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Following marginal stability manifolds in quasilinear dynamical reductions of multiscale flows in two space dimensions

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Physical Review E 2025年第2期111卷 025105-025105页

作者： Alessia Ferraro Gregory P. Chini T. M. Schneider Emergent Complexity in Physical Systems Laboratory (ECPS) École Polytechnique Fédérale de Lausanne CH-1015 Lausanne Switzerland Nordita Royal Institute of Technology and Stockholm University Stockholm 106 91 Sweden Department of Mechanical Engineering and Program in Integrated Applied Mathematics University of New Hampshire Durham New Hampshire 03824 USA

We derive a two-dimensional (2D) extension of a recently developed formalism for slow-fast quasilinear (QL) systems subject to fast instabilities. The emergent dynamics of these systems is characterized by a slow evolution of (suitably defined) mean fields coupled to marginally stable, fast fluctuation fields. By exploiting this scale separation, an efficient hybrid fast-eigenvalue/slow-initial-value solution algorithm can be developed in which the amplitude of the fast fluctuations is slaved to the slowly evolving mean fields to ensure marginal stability—and temporal scale separation—is maintained. For 2D systems, the fluctuation eigenfunctions are labeled by their Fourier wave numbers characterizing spatial variability in that extended spatial direction, and the marginal mode(s) must coincide with the fastest-growing mode(s) over all admissible Fourier wave numbers. Here we derive an ordinary differential equation governing the slow evolution of the wave number of the fastest-growing fluctuation mode that simultaneously must be slaved to the mean dynamics to ensure the mode has zero growth rate. We illustrate the procedure in the context of a 2D model partial differential equation that shares certain attributes with the equations governing strongly stratified shear flows and other strongly constrained forms of geophysical turbulence in extreme parameter regimes. The slaved evolution follows one or more marginal stability manifolds, which constitute select state-space structures that are not invariant under the full flow dynamics yet capture quasicoherent structures in physical space in a manner analogous to invariant solutions identified in, e.g., transitionally turbulent shear flows. Accordingly, we propose that marginal stability manifolds are central organizing structures in a dynamical systems description of certain classes of multiscale flows in which scale separation justifies a QL approximation of the dynamics.

关键词： Shear flow

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Spatio-temporal characterization of nonlinear forcing and response in turbulent channel flow

arXiv

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arXiv 2025年

作者： Huang, Yuting Toedtli, Simon S. Chini, Gregory P. McKeon, Beverley J. Mechanical and Civil Engineering California Institute of Technology PasadenaCA91125 United States National Center for Atmospheric Research BoulderCO80301 United States Program in Integrated Applied Mathematics Department of Mechanical Engineering University of New Hampshire DurhamNH03824 United States Department of Mechanical Engineering Center for Turbulence Research Stanford University StanfordCA94305 United States

The quadratic convection term in the incompressible Navier-Stokes equations is considered as a nonlinear forcing to the linear resolvent operator, and it is studied in the Fourier domain through the analysis of interactions between triadically compatible wavenumber-frequency triplets. A framework to quantify the triadic contributions to the forcing and response by each pair of triplets is developed and applied to data from direct numerical simulations of a turbulent channel at Reι ≈ 550. The linear resolvent operator is incorporated to provide the missing link from energy transfer between modes to the effect on the spectral turbulent kinetic energy. The coefficients highlight the importance of interactions involving large-scale structures, providing a natural connection to the modeling assumptions in quasi-linear (QL) and generalized quasi-linear (GQL) analyses. Specifically, it is revealed that the QL and GQL reductions efficiently capture important triadic interactions in the flow, especially when including of a small number of wavenumbers into the GQL large-scale base flow. Additionally, spatio-temporal analyses of the triadic contributions to a single mode representative of the near-wall cycle demonstrate the spatio-temporal nature of the triadic interactions and the effect of the resolvent operator, which selectively amplifies certain forcing profiles. The tools presented are expected to be useful for improving modeling of the nonlinearity, especially in QL, GQL, and resolvent analyses, and understanding the amplitude modulation mechanism relating large-scale fluctuations to the modulation of near-wall structures. © 2025, CC BY.

关键词： Navier Stokes equations

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Utilization of nanohydroxyapatite-kaolin composites as a slow-release materials of urea

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Materials Chemistry and Physics 2025年 342卷

作者： Noviyanti, Atiek Rostika Fajrina, Yulia Eddy, Diana Rakhmawaty Irkham Hartati, Yeni Wahyuni Rupaedah, Bedah Suryana Permana, Muhamad Diki Karnjanakom, Surachai Guan, Guoqing Kurnia, Irwan Department of Chemistry Faculty of Mathematics and Natural Sciences Universitas Padjadjaran Jl. Raya Bandung-Sumedang Km 21 Jatinangor West Java Sumedang45363 Indonesia Research Center for Applied Microbiology National Research and Innovation Agency Jl. Raya Jakarta-Bogor Km. 46 Cibinong West Java Bogor16911 Indonesia Department of Biology Faculty of Mathematics and Natural Sciences Universitas Padjadjaran Jl. Raya Bandung-Sumedang Km 21 Jatinangor West Java Sumedang45363 Indonesia Special Educational Program for Green Energy Conversion Science and Technology Integrated Graduate School of Medicine Engineering and Agricultural Sciences University of Yamanashi Kofu400-8511 Japan Center for Crystal Science and Technology University of Yamanashi Kofu400-8511 Japan Department of Chemistry Faculty of Science Rangsit University 52/347 Phahonyothin Road Pathum Thani 12000 Thailand Institute of Regional Innovation Hirosaki University 3-Bunkyocho Hirosaki036-8561 Japan

