Wavetet transform was used to analyze the scaling law of temperature data (passive scalar) in Rayleigh-Bénard convection flow from two aspects. The first one was to utilize the method of extended self similarity,...Wavetet transform was used to analyze the scaling law of temperature data (passive scalar) in Rayleigh-Bénard convection flow from two aspects. The first one was to utilize the method of extended self similarity, presented first by Benzi et al., to study the scaling exponent of temperature data. The obtained results show that the inertial range is much wider than that one determined directly from the conventional structure function, and find the obtained scaling exponent agrees well with the one obtained from the temperature data in an experiment of wind tunnel. The second one was that, by extending the formula which was proposed by A. Arneodo et al. for extracting the scaling exponent ζ(q) of velocity data to temperature data, a newly defined formula which is also based on wavelet transform, and can determine the scaling exponent ξ(q) of temperature data was proposed. The obtained results demonstrate that by using the method which is named as WTMM (wavelet transform maximum modulus) ξ(q) correctly can be extracted.展开更多
The author of this paper once attempted to propose a unified framework for gauge fields based on the mathematical and physical picture of the principal fiber bundle: that is, to believe that our universe may have more...The author of this paper once attempted to propose a unified framework for gauge fields based on the mathematical and physical picture of the principal fiber bundle: that is, to believe that our universe may have more fundamental interactions than the four, and these fundamental gauge fields are only components on the bottom manifold (i.e. our universe) projected by a unified gauge potential of the principal fiber bundle manifold;these components can satisfy the transformation of gauge potential, or even be transformed from one basic interaction gauge potential to another basic interaction gauge potential, and can be summarized into a unified equation, namely the generalized gauge equation expression, corresponding to gauge transformation invariance;so the invariance of gauge transformation is a necessary condition for unified field theory, and the four (or more) fundamental interaction fields of the universe are unified in a unified gauge field defined by the connection on the principal fiber bundle. In this paper, the author continues to propose a model of large-scale (gravitational) fundamental interactions in the universe based on the mathematical and physical picture of the principal fiber bundle, attempting to explain that dark matter and dark energy are merely reflections of these gravitational fundamental interactions that deviate in intensity from the gravitational fundamental interactions of the solar system at galaxy scales or some cosmic scales which are much larger than the solar system. All these “gravitational” fundamental interactions originate from the unified gauge field of the universe, namely the connection or curvature on the principal fiber bundle. These interactions are their projected representations on the bottom manifold (i.e. our universe) by different cross-sections (gauge transformations). These projection representations of the universe certainly are described by the generalized gauge equation or curvature similarity equation, and under the guidance of curvature gauge transformation factors, oscillate and evolve between the curvatures 1→0→-1→0→1 of the universe.展开更多
Similarity measurement has been a prevailing research topic geographic information science.Geometric similarity measurement inin scaling transformation(GSM_ST)is critical to ensure spatial data quality while balancing...Similarity measurement has been a prevailing research topic geographic information science.Geometric similarity measurement inin scaling transformation(GSM_ST)is critical to ensure spatial data quality while balancing detailed information with distinctive features.However,GSM_ST is an uncertain problem due to subjective spatial cognition,global and local concerns,and geometric complexity.Traditional rule-based methods considering multiple consistent conditions require subjective adjustments to characteristics and weights,leading to poor robustness in addressing GSM_ST.This study proposes an unsupervised representation learning framework for automated GSM_ST,using a Graph Autoencoder Network(GAE)and drainage networks as an example.The framework involves constructing a drainage graph,designing the GAE architecture for GSM_ST,and using Cosine similarity to measure similarity based on the GAE-derived drainage embeddings in different scales.We perform extensive experiments and compare methods across 71 drainage networks duringfive scaling transformations.The results show that the proposed GAE method outperforms other methods with a satisfaction ratio of around 88%and has strong robustness.Moreover,our proposed method also can be applied to other scenarios,such as measuring similarity between geographical entities at different times and data from different datasets.展开更多
文摘Wavetet transform was used to analyze the scaling law of temperature data (passive scalar) in Rayleigh-Bénard convection flow from two aspects. The first one was to utilize the method of extended self similarity, presented first by Benzi et al., to study the scaling exponent of temperature data. The obtained results show that the inertial range is much wider than that one determined directly from the conventional structure function, and find the obtained scaling exponent agrees well with the one obtained from the temperature data in an experiment of wind tunnel. The second one was that, by extending the formula which was proposed by A. Arneodo et al. for extracting the scaling exponent ζ(q) of velocity data to temperature data, a newly defined formula which is also based on wavelet transform, and can determine the scaling exponent ξ(q) of temperature data was proposed. The obtained results demonstrate that by using the method which is named as WTMM (wavelet transform maximum modulus) ξ(q) correctly can be extracted.
文摘The author of this paper once attempted to propose a unified framework for gauge fields based on the mathematical and physical picture of the principal fiber bundle: that is, to believe that our universe may have more fundamental interactions than the four, and these fundamental gauge fields are only components on the bottom manifold (i.e. our universe) projected by a unified gauge potential of the principal fiber bundle manifold;these components can satisfy the transformation of gauge potential, or even be transformed from one basic interaction gauge potential to another basic interaction gauge potential, and can be summarized into a unified equation, namely the generalized gauge equation expression, corresponding to gauge transformation invariance;so the invariance of gauge transformation is a necessary condition for unified field theory, and the four (or more) fundamental interaction fields of the universe are unified in a unified gauge field defined by the connection on the principal fiber bundle. In this paper, the author continues to propose a model of large-scale (gravitational) fundamental interactions in the universe based on the mathematical and physical picture of the principal fiber bundle, attempting to explain that dark matter and dark energy are merely reflections of these gravitational fundamental interactions that deviate in intensity from the gravitational fundamental interactions of the solar system at galaxy scales or some cosmic scales which are much larger than the solar system. All these “gravitational” fundamental interactions originate from the unified gauge field of the universe, namely the connection or curvature on the principal fiber bundle. These interactions are their projected representations on the bottom manifold (i.e. our universe) by different cross-sections (gauge transformations). These projection representations of the universe certainly are described by the generalized gauge equation or curvature similarity equation, and under the guidance of curvature gauge transformation factors, oscillate and evolve between the curvatures 1→0→-1→0→1 of the universe.
基金supported by the National Natural Science Foundation of China[grant number 41531180]the National Natural Science Foundation of China[grant number 42071450]the China Scholarship Council(CSC)[grant number 202206270076].
文摘Similarity measurement has been a prevailing research topic geographic information science.Geometric similarity measurement inin scaling transformation(GSM_ST)is critical to ensure spatial data quality while balancing detailed information with distinctive features.However,GSM_ST is an uncertain problem due to subjective spatial cognition,global and local concerns,and geometric complexity.Traditional rule-based methods considering multiple consistent conditions require subjective adjustments to characteristics and weights,leading to poor robustness in addressing GSM_ST.This study proposes an unsupervised representation learning framework for automated GSM_ST,using a Graph Autoencoder Network(GAE)and drainage networks as an example.The framework involves constructing a drainage graph,designing the GAE architecture for GSM_ST,and using Cosine similarity to measure similarity based on the GAE-derived drainage embeddings in different scales.We perform extensive experiments and compare methods across 71 drainage networks duringfive scaling transformations.The results show that the proposed GAE method outperforms other methods with a satisfaction ratio of around 88%and has strong robustness.Moreover,our proposed method also can be applied to other scenarios,such as measuring similarity between geographical entities at different times and data from different datasets.
