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Momentum mapping of continuum-electron wave-packet interference

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Physical Review A 2016年第4期94卷 043419-043419页

作者： Weifeng Yang Huatang Zhang Cheng Lin Jingwen Xu Zhihao Sheng Xiaohong Song Shilin Hu Jing Chen Department of Physics College of Science Shantou University Shantou Guangdong 515063 China CAPT HEDPS and IFSA Collaborative Innovation Center of MoE College of Engineering Peking University Beijing 100084 China Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 China

We analyze the two-dimensional photoelectron momentum distribution of an Ar atom ionized by midinfrared laser pulses and mainly concentrate on the energy range below 2Up. By using a generalized quantum trajectory Monte Carlo simulation and comparing with the numerical solution of the time-dependent Schrödinger equation, we demonstrate that a profound ringlike pattern coming from the interplay between the intra- and the intercycle interferences of electron trajectories can be observed in the deep tunneling ionization regime. Moreover, we found that the rescattered electrons play a negligible role on the formation of a ringlike interference pattern, and the appearance of the ringlike interference pattern masks the holographic interference structure. Our results provide an appropriate experimental condition for the observation of the photoelectron holography and help to gain physical insight into the corresponding ultrafast electron dynamic process with attosecond temporal resolution.

关键词： Atomic & molecular processes in external fields Multiphoton or tunneling ionization & excitation Quantum Monte Carlo

The marginal value formula on regions of stability

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Optimization 1993年第1-2期27卷 17-42页

作者： Van Rooyen, M. Zlobec, S. University of the Witwatersrand Department of Computational & Applied Mathematics 2001 Johannesburg 1 Jan Smuts Avenue South Africa McGill University Department of Mathematics and Statistics Montreal Quebec H3A 2K6 Burnside Hall 805 Sherbrooke Street West Canada

A marginal value formula has recently been introduced for bi-convex mathematical programming models on a particular region of stability. In this paper, first we show that the formula remains valid for convex models and on every region of stability, where a certain point to set mapping is lower semicontinuous. These significantly weaker assumptions enable us to use the formula in new situations, such as interactive methods of multiobjective optimization. One term in the formula contains the directional derivative of the optimal solution function. We find sufficient conditions for the upper Lipschitzian behaviour of the solution set on regions of stability. Finally, we give the marginal value estimates for the case when the saddle points are not unique. Our approach is different from the ones described in the literature because we work with arbitrary stable perturbations and do not assume any constraint qualification. Instead of employing the Fritz John condition we use complete characterizations of optimality. © 1993, Taylor & Francis Group, LLC. All right reserved.

关键词： Lagrange multipliers marginal value optimal solution set Optimal value function point-to-set mapping region of stability

Microstructural and Transport Characteristics of Triply Periodic Bicontinuous Materials

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arXiv 2024年

作者： Torquato, Salvatore Kim, Jaeuk Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Three-dimensional (3D) bicontinuous two-phase materials are increasingly gaining interest because of their unique multifunctional characteristics and advancements in techniques to fabricate them. Because of their complex topological and structural properties, it still has been nontrivial to develop explicit microstructure-dependent formulas to predict accurately their physical properties. A primary goal of the present paper is to ascertain various microstructural and transport characteristics of five different models of triply periodic bicontinuous porous materials at a porosity 1 = 1/2: those in which the two-phase interfaces are the Schwarz P, Schwarz D and Schoen G minimal surfaces as well as two different pore-channel structures. We ascertain their spectral densities, pore-size distribution functions, local volume-fraction variances, and hyperuniformity order metrics and then use this information to estimate certain effective steady-state as well as time-dependent transport properties via closed-form microstructure-property formulas. Specifically, the recently introduced time-dependent diffusion spreadability is determined exactly from the spectral density. Moreover, we accurately estimate the fluid permeability of such porous materials from a closed-form formula that depends on the second moment of the pore-size function and the formation factor, a measure of the tortuosity of the pore space, which is exactly obtained for the three minimal-surface structures. We also rigorously bound the permeability from above using the spectral density. For the five models with identical cubic unit cells, we find that the permeability, inverse of the specific surface, hyperuniformity order metric, pore-size second moment and long-time spreadability behavior are all positively correlated and rank order the structures in exactly the same way. We also conjecture what structures maximize the fluid permeability for arbitrary porosities and show that this conjecture must be true in

关键词： Pore size

Sequences in overpartitions

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arXiv 2021年

作者： Andrews, George E. Uncu, ALI Kemal Pennsylvania State University Department of Mathematics University ParkPA16802 United States Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Science Altenbergerstraße 69 LinzA-4040 Austria University of Bath Faculty of Science Department of Computer Science BathBA2 7AY United Kingdom

This paper is devoted to the study of sequences in overpartitions and their relation to 2-color partitions. An extensive study of a general class of double series is required to achieve these *** Codes Primary 11B65, Secondary 11C08, 11C20, 11P81, 11P84, 05A10, 05A15, 05A17 Copyright © 2021, The Authors. All rights reserved.

