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The phase diagram of a deep potential water model

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arXiv 2021年

作者： Zhang, Linfeng Wang, Han Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Beijing Institute of Big Data Research Beijing100871 China

Using the Deep Potential methodology, we construct a model that reproduces accurately the potential energy surface of the SCAN approximation of density functional theory for water, from low temperature and pressure to about 2400 K and 50 GPa, excluding the vapor stability region. The computational efficiency of the model makes it possible to predict its phase diagram using molecular dynamics. Satisfactory overall agreement with experimental results is obtained. The fluid phases, molecular and ionic, and all the stable ice polymorphs, ordered and disordered, are predicted correctly, with the exception of ice III and XV that are stable in experiments, but metastable in the model. The evolution of the atomic dynamics upon heating, as ice VII transforms first into ice VII′′ and then into an ionic fluid, reveals that molecular dissociation and breaking of the ice rules coexist with strong covalent fluctuations, explaining why only partial ionization was inferred in experiments. © 2021, CC BY-NC-ND.

关键词： Phase diagrams

Energy stability of the Charney-DeVore quasi-geostrophic equation for atmospheric blocking

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arXiv 2021年

作者： Chen, Zhi-Min Xiong, Xiangming School of Mathematics and Statistics Shenzhen University Shenzhen518060 China The Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Charney and DeVore [J. Atmos. Sci. 36 (1979), 1205-1216] found multiple equilibrium states as a consequence of bottom topography in their pioneering work on the quasi-geostrophic barotropic flow over topography in a β-plane channel. In the present paper, we prove that the basic flow is asymptotically stable in a parameter region, including the flat topography situation, which excludes the existence of multiple equilibrium states therein. Moreover, we show that an additional condition on the average zonal force or the average zonal velocity is indispensable to the well-posedness of the Charney–DeVore quasi-geostrophic equation. Coexistence of at least three equilibrium states is confirmed by a pseudo-arclength continuation method for different topographic amplitudes. The stabilities of the equilibrium states are examined by high-resolution direct numerical simulations. © 2021, CC BY-NC-ND.

关键词： Astrophysics

Can One Hear the Shape of a Crystal?

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arXiv 2025年

作者： Wang, Haina Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics PrincetonNJ08544 United States

Isospectrality is a general fundamental concept often involving whether various operators can have identical spectra, i.e., the same set of eigenvalues. In the context of the Laplacian operator, the famous question "Can one hear the shape of a drum?" concerns whether different shaped drums can have the same vibrational modes. The isospectrality of a lattice in d-dimensional Euclidean space Rd is a tantamount to whether it is uniquely determined by its theta series, i.e., the radial distribution function g2(r). While much is known about the isospectrality of Bravais lattices across dimensions, little is known about this question of more general crystal (periodic) structures with an n-particle basis (n ≥ 2). Here, we ask, What is nmin(d), the minimum value of n for inequivalent (i.e., unrelated by isometric symmetries) crystals with the same theta function in space dimension d? To answer these questions, we use rigorous methods as well as a precise numerical algorithm that enables us to determine the minimum multi-particle basis of inequivalent isospectral crystals. Our algorithm identifies isospectral 4-, 3- and 2-particle bases in one, two and three spatial dimensions, respectively. For many of these isospectral crystals, we rigorously show that they indeed possess identical g2(r) up to infinite r. Based on our analyses, we conjecture that nmin(d) = 4, 3, 2 for d = 1, 2, 3, respectively. The identification of isospectral crystals enables one to study the degeneracy of the ground-state under the action of isotropic pair potentials. Indeed, using inverse statistical-mechanical techniques, we find an isotropic pair potential whose low-temperature configurations in two dimensions obtained via simulated annealing can lead to both of two isospectral crystal structures with n = 3, the proportion of which can be controlled by the cooling rate. Our findings provide general insights into the structural and ground-state degeneracies of crystal structures as determined by radia

关键词： Eigenvalues and eigenfunctions

Ground state phases of the two-dimension electron gas with a unified variational approach

