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Translation of a sphere towards a rigid plane in an Oldroyd-B fluid

Physical Review Fluids 2024年第8期9卷 083303页

作者： Tachin Ruangkriengsin Rodolfo Brandão Bimalendu Mahapatra Evgeniy Boyko Howard A. Stone Program in Applied and Computational Mathematics Department of Mechanical and Aerospace Engineering Faculty of Mechanical Engineering

We analyze the low-Reynolds-number translation of a sphere towards or away from a rigid plane in an Oldroyd-B fluid under two scenarios: prescribing the sphere's translational velocity, and prescribing the force on the sphere. Leveraging the lubrication approximation and a perturbation expansion in powers of the Deborah number, we develop a comprehensive theoretical analysis that yields analytical approximations for velocity fields, pressures, and forces acting on the sphere. Our framework aids in understanding temporal microstructural changes as the particle-wall gap evolves over time. In particular, we show that alterations in the polymer conformation tensor in response to geometric changes induce additional forces on the sphere. For cases with prescribed velocity, we present a theoretical approach for calculating resistive forces at any order in the Deborah number and utilize a reciprocal theorem to obtain higher-order corrections based on velocity fields in the previous orders. When the sphere translates with a constant velocity, the fluid viscoelasticity decreases the resistive force at the first order. However, at the second-order correction, the direction of the sphere's movement determines whether viscoelasticity increases or decreases the resistive force. For cases with prescribed force, we show that understanding the influence of viscoelasticity on the sphere's translational velocity necessitates a more intricate analysis even at low Deborah numbers. Specifically, we introduce an ansatz for constant force scenarios, and we derive solution forms for general prescribed forces using the method of multiple scales. We find that when a sphere undergoes sedimentation due to its own weight, the fluid viscoelasticity results in a slower settling process, reducing the leading-order sedimentation rate.

关键词： Complex fluids Low Reynolds number flows Lubrication theory Polymer conformation changes Rheology

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Spectral bounds for independent cascade model with sensitive edges

Spectral bounds for independent cascade model with sensitive...

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Annual Conference on Information Sciences and Systems (CISS)

作者： Eun Jee Lee Sudeep Kamath Emmanuel Abbe Sanjeev R. Kulkarni Program in Applied and Computational Mathematics Department of Electrical Engineering Princeton University

This paper studies independent cascade models where influence propagates from seed-nodes along edges with independent probabilities. Upper-bounds for the expected number of influenced nodes were previously proposed using the spectral norm of a Hazard matrix. However, these bounds turn out loose in many cases, in particular with respect to sensitive edges such as bottlenecks, seed adjacent, and high probability edges. This paper proposes a similar bound that improves in such cases by handling sensitives edges more carefully.

关键词： Hazards Upper bound Stochastic processes Information science Merging computational modeling Mathematical model

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Convolutional neural networks with low-rank regularization 4

Convolutional neural networks with low-rank regularization

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4th International Conference on Learning Representations, ICLR 2016

作者： Tai, Cheng Xiao, Tong Zhang, Yi Wang, Xiaogang Weinan, E. Program in Applied and Computational Mathematics Princeton University United States Department of Electronic Engineering Chinese University of Hong Kong Hong Kong Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor United States

Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have been used for speeding up CNNs. In this paper, we further develop the tensor decomposition technique. We propose a new algorithm for computing the low-rank tensor decomposition for removing the redundancy in the convolution kernels. The algorithm finds the exact global optimizer of the decomposition and is more effective than iterative methods. Based on the decomposition, we further propose a new method for training low-rank constrained CNNs from scratch. Interestingly, while achieving a significant speedup, sometimes the low-rank constrained CNNs delivers significantly better performance than their non-constrained counterparts. On the CIFAR-10 dataset, the proposed low-rank NIN model achieves 91.31% accuracy (without data augmentation), which also improves upon state-of-the-art result. We evaluated the proposed method on CIFAR-10 and ILSVRC12 datasets for a variety of modern CNNs, including AlexNet, NIN, VGG and GoogleNet with success. For example, the forward time of VGG-16 is reduced by half while the performance is still comparable. Empirical success suggests that low-rank tensor decompositions can be a very useful tool for speeding up large CNNs. © ICLR 2016: San Juan, Puerto Rico. All Rights Reserved.

