MATLAB Code Research Articles

MÔ PHỎNG XOÁY TÁCH RỜI TRONG NGHIÊN CỨU CÁC ĐẶC TRƯNG KHÍ ĐỘNG CỦA DÒNG CHẢY RỐI TRÊN VÙNG TƯƠNG TÁC

The turbulent mixing layer is a phenomenon that occurs and has many applications in aeronautical engineering. The study of mixing layer turbulence by the numerical method is suitable under domestic conditions. Two numerical simulation methods are used in most studies including, direct numerical simulation DNS and large eddy simulation LES, while there are very few studies using detached eddy simulation DES. In this article, the authors use numerical simulation methods evolving Reynolds average Navier-Stokes simulation RANS and detached eddy simulation DES to propose a numerical simulation model that allows to study of the aerodynamic characteristics of the turbulent flow interaction. RANS is used to evaluate grid independence. With the selected mesh, two models counting the DES-2D model and the DES-3D model are conducted. Processing velocity field data with Matlab code, the results show that the average flow behavior has closely followed the experimental results, while the turbulent kinetic energy still has a large error. POD and Q-criterion analysis has shown some large coherent structures in the interaction region.

An Efficient Design for the DVB-S2 Forward Link System Outer Layer Encoding Based on PCC Turbo Coding Across Fading Channel

The most significant challenges wireless broadcasting systems face are channel effects and Inter Symbol Interference (ISI). Many different kinds of channel coding are employed to get around these issues. Digital Video Broadcasting for Satellite Telecommunication Second Generation (DVB-S2) uses a serial concatenation of Bose, Ray-Chaudhuri, and Hocquenghem (BCH) code and Low-Density Parity-Check (LDPC) code as a Forward Error Correction (FEC) for error detection purpose and correction. In this work, a MATLAB code (m-files) is constructed to simulate the standard DVB-S2 Bit-Interleaved Coded Modulation (BICM) system according to the ETSI Technical Report (EN 302 307 1). Then, the traditional design is redesigned with a Parallel Concatenation Convolutional (PCC) Turbo coding in concatenation with LDPC coding to enhance the (FEC). The two approaches have been tested under the official modulation types QPSK, 8PSK, 16APSK, and 32APSK with 2/3, 3/4, 3/5, 4/5, and 5/6 code rates (RC). Over a Rayleigh Fading channel, the two models are compared. The proposed model performed better than the standard model regarding bit error rate (BER) mitigation when operating at varying signal-to-noise ratio (SNR) levels, especially in 8PSK 3/5 MODCODE. The proposed model achieved (2.6272×10-3) BER mitigation value with power gain equal to 4 dB.

In silico study of luminal transport of bile salts from the duodenum to the gastric mucosa: Role of small intestinal peristalsis

Biliary reflux plays a key role in the progression of gastric carcinoma over the long term. The reflux of alkaline duodenal contents (Duodenogastric Reflux) is presumed to be mediated by changes in the gastroduodenal motility, with no clear insights into the mechanisms. Considering mechanism comes under the perspective of fluid transport, a mathematical model is formulated for investigating the transport of the bile as a non-reactive species, assuming non-Newtonian nature as the power law fluids in the antropyloroduodenal segment using lubrication approximation. An analytical approach is employed to derive the exact solutions, and further computational results are simulated using MATLAB coding. To assess the pathophysiology of reflux, transport of the bile salt was quantified for various duodenal motility patterns by considering the following peristalsis parameters, such as elementary contraction (Antegrade Propagating Wave, Retrograde Propagating Wave, and Stationary Wave), wavelength, velocity and occlusion of the wave, and frequency of the contraction. Results of the bile transport are presented for the duodenal peristalsis and analyzed for the relative displacement from its initial position across various motility patterns. The particle transport is driven by wave traversal in the vicinity at the duodenum, whereas at the pylorus and proximal pylorus, transport of the imaginary particles, such as bile salts, is accelerated by increased occlusion of the wave (particles travel longer distances owing to higher occlusion, with 90% occlusion showing more transit than 70% occlusion) and wave speed, with pylorus contributing to hydrodynamic hindrance (owing to pyloric channel width, where the resistance scales to 1/R4) with oscillatory excursion.