Urea is widely used as a nitrogen-source fertilizer in agriculture, but its leaching due to rainwater leads to eutrophication and environmental pollution. To address this, urea was incorporated into nanohydroxyapatite (nHA)–kaolin (KA) composites (HKs) that were synthesized via a two-step hydrothermal method as a slow-release materials (SRMs). Among the composites, HK1 (nHA:KA 75:25) is the most promising slow-release material with a urea release rate of 57.0 μgurea min−1 (20.3 % for 240 min), which is 4.6 times slower than urea release rate of nHA-urea for 262.9 μgurea min−1 (93.5 %, 240 min). This enhanced slow-release behavior is attributed to synergistic interactions between nHA and KA, as reflected on their zeta potentials. These findings suggest that HKs are promising slow-release materials for improving fertilizer efficiency and mitigating environmental impact in agricultural applications. © 2025 Elsevier B.V.

关键词： Urea fertilizers

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A FOCUS VERNIER FOR OPTICAL LITHOGRAPHY 7

A FOCUS VERNIER FOR OPTICAL LITHOGRAPHY

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7TH ANNUAL CONF ON integrated CIRCUIT METROLOGY, INSPECTION, AND PROCESS CONTROL

作者： ARNOLD, WH BAROUCH, E HOLLERBACH, U ORSZAG, SA Advanced Micro Devices Inc. Integrated Technology Division MS 79 901 Thompson Place Sunnyvale 94088-3453 CA United States Program in Applied and Computational Mathematics Princeton University Princeton 08544-1000 NJ United States

ISBN: (纸本)0819411604

As the depth of focus of optical steppers grows smaller, it becomesmore important to determine the position of best focus accurately andquickly. This paper describes the use of phase-shifted mask technologyto form a focus vernier: a phase pattern on the stepper reticle which,when imaged in resist, cangive both the magnitude and the direction ofthe focus error. In this, the focus vernier structure is analogous to3overlay verniers. Thus the determination of focus error can be treatedas an alignment problem in the z-axis. This technique is an improvementon previous schemes for the determination of best focus from resistimages as it can indicate both the magnitude of the error and itsdirection in a single exposure. © 1993 Proceedings of SPIE - The International Society for Optical Engineering. All rights reserved.

关键词： Errors

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Null Space Properties of Neural Networks with Applications to Image Steganography

arXiv

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arXiv 2023年

作者： Li, Xiang Short, Kevin M. Integrated Applied Mathematics Program Department of Mathematics and Statistics University of New Hampshire DurhamNH03824 United States

This paper explores the null space properties of neural networks. We extend the null space definition from linear to nonlinear maps and discuss the presence of a null space in neural networks. The null space of a given neural network can tell us the part of the input data that makes no contribution to the final prediction so that we can use it to trick the neural network. This reveals an inherent weakness in neural networks that can be exploited. One application described here leads to a method of image steganography. Through experiments on image datasets such as MNIST, we show that we can use null space components to force the neural network to choose a selected hidden image class, even though the overall image can be made to look like a completely different image. We conclude by showing comparisons between what a human viewer would see, and the part of the image that the neural network is actually using to make predictions and, hence, show that what the neural network "sees" is completely different than what we would expect. Copyright © 2023, The Authors. All rights reserved.

关键词： Machine learning

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Reduced modeling of transitional exact coherent states in shear flow 15

Reduced modeling of transitional exact coherent states in sh...

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15th European Turbulence Conference, ETC 2015

作者： Beaume, Cédric Chini, Greg P. Julien, Keith Knobloch, Edgar Department of Aeronautics Imperial College London LondonSW7 2AZ United Kingdom Department of Mechanical Engineering and Program in Integrated Applied Mathematics University of New Hampshire DurhamNH03824 United States Department of Applied Mathematics University of Colorado at Boulder BoulderCO80309 United States Department of Physics University of California BerkeleyCA94720 United States

In parallel shear flows, the lower branch solution follows simple streamwise dynamics. A decomposition of this solution into Fourier modes in this direction yields modes whose amplitudes scale with inverse powers of the Reynolds number. We use this scaling to derive a reduced model for exact coherent structures in general parallel shear flows. The reduced model is regularized by retaining higher order viscous terms. Both lower branch and upper branch solutions are captured and studied. © TU Delft.

