Set Of Equations Research Articles

A combined transport-defect evolution model of microstructure damage in silicon carbide induced by precise irradiation of focused helium ion beams

In this paper, a combined transport-defect evolution multiscale model describing the generation and the evolution of microstructure damage in silicon carbide (SiC) induced by focused helium ion beams is developed. In the proposed model, the transport of helium ions and displaced atoms in the SiC substrate and the generation of point defects are described by the Boltzmann transport equations, while the subsequent defect evolution is characterized by a set of rate equations with the contributions of the modeling of the bubble coalescence as well as the substrate swelling. The validity and superiority of the transport equations are verified by comparing the simulation results with the data from experimental measurements and available simulation methods. The subsurface amorphous profile, onsurface swelling profile, and the spatial and size distribution of helium bubbles in a SiC substrate irradiated by focused helium ion beams are simulated using the proposed multiscale model. The damage morphology simulated by the proposed model is in good agreement with the transmission electron microscopy images at different beam energies and doses. This work provides an effective tool for full-stage modeling of complex evolutionary mechanisms of microstructure damage induced by precise and high-throughput helium irradiation.

Application of the iteratively regularized Gauss–Newton method to parameter identification problems in Computational Fluid Dynamics

Field Inversion and Machine Learning is an active field of research in Computational Fluid Dynamics (CFD). This approach can be leveraged to obtain a closed-form correction for a given turbulence model to improve the predictions. The fundamental approach is to insert a parameter into the system of RANS equations and determine it in a way such that, for example, a given pressure distribution is better approximated compared to the one obtained with the original set of equations. The goal of this article is twofold. Numerical arguments are presented that these kinds of problems can be severely ill-posed. In the second part, an approach is presented to directly reconstruct the turbulent viscosity field along with an example. The Iteratively Regularized Gauss-Newton Method (IRGNM) is used for a realization. The construction of a problem-adapted norm for a finite volume method is presented. Finally, an outlook is presented on how this approach can be used to possibly modify or improve turbulence models such that not only one, but a larger number of test cases are considered.

Singularity analysis for V‐notches in a piezoelectric multimaterial and functionally graded piezoelectric materials

AbstractThis study develops a novel singularity analysis method that addresses the limitations posed by piezoelectric material quantity and the variation patterns of property functions in functionally graded piezoelectric materials (FGPMs). Given that piezoelectric composite materials consist of multiple materials, the material properties of FGPMs vary with respect to angle. By introducing the asymptotic assumption that governs the physical fields close to the notch vertex into the static equilibrium equations, a comprehensive set of characteristic equations is formulated. All singularity orders and corresponding characteristic angle functions of the notch are determined by numerically solving the established characteristic equations. The effects of the notch opening angle, piezoelectric material polarization direction, and boundary conditions on the electromechanical field singularity at the notch are assessed. The judicious selection of material variation patterns can alleviate notch singularity in FGPMs.

Thermal dynamics of nanoparticle aggregation in MHD dissipative nanofluid flow within a wavy channel: Entropy generation minimization

This paper examines how nanoparticle aggregation and a consistent magnetic field influence the peristaltic movement of a dissipative nanofluid, which is caused by the sinusoidal deformation of the boundary. The viscosity of TiO2/H2O nanofluids is accurately determined by the Krieger-Dougherty model with nanoparticle aggregation, while thermal conductivity (TC) is estimated through the Bruggeman model. The set of governing equations are modeled in a fixed frame by utilizing the conservation laws of energy, mass and momentum. Galilean transformation is utilized to transform the system of equations into a wave frame, which is then converted into a dimensionless form. The assumption of a small Reynolds number and long wavelength serve to further simplify the set of equations, which are subsequently addressed through the implementation of the differential quadrature method (DQM), a highly effective numerical technique. Quantities of interest, namely velocity, pressure gradient, temperature, trapping phenomena, heat transfer, and volumetric entropy generation are analyzed across a range of physical parameters, including the solid volume fraction (Φ=0.01−0.04), Eckert number (Ec=0.0−0.1), Hartman number (Mh=0.2−2.2), Grashof number (Gr=1.0−3.0) and temperature ratio parameter (θd=0.5−2.5). A comparative analysis is conducted between the scenario involving aggregation and the one without aggregation. It is observed that nanoparticle aggregation significantly alters these quantities.