Estimating insulin sensitivity and β-cell function from the oral glucose tolerance test: validation of a new insulin sensitivity and secretion (ISS) model.

Efficient and accurate methods to estimate insulin sensitivity (SI) and β-cell function (BCF) are of great importance for studying the pathogenesis and treatment effectiveness of type 2 diabetes (T2D). Existing methods range in sensitivity, input data, and technical requirements. Oral glucose tolerance tests (OGTTs) are preferred because they are simpler and more physiological than intravenous methods. However, current analytical methods for OGTT-derived SI and BCF also range in complexity; the oral minimal models require mathematical expertise for deconvolution and fitting differential equations, and simple algebraic surrogate indices (e.g., Matsuda index, insulinogenic index) may produce unphysiological values. We developed a new insulin secretion and sensitivity (ISS) model for clinical research that provides precise and accurate estimates of SI and BCF from a standard OGTT, focusing on effectiveness, ease of implementation, and pragmatism. This model was developed by fitting a pair of differential equations to glucose and insulin without need of deconvolution or C-peptide data. This model is derived from a published model for longitudinal simulation of T2D progression that represents glucose-insulin homeostasis, including postchallenge suppression of hepatic glucose production and first- and second-phase insulin secretion. The ISS model was evaluated in three diverse cohorts across the lifespan. The new model had a strong correlation with gold-standard estimates from intravenous glucose tolerance tests and insulin clamps. The ISS model has broad applicability among diverse populations because it balances performance, fidelity, and complexity to provide a reliable phenotype of T2D risk.NEW & NOTEWORTHY The pathogenesis of type 2 diabetes (T2D) is determined by a balance between insulin sensitivity (SI) and β-cell function (BCF), which can be determined by gold standard direct measurements or estimated by fitting differential equation models to oral glucose tolerance tests (OGTTs). We propose and validate a new differential equation model that is simpler to use than current models and requires less data while maintaining good correlation and agreement with gold standards. Matlab and Python code is freely available.

Comparative exergy and economic analyses of single slope solar desalination unit combined with concentrator integrated evacuated collectors

This paper deals with the exergy analysis of single slope solar desalination unit combined with N number of compound parabolic concentrator integrated evacuated tubular collectors (NCPCETC-SU) considering New Delhi climate. An exhaustive computation considering each month of year is carried out. The methodology consists of feeding all fundamental equations with relevant data to MATLAB code and presenting the output in the suitable form. Results of NCPCETC-SU are compared with results of SU incorporated with evacuated tubular collectors (NETC-SU). Concludingly, the annual exergy and daily exergy efficiency for NCPCETC-SU are higher by 36.51% and 30.81% than NETC-SU for same mass flow rate, N and water depth under similar climatic situation. The annual freshwater output is higher by 16.81% and freshwater cost is higher by 9.85% at 2% rate of interest for NCPCETC-SU than NETC-SU respectively. Further, the freshwater cost of NCPCETC-SU can be diminished by increasing the concentration ratio.

Numerical Solution of Two-Dimensional Nonlinear Unsteady Advection-Diffusion-Reaction Equations with Variable Coefficients

The advection-diffusion-reaction (ADR) equation is a fundamental mathematical model used to describe various processes in many different areas of science and engineering. Due to wide applicability of the ADR equation, finding accurate solution is very important to better understand a physical phenomenon represented by the equation. In this study, a numerical scheme for solving two-dimensional unsteady ADR equations with spatially varying velocity and diffusion coefficients is presented. The equations include nonlinear reaction terms. To discretize the ADR equations, the Crank–Nicolson finite difference method is employed with a uniform grid. The resulting nonlinear system of equations is solved using Newton’s method. At each iteration of Newton’s method, the Gauss–Seidel iterative method with sparse matrix computation is utilized to solve the block tridiagonal system and obtain the error correction vector. The consistency and stability of the numerical scheme are investigated. MATLAB codes are developed to implement this combined numerical approach. The validation of the scheme is verified by solving a two-dimensional advection-diffusion equation without reaction term. Numerical tests are provided to show the good performances of the proposed numerical scheme in simulation of ADR problems. The numerical scheme gives accurate results. The obtained numerical solutions are presented graphically. The result of this study may provide insights to apply numerical methods in solving comprehensive models of physical phenomena that capture the underlying situations.

