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SSRN 2024年

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

Phase mixing and separation phenomena abound in the formation of natural and synthetic material systems, including alloys, composites, granular media, geological media, complex fluids, and biological media. While characterizing phase mixing is critical to understanding material microstructure formation and physical properties, previous metrics that measure the degree of mixing in condensed phases often rely on empirical observation, are applicable only to certain microstructures, and/or fail to detect nontrivial changes in mixing with respect to length scale. To overcome these shortcomings, we introduce and study a mixing metric that is applicable to a broad spectrum of complex microstructures and leverages the hyperuniformity concept to provide a unifying framework to rank and classify mixing in materials across both length and time scales. Specifically, we employ the local phase volume-fraction/field-intensity variance [[EQUATION]] associated with a spherical sampling window of radius [[EQUATION]] at time [[EQUATION]] as our metric. We demonstrate that of [[EQUATION]] provides a sensitive measure of mixing across both length and time scales of a structurally diverse set of real and simulated material microstructures: exotic disordered multihyperuniform avian retina photoreceptor cell patterns, time-evolving spinodal decomposition patterns, and a model material mixed via the baker's transformation. We also describe how this metric can be used to guide future work on fabricating materials whose bulk properties can be controlled by tuning their mixing characteristics across length and time scales. © 2024, The Authors. All rights reserved.

关键词： Blending

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Thermodynamics of the Solid-Liquid Phase Equilibrium of a Binary System: Effect of a Chemical Reaction in the Liquid and Epitaxial Strain in the Solid

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SSRN 2023年

作者： Deymier, Alix C. Deymier, Pierre Alix Muralidharan, Krishna Latypov, Marat I. Department of Biomedical Engineering UConn Health FarmingtonCT06030 United States Department of Materials Science and Engineering University of Arizona TucsonAZ85721 United States Graduate Interdisciplinary Program in Applied Mathematics University of Arizona TucsonAZ85721 United States

We introduce two thermodynamics models of solid-liquid phase equilibrium of a binary system in the presence of (a) a chemical reaction in the liquid involving only one of the binary components and, (b) strain-inducing epitaxial conditions on the solid in addition to the chemical reaction in the liquid. These models show the existence of the counter intuitive behavior that epitaxy may promote recrystallization of the solid in spite of the reaction driving dissolution. The conditions for this recrystallization behavior are determined by the value of the epitaxial lattice matching composition, the temperature and the overall composition of the binary solid-liquid system. © 2023, The Authors. All rights reserved.

关键词： Chemical reactions

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GRAMMCell: Docking-based Cell Modeling Resource

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Journal of Molecular Biology 2025年第15期437卷 169085页

作者： Singh, Amar Tytarenko, Andrii M. Ambati, Vineeth Kumar Copeland, Matthew M. Kundrotas, Petras J. Kasyanov, Pavlo O. Feinberg, Eugene A. Vakser, Ilya A. Computational Biology Program The University of Kansas Lawrence 66045 KS United States Institute for Applied System Analysis at the Igor Sikorsky Kyiv Polytechnic Institute Kyiv 03056 Ukraine Department of Applied Mathematics and Statistics Stony Brook University Stony Brook 11794 NY United States Department of Molecular Biosciences The University of Kansas Lawrence 66045 KS United States

The environment inside biological cells is densely populated by macromolecules and other cellular components. The crowding has a significant impact on folding and stability of macromolecules, and on kinetics of molecular interactions. Computational approaches to cell modeling, such as molecular dynamics, provide details of macromolecular behavior in concentrated solutions. However, such simulations are either slow, when carried out at atomic resolution, or significantly coarse-grained. Protein docking has been widely used for predicting structures of protein complexes. Systematic docking approaches, such as those based on Fast Fourier Transform (FFT), map the entire intermolecular energy landscape by determining the position and depth of the energy minima. The GRAMMCell web server implements docking-based approach for simulating cell crowded environment by sampling the intermolecular energy landscape generated by GRAMM (Global RAnge Molecular Matching). GRAMM systematically maps the landscape by a spectrum of docking poses corresponding to stable (deep energy minima) and transient (shallow minima) protein interactions. The sampling of these energy landscapes of a large system of proteins is performed in GRAMMCell using highly optimized Markov Chain Monte Carlo protocol. The procedure allows simulation of extra-long trajectories of large, crowded protein systems with atomic resolution accuracy. GRAMMCell is available at https://***. © 2025 The Author(s)

