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Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…

经典物理 · 物理学 2025-07-14 Sergej Pankratow

The design of functional materials with desired properties is essential in driving technological advances in areas like energy storage, catalysis, and carbon capture. Generative models provide a new paradigm for materials design by directly…

Machine learning has been increasingly applied in climate modeling on system emulation acceleration, data-driven parameter inference, forecasting, and knowledge discovery, addressing challenges such as physical consistency, multi-scale…

The Mat\'ern model has been a cornerstone of spatial statistics for more than half a century. More recently, the Mat\'ern model has been central to disciplines as diverse as numerical analysis, approximation theory, computational…

统计理论 · 数学 2023-03-07 Emilio Porcu , Moreno Bevilacqua , Robert Schaback , Chris J. Oates

Machine learning force fields have emerged as promising tools for molecular dynamics (MD) simulations, potentially offering quantum-mechanical accuracy with the efficiency of classical MD. Inspired by foundational large language models,…

计算物理 · 物理学 2025-11-14 Denan Li , Jiyuan Yang , Xiangkai Chen , Lintao Yu , Shi Liu

Molecular machines consist of either a single protein or a macromolecular complex composed of protein and RNA molecules. Just like their macroscopic counterparts, each of these nano-machines has an engine that "transduces" input energy into…

生物物理 · 物理学 2012-03-15 Debashish Chowdhury

Materials design and development typically takes several decades from the initial discovery to commercialization with the traditional trial and error development approach. With the accumulation of data from both experimental and…

材料科学 · 物理学 2017-07-18 Xiaojiao Yu

In this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The fibers are explicitly modeled with highly…

计算工程、金融与科学 · 计算机科学 2023-08-25 Ivo Steinbrecher , Matthias Mayr , Maximilian J. Grill , Johannes Kremheller , Christoph Meier , Alexander Popp

Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…

凝聚态物理 · 物理学 2007-05-23 Boris Neubert , Michel Pleimling , Rolf Siems

Atomistic or ab-initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such…

Despite the intense activity at the electronic and atomistic resolutions, coarse grained (CG) modeling of MOFs remains largely unexplored. One of the main reasons for this is the lack of adequate CG force fields. In this work, we present…

材料科学 · 物理学 2023-12-11 Cecilia M. S. Alvares , Rocio Semino

The Majorana neutrino mass matrix combines information from the neutrino masses and the leptonic mixing in the flavor basis. Its invariance under some transformation matrices indicates the existence of certain residual symmetry. We offer an…

高能物理 - 唯象学 · 物理学 2015-06-15 Xinyi Zhang , Bo-Qiang Ma

Granular materials -- aggregates of many discrete, disconnected solid particles -- are ubiquitous in natural and industrial settings. Predictive models for their behavior have wide ranging applications, e.g. in defense, mining,…

软凝聚态物质 · 物理学 2023-09-01 Aaron S. Baumgarten , Justin Moreno , Brett Kuwik , Sohanjit Ghosh , Ryan Hurley , K. T. Ramesh

Data-driven techniques have a large potential to transform and accelerate the chemical sciences. However, chemical sciences also pose the unique challenge of very diverse, small, fuzzy datasets that are difficult to leverage in conventional…

Over the past seven years, full-field analyses of a wide range of classical as well as modern quasi-static fracture experiments on nominally elastic brittle materials -- ranging from hard ceramics to soft elastomers -- have repeatedly…

材料科学 · 物理学 2024-11-26 Yangyuanchen Liu , Oscar Lopez-Pamies , John E. Dolbow

Developing physics-based models for molecular simulation requires fitting many unknown parameters to diverse experimental datasets. Traditionally, this process is piecemeal and difficult to reproduce, leading to a fragmented landscape of…

生物物理 · 物理学 2025-04-10 Ryan K. Krueger , Megan C. Engel , Ryan Hausen , Michael P. Brenner

Over the past decade inter-atomic potentials based on machine-learning (ML) techniques have become an indispensable tool in the atomic-scale modeling of materials. Trained on energies and forces obtained from electronic-structure…

材料科学 · 物理学 2022-08-15 Michele Ceriotti

Machine learning models of vastly different modalities and architectures are being trained to predict the behavior of molecules, materials, and proteins. However, it remains unclear whether they learn similar internal representations of…

机器学习 · 计算机科学 2025-12-04 Sathya Edamadaka , Soojung Yang , Ju Li , Rafael Gómez-Bombarelli

In recent years, the use of Machine Learning (ML) in computational chemistry has enabled numerous advances previously out of reach due to the computational complexity of traditional electronic-structure methods. One of the most promising…

The formalism of the models with Petri networks provides a sound theoretical base, supported by powerful mathematical methods able to extract information necessary for the formalism and simulation of the real system that provides features…

其他计算机科学 · 计算机科学 2009-03-26 Alexandra Emilia Fortis