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arXiv 2024年

作者： Smith, Conor Chen, Yixiao Levy, Ryan Yang, Yubo Morales, Miguel A. Zhang, Shiwei Center for Computational Quantum Physics Flatiron Institute New YorkNY10010 United States Department of Electrical and Computer Engineering University of New Mexico AlbuquerqueNM87131 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The two-dimensional electron gas (2DEG) is a fundamental model, which is drawing increasing interest because of recent advances in experimental and theoretical studies of 2D materials. Current understanding of the ground state of the 2DEG relies on quantum Monte Carlo calculations, based on variational comparisons of different ansatze for different phases. We use a single variational ansatz, a general backflow-type wave function using a message-passing neural quantum state architecture, for a unified description across the entire density range. The variational optimization consistently leads to lower ground-state energies than previous best results. Transition into a Wigner crystal (WC) phase occurs automatically at rs = 37±1, a density lower than currently believed. Between the liquid and WC phases, the same ansatz and variational search strongly suggest the existence of intermediate states in a broad range of densities, with enhanced short-range nematic spin correlations. Copyright © 2024, The Authors. All rights reserved.

关键词： Message passing

HiPoNet: A Topology-Preserving Multi-View Neural Network For High Dimensional Point Cloud and Single-Cell Data

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arXiv 2025年

作者： Viswanath, Siddharth Madhu, Hiren Bhaskar, Dhananjay Kovalic, Jake Johnson, Dave Ying, Rex Tape, Christopher Adelstein, Ian Perlmutter, Michael Krishnaswamy, Smita Department of Computer Science Yale University New Haven United States Department of Genetics Yale University New Haven United States Department of Applied Physics Yale University New Haven United States Program in Computing Boise State University Idaho United States Cell Communication Lab Department of Oncology University College London Cancer Institute London United Kingdom Department of Mathematics Yale University New Haven United States Department of Mathematics Boise State University Idaho United States Computational Biology and Bioinformatics Program Yale University New Haven United States Wu-Tsai Institute Yale University New Haven United States Program for Applied Math Yale University New Haven United States

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Single-cell data can have high dimensionality exceeding the capabilities of existing methods for point clouds which are tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e. one on every patient), necessitating models that can process large, high-dimensional point clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric information. In contrast, HiPoNet forms higher-order simplicial complexes through learnable feature reweighting, generating multiple data views that disentangle distinct biological processes. It then employs simplicial wavelet transforms to extract multiscale features—capturing both local and global topology. We empirically show that these components preserve topological information in the learned representations, and that HiPoNet significantly outperforms state-of-the-art point-cloud and graph-based models on single cell. We also show an application of HiPoNet on spatial transcriptomics datasets using spatial co-ordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis. © 2025, CC BY.

关键词： Network topology

NOMAD: Nonlinear Manifold Decoders for Operator Learning

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arXiv 2022年

作者： Seidman, Jacob H. Kissas, Georgios Perdikaris, Paris Pappas, George J. Graduate Program in Applied Mathematics and Computational Science University of Pennsylvania United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania United States Department of Electrical and Systems Engineering University of Pennsylvania United States

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps (operators) between infinite dimensional function spaces, these models are able to learn discretization invariant representations of target functions. A common approach is to represent such target functions as linear combinations of basis elements learned from data. However, there are simple scenarios where, even though the target functions form a low dimensional submanifold, a very large number of basis elements is needed for an accurate linear representation. Here we present NOMAD, a novel operator learning framework with a nonlinear decoder map capable of learning finite dimensional representations of nonlinear submanifolds in function spaces. We show this method is able to accurately learn low dimensional representations of solution manifolds to partial differential equations while outperforming linear models of larger size. Additionally, we compare to state-of-the-art operator learning methods on a complex fluid dynamics benchmark and achieve competitive performance with a significantly smaller model size and training cost. © 2022, CC BY-NC-SA.

关键词： Benchmarking

Earthquake relocation to understand the megathrust segments along the Sumatran subduction zone 12

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Earthquake relocation to understand the megathrust segments ...

