Mathematical Equations Research Articles

Lid driven flow and heat transfer due to various positions of slit in a square cavity: FEM approach

A detailed analysis of flow and heat transfer due to moving slit within the various positions of the square cavity is discussed. The slit is strategically positioned and examined at three distinct locations within the square cavity i.e. left, middle and right. Constraints of the square cavity are defined for horizontal and vertical walls. The top horizontal wall is considered to be adiabatic while the other three walls of the cavity are cold. The upper surface of slit is heated and movable towards the left side of the square cavity while the other three walls are immovable and cold. The fluid flow dynamics and heat transfer within the enclosed cavity are governed by fundamental principles of mass, momentum and energy conservation. These governing principles manifest as intricate mathematical equations, specifically nonlinear partial differential equations accompanied with boundary conditions. The key parameters under consideration include the Reynolds number (250≤Re≤1500) and Richardson number (0.01≤Ri≤5) at a fixed Prandtl number (Pr=6.2). These parameters are analysed through variations in velocities, temperature profiles, isotherms and streamlines. In the computational framework, the momentum and temperature equations are addressed through quadratic interpolation, while linear interpolation is applied to handle the pressure equation. The numerical solution, utilizing Newton's technique and the PARADISO solver, is rigorously validated against existing research methodologies, establishing its methodological reliability. Higher Reynolds numbers shift the primary vortex towards the middle and create corner recirculation zones, more uniform heat distribution, while higher Richardson numbers increase buoyancy forces, reducing isotherm contours and affecting heat distribution. The local Nusselt number increases with the increase in Reynolds numbers but shows small changes with the increase in Richardson number. The value of Nusselt number decreases as the position of slit changes from left to right.

Developmet of Android E-book Forms of Energy to Improve Students' Critical Thinking and Mathematical Representation Skills

Critical thinking and mathematical representation skills play an important role for students, especially in physics. This research’ aims are to study the feasibility and effectiveness of the android e-book forms of energy to improve students' critical thinking and mathematical representation skills. This research was developed using the ADDIE model. The experimental design was one group pretest posttest. This research found that the E-book were feasible to be applied in physics learning. It content qualify the writing and content requirements for a physics E-book. The android e-book is effective for improving students' ability in interpretation and explanation, effective enough in analyze, and less effectively in the inference and argument and evaluation aspects. E-book is less effective in the aspect use pictures, graphs, tables, or diagrams to solve problems and effective enough in training students use symbols or mathematical equations in solving problems and explain data or other representations in sentence form. The global N-Gain value shows that the Android e-book forms of energy is effective enough to improve critical thinking and mathematical representation skills.

Decomposition-assisted analysis of transmission in periodic resonator arrays using mode-matching method.

This paper focuses on analysing acoustic structures containing locally reacting resonators, aiming to establish a framework for discussing sound properties related to scattering and transmission in a periodic resonator array. The paper introduces an analytical model for the input surface impedance of non-uniform resonator arrays, which is a challenging task when addressing sound propagation to the opposite side of the array. To address this challenge, a mode-matching method is employed within a one-dimensional periodic structure combined with the decomposition of the initial mirror-symmetric system into symmetric and antisymmetric sub-systems. This procedure leads to simplified analytical solutions of transmission problems about non-uniform resonator arrays, and its accuracy is verified through numerical simulations. The proposed method provides insights into mode shapes and amplitudes, thereby complementing numerical simulations and enabling a comprehensive understanding of sound fields beyond conventional results such as pressure fields and sound absorption coefficients alone. The model of a periodic varying-height resonator array presented herein involves developing mathematical equations or simulations to capture the physical characteristics and interactions of the resonators. This approach empowers researchers to predict and comprehend the non-uniform array's transmission behaviour and performance characteristics, with diverse applications spanning various systems, including electromagnetic devices.