VDR decomposition of Chebyshev-Vandermonde matrices with the Arnoldi Process

This paper introduces the VDR decomposition of Chebyshev-Vandermonde matrices, where V represents an ordinary Vandermonde matrix, D is diagonal, and R is upper triangular. Our motivation for this work stems from the study by Brubeck et al. [Vandermonde with Arnoldi. SIAM Rev. 2021;63(2):405–415]. We explore the VDR decomposition and combine it with a QR decomposition of V for Chebyshev-Vandermonde matrices. Furthermore, we demonstrate that the upper triangular factor in the QR decomposition can be recursively obtained from the upper Hessenberg matrix in the Arnoldi process. To compare our approach with the results obtained using the default QR code in Matlab, we present experimental results. Finally, we provide an algorithm for solving linear systems with Chebyshev-Vandermonde matrices as coefficient matrices, and experimental results for an upper bound on the relative error by applying an a posteriori error analysis for the computed solutions of the systems.

SOLVING STOCHASTIC TRANSPORTATION ELECTRICITY PROBLEM WITH FUZZY INFORMATION ON PROBABILITY DISTRIBUTION USING MATLAB PROGRAM

This study focuses on MATLAB code programs of the entire stages of solving Stochastic Transportation Linear Programming Problems with Fuzzy Uncertainty Information on Probability Distribution Space (STLPPFI) with its algorithm outlines. A MATLAB code program of STLPPFI problem solver with algorithm outlines are proposed to solve STLPPFI model problems, and it utilizes many concepts as Alpha-Cut technique, Truth Degrees technique, Linear Fuzzy Membership Function (LFMF), Trapezoidal Fuzzy Number , Triangular Fuzzy Number , Linear Fuzzy Ranking Function (LFRF), Expectation Weighted Summation technique (EWS) and analyzing cases via second condition test of alpha-cut technique. The STLPPFI problem solver is utlized to convert STLPPFI into its corresponding equivalent Deterministic Transportation Linear Programming Problem (DTLPP) via defuzzifying from fuzziness on probability distribution space and derandomization randomness of problem formulation respectively. In addition, Dual-Simplex algorithm method with Vogel Approximation Algorithm Method (VAM) are used to obtain optimal solution from DTLPP. All MATLAB code programs with their proposed algorithm outlines are new except Dual-Simplex and VAM. The MATLAB code program of STLPPFI problem solver are more efficient along with a numerical example on electricity field illustrating practicability of this proposed MATLAB code program with its algorithm. Finally, the solution procedure illustrates the MATLAB code program of the proposed method is practical and applicable in the fields of energy and industry as it facilitates the method of transforming the energy at the lowest cost, least time running and is commercially applicable. Comparative comments are provided between Dual-Simplex and VAM in solution process.

Low-velocity impact simulation of carbon fiber reinforced composite laminate using IFF-criterion based on BP-ANN

Damage characteristics of composite materials after low-velocity impacts are hard to predict and numerical simulation is time-consuming. This paper explores a study in carbon fiber reinforced composite (CFRP) laminates low-velocity impact (LVI) simulation with Puck inter-fiber failure (IFF) criterion based on the back-propagation neural network (BP-ANN) model. LVI numerical simulations under three different energy levels were conducted and the resulting element stress components were extracted. After data screening and stratified sampling, a training set including five stress tractions as input and the corresponding fracture angle as output was generated. With this dataset, a fracture angle search algorithm based on the BP-ANN model containing three hidden layers was established. Through Matlab coding and ABAQUS subroutine tests, the algorithm exhibits high efficiency compared with other common algorithms and distinctly accelerates the simulation progress (reduce cost time 22.75% and 38.06% compared with Puck's method and SRGSS algorithm). In addition, the simulation results, including the predicted damage size, impact force, displacement and absorbed energy, are in good agreement with experimental results. This work provided a referable thought to accelerate the impact simulation process with the fracture angle-based criteria.

