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Semiclassical trajectory perspective of glory rescattering in strong-field photoelectron holography

Physical Review A 2022年第5期105卷 053115-053115页

作者： L. G. Liao Q. Z. Xia J. Cai J. Liu School of Physics Peking University Beijing 100871 China CAPT HEDPS and IFSA Collaborative Innovation Center of MoE Peking University Beijing 100871 China National Laboratory of Science and Technology on Computational Physics Institute of Applied Physics and Computational Mathematics Beijing 100088 China School of Physics and Electronic Engineering Jiangsu Normal University Xuzhou 221116 China Graduate School of China Academy of Engineering Physics Beijing 100193 China

We investigate theoretically the photoelectron momentum distribution (PMD) of ionized atoms irradiated by a linearly polarized intense laser, focusing on the holography interference patterns in PMD that carry important information of the initial wavefunction of a tunneled electron and its experienced atomic potential in rescattering. With the help of Dyson series and a semiclassical propagator, we calculate the scattering amplitudes in the cylindrical coordinate representation. In contrast to conventional recognitions that photoelectron holography is the interference of two branches of electron trajectories, however, we find strikingly that infinitely many semiclassical trajectories can be deflected by the combined Coulomb potential and laser field into the same final momentum. The initial momenta are found to be distributed on a ring-shaped curve in the transverse momentum plane and the initial positions of these trajectories are perpendicular to their initial momentum vectors. For the zero final transverse momentum, the above ring-source trajectories degenerate into the point-source axial caustic trajectories (or glory trajectories) and the quantum interference of these trajectories will dramatically alter the scattering amplitudes, which is termed the glory rescattering effect. By following Berry's spirit of uniform approximation for glory scattering in optics, we can finally derive a uniform formulation of the rescattering amplitude in the Bessel functions for the strong-field photoelectron holography patterns. Our results are in good agreement with solutions of the time-dependent Schrödinger equation and can account for recent photoelectron holography experiments. Important applications of our theory are also discussed.

关键词： Strong-field-induced spectra Atoms Semiclassical methods

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DATA-DRIVEN MORI-ZWANZIG: REDUCED ORDER MODELING OF SPARSE SENSORS MEASUREMENTS FOR BOUNDARY LAYER TRANSITION

arXiv

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arXiv 2023年

作者： Woodward, Michael Tian, Yifeng Mohan, Arvind Lin, Yen Ting Hader, Christoph Fasel, Hermann Chertkov, Michael Livescu, Daniel Computer Computational and Statistical Sciences Division Los Alamos National Laboratory Los AlamosNM87544 United States Graduate Interdisciplinary Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ85721 United States Department of Aerospace and Mechanical Engineering University of Arizona TucsonAZ85721 United States

Understanding, predicting and controlling laminar-turbulent boundary-layer transition is crucial for the next generation aircraft design. However, in real flight experiments, or wind tunnel tests, often only sparse sensor measurements can be collected at fixed locations. Thus, in developing reduced models for predicting and controlling the flow at the sensor locations, the main challenge is in accounting for how the surrounding field of unobserved (or unresolved) variables interacts with the observed (or resolved) variables at the fixed sensor locations. This makes the Mori-Zwanzig (MZ) formalism a natural choice, as it results in the Generalized Langevin Equations which provides a mathematically sound framework for constructing non-Markovian reduced-order models that include the effects the unresolved variables have on the resolved variables. These effects are captured in the so called memory kernel and orthogonal dynamics, which, when using Mori's linear projection, provides a higher order approximation to the traditional approximate Koopman learning methods. In this work, we explore recently developed data-driven methods for extracting the MZ operators to two boundary-layer flows obtained from high resolution data;a low speed incompressible flow over a flat plate exhibiting bypass transition;and a high speed compressible flow over a flared cone at Mach 6 and zero angle of attack where transition was initiated using a broadband forcing approach ("natural" transition). In each case, an array of "sensors" are placed near the surface of the solid boundary, and the MZ operators are learned and the predictions are compared to the Extended Dynamic Mode Decomposition (EDMD), both using delay embedded coordinates. Further comparisons are made with Long Short-Term Memory (LSTM) and a regression based projection framework using neural networks for the MZ operators. First, we compare the effects of including delay embedded coordinates with EDMD and Mori based MZ and provide

关键词： Dynamic mode decomposition

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Periodicity Scoring of Time Series Encodes Dynamical Behavior of the Tumor Suppressor p53 ⁎ ⁎

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IFAC-PapersOnLine 2021年第9期54卷 488-495页

