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Hamiltonian bridge: A physics-driven generative framework for targeted pattern control

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arXiv 2024年

作者： Krishnan, Vishaal Sinha, Sumit Mahadevan, L. School of Engineering and Applied Sciences Harvard University CambridgeMA02138 United States Department of Data Science Dana-Farber Cancer Institute BostonMA United States Departments of Physics and Organismic and Evolutionary Biology Harvard University CambridgeMA02138 United States

Patterns arise spontaneously in a range of systems spanning the sciences, and their study typically focuses on mechanisms to understand their evolution in space-time. Increasingly, there has been a transition towards controlling these patterns in various functional settings, with implications for engineering. Here, we combine our knowledge of a general class of dynamical laws for pattern formation in non-equilibrium systems, and the power of stochastic optimal control approaches to present a framework that allows us to control patterns at multiple scales, which we dub the "Hamiltonian bridge". We use a mapping between stochastic many-body Lagrangian physics and deterministic Eulerian pattern forming PDEs to leverage our recent approach utilizing the Feynman-Kac-based adjoint path integral formulation for the control of interacting particles and generalize this to the active control of patterning fields. We demonstrate the applicability of our computational framework via numerical experiments on the control of phase separation with and without a conserved order parameter, self-assembly of fluid droplets, coupled reaction-diffusion equations and finally a phenomenological model for spatio-temporal tissue differentiation. We interpret our numerical experiments in terms of a theoretical understanding of how the underlying physics shapes the geometry of the pattern manifold, altering the transport paths of patterns and the nature of pattern interpolation. We finally conclude by showing how optimal control can be utilized to generate complex patterns via an iterative control protocol over pattern forming pdes which can be casted as gradient flows. All together, our study shows how we can systematically build in physical priors into a generative framework for pattern control in non-equilibrium systems across multiple length and time scales. Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

Self-generated magnetic field in three-dimensional ablative Rayleigh-Taylor instability

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arXiv 2024年

作者： Zhang, Dehua Jiang, Xian Tao, Tao Li, Jun Yan, Rui Sun, De-Jun Zheng, Jian Department of Modern Mechanics University of Science and Technology of China Hefei230026 China Department of Plasma Physics and Fusion Engineering University of Science and Technology of China Anhui Hefei230026 China Institute of Applied Physics and Computational Mathematics Beijing100094 China IFSA Collaborative Innovation Center Shanghai Jiao Tong University Shanghai200240 China

The self-generated magnetic field in three-dimensional (3D) single-mode ablative Rayleigh-Taylor instabilities (ARTI) relevant to the acceleration phase of a direct-drive inertial confinement fusion (ICF) implosion is investigated. It is found that stronger magnetic fields up to a few thousands of T can be generated by 3D ARTI than by its two-dimensional (2D) counterpart. The Nernst effects significantly alter the magnetic fields convection and amplify the magnetic fields. The scaling law for the magnetic flux obtained in the 2D simulations performs reasonably well in the 3D cases. While the magnetic field significantly accelerates the bubble growth in the short-wavelength 2D modes through modifying the heat fluxes, the magnetic field mostly accelerates the spike growth but has little influence on the bubble growth in 3D ARTI. Copyright © 2024, The Authors. All rights reserved.

关键词： Acceleration

Generalized quantum asymptotic equipartition

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arXiv 2024年

作者： Fang, Kun Fawzi, Hamza Fawzi, Omar School of Data Science The Chinese University of Hong Kong Guangdong Shenzhen518172 China Department of Applied Mathematics and Theoretical Physics University of Cambridge CambridgeCB3 0WA United Kingdom Inria ENS de Lyon UCBL LIP Lyon69342 Cedex 07 France

