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Isotope effects in x-ray absorption spectra of liquid water

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arXiv 2020年

作者： Zhang, Chunyi Zhang, Linfeng Xu, Jianhang Tang, Fujie Santra, Biswajit Wu, Xifan Department of Physics Temple University PhiladelphiaPA19122 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The isotope effects in x-ray absorption spectra of liquid water are studied by a many-body approach within electron-hole excitation theory. The molecular structures of both light and heavy water are modeled by path-integral molecular dynamics based on the advanced deep-learning technique. The neural network is trained on ab initio data obtained with SCAN density functional theory. The experimentally observed isotope effect in x-ray absorption spectra is reproduced semi-quantitatively in theory. Compared to the spectrum in normal water, the blueshifted and less pronounced pre- and main-edge in heavy water reflect that the heavy water is more structured at short- and intermediate-range of the hydrogen-bond network. In contrast, the isotope effect on the spectrum is negligible at post-edge, which is consistent with the identical long-range ordering in both liquids as observed in the diffraction experiment. Copyright © 2020, The Authors. All rights reserved.

关键词： Heavy water

A Probabilistic Approach to Discounted Infinite Horizon and Invariant Mean Field Games

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arXiv 2024年

作者： Carmona, René Tangpi, Ludovic Zhang, Kaiwen Operations Research and Financial Engineering Program in Applied and Computational Mathematics Princeton University United States Operations Research and Financial Engineering Princeton University United States

This paper considers discounted infinite horizon mean field games by extending the probabilistic weak formulation of the game as introduced in [16]. Under similar assumptions as in the finite horizon game, we prove existence and uniqueness of solutions for the extended infinite horizon game. The key idea is to construct local versions of the previously considered stable topologies. Further, we analyze how sequences of finite horizon games approximate the infinite horizon one. Under a weakened Lasry-Lions monotonicity condition, we can quantify the convergence rate of solutions for the finite horizon games to the one for the infinite horizon game using a novel stability result for mean field games. Lastly, applying our results allows to solve the invariant mean field game as well. Copyright © 2024, The Authors. All rights reserved.

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Thermal disorder and phonon softening in the ferroelectric phase transition of lead titanate

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arXiv 2024年

作者： Xie, Pinchen Chen, Yixiao Weinan, E. Car, Roberto Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States AI for Science Institute Beijing China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing China Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Materials Institute Princeton University PrincetonNJ08544 United States

We report an extensive molecular dynamics study of ab-initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium upon crossing the transition temperature. We find that the macroscopic polarization appears/disappears due to dipolar switching at the nanometer scale. We also compute the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. For a long time, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation due to the thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases. © 2024, CC BY.

关键词： Ferroelectricity

Cluster synchronization of diffusively-coupled nonlinear systems: A contraction based approach

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arXiv 2017年

作者： Aminzare, Zahra Dey, Biswadip Davison, Elizabeth N. Leonard, Naomi Ehrich Program in Applied and Computational Mathematics Princeton University NJ08544 United States Department of Mechanical and Aerospace Engineering Princeton University NJ08540 United States

Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with neuronal spiking dynamics, we show that our new sufficient condition is tighter than those found in previous analyses which used nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex oscillatory systems. Copyright © 2017, The Authors. All rights reserved.

关键词： Synchronization

Hyperuniform states of matter

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arXiv 2018年

作者： Torquato, Salvatore 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

Hyperuniform states of matter are correlated systems that are characterized by an anomalous suppression of long-wavelength (i.e., large-length-scale) density fluctuations compared to those found in garden-variety disordered systems, such as ordinary fluids and amorphous solids. All perfect crystals, perfect quasicrystals and special disordered systems are hyperuniform. Thus, the hyperuniformity concept enables a unified framework to classify and structurally characterize crystals, quasicrystals and the exotic disordered varieties. While disordered hyperuniform systems were largely unknown in the scientific community over a decade ago, now there is a realization that such systems arise in a host of contexts across the physical, materials, chemical, mathematical, engineering, and biological sciences, including disordered ground states, glass formation, jamming, Coulomb systems, spin systems, photonic and electronic band structure, localization of waves and excitations, self-organization, fluid dynamics, number theory, stochastic point processes, integral and stochastic geometry, the immune system, and photoreceptor cells. Such unusual amorphous states can be obtained via equilibrium or nonequilibrium routes, and come in both quantum-mechanical and classical varieties. The connections of hyperuniform states of matter to many different areas of fundamental science appear to be profound and yet our theoretical understanding of these unusual systems is only in its infancy. The purpose of this review article is to introduce the reader to the theoretical foundations of hyperuniform ordered and disordered systems. Special focus will be placed on fundamental and practical aspects of the disordered kinds, including our current state of knowledge of these exotic amorphous systems as well as their formation and novel physical properties. Copyright © 2018, The Authors. All rights reserved.