Unraveling mudstone compaction at microscale: A combined approach of nanoindentation mapping and machine learning data analysis

Compaction processes within mudstone samples across varying depths (723.5–3213.5 m) in the Vienna Basin were investigated, focusing on porosity changes and the resulting micromechanical response in the clay-rich, fine-grained fraction (“clay matrix”). A novel approach combining nanoindentation mapping with machine learning data analysis was developed to efficiently extract representative micromechanical parameters of the clay matrix. Emphasis was put on capturing the properties of the fine-grained, clay-dominated composite rather than individual mineral phases, enabling the analysis of compaction-induced strength changes at microscale. A significant enhancement in the mechanical strength of the clay matrix with increasing burial depth was observed. Reduced elastic modulus (Er) and hardness (H) increased from 6.8 ± 3.4 to 22.6 ± 7.5 GPa and from 0.2 ± 0.2 to 0.9 ± 0.2 GPa, respectively, over the depth interval of 2490 m. Moreover, a strong correlation between depth and porosity and consequently micromechanical properties of the clay matrix exists. This highlights the substantial influence of intra-clay porosity on mechanical properties, which follow a general compaction trend with depth. Broad ion beam-scanning electron microscopy (BIB-SEM) analysis was used for textural investigations at micro-to nanoscale and indicated that the reduction in porosity predominantly resulted from mechanical compaction rather than mineral diagenesis, which would have been noticeable by signs of significant dissolution or cementation. The correlation coefficient matrix between multiscale porosity measurements and nanoindentation affirmed that the porosity loss was closely linked to the enhanced mechanical properties of the fine-grained composite clay matrix, while other compositional variables like total clay mineral content showed weak correlations. Empirical mathematical equations were derived to describe the mechanical properties as generalized functions of depth and porosity. These may be used as geomechanical input for future basin analysis and geoenergy applications (e.g., seal rock studies in a geological storage context). This study introduces a new approach to unravel compaction processes in fine-grained rocks at microscale, emphasizing the interplay between intra-clay porosity and micromechanical changes during proceeding burial.

Adaptive current decoupling control scheme based on online multi-parameter identification for high-speed permanent magnet synchronous motor in fuel cell

The precise control of centrifugal hydrogen compressor (CHC) driven by high-speed permanent magnet synchronous motor (PMSM) is the key to the stable and efficient operation of hydrogen fuel cell (HFC). In this paper, an adaptive current deviation decoupling control (CDDC) strategy based on variable step size affine projection algorithm (VSS-APAs) is proposed to solve the high-speed PMSM control problem caused by current cross-coupling and parameter perturbation under complex operating conditions. Firstly, the step size is dynamically adjusted by VSS-APA through a normalized gradient descent to respond to system fluctuations, achieving rapid parameter identification during dynamic changes and accurate tracking in steady states. Secondly, stator inductance, magnetic flux linkage, stator resistance, and disturbance torque are identified in two-time-scale based on the characteristics of parameter changes, overcoming the rank deficiency in motor mathematical equations. Finally, utilizing online-identified motor parameters, the gains of the CDDC are adjusted, and compensation is applied for back electromotive force (BEMF) and disturbance torque, thereby ensuring the control accuracy of the motor under parameter perturbations and system disturbances. Experimental results demonstrate that the proposed method enhances the responsiveness and accuracy of the control strategy through efficient parameters identification. Consequently, it guarantees high-efficiency and stable performance of the CHC across different working conditions, markedly advancing the overall functionality and dependability of hydrogen energy system.

Bond strength prediction of externally bonded reinforcement on groove method (EBROG) using MARS-POA

The Externally Bonded Reinforcement on Grooves (EBROG) method represents an advancement in externally bonded reinforcement (EBR) techniques, specifically addressing the challenge of premature debonding often encountered in conventional Fiber Reinforced Polymer (FRP) applications directly bonded to concrete. This article introduces a novel and straightforward mathematical equation for predicting bond strength in the EBROG method using soft computing techniques for the first time. The study delves into the combined potential of the Multivariate Adaptive Regression Spline (MARS) model and the Pelican Optimization Algorithm (POA) for bond strength prediction in this method. The input parameters include FRP width, FRP thickness, elasticity modulus of FRP, concrete strength, groove length, groove width, and groove depth, while the output is EBROG bond strength. The study demonstrates exceptional accuracy with R2 values of 0.9629 for training and 0.9623 for testing, highlighting the model’s precision. The proposed bond strength prediction equation for the EBROG method undergoes validation against existing models, encompassing thirteen equations for EBR and a recent one specific to EBROG. Statistical metrics confirm the accuracy and reliability of the proposed equation. Notably, FRP stiffness emerges as the parameter with the highest relative importance, while groove width exhibits the lowest impact on bond strength.