On split-octonionic curves

Abstract In this paper, we first define the vector product in Minkowski space $\mathbb{R}_{4}^{7}$, which is identified with the space of spatial split-octonions. Next, we derive the $G_{2}-$ frame formulae for a seven dimensional Minkowski curve by using the spatial split-octonions and the vector product. We show that Frenet–Serret formulas are satisfied for a spatial split octonionic curve. We obtain the congruence of two spatial split octonionic curves and give relationship between the $G_{2}-$ frame and Frenet–Serret frame. Furthermore, we present the Frenet–Serret frame with split octonions in $\mathbb{R}_{4}^{8}$. Finally, we give illustrative examples with Matlab codes.

Comparison of non-linear vibration of outer race defective ball bearing using two defect functions

The aim of this article is to study the effects of evolution in defect size on vibration of a ball bearing by simulation of a ball bearing by developing a 2-DOF mathematical model and to compare the vibration responses of defective bearings obtained for two widely used defect functions, viz., rectangular function and half-sine wave function. MATLAB codes are developed to prepare a mathematical model of a ball bearing and to solve the differential equations of the model using the Runge-Kutta method. In the model, the mass supported by the bearing is considered as a lumped mass, and the contact between the races and the balls is considered as a series of springs, whose spring stiffness is obtained by using Hertz’s contact deformation theory. This model considers the contact deformation between the balls and the races and the additional displacement between the balls and the inner race due to radial clearance and defect geometry. The maximum possible radial displacement of the ball into the defect is obtained analytically and graphically from the race-ball-defect geometry. First, the impulses generated due to an outer race defect in the ball bearing are modeled using two different defect functions separately and their vibration responses are compared. Secondly, the effects of increase in defect length on vibration of the bearing are simulated separately for two defect functions, and then their responses are compared and analyzed. The results show that when the defect is modeled with a rectangular defect function, the vibration responses obtained are greater than when the defect is modeled with a half-sine wave defect function. And, vibration responses increase rapidly up to a certain level of defect length and then decrease with a further increase in defect length. The vibration analysis performed for different defect lengths can provide good support to vibration analysts and researchers.

Stability analysis and vibration suppression in an overhung rotor system using active magnetic damper

The present work demonstrates the effectiveness of an active magnetic damper (AMD) in improving the vibration characteristics of an overhung rotor system (ORS) considering the effects of synchronous mass-unbalance, rotor bow, and viscous internal damping. A finite element-based rotordynamic analysis has been conducted to evaluate the system response using state-space formulation. MATLAB codes are developed for the numerical implementation of the rotordynamic model pertaining to the flexible ORS integrated with an AMD consisting of three parallel feedback loops. The internal damping is found to reduce the vibration amplitudes at the bearing and disk locations. However, it leads to system instability in the absence of AMD beyond the first critical speed (670 RPM) which is indicated by the change in the real part of eigenvalues. Under these circumstances, the use of AMD causes a remarkable improvement and the system stabilizes for almost the entire speed range considered here, 320–10,000 RPM. In addition, the AMD causes a maximum reduction of 95.8%, 96.5%, and 83.3% in the vibration amplitudes at the locations of Bearing 1, Bearing 2, and the overhung disk, respectively. Using an appropriate set of AMD parameters, the system characteristics can be altered effectively as per the requirement.

Smart distribution network voltage estimation using PMU technology considering zero injection constraints.