Observation and Classification of Low-Altitude Haze Aerosols Using Fluorescence–Raman–Mie Polarization Lidar in Beijing during Spring 2024

Haze aerosols have a profound impact on air quality and pose serious health risks to the public. Due to its geographical location, Beijing experienced haze events in the spring of 2024. Lidar is an active remote sensing technology with a high spatiotemporal resolution and the ability to classify aerosols, and it is essential for effective haze monitoring. This study utilizes fluorescence–Raman–Mie polarization lidar with an emission wavelength of 355 nm, employing the δp-Gf method based on the particle depolarization ratio at 355 nm (δp355) and the fluorescence capacity (Gf), and combines meteorological data and backward-trajectory analysis to observe and classify low-altitude haze aerosols in Beijing during the spring of 2024. Notably, a mining dust event with strong fluorescence backscatter was detected. The haze aerosols were categorized into three types: pollution aerosols, desert dust, and mining dust. Their optical properties were summarized and compared. Desert dust showed a particle depolarization ratio range of 0.23–0.39 and a fluorescence capacity range from 0.18 × 10−4 to 0.63 × 10−4. Pollution aerosols had a larger fluorescence capacity but a lower depolarization ratio compared to desert dust, with a fluorescence capacity ranging from 0.55 × 10−4 to 1.10 × 10−4 and a depolarization ratio ranging from 0.10 to 0.17. Mining dust shared similar depolarization characteristics with desert dust but had a larger fluorescence capacity, ranging from 0.71 × 10−4 to 1.23 × 10−4, with a depolarization ratio range of 0.30–0.39. This study validates the effectiveness of the δp355-Gf method in classifying low-altitude haze aerosols in Beijing. Additionally, it offers a new perspective for more detailed dust classification using lidar. Furthermore, utilizing the δp355-Gf classification method and the δp355-Gf distributions of three typical aerosol samples, we developed a set of equations for the analysis of mixed aerosols. This method facilitates the separation and fraction analysis of aerosol components under various mixing scenarios. It enables the characterization of variations in the three types of haze aerosols at different altitudes and times, offering valuable insights into the interactions between desert dust, mining dust, and pollution aerosols in Beijing.

On the Behavior of a Non-Linear Bandpass Filter with Self Voltage-Controlled Resistors

In this work, we explore the behavior of a classical RLC resonance-based bandpass filter, which includes two resistors (one of which is associated with a non-ideal inductor), when either of these resistors is self voltage-controlled. In particular, self-feedback control is achieved by using the voltage developed across the inductor or the capacitor to dynamically change the value of the controlled resistor. This results in a multiplication-type non-linearity, which transforms the linear filter into a non-linear filter described by a set of non-linear differential equations. When gradually increasing the strength of the non-linearity, a notch-like behavior is observed at twice the resonance frequency. However, the non-linear filter can lose its stability with excessive feedback. Simulations and experimental results are provided to support the theory.

A novel compartmental approach for modeling stomach motility and gastric emptying