Analysis of the behavior of structures under the effect of progressive rupture of a cavity

Abstract The ground movements related to the presence of old underground cavities are often damaging to structures and infrastructures. Considering these ground movements in calculations will prevent considerable human loss and material damage. Many areas, both in Algeria and in abroad, are prone to instability caused by ground rupture and the phenomenon of sinkhole progression. The objectives of this work are first to numerically simulate the process of cavity collapse and second to analyze the impact of cavity properties on structure stability. A finite element model was established to analyze the influence of several cavity parameters (dimensions, volume, and spacing). Validation of the model relied on comparing numerical results with experimental data from scientific research, as well as those from analytical approaches. Adequate correlation was achieved. The study allowed deriving mathematical equations relating to several parameters, including cavity dimensions and position in the soil, soil characteristics, and footing width. These results will be considered to reduce the risk of surface structure instability.

Dynamics of a horizontal magnetic pendulum in a repulsive magnetic field and driven by two coil magnets

We studied theoretically and experimentally in this work the nonlinear dynamics of a horizontal magnetic pendulum in a repulsive magnetic field controlled by two coil magnets. The mathematical equations of the system are derived using the magnetic charges interaction model. The system presents a single equilibrium point which is stable if the currents through the coils are positive. Considering the situation where the current through the coils is sinusoidal with a DC component, analytical calculations using the harmonic balance method and numerical simulations are also carried out. The results obtained are shown in terms of amplitude responses, time–displacement diagrams, and phase portraits. The two-parameter bifurcation diagrams are plotted showing the different dynamical behaviors considering the current amplitudes, frequency, angle between the coil magnets, and the modulation indexes as the control parameters. Amplitude jumps, hysteresis, and multistability are also observed. In the experimental part, the modulated current sources that can provide the required current in the coil magnets have been designed and implemented. The complete experimental setup of the magnetic pendulum is also presented. Good agreements are found between our theoretical results and experimental ones.

Advancing Climate Modeling through High-Performance Computing: Towards More Accurate and Efficient Simulations

A crucial branch of science called climate modeling uses mathematical equations and computer simulations to study and forecast the Earth's climate sys- tem. The main elements of climate modeling, such as general circulation models (GCMs), data assimilation methods, and numerical formulations, are outlined in this paper. GCMs, which include grid point and spectral models, are effective instruments for examining the behavior of the climate. Four-Dimensional Data Assimilation (4D-Var) is one example of a data assimilation technique that in- corporates observational data into models to improve their correctness. Numeri cal methods, ocean dynamics, heat transport, radiative transfer, and atmospheric dynamics are all included in numerical formulations. The simulation of different climate processes is possible because to these mathematical representations. Fur thermore, the detection of precipitation patterns within climate modeling is using machine learning techniques like Random Forest more frequently. This paper highlights the importance of high-performance computing (HPC) in climate modeling, boosting efficiency and simulations, in the context of research technique. Advanced data assimilation and validation techniques are also examined, as well as the influence of high-resolution modeling on small-scale climatic processes. On HPC platforms, accessibility to climate modeling is addressed. It is shown how climate modeling crosses physics, mathematics, computer science, and engineering to be interdisciplinary. A comprehensive understanding of the Earth's intricate climate system gains from the integration of all its parts, from atmospheric dynamics to data assimilation. We explore the consequences of these research approaches, their contribution to enhancing climate prediction models, and the influence of various factors on climatic variables in the debate. Climate modeling becomes an essential tool for studying precipitation patterns and climate change, ultimately improving our comprehension of the complex cli- mate system on Earth.

Determination of antibacterial performance of boric acid ester in the paint industry

ABSTRACT This study aims to assess the antibacterial activity of boric acid ester derived from boron mines, which is utilised as an active component in the paint industry. Multiple product variations were obtained by adding boric acid ester to the base, referred to as the reference sample, known as silk matte paint, and used as an interior paint with active substance concentrations ranging from 0.005% to 0.6%. Escherichia coli (ATCC10536) bacteria were inoculated at 78000 cfu cm−2 into samples with 0.005- 0.075% active substance, and at 24000 cfu cm−2 into samples containing 0.15- 0.6% of the active substance, and the reduction rates were determined by a mathematical equation via multivariate linear regression analysis, relating Escherichia coli reduction percentages, surface energy values, and pH measurements, including the power percentages and gloss values for the reference sample. The highest level of antibacterial effect was observed in the sample containing 0.075% active substance.