关键词： cell-modelling energy landscape protein docking protein–protein interactions web-based resource

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On the Origin of Dust Structures in Protoplanetary Disks: Constraints from the Rossby Wave Instability

arXiv

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arXiv 2023年

作者： Chang, Eonho Youdin, Andrew N. Krapp, Leonardo Graduate Interdisciplinary Program in Applied Mathematics University of Arizona TucsonAZ85721 United States Department of Astronomy Steward Observatory University of Arizona TucsonAZ85721 United States The Lunar and Planetary Laboratory University of Arizona TucsonAZ85721 United States

High resolution sub-mm observations of protoplanetary disks with ALMA have revealed that dust rings are common in large, bright disks. The leading explanation for these structures is dust-trapping in a local gas pressure maximum, caused by an embedded planet or other dynamical process. Independent of origin, such dust traps should be stable for many orbits to collect significant dust. However, ring-like perturbations in gas disks are also known to trigger the Rossby Wave Instability (RWI). We investigate whether axisymmetric pressure bumps can simultaneously trap dust and remain stable to the RWI. The answer depends on the thermodynamic properties of pressure bumps. For isothermal bumps, dust traps are RWI-stable for widths from ∼1 to several gas scale-heights. Adiabatic dust traps are stable over a smaller range of widths. For temperature bumps with no surface density component, however, all dust traps tend to be unstable. Smaller values of disk aspect ratio allow stable dust trapping at lower bump amplitudes and over a larger range of widths. We also report a new approximate criterion for RWI. Instability occurs when the radial oscillation frequency is . 75% of the Keplerian frequency, which differs from the well-known Lovelace necessary (but not sufficient) criterion for instability. Our results can guide ALMA observations of molecular gas by constraining the resolution and sensitivity needed to identify the pressure bumps thought to be responsible for dust rings. © 2023, CC BY.

关键词： Dust

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Composite B-Spline Regularized Delta Functions for the Immersed Boundary Method: Divergence-Free Interpolation and Gradient-Preserving Force Spreading

arXiv

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arXiv 2024年

作者： Gruninger, Cole Griffith, Boyce E. Department of Mathematics University North Carolina Chapel HillNC United States Department of Applied Physical Sciences University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

This paper presents an approach to enhance volume conservation in the immersed boundary (IB) method by employing regularized delta functions derived from composite B-splines. These delta functions are constructed using tensor product kernels, similar to the conventional IB method. However, the kernels are B-splines whose polynomial degree varies according to the normal and tangential directions of each velocity component. The conventional IB method, while effective for fluid-structure interaction applications, has long been challenged by poor volume conservation, particularly evident in simulations of pressurized, closed membranes. We demonstrate that composite B-spline regularized delta functions significantly enhance volume conservation through two complementary properties: they provide continuously divergence-free velocity interpolants and maintain the gradient character of forces corresponding to mean pressure jumps across interfaces. By correctly representing these forces as discrete gradients, they eliminate a key source of spurious flows that typically plague immersed boundary computations. Our approach maintains the local nature of the classical IB method, avoiding the computational overhead associated with the non-local Divergence-Free Immersed Boundary (DFIB) method’s construction of an explicit velocity potential which requires additional Poisson solves for interpolation and force spreading operations. Through a series of numerical experiments, we show that sufficiently regular composite B-spline kernels can maintain initial volumes to within machine precision. We provide a detailed analysis of the relationship between kernel regularity and the accuracy of force spreading and velocity interpolation operations. Our findings indicate that composite B-splines of at least C1 regularity produce results comparable to the DFIB method in dynamic simulations, with errors in volume conservation primarily dominated by truncation error of the employed time-stepping s

关键词： Delta functions

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Local Divergence-Free Immersed Finite Element-Difference Method Using Composite B-Splines

arXiv

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arXiv 2024年

作者： Li, Lianxia Gruninger, Cole Lee, Jae H. Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

