MATLAB Functions Research Articles

Entropy optimized flow of hydromagnetic Reiner–Philippoff fluid over a stretching surface

Here, we investigate magnetohydrodynamic flow of an incompressible Reiner–Philippoff fluid over a stretched surface. The stretching property of the sheet induced flow. Joule heating and dissipation effects are considered in energy communication. The energy equation is developed through the first law of thermodynamics. Irreversibility analysis is constructed. Furthermore, the first-order chemical reaction is also accounted. Adequate transformation is used to get the ordinary differential system tackled through a local non-similar technique via the built-in Matlab function bvp4c. Prominent characteristics of flow parameters on the entropy rate, temperature, velocity, and concentration are studied. Thermal and solutal transport rates are studied. Reverse impacts for velocity and temperature are noted for the Reiner–Philippoff liquid parameter. Reduction in velocity is seen for the Bingham number. A larger Prandtl number reduces temperature distribution. Concentration is decreased for both the Lewis number and chemical reaction parameter. A reverse trend is observed for the entropy rate against Brinkman and Bingham numbers. A larger magnetic variable enhances entropy generation.

Insights of Heat and Mass Transfer in Magneto-Mixed Convective Sisko Nanofluid over a Wedge with Viscous Dissipation

The current analysis provides the important insights of Sisko nanofluid flow over a wedge with thermal radiation and viscous dissipation effects. The Buongiorno nanofluid model, which includes Brownian movement and thermophoresis, is taken into consideration. Momentum, temperature, and nanoparticle concentration equations are used to simulate the current problem. The suitable similarity variables are applied to the governing partial differential equations (PDEs) which yield the dimensionless ordinary differential equations (ODEs). The MATLAB function bvp4c has been used to resolve the resulting ODEs. The attributes of various flow parameters on the transfer rate of mass, heat, temperature, velocity, and nanoparticle concentration have been explored. The pressure gradient parameter boosts the mass transfer and velocity. Moreover, mixed convection leads to the decrement in thermal and nanoparticle concentration boundary layer. The obtained numerical findings are compared to published results in the literature by considering the particular cases to validate the current study and are seen to be in perfect accord.

Numerical solution of magnetohydrodynamics radiative flow of Oldroyd‐B nanofluid toward a porous stretched surface containing gyrotactic microorganisms

AbstractIn this article, we explore an incompressible steady flow of Oldroyd‐B nanofluid near a plan porous stretched surface considering the influence of thermophoresis, Brownian motion, and thermal radiation. Moreover, the constant magnetic field of intensity B0 is implemented with a low Reynolds number as well as the induced magnetic effect and the electric fields are ignored. The suitable similarity variables are applied to the governing partial differential equations (PDEs) which yield the dimensionless ordinary differential equations (ODEs). The MATLAB function bvp4c has been used to resolve the resulting ODEs. The attributes of various flow parameters on the transfer rate of mass, heat, density number of motile microorganisms, motile density, temperature, velocity, and nanoparticles concentration have been explored. It is determined that the boosting values of Prandtl number, solutal stratified, and the radiation parameter supports the boosting of heat transfer rate, and their reduction is assisted by the boosting values of thermal stratified and Brownian motion parameter. Moreover, the higher values of Brownian motion parameters and Schmidt number are more effective in the boosting of Sherwood number, although an opposite behavior is spotted for the boosting values of the thermophoresis and solutal stratified parameter. In the same way, the fluid velocity declines with the escalation of Deborah numbers, Hartmann number, and porosity parameter as well as the fluid temperature minimizes for the inclination of Prandtl number and thermal stratified parameter although it is magnified for the inclination of radiation parameter.