作者： Caroline Moosmüller Christopher J. Tralie Mahdi Kooshkbaghi Zehor Belkhatir Maryam Pouryahya José Reyes Joseph O. Deasy Allen R. Tannenbaum Ioannis G. Kevrekidis C. Moosmüller and C. Tralie contributed equally to this work Department of Mathematics University of California San Diego La Jolla CA 92093 USA Department of Medical Physics Memorial Sloan-Kettering Cancer Center NY USA Department of Chemical and Biomolecular Engineering Johns Hopkins University Baltimore MD 21218 USA Department of Mathematics and Computer Science Ursinus College Collegeville PA USA Program in Applied and Computational Mathematics Princeton University NJ USA School of Engineering and Sustainable Development De Montfort University Leicester UK Cancer Biology and Genetics Program and Computational and Systems Biology Program Memorial Sloan-Kettering Cancer Center New York NY 10065 USA and Department of Systems Biology Harvard Medical School Boston MA 02115 USA Departments of Computer Science and Applied Mathematics & Statistics Stony Brook University NY USA

In this paper we analyze the dynamical behavior of the tumor suppressor protein p53, an essential player in the cellular stress response, which prevents a cell from dividing if severe DNA damage is present. When this response system is malfunctioning, e.g. due to mutations in p53, uncontrolled cell proliferation may lead to the development of cancer. Understanding the behavior of p53 is thus crucial to prevent its failing. It has been shown in various experiments that periodicity of the p53 signal is one of the main descriptors of its dynamics, and that its pulsing behavior (regular vs. spontaneous) indicates the level and type of cellular stress. In the present work, we introduce an algorithm to score the local periodicity of a given time series (such as the p53 signal), which we call Detrended Autocorrelation Periodicity Scoring (DAPS). It applies pitch detection (via autocorrelation) on sliding windows of the entire time series to describe the overall periodicity by a distribution of localized pitch scores. We apply DAPS to the p53 time series obtained from single cell experiments and establish a correlation between the periodicity scoring of a cell’s p53 signal and the number of cell division events. In particular, we show that high periodicity scoring of p53 is correlated to a low number of cell divisions and vice versa. We show similar results with a more computationally intensive state-of-the-art periodicity scoring algorithm based on topology known as Sw1PerS. This correlation has two major implications: It demonstrates that periodicity scoring of the p53 signal is a good descriptor for cellular stress, and it connects the high variability of p53 periodicity observed in cell populations to the variability in the number of cell division events.

关键词： Systems biology cellular systems time series modeling bioinformatics computational biology

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Nonuniform 3D finite difference elastic wave simulation on staggered grids

arXiv

引用

arXiv 2020年

作者： Gao, Longfei Ghattas, Omar Keyes, David Oden Institute for Computational Engineering and Sciences The University of Texas at Austin AustinTX78712 United States Oden Institute for Computational Engineering and Sciences Jackson School of Geosciences Department of Mechanical Engineering The University of Texas at Austin AustinTX78712 United States Applied Mathematics and Computational Science Program Extreme Computing Research Center King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

We present an approach to simulate the 3D isotropic elastic wave propagation using nonuniform finite difference discretization on staggered grids. Specifically, we consider simulation domains composed of layers of uniform grids with different grid spacings, separated by nonconforming interfaces. We demonstrate that this layer-wise finite difference discretization has the potential to significantly reduce the simulation cost, compared to its fully uniform counterpart. Stability of such a discretization is achieved by using specially designed difference operators, which are variants of the standard difference operators with adaptations near boundaries or interfaces, and penalty terms, which are appended to the discretized wave system to weakly impose boundary or interface conditions. Combined with specially designed interpolation operators, the discretized wave system is shown to preserve the energy conserving property of the continuous elastic wave equation, and a fortiori ensure the stability of the simulation. Numerical examples are presented to demonstrate the efficacy of the proposed simulation approach. © 2020, CC BY.

关键词： Elastic waves

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Mori–Zwanzig Modal Decomposition

arXiv

引用

arXiv 2023年

作者： Woodward, Michael Tian, Yifeng Lin, Yen Ting Hader, Christoph Fasel, Hermann Livescu, Daniel Graduate Interdisciplinary Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ85721 United States Computer Computational and Statistical Sciences Division Los Alamos National Laboratory Los AlamosNM87544 United States Department of Aerospace and Mechanical Engineering University of Arizona TucsonAZ85721 United States