The stomach, a central organ in the Gastrointestinal (GI) tract, regulates the processing of ingested food through gastric motility and emptying. Understanding the stomach function is crucial for treating gastric disorders. Experimental studies in this field often face difficulties due to limitations and invasiveness of available techniques and ethical concerns. To counter this, researchers resort to computational and numerical methods. However, existing computational studies often isolate one aspect of the stomach function while neglecting the rest and employ computationally expensive methods. This paper proposes a novel cost-efficient multi-compartmental model, offering a comprehensive insight into gastric function at an organ level, thus presenting a promising alternative.The proposed approach divides the spatial geometry of the stomach into four compartments: Proximal/Middle/Terminal antrum and Pyloric sphincter. Each compartment is characterized by a set of ordinary differential equations (ODEs) with respect to time to characterize the stomach function. Electrophysiology is represented by simplified equations reflecting the “slow wave behavior” of Interstitial Cells of Cajal (ICC) and Smooth Muscle Cells (SMC) in the stomach wall. An electro-mechanical coupling model translates SMC “slow waves” into smooth muscle contractions. Muscle contractions induce peristalsis, affecting gastric fluid flow velocity and subsequent emptying when the pyloric sphincter is open. Contraction of the pyloric sphincter initiates a retrograde flow jet at the terminal antrum, modeled by a circular liquid jet flow equation.The results from the proposed model for a healthy human stomach were compared with experimental and computational studies on electrophysiology, muscle tissue mechanics, and fluid behavior during gastric emptying. These findings revealed that each “ICC” slow wave corresponded to a muscle contraction due to electro-mechanical coupling behavior. The rate of gastric emptying and mixing efficiency decreased with increasing viscosity of gastric liquid but remained relatively unchanged with gastric liquid density variations. Utilizing different ODE solvers in MATLAB, the model was solved, with ode15s demonstrating the fastest computation time, simulating 180 s of real-time stomach response in just 2.7 s. This multi-compartmental model signifies a promising advancement in understanding gastric function, providing a cost-effective and comprehensive approach to study complex interactions within the stomach and test innovative therapies like neuromodulation for treating gastric disorders.

Existence, uniqueness and Ulam–Hyers stability result for variable order fractional predator-prey system and it's numerical solution

This study presents an approximate numerical technique for solving time fractional advection-diffusion-reaction predator-prey equations with variable order (VO), where the analyzed fractional derivatives of VO are in the Caputo sense. Results for Ulam–Hyers stability are shown, as well as the existence and uniqueness of solutions. It is suggested to use a numerical approximation based on the shifted second kind of airfoil polynomials to solve the equations under consideration. A fractional derivative operational matrix with VO is derived for shifted airfoil polynomials, which will be used to compute the unknown function. The main equations are transformed into a set of algebraic equations by substituting the aforementioned operational matrix into the equations under consideration and utilizing the properties of the shifted airfoil polynomial along with the collocation points. A numerical solution is obtained by solving the acquired set of algebraic equations. To verify the accuracy and efficiency of the discussed scheme, several illustrative examples have been considered. The results obtained by the proposed method demonstrate the efficiency and superiority of the method compared to other existing methods.

Linear quadratic optimal control of stochastic 2-D Roesser models

This paper investigates the linear quadratic (LQ) optimal control problem for the stochastic two-dimensional (2-D) systems governed by Roesser models with multiplicative noise. The main contribution is to give the necessary and sufficient optimality condition by proposing a set of novel forward and backward stochastic partial difference equations (FBSPDE), and to further present the explicitly optimal feedback control laws on the finite horizon and on the infinite horizon based on the Riccati-like difference equations and the algebraic equation, respectively. Several numerical simulations are provided to illustrate the performance of the designed controllers.

Entropy optimization in multigrade motor oil based nanofluid: a spectral and sensitivity analysis with particle shape and dispersion effects

PurposeThis study aims to enhance heat transfer efficiency while minimizing friction factor and entropy generation in the flow of Nickel zinc ferrite (NiZnFe2O4) nanoparticles suspended in multigrade 20W-40 motor oil (as specified by the Society of Automotive Engineers). The investigation focuses on the effects of the melting process, nonspherical particle shapes, thermal dispersion and viscous dissipation on the nanofluid flow.Design/methodology/approachThe fundamental governing equations are transformed into a set of similarity equations using Lie group transformations. The resulting set of equations is numerically solved using the spectral local linearization method. Additionally, sensitivity analysis using response surface methodology (RSM) is conducted to evaluate the influence of key parameters on response function.FindingsHigher dispersion reduces entropy production. Needle-shaped particles significantly enhance heat transfer by 27.65% with melting and reduce entropy generation by 45.32%. Increasing the Darcy number results in a reduction of friction by 16.06%, lower entropy by 31.72% and an increase in heat transfer by 17.26%. The Nusselt number is highly sensitive to thermal dispersion across melting and varying volume fraction parameters.Originality/valueThis study addresses a significant research gap by exploring the combined effects of melting, particle shapes and thermal dispersion on nanofluid flow, which has not been thoroughly investigated before. The focus on practical applications such as fuel cells, material processing, biomedicine and various cooling systems underscores its relevance to sectors such as nuclear reactors, tumor treatments and manufacturing. The incorporation of RSM for friction factor analysis introduces a unique dimension to the research, offering novel insights into optimizing nanofluid performance under diverse conditions.