The asymptotic equipartition property (AEP) states that in the limit of a large number of independent and identically distributed (i.i.d.) random experiments, the output sequence is virtually certain to come from the typical set, each member of which is almost equally likely. This property is a form of the law of large numbers and lies at the heart of information theory. In this work, we prove a generalized quantum AEP beyond the i.i.d. framework where the random samples are drawn from two sets of quantum states. In particular, under suitable assumptions on the sets, we prove that all operationally relevant divergences converge to the quantum relative entropy between the sets. More specifically, both the quantum hypothesis testing relative entropy (a smoothed form of the min-relative entropy) and the smoothed max-relative entropy approach the regularized relative entropy between the sets. Notably, the asymptotic limit has explicit convergence guarantees and can be efficiently estimated through convex optimization programs, despite the regularization, provided that the sets have efficient descriptions. As the first application, the generalized AEP directly implies a new generalized quantum Stein’s lemma for conducting quantum hypothesis testing between two sets of quantum states. This addresses open questions raised by Brandão et al. [IEEE TIT 66(8):5037–5054, 2020] and Mosonyi et al. [IEEE TIT 68(2):1032-1067, (2022)], which seek a Stein’s lemma with computational efficiency. Moreover, we propose a new framework for quantum resource theory in which state transformations are performed without requiring precise characterization of the states being manipulated, making it more robust to imperfections. We demonstrate the reversibility (also referred to as the second law) of such a theory and identify the regularized relative entropy as the "unique" measure of the resource in this new framework. As the second application, we introduce a quantum version of adversarial hypo

关键词： Quantum channel

Discrete Boltzmann modeling of Rayleigh-Taylor instability: Effects of interfacial tension, viscosity, and heat conductivity

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Physical Review E 2022年第1期106卷 015102-015102页

作者： Jie Chen Aiguo Xu Dawei Chen Yudong Zhang Zhihua Chen Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics P.O. Box 8009-26 Beijing 100088 China Key Laboratory of Transient Physics Nanjing University of Science and Technology Nanjing 210094 China State Key Laboratory of Explosion Science and Technology Beijing Institute of Technology Beijing 100081 China HEDPS Center for Applied Physics and Technology and College of Engineering Peking University Beijing 100871 China School of Mechanics and Safety Engineering Zhengzhou University Zhengzhou 450001 China

The two-dimensional Rayleigh-Taylor instability (RTI) in compressible flow with intermolecular interactions is probed via the discrete Boltzmann method. The effects of interfacial tension, viscosity, and heat conduction are investigated. It is found that the influences of interfacial tension on the perturbation amplitude, bubble velocity, and two kinds of entropy production rates all show differences at different stages of RTI evolution. It inhibits the RTI evolution at the bubble acceleration stage, while at the asymptotic velocity stage, it first promotes and then inhibits the RTI evolution. Viscosity and heat conduction inhibit the RTI evolution. Viscosity shows a suppressive effect on the entropy generation rate related to heat flow at the early stage but a first promotive and then suppressive effect on the entropy generation rate related to heat flow at a later stage. Heat conduction shows a promotive effect on the entropy generation rate related to heat flow at an early stage. Still, it offers a first promotive and then suppressive effect on the entropy generation rate related to heat flow at a later stage. By introducing the morphological boundary length, we find that the stage of exponential growth of the interface length with time corresponds to the bubble acceleration stage. The first maximum point of the interface length change rate and the first maximum point of the change rate of the entropy generation rate related to viscous stress can be used as a criterion for RTI to enter the asymptotic velocity stage.

关键词： Complex fluids Entropy production Flow instability Interface & surface thermodynamics Nonequilibrium & irreversible thermodynamics Rayleigh-Taylor instability Thermodynamics of mixing

Semisupervised regression in latent structure networks on unknown manifolds

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arXiv 2023年

作者： Acharyya, Aranyak Agterberg, Joshua Trosset, Michael W. Park, Youngser Priebe, Carey E. Department of Applied Mathematics and Statistics Johns Hopkins University Baltimore United States Institute for Data Engineering and Science Department of Electrical and Systems Engineering Department of Statistics and Data Science University of Pennsylvania PA United States Department of Statistics Indiana University Bloomington United States Centre for Imaging Science Johns Hopkins University Baltimore United States

