR. Waste was converted to two types of adsorbents, with and without subjecting it to pyrolysis. Both the adsorbents were characterized for functionality and crystallinity and used for conducting adsorption studies. Removal of dye was evaluated by intrinsic strategy of monitoring the model solutions under pre‐ and post‐adsorption conditions. Removal percentage of dye was determined by calculating its initial (Co) and final (Cf) concentrations in solution using the formula (see Eq. (1)). Various reaction parameters important for adsorption, viz. pH, adsorbent dose, residence time, reaction temperature and particle size were optimized. Results indicate that ~80 % and >92 % dye could be removed using 0.5 g/L adsorbent before and after pyrolysis respectively in 3.5 h from its 2 ppm concentration in modelled water.

Education 4.0 framework for sustainable entrepreneurship through transdisciplinary and abductive thinking: a case study

The global challenges and problems that threaten sustainability and human well-being demand the provision of creative, innovative, and affordable solutions so that they are within the reach of different levels of society. From the point of view of Higher Education, this is a major challenge since it is responsible for training new generations with the competencies and knowledge that allow them to respond to contemporary challenges and problems. This study provides a framework to promote sustainable entrepreneurship through transdisciplinary and abductive thinking. This combination of approaches will allow students to identify, analyze, and understand contemporary problems and, through a systematized process based on the “design thinking” design model, propose creative, innovative, and affordable solutions that can be implemented through entrepreneurship mechanisms. The identified findings that will be presented in this work are (i) the relevance of the Education 4.0 model as a reference to promote transdisciplinarity in a current teaching-learning context, (ii) The relevance of “design for sustainable development” as a trigger for sustainable entrepreneurship, (iii) The formation of desirable competencies in the profile of the higher education student based on transdisciplinarity and abductive thinking within the active learning process, and (iv) quantitative and qualitative measurement that allows measuring acceptance and evaluation of the long-term sustainability of the solutions obtained. This work will present the implementation of the proposed framework through a case study. This case study allowed us to identify elements of the proposed reference framework. The case study will address the problem of water scarcity and pollution, describing initiatives to achieve ODS 6, where it explains how sustainable and visionary solutions can be forged through transdisciplinary collaboration and abductive thinking. The project named “STEAM-mural fountain” done by a transdisciplinary working team between academia-society-industry is described, which aims to make technological advances in water treatment and monitoring visible to society.

AN EFFICIENT SPECTRAL METHOD FOR NONLINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS

For Volterra integro-differential equations (VIDEs) with weakly singular kernels, their solutions are singular at the initial time. This property brings a great challenge to traditional numerical methods. Here, we investigate the numerical approximation for the solution of the nonlinear model with weakly singular kernels. Due to its characteristic, we split the interval and focus on the first one to save operation. We employ the corresponding singular functions as basis functions in the first interval to simulate its singular behavior, and take the Legendre polynomials as basis functions in the other one. Then the corresponding hp-version spectral method is proposed, the existence and uniqueness of solution to the numerical scheme are proved, the hp-version optimal convergence is derived. Numerical experiments verify the effectiveness of the proposed method.

A Comprehensive Fuzzy Model for Understanding Neuronal Calcium Distribution in Presence of VGCC, Na+/Ca2+ Exchanger, Buffer, and ER Fluxes.

Free Calcium ions in the cytosol are essential for many physiological and physical functions. The free calcium ions are commonly regarded as a second messenger, are an essential part of brain communication. Numerous physiological activities, such as calcium buffering and calcium ion channel flow, etc. influence the cytosolic calcium concentration. In light of the above, the primary goal of this study is to develop a model of calcium distribution in neuron cells when a Voltage-Gated Calcium Channel and Sodium Calcium Exchanger are present. As we know, decreased buffer levels and increased calcium activity in the Voltage-Gated Calcium Channel and Sodium Calcium Exchanger lead to Alzheimer's disease. Due to these changes, the calcium diffusion in that location becomes disrupted and impacted by Alzheimer's disease. The model has been constructed by considering key factors like buffers and ER fluxes when Voltage-Gated Calcium Channels and Sodium Calcium Exchangers are present. Based on the physiological conditions of the parameters, appropriate boundary conditions have been constructed in the fuzzy environment. This model is considered a fuzzy boundary value problem with the source term and initial boundary conditions are modeled by triangular fuzzy functions. In this, paper we observed the approximate solution of the mathematical model which was investigated by the fuzzy undetermined coefficient method. The solution has been performed through MATLAB and numerical results have been computed using simulation. The observation made that the proper operation of the Voltage-Gated Calcium Channel and Sodium Calcium Exchanger is critical for maintaining the delicate equilibrium of calcium ions, which regulates vital cellular activities. Dysregulation of Voltage-Gated Calcium Channel and Sodium Calcium Exchanger activity has been linked to neurodegenerative illnesses like Alzheimer's disease.