Euler–Euler modeling of turbulent annular regime

Euler–Euler methods are one of the many approaches available in literature for modeling droplet-laden flows. These models consider both the gas and droplet phases as inter-penetrating continua, thereby separate sets of transport equations are solved for these phases. The current work focuses on modeling of thin liquid films on solid surfaces in the context of the two-fluid approach to multiphase simulation. In majority of the literature, liquid films are modeled using a 2D Laminar approximation with a parabolic profile for the velocity across the film. However, a number of industrial applications demonstrate a turbulent behavior of the film which would affect the effective viscosity and thereby the thickness of the film. In the current work, a turbulent model for liquid films is proposed based on the Universal Velocity Profile. Additional models are employed to capture the deposition of droplets onto solid surface and stripping off of droplets from the film due to surface waves. The liquid film model is validated on experimental data from available literature. Finally, the newly implemented turbulent film model is applied to study the flow over a fuel rod assembly in a Boiling Water Reactor.

Accuracy and scalability of incompressible inductionless MHD codes applied to fusion technologies

Abstract It is well-known that magnetohydrodynamics (MHD) dominates the dynamic of the liquid metal flows inside the breeding blankets (BB) of future nuclear fusion plants by magnetic confinement. MHD is a multiphysics phenomenon involving both electromagnetism and incompressible fluid mechanics. From the computational point of view, the simulation of MHD flows in fusion relevant conditions entails a significant challenge. Indeed, due to the shape of the induced electrical currents inside the bulk of the fluid, high spatial resolutions are needed to capture the large gradients found in boundary layers and 3D effects. Besides, solving the equations accurately typically requires very small time steps for the transient algorithms. Over the past few decades, some parallel MHD codes have been developed with success to simulate complex flows in increasingly realistic geometries. Among them, the MHD tools of commercial CFD platforms have attracted attention due to their relatively soft learning curve. Most of these codes are based on the so called ϕ-formulation which, by applying the divergence free condition of the current density to the Ohms law, reduces the electromagnetic part of the problem to a single Poisson equation. As a downside, the approach segregates the fluid and electromagnetic problem. In practice, this establishes important limits to the mesh element size, to the mesh quality and to the time-step needed to obtain accurate and stable solutions that maintains charge conservation at a discrete level. In this work, these limits are explored for the commercial platform ANSYS-Fluent using a test geometry under different conditions. As an alternative, a new code based on Finite Element Methods (FEM) is introduced as well. This open-source code, called GridapMHD (https://github.com/gridapapps/GridapMHD.jl), aims at solving the full set of MHD equations using a monolithic approach. GridapMHD is still in early stages of development but it has already shown promising results.

Viability for impulsive stochastic differential inclusions driven by fractional Brownian motion

In this paper, we prove necessary and sufficient conditions for the viability for an impulsive stochastic functional differential inclusion driven by a fractional Brownian motion. The viable property is of interest since it reflects the stability of the model under consideration. The fractional Brownian motion provides a memory effect to the model. Whereas, the appearance of the impulsive factor introduces jumps to the solutions and is new to the analysis of this type. Hence our results are new even in the special case of stochastic differential equation setting.

