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arXiv 2021年

作者： Chini, Gregory P. Michel, Guillaume Julien, Keith Rocha, Cesar B. Caulfield, Colm-Cille P. Program in Integrated Applied Mathematics University of New Hampshire DurhamNH03824 United States Department of Mechanical Engineering University of New Hampshire DurhamNH03824 United States Institut Jean Le Rond d’Alembert Sorbonne Université CNRS UMR 7190 ParisF-75005 France Department of Applied Mathematics University of Colorado BoulderCO80309 United States Department of Marine Sciences University of Connecticut StorrsCT06269 United States BP Institute Department of Applied Mathematics & Theoretical Physics Cambridge University CambridgeCB3 0WA United Kingdom

A multiscale reduced description of turbulent free shear flows in the presence of strong stabilizing density stratification is derived via asymptotic analysis of the Boussinesq equations in the simultaneous limits of small Froude and large Reynolds numbers. The analysis explicitly recognizes the occurrence of dynamics on disparate spatiotemporal scales, yielding simplified partial differential equations governing the coupled evolution of slow large-scale hydrostatic flows and fast small-scale isotropic instabilities and internal waves. The dynamics captured by the coupled reduced equations is illustrated in the context of two-dimensional strongly stratified Kolmogorov flow. A noteworthy feature of the reduced model is that the fluctuations are constrained to satisfy quasilinear (QL) dynamics about the comparably slowly-varying large-scale fields. Crucially, this QL reduction is not invoked as an ad hoc closure approximation, but rather is derived in a physically relevant and mathematically consistent distinguished limit. Further analysis of the resulting slow-fast QL system shows how the amplitude of the fast stratified-shear instabilities is slaved to the slowly-evolving mean fields to ensure the marginal stability of the latter. Physically, this marginal stability condition appears to be compatible with recent evidence of self-organized criticality in both observations and simulations of stratified turbulence. Algorithmically, the slaving of the fluctuation fields enables numerical simulations to be time-evolved strictly on the slow time scale of the hydrostatic flow. The reduced equations thus provide a solid mathematical foundation for future studies of three-dimensional strongly stratified turbulence in extreme parameter regimes of geophysical relevance and suggest avenues for new sub-grid-scale parameterizations. Copyright © 2021, The Authors. All rights reserved.

关键词： Asymptotic analysis

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Nonequilibrium and morphological characterizations of Kelvin-Helmholtz instability in compressible flows

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Frontiers of physics 2019年第4期14卷 83-99页

作者： Yan-Biao Gan Ai-Guo Xu Guang-Cai Zhang Chuan-Dong Lin Hui-Lin Lai Zhi-Peng Liu North China Institute of Aerospace Engineering Langfang 065000 China College of Mathematics and Informatics & FJKLMAA Fujian Normal University Fuzhou 350007 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics P. O. Box 8009-26 Beijing 100088 China State Key Laboratory of Explosion Science and Technology Beijing Institute of Technology Beijing 100081 China Center for Applied Physics and Technology MOE Key Center for High Energy Density Physics Simulations College of Engineering Peking University Beijing 100871 China Center for Combustion Energy Key Laboratory for Thermal Science and Power Engineering of Ministry of Education Department of Energy and Power Engineering Tsinghua University Beijing 100084 China Department of Physics School of Science Tianjin Chengjian University Tianjin 300384 China

We investigate the effects of viscosity and heat conduction on the onset and growth of Kelvin-Helmholtz instability (KHI) via an efficient discrete Boltzmann ***,two effective approaches are presented to quantitatively analyze and understand the configurations and kinetic *** is to determine the thickness of mixing layers through tracking the distributions and evolutions of the thermodynamic nonequilibrium (TNE) measures;the other is to evaluate the growth rate of KHI from the slopes of morphological ***,it is found that the time histories of width of mixing layer,TNE intensity,and boundary length show high correlation and attain their maxima *** viscosity effects are twofold,stabilize the KHI,and enhance both the local and global TNE *** to the monotonically inhibiting effects of viscosity,the heat conduction effects firstly refrain then enhance the evolution *** physical reasons are analyzed and presented.

关键词： Kelvin-Helmholtz instability discrete Boltzmann method thermodynamic nonequilibrium effect morphological characterization

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Comparison of volume transport in the Halmahera Sea between la Nina 2011 and El Nino 2015 events based on numerical model 2

Comparison of volume transport in the Halmahera Sea between ...