关键词： Iterative methods

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Threshold and decay properties of transient isolated turbulent band in plane Couette flow

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applied mathematics and Mechanics(English Edition) 2019年第10期40卷 1449-1456页

作者： Jianzhou LU Jianjun TAO Weitao ZHOU Xiangming XIONG CAPT-HEDPS SKLTCS Collaborative Innovation Center of IFSA Department of Mechanics and Engineering Science College of Engineering Peking University Beijing 100871 China The Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 U. S.A.

By direct numerical simulations of the plane Couette flow (PCF) in a large computational domain, it is shown that an isolated turbulent band decays monotonically at low Reynolds numbers but experiences transient growth before the eventual relaminarization at moderate Reynolds numbers. The lower bound Reynolds number of the transient-growth regime is determined as 286. The width, length, and tilt angle of the iso- lated band structure are defined based on the disturbance kinetic energy in the mid-plane, and the geometric characteristics of the band can be described with a tilted rectangle. It is illustrated that before its eventual fragmentation, the isolated turbulent band decays in a style of longitudinal contraction, where the center, width, and tilt angle of the band keep almost constant but the band length contracts with a statistically constant velocity.

关键词： plane Couette flow (PCF) subcritical transition turbulent band

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Reliability-based risk-metric computation for energy trading

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作者： Mínguez, Roberto Conejo, Antonio J. García-Bertrand, Raquel Castillo, Enrique Department of Applied Mathematics University of Castilla La Mancha Spain Department of Electrical Engineering University of Castilla La Mancha Spain Department of Applied Mathematics and Computational Sciences University of Cantabria Spain

ISBN: (纸本)9780415485135

Due to the stochastic nature of many of the variables involved in energy markets, asset operators, producers and consumers have to deal with a high level of financial risk. Therefore, the positioning with respect to the market is critical for successful trading. Different techniques from financial engineering have been used to manage market financial risks, e.g., Value-at-Risk (VaR) or Conditional-Value-at-Risk (CVaR). In this paper, those risk metrics are presented within a unified approach using reliability-based techniques, which allow obtaining the relationships among them easily. Additionally, First-Order-Reliability-Methods (FORM) are introduced as a tool to compute risk metrics. The proposed method uses standard optimization models to compute risk metrics even in cases that include dependent stochastic variables. Relevant results from an illustrative example are discussed and conclusions are finally drawn. © 2009 Taylor & Francis Group.

关键词： Risk analysis

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Time-frequency and time-scale canonical representations of doubly spread channels 12

Time-frequency and time-scale canonical representations of d...

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12th European Signal Processing Conference, EUSIPCO 2004

作者： Balan, Radu Vincent Poor, H. Rickard, Scott Verdú, Sergio Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Siemens Corporate Research PrincetonNJ United States Electronic and Electrical Engineering Department University College Dublin Ireland

ISBN: (纸本)9783200001657

A general technique for the generation of canonical channel models and demonstrate the application of the technique to time-frequency and time-scale integral kernel operators is developed. As an example, the derivation of Sayeed/Aazhang's time-frequency canonical channel characterization that forms the basis for the time-frequency RAKE receiver is shown. Then, a canonical time-scale channel model for wideband communication is developed. © 2004 EUSIPCO.