Multi-fidelity graph neural networks for efficient power flow analysis under high-dimensional demand and renewable generation uncertainty

The modernization of power systems faces uncertainties due to fluctuating renewable energy sources, electric vehicle expansion, and demand response initiatives. These uncertainties require consideration in power flow analyses by calculating power flow across a spectrum of generation and load values. Traditional power flow methods, which rely on iterative solutions of non-linear equation sets, become computationally burdensome under these uncertain conditions. Surrogate models have been used to reduces the computational cost of power flow analysis under uncertainty. Recently, graph neural networks (GNNs) have gained increasing attention as surrogates for power system simulations. However, GNNs, similar to other machine learning models, require significant amounts of training data. This paper proposes an innovative approach combining a multi-fidelity methodology with a GNN-based surrogate model for efficient power flow calculations. This model is trained using both high-fidelity power flow simulations and low-fidelity power flow simulations. Our multi-fidelity GNN model not only reduces the cost of generating training data, but also outperforms both single-fidelity GNN models trained solely on high-fidelity data and conventional neural network models. Additionally, the proposed model exhibits robustness to minor topology changes and achieves reasonable performance with unseen topologies. The model’s effectiveness is validated through simulations on standard IEEE systems.

Thermo-Mechanical Jitter in Slender Space Structures: A Simplified Modeling Approach

Thermally induced vibrations usually affect spacecraft equipped with light and slender appendages such as booms, antennas or solar panels. This phenomenon occurs when a thermal shock, resulting from the sudden cooling and warming phases at the entrance and exit from eclipses, triggers mechanical vibrations. The study proposed hereafter concerns the modeling and prediction of jitter of thermal origin in a long and thin plate with a sun-pointing attitude in geostationary orbit. The system’s temperature and dynamics are described by a set of equations expressing the two-way coupling between the thermal bending moment and the shape of the panel. The structure is discretized and reduced to a one-degree-of-freedom simplified model able to identify a mechanism of thermal pumping that could lead to instability. Finally, the results of the analysis are compared with those obtained with a more accurate FEM modelization.

Solution of the plane thermoelasticity problems based on a new set of equations

The interaction of thermal and mechanical fields in modern technologies for the synthesis and processing of materials attracts more and more attention. This is due to the need to predict the behavior and properties of new materials and products depending on the conditions of their creation. In the present work, attention is focused on the comparison of the solutions to the thermoelasticity plane problems with and without accounting for the temperature dependence of the material properties. It is assumed that an external heat source traveling over the surface with a specific velocity and following a given trajectory is responsible for a significant temperature increase. It may correspond to a laser source, for example. The new way of problem formulation in stresses is used. The temperature dependence of the characteristics leads to nonlinear thermoelasticity equations when the equilibrium equations, the requirement of strain compatibility, and the Duhamel-Neuman relation for the plane stress state case are combined. To determine the temperature field, a nonlinear thermal conductivity equation is used. To solve the problem numerically, the use of an implicit finite-difference scheme and coordinate splitting for the thermal conductivity equation and the finite-difference method of successive over-relaxation with Chebyshev acceleration for the equations for stresses was made. As a result, the difference in the solution of linear and nonlinear problems is demonstrated for the considered cases. Using the example of a mixture of titanium and aluminum powders, numerical modeling demonstrated that some stress components can reach values up to 3.5 times higher than those obtained in the case of temperature-independent material properties when there is a 500-degree local temperature increase.

Techno-Economic Assessment of Coaxial HTS HVAC Transmission Cables with Critical Current Grading between Phases Using the OSCaR Tool