Mathematical Modelling of the Thermosolutal Effect on Blood Flow through a Micro-Channel in the Presence of a Magnetic Field

Substances such as mass concentrations in the blood cause circulation challenges. Blood is a substance made up of 55% plasma and 45% hemoglobin, which flows through the blood vessels and is aided by the heart in pumping to all organs and other tissues and cells in the human body. Mathematical modelling plays an important role in understanding the blood circulation problem in the human body, and it helps transform the real-life cardiovascular problem into a system of mathematical equations. In this research, we transformed the real-life cardiovascular problem of the heat effect on mass concentration and blood flow through blood vessels into a system of partial differential equations representing blood momentum, energy, and mass concentration equations after modifying the Navier-Stoke equation. The models are scaled from dimensional to dimensionless using specific scaling parameters. The scaled dimensionless equations were further perturbed and reduced to a system of ordinary differential equations, and the system of ODEs was solved using the Laplace method, where mathematical models representing blood velocity profiles, temperature profiles, and mass concentration profiles were obtained. A numerical simulation was performed using Wolfram Mathematica, version 12, where the effect of the pertinent parameters on the flow profiles was investigated and the results were presented graphically. The variation of the pertinent parameters such as the Grashof number, solutal Grashof number, Prandtl number, Soret number, Schmidt number, Darcy number, and magnetic field affect the flow profile such that the increase in Grashof number and solutal Grashof number causes the blood velocity to increase substantially at the centre of the vessel before decreasing to zero as the wall boundary layer increases, while the increase in Prandtl number and Soret number increases the blood temperature and velocity.

To What Extent Does Computational Modeling Help Understanding Dementia?

Dementia refers to a set of neurodegenerative illnesses defined by a decline in cognitive functions, such as thinking, reasoning, memory recall, and the ability to carry out daily tasks. In recent years, there have been significant advancements in dementia research. However, many aspects of dementia, including its underlying etiology, remain unknown. Thus, it is critical to use new approaches and technologies to uncover unresolved issues about these diseases. Computational modeling is used in various scientific, engineering, and problem-solving disciplines to simulate and study complex systems or events using computer algorithms and mathematical equations. It entails developing a simplified model of a real-world system to acquire insights, make predictions, test hypotheses, and optimize operations. This paper discusses recent case studies and computational models to understand how computational modeling can aid in uncovering the characteristics of visual hallucinations related to Lewy body dementia and the etiology of Alzheimer’s disease.

Teacher-centered analysis with TIMSS and PIRLS data: weighting approaches, accuracy, and precision

This paper extends existing work on teacher weighting in student-centered surveys by looking into aspects of practical implementation of deriving and using weights for teacher-centered analysis in the Trends in International Mathematics and Science Study (TIMSS) and the Progress in International Reading Literacy Study (PIRLS). The formal conditions to compute teacher-centered weights are detailed, including mathematical equations. We provide a proposal on how to define the targeted populations as well as how to collect data that is needed to derive teacher-centered weights, yet currently unavailable. We also tackle the issue of teacher nonresponse by proposing a respective adjustment factor, as well as mentioning the challenge of multiple selection probabilities when teachers teach in multiple schools. The core part of the paper focuses on studying the level of accuracy that can be expected when estimating teacher population characteristics. We use TIMSS 2019 data and simulate likely scenarios regarding the variance in weights. The results show that (i) the different weighting scenarios lead to relatively similar estimates; however, the differences between the scenarios are sufficient to justify the recommendation to use correctly derived teacher weights; (ii) differences between estimated standard errors based on complex sampling and corresponding estimates based on simple random sampling are sufficiently consistent to support use of a procedure to estimate standard errors that accounts for both sample weights and the complex sampling design; (iii) sample sizes and variance in weights significantly limit estimate precision, so that total population estimates with sufficient precision are available in the majority of countries but subpopulation features are generally not sufficiently precise. To provide a critical evaluation of our results, we recommend implementation of the proposed method in one or more countries. This recommended study will permit examination of logistical considerations in implementation of required changes in data acquisition and will provide data to replicate the analysis with teacher-centered weights.