To properly control the network of the power system and ensure its protection, Phasor measurement units (PMUs) must be used to monitor the network's operation. PMUs can provide synchronized real-time measurements. These measurements can be used for state estimation, fault detection and diagnosis, and other grid control applications. Conventional state estimation methods use weighting factors to balance the different types of measurements, and zero injection measurements can lead to large weighting factors that can introduce computational errors. The offered methods are designed to ensure that these zero injection criteria can be strictly satisfied while calculating the voltage profile and observability of the various distribution networks without sacrificing computing efficiency. The proposed method's viability is assessed using standard IEEE distribution networks. MATLAB coding is used to simulate the case analyses. Overall, the study provides a valuable contribution to the field of power distribution system monitoring and control by simplifying the process of determining the optimal locations for PMUs in a distribution network and assessing the impact of ZI buses on the voltage profile of the system.

Newtonian Heating on Casson Mixed Convection Transport by Ternary Hybrid Nanofluids over Vertical Stretching Sheet: Numerical Study

Numerous physical characteristics occurring from the structure and micro-motions of fluid nanoparticles can be examined using the governing models of nanofluids. Also, It can describe the demeanor of a vast field of actual fluids. This achieved a significant turn in the enhancement of heat transfer that improves manufacturing and engineering modernization. Depending on that, the assumptions that form our aims are numerically examining energy transport and heat transfer via Casson ternary hybrid nanofluids that contain the states of combined convection flow over a vertical stretching sheet. Also, Newtonian heating boundary conditions and magnetohydrodynamics (MHD) effects are investigated. Mathematical models (governing equations) that emulate and construct the conduct of these boosted ternary hybrid nanofluids are formed by developing the Tiwari and Das models. These governing equations are converted to partial differential equations (PDEs) employing appropriate substitutions. An accurate and efficient method called the Keller box numerical method is executed to get outcomes to the physical model. These numerical calculations are found and presented by employing MATLAB codes, to acquire tables of numerical outcomes, and graphic exhibits, which provide the impacts of important parameters on the physical quantities supporting heat transfer. Furthermore, the new results, in the Newtonian fluid case, were compared with prior literature, which were in excellent agreement. The studied problem parameters are examined at a Casson parameter domain of 1 to 5, a mixed convection parameter domain of -1 to 3, a conjugate parameter of 0.2 to 1, a magnetic parameter domain of 0.1 to 5, and a nanoparticle volume fraction parameter of 0.001 to 0.008. The numerical consequences deduced that the local skin friction rises when the conjugate and mixed convection parameters are increased. But the opposite case happens when the effects are obtained for the nanoparticle volume fraction, magnetic, and Casson parameters. Also, the Nusselt number rises with growing nanoparticle volume fraction and Casson parameters.

A 2D stability analysis of the rock surrounding underground liquified natural gas storage cavern based on COMSOL Multiphysics

Underground liquified natural gas (LNG) storage is essential in guaranteeing national energy strategic reserves, and its construction is being accelerated. The stability of surrounding rock of underground LNG storage caverns under stress-low temperature coupling effect is the key factor determining the feasibility of LNG storage. First, a mathematical model used for controlling the stress-low temperature coupling and the processes of rock damage evolution is given, followed by a 2-D numerical execution process of the mathematical model mentioned above described based on Comsol Multiphysics and Matlab code. Finally, a series of 2-D simulations are performed to study the influence of LNG storage cavern layout, burial depth, temperature and internal pressure on the stability of surrounding rocks of these underground storage caverns. The results indicate that all the factors mentioned above affect the evolution of deformation and plastic zone of surrounding rocks. The research results contribute to the engineering design of underground LNG storage caverns.

The Solution of Traveling Salesman Problem with Time Windows by MILP in Matlab Code

A delivery driver uses his truck to distribute ordered goods from the warehouse (depot) to n customers. Each customer determines the delivery point (by GPS coordinates) and time window for the distribution of goods. This problem can be called the traveling salesman problem with time windows (TSPTW). The objective of the solution is to select the sequence of delivery points so that the travel distance and the total travel time are minimal. The necessary condition is that the deliverer leaves the warehouse, visits all delivery points (where he arrives at the required time windows), and returns to the warehouse. In this article, one exact robust solution of the TSPTW is presented by using mixed integer linear programming implemented in Matlab code. The created algorithm can be used for any number n of customers.

