Ms. Jiayi Hu Profile

Jiayi Hu

at Columbia Univ

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Proceedings Article | 29 November 2023 Paper

Nonlinear prediction models and cluster analysis for global plastic waste management

Jiayi Hu, Maoxu Wang, Xue Han

Proceedings Volume 12937, 129370M (2023) https://doi.org/10.1117/12.3013290

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Highlighted by durability and availability, plastic product has become an indispensable part from industry to our daily lives. However, the amount of plastic waste far exceeds the amount that humans can safely dispose of. Through Least Squares, our model estimates that the maximum level for plastic waste that can be mitigated is about 11.7 million tons by fitting the data from 1980 to 2015. In the following discussion, we take the situation of each country into account, amend the model results and obtain the conjecture that the amount of disposable plastic waste reduced to the environmentally safe level is 380 million tons. The attempt to achieve the goal affects people’s quality of life and job opportunities to some extent, but it will have great benefits to the ecological environment and human health. In our models, PCA is applied to calculate the Severity Index. To improve equity, we designed a model to categorize countries by their capability to dispose plastic waste. For unsupervised clustering, t-SNE is used to divide countries into three categories. The results make sense and offer policy makers the basis to distribute the burden to every country more reasonably. We strongly recommend that countries with higher income and waste disposal capacity (Category 1) help countries with weaker integrated capacity (Category 2) by investing funds and technology. For middle-income countries (Category 0) with great potential to contribute, we should encourage them to develop sustainable economies, although the rate of economic development may decline in the process.

Proceedings Article | 22 April 2022 Paper

Numerical methods and comparison for soliton solutions of the nonlinear Schrödinger equation

Jiayi Hu

Proceedings Volume 12163, 121631Q (2022) https://doi.org/10.1117/12.2628213

KEYWORDS: Solitons, Numerical analysis, Neodymium, Finite difference methods, Quantum mechanics, Particles, Elementary particles, Complex systems, Quantum physics, Physics

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The Schrödinger equation is a basic and key equation in quantum mechanics. In this thesis, we focus on the one-dimensional cubic-quintic nonlinear Schrödinger equation (CQNLSE). First, we introduce the general formulation of Schrödinger equation as well as some dynamic properties of the general nonlinear Schrödinger equation, including the mass and energy conservation. Second, we present four types of analytical solutions to the normalized CQNLSE and prove the conservation of energy of the CQNLSE. Third, we provide and analyze numerical methods, mainly finite difference methods and pseudo-spectral methods, for the CQNLSE under the zero far-field condition. Finally, we simulate the interaction of two bright solitons and dissect their condition and behavior before and after the collision.

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