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Asymptotic Analysis of Quantum Dynamics in Crystals: the Bloch-Wigner Transform, Bloch Dynamics and Berry Phase

Acta Mathematicae Applicatae Sinica 2013年第3期29卷 465-476页

作者： Weinan E Jian-feng LU Xu YANG Department of Mathematics Princeton University Program in Applied and Computational Mathematics Princeton University School of Mathematical Sciences Peking University

We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.

关键词： semiclassical limit Bloch-Wigner transform Bloch dynamics Berry phase asymptotic analysis

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Carbon-modified zeolite derivates based filler in mixed matrix membrane adsorbers (MMMAs) for enhancing urea and creatinine removal from hemodialysis spent dialysate

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Journal of Industrial and Engineering Chemistry 2025年 147卷 584-597页

作者： Widiastuti, Nurul Rahman, Reca Ardiyanti Cipta Dharma, Hadi Nugraha Widyanto, Alvin Rahmad Nareswari, Cininta Kayadoe, Victor Raharjo, Yanuardi Saiful Nomura, Mikihiro Department of Chemistry Faculty of Science and Data Analytics Institut Teknologi Sepuluh Nopember Kampus ITS Keputih-Sukolilo Jl. Arif Rahman Hakim Surabaya60111 Indonesia Advanced Nanolithography Lab Department of System Semiconductor Science Dongguk University 30 Pildong-ro 1-gil Jung-gu Seoul04620 Korea Republic of Department of Applied Chemistry Shibaura Institute of Technology 3-7-5 Toyosu Koto-ku Tokyo135-8548 Japan Chemical Education Study Program Faculty of Teaching and Education Sciences University of Pattimura Ambon97233 Indonesia Chemistry Department Faculty of Science and Technology Universitas Airlangga Surabaya Indonesia Chemistry Department Faculty of Mathematics and Natural Science Universitas Syiah Kuala Banda Aceh Indonesia

Conventional dialysate recycling methods struggle to effectively remove creatinine, urea, and other minor contaminants. This study explores mixed matrix membrane adsorbers (MMMAs) as a novel approach to address these challenges. MMMAs, which integrate adsorbents into filtration membranes, function as both filters and impurity scavengers. Zeolite carbon composite (ZCC) and zeolite-templated carbon (ZTC) were incorporated into MMMAs using the non-solvent induced phase separation (NIPS) technique. Characterization by SEM and XRD confirmed the successful synthesis of ZCC and ZTC, retaining the zeolite-Y structure and amorphous nature, with notable differences in particle sizes (680 and 379 nm) and crystallite sizes (0.45 and 0.02 nm). FTIR revealed hydrogen bonding interactions between ZCC and PVP, absent in ZTC. SEM and AFM analyses of the membranes indicated increased hydrophilicity and porosity with ZCC, while ZTC reduced surface roughness. MMMAs significantly outperformed pristine membranes in removing urea and creatinine. The PPK-0.2 membrane achieved superior rejection rates (93.05 % for urea and 98.95 % for creatinine), attributed to microporous entrapment of ZTC and polymer matrix adsorption. In contrast, PPZ-0.2 showed lower rejection rates (84.24 % for urea and 85.79 % for creatinine), relying solely on physical adsorption. These findings highlight MMMAs, especially ZTC-based ones, as promising candidates for enhancing dialysate reuse efficiency. © 2024 The Korean Society of Industrial and Engineering Chemistry

关键词： Hydrogen bonds

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Optimization of Crop Yields in Sustainable Agriculture: Application of Big Data Analytics and Artificial Intelligence

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Remote Sensing in Earth Systems Sciences 2025年 1-12页

作者： Nimma, Divya Dhanke, Jyoti A. Murthy, G.S.N. Khandekar, Sachin Dadu Hymavathi, J. Jangir, Pradeep Singh, Mahesh Department of Computational Science University of Southern Mississippi Hattiesburg 39406 MS United States Department of Engineering Science (Mathematics) Bharati Vidyapeeth’s College of Engineering Lavale Maharashtra Pune India Department of CSE Aditya University Surampalem India Department of Civil Engineering Sinhgad College of Engineering Maharashtra Pune India Department of CSE Koneru Lakshmaiah Education Foundation Andhra Pradesh Vaddeswaram India Department of Biosciences Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Chennai India Hourani Center for Applied Scientific Research Al-Ahliyya Amman University Amman 19328 Jordan Department of Robotics and Automation Symbiosis Institute of Technology Pune Campus Symbiosis International (Deemed University) Pune India