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Theoretical Prediction of the Effective Dynamic Dielectric Constant of Disordered Hyperuniform Anisotropic Composites Beyond the Long-Wavelength Regime

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arXiv 2023年

作者： Kim, Jaeuk Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Torquato and Kim [Phys. Rev. X 11, 296 021002 (2021)] derived exact nonlocal strong-contrast expansions of the effective dynamic dielectric constant tensor Εe(kq, ω) that treat general three-dimensional (3D) two-phase composite microstructures, which are valid well beyond the long-wavelength regime. Here, we demonstrate that truncating this general rapidly converging expansion at the two- and three-point levels is a powerful theoretical tool from which one can extract accurate approximations suited for various microstructural symmetries. Among other results, we show that such truncations yield closed-form formulas applicable to transverse polarization in layered media and transverse magnetic polarization in transversely isotropic media, respectively. We apply these formulas to estimate Εe(kq, ω) for models of 3D disordered hyperuniform layered and transversely isotropic media: nonstealthy hyperuniform media and stealthy hyperuniform media. In particular, we show that stealthy hyperuniform layered and transversely isotropic media are perfectly transparent (trivially implying no Anderson localization, in principle) within finite wave number intervals through the third-order terms. For all models considered here, we validate that the second-order formulas, which depend on the spectral density, are already very accurate well beyond the long-wavelength regime by showing very good agreement with the finite-difference time-domain (FDTD) simulations. The high predictive power of the second-order formula is due to the fact that higher-order contributions are negligibly small, implying that it very accurately approximates multiple scattering through all orders. This implies that there can be no Anderson localization within the predicted perfect transparency interval in stealthy hyperuniform layered and transversely isotropic media in practice because the localization length (associated with only possibly negligibly small higher-order contributions) should be very large compar

关键词： Spectral density

ON FINITE ANALOGS of SCHMIDT'S PROBLEM and ITS VARIANTS

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arXiv 2022年

作者： Berkovich, Alexander Uncu, Ali Kemal Department of Mathematics University of Florida 358 Little Hall GainesvilleFL32611 United States University of Bath Faculty of Science Department of Computer Science BathBA2 7AY United Kingdom Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Science Altenbergerstraße 69 LinzA-4040 Austria

We refine Schmidt's problem and a partition identity related to 2-color partitions which we will refer to as Uncu-Andrews-Paule theorem. We will approach the problem using Boulet-Stanley weights and a formula on Rogers-Szego polynomials by Berkovich-Warnaar, and present various Schmidt's problem alike theorems and their refinements. Our new Schmidt type results include the use of even-indexed parts' sums, alternating sum of parts, and hook lengths as well as the odd-indexed parts' sum which appears in the original Schmidt's problem. We also translate some of our Schmidt's problem alike relations to weighted partition counts with multiplicative weights in relation to Rogers-Ramanujan *** Codes 05A15, 05A17, 05A19, 11B34, 11B75, 11P81 Copyright © 2022, The Authors. All rights reserved.

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Two-body fragmentation dynamics of N2Oq+ (q=2,3) induced by electron-capture collisions with 5.7−keV/uXe15+

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Physical Review A 2019年第1期99卷 012710-012710页

作者： Lei Chen Xu Shan Xi Zhao Xiaolong Zhu Xiaoqing Hu Yong Wu Wentian Feng Dalong Guo Ruitian Zhang Yong Gao Zhongkui Huang Jianguo Wang Xinwen Ma Xiangjun Chen Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics University of Science and Technology of China Hefei 230026 China Institute of Modern Physics Chinese Academy of Sciences Lanzhou 730000 China Institute of Applied Physics and Computational Mathematics Chinese Academy of Engineering Physics Beijing 100094 China

Two-body fragmentation of N2Oq+ (q=2,3) induced by electron-capture collision of 5.7−keV/uXe15+ is studied. Through the triply coincident measurement on ion-pair fragments with the scattered projectile and the correlation analysis on the ion-pair time of flight and momentum conservation, we have clearly identified 12 reaction channels for the formation and dissociation of N2O2+ and N2O3+. The fraction ratios for these channels and the corresponding kinetic energy release (KER) distributions for the ion-pair products have been obtained. Calculations of the potential energy curves of N2O3+ for the N-N and N-O bond stretches are performed using the complete active space self-consistent field method. The KER spectra for the two-body fragmentation of N2O2+→N++NO+ and N2++O+ can be explained by the decay via the XΣ−3 and 1Π3 states, and the major peaks or structures observed in the KER spectra for N2O3+→N++NO2+ can be attributed to the 1Π2, 2Π2, and 2Σ−2 states, whereas those in the KER spectra for N2O3+→O++N22+ are mainly contributed from the 1Π2, 3Π2, and 4Π2 states. In addition, we found that the KER structures for the same ion-pair products are not sensitive to the number of electrons stabilized at the projectile, but the KER intensities are clearly dependent on it. The mechanism of multielectron captures of the projectile to form the transient multicharged molecular ions and the following projectile stabilization with or without autoionizing cascades is proposed to explain it.