In recent years, the scientific and industrial interest regarding alternative technologies for transmission cables has increased. These conductors should efficiently transmit significant amounts of power between grid nodes, which are expected to be particularly congested due to the projected global increase in electricity production. Superconducting cables are considered a promising solution in this context, offering the potential to transmit large amounts of energy with minimal losses and compact dimensions, thereby potentially benefiting the environment. To evaluate the feasibility of integrating superconducting cables into existing grids, techno-economic approaches should be adopted. Such techniques enable the conceptual design of a specific cable structure, allowing users to explore a wide range of operating parameters to derive optimal designs. This paper reports a comprehensive techno-economic analysis of High Voltage Alternating Current (HVAC) cables realized with High-Temperature Superconducting (HTS) tapes, with the aim to transmit extremely high-power level. The optimal coaxial design is selected using Optimization Tool for Superconducting Cable Research (OSCaR) by implementing a graded approach to the critical current of the HTS tapes used for the different phases. This optimization aims to achieve the most effective balance between the cost of the coated conductors and their electrical properties. The whole set of model equations, the user-defined parameters, and the applied constraints are detailed. The OSCaR tool is then applied to assess the impact on the optimized design of the cable system and the corresponding cost indexes of several crucial parameters, such as the maximum transmitted power, the voltage level, and the line length.

Effects of trapped charge transitions between localized levels on the optical properties of thermoluminescent materials: A study of fading and thermal quenching

The current theoretical knowledge about thermoluminescence allows its study through numerical simulations, by solving a set of differential equations that describe system properties. These models, based on experimental evidence, have been used to reproduce the phenomenon of fading and thermal quenching suffered by materials used by Radiation Dosimetry Services such as LiF:Mg;Ti, commercially called TLD-100. These studies have been carried out by adding both possible charge transitions between localized and delocalized levels and complex thermoluminescence models that allow charge transitions between localized levels.

Mathematical modeling of the thermal process of arc erosion with current carrying heating effect in a temperature gradient

This paper presents a mathematical model aimed at comprehensively understanding the thermal processes associated with arc erosion of closed electrical contacts triggered by the instantaneous explosion of micro-asperities including Thomson effect and Joule heat source. The phenomenon involves vaporization and liquid zones, and the temperature distribution is governed by a generalized heat equation, accounting for the heating effect due to current flow in temperature gradients and effect of heat source. The proposed model allows for a nuanced analysis of the thermal dynamics, shedding light on the complex phenomena involved in arc erosion. The proposed method in this paper employs similarity transformation techniques to effectively reduce the complexity of the problem, transforming it into a set of manageable ordinary differential equations. The study establishes the existence and uniqueness of the solution through rigorous analysis. The behavior of the solution of the problem is successfully considered for special cases of Thomson and thermal coefficients. By leveraging similarity transformations, the paper offers a powerful approach for unraveling the intricacies of the thermal processes in arc erosion of closed electrical contacts, providing valuable insights into the phenomena associated with current-carrying heating in the presence of temperature gradients.

Diffusion-thermo and thermo-diffusion impacts on MHD natural convection flow of maxwell nanofluids over a stretching sheet

The present study carried out significant importance in its magnetic field and crosswise diffusion influenced the Maxwell nanofluid flow past a nonlinear stretching sheet. This investigation aimed to shed light on the behavior of critical parameters, particularly in the presence of thermophoresis and Brownian motion. The primary aim is to investigate the impact of thermal diffusion, diffusion-thermo, and various influencing factors on a Maxwell nanofluid near a stretching sheet in the magnetic field, and the impact of three distinct slip conditions (velocity, thermal, and solutal). The partial differential equations by the nonlinear coefficients are utilized in obtaining the most important equations. These equations are distorting to beneficial nonlinear ordinary differential equations making use of the appropriate transformations variables and transformation coefficients. To investigating the computational solutions for the reducing sets of the nonlinear ordinary differential equations, these were developing and utilized the Keller box methodology. The simulations are carried out the nanofluids velocity, temperature, concentration, skin friction coefficients, the rate of temperature transport, in addition to the rate of mass transportation, amongst previous variables. The validations of this methodology are displayed via the comparison of the present outputs through the preceding judgments into the literatures. The major conclusions drawn from this study are the concentration profiles exhibited opposing behaviours as concentration slip parameter increased. However, the temperature profile increases for Brownian motion parameter and thermophoresis parameter parameters. Secondly, concentration displayed an increasing behavior as the Soret number increased.