We introduce the Mori-Zwanzig (MZ) Modal Decomposition (MZMD), a novel technique for performing modal analysis of large scale spatio-temporal structures in complex dynamical systems, and show that it represents an efficient generalization of Dynamic Mode Decomposition (DMD). The MZ formalism provides a mathematical framework for constructing non-Markovian reduced-order models of resolved variables from high-dimensional dynamical systems, incorporating the effects of unresolved dynamics through the memory kernel and orthogonal dynamics. We present a formulation and analysis of the modes and spectrum from MZMD and compare it to DMD when applied to a complex flow: a Direct Numerical Simulation (DNS) data-set of laminar-turbulent boundary-layer transition flow over a flared cone at Mach 6. We show that the addition of memory terms by MZMD improves the resolution of spatio-temporal structures within the transitional/turbulent regime, which contains features that arise due to nonlinear mechanisms, such as the generation of the so-called "hot" streaks on the surface of the flared cone. As a result, compared to DMD, MZMD improves future state prediction accuracy, while requiring nearly the same computational cost. Copyright © 2023, The Authors. All rights reserved.

关键词： Dynamic mode decomposition

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Data-Driven Mori-Zwanzig: Approaching a Reduced Order Model for Hypersonic Boundary Layer Transition

arXiv

引用

arXiv 2023年

作者： Woodward, Michael Tian, Yifeng Mohan, Arvind Lin, Yen Ting Hader, Christoph Fasel, Hermann Chertkov, Misha Livescu, Daniel Graduate Interdisciplinary Program in Applied Mathematics Department of Mathematics University of Arizona TucsonAZ85721 United States Computer Computational and Statistical Sciences Division Los Alamos National Laboratory Los AlamosNM87544 United States Department of Aerospace and Mechanical Engineering University of Arizona TucsonAZ85721 United States

In this work, we apply, for the first time to spatially inhomogeneous flows, a recently developed data-driven learning algorithm of Mori-Zwanzig (MZ) operators, which is based on a generalized Koopman’s description of dynamical systems. The MZ formalism provides a mathematically exact procedure for constructing non-Markovian reduced-order models of resolved variables from high-dimensional dynamical systems, where the effects due to the unresolved dynamics are captured in the memory kernel and orthogonal dynamics. The algorithm developed in this work applies Mori’s linear projection operator and an SVD based compression to the selection of the resolved variables (equivalently, a low rank approximation of the two time covariance matrices). We show that this MZ decomposition not only identifies the same spatio-temporal structures found by DMD, but it can also be used to extract spatio-temporal structures of the hysteresis effects present in the memory kernels. We perform an analysis of these structures in the context of a laminar-turbulent boundary-layer transition flow over a flared cone at Mach 6, and show the dynamical relevance of the memory kernels. Additionally, by including these memory terms learned in our data-driven MZ approach, we show improvement in prediction accuracy over DMD at the same level of truncation and at a similar computational cost. Furthermore, an analysis of the spatio-temporal structures of the MZ operators shows identifiable structures associated with the nonlinear generation of the so-called "hot" streaks on the surface of the flared cone, which have previously been observed in experiments and direct numerical simulations. Copyright © 2023, The Authors. All rights reserved.

关键词： Dynamic mode decomposition

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Velocity-gauge Real-time Time-dependent Density Functional Tight-binding for Large-scale Condensed Matter Systems

arXiv

引用

arXiv 2023年

作者： Xu, Qiang Del Ben, Mauro Okyay, Mahmut Sait Choi, Min Ibrahim, Khaled Z. Wong, Bryan M. Materials Science & Engineering Program Department of Chemistry Department of Physics & Astronomy University of California-Riverside RiversideCA92521 United States Applied Mathematics & Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

We present a new velocity-gauge real-time, time-dependent density functional tight-binding (VG-rtTDDFTB) implementation in the open-source DFTB+ software package (https://***) for probing electronic excitations in large, condensed matter systems. Our VG-rtTDDFTB approach enables real-time electron dynamics simulations of large, periodic, condensed matter systems containing thousands of atoms with a favorable computational scaling as a function of system size. We provide computational details and benchmark calculations to demonstrate its accuracy and computational parallelizability on a variety of large material systems. As a representative example, we calculate laser-induced electron dynamics in a 512-atom amorphous silicon supercell to highlight the large periodic systems that can be examined with our implementation. Taken together, our VG-rtTDDFTB approach enables new electron dynamics simulations of complex systems that require large periodic supercells, such as crystal defects, complex surfaces, nanowires, and amorphous materials. Copyright © 2023, The Authors. All rights reserved.

关键词： Gages

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Novel linear algebraic theory and one-hundred-million-atom quantum material simulations on the K computer 1

Novel linear algebraic theory and one-hundred-million-atom q...