Random graphs are increasingly becoming objects of interest for modeling networks in a wide range of applications. Latent position random graph models posit that each node is associated with a latent position vector, and that these vectors follow some geometric structure in the latent space. In this paper, we consider random dot product graphs, in which an edge is formed between two nodes with probability given by the inner product of their respective latent positions. We assume that the latent position vectors lie on an unknown one-dimensional curve and are coupled with a response covariate via a regression model. Using the geometry of the underlying latent position vectors, we propose a manifold learning and graph embedding technique to predict the response variable on out-of-sample nodes, and we establish convergence guarantees for these responses. Our theoretical results are supported by simulations and an application to Drosophila brain data. © 2023, CC BY.

关键词： Vectors

Experimental studies of three-nucleon-system dynamics in proton-induced deuteron breakup at 108 MeV

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Physical Review C 2025年第5期111卷 054001-054001页

作者： A. Łobejko E. Stephan I. Ciepał J. Golak N. Kalantar–Nayestanaki S. Kistryn B. Kłos A. Kozela P. Kulessa W. Parol R. Skibiński I. Skwira-Chalot A. Szadziński A. Wilczek H. Witała B. Włoch J. Zejma Institute of Physics University of Silesia PL-41500 Chorzów Poland Institute of Experimental Physics Faculty of Mathematics Physics and Informatics University of Gdańsk PL-80308 Gdańsk Poland Institute of Nuclear Physics PAS PL-31342 Kraków Poland Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University PL-30348 Kraków Poland ESRIG University of Groningen 9747 AA Groningen The Netherlands Faculty of Physics University of Warsaw PL-02093 Warszawa Poland Université de Bordeaux CNRS LP2I Bordeaux FR-33170 Gradignan France

The differential cross sections for the H2(p,pp)n reaction have been measured for 84 angular configurations of the outgoing protons in the range of polar angles from 13∘ to 33∘ with a proton beam of 108 MeV. data have been collected in the Cyclotron Center Bronowice at the institute of Nuclear physics PAS in Kracow using the BINA detector setup. Analysis leading to determination of the breakup cross-section values is described. Absolute normalization is obtained by normalization to the simultaneously measured H2(p,d)p scattering events. Experimental results are compared to the state-of-the-art theoretical calculations. Global analysis shows significant influence of the Coulomb interaction and small effects of three-nucleon force in the studied phase-space region.

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Measurements of the ^(107)Ag neutron capture cross sections with pulse height weighting technique at the CSNS Back-n facility

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Chinese physics B 2022年第3期31卷 109-116页

作者： Xin-Xiang Li Long-Xiang Liu Wei Jiang Jie Ren Hong-Wei Wang Gong-Tao Fan Jian-Jun He Xi-Guang Cao Long-Long Song Yue Zhang Xin-Rong Hu Zi-Rui Hao Pan Kuang Bing Jiang Xiao-He Wang Ji-Feng Hu Jin-Cheng Wang De-Xin Wang Su-Yalatu Zhang Ying-Du Liu Xu Ma Chun-Wang Ma Yu-Ting Wang Zhen-Dong An Jun Su Li-Yong Zhang Yu-Xuan Yang Wen-Bo Liu Wan-Qing Su Sheng Jin Kai-Jie Chen Shanghai Institute of Applied Physics Chinese Academy of SciencesShanghai 201800China University of Chinese Academy of Sciences Beiing 100049China Shanghai Advanced Research Institute Chinese Academy of SciencesShanghai 201210China Institute of High Energy Physics Chinese Academy of SciencesBeijing 100049China China Spallation Neutron Source Dongguan 523803China China Institute of Atomic Energy Beijing 102413China Key Laboratory of Beam Technology and Material Modification of Ministry of Education College of Nuclear Science and TechnologyBeijing Normal UniversityBeijing 100875China Beijing Radiation Center Bejing 100875China College of Mathematics and Physics Inner Mongolia Minzu UniversityTongliao 0280000 China Xiangtan University Xiangtan 411105China Henan Normal University Xinxiang 453007China Sun Yat-sen University Zhuhai 510275China ShanghaiTech University Shanghai 200120China