SCTBEM: A scaled coordinate transformation boundary element method with 99-line MATLAB code for solving Poisson's equation

This study introduces the scaled coordinate transformation boundary element method (SCTBEM), a novel boundary-type method for solving three-dimensional potential problems. To apply the BEM to complex problems, it is common practice to use the fundamental solution corresponding to the partial governing equation operator to establish the integral equation. However, this approach introduces the domain integral, which may jeopardize the dimensionality reduction advantages of BEM. To preserve the benefits of dimensionality reduction, this study proposes a novel domain integral transformation method named SCT. The SCT is purely a mathematical operation that does not rely on a particular solution of the operators, which requires only discretization on the surface of the structure while remaining analytical in the radial direction. An even more significant advantage is that the lower-order singularity can be eliminated by the coordinate translation technique. To facilitate the wider adoption of BEM, the authors present an open-source 99-line MATLAB code. Numerical results demonstrate that the SCTBEM exhibits high numerical accuracy even when dealing with complex models.

A ChatGPT-MATLAB framework for numerical modeling in geotechnical engineering applications

ChatGPT has recently emerged as a representative of Large Language Models (LLMs) that have brought evolutionary changes to our society, and the effectiveness of ChatGPT in various applications has been increasingly reported. This study aimed to explore the potential of employing programming performance driven by ChatGPT responses to conversational prompts in the field of geotechnical engineering. The tested examples included the analysis of seepage flow and slope stability, and the image processing of X-ray computed tomographic image for partially saturated sand. For each case, the prompt was initially fed by a narrative explanation of the problem attributes such as geometry, initial conditions, and boundary conditions to generate the MATLAB code that was in turn executed to evaluate the correctness and functionality. Any errors and unanticipated results were further refined by additional prompts until the correct outcome was achieved. ChatGPT was able to generate the numerical code at a considerable level, demonstrating creditable awareness of the refining process, when meticulous prompts were provided based on a comprehensive understanding of given problems. While ChatGPT may not be able to replace the entire process of programming, it can help minimize sloppy syntax errors and assist in designing a basic framework for logical programming.

Do the feet of male and female netball players differ in shape? Implications for shoe design

ABSTRACT A large proportion of netball players suffer foot-related problems and pain and are dissatisfied with current netball-specific footwear. To improve the fit and functionality of netball-specific shoes, we must understand the shape of these players’ feet and determine whether any sex differences exist. Five hundred and two representative-level netball players (n = 251 male; n = 251 female) had their feet three-dimensionally scanned. We then used a validated MATLAB code to automatically extract 10 measurements to characterise each participant’s foot shape. Differences between men and women for the absolute values and those normalised to foot length and stature were identified using independent samples t-tests with a Bonferroni adjusted alpha level. The size and shape of male netball players’ feet differed significantly from their female counterparts. Males had significantly larger absolute and normalised foot measurements than females, notably at the ball of the foot, heel and instep (p < 0.001). Netball shoe manufacturers should develop unique lasts for each sex and foot size and should offer a more extensive range of shoe lengths and widths to netball players. Such considerations will help optimise shoe fit and comfort and, in turn, reduce foot-related problems and pain associated with ill-fitting footwear.

A new solution of the fractional neutron point kinetics equations using symmetry and the Heaviside's expansion formula

A new analytical solution of the Fractional Neutron Point Kinetics Equations is developed in the present work, considering multi-groups of precursors of delayed neutrons as well as a constant reactivity. Such solution is obtained in a short way, as a direct generalization of the integer case, being only necessary to use an elementary change of variable as well as the Heaviside's Expansion Formula. One of the most relevant novelties of the developed solution is that it has the same structure and mathematical form of the solution of the integer case. This symmetry property is an important advantage over other reported solutions because it allows extending, in a straightforward way, computational algorithms that are used for the integer case to the fractional one. A MATLAB code implementation of the developed solution is also provided, as well as numerical experiments, where the proposed analytical solution is applied to several cases and scenarios, observing a sub-diffusive behavior for step reactivities, a mixed profile for ramp simulations, as well as a displacement of the peaks in the case of feedback reactivities.