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2nd Maritime Science and Advanced Technology: Marine Science and Technology in Framework of The Sustainable Development Goals, MSAT 2019

作者： Riza, Muhammad Putri, Mutiara R. Mandang, Idris Department of Earth Science Faculty of Earth Science and Technology Bandung Institute of Technology Jalan Ganesha No 10 Bandung40132 Indonesia Hydro-Atmosphere Environment Research Group Physical Oceanography and Computational Modeling Laboratory Program Study of Physics Faculty of Mathematics and Natural Sciences Mulawarman University Jalan Barong Tongkok No 04 Samarinda75123 Indonesia

Variations of volume transport in the Halmahera Sea are strongly influenced by the El Nino Southern Oscillation (ENSO). Based on the Southern Oscillation Index (SOI), in 2011 La Nina event took place with a strength of 3.02, while in 2015 El Nino occurred with a strength of -2.6. This paper discusses the variation of transport volume caused by the ENSO phenomenon based on the results of the Regional Ocean Model System (ROMS). On the Halmahera Sea at a latitude of 0.3°S with a width of 67 km and a depth of down to 200 m, net volume transport always moves southward. The largest volume transport in La Nina 2011 occurred in September-October, which was -8.9 Sv. Meanwhile, in El Nino 2015 the largest volume transport occurred in July-August, which was equal to -4.9 Sv. The cross correlation coefficient between volume transport and SOI in 2011 and 2015 was r = 0.55 and r = 0.61 respectively, where these results indicate a strong relationship. © Published under licence by IOP Publishing Ltd.

关键词： Numerical models

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Breaking Mechanical Holography in Combinatorial Metamaterials

arXiv

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arXiv 2024年

作者： Sirote-Katz, Chaviva Palti, Ofri Spiro, Naomi Kálmán, Tamás Shokef, Yair Department of Biomedical Engineering Tel Aviv University Tel Aviv69978 Israel The Future Scientists Center Alpha Program Tel Aviv Youth University Tel Aviv69978 Israel University of Illinois at Urbana-Champaign UrbanaIL61801 United States Department of Mathematics Institute of Science Tokyo H-214 2-12-1 Ookayama Tokyo Meguro-ku152-8551 Japan Hiroshima University Higashi-Hiroshima Hiroshima739-8526 Japan School of Mechanical Engineering Tel Aviv University Tel Aviv69978 Israel Center for Computational Molecular and Materials Science Tel Aviv University Tel Aviv69978 Israel Center for Physics and Chemistry of Living Systems Tel Aviv University Tel Aviv69978 Israel

Combinatorial mechanical metamaterials are made of anisotropic, flexible blocks, such that multiple metamaterials may be constructed using a single block type, and the system’s response strongly depends on the mutual orientations of the blocks within the lattice. We study a family of possible block types for the square, honeycomb, and cubic lattices. Blocks that are centrally symmetric induce holographic order, such that mechanical compatibility (meaning that blocks do not impede each other’s motion) implies bulk-boundary coupling. With them, one can design a compatible metamaterial that will deform in any desired texture only on part of its boundary. With blocks that break holographic order, we demonstrate how to design the deformation texture on the entire boundary. Correspondingly, the number of compatible holographic metamaterials scales exponentially with the boundary, while in non-holographic cases we show that it scales exponentially with the bulk. © 2024, CC BY.

关键词： Holography

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Preconditioned BFGS-based uncertainty quantification in elastic full waveform inversion

arXiv

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arXiv 2020年

作者： Liu, Qiancheng Beller, Stephen Lei, Wenjie Peter, Daniel Tromp, Jeroen Department of Geosciences Princeton University PrincetonNJ08544 United States Thuwal Saudi Arabia Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Full Waveform Inversion (FWI) has become an essential technique for mapping geophysical subsurface structures. However, proper uncertainty quantification is often lacking in current applications. In theory, uncertainty quantification is related to the inverse Hessian (or the posterior covariance matrix). Even for common geophysical inverse problems its calculation is beyond the computational and storage capacities of the largest high-performance computing systems. In this study, we amend the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to perform uncertainty quantification for large-scale applications. For seismic inverse problems, the limited-memory BFGS (L-BFGS) method prevails as the most efficient quasi-Newton method. We aim to augment it further to obtain an approximate inverse Hessian for uncertainty quantification in FWI. To facilitate retrieval of the inverse Hessian, we combine BFGS (essentially a full-history L-BFGS) with randomized singular value decomposition to determine a low-rank approximation of the inverse Hessian. Setting the rank number equal to the number of iterations makes this solution efficient and memory-affordable even for large-scale problems. Furthermore, based on the Gauss-Newton method, we formulate different initial, diagonal Hessian matrices as preconditioners for the inverse scheme and compare their performances in elastic FWI applications. We highlight our approach with the elastic Marmousi benchmark model, demonstrating the applicability of preconditioned BFGS for large-scale FWI and uncertainty quantification. Copyright © 2020, The Authors. All rights reserved.