SCELT (symbolic computation aided eigenvalue and linear code for tokamaks): A full MHD eigenvalue code in toroidal geometry developed with the use of a symbolic computation technique

In this work, we report the construction of an eigenvalue computer code largely in C++ language, SCELT, by using the symbolic computation technique for the first time to solve the linearized single fluid magnetohydrodynamic (MHD) eigenvalue problem in toroidal geometry. A symbolic vector analysis module is developed to function the automatic derivation of the tedious linearized full MHD equations in the magnetic flux coordinate system. Furthermore, another module is developed to implement the automatic numerical discretization. These two modules dramatically reduce the human workload and obviate the possibility of a mistake during code development. The tools provide a means of constructing matrices from differential operations and can be used for (generalized) linear problems, such as source driven and eigenvalue problems. Demo uses of both the symbolic vector analysis module and automatic numerical discretization module, such as the Poisson equation and tokamak equilibrium equation, are presented to demonstrate their advantages and potential broad applications. The full MHD eigenvalue code developed with these two modules is verified by the internal kink mode and tearing mode tests. Program summaryProgram Title: SCELT (Symbolic Computation aided Eigenvalue and Linear code for Tokamaks)CPC Library link to program files:https://doi.org/10.17632/35h3xmc28k.1Licensing provisions: GNU General Public License 3.0Programming language: C++, MATLABExternal routines/libraries:• EIGEN (https://eigen.tuxfamily.org/index.php?title=Main_Page)Nature of problem: The eigenvalue full MHD model determines a wide range of physical phenomena arising from the basic destabilizing forces, which are of considerable both fundamental and practical importance for magnetic fusion plasmas. From the viewpoint of physics, solving the model is equivalent to finding the spectrum of the system, and for realistic tokamak geometry, it becomes possible only with the help of computer simulation. From the viewpoint of mathematics, it is actually a problem of solving a set of partial differential equations in a general curvilinear coordinate system.Solution method: Different from the conventional method, a symbolic vector analysis module using the symbolic computation technique is developed to conduct the automatic expansion of the full MHD equations in the magnetic flux coordinate system. In addition, an automatic numerical discretization module is developed to automatically implement the numerical discretization. Facilitated by the two modules, the coefficients of the matrices of the eigenvalue equation will be automatically generated and passed to the linear eigenvalue solver (eig function of MATLAB). The eigenvalues and eigenvectors are resolved by the solver.Additional comments including restrictions and unusual features: As originally motivated by the development of an eigenvalue full MHD code, a symbolic vector analysis module by using symbolic computation technique and a closely related automatic numerical discretization module are developed and directly applied to physics code development for the first time at least in the fusion field. Many (generalized) linear physics problems can benefit from the standalone or integrated application of these two modules. The tokamak equilibrium and eigenvalue MHD problems presented in the paper can be considered two important and practical examples.

Second-order conic programming for data envelopment analysis models

Data envelopment analysis (DEA) is a widely used benchmarking technique. Its strength stems from the fact that it can include several inputs and outputs of not necessarily the same type to evaluate efficiency scores. Indeed, the aforesaid method is based on mathematical optimization. This paper constructs a second-order conic optimization problem unifying several DEA models. Moreover, it presents an algorithm that solves the former problem, and provides a MATLAB function associated with it. As far as known, no MATLAB function solves DEA models. Among different types of DEA, this function can handle deterministic, Malmquist index, and stochastic models. In fact, DEA is involved in various practical applications, thus, this work will provide some possible future extensions, not only for MATLAB but also for any programming software in applications of decision science and efficiency analysis.

