The study investigated Taylor vortex flow between rotating double cylinders using a convolutional neural network (CNN). By combining numerical results of vortex flow for specific periods after vortex onset, the resear...The study investigated Taylor vortex flow between rotating double cylinders using a convolutional neural network (CNN). By combining numerical results of vortex flow for specific periods after vortex onset, the researchers aimed to determine if mode discrimination was possible in the combined images. They used images taken at various intervals: 20 images at 1 second, 30 images at 1.5 seconds, 40 images at 2 seconds, 50 images at 2.5 seconds, 60 images at 3 seconds, and 67 images at 3.35 seconds after vortex onset. The goal was to compare the accuracy rates in predicting the mode development process of the vortex. The study concluded that the mode development process of the Taylor vortex can be discriminated by combining images taken at specific time intervals after the vortex occurs and training the CNN with these images as teacher data. The results showed that the most efficient prediction of the mode development process was achieved when 50 images taken at 2.5 seconds were used for learning. This highlights the potential of using CNNs in fluid dynamics research, specifically in analyzing and predicting the behavior of vortex flows.展开更多
To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’...To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.展开更多
文摘The study investigated Taylor vortex flow between rotating double cylinders using a convolutional neural network (CNN). By combining numerical results of vortex flow for specific periods after vortex onset, the researchers aimed to determine if mode discrimination was possible in the combined images. They used images taken at various intervals: 20 images at 1 second, 30 images at 1.5 seconds, 40 images at 2 seconds, 50 images at 2.5 seconds, 60 images at 3 seconds, and 67 images at 3.35 seconds after vortex onset. The goal was to compare the accuracy rates in predicting the mode development process of the vortex. The study concluded that the mode development process of the Taylor vortex can be discriminated by combining images taken at specific time intervals after the vortex occurs and training the CNN with these images as teacher data. The results showed that the most efficient prediction of the mode development process was achieved when 50 images taken at 2.5 seconds were used for learning. This highlights the potential of using CNNs in fluid dynamics research, specifically in analyzing and predicting the behavior of vortex flows.
文摘To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.