关键词： Uncertainty analysis

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Inertial proximal ADMM for separable multi-block convex optimizations and compressive affine phase retrieval

arXiv

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arXiv 2020年

作者： Li, Peng Chen, Wengu Sun, Qiyu School of Mathematics and Statistics Lanzhou University LanzhouGansu China Graduate School China Academy of Engineering Physics Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Department of Mathematics University of Central Florida OrlandoFL32816 United States

Separable multi-block convex optimization problem appears in many mathematical and engineering fields. In the first part of this paper, we propose an inertial proximal ADMM to solve a linearly constrained separable multi-block convex optimization problem, and we show that the proposed inertial proximal ADMM has global convergence under mild assumptions on the regularization matrices. Affine phase retrieval arises in holography, data separation and phaseless sampling, and it is also considered as a nonhomogeneous version of phase retrieval that has received considerable attention in recent years. Inspired by convex relaxation of vector sparsity and matrix rank in compressive sensing and by phase lifting in phase retrieval, in the second part of this paper, we introduce a compressive affine phase retrieval via lifting approach to connect affine phase retrieval with multi-block convex optimization, and then based on the proposed inertial proximal ADMM for multi-block convex optimization, we propose an algorithm to recover sparse real signals from their (noisy) affine quadratic measurements. Our numerical simulations show that the proposed algorithm has satisfactory performance for affine phase retrieval of sparse real *** Codes 65K10, 94A12, 42C15, 52A41 Copyright © 2020, The Authors. All rights reserved.

关键词： Convex optimization

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Instability waves and low-frequency noise radiation in the subsonic chevron jet

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Acta Mechanica Sinica 2018年第3期34卷 421-430页

作者： Lingke Ran Chuangchao Ye Zhenhua Wan Haihua Yang Dejun Sun Department of Modern Mechanics University of Science and Technology of ChinaHefei 230027China Institute of Applied Physics and Computational Mathematics Beijing 100088China

Spatial instability frequency noise radiation at waves associated with low- shallow polar angles in the chevron jet are investigated and are compared to the round counterpart. The Reynolds-averaged Navier-Stokes equations are solved to obtain the mean flow fields, which serve as the baseflow for linear stability analysis. The chevron jet has more complicated instability waves than the round jet, where three types of instability modes are identified in the vicinity of the nozzle, corresponding to radial shear, azimuthal shear, and their integrated effect of the baseflow, respectively. The most unstable frequency of all chevron modes and round modes in both jets decrease as the axial location moves downstream. Besides, the azimuthal shear effect related modes are more unstable than radial shear effect related modes at low frequencies. Compared to a round jet, a chevron jet reduces the growth rate of the most unstable modes at down- stream locations. Moreover, linearized Euler equations are employed to obtain the beam pattern of pressure generated by spatially evolving instability waves at a dominant low frequency St = 0.3, and the acoustic efficiencies of these linear wavepackets are evaluated for both jets. It is found that the acoustic efficiency of linear wavepacket is able to be reduced greatly in the chevron jet, compared to the round jet.

关键词： Instability waves Chevron jet Wavepacket Far-field noise

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Competing electronic states emerging on polar surfaces

arXiv

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arXiv 2022年

作者： Reticcioli, Michele Wang, Zhichang Schmid, Michael Wrana, Dominik Boatner, Lynn A. Diebold, Ulrike Setvin, Martin Franchini, Cesare University of Vienna Faculty of Physics Center for Computational Materials Science Vienna Austria Institute of Applied Physics Technische Universität Wien Vienna Austria State Key Laboratory for Physical Chemistry of Solid Surfaces Collaborative Innovation Center of Chemistry for Energy Materials Department of Chemistry College of Chemistry and Chemical Engineering Xiamen University Xiamen China Department of Surface and Plasma Science Faculty of Mathematics and Physics Charles University Prague 8180 00 Czech Republic Materials Science and Technology Division Oak Ridge National Laboratory Oak Ridge United States Dipartimento di Fisica e Astronomia Università di Bologna Bologna40127 Italy

