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Gap sensitivity reveals universal behaviors in optimized photonic crystal and disordered networks

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arXiv 2021年

作者： Klatt, Michael Andreas Steinhardt, Paul J. Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Institut für Theoretische Physik University of Erlangen-Nürnberg Staudtstr. 7 Erlangen91058 Germany Department of Chemistry Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Through an extensive series of high-precision numerical computations of the optimal complete photonic band gap (PBG) as a function of dielectric contrast α for a variety of crystal and disordered heterostructures, we reveal striking universal behaviors of the gap sensitivity S(α) ≡ d∆(α)/dα, the first derivative of the optimal gap-to-midgap ratio ∆(α). In particular, for all our crystal networks, S(α) takes a universal form that is well approximated by the analytic formula for a one-dimensional quarter-wave stack, SQWS(α). Even more surprisingly, the values of S(α) for our disordered networks converge to SQWS(α) for sufficiently large α. A deeper understanding of the simplicity of this universal behavior may provide fundamental insights about PBG formation and guidance in the design of novel photonic *** Codes 78A48, 78M50 (Primary) 82D25, 82D30, 52C99 (Secondary) © 2021, CC BY-SA.

关键词： Photonic band gap

Symplectic model reduction of Hamiltonian systems using data-driven quadratic manifolds

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arXiv 2023年

作者： Sharma, Harsh Mu, Hongliang Buchfink, Patrick Geelen, Rudy Glas, Silke Kramer, Boris Department of Mechanical and Aerospace Engineering University of California San DiegoCA United States Department of Applied Mathematics University of Twente Enschede Netherlands Institute of Applied Analysis and Numerical Simulation University of Stuttgart Stuttgart Germany Oden Institute for Computational Engineering and Sciences University of Texas AustinTX United States

This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical symplectic model reduction approaches employ linear symplectic subspaces for representing the high-dimensional system states in a reduced-dimensional coordinate system. While these approximations respect the symplectic nature of Hamiltonian systems, linear basis approximations can suffer from slowly decaying Kolmogorov N-width, especially in wave-type problems, which then requires a large basis size. We propose two different model reduction methods based on recently developed quadratic manifolds, each presenting its own advantages and limitations. The addition of quadratic terms to the state approximation, which sits at the heart of the proposed methodologies, enables us to better represent intrinsic low-dimensionality in the problem at hand. Both approaches are effective for issuing predictions in settings well outside the range of their training data while providing more accurate solutions than the linear symplectic reduced-order models. © 2023, CC BY.

关键词： Hamiltonians

Orbital-selective Kondo entanglement and antiferromagnetic order in USb2

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arXiv 2019年

作者： Chen, Q.Y. Luo, X.B. Xie, D.H. Li, M.L. Ji, X.Y. Zhou, R. Huang, Y.B. Zhang, W. Feng, W. Zhang, Y. Zhu, X.G. Hao, Q.Q. Liu, Q. Huang, L. Zhang, P. Lai, X.C. Si, Q. Tan, S.Y. Science and Technology on Surface Physics and Chemistry Laboratory Mianyang621908 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Shanghai Institute of Applied Physics CAS Shanghai201204 China Department of Physics and Astronomy Rice University HoustonTX77005 United States

In heavy-fermion compounds, the dual character of f electrons underlies their rich and often exotic properties like fragile heavy quasipartilces, variety of magnetic orders and unconventional superconductivity. 5f-electron actinide materials provide a rich setting to elucidate the larger and outstanding issue of the competition between magnetic order and Kondo entanglement and, more generally, the interplay among different channels of interactions in correlated electron systems. Here, by using angle-resolved photoemission spectroscopy, we present detailed electronic structure of USb2 and observed two different kinds of nearly flat bands in the antiferromagnetic state of USb2. Polarization-dependent measurements show that these electronic states are derived from 5f orbitals with different characters;in addition, further temperature-dependent measurements reveal that one of them is driven by the Kondo correlations between the 5f electrons and conduction electrons, while the other reflects the dominant role of the magnetic order. Our results on the low-energy electronic excitations of USb2 implicate orbital selectivity as an important new ingredient for the competition between Kondo correlations and magnetic order and, by extension, in the rich landscape of quantum phases for strongly correlated f electron systems. Copyright © 2019, The Authors. All rights reserved.