Travelling waves for a fast reaction limit of a discrete coagulation-fragmentation model with diffusion and proliferation.

We study traveling wave solutions for a reaction-diffusion model, introduced in the article Calvez et al. (Regime switching on the propagation speed of travelling waves of some size-structured myxobacteriapopulation models, 2023), describing the spread of the social bacterium Myxococcus xanthus. This model describes the spatial dynamics of two different cluster sizes: isolated bacteria and paired bacteria. Two isolated bacteria can coagulate to form a cluster of two bacteria and conversely, a pair of bacteria can fragment into two isolated bacteria. Coagulation and fragmentation are assumed to occur at a certain rate denoted by k. In this article we study theoretically the limit of fast coagulation fragmentation corresponding mathematically to the limit when the value of the parameter k tends to . For this regime, we demonstrate the existence and uniqueness of a transition between pulled and pushed fronts for a certain critical ratio between the diffusion coefficient of isolated bacteria and the diffusion coefficient of paired bacteria. When the ratio is below , the critical front speed is constant and corresponds to the linear speed. Conversely, when the ratio is above the critical threshold, the critical spreading speed becomes strictly greater than the linear speed.

The resurgence of the G(2) group for the strong sector and the emergence of dark matter

G(2) is the smallest exceptional group and it is the simplest and viable gauge group to minimally extend the strong interaction sector: G(2) includes the group SU(3) of Quantum Chromodynamics (QCD) as a maximal subgroup and it is equipped with six additional gluons that can acquire mass via a Higgs mechanism driven by a new Higgs particle and constitute dark matter. In this article I want to describe how the exceptional G(2) group can be a physical gauge group, capable of extending the Standard Model (SM) of particles and including a versatile dark sector, which is compatible with experimental observations. In fact, due to its peculiar mathematical features, the group G(2) manifests some complex features, not properly considered in literature, which guarantee its correct use in physics, as its {3}⊕{3‾} decompositions w.r.t. SU(3) can acquire a complex structure. The resulting framework can be a solid Beyond Standard Model (BSM) solution for the dark matter (DM) problem, in the form of massive complex scalar glueballs, and it includes the proper color representations for quarks and leptons. Several quantum field theory features are discussed, like the G(2) coupling constant running and its spectrum before and after the phase transition, along with all the DM astrophysical realizations, in order to present the unexpected potential of this gauge group.

On the use of the Astarita flow field for viscoelastic fluids to develop a generalised Newtonian fluid model incorporating flow type (GNFFTy)

The two-dimensional, steady, homogeneous flow field proposed by Astarita (J. Rheol., vol. 35, 1991, pp. 687–689) is studied for a range of viscoelastic constitutive equations of differential form including the models due to Oldroyd (the upper and lower convected Maxwell; UCM/LCM), Phan-Thien and Tanner (simplified, linear form; sPTT) and Giesekus. As the flow is steady and homogeneous, the sPTT model results also give the FENE-P model solutions via a simple transformation of parameters. The flow field has the interesting feature that a scalar parameter may be used to vary the flow ‘type’ continuously from solid-body rotation to simple shearing to planar extension whilst the rate of deformation tensor $\boldsymbol{\mathsf{D}}$ remains constant (i.e. independent of flow type). The response of the models is probed in order to determine how a scalar ‘viscosity’ function may be rigorously constructed which includes flow-type dependence. We show that for most of these models – the Giesekus being the exception – the first and second invariants of the resulting extra stress tensor are linearly related, and for models based on the upper convected derivative, this link is simply via a material property, i.e. half the modulus. By defining a frame-invariant coordinate system with respect to the eigenvectors of $\boldsymbol{\mathsf{D}}$ , we associate a ‘viscosity’ for each of the flows to a deviatoric stress component and show how this quantity varies with the flow-type parameter. For elliptical motions, rate thinning is always observed and all models give essentially the UCM response. For strong flows, i.e. flow types containing at least some extension, thickening occurs and only a small element of extension is required to remove any shear thinning inherent in the model (e.g. as occurs in steady simple shearing for the sPTT/Giesekus models). Finally, a functional form of a viscosity equation which could incorporate flow type, but be otherwise inelastic, the so-called GNFFTy (generalised Newtonian fluid model incorporating flow type, pronounced ‘nifty’), is proposed. In the frame-invariant coordinate system proposed, this model is also capable of capturing normal-stress differences.