Silver indium cadmium(Ag–In–Cd) control rod is widely used in pressurized water reactor nuclear power plants,and it is continuously consumed in a high neutron flux environment. The mass ratio of ^(107)Ag in the Ag–In–Cd control rod is 41.44%. To accurately calculate the consumption value of the control rod, a reliable neutron reaction cross section of the ^(107)Ag is required. Meanwhile,^(107)Ag is also an important weak r nucleus. Thus, the cross sections for neutron induced interactions with ^(107)Ag are very important both in nuclear energy and nuclear astrophysics. The(n, γ) cross section of ^(107)Ag has been measured in the energy range of 1–60 eV using a back streaming white neutron beam line at China spallation neutron source. The resonance parameters are extracted by an R-matrix code. All the cross section of ^(107)Ag and resonance parameters are given in this paper as datasets. The datasets are openly available at http://***/10.11922/sciencedb.j00113.00010.

关键词： neutron capture cross section pulse height weighting technique(PHWT) ^(107)Ag(n γ)^(108)Ag the China spallation neutron source(CSNS)Back-n facility

Current-induced second harmonic generation of Dirac or Weyl semimetals in a strong magnetic field

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Physical Review B 2021年第4期103卷 L041301-L041301页

作者： Yang Gao Furu Zhang College of Computer Science and Engineering Anhui University of Science and Technology Huainan 232001 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

We theoretically investigate the second harmonic generation (SHG) of Dirac or Weyl semimetals under parallel DC electric and strong magnetic fields using the Boltzmann equation approach. The DC current-induced SHG process originates from the optical intraband transitions of the Landau subbands. It is a remarkable fingerprint of three-dimensional Dirac or Weyl dispersions and absent in other materials. An analytical formula for the SHG tensor is derived, and it shows chirality independence. The second-order nonlinear optical susceptibility is proportional to the DC field, giving strong optical nonlinearity up to 105pm/V with THz light, which is several orders larger than that of the usual materials. More interesting, the second harmonic conductivity is found to exhibit periodicity in magnetic field 1/B oscillations, which are similar to the Shubnikov–de Haas oscillations. Thus our work proposes another approach for SHG and potential applications of Dirac or Weyl semimetals in nonlinear optics.

关键词： Landau levels Nonlinear optical susceptibility Photoconductivity Semimetals Boltzmann theory Optical second-harmonic generation

Fidelity-enhanced variational quantum optimal control

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Physical Review A 2025年第5期111卷 052625-052625页

作者： R. J. P. T. de Keijzer L. Y. Visser O. Tse S. J. J. M. F. Kokkelmans Department of Applied Physics Eindhoven University of Technology P.O. Box 513 5600 MB Eindhoven The Netherlands Eindhoven Hendrik Casimir Institute Eindhoven University of Technology P.O. Box 513 5600 MB Eindhoven The Netherlands Department of Mathematics and Computer Science Eindhoven University of Technology P.O. Box 513 5600 MB Eindhoven The Netherlands

Creating robust quantum operations is a major challenge in the current noisy intermediate-scale quantum computing era. Recently, the importance of noise-resilient control methods has become more pronounced in the field. Ordinarily, noisy quantum systems are described by the Lindblad equation. However, minimizing noise susceptibility using this equation has proven challenging because of its irreversibility. In this study, we propose a method for creating robust pulses based on the stochastic Schrödinger equation. This equation describes individual noise realizations under any colored noise process, contrary to the Lindblad equation, which describes mean system behavior under white noise. Using stochastic optimal control techniques, our method, fidelity-enhanced variational quantum optimal control, is able to construct higher-fidelity paths than its nonstochastic counterpart. By accounting for both environmental noise sources as well as noise sources inherent to the control system, highly significant increases in fidelity are noted for both single- and multiple-qubit state preparations.

关键词： Schrodinger equation