引用

1st International Workshop on computational science and Engineering, IWCSE 2013

作者： Hoshi, Takeo Sogabe, Tomohiro Miyata, Takafumi Lee, Dongjin Zhang, Shao-Liang Imachi, Hiroto Kawai, Yoshifumi Akiyama, Yohei Yamazaki, Keita Yokoyama, Seiya Department of Applied Mathematics and Physics Tottori University Koyama Minami Tottori680-8550 Japan 5 Sanbancho Chiyoda-ku Tokyo102-0075 Japan Graduate School of Information Science and Technology Aichi Prefectural University 1522-3 Ibaragabasama Kumabari Nagakute-cho Aichi-gun Aichi480-1198 Japan Department of Computational Science and Engineering Nagoya University Furo-cho Chikusa-ku Nagoya464-8603 Japan Center for Research and Development of Higher Education University of Tokyo Bunkyo-ku Tokyo113-8656 Japan

The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are Krylov-subspace (iterative) solvers for generalized shifted linear equations, in the form of (zS-H)x = b, in stead of conventional generalized eigen-value equation. The method was implemented in our order-N calculation code ELSES (http://***/) with modelled systems based on ab initio calculations. The code realized one-hundred-million-atom, or 100-nm-scale, quantum material simulations on the K computer in a high parallel efficiency with up to all the built-in processor cores. The present paper also explains several methodological aspects, such as use of XML files and 'novice' mode for general users. A sparse matrix data library in our real problems (http://***/matrix/) was prepared. Internal eigen-value problem is discussed as a general need from the quantum material simulation. The present study is a interdisciplinary one and is sometimes called 'Application-Algorithm-Architecture co-design'. The co-design will play a crucial role in exa-scale scientific computations. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.

关键词： Iterative methods

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Controlling multiple filaments by relativistic optical vortex beams in plasmas

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Physical Review E 2016年第3期94卷 033202-033202页

作者： L. B. Ju T. W. Huang K. D. Xiao G. Z. Wu S. L. Yang R. Li Y. C. Yang T. Y. Long H. Zhang S. Z. Wu B. Qiao S. C. Ruan C. T. Zhou Graduate School China Academy of Engineering Physics Beijing 100088 People's Republic of China Institute of Applied Physics and Computational Mathematics Beijing 100094 People's Republic of China HEDPS Center for Applied Physics and Technology and School of Physics Peking University Beijing 100871 People's Republic of China College of Electronic Science and Technology Shenzhen University Shenzhen 518060 People's Republic of China

Filamentation dynamics of relativistic optical vortex beams (OVBs) propagating in underdense plasma is investigated. It is shown that OVBs with finite orbital angular momentum (OAM) exhibit much more robust propagation behavior than the standard Gaussian beam. In fact, the growth rate of the azimuthal modulational instability decreases rapidly with increase of the OVB topological charge. Thus, relativistic OVBs can maintain their profiles for significantly longer distances in an underdense plasma before filamentation occurs. It is also found that an OVB would then break up into regular filament patterns due to conservation of the OAM, in contrast to a Gaussian laser beam, which in general experiences random filamentation.

关键词： Self-focusing & filamentation in plasmas

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Irregular oscillatory-patterns in the early-time region of coherent phonon generation in silicon

arXiv

引用

arXiv 2017年

作者： Watanabe, Yohei Hino, Ken-Ichi Hase, Muneaki Maeshima, Nobuya Doctoral Program in Materials Science Graduate School of Pure and Applied Sciences University of Tsukuba Tsukuba Ibaraki305-8573 Japan Division of Materials Science Faculty of Pure and Applied Sciences University of Tsukuba Tsukuba305-8573 Japan Center for Computational Sciences University of Tsukuba Tsukuba305-8577 Japan Division of Applied Physics Faculty of Pure and Applied Sciences University of Tsukuba Tsukuba305-8573 Japan

Coherent phonon (CP) generation in an undoped Si crystal is theoretically investigated to shed light on unexplored quantum-mechanical effects in the early-time region immediately after the irradiation of ultrashort laser pulse. One examines time signals attributed to an induced charge density of an ionic core, placing the focus on the effects of the Rabi frequency ωocvon the signals;this frequency corresponds to the peak electric-field of the pulse. It is found that at specific ωocv's where the energy of plasmon caused by photoexcited carriers coincides with the longitudinal-optical phonon energy, the energetically resonant interaction between these two modes leads to striking anticrossings, revealing irregular oscillations with anomalously enhanced amplitudes in the observed time signals. Also, the oscillatory pattern is subject to the Rabi flopping of the excited carrier density that is controlled by ωocv. These findings show that the early-time region is enriched with quantum-mechanical effects inherent in the CP generation, though experimental signals are more or less masked by the so-called coherent artifact due to nonlinear optical effects. Copyright © 2017, The Authors. All rights reserved.

关键词： Ultrashort pulses

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