关键词： Shear flow

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Symmetry groups and invariant solutions of plane Poiseuille flow

arXiv

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arXiv 2024年

作者： Aghor, Pratik P. Gibson, John F. School of Earth and Atmospheric Sciences Georgia Institute of Technology United States Integrated Applied Mathematics Program Department of Mathematics & Statistics University of New Hampshire United States

Equilibrium, traveling-wave, and periodic-orbit solutions of the Navier-Stokes equations provide a promising avenue for investigating the structure, dynamics, and statistics of transitional flows. Many such invariant solutions have been computed for wall-bounded shear flows, including plane Couette, plane Poiseuille, and pipe flow. However, the organization of invariant solutions is not well understood. In this paper we focus on the role of symmetries in the organization and computation of invariant solutions of plane Poiseuille *** show that enforcing symmetries while computing invariant solutions increases the efficiency of the numerical methods, and that redundancies between search spaces can be eliminated by consideration of equivalence relations between symmetry subgroups. We determine all symmetry subgroups of plane Poiseuille flow in a doubly-periodic domain up to translations by half the periodic lengths and classify the subgroups into equivalence classes, each of which represents a physically distinct set of symmetries and an associated set of physically distinct invariant *** calculate fifteen new traveling waves of plane Poiseuille flow in seven distinct symmetry groups and discuss their relevance to the dynamics of transitional turbulence. We present a few examples of subgroups with fractional shifts other than half the periodic lengths and one traveling wave solution whose symmetry involves shifts by one-third of the periodic lengths. We conclude with a discussion and some open questions about the role of symmetry in the behavior of shear flows. © 2024, CC BY.

关键词： Navier Stokes equations

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Two-stage likelihood robust linear program with application to water allocation under uncertainty 13

Two-stage likelihood robust linear program with application ...

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Simulation Winter Conference

作者： David Love Güzin Bayraksan Program in Applied Mathematics University of Arizona Tucson AZ USA Integrated Systems Engineering The Ohio State University Columbus OH USA

ISBN: (纸本)9781479920778

We adapt and extend the likelihood robust optimization method recently proposed by Wang, Glynn, and Ye for the newsvendor problem to a more general two-stage setting. We examine the value of collecting additional data and the cost of finding a solution robust to an ambiguous probability distribution. A decomposition-based solution algorithm to solve the resulting model is given. We apply the model to examine a long-term water allocation problem in the southeast area of Tucson, AZ under ambiguous distribution of future available supply and demand and present computational results.

关键词： Robustness Stochastic processes Computational modeling Uncertainty Resource management Optimization

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Cupolets in a Chaotic Neuron Model

arXiv

引用

arXiv 2022年

作者： Parker, John E. Short, Kevin M. Department of Mathematics University of Pittsburgh PittsburghPA15260 United States Integrated Applied Mathematics Program Department of Mathematics and Statistics University of New Hampshire DurhamNH03824 United States

This paper reports the first finding of cupolets in a chaotic Hindmarsh-Rose neural model. Cupolets (chaotic, unstable, periodic, orbit-lets) are unstable periodic orbits that have been stabilized through a particular control scheme applying a binary control sequence. We demonstrate different neural dynamics (periodic or chaotic) of the Hindmarsh-Rose model through a bifurcation diagram where the external input current, I, is the bifurcation parameter. We select a region in the chaotic parameter space and provide the results of numerical simulations. In this chosen parameter space, a control scheme is applied when the trajectory intersects with either of the two control planes. The size of the control is determined by a bit in a binary control sequence. The control is either a small microcontrol (0) or a large macrocontrol (1) that adjusts the future dynamics of the trajectory. We report the discovery of many cupolets with corresponding control sequences and comment on the differences with previously reported cupolets in the double scroll system. We provide some examples of the generated cupolets and conclude by discussing potential implications for biological neurons. © 2022, CC BY.

关键词： Bifurcation (mathematics)

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Wall to wall optimal transport 15

Wall to wall optimal transport

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15th European Turbulence Conference, ETC 2015

作者： Doering, Charles R. Souza, Andre N. Chini, Gregory P. Hassanzadeh, Pedram Department of Physics University of Michigan United States Department of Mathematics University of Michigan United States Center for the Study of Complex Systems University of Michigan United States Department of Mechanical Engineering Program in Integrated Applied Mathematics and Center for Fluid Physics University of New Hampshire United States Centre for the Environment Department of Earth and Planetary Sciences Harvard University United States

The calculus of variations is employed to find steady divergence-free velocity fields that maximize transport of a tracer between two parallel walls held at fixed concentration for one of two constraints on flow strength: a fixed value of the kinetic energy or a fixed value of the enstrophy (the mean square rate of strain in this situation). The optimizing flows realize upper limits on convective transport in this scenario. We interpret the results in the context of buoyancy-driven Rayleigh–Bénard convection problems that satisfy the flow intensity constraints, enabling us to investigate how optimal transport scalings compare with upper bounds on Nu expressed as a function of the Rayleigh number Ra. © TU Delft.

关键词： Kinetic energy

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