Apatite-related Na+, Cu2+, Zn2+, CO3 2− containing calcium phosphates nanoparticles: synthesis, characterization and antibacterial properties for medical application

The aim of this study was to prepare and characterize the calcium phosphates modified by different amount of Na+, Cu2+, Zn2+ and CO3 2−, and to investigate their activity in model solution (at pH = 7.45 and 37 °C) and antibacterial properties against Streptococcus pyogenes. According to XRD and FTIR spectroscopy data the apatite-related phases with partial substitution РО4 3− → СО3 2− (B-type) have been prepared. Presence of sodium and carbonate ions led to increase of solubility in model solution during the first 48 h, while modification with both Cu2+ and Zn2+ cations (up to 0.6 wt%) significantly improved antimicrobial properties against Streptococcus pyogenes.

Dynamics of propagation patterns: An analytical investigation into fractional systems

Recent years have seen a growing interest in fractional differential equations, particularly the fractional Chaffee-Infante ([Formula: see text]) equation, pivotal for understanding dynamics governed by fractional orders in specific physical systems. Exploring solitary wave solutions, this study employs the extended Khater method and truncated Mittag-Leffler function properties to formulate tailored solutions for the ([Formula: see text]) model. Through a traveling wave ansatz, the equation transforms into a nonlinear ordinary differential equation, revealing intricate propagation patterns of solitary waves. Visual representations aid comprehension, while rigorous validation ensures solution precision, ultimately providing a comprehensive understanding of system responses to external stimuli. This study effectively integrates analytical and numerical methodologies to derive precise solitary wave solutions, with significant implications for advancing comprehension of complex phenomena in various disciplines governed by fractional-order dynamics.

Mathematical modelling of impurity deposition during evaporation of dirty liquid in a porous material

When a contaminated liquid evaporates from within a porous material, the impurities or dirt accumulate and deposit within the pore space. This occurs during the cleaning of filters and fouling of textiles, and is related to the ‘coffee-ring’ problem. To investigate how and where dirt is deposited in the pore space, we present a model for the motion of an evaporation front through a porous material, and the related accumulation, transport, and deposition of dirt, assuming that the liquid remains stationary. For physically relevant parameters, vapour transport out of the porous material is quasi-steady and we derive a single ordinary differential equation describing the motion of the evaporation front in time. Model solutions exhibit spatially non-uniform profiles of the deposited dirt-layer thickness through the porous material. The dirt accumulation and evaporation problems are coupled: deposited dirt hinders vapour transport through the porous material, slowing the evaporation. We identify two scenarios in which the porous material becomes clogged with dirt. Accumulation of suspended dirt at the evaporating interface along with slow dirt diffusion results in the deposited dirt layers clogging the pores at the evaporating interface, halting the drying and trapping liquid in the porous material. Alternatively, slow dirt deposition results in the suspended dirt being pushed far into the porous material by the evaporation, eventually leaving only dirt (with no liquid) in the pore space. We investigate the dynamics of both clogging scenarios, characterising the parameter regimes for which each occurs. Both clogging scenarios must be avoided in practice since they may be detrimental to future filter efficacy or textile breathability.

Analytical Solutions of the 3-DOF Gyroscope Model

The motion of a rigid body (a gyroscope) is one of the key issues in classical mechanics. It remains a significant challenge, as evidenced by its extensive practical implementations in various scientific disciplines and engineering operations. It is important to obtain analytical solutions, as they provide solutions that depend directly on the system’s parameters, which can be definitively interpreted. The coupling of numerical and analytical solutions allows for a more precise representation of the real phenomenon. The main objective of the article was to formulate analytical solutions for the motion of a Cardan suspension gyroscope subjected to controlling torque moments. Analytical solutions for the proposed mathematical model were developed using the Laplace transform and Green’s function. Subsequently, they were validated by numerical tests. The obtained analytical solutions are universally applicable, regardless of the type of controlling moments.