关键词： Electronic structure

Erratum to: The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 1: polycrystalline plasticity

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Continuum Mechanics and Thermodynamics 2011年第1期24卷 79-79页

作者： B. D. Reddy Department of Mathematics and Applied Mathematics and Centre for Research in Computational and Applied Mechanics University of Cape Town Rondebosch South Africa

Disordered Heterogeneous Universe: Galaxy Distribution and Clustering across Length Scales

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Physical Review X 2023年第1期13卷 011038-011038页

作者： Oliver H. E. Philcox Salvatore Torquato Department of Astrophysical Sciences Princeton University Princeton New Jersey 08540 USA School of Natural Sciences Institute for Advanced Study 1 Einstein Drive Princeton New Jersey 08540 USA Center for Theoretical Physics Department of Physics Columbia University New York New York 10027 USA Simons Foundation New York New York 10010 USA Department of Chemistry Department of Physics Princeton Materials Institute and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA

The studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the disordered distribution of particles and/or building blocks at microscales to predict physical properties of the medium at macroscales, whether it be a liquid, colloidal suspension, composite material, galaxy cluster, or entire Universe. The theory of disordered heterogeneous media provides an array of theoretical and computational techniques to characterize a wide class of complex material microstructures. In this work, we apply them to describe the disordered distributions of galaxies obtained from recent suites of dark matter simulations. We focus on the determination of lower-order correlation functions, void and particle nearest-neighbor functions, certain cluster statistics, pair-connectedness functions, percolation properties, and a scalar order metric to quantify the degree of order. Compared to analogous homogeneous Poisson and typical disordered systems, the cosmological simulations exhibit enhanced large-scale clustering and longer tails in the void and particle nearest-neighbor functions, due to the presence of quasi-long-range correlations imprinted by early Universe physics, with a minimum particle separation far below the mean nearest-neighbor distance. On large scales, the system appears hyperuniform, as a result of primordial density fluctuations, while on the smallest scales, the system becomes almost antihyperuniform, as evidenced by its number variance. Additionally, via a finite-scaling analysis, we compute the percolation threshold of the galaxy catalogs, finding this to be significantly lower than for Poisson realizations (at reduced density ηc=0.25 in our fiducial analysis compared to ηc=0.34), with strong dependence on the mean density; this is consistent with the observation that the galaxy distribution contains voids of up to 50% larger radius. However, the two sets of simulations appear to share the same fractal dimension on scales much l

关键词： Large scale structure of the Universe

SPACE: 3D parallel solvers for Vlasov-Maxwell and Vlasov-Poisson equations for relativistic plasmas with atomic transformations

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arXiv 2021年

作者： Yu, Kwangmin Kumar, Prabhat Yuan, Shaohua Cheng, Aiqi Samulyak, Roman Computational Science Initiative Brookhaven National Laboratory UptonNY11973 United States Center for Computational Sciences and Engineering Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Applied Mathematics and Statistics Stony Brook University Stony BrookNY11794 United States

A parallel, relativistic, three-dimensional particle-in-cell code SPACE has been developed for the simulation of electromagnetic fields, relativistic particle beams, and plasmas. In addition to the standard second-order Particle-in-Cell (PIC) algorithm, SPACE includes efficient novel algorithms to resolve atomic physics processes such as multi-level ionization of plasma atoms, recombination, and electron attachment to dopants in dense neutral gases. SPACE also contains a highly adaptive particle-based method, called Adaptive Particle-in-Cloud (AP-Cloud), for solving the Vlasov-Poisson problems. It eliminates the traditional Cartesian mesh of PIC and replaces it with an adaptive octree data structure. The code’s algorithms, structure, capabilities, parallelization strategy and performances have been discussed. Typical examples of SPACE applications to accelerator science and engineering problems are also *** Codes I.6, D.2 © 2021, CC BY.