Design and Modelling of a Modified High Gain Printed Vivaldi Antenna for EMC Measurements

This paper demonstrates the design, modeling, and analysis of a small size 180 × 165 × 1.6 mm3 printed broadband Vivaldi antenna for electromagnetic compatibility measurements. The proposed antenna is intended to be utilized as a reference antenna for emission and immunity tests inside the EMC Chamber through the band (0.8–5.5 GHz). Exponentially tapered slots were created based on mathematical equations to form an end-fire radiation antenna. Furthermore, microstrip and slot line stubs were employed to tune the impedance bandwidth. This antenna could be considered a 2-D Horn antenna with a size reduction of 64% and 67% since both antennas, Vivaldi and Horn are based on the same principle. Two rectangular slots were engraved near the feeding point to reshape and enhance the gain at lower frequency bands. Furthermore, the realized gain has been improved by approximately 3.5 dB and reached up to 10.7 dBi by introducing a pair of triangular reversal slots at the top edges of the structure. Moreover, this antenna has specifications that make it a suitable candidate to work as a reference antenna inside the EMC chamber compared to the classical Horn antenna offered for sale (PowerLOG® PRO 30800 and TBMA4).

Fundamental equations and hypotheses governing glomerular hemodynamics.

The glomerular filtration rate (GFR) is the outcome of glomerular hemodynamics, influenced by a series of parameters: renal plasma flow, resistances of afferent arterioles and efferent arterioles (EAs), hydrostatic pressures in the glomerular capillary and Bowman's capsule, and plasma colloid osmotic pressure in the glomerular capillary. Although mathematical models have been proposed to predict the GFR at both the single-nephron level and the two-kidney system level using these parameters, mathematical equations governing glomerular filtration have not been well-established because of two major problems. First, the two-kidney system-level models are simply extended from the equations at the single-nephron level, which is inappropriate in epistemology and methodology. Second, the role of EAs in maintaining the normal GFR is underappreciated. In this article, these two problems are concretely elaborated, which collectively shows the need for a shift in epistemology toward a more holistic and evolving way of thinking, as reflected in the concept of the complex adaptive system (CAS). Then, we illustrate eight fundamental mathematical equations and four hypotheses governing glomerular hemodynamics at both the single-nephron and two-kidney levels as the theoretical foundation of glomerular hemodynamics. This illustration takes two steps. The first step is to modify the existing equations in the literature and establish a new equation within the conventional paradigm of epistemology. The second step is to formulate four hypotheses through logical reasoning from the perspective of the CAS (beyond the conventional paradigm). Finally, we apply the new equation and hypotheses to comprehensively analyze glomerular hemodynamics under different conditions and predict the GFR. By doing so, some concrete issues are eliminated. Unresolved issues are discussed from the perspective of the CAS and a desinger's view. In summary, this article advances the theoretical study of glomerular dynamics by 1) clarifying the necessity of shifting to the CAS paradigm; 2) adding new knowledge/insights into the significant role of EAs in maintaining the normal GFR; 3) bridging the significant gap between research findings and physiology education; and 4) establishing a new and advanced foundation for physiology education.

Force-electric characteristics of model rock-filled concrete under uniaxial compression with different curing ages and rock-filled ratios

By analyzing the force-electric properties of rock-filled concrete under uniaxial compression, the precursor information and characteristics of deformation and failure of rock-filled concrete can be mastered, and the reliability and safety of rock-filled concrete structures at an early age can be ensured. This study investigated four variations of model rock-filled concrete, each with a distinct rock-filled ratio. Using the two-electrode alternating current test method, we analyzed the electrical resistivity properties of rock-filled concrete under uniaxial compression at various curing ages (1 d, 3 d, 7 d, 14 d, and 28 d). Additionally, the microscopic pore structure was examined using low-field nuclear magnetic resonance technology. The results showed that with increasing curing age or rock-filled ratio, the compressive strength and electrical resistivity of rock-filled concrete showed a nonlinear growth trend. In contrast, the porosity showed a nonlinear decrease, with the internal pore structure gradually becoming more refined. A mathematical model was established to describe the electrical resistivity of rock-filled concrete at various curing ages and rock-filled ratios. During uniaxial compression, the electrical resistivity of rock-filled concrete followed a pattern of rapid decline, slow decline, stable, and slow increase with strain. These phases corresponded to the development of internal pores and cracks and changes in the crack resistance performance of the rockfill skeleton in the concrete. Moreover, a mathematical equation was formulated to elucidate the relationship among the damage variable, the rock-filled ratio, and the electrical resistivity of model rock-filled concrete, thereby enabling the prediction of the extent of damage to the model rock-filled concrete under stress conditions.