关键词： Atomic & molecular collisions Ions Molecules Spectroscopy

Strength outlooks for the El Niño-Southern Oscillation

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Weather and Forecasting 2019年第1期34卷 165-175页

作者： L'Heureux, Michelle L. Tippett, Michael K. Takahashi, Ken Barnston, Anthony G. Becker, Emily J. Bell, Gerald D. Di Liberto, Tom E. Gottschalck, Jon Halpert, Michael S. Hu, Zeng-Zhen Johnson, Nathaniel C. Xue, Yan Wang, Wanqiu NOAA/NWS/NCEP/Climate Prediction Center College ParkMD United States Department of Applied Physics and Applied Mathematics Columbia University New YorkNY United States Servicio Nacional de Meteorología e Hidrología del Perú Instituto Geofísico del Perú Lima Peru International Research Institute for Climate and Society Columbia University New YorkNY United States Innovim College ParkMD United States NOAA/Climate Program Office Silver SpringMD United States CollabraLink Technologies Silver SpringMD United States NOAA/Geophysical Fluid Dynamics Laboratory PrincetonNJ United States Atmospheric and Oceanic Sciences Program Princeton University PrincetonNJ United States

Three strategies for creating probabilistic forecast outlooks for El Niño-Southern Oscillation (ENSO) are compared. One is subjective and is currently used by the NOAA/Climate Prediction Center (CPC) to produce official ENSO outlooks. A second is purely objective and is based on the North American Multimodel Ensemble (NMME).Anew third strategy is proposed in which the forecaster only provides the expected value of the Niño-3.4 index, and then categorical probabilities are objectively determined based on past skill. The new strategy results in more confident probabilities compared to the subjective approach and higher verification scores, while avoiding the significant forecast busts that sometimes afflict the NMME-based objective approach. The higher verification scores of the new strategy appear to result from the added value that forecasters provide in predicting the mean, combined with more reliable representations of uncertainty, which is difficult to represent because forecasters often assume less confidence than is justified. Moreover, the new approach can produce higher-resolution probabilistic forecasts that include ENSO strength information and that are difficult, if not impossible, for forecasters to produce. To illustrate, a nine-category ENSO outlook based on the new strategy is assessed and found to be skillful. The new approach can be applied to other outlooks where users desire higher-resolution probabilistic forecasts, including the extremes. © 2019 American Meteorological Society.

关键词： Forecasting

Double-exchange theory of ferroelectric polarization in orthorhombic manganites with twofold periodic magnetic texture

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Physical Review B 2013年第14期87卷 144424-144424页

作者： I. V. Solovyev S. A. Nikolaev Computational Materials Science Unit National Institute for Materials Science 1-2-1 Sengen Tsukuba Ibaraki 305-0047 Japan Department of Theoretical Physics and Applied Mathematics Ural Federal University Mira str. 19 620002 Ekaterinburg Russia

We argue that many aspects of improper ferroelectric (FE) activity in orthorhombic manganites can be rationalized by considering the limit of infinite intra-atomic splitting between majority- and minority-spin states (or the double-exchange limit), which reduces the problem to the analysis of a spinless double-exchange (DE) Hamiltonian. We apply this strategy to the low-energy model, derived from the first-principles electronic-structure calculations, and combine it with the Berry-phase theory of electric polarization. We start with the analysis of the simplest two-orbital model, describing the behavior of the eg bands, and apply it to the E-type antiferromagnetic (AFM) phase, which in the DE limit effectively breaks up into one-dimensional zigzag chains. We derive an analytical expression for the electronic polarization (Pel) and explain how it depends on the orbital ordering and the energy splitting Δ between eg states. Then, we evaluate parameters of this model for the series of manganites. For these purposes, we start from a more general five-orbital model for all Mn 3d bands and construct a new downfolded model for the eg bands. From the analysis of these parameters, we conclude that the behavior of Pel in realistic manganites always corresponds to the limit of large Δ. This property holds for all considered compounds even in the local-density approximation, which typically underestimates Δ. We further utilize this property in order to derive an analytical expression for Pel in a general twofold periodic magnetic texture, based on the five-orbital model and the perturbation-theory expansion for the Wannier functions in the first order of 1/Δ. This expression explains the functional dependence of Pel on the relative directions of spins. Furthermore, it suggests that Pel is related to the asymmetry of transfer integrals, which should have simultaneously symmetric and antisymmetric components in the crystal-field representation. The main contribution to this asymm

关键词： FERROELECTRIC materials MANGANITE POLARIZATION (Electricity) SPINTRONICS HAMILTONIAN systems ELECTRONIC structure GEOMETRIC quantum phases ANTIFERROMAGNETIC materials