A Class of Embedded DG Methods for Dirichlet Boundary Control of Convection Diffusion PDEs

We investigated an hybridizable discontinuous Galerkin (HDG) method for a convection diffusion Dirichlet boundary control problem in our earlier work [SIAM J. Numer. Anal. 56 (2018) 2262-2287] and obtained an optimal convergence rate for the control under some assumptions on the desired state and the domain. In this work, we obtain the same convergence rate for the control using a class of embedded DG methods proposed by Nguyen, Peraire and Cockburn [J. Comput. Phys. vol. 302 (2015), pp. 674-692] for simulating fluid flows. Since the global system for embedded DG methods uses continuous elements, the number of degrees of freedom for the embedded DG methods are smaller than the HDG method, which uses discontinuous elements for the global system. Moreover, we introduce a new simpler numerical analysis technique to handle low regularity solutions of the boundary control problem. We present some numerical experiments to confirm our theoretical results

Removal Effects on Nitrogen, Phosphorus and COD in Water Body of Shanghu Lake Ecological Wetland in Taihu Lake Watershed

AbstractShanghu ecological lake wetland is mostly made up of woody plants. So far, its removal effects on nitrogen and phosphorus are unknown. The removal effects on TN, TP, AmmN and COD in wastewater of Shanghu lake wetland were studied from July, 2008 to May, 2009. The relationship between removal effects on pollutants and temperatures of water body was studied too.192 samples were collected from input point, output point, and 6 points in water body. The results show that the wetland has always a good removal effect on TN, TP and AmmN under different water temperature, the water temperature has influence on removal effects to various extents. First report to removal effects on nitrogen and phosphorus of Shanghu lake wetland and woody plants wetland in China

First order least squares method with weakly imposed boundary condition for convection dominated diffusion problems

We present and analyze a first order least squares method for convection dominated diffusion problems, which provides robust L2 a priori error estimate for the scalar variable even if the given data f in L2 space. The novel theoretical approach is to rewrite the method in the framework of discontinuous Petrov - Galerkin (DPG) method, and then show numerical stability by using a key equation discovered by J. Gopalakrishnan and W. Qiu [Math. Comp. 83(2014), pp. 537-552]. This new approach gives an alternative way to do numerical analysis for least squares methods for a large class of differential equations. We also show that the condition number of the global matrix is independent of the diffusion coefficient. A key feature of the method is that there is no stabilization parameter chosen empirically. In addition, Dirichlet boundary condition is weakly imposed. Numerical experiments verify our theoretical results and, in particular, show our way of weakly imposing Dirichlet boundary condition is essential to the design of least squares methods - numerical solutions on subdomains away from interior layers or boundary layers have remarkable accuracy even on coarse meshes, which are unstructured quasi-uniform

Identification of precipitation onset based on Cloudsat observations

AbstractObservations of cloud vertical structure by Cloud Profiling Radar on CloudSat satellite provide a unique opportunity to globally identify the onset of precipitation. In this study, based on a conceptual model for an adiabatic cloud, a new method to determine the onset of precipitation in marine warm clouds is developed. The new method uses the slope of radar reflectivities near the cloud top, which gradually reverses its signs as drizzle occurs. By analyzing multiyear CloudSat data, it is found that globally the radar reflectivity threshold for precipitation onset varies from −18 to −13dBZ with an average value of −16dBZ. The corresponding liquid water path threshold for precipitation onset is also studied by analyzing satellite microwave observations collocated with CloudSat data. Results show that the liquid water path threshold is 190gm−2 as a global mean, varying from 150 to over 300gm−2 depending on regions

Neural Vector Fields: Generalizing Distance Vector Fields by Codebooks and Zero-Curl Regularization