Making informed economic decisions based on agricultural data is challenging without proper crop management. Data has become the single most important part of modern farming, and its rapid evolution is a major contributor to the rise of “smart farming.” Using sensors to gather objective data with the end aim of increasing productivity and sustainability has several advantages. Information that might boost productivity while decreasing resource waste and pollution levels is essential for managed farms. The cornerstone of future sustainable farming will be data-driven agriculture using robotic solutions based on AI-based techniques. This paper examines the current state of advanced farm management systems, discussing topics like data acquisition in crop fields and variable rate applications, to assist farmers in saving money, protecting the environment, and transforming food production so that it can sustainably keep up with the expected increase in population. The advent of machine learning, big data technologies, and high-performance computers has opened up new avenues for data-intensive research in the interdisciplinary subject of agro technology. These avenues of exploration have been aided by the development of more capable computers. A comprehensive literature review on the issue of the applications of machine learning in agricultural manufacturing is provided in this research. Machine learning has shown its utility in agriculture via two applications: filtering and categorizing products. The use of machine learning on sensor data is transforming conventional farm management systems into AI-enabled programs. These services provide farmers instantaneous, complete access to ideas and insights that may guide their decisions. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

关键词： Artificial intelligence Big data analytics Optimize crop yields Sustainable agriculture

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Existence of Weak Solutions to the Three-dimensional Steady Compressible Magnetohydrodynamic Equations

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Acta Mathematica Sinica,English Series 2012年第12期28卷 2431-2442页

作者： Chun Hui ZHOU Department of Mathematics Southeast University LCP Institute of Applied Physics and Computational Mathematics

The purpose of this paper is to prove the existence of a spatially periodic weak solution to the steady compressible isentropic MHD equations in R3 for any specific heat ratio γ〉 1. The proof is based on the weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density, and the method of weak convergence. According to the author＇s knowledge, it is the first result that treats in three dimensions the existence of weak solutions to the steady compressible MHD equations with γ〉1.

关键词： Steady compressible Magnetohydrodynamic equations existence for γ〉 1 weighted estimate viscous flux

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EXISTENCE OF TIME PERIODIC SOLUTIONS FOR A DAMPED GENERALIZED COUPLED NONLINEAR WAVE EQUATIONS

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applied mathematics and Mechanics(English Edition) 2003年第6期24卷 673-683页

作者：房少梅郭柏灵 Department of Mathematics Shaoguan University Shaoguan Institute of Applied Physics and Computational Mathematics

The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray_Schauder fixed point theorem to prove the convergence of the approximate solutions, the existence of time periodic solutions for a damped generalized coupled nonlinear wave equations can be obtained.

关键词： nonlinear wave equations priori estimate time periodic solution

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Stability theorems for Fourier frames and wavelet Riesz bases

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JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 1997年第5期3卷 499-504页

作者： Balan, R Program in Applied and Computational Mathematics Princeton University Princeton

In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type constant for nonharmonic series given by Duffin and Schaefer in [6] and used recently in some applications (see (3]). In the case of an orthonormal basis, our estimate reduces to Kadec' optimal 1/4 result. The second application proves that a phenomenon discovered by Daubechies and Tchamitchian [4] for the orthonormal Meyer wavelet basis (stability of the Riesz basis property under small changes of the translation parameter) actually holds for a large class of wavelet Riesz bases.

关键词： frames Riesz basis nonharmonic series wavelets

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EHands: Quantum Protocol for Polynomial Computation on Real-Valued Encoded States

arXiv

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arXiv 2025年

作者： Balewski, Jan Amankwah, Mercy G. Bethel, E. Wes Perciano, Talita Van Beeumen, Roel National Energy Research Scientific Computing Center Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Mathematics Applied Mathematics and Statistics Case Western Reserve University ClevelandOH44106 United States Computer Science Department San Francisco State University San FranciscoCA94132 United States Scientific Data Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

The novel constructive EHands protocol defines a universal set of quantum operations for multivariable polynomial transformations on quantum processors by introducing four basic subcircuits—multiplication, addition, negation, and parity flip—and by using expectation-value encoding (EVEN) to represent real numbers in quantum states. These elementary arithmetic operations can be systematically composed to compute degree-d polynomials, Pd(x), on a QPU. The resulting quantum circuit structure closely mirrors the stepwise evaluation of polynomials on a classical calculator, providing an intuitive and efficient approach to polynomial computation on quantum hardware. By enabling direct, predictable polynomial and nonlinear data transformations on a QPU, our method reduces dependence on classical post-processing in hybrid quantum-classical algorithms, enabling advancements in many quantum algorithms. The EHands quantum circuits are compact enough to deliver meaningful and accurate results on today’s noisy quantum processors. We present a detailed implementation of P4(x) and report experimental results for polynomial approximations of common functions, obtained using IBM’s Heron-class quantum processors and an ideal Qiskit simulator. Copyright © 2025, The Authors. All rights reserved.

