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Wigner non-negative states that verify the Wigner entropy conjecture

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arXiv 2024年

作者： Qian, Qipeng Gagatsos, Christos N. Program in Applied Mathematics The University of Arizona TucsonAZ85721 United States Department of Electrical and Computer Engineering The University of Arizona TucsonAZ85721 United States Wyant College of Optical Sciences The University of Arizona TucsonAZ85721 United States

We present further progress, in the form of analytical results, on the Wigner entropy conjecture set forth in [Phys. Rev. A 104, 042211 (2021)] and [J. Phys. A: Math. Theor. 50 385301]. Said conjecture asserts that the differential entropy defined for non-negative, yet physical, Wigner functions is minimized by pure Gaussian states while the minimum entropy is equal to 1 + ln π. We prove this conjecture for the qubits formed by Fock states |0) and |1) that correspond to non-negative Wigner functions. In particular, we derive an explicit form of the Wigner entropy for those states lying on the boundary of the set of Wigner non-negative qubits. We then consider general mixed states and derive a sufficient condition for the conjecture’s validity. Lastly, we elaborate on the states which are in accordance with our condition. Copyright © 2024, The Authors. All rights reserved.

关键词： Entropy

Matlab-Based program for the Parametric Study of Piping Systems

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Journal of engineering Science and Technology Review 2023年第6期16卷 161-169页

作者： Carvajal, Diego Alexander Obregón, Luis Guillermo Candezano, M.A.C. Research Group on Sustainable Chemical and Biochemical Processes Chemical Engineering Program Universidad del Atlántico Carrera 30 # 8-49 Puerto Colombia Atlántico Colombia Department of Mathematics Universidad del Atlántico Carrera 30 # 8-49 Puerto Colombia Atlántico Colombia

Educative computational tools for education in chemical engineering has been increasing in the last decade due to the advance in technology. This branch of engineering has many subjects that make it difficult to have only one robust software that contains all the main subjects. It involves the creation of special programs dedicated to specific areas of study. One of the main subjects in chemical engineering programs is fluid mechanics. This study presents the application of a graphical user interface developed in Matlab for the study of piping systems where the flow rate, pump power, and pressure drops are determined as a function of the material, diameter, length, and elevation of the pipe, as well as the number and type of pipe couplings. The software is based on an algorithm that allows the solution of piping systems with elevation using energy balances, specific equations of fluid mechanics, and specific geometric parameters. Three relevant case studies were developed, showing the behavior of the energy expenses of the pumps. It was found an increase in the pump power from 91.4% to 3713.4% when a pipe diameter of 2 1/2 inches is increased from 20% to 60%. It was observed that the effect of the length of the pipe on the energy consumption of the pump is not significant for flows lower than 8 L/s. When the flow rate in the pipeline is 15 L/s and a change of pipeline is made from a 2-inch pipe - PVC schedule 40 to one of PVC schedule 80 of the same size, a 26.5% increase in pump power is needed. For steel pipes with schedule 40 and schedule 80, a rise of 30% and 67.8% was required, respectively. © 2023 School of Science, IHU. All rights reserved.

关键词： Polyvinyl chlorides

Measuring 3D Chemistry at 1 nm Resolution with Fused Multi-Modal Electron Tomography

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Microscopy and microanalysis : the official journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada 2023年第1期29卷 1394-1395页

作者： Schwartz, Jonathan Di, Zichao Wendy Jiang, Yi Cho, Min Gee Qian, Yiwen Gu, Junsi Rozeveld, Steve Ercius, Peter Fessler, Jeffrey A. Xu, Ting Scott, Mary Hovden, Robert Department of Materials Science and Engineering University of Michigan Ann Arbor MI United States Mathematics and Computer Science Division Argonne National Laboratory Lemont IL United States Advanced Photon Source Argonne National Laboratory Lemont IL United States Department of Materials Science and Engineering University of California at Berkeley Berkeley CA United States National Center for Electron Microscopy Lawrence Berkeley National Laboratory Berkeley CA United States Dow Chemical Co. Midland MI United States Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor MI United States Materials Science Division Lawrence Berkeley National Laboratory Berkeley CA United States Applied Physics Program University of Michigan Ann Arbor MI United States

Cyclodextrin-modified layered double hydroxide thin-film nanocomposite desalination membrane for boron removal

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Cyclodextrin-modified layered double hydroxide thin-film nan...

2023 AIChE Annual Meeting

作者： Ee, Liang Ying Zhao, Qipeng Gao, Jie Lim, Chit Kai Xue, Kai Chin, Sze Yuet Li, Sam Fong Yau Chung, Tai-Shung Chen, Shing Bor Department of Chemical and Biomolecular Engineering College of Design and Engineering National University of Singapore 4 Engineering Drive 4 Singapore117585 Singapore Department of Chemistry College of Humanities and Sciences National University of Singapore 3 Science Drive 3 Singapore117543 Singapore Chemical Engineering Program Physical Science and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Centre of High Field NMR Spectroscopy and Imaging School of Physical and Mathematical Sciences College of Science Nanyang