关键词： Time measurement

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MatterChat: A Multi-Modal LLM for Material Science

arXiv

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arXiv 2025年

作者： Tang, Yingheng Xu, Wenbin Cao, Jie Ma, Jianzhu Gao, Weilu Farrell, Steve Erichson, Benjamin Mahoney, Michael W. Nonaka, Andy Yao, Zhi Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA United States National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA United States NSF National AI Institute for Student-AI Teaming University of Colorado at Boulder Boulder United States Institute for AI Industry Research Tsinghua University Beijing China Department of Electrical and Computer Engineering The University of Utah Salt Lake CityUT United States Scientific Data Division Lawrence Berkeley National Laboratory BerkeleyCA United States International Computer Science Institute BerkeleyCA United States Department of Statistics University of California at Berkeley BerkeleyCA United States

Understanding and predicting the properties of inorganic materials is crucial for accelerating advancements in materials science and driving applications in energy, electronics, and beyond. Integrating material structure data with language-based information through multi-modal large language models (LLMs) offers great potential to support these efforts by enhancing human–AI interaction. However, a key challenge lies in integrating atomic structures at full resolution into LLMs. In this work, we introduce MatterChat, a versatile structure-aware multi-modal LLM that unifies material structural data and textual inputs into a single cohesive model. MatterChat employs a bridging module to effectively align a pretrained machine learning interatomic potential with a pretrained LLM, reducing training costs and enhancing flexibility. Our results demonstrate that MatterChat significantly improves performance in material property prediction and human-AI interaction, surpassing general-purpose LLMs such as GPT-4. We also demonstrate its usefulness in applications such as more advanced scientific reasoning and step-by-step material synthesis. © 2025, CC BY.

关键词： Materials properties

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Analysis of the linear stability of compressible boundary layers using the PSE

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Theoretical and computational Fluid Dynamics 1991年第2期3卷 117-124页

作者： Bertolotti, F.P. Herbert, Th. Program in Applied and Computational Mathematics Princeton University Princeton 08544 NJ United States Department of Mechanical Engineering Ohio State University Columbus 43210 OH United States

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A granular model for crowd motion and pedestrian flow

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Journal of the London Mathematical Society 2025年第5期111卷

作者： Noureddine Igbida José Miguel Urbano Institut de recherche XLIM UMR-CNRS 7252 Faculté des Sciences et Techniques Université de Limoges Limoges France Applied Mathematics and Computational Sciences (AMCS) Computer Electrical and Mathematical Sciences and Engineering Division (CEMSE) King Abdullah University of Science and Technology (KAUST) Thuwal Saudi Arabia CMUC Department of Mathematics University of Coimbra Coimbra Portugal

We study a granular model for congested crowd motion and pedestrian flow. Our approach is based on an approximation through a Hele-Shaw type equation involving a degenerate operator of p $p $ -Laplacian type and a linear drift, for which we prove existence and uniqueness using nonlinear semigroup methods and the doubling variables technique. Our main result shows that, as p → ∞ $p \rightarrow \infty$ , the weak solutions of the p $p$ -problem converge to a solution of the congested crowd motion problem interpreted in a variational sense.

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Detecting community structures in Hi-C genomic data

Detecting community structures in Hi-C genomic data

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Annual Conference on Information Sciences and Systems (CISS)

作者： Irineo Cabreros Emmanuel Abbe Aristotelis Tsirigos Program in Applied and Computational Mathematics Princeton University Program in Applied and Computational Mathematics and Department of Electrical Engineering Princeton University Department of Pathology NYU Langone Medical Center

Community detection (CD) algorithms are applied to Hi-C data to discover new communities of loci in the 3D conformation of human and mouse DNA. We find that CD has some distinct advantages over pre-existing methods: (1) it is capable of finding a variable number of communities, (2) it can detect communities of DNA loci either adjacent or distant in the 1D sequence, and (3) it allows us to obtain a principled value of k, the number of communities present. Forcing k = 2, our method recovers earlier findings of Lieberman-Aiden, et al. (2009), but letting k be a parameter, our method obtains as optimal value k* = 6, discovering new candidate communities. In addition to discovering large communities that partition entire chromosomes, we also show that CD can detect small-scale topologically associating domains (TADs) such as those found in Dixon, et al. (2012). CD thus provides a natural and flexible statistical framework for understanding the folding structure of DNA at multiple scales in Hi-C data.

关键词： DNA Biological cells Three-dimensional displays Hidden Markov models Principal component analysis Algorithm design and analysis Genomics

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