关键词： Beam plasma interactions

Optimized large hyperuniform binary colloidal suspensions in two dimensions

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arXiv 2020年

作者： Ma, Zheng Lomba, Enrique Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Instituto de Química Física Rocasolano CSIC Calle Serrano 119 MadridE-28006 Spain Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The creation of disordered hyperuniform materials with potentially extraordinary optical properties requires a capacity to synthesize large samples that are effectively hyperuniform down to the nanoscale. Motivated by this challenge, we propose a fabrication protocol using binary paramagnetic colloidal particles confined in a 2D plane. The strong and long-ranged dipolar interaction induced by a tunable magnetic field is free from screening effects that attenuates long-ranged electrostatic interactions in charged colloidal systems. Specifically, we find a family of optimal size ratios that makes the two-phase system effectively hyperuniform. We show that hyperuniformity is a general consequence of low isothermal compressibilities, which makes our protocol suitable to systems with other long-ranged soft interactions, dimensionalities and/or polydispersity. Our methodology paves the way to synthesize large photonic hyperuniform materials that function in the visible to infrared range and hence may accelerate the discovery of novel photonic materials. Copyright © 2020, The Authors. All rights reserved.

关键词： Suspensions (fluids)

Data-driven modeling of rotating detonation waves

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arXiv 2020年

作者： Mendible, Ariana Koch, James Lange, Henning Brunton, Steven L. Kutz, J. Nathan Department of Mechanical Engineering University of Washington SeattleWA98195 United States Oden Institute for Computational and Engineering Sciences University of Texas AustinTX78712 United States Department of Applied Mathematics University of Washington SeattleWA98195 United States

The direct monitoring of a rotating detonation engine (RDE) combustion chamber has enabled the observation of combustion front dynamics that are composed of a number of co- and/or counter-rotating coherent traveling shock waves whose nonlinear mode-locking behavior exhibit bifurcations and instabilities which are not well understood. computational fluid dynamics simulations are ubiquitous in characterizing the dynamics of RDE's reactive, compressible flow. Such simulations are prohibitively expensive when considering multiple engine geometries, different operating conditions, and the long-time dynamics of the mode-locking interactions. Reduced-order models (ROMs) provide a critically enabling simulation framework because they exploit low-rank structure in the data to minimize computational cost and allow for rapid parameterized studies and long-time simulations. However, ROMs are inherently limited by translational invariances manifest by the combustion waves present in RDEs. In this work, we leverage machine learning algorithms to discover moving coordinate frames into which the data is shifted, thus overcoming limitations imposed by the underlying translational invariance of the RDE and allowing for the application of traditional dimensionality reduction techniques. We explore a diverse suite of data-driven ROM strategies for characterizing the complex shock wave dynamics and interactions in the RDE. Specifically, we employ the dynamic mode decomposition and a deep Koopman embedding to give new modeling insights and understanding of combustion wave interactions in RDEs. Copyright © 2020, The Authors. All rights reserved.

关键词： Learning algorithms

Flagellum Pumping Efficiency in Shear-Thinning Viscoelastic Fluids

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arXiv 2023年

作者： Barrett, Aaron Fogelson, Aaron L. Gregory Forest, M. Gruninger, Cole Lim, Sookkyung Griffith, Boyce E. Department of Mathematics University of Utah Salt Lake CityUT United States Departments of Mathematics and Biomedical Engineering University of Utah Salt Lake CityUT United States Department of Mathematics University of 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 Department of Mathematical Sciences University of Cincinnati CincinnatiOH 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

Microorganism motility often takes place within complex, viscoelastic fluid environments, e.g., sperm in cervicovaginal mucus and bacteria in biofilms. In such complex fluids, strains and stresses generated by the microorganism are stored and relax across a spectrum of length and time scales and the complex fluid can be driven out of its linear response regime. Phenomena not possible in viscous media thereby arise from feedback between the swimmer and the complex fluid, making swimming efficiency co-dependent on the propulsion mechanism and fluid properties. Here we parameterize a flagellar motor and filament properties together with elastic relaxation and nonlinear shear-thinning properties of the fluid in a computational immersed boundary model. We then explore swimming efficiency, defined as a particular flow rate divided by the torque required to spin the motor, over this parameter space. Our findings indicate that motor efficiency (measured by the volumetric flow rate) can be boosted or degraded by relatively moderate or strong shear-thinning of the viscoelastic environment. Copyright © 2023, The Authors. All rights reserved.

关键词： Shear thinning