Metastable states arise in a range of quantum systems and can be observed in various dynamical scenarios, including decay, bubble nucleation, and long-lived oscillations. The phenomenology of metastable states has bee...
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Estimating the rank of a corrupted data matrix is an important task in data analysis, most notably for choosing the number of components in PCA. Significant progress on this task was achieved using random matrix theor...
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We study the solutions of the one-phase supercooled Stefan problem with kinetic undercooling, which describes the freezing of a supercooled liquid, in one spatial dimension. Assuming that the initial temperature lies ...
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We report on an extensive study of the viscosity of liquid water at near-ambient conditions, performed within the Green-Kubo theory of linear response and equilibrium ab initio molecular dynamics (AIMD), based on dens...
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The development of powerful natural language models have increased the ability to learn meaningful representations of protein sequences. In addition, advances in high-throughput mutagenesis, directed evolution, and ne...
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Modeling fracture is computationally expensive even in computational simulations of two-dimensional problems. Hence, scaling up the available approaches to be directly applied to large components or systems crucial fo...
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Modeling fracture is computationally expensive even in computational simulations of two-dimensional problems. Hence, scaling up the available approaches to be directly applied to large components or systems crucial for real applications become challenging. In this work. we propose domain decomposition framework for the variational physics-informed neural networks to accurately approximate the crack path defined using the phase field approach. We show that coupling domain decomposition and adaptive refinement schemes permits to focus the numerical effort where it is most needed: around the zones where crack propagates. No a priori knowledge of the damage pattern is required. The ability to use numerous deep or shallow neural networks in the smaller subdomains gives the proposed method the ability to be parallelized. Additionally, the framework is integrated with adaptive non-linear activation functions which enhance the learning ability of the networks, and results in faster convergence. The efficiency of the proposed approach is demonstrated numerically with three examples relevant to engineering fracture mechanics. Upon the acceptance of the manuscript, all the codes associated with the manuscript will be made available on Github. Impact Statement—Machine learning techniques have been increasingly used for modeling of engineering problems. In particular, physics informed neural networks (PINNs) have been shown to be a promising approach for discretizing and solving partial differential equations. However, PINNs are best suited for smooth function approximations and have some difficulties dealing with discontinuities and rapidly changing gradients in the solution. Here, we propose a framework for the simulation of nucleation and propagation of cracks under brittle fracture using a subdomain-based phase-field approach. By subdividing the domain into smaller regions and considering an energy minimization formulation, the discontinuous displacements and singular stress
The surface of a three-dimensional topological insulator (TI) hosts two-dimensional massless Dirac fermions (DFs), the gapless and spin-helical nature of which yields many exotic phenomena, such as the immunity of top...
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Aworld-renowned expert on non-conforming finite elementmethods,***-Ci Shi,had left a lasting impact on the overarching development of Chinese computationalmathematics and scientific computing as well as computational...
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Aworld-renowned expert on non-conforming finite elementmethods,***-Ci Shi,had left a lasting impact on the overarching development of Chinese computationalmathematics and scientific computing as well as computationalmathematics worldwide through his tireless and visionary *** dedication to developing academic programs in many leading Chinese universities and institutions,along with his stewardship in establishing national computational research programs,played a fundamental role in elevating Chinese computational research status to a global *** generations of Chinese scholars benefited from his guidance and teaching,and this focused issue of original research contributions from 33 Chinese and international scientist teams bears witness to the profound influence of *** on their research careers by his lifetime of work spanning over six *** being an accomplished mathematician,*** had lived a life of a cultured man who radiated vigor and warmth,imbuing his life with heartiness,openness,and honesty.
Fast and accurate hourly forecasts of wind speed and power are crucial in quan-tifying and planning the energy budget in the electric grid. Modeling wind at a high resolution brings forth considerable challenges given...
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Quantum computers hold great promise for exact simulations of nuclear dynamical processes (e.g., scattering and reactions), which are paramount to the study of nuclear matter at the limit of stability and in the forma...
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