Flow-Engineered 3-D Printed Electrodes for Alkaline Water Electrolysis

Initially, industrial alkaline electrolyzers had 2-D bipolar plates as electrodes in a configuration in which there is an important physical gap between the electrodes (e.g., 2 mm). This setup presented a high ohmic resistance and is commonly limited to a current density in the order of 0.5 A·cm-2 due to gas screening, i.e., the produced gases form a non-conductive layer over the entire electrode surface, limiting current density. The more advanced designs of today include the use of a zero-gap cell where the interelectrode distance is limited to the thickness of the separator (hundreds of micrometers for diaphragms and tens of micrometers for membranes). Commonly, 2-D electrodes such as perforated plates or an expanded metal mesh are used. As the electrode is pressed against the separator, the gases are forced to be evacuated at the backside of the electrode, avoiding the screening effect. As a consequence, much higher current densities can be achieved. More recently, there has been an increasing interest in the integration of 3-D electrodes in the zero-gap configuration, as they present higher surface areas than their counterpart 2-D electrodes. Nevertheless, bubbles can get trapped inside the intricate 3-D electrode structures. Several strategies are used to mitigate bubble entrapment, including the use of a forced electrolyte flow.The current study aims to investigate the possible electrochemical performance improvement of a single alkaline water electrolysis cell by using 3-D printed electrodes with graded structures, engineered to enhance bubble removal under the effect of a forced electrolyte flow. As the majority of the current is concentrated near the separator, the tailored 3-D printed electrodes present low strut distances and, consequently, a high surface area in this region. Further away from the separator, the distance between the struts gradually increases, decreasing flow-related energy dissipation and avoiding bubble entrapment. This tailored laterally graded structure promotes a difference in pressure along the direction perpendicular to the separator, allowing to extract bubbles from the region near the separator and to evacuate them towards the region with higher strut distances more efficiently. Furthermore, our flow cell was designed to promote a homogeneous upstream flow at the entrance of the electrode. Based on previous findings [1], a Schwarz triply periodic minimum surface was chosen as electrode geometry, as this geometry can channel the flow and reduce bubble-induced ohmic resistance. This geometry is defined by the following mathematical equation: t = sin(2·π·z/L)·sin(2·π·x/L) - 0.4·sin(2.4·π·y/L)·cos(2·π·z/L)·cos(2·π·x/L)with L the periodicity (e.g., an L = 1 mm means that the structure repeats itself in the space at each 1 mm), and t relates to void fraction.Different electrodes with a Schwarz geometry were analyzed in a combined experimental and simulation approach. Electrodes were 3-D printed using selective laser melting, and a strut in the order of 500 μm was achieved. Explicit computational fluid dynamics simulations were performed to estimate bubble residence time and path. Experimental analyses were conducted in a flow-through setup operating under industrial standard conditions of 30 wt% KOH electrolyte at 70°C to elucidate the performance disparities between these structures. Our findings indicate that such tailored 3-D printed electrodes are capable of significantly outperforming previously reported performances in the literature using more stochastic 3-D electrodes like foams. Furthermore, results show that the printed structures are more sensitive to electrolyte flow, presenting an important overvoltage reduction with increase in electrolyte flow rate. We also identified the most critical structural parameters controlling bubble evacuation, thereby significantly reducing the cell's ohmic resistance. Ultimately, this study also emphasizes the critical role of efficient gas evacuation for high-rate alkaline electrolysers using a zero-gap design.[1] Rocha F, Delmelle R, Georgiadis C, Proost J. Electrochemical Performance Enhancement of 3D Printed Electrodes Tailored for Enhanced Gas Evacuation during Alkaline Water Electrolysis. Advanced Energy Materials 2022;13:2203087.