MatNERApor—A Matlab Package for Numerical Modeling of Nonlinear Response of Porous Saturated Soil Deposits to P- and SH-Waves Propagation

The paper is devoted to the problem of numerical modeling of earthquake response of porous saturated soil deposits to seismic waves propagation. Site-specific earthquake response analysis is a necessary and important component of seismic hazard assessment. Accounting for the complex structure of porous saturated soils, i.e., the content in them, in addition to the solid matrix, pore water, gas mixture and ice, is especially important for the water areas in the zones of continuous or sparse permafrost, as well as the massive release of bubble gas from bottom sediments. The purpose of this study is to introduce an algorithm and its Matlab implementation for numerical modeling of the nonlinear response of porous saturated soil deposits to vertical P- and SH-waves propagation. The presented MatNERApor package consists of a set of Matlab scripts and functions. The package was tested and verified using the records of vertical seismic arrays of the Kik-net network. In addition, the records of local earthquakes obtained by ocean bottom seismographs in the Laptev Sea in 2019–2020 were used to demonstrate the effect of the water layer above the seabed sites on the reduction of vertical motions spectra. The results of the calculations showed good agreement with the data obtained from real seismic records, which justifies the correctness of the theoretical basis of the presented algorithm and its software implementation.

Improved heat coefficients for joint-space metabolic energy expenditure model during level, uphill, and downhill walking.

A previously developed joint-space metabolic energy expenditure (MEE) model includes subject-specific parameters and was validated using level walking gait data. In this work, we determine how well this joint-space model performs during various walking grades (-8%, 0%, and 8%) at 0.8 m·s ⁻1 and 1.3 m·s ⁻1 using published gait data in the literature. In response to those results, we formulate an optimization problem and solve it through the particle swam method plus fmincon function in MATLAB to identify a new optimal weighting parameter set for each grade that produces more accurate predicted MEE and we compare our new findings with seven other MEE models in the literature. The current study matched the measured MEE the best with the lowest RMSE values for level (0.45 J·kg ⁻1·m ⁻1) and downhill (0.82 J·kg ⁻1·m ⁻1) walking and the third lowest RMSE value for uphill (1.56 J·kg ⁻1·m ⁻1) walking, where another MEE model, Looney et al., had the lowest RMSE for uphill (1.27 J·kg ⁻1·m ⁻1) walking. Bland-Altman plots and three independent-samples t-tests show that there was no statistical significant difference between experimentally measured MEE and estimated MEE during the three walking conditions, meaning that the three new optimal weighting parameter sets can be used with 6 degree of freedom (DOF) lower extremity motion data to better estimate whole body MEE in those scenarios. We believe that this work is a step towards identifying a single robust parameter set that allows for accurate estimation of MEE during any task, with the potential to mitigate a limitation of indirect calorimetry requiring lengthy steady state motion.

Optimization of University Campus Microgrid for Cost Reduction: A Case Study

This paper presents an optimization model to minimize the fuel cost and CO2 emision on university campuses using an hybrid power system (HPS). The HPS is made up of solar photovoltaic (PV), diesel generator (DG), wind turbine (WT) and battery energy storage system (BESS). Two university campuses are used as case study to investigate the efficiency of the proposed HPS. The objective function is formulated such that each campus load is met by the renewable energy source (RES) when available and the DG only swicthes on when the output of the RES is not eneough to meet the load. The resulting non linear optimization problem is solved using a function in MATLAB called “quadprog”. The results of the simulation are analyzed and compared with the base case in which the DG is used exclusively to meet the entire load. The results show the effectiveness of the optimized HPS in saving fuel when compared to the base case and reflect the effects of seasonal variations in fuel costs.

Stability analysis and Simulation of power system based on Matlab

Abstract Abstact: The stability analysis of power system is an important process to measure the security and stability level of the power system and the construction and development plan. The stability of the power system is divided into static stability, transient stability and dynamic stability. The stability of the system is judged by different analysis methods for different forms and sizes of interference. The construction of large power grid is developing rapidly, and the powerful computing function of Matlab can adapt to the more and more huge power system stability calculation tasks. As a Matlab sub module, Simulink can properly assist the stability calculation of power system with its powerful and stable computing function and simple visual modular graphics. In this paper, the concept of power system stability is first proposed, the static stability and transient stability of power system are briefly introduced. Secondly, the static / transient stability of power system is simulated with Simulink, and the measures to improve the static / transient stability of power system are proposed.

