Construction of geodesics on Teichm\"uller spaces of Riemann surfaces with Z\mathbb Z action

Teichm\"uller space $\mathrm{Teich}(R)$ of a Riemann surface $R$ is a deformation space of $R$. In this paper, we prove a sufficient condition for extremality of the Beltrami coefficients when $R$ has the $\mathbb Z$ action. As an application, we discuss the construction of geodesics. Earle-Kra-Krushka\'l proved that the necessary and sufficient conditions for the geodesics connecting $[0]$ and $[\mu]$ to be unique are $\| \mu_0 \|_{\infty} = | \mu_0 | ( z )$ (a.e.$z$) and ``unique extremality''. As a byproduct of our results, we show that we cannot exclude ``unique extremality''.To show the above claim, we construct a point $[\mu_0]$ in $\mathrm{Teich}(\mathbb C \setminus \mathbb Z)$, satisfying $\| \mu_0 \|_{\infty} = | \mu_0 | ( z )$ (a.e.$z$) and there exists a family of geodesics $\{ \gamma_\lambda \} _{\lambda \in D}$ connecting $[0]$ and $[\mu_0]$ with complex analytic parameter, where $D$ is an open set in $l^{\infty}$.Comment: 16 page

Sound field decomposition based on two-stage neural networks

A method for sound field decomposition based on neural networks is proposed. The method comprises two stages: a sound field separation stage and a single-source localization stage. In the first stage, the sound pressure at microphones synthesized by multiple sources is separated into one excited by each sound source. In the second stage, the source location is obtained as a regression from the sound pressure at microphones consisting of a single sound source. The estimated location is not affected by discretization because the second stage is designed as a regression rather than a classification. Datasets are generated by simulation using Green's function, and the neural network is trained for each frequency. Numerical experiments reveal that, compared with conventional methods, the proposed method can achieve higher source-localization accuracy and higher sound-field-reconstruction accuracy.Comment: 31 pages, 16 figure

Josephson Plasma Mode in Fields Parallel to Layers of Bi_2Sr_2CaCu_2O_{8+\delta}

Josephson plasma resonance measurements under magnetic fields parallel to the CuO_2 layers as functions of magnetic field, temperature, and microwave frequency have been performed in Bi_2Sr_2CaCu_2O_{8+\delta} single crystals with doping range being from optimal to under-doped side. The feature of the resonance is quite unique and cannot be explained by the conventional understandings of the Josephson plasma for H \parallel c, that requires a new theory including coupling effect between Josephson vortex lattice and Josephson plasma.Comment: 2 pages, 2 figure

Super-Resolution Simulation for Real-Time Prediction of Urban Micrometeorology

We propose a super-resolution (SR) simulation system that consists of a physics-based meteorological simulation and an SR method based on a deep convolutional neural network (CNN). The CNN is trained using pairs of high-resolution (HR) and low-resolution (LR) images created from meteorological simulation results for different resolutions so that it can map LR simulation images to HR ones. The proposed SR simulation system, which performs LR simulations, can provide HR prediction results in much shorter operating cycles than those required for corresponding HR simulation prediction system. We apply the SR simulation system to urban micrometeorology, which is strongly affected by buildings and human activity. Urban micrometeorology simulations that need to resolve urban buildings are computationally costly and thus cannot be used for operational real-time predictions even when run on supercomputers. We performed HR micrometeorology simulations on a supercomputer to obtain datasets for training the CNN in the SR method. It is shown that the proposed SR method can be used with a spatial scaling factor of 4 and that it outperforms conventional interpolation methods by a large margin. It is also shown that the proposed SR simulation system has the potential to be used for operational urban micrometeorology predictions

Three-Dimensional Super-Resolution of Passive-Scalar and Velocity Distributions Using Neural Networks for Real-Time Prediction of Urban Micrometeorology

In future cities, micrometeorological predictions will be essential to various services such as drone operations. However, the real-time prediction is difficult even by using a super-computer. To reduce the computation cost, super-resolution (SR) techniques can be utilized, which infer high-resolution images from low-resolution ones. The present paper confirms the validity of three-dimensional (3D) SR for micrometeorology prediction in an urban city. A new neural network is proposed to simultaneously super-resolve 3D temperature and velocity fields. The network is trained using the micrometeorology simulations that incorporate the buildings and 3D radiative transfer. The error of the 3D SR is sufficiently small: 0.14 K for temperature and 0.38 m s-1for velocity. The computation time of the 3D SR is negligible, implying the feasibility of real-time predictions for the urban micrometeorology

Super-Resolution of Three-Dimensional Temperature and Velocity for Building-Resolving Urban Micrometeorology Using Physics-Guided Convolutional Neural Networks with Image Inpainting Techniques

Atmospheric simulations for urban cities can be computationally intensive because of the need for high spatial resolution, such as a few meters, to accurately represent buildings and streets. Deep learning has recently gained attention across various physical sciences for its potential to reduce computational cost. Super-resolution is one such technique that enhances the resolution of data. This paper proposes a convolutional neural network (CNN) that super-resolves instantaneous snapshots of three-dimensional air temperature and wind velocity fields for urban micrometeorology. This super-resolution process requires not only an increase in spatial resolution but also the restoration of missing data caused by the difference in the building shapes that depend on the resolution. The proposed CNN incorporates gated convolution, which is an image inpainting technique that infers missing pixels. The CNN performance has been verified via supervised learning utilizing building-resolving micrometeorological simulations around Tokyo Station in Japan. The CNN successfully reconstructed the temperature and velocity fields around the high-resolution buildings, despite the missing data at lower altitudes due to the coarseness of the low-resolution buildings. This result implies that near-surface flows can be inferred from flows above buildings. This hypothesis was assessed via numerical experiments where all input values below a certain height were made missing. This research suggests the possibility that building-resolving micrometeorological simulations become more practical for urban cities with the aid of neural networks that enhance computational efficiency