Reconstructing the Pseudo-2-Dimensional (p2D) Model in Comsol Multiphysics Using Mathematical Interfaces

The classic ‘pseudo-2-dimensional’ (p2D) model of Newman and co-workers (also known as the DFN model), with its different efficient implementations, is the state-of-the-art physics-based electrochemical model for lithium-ion batteries. COMSOL Multiphysics (COMSOL) is a popular modeling software for multiphysics simulations, and its Battery Design Module for Li-ion batteries is widely used in the battery modeling community. This work presents a step-wise model development for reconstructing the detailed p2D model equations. This includes variable model parameters and weak-form implementation for the solid-phase diffusion, eliminating the need for non-local couplings and approximations for modeling the pseudo radial-dimension in the solid-phase.To model and understand the effect of capacity degradation on lithium-ion cells, the battery models in COMSOL need to incorporate additional degradation mechanisms. In this work, we have followed the approach of equation-based modeling in COMSOL, which enables us to formulate the p2D model using the mathematical PDE interfaces. This approach provides us with a lot of flexibility in terms of battery degradation model formulation and helps develop a clearer understanding of the p2D model equation in light of the assumptions involved.The steps in the model development involved writing the conservation equations in the generic mathematics interfaces coupled with the additional equations for the degradation mechanisms. The efforts were centered on developing cycling simulations based on Events for practically relevant operating conditions. This custom model was validated against the results from COMSOL’s Battery Interface, in-house codes, and baseline cycle data from the experiments and further developed as a physicochemical degradation model for automotive, large-format Lithium-ion batteries.This equation-based COMSOL model with cycling works without the requirement for Battery Design Module, LiveLink and Application Builder and can be adopted for a variety of electrochemical modeling applications by the electrochemical modeling community.

Influence of solid cylinders on fluid flow and thermal analysis in a curved channel with constant magnetic field

The current study explores the numerical simulation of constant mixed convection heat transfer and fluid flow within a channel, driven by the inlet velocity. The investigation focuses on a curved irregular channel where the presence of three differently sized circular obstacles introduces an unpredictable element to the heat transfer process. For the two-dimensional physical scenario, mathematical equations are formulated to analyze velocity and temperature. Employing appropriate dimensional variables, the coupled partial differential equations are transformed into dimensionless form. Subsequently, the Finite Element Method (FEM) is employed to simulate the results for non-dimensional physical parameters such as Reynolds number, Richardson number, Hartmann number, nanoparticles' volume fraction, and various states of the circular obstacles on heated lines, flow structure, velocities, and temperatures at mean positions generating isotherms, streamlines, velocity, and temperature profiles for various parameter increments. The analysis reveals significant influences of Reynolds number (Re) and heated circular obstacles on the temperature profile, manifesting as heated lines within the system. The analysis brings to light the substantial impacts of nanoparticles on the temperature profile at both the vertical and horizontal mean positions. An elevated Hartmann number signifies a more robust magnetic field than viscous forces. A heightened magnetic field can hinder fluid movement and modify the patterns of heat transfer. Based on the graphical results, we infer that temperature differences tend to arise between strata as the Richardson number increases, leading to a heightened and more evident stratification.

Dynamic Mutation Strategy Selection in Differential Evolution Using Perturbed Adaptive Pursuit

Diverse mutant vectors play a significant role in the performance of the Differential Evolution (DE). A mutant vector is generated using a stochastic mathematical equation, known as mutation strategy. Many mutation strategies have been proposed in the literature. Utilizing multiple mutation strategies with the help of an adaptive operator selection (AOS) technique can improve the quality of the mutant vector. In this research, one popular AOS technique known as perturbation adaptive pursuit (PAP) is integrated with the DE algorithm for managing a pool of mutation strategies. A community-based reward criterion is proposed that rewards the cumulative performance of the whole population. The proposed approach is called ‘Dynamic Mutation Strategy Selection in Differential Evolution using Perturbed Adaptive Pursuit (dmss-DE-pap)’. The performance of dmss-DE-pap is evaluated over the 30D and 50D optimization problems of the CEC 2014 benchmark test suite. Results are competitive when compared with other state-of-the-art evolutionary algorithms and some recent DE variants.