Solution Of Model Research Articles

A theoretical description for competitive adsorption at the Solid/Solution interface

Wastewaters usually contain several solutes, and the adsorption process for removing pollutants from the solutions is usually competitive. Kinetic modeling of adsorption systems is a useful tool to obtain some information about the behavior of the system at the same time or in the future. The provided rate equations for binary adsorption are in differential form, and their solutions are approximated numerically using computers. In the present work, the kinetics of competitive adsorption at the solid/solution interface is studied. The new equation shows an exponential relation between time and surface coverage. This new equation is the first analytical solution of the kinetics Langmuir model of competitive adsorption. The simulated and experimental data confirm the provided equation is suitable to study the rate of binary adsorption.

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.

Modeling transient temperature coupled pressure behaviour for waterflooding well with induced fractures: Semi-analytical model, numerical model, and case studies

Waterflooding is a widely used technique for developing unconventional reservoirs. Long-term waterflooding can lead to the formation of multiple induced fractures. Accurately tracking the location, extent, and dynamic behavior of these induced fractures is crucial. To enhance monitoring capabilities, data obtained from distributed temperature sensors are used to track temperature variations within the wellbore and at the bottom of the well. Combining temperature and pressure inversion techniques helps mitigate the issue of multiple solutions while offering a more comprehensive characterization of multi-induced fractures from various perspectives. In this study, this work presents a model for temperature coupled pressure (TCP) transient analysis. Additionally, this work utilizes COMSOL Multiphysics software to develop and solve a dynamic wellbore temperature (DWT) model. This work proposes a workflow that describes the dynamic behaviour of multi-induced fractures. During model development and solution, this work employs both pressure and temperature transient analysis methods, examining time-dependent non-linear pressure drop and heat transfer variations. Our results reveal that induced fractures exhibit convective heat exchange with the wellbore, resulting in significantly higher temperatures at the induced fracture locations compared to other wellbore locations. By analyzing temperature-wellbore location curves, this work can accurately identify the locations of induced fractures. The TCP model successfully extracts characteristic parameters of induced fractures, while the DWT model allows for monitoring the locations and heights of these fractures. By combining the workflows of both models, this work achieves a comprehensive characterization of the physical properties of induced fractures. In conclusion, this advancement empowers engineers to manage the development of such fractures effectively, thereby averting potential adverse effects on production well performance and preventing the need for well abandonment.

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 integration method of a hybrid genetic algorithm and the Levenberg–Marquardt algorithm for ultrasonic testing

The accurate measurement of time-of-flight (TOF) is essential in ultrasonic testing. Further, noise interference is the key factor affecting the measurement accuracy. Therefore, to develop a reliable computational method of TOF for test pieces working in noisy environments, an integration method of a hybrid genetic algorithm and the Levenberg–Marquardt algorithm (GA–LM) for ultrasonic thickness measurement is proposed in the present research. A Gaussian model is first established for an echo signal. Further, the model-based parameter estimation is converted into a nonlinear optimization problem by applying the least square method. As the parameter estimation methods are easily affected by the initial value, an integrating innovation of the GA–LM algorithm is proposed. The initial values of the model parameters are selected by GA to obtain an approximate global optimal solution. Subsequently, this approximate solution is used as the initial value for the LM algorithm to perform iterations. The accurate global optimal solution of the Gaussian model is obtained through these iterations. Finally, the measuring accuracy and robustness of the GA–LM algorithm for TOF computation are verified by both numerical simulation and experiment data

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.

Miscanthus x giganteus biochar: Effective adsorption of pharmaceuticals from model solution and hospital wastewater

This study investigated the adsorption of pharmaceuticals, including atenolol (AT), 17-α-ethinylestradiol (EE2), and sulfamethoxazole (SMX), in model solutions and in the effluent from a hospital wastewater treatment plant. The pharmaceuticals were adsorbed on biochar prepared from Miscanthus x giganteus biomass obtained from the phytoremediation of contaminated or marginal soil. The feedstock was pyrolyzed at 360 °C (M-3) and 500 °C (M-5). The representation of functional groups, specific surface area, porosity, and pore volume were lower for M-5. Pore diameters were comparable, but their depth decreased for M-5. The specific surface area and porosity surface area of M-5 were 30 times higher after 4 h of shaking compared to properties without shaking. The biochar leachate pH was 9.8 ± 1.0 (M-3), and 11.1 ± 1.1 (M-5). No desorption of potentially risk organic compounds was detected. M-3 was generally a better adsorption material. The removal of EE2, AT and SMX was greater than 90%, 70% and 30 % respectively after 4 h in model waters. There was no evidence of a linear relationship between the sorption efficiency of pharmaceuticals and the biochar dose. Sorption experiments with real wastewater from a hospital wastewater treatment plant demonstrated high removal rates of monitored pharmaceuticals, including e.g. SMX (80%), trimethoprim (91%), venlafaxine (100%), clarithromycin (96%), tramadol (93%), diclofenac (86%). It was proven that the efficiency of the adsorption process is influenced not only by the dose or physico-chemical properties of the biochar, but also by the initial concentration of the pharmaceutical and its properties. The presence of other components of real wastewater, which can cause competitive sorption and overlapping of active centers on the surface of the biochar, also decreased the efficiency. The results demonstrate that both biochars are suitable for tertiary or quaternary water treatment for pharmaceutical removal. Due to the lower energetic, and therefore economic, costs of pyrolysis, a lower pyrolysis temperature can be preferred.

The Determining Role of Covariances in Large Networks of Stochastic Neurons.

Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active and refractory neurons in the network's populations. We do so by describing the evolution of the states of individual neurons with a continuous-time Markov chain, from which we formally derive a low-dimensional dynamical system. This is done by solving a moment closure problem in a way that is compatible with the nonlinearity and boundedness of the activation function. Our dynamical system captures the behavior of the high-dimensional stochastic model even in cases where the mean-field approximation fails to do so. Taking into account the second-order moments modifies the solutions that would be obtained with the mean-field approximation and can lead to the appearance or disappearance of fixed points and limit cycles. We moreover perform numerical experiments where the mean-field approximation leads to periodically oscillating solutions, while the solutions of the second-order model can be interpreted as an average taken over many realizations of the stochastic model. Altogether, our results highlight the importance of including higher moments when studying stochastic networks and deepen our understanding of correlated neuronal activity.

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.