Homogenization of earthquake magnitudes using bivariate fit shell approach: Eastern Himalaya region

An earthquake catalog is an essential requirement for seismic hazard estimation, which contains data from various sources or agencies (e.g., ISC, NEIC, HRVD). A myriad of earthquake magnitude scales (e.g., MS, mb MW) are given in these catalogs. These different magnitudes need to be homogenized for seismic hazard assessment. Here, we studied seismicity of the Eastern Himalayan region, within latitudes 26°N-30°N and longitudes 89°E −98°E, to obtain a set of relations for the homogenization. Development of regression relationships using Williamson-York Iterative Bivariate Fit shell method is executed. The conversions are implemented to magnitude scales MS and mb, and homogenized to moment magnitude MW, which is accepted as a more stable magnitude scale. This study further involves the development of a robust function in MATLAB that makes the homogenization of an extensive data set much more effective and more accessible. The earthquake catalog data for the period 1900–2020 are compiled for homogenization to MW. The code and the homogenized earthquake catalog would be helpful for seismic hazard assessment studies in the Eastern Himalayan region.

Thermolab: A Thermodynamics Laboratory for Nonlinear Transport Processes in Open Systems

AbstractWe developed a numerical thermodynamics laboratory called “Thermolab” to study the effects of the thermodynamic behavior of nonideal solution models on reactive transport processes in open systems. The equations of the state of internally consistent thermodynamic data sets are implemented in MATLAB functions and form the basis for calculating Gibbs energy. A linear algebraic approach is used in Thermolab to compute Gibbs energy of mixing for multicomponent phases to study the impact of the nonideality of solution models on transport processes. The Gibbs energies are benchmarked with experimental data, phase diagrams, and other thermodynamic software. Constrained Gibbs minimization is exemplified with MATLAB codes and iterative refinement of composition of mixtures may be used to increase precision and accuracy. All needed transport variables such as densities, phase compositions, and chemical potentials are obtained from Gibbs energy of the stable phases after the minimization in Thermolab. We demonstrate the use of precomputed local equilibrium data obtained with Thermolab in reactive transport models. In reactive fluid flow the shape and the velocity of the reaction front vary depending on the nonlinearity of the partitioning of a component in fluid and solid. We argue that nonideality of solution models has to be taken into account and further explored in reactive transport models. Thermolab Gibbs energies can be used in Cahn‐Hilliard models for nonlinear diffusion and phase growth. This presents a transient process toward equilibrium and avoids computational problems arising during precomputing of equilibrium data.

Modeling, Simulation and Development of Grid-Connected Voltage Source Converter with Selective Harmonic Mitigation: HiL and Experimental Validations

This paper elaborates on a development technique for the grid-connected voltage source converter (VSC). We propose a simulation technique in the MATLAB/Simulink environment that emulates the operation of the discrete-time controlled grid-connected VSC. The switched-circuit modeling approach is used for simulation of the power stage in the continuous-time domain with the physical unit scale. The discrete-time control algorithm is implemented in an interpreted MATLAB function in the per-unit scale, which synchronizes with the switching period. Such a control algorithm is easily translated into the C language for programing of the 32-bit C2000 DSP controller with the same regulators’ parameters. The proposed platform was validated with a hardware-in-the-loop real-time simulator and with a 5-kVA 3-phase LCL-filtered grid-connected VSC. The discrete-time control scheme was implemented in the synchronous reference frame control with proportional-integral with multi-resonant controllers at harmonic orders 6th and 12th for suppression of the grid voltage harmonic orders 5th, 7th, 11th, and 13th. The experimental results closely agreed with the simulation results. The experimental grid currents complied with the IEEE 1547 standard thanks to the multi-resonant controllers. The proposed platform provides a smooth transition from implementation to a near-commercial prototype with a low investment cost in simulation and rapid prototyping tools. A MATLAB/Simulink VSC model is provided as an attachment of this paper.