In the class of immersed boundary (IB) methods, the choice of the regularized delta function plays a crucial role in transferring information between fluid and solid domains through interpolation and spreading operators. Most prior work using the IB method has used isotropic kernels that do not preserve the divergence-free condition of the velocity field, leading to loss of incompressibility of the solid when interpolating the Eulerian velocity to Lagrangian markers. To address this issue, in simulations involving large deformations of incompressible hyperelastic structures immersed in fluid, researchers often use a volumetric stabilization approach such as adding a volumetric energy term and using modified invariants in the constitutive model of the immersed structure. Composite B-spline (CBS) kernels offer an alternative approach by inherently maintaining the discrete divergence-free property. This work evaluates the performance of CBS kernels in terms of their volume conservation and accuracy, comparing them with several traditional isotropic kernel functions using a construction introduced by Peskin (referred to as IB kernels) and B-spline (BS) kernels. Benchmark tests include pressure-loaded and shear-dominated flows, such as an elastic band under differential pressure loads, a pressurized membrane, a compressed block, Cook’s membrane, a slanted channel flow, and a modified Turek-Hron problem. Additionally, we validate our methodology using a complex fluid-structure interaction model of bioprosthetic heart valve dynamics in a pulse duplicator. Results demonstrate that CBS kernels achieve superior volume conservation compared to conventional isotropic kernels, eliminating the need for additional volumetric stabilization techniques typically required to address instabilities arising from volume conservation errors. Further, CBS kernels achieve convergence on coarser fluid grids, while IB and BS kernels need finer grids for comparable accuracy. Unlike IB and BS ke

关键词： Delta functions

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Rapid and accurate mosquito abundance forecasting with Aedes-AI neural networks

arXiv

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arXiv 2024年

作者： Kinney, Adrienne C. Barrera, Roberto Lega, Joceline Interdisciplinary Program in Applied Mathematics The University of Arizona TucsonAZ85721 United States Department of Mathematics The University of Arizona TucsonAZ85721 United States Department of Epidemiology and Biostatistics The University of Arizona TucsonAZ85721 United States BIO5 Institute The University of Arizona TucsonAZ85721 United States Entomology and Ecology Activity Dengue Branch Centers for Disease Control and Prevention 1324 Calle Cañada Puerto Rico San Juan00920 Puerto Rico

We present a method to convert weather data into probabilistic forecasts of Aedes aegypti abundance. The approach, which relies on the Aedes-AI suite of neural networks, produces weekly point predictions with corresponding uncertainty estimates. Once calibrated on past trap and weather data, the model is designed to use weather forecasts to estimate future trap catches. We demonstrate that when reliable input data are used, the resulting predictions have high skill. This technique may therefore be used to supplement vector surveillance efforts or identify periods of elevated risk for vector-borne disease outbreaks. © 2024, CC BY.

关键词： Prediction models

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Scaling positive random matrices: Concentration and asymptotic convergence

arXiv

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arXiv 2020年

作者： Landa, Boris Program in Applied Mathematics Department of Mathematics Yale University United States

It is well known that any positive matrix can be scaled to have prescribed row and column sums by multiplying its rows and columns by certain positive scaling factors (which are unique up to a positive scalar). This procedure is known as matrix scaling, and has found numerous applications in operations research, economics, image processing, and machine learning. In this work, we investigate the behavior of the scaling factors and the resulting scaled matrix when the matrix to be scaled is random. Specifically, letting Ã∈ RM×N be a positive and bounded random matrix whose entries assume a certain type of independence, we provide a concentration inequality for the scaling factors of Ã around those of A = E[Ã]. This result is employed to bound the convergence rate of the scaling factors of Ã to those of A, as well as the concentration of the scaled version of Ã around the scaled version of A in operator norm, as M, N → ∞. When the entries of Ã are independent, M = N, and all prescribed row and column sums are 1 (i.e., doubly-stochastic matrix scaling), both of the previously-mentioned bounds are O(√log N/N) with high probability. We demonstrate our results in several *** Codes 60B20, 60F10, 65F35 Copyright © 2020, The Authors. All rights reserved.