关键词： Ground state

Hardware software co-design of a fast bilateral filter in FPGA

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Hardware software co-design of a fast bilateral filter in FP...

Annual IEEE India Conference

作者： Chandrajit Pal Kunal N. Chaudhury Asit Samanta Amlan Chakrabarti Ranjan Ghosh A.K Choudhury School of Information Technology University of Calcutta Program in Applied and Computational Mathematics (PACM) Princeton University Institute of RadioPhysics and Electronics University of Calcutta

ISBN: (纸本)9781479922765

Bilateral filters are widely used in computer vision and digital imaging applications such as denoising, video abstraction, demosaicing, optical-flow estimation etc. to name a few. Its smoothing and edge preserving characteristics suites perfectly for image and video processing applications, yet its high computational complexity makes real-time hardware implementation a challenging task. This paper provides an efficient Field programmable Gate Array (FPGA) based implementation of an edge preserving fast bilateral filter on a hardware software co-design environment of a most recent algorithm preserving the boundaries, spikes and canyons in presence of noise. Further, the four stage parallel pipelined architecture greatly improves the speed of operation. Moreover, our separable kernel implementation of the filtering hardware increases the speed of execution by almost five times than the traditional convolution filtering, while utilizing less hardware resource.

关键词： Bilateral filter edge-preserving smoothing constant-time algorithm O(1) complexity raised cosines FPGA system generator VHDL

Unbiased and Multilevel Methods for a Class of Diffusions Partially Observed via Marked Point Processes

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arXiv 2023年

作者： Alvarez, Miguel Jasra, Ajay Ruzayqat, Hamza Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this article we consider the filtering problem associated to partially observed diffusions, with observations following a marked point process. In the model, the data form a point process with observation times that have its intensity driven by a diffusion, with the associated marks also depending upon the diffusion process. We assume that one must resort to time-discretizing the diffusion process and develop particle and multilevel particle filters to recursively approximate the filter. In particular, we prove that our multilevel particle filter can achieve a mean square error (MSE) of O(∈2) (∈ > 0 and arbitrary) with a cost of O(∈-2.5) versus using a particle filter which has a cost of O(∈-3) to achieve the same MSE. We then show how this methodology can be extended to give unbiased (that is with no time-discretization error) estimators of the filter, which are proved to have finite variance and with high-probability have finite cost. Finally, we extend our methodology to the problem of online static-parameter estimation. Key words: Unbiased Methods, Multilevel Monte Carlo, Non-Linear Filtering, Point Processes, Parameter *** Codes 60G55, 60G35, 62M20, 62F30 © 2023, CC BY.

关键词： Diffusion

Three-Dimensional Instability of Elliptical Flow

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Physical Review Letters 1986年第17期57卷 2160-2160页

作者： B. J. Bayly Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 United States Courant Institute of Mathematical Sciences New York NY 10012 251 Mercer Street United States

A theory is presented for Pierrehumbert's three-dimensional short-wave inviscid instability of the simple two-dimensional elliptical flow with velocity field u(x,y,z)=Ω(−Ey,E−1x,0). The fundamental modes, which are also exact solutions of the nonlinear equations, are plane waves whose wave vector rotates elliptically around the z axis with period 2πΩ. The growth rates are the exponents of a matrix Floquet problem, and agree with those calculated by Pierrehumbert.

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Image Recovery from Rotational And Translational Invariants

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Image Recovery from Rotational And Translational Invariants

IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Nicholas F. Marshall Ti-Yen Lan Tamir Bendory Amit Singer Department of Mathematics Princeton University Princeton NJ USA The Program in Applied and Computational Mathematics Princeton University Princeton NJ USA School of Electrical Engineering Tel Aviv University Tel Aviv Israel

ISBN: (数字)9781509066315

ISBN: (纸本)9781509066322

We introduce a framework for recovering an image from its rotationally and translationally invariant features based on autocorrelation analysis. This work is an instance of the multi-target detection statistical model, which is mainly used to study the mathematical and computational properties of single-particle reconstruction using cryo-electron microscopy (cryo-EM) at low signal-to-noise ratios. We demonstrate with synthetic numerical experiments that an image can be reconstructed from rotational and translational invariants and show that the reconstruction is robust to noise. These results constitute an important step towards the goal of structure determination of small biomolecules using cryo-EM.

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