More accurate and strengthened forms of half-discrete Hilbert inequality

In this work, by introducing a new half-discrete kernel function with parameters, and using the method of weight coefficient, Euler-Maclaurin summation formula and some other techniques of real analysis, a more accurate half-discrete Hilbert-type inequality as well as its strengthened form are established. Additionally, some equivalent inequalities in Hardy's form are also considered. Furthermore, it is proved that the constant factors in the newly obtained inequalities are the best possible. At last, by taking some special values of parameters and using the numerical calculation function of Matlab, some special cases are presented at the end of the paper.

Computing Color Transforms with Applications to Image Editing

This paper deals with the implementation of various MATLAB functions present in image processing toolbox of MATLAB and using the same to create a basic image processor having different features like, viewing the red, green and blue components of a color image separately, color detection and various other features (noise addition and removal, edge detection, cropping, resizing, rotation, histogram adjust, brightness control, etc.) that is used in a basic image editor along with object detection and tracking.

Ensuring stability of inverse functions and minimized models in MATLAB

Plotting of inverse functions of high-order models in MATLAB can generate positive zeros that distort the dynamic properties of the model. Minimizing the dimension of models with the "mineral" function in MATLAB significantly reduces the computation time, but creates additional zeros and generates positive poles, leading to instability of the model. Variants of constructing models with inverse functions and minimizing the dimension of models in MATLAB, which do not create additional zeros and poles, are proposed. Keywords: MATLAB, ADAMS software, inversion, minimization, dynamic model. v123std@mail.ru

Physics-Based Guidelines for Accepting Reasonable Dynamic Simulations of Movement.

During dynamic simulations, residuals are nonphysical generalized forces/moments that dynamically balance external and inertial forces/moments, accounting for data processing and modelling errors. Hicks et al. (2015) made the original residual threshold recommendations for an acceptable simulation, but these thresholds are not based on the dynamic, physics-based movement characteristics. In this study, we present three new, physics-based guidelines for accepting dynamic simulations of movement using zero moment point computations and thresholds for forces, center of pressure, and free moment. We formulate new guidelines and evaluate them alongside the original 2015 recommendations using two movements: single-leg jump-landing (SLJL) and walking gait. We also present a MATLAB function for users to test if their simulations meet these guidelines. We found that on average, only 4.3% (SLJL) and 8.2% (walking gait) of the original 2015 residuals volume met all the new physics-based guidelines. The free-moment guideline was the most restrictive for reasonable simulations, especially for high-velocity movements at times with lower vertical ground reaction forces. Additionally, some of the new recommended residuals volume fell outside of the original 2015 recommendations. Moreover, accepting reasonable simulations using different thresholds leads to different joint torques as high as 24 Nm (SLJL) and 8.2 Nm (walking gait). The physics-based guidelines are overall more restrictive than the original 2015 recommendations and elicit different simulation kinetics. Using different guidelines may lead to different conclusions and clinical interpretations. We advocate for the physics-based guidelines as they are built upon the dynamic, physics-based characteristics of the movement.

Evaluation of Eleven Numerical Methods for Determining Weibull Parameters for Wind Energy Generation in the Caribbean Region of Colombia

The two-parameter Weibull probability density function (PDF) is widely utilized by different researchers and engineers to fit wind speed data for statistical analysis and modeling. The characterization of wind resources in the frequency and probability domain is necessary to estimate the power output potential of new wind energy projects. Considering that exist a variety of Weibull equations evidenced in the literature review, this article evaluates 11 different methods to calculate the shape and scale parameters of the Weibull PDF. In this sense, it was written an algorithm within a Matlab function that solves the 11 methods for calculating the Weibull PDF parameters. Wind speed data extracted from the ERA5 database was used as input data for applying the proposed algorithm, and statistical parameters such as the Root Mean Square Error (RMSE), the Relative Root Mean Square Error (RRMSE), and chi-square test (X2) we utilized for assessing the performance of each one of the 11 methods for modeling the wind distribution. The statistical results pointed that the numerical iteration methods (e.g. maximum likelihood method) showed better results than parameterized equations such as the Graphical Method, hence, this research recommends the implicit methods for determining Weibull PDF parameters of wind speed data.