关键词： Polynomial approximation

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LOCAL DISCONTINUOUS GALERKIN METHOD FOR ELLIPTIC INTERFACE PROBLEMS

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Acta Mathematica Scientia 2017年第5期37卷 1519-1535页

作者：张志娟蔚喜军常延贞 Department of Mathematics Nanchang University Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Department of Mathematics Beijing University of Chemical Technology

In this paper,the minimal dissipation local discontinuous Galerkin method is studied to solve the elliptic interface problems in two-dimensional *** interface may be arbitrary smooth *** is shown that the error estimates in L;-norm for the solution and the flux are O（h;|log h|）and O(h|log h|;),*** numerical experiments,the successive substitution iterative methods are used to solve the LDG *** results verify the efficiency and accuracy of the method.

关键词： elliptic interface problem minimal dissipation local discontinuous Galerkin method error estimates

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GRAMMCell: Docking-based Cell Modeling Resource

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Journal of Molecular Biology 2025年 169085页

作者： Singh, Amar Tytarenko, Andrii M. Ambati, Vineeth Kumar Copeland, Matthew M. Kundrotas, Petras J. Kasyanov, Pavlo O. Feinberg, Eugene A. Vakser, Ilya A. Computational Biology Program The University of Kansas Lawrence 66045 KS United States Institute for Applied System Analysis at the Igor Sikorsky Kyiv Polytechnic Institute Kyiv 03056 Ukraine Department of Applied Mathematics and Statistics Stony Brook University Stony Brook 11794 NY United States Department of Molecular Biosciences The University of Kansas Lawrence 66045 KS United States

The environment inside biological cells is densely populated by macromolecules and other cellular components. The crowding has a significant impact on folding and stability of macromolecules, and on kinetics of molecular interactions. computational approaches to cell modeling, such as molecular dynamics, provide details of macromolecular behavior in concentrated solutions. However, such simulations are either slow, when carried out at atomic resolution, or significantly coarse-grained. Protein docking has been widely used for predicting structures of protein complexes. Systematic docking approaches, such as those based on Fast Fourier Transform (FFT), map the entire intermolecular energy landscape by determining the position and depth of the energy minima. The GRAMMCell web server implements docking-based approach for simulating cell crowded environment by sampling the intermolecular energy landscape generated by GRAMM (Global RAnge Molecular Matching). GRAMM systematically maps the landscape by a spectrum of docking poses corresponding to stable (deep energy minima) and transient (shallow minima) protein interactions. The sampling of these energy landscapes of a large system of proteins is performed in GRAMMCell using highly optimized Markov Chain Monte Carlo protocol. The procedure allows simulation of extra-long trajectories of large, crowded protein systems with atomic resolution accuracy. GRAMMCell is available at https://***. © 2025 The Author(s)

关键词： cell-modelling energy landscape protein docking protein–protein interactions web-based resource

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Dynamic thermo-mechanical coupled simulation of statistically inhomogeneous materials by statistical second-order two-scale method

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Acta Mechanica Sinica 2015年第5期31卷 762-776页

作者： Zihao Yang Junzhi Cui Yufeng Nie Zhiqiang Huang Meizhen Xiang Department of Applied Mathematics Northwestern Polytechnical University LSEC ICMSECAcademy of Mathematics and Systems ScienceChinese Academy of Sciences Institution of Applied Physics and Computational Mathematics

In this paper,a statistical second-order twoscale（SSOTS） method is developed to simulate the dynamic thcrmo-mechanical performances of the statistically inhomogeneous *** this kind of composite material,the random distribution characteristics of particles,including the shape,size,orientation,spatial location,and volume fractions,are all ***,the *** for the microscopic configuration of the statistically inhomogeneous materials is ***,the SSOTS formulation for the dynamic thermo-mechanical coupled problem is proposed in a constructive way,including the cell problems,effective thermal and mechanical parameters,homogenized problems,and the SSOTS formulas of the temperatures,displacements,heat flux densities and *** then the algorithm procedure corresponding to the SSOTS method is brought *** numerical results obtained by using the SSOTS algorithm are compared with those by classical *** addition,the thermo-mechanical coupling effect is studied by comparing the results of coupled case with those of uncoupled *** demonstrates that the coupling effect on the temperatures,heat flux densities,displacements,and stresses is very *** results show that the SSOTS method is valid to predict the dynamic thermo-mechanical coupled performances of statistically inhomogeneous materials.

关键词： Statistically inhomogeneous materials Dynamic thermo-mechanical coupled performances The SSOTS method The thermo-mechanical coupling effect

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