Recent neural networks based surface reconstruction can be roughly divided into two categories, one warping templates explicitly and the other representing 3D surfaces implicitly. To enjoy the advantages of both, we propose a novel 3D representation, Neural Vector Fields (NVF), which adopts the explicit learning process to manipulate meshes and implicit unsigned distance function (UDF) representation to break the barriers in resolution and topology. This is achieved by directly predicting the displacements from surface queries and modeling shapes as Vector Fields, rather than relying on network differentiation to obtain direction fields as most existing UDF-based methods do. In this way, our approach is capable of encoding both the distance and the direction fields so that the calculation of direction fields is differentiation-free, circumventing the non-trivial surface extraction step. Furthermore, building upon NVFs, we propose to incorporate two types of shape codebooks, \ie, NVFs (Lite or Ultra), to promote cross-category reconstruction through encoding cross-object priors. Moreover, we propose a new regularization based on analyzing the zero-curl property of NVFs, and implement this through the fully differentiable framework of our NVF (ultra). We evaluate both NVFs on four surface reconstruction scenarios, including watertight vs non-watertight shapes, category-agnostic reconstruction vs category-unseen reconstruction, category-specific, and cross-domain reconstruction

The Application of Carbon Footprint Analysis in Hunan Province

Based on interpreting carbon footprint’s definition and its effecting factors, making positive analyses by using the data of cities in Hunan Province from 2005 to 2009, this paper constructs the calculating model of carbon footprint and analyses the relationship between carbon footprint and population, economy development level, industrial structure and energy structure. Meanwhile, on the basis of above analyses, this paper puts forward effective ways to advance the low-carbon development of Hunan Province from four aspects

Neural Vector Fields: Implicit Representation by Explicit Learning

Deep neural networks (DNNs) are widely applied for nowadays 3D surface reconstruction tasks and such methods can be further divided into two categories, which respectively warp templates explicitly by moving vertices or represent 3D surfaces implicitly as signed or unsigned distance functions. Taking advantage of both advanced explicit learning process and powerful representation ability of implicit functions, we propose a novel 3D representation method, Neural Vector Fields (NVF). It not only adopts the explicit learning process to manipulate meshes directly, but also leverages the implicit representation of unsigned distance functions (UDFs) to break the barriers in resolution and topology. Specifically, our method first predicts the displacements from queries towards the surface and models the shapes as \textit{Vector Fields}. Rather than relying on network differentiation to obtain direction fields as most existing UDF-based methods, the produced vector fields encode the distance and direction fields both and mitigate the ambiguity at "ridge" points, such that the calculation of direction fields is straightforward and differentiation-free. The differentiation-free characteristic enables us to further learn a shape codebook via Vector Quantization, which encodes the cross-object priors, accelerates the training procedure, and boosts model generalization on cross-category reconstruction. The extensive experiments on surface reconstruction benchmarks indicate that our method outperforms those state-of-the-art methods in different evaluation scenarios including watertight vs non-watertight shapes, category-specific vs category-agnostic reconstruction, category-unseen reconstruction, and cross-domain reconstruction. Our code is released at https://github.com/Wi-sc/NVF.Comment: Accepted by CVPR2023. Video: https://www.youtube.com/watch?v=GMXKoJfmHr

The Roles of Social Capital in Online P2P Lending Markets Under Different Cultures: A Comparison of China and America

Online P2P (People-to-People or Peer-to-Peer) lending has very rapid development since it was appeared in 2005. In order to mitigate asymmetric information between borrowers and lenders, some online P2P market allows members building their social networks (such as Prosper, CommunityLend, PPDai etc). By empirical analyzing the transaction data of Prosper (largest P2P market in US) and PPDai (largest P2P market in China), the paper verifies that the social capital systems have a positive influence on borrower’s loan performance on the markets. However, on both markets, the loan interest rate mainly dependents on borrower’s hard information rather than their social capital. Furthermore, it concludes that borrower’ social network in PPDai is much more useful and effective than in Prosper by comparing the empirical results, which could be helpful for the credit system development of Chinese online P2P lending markets based on the conclusions

Research and Development of Carbon Footprint Analysis In Hunan Province

AbstractBased on the definition of carbon footprint and elements that affect it, a model was constructed for empirical research, using data of cities in Hunan Province from 2005 to 2009, to calculate the amount of carbon footprint and to analyze the relationships between carbon footprint and each of the elements, including population, level of economic development, industrial structure and energy structure. In addition, this paper also puts forward solutions to further low-carbon development of Hunan Province in the areas of low-carbon development mechanism energy structure low carbon life style and talent development