12th ACEH International Workshop on Sustainable Tsunami Disaster Recovery: Sharing Experience, Knowledge and Culture 2019, AIWEST-DR 2019

作者： Jihad, Abdi Muksin, Umar Syamsidik Ramli, Marwan Doctoral Program of Mathematics and Applied Sciences Universitas Syiah Kuala Banda Aceh Indonesia Geophysical of Aceh Besar Station Meteorological Climatological And Geophysical Agency BMKG Roadway Aceh23352 Indonesia Universitas Syiah Kuala Indonesia

Historical seismicity shows the presence of mega-thrust segments along the Sumatran subduction zone that could generate large earthquakes. The segments include the Aceh-Andaman, Nias-Seumeuleu, Batu, Siberut, Mentawai-Pagai, Enggano, and Sunda Strait. Shallow and large earthquakes with magnitudes larger than 7.5 can occur along the segments thus trigger tsunamis. The accurate seismicity distribution along the subduction zone can be used to characterize the segments. The objective of the research is to precisely relocate the earthquakes in order to investigate the properties of the Sumatran subduction zone. Among more than 5000 preliminary located earthquakes occurring in 1980-2018 obtained from the Indonesian Agency for Geophysics (BMKG), only earthquakes with azimuthal gap angle less than 180 and recorded by at least 4 stations are used in the data analysis. We applied double difference method in order to relocate the seismic events. The result shows a zone with significantly less earthquakes along the subduction in West Aceh interpreted as a seismic gap zone. This zone is expected to accumulate energy which could be released in the form of a large earthquake. The new earthquake locations mimic shallower Sumatran subduction zone further north therefore closer to people inland. The closer earthquake the higher intensity of an earthquake felt by people which higher level of hazard. The pattern of the subduction zone derived from the relocated seismicity can be used as better source information for tsunami modeling. © 2021 Institute of Physics Publishing. All rights reserved.

关键词： Earthquakes

Angklung Smart Band: An IoT-Based System to Support Music Activities for Elderly in Thailand

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Angklung Smart Band: An IoT-Based System to Support Music Ac...

2022 IEEE European Technology and Engineering Management Summit, E-TEMS 2022

作者： Hiranpanthaporn, Saranya Phoasavadi, Pornprapit Cooharojananone, Nagul Technopreneurship and Innovation Management Program Graduate School Chulalongkorn University Bangkok Bangkok Thailand Emili Sagol Creative Arts Research and Innovation for Well-being Center Chulalongkorn University Faculty of Fine and Applied Arts Department of Thai Music Bangkok Bangkok Thailand Chulalongkorn University Faculty of Science Department of Mathematics and Computer Science Bangkok Bangkok Thailand

ISBN: (数字)9781665411004

ISBN: (纸本)9781665411004

Organizing music activities for the elderly is another way that supports their well-being. Angklung, an Indonesian musical instrument, has been used for music activities for the elderly in Thailand with the hand signs method. Unfortunately, music activity is not widely used because the experts with the hand sign skills are few and not enough for demanding in the aging healthcare. At the same time, technologies of remote systems using the Internet of Things (IoT) have been developed to assist the elderly in supporting and improving their quality of life. This paper will introduce 'Angklung Smart Band,' an IoT-based system to support Angklung music activities for the elderly in Thailand. This work aims at setting up Angklung music activities for the elderly by using technology instead of hand signs. The system is composed of a web application, IoT devices, and Angklung musical instruments connected together via a wireless network. We did a preliminary study with the experts to improve experiences and system performance. After that, we asked the music experts to use the smart band to conduct the music activities experiment with the elderly for three days and give us feedback. The results found that the smart band could assist the Angklung music experts and help with the shortage of music expertise in aged care facilities or nursing homes. © 2022 IEEE.

关键词： Music

Preconditioning hyperbolic 5-equation two-phase model in intermittent pipe flow simulations

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AIP Conference Proceedings 2024年第1期3094卷

作者： Farhad Nikfarjam Hamid Reza Anbarlooei Daniel O. A. Cruz Department of Applied Mathematics Institute of Mathematics Federal University of Rio de Janeiro RJ Brazil Mechanical Engineering Program Institute of Mathematics Federal University of Rio de Janeiro RJ Brazil

The 5-equation unconditionally hyperbolic formulation of the two-fluid model solved by Roe’s method is studied. It is well-known that the 5-equation upwind methods experience loss of accuracy at low Mach numbers. To address this issue, a preconditioning technique is developed to control the numerical dissipation at low velocities. The resulting method is evaluated on different test cases, and is observed that the preconditioned first order Roe method limits the numerical dissipation, comparable to the second order method without preconditioning. The method is used to study 1D intermittent two-phase flow in pipelines. Our method successfully captures the slugs and predicts the statistics of the flow accurately, for the cases where other methods could not capture a slug flow at all or have serious shortcomings.

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