Failure Analysis of Tubing Collapse in a Gas WellRead the full article
Mathematical Problems in Engineering is a broad-based journal publishing results of rigorous engineering research across all disciplines, carried out using mathematical tools.
Chief Editor, Professor Guangming Xie, is currently a full professor of dynamics and control with the College of Engineering, Peking University. His research interests include complex system dynamics and control and intelligent and biomimetic robots.
Latest ArticlesMore articles
Optimize Ranking and Load Shedding in Microgrid Considering Improved Analytic Hierarchy Process Algorithm and Power Stability Index
This paper proposes a load shedding model for the island microgrid based on the ranking of loads and the power stability index (PSI). Loads are ranked based on the improved analytic hierarchy process (AHP) algorithm. Real-time measurement systems have the function of collecting data for very important, important, and less-important loads at each bus load. From this data, the improved AHP method is applied to rank the loads. The advantage of this method is that the subjectivity is eliminated and not depending on the expertise of the system operator when implementing the traditional AHP method. Besides, the minimum amount of load shedding power is calculated, taking into account both primary and secondary control methods. The objective is to minimize the impact on power consumers and ensure that the frequency returns to an acceptable range. In addition, when implementing load shedding, voltage quality, and stability are considered. The PSI serves as a crucial parameter for assessing the voltage stability of microgrid buses. This index is combined with load ranking weights to obtain combined weights for the load shedding plan. Consequently, the proposed load shedding plan prioritizes minimizing damage to customers, improving voltage quality and stability, and ensuring frequency is within permissible limits. The 16-bus microgrid system is applied to compare with traditional methods and to prove the efficiency of the suggested technique.
Dynamics and Control of a Discrete Predator–Prey Model with Prey Refuge: Holling Type I Functional Response
In this study, we examine the dynamics of a discrete-time predator–prey system with prey refuge. We discuss the stability prerequisite for effective fixed points. The existence criteria for period-doubling (PD) bifurcation and Neimark–Sacker (N–S) bifurcation are derived from the center manifold theorem and bifurcation theory. Examples of numerical simulations that demonstrate the validity of theoretical analysis, as well as complex dynamical behaviors and biological processes, include bifurcation diagrams, maximal Lyapunov exponents, fractal dimensions (FDs), and phase portraits, respectively. From a biological perspective, this suggests that the system can be stabilized into a locally stable coexistence by the tiny integral step size. However, the system might become unstable because of the large integral step size, resulting in richer and more complex dynamics. It has been discovered that the parameter values have a substantial impact on the dynamic behavior of the discrete prey–predator model. Finally, to control the chaotic trajectories that arise in the system, we employ a feedback control technique.
Developing Control Strategy for PV-Based Distributed Generator for Enhancing Frequency Regulation of Microgrid
This paper presents a control strategy for a photovoltaic (PV)-based distributed generator (DG) to enhance the frequency regulation of a microgrid. A microgrid is a small-scale power system that integrates distributed energy sources and interconnected loads, which can operate independently or in parallel with the main grid. However, the high integration of DGs poses stability problems, particularly the frequency regulation under contingencies in the microgrid. For example, the shutdown of one generating unit or the reduction of system inertia owing to the high integration of converter-based DGs will increase the risk of instability of the microgrid and the main grid. Therefore, maintaining and increasing the frequency regulation capability is crucial in microgrid operation. This paper focuses on developing a controller for PV DG based on virtual inertia control combined with the conventional control method of a converter in order to regulate the microgrid frequency under contingency. The proposed control strategy for a PV-based DG is then verified through simulation of the 14-bus microgrid model using MATLAB/Simulink, showing regulation in frequency under island mode operation of the microgrid. In addition, comparisons between the original and proposed control strategy microgrid model are then carried out.
Finite Element and Vibration Frequency Analysis of Cracked Solid Beams: A Comparison of Iron, Steel, and Titanium Materials
Different solid materials are widely used in various constructions due to their availability and low cost. However, cracks or conversions in the structures can affect their stiffness and vibration signatures. This research aims to evaluate the load distribution, deformation, and the effects of the cracks on the natural frequencies and deformations of iron, steel, and titanium beams. A finite element-based model and COMSOL Multiphysics software were employed to measure and compare the frequencies and strengths of the beams. The results showed that the frequencies increased with the load, and titanium beams had the highest frequencies and deflections, while steel beams had the highest stress resistance. This frequency analysis can help to detect very small cracks (less than 0.05 mm) in the beams. The study concluded that steel is the most suitable material for construction due to its elasticity, availability, and low cost.
Soliton Solutions to the BA Model and (3 + 1)-Dimensional KP Equation Using Advanced -Expansion Scheme in Mathematical Physics
In this manuscript, the primary motivation is the implementation of the advanced -expansion method to construct the soliton solution, which contains some controlling parameters of two distinct equations via the Biswas–Arshed model and the (3 + 1)-dimensional Kadomtsev–Petviashvili equation. Here, the solutions’ behaviors are presented graphically under some conditions on those parameters. The height of the wave, wave direction, and angle of the obtained wave is formed by substituting the particular values of the considerations over showing figures with the control plot. With the collaboration of the advanced -expansion method, we construct entirely the solitary wave results as well as rogue type soliton, combined singular soliton, kink, singular kink, bright and dark soliton, periodic shape, double periodic shape soliton, etc. Therefore, it is remarkable to perceive that the advanced -expansion technique is a simple, viable, and numerical solid apparatus for clarifying careful outcomes to the other nonstraight equivalences.
Mathematical Analysis of the Impact of French Standardization Strategy and Electric Vehicle Development on the Breakthrough Development of EVs in China
The problems of operating range and costs are the two most critical bottlenecks restricting the extensive application of electric vehicles (EVs) in China and some other countries. There are also some prominent problems in China’s EVs, which lead to poor competitiveness of EVs compared with traditional internal combustion engine vehicles. This paper analyzes the key mathematical factors restricting the development and popularization of EVs in China from the aspects of strategic policy, sales situation, and self-problems. For the best-selling family cars in China, select the representative models with the same body structure, and make statistics on various parameters most concerned by consumers, establish a database through data statistics and analysis software. Through summarizing France’s standardization development strategy and relevant issues reflected by the development data of its EVs, this paper puts forward the hypothesis leading the development of EVs through standardization to enhance their competitiveness, gives the specific suggestions, and briefly analyzes the feasibility from the aspects of product situation. The research content of this paper provides a certain basis and ideas for the future research work.