Excess charge on polar surfaces of ionic compounds is commonly described by the two-dimensional electron gas (2DEG) model, a homogeneous distribution of charge, spatially-confined in a few atomic layers. Here, by combining scanning probe microscopy with density functional theory calculations, we show that excess charge on the polar TaO2 termination of KTaO3(001) forms more complex electronic states with different degrees of spatial and electronic localization: charge density waves (CDW) coexist with strongly-localized electron polarons and bipolarons. These surface electronic reconstructions, originating from the combined action of electron-lattice interaction and electronic correlation, are energetically more favorable than the 2DEG solution. They exhibit distinct spectroscopy signals and impact on the surface properties, as manifested by a local suppression of ferroelectric distortions. Controlling the degree of charge ordering and the transition from ferroelectric to paraelectric states could be of great benefit for the generation and transport of carriers in electronic applications. Copyright © 2022, The Authors. All rights reserved.

关键词： Electronic states

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Numerical study on the turbulent mixing of planar shock-accelerated triangular heavy gases interface

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Acta Mechanica Sinica 2018年第5期34卷 855-870页

作者： Wei-Gang Zeng Jian-Hua Pan Yu-Xin Ren Yu-Tao Sun Department of Engineering Mechanics School of AerospaceTsinghua UniversityBeijing 100084China Institute of Applied Physics and Computational Mathematics Beijing 100094China

The interaction of a planar shock wave with a triangle-shaped sulfur hexafluoride (SF6) cylinder surrounded by air is numerically studied using a high resolution finite volume method with minimum dispersion and controllable dissipation *** vortex dynamics of the Richtmyer-Meshkov instability and the turbulent mixing induced by the KelvinHelmholtz instability are discussed.A modified reconstruction model is proposed to predict the circulation for the shock triangular gas-cylinder interaction *** typical stages leading the shock-driven inhomogeneity flow to turbulent mixing transition are *** the decoupled length scales and the broadened inertial range of the turbulent kinetic energy spectrum in late time manifest the turbulent mixing transition for the present *** analysis of variable-density energy transfer indicates that the flow structures with high wavenumbers inside the Kelvin-Helmholtz vortices can gain energy from the mean flow in ***,small scale flow structures are generated therein by means of nonlinear ***,the occasional 'pairing' between a vortex and its neighboring vortex will trigger the merging process of vortices and,finally,create a large turbulent mixing zone.

关键词： Richtmyer-Meshkov instability Kelvin-Helmholtz instability Length scale Turbulent mixing

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Bayesian quantum phase estimation with fixed photon states

arXiv

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arXiv 2023年

作者： Zhou, Boyu Guha, Saikat Gagatsos, Christos N. Department of Physics The University of Arizona 1118 E 4th St TucsonAZ85721 United States Department of Electrical and Computer Engineering University of Maryland 2410 A.V. Williams Building College ParkMD20742 United States Wyant College of Optical Sciences The University of Arizona 1630 E University Blvd TucsonAZ85721 United States Department of Electrical and Computer Engineering The University of Arizona 1230 E Speedway Blvd TucsonAZ85721 United States Program in Applied Mathematics The University of Arizona 617 N. Santa Rita TucsonAZ85721 United States

We consider a two-mode bosonic state with fixed photon number n ∈ N, whose upper and lower modes pick up a phase and − respectively. We compute the optimal Fock coefficients of the input state, such that the mean square error (MSE) for estimating is minimized while the minimum MSE is always attainable by a measurement. Our setting is Bayesian, i.e., we consider to be a random variable that follows a prior probability distribution function (PDF). Initially, we consider the flat prior PDF and we discuss the well-known fact that the MSE is not an informative tool for estimating a phase when the variance of the prior PDF is large. Therefore, we move on to study truncated versions of the flat prior in both single-shot and adaptive approaches. For our adaptive technique we consider n = 1 and truncated prior PDFs. Each subsequent step utilizes as prior PDF the posterior probability of the previous step and at the same time we update the optimal state and optimal measurement. Copyright © 2023, The Authors. All rights reserved.

关键词： Distribution functions

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