Homoclinic orbits in the Euler problem of two fixed centers
We give a complete description of the shapes and the behavior of all homoclinic orbits in the Euler problem of two fixed centers.
math.SG↗
arXiv subjects
Seongchan Kim
Publications and source records attributed to Seongchan Kim.
On a convex embedding of the Euler problem of two fixed centers
In this article, we study a convex embedding for the Euler problem of two fixed centers for energies below the critical energy level. We prove that the doubly-covered elliptic coordinates provide a 2-to-1 symplectic embedding such that the image of the bounded component near the lighter primary of the regularized Euler problem is convex for any energy below the critical Jacobi energy. This holds true if the two primaries have the equal mass, but does not holds near the heavier body.
math.SG↗
PSIque: Next Sequence Prediction of Satellite Images using a Convolutional Sequence-to-Sequence Network
Predicting unseen weather phenomena is an important issue for disaster management. In this paper, we suggest a model for a convolutional sequence-to-sequence autoencoder for predicting undiscovered weather situations from previous satellite images. We also propose a symmetric skip connection between encoder and decoder modules to produce more comprehensive image predictions. To examine our model performance, we conducted experiments for each suggested model to predict future satellite images from historical satellite images. A specific combination of skip connection and sequence-to-sequence autoencoder was able to generate closest prediction from the ground truth image.
cs.CV↗
DeepRain: ConvLSTM Network for Precipitation Prediction using Multichannel Radar Data
Accurate rainfall forecasting is critical because it has a great impact on people's social and economic activities. Recent trends on various literatures show that Deep Learning (Neural Network) is a promising methodology to tackle many challenging tasks. In this study, we introduce a brand-new data-driven precipitation prediction model called DeepRain. This model predicts the amount of rainfall from weather radar data, which is three-dimensional and four-channel data, using convolutional LSTM (ConvLSTM). ConvLSTM is a variant of LSTM (Long Short-Term Memory) containing a convolution operation inside the LSTM cell. For the experiment, we used radar reflectivity data for a two-year period whose input is in a time series format in units of 6 min divided into 15 records. The output is the predicted rainfall information for the input data. Experimental results show that two-stacked ConvLSTM reduced RMSE by 23.0% compared to linear regression.
cs.LG↗
GlobeNet: Convolutional Neural Networks for Typhoon Eye Tracking from Remote Sensing Imagery
Advances in remote sensing technologies have made it possible to use high-resolution visual data for weather observation and forecasting tasks. We propose the use of multi-layer neural networks for understanding complex atmospheric dynamics based on multichannel satellite images. The capability of our model was evaluated by using a linear regression task for single typhoon coordinates prediction. A specific combination of models and different activation policies enabled us to obtain an interesting prediction result in the northeastern hemisphere (ENH).
cs.NE↗
Dynamical convexity of the Euler problem of two fixed centers
We give thorough analysis for the rotation functions of the critical orbits from which one can understand bifurcations of periodic orbits. Moreover, we give explicit formulas of the Conley-Zehnder indices of the interior and exterior collision orbits and show that the universal cover of the regularized energy hypersurface of the Euler problem is dynamically convex for energies below the critical Jacobi energy.
math.SG↗