关键词： Operations research

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Correlations between student connectivity and academic performance: A pandemic follow-up

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Physical Review Physics Education Research 2023年第1期19卷 010106-010106页

作者： Nathan Crossette Lincoln D. Carr Bethany R. Wilcox Department of Physics University of Colorado Boulder Boulder Colorado 80309 USA Quantum Engineering Program Colorado School of Mines Golden Colorado 80401 USA Department of Physics Colorado School of Mines Golden Colorado 80401 USA Department of Applied Mathematics and Statistics Colorado School of Mines Golden Colorado 80401 USA

Social network analysis (SNA) has been gaining traction as a technique for quantitatively studying student collaboration. We analyze networks, constructed from student self-reports of collaboration on homework assignments, in two courses from the University of Colorado Boulder and one course from the Colorado School of Mines. All three courses occurred during the COVID-19 pandemic, which allows for a comparison between the course at the Colorado School of Mines (in a fully remote format) with results from a previous pre-pandemic study of student collaboration at the Colorado School of Mines (in an in-person format), as well as comparison between the Mines results with the two University of Colorado courses (in a hybrid format). We compute nodal centrality measures and calculate the correlation between student centrality and performance. Results varied widely between each of the courses studied. The course at the Colorado School of Mines had strong correlations between many centrality measures and performance which matched the patterns seen in the pre-pandemic study. The courses at the University of Colorado Boulder showed weaker correlations, and one course showed nearly no correlations at all between students’ connectivity to their classmates and their performance. Taken together, the results from the trio of courses indicate that the context and environment in which the course is situated play a more important role in fostering a correlation between student collaboration and course performance than the format (remote, hybrid, in-person) of the course, a finding which has implications for the broader use of SNA within physics education research. Additionally, we conducted a short study on the effect that missing nodes may have on the correlations calculated from the measured networks, an analysis largely missing from the SNA literature within PER. This investigation showed that missing nodes tend to shift correlations towards zero, providing evidence that the stati

关键词： Learning environment Research methodology Upper undergraduate students

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The Smart Analysis of Performing Scalable Inference for Big Data Analytics

The Smart Analysis of Performing Scalable Inference for Big ...

引用

2023 International Conference on Power Energy, Environment and Intelligent Control, PEEIC 2023

作者： Bhandarkar, Vishakha D. Rongali, Aruna Sri Shamout, Mohamed Dawood Pund, Sachin Nama, Gigih Forda Patil, Shrishailappa Yeshwantrao Chavan College of Engineering Applied Mathematics and Humanities India University of the Cumberlands Graduate Doctoral Information Technology Information Technology Emphasis/Information Technology United States College of Business Administration University of Sharjah Department of Management Sharjah United Arab Emirates Shri Ramdeobaba College of Engineering and Management Department of Industrial Engineering Maharashtra Nagpur India Doctoral Program of Environtmental Science University of Lampung Department of Informatics Bandar Lampung Indonesia Vishwakarma Institute of Technology Computer Engineering Pune India

ISBN: (纸本)9798350357769

This paper examines the reproducibility of massive information analytics under particular factors. The paper proposes the 'performing Scalable Inference' technique to cope with scalability troubles and to exploit current big statistics platforms for efficient computing and statistics garage of the statistics. In particular, the paper describes how to perform leak-free, parallelizable visible analytics over massive datasets using present extensive records analytics frameworks such as Apache Flink. This method presents an automated manner to execute analytics that preserves reproducibility and the ability to make adjustments without re-running the entire technique. The paper also demonstrates how these analytics may help several real-world use instances, explore affected person cohorts for studies, and develop stratified patient cohorts for hospital therapy. In the end, the paper observes how the proposed method may be exercised within the real world. Actively scalable inference for massive information analytics is pivotal in optimizing decision-making and allocation of assets. Typically, such inferences are made based on information accumulated from numerous sources, databases, unstructured data, and different digital sources. So one can ensure scalability, a complete cloud-primarily based platform has to be hired. This solution will permit the ***, deploying the essential records series and evaluation algorithms are prime here. It could permit the platform to recognize the styles inside the statistics and discover any ability correlations or traits. Additionally, predictive analytics and system mastering strategies may be incorporated to provide insights into the results of the information. In the long run, by leveraging those techniques, the platform can draw efficient inferences and appropriately compare situations in an agile and green way.. © 2023 IEEE.

关键词： adjustments an a lytics automated preserves statistics

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