Unsteady three dimensional bioconvective flow of Maxwell nanofluid over an exponentially stretching sheet with variable thermal conductivity and chemical reaction

An unsteady three-dimensional bio-convective Maxwell nanofluid flow through an exponentially stretched sheet with the convective boundary condition is the focus of this study. In the presence of variable thermal conductivity, the characteristic of heat transfer is performed. By changing the similarity variable, the model flow problem becomes a nonlinear form of coupled ordinary differential equations. The numerical results are calculated using Matlab's bvp4c function. The effect of various factors on velocity, temperature, concentration, and microorganism distribution is represented graphically. The physical quantities are examined in detail using graphs and tabulated data. For increasing values of Deborah number, the Nusselt number shrinks, whereas the convective parameter shows the opposite effect.

Natural bio-convective flow of Maxwell nanofluid over an exponentially stretching surface with slip effect and convective boundary condition

The under-consideration article mainly focuses an unsteady three-dimensional Maxwell bio-convective nanomaterial liquid flow towards an exponentially expanding surface with the influence of chemical reaction slip condition. The feature of heat transport is achieving in the existenceof convective boundary condition and variable thermal conductivity. With the help of similarity variables, the flow form of equations is turned into a nonlinear form of coupled ODEs. The numerical solutions are calculated by adopting bvp4c function of MATLAB. Impact of distinct characteristics on the temperature, velocity microorganism and concentration field is graphically evaluated. Moreover, physical quantities are observed via graphs and tabulated data in details. It has been seen by the observation that the involvement of unsteadiness parameter restricts the change of laminar to turbulent flow. Further, for increasing velocity slip parameter velocity component in both directions shows lessening behavior. The Nusselt number exhibits diminishing behavior for larger values of Deborah number, and it shows the opposite behavior for larger values of convective parameter.

MHD flow of a nanofluid due to a nonlinear stretching/shrinking sheet with a convective boundary condition: Tiwari–Das nanofluid model

PurposeNanofluid research has piqued the interest of scientists due to its intriguing applications in nanoscience, biomedical and electrical engineering, medication delivery, biotechnology, food processing, chemotherapy and other fields. This paper aims to inspect the behavior of the mixed convection magnetohydrodynamic flow and heat transfer induced by a nonlinear stretching/shrinking sheet in a nanofluid with a convective boundary condition. Tiwari and Das mathematical nanofluid model is incorporated in the analysis.Design/methodology/approachThe mathematical model is initially transformed to a nondimensional form by using dimensionless variables. Then the nondimensional partial differential equations are further transformed to a set of similarity equations by using the similarity technique. These equations are solved numerically by the bvp4c function in MATLAB software.FindingsFor a certain range of the stretching/shrinking parameter, two solutions are obtained. The friction factor and the heat transfer rate escalate due to suction parameter with adding nanoparticles volume fraction by almost 27.15% and 0.153% for the upper branch solution, while the friction factor declines by almost 30.10% but the heat transfer rate augments by 0.145% for the lower branch solution. Furthermore, the behavior of the nanoparticle volume fractions on the heat transfer rate behaves differently in the presence of the mixed convection effect. The temperature of fluid augments with increasing Biot number for both solutions.Originality/valueThe present work considers the flow and heat transfer induced by a stretching/shrinking sheet in a nanofluid using the Tiwari–Das nanofluid model with a convective boundary condition, where the effect of the buoyancy force is taken into consideration. It is shown that two solutions are found for a certain range of the shrinking strength, while the solution is unique for the stretching case. This study is important for scientists working in the growing field of nanofluids to become familiar with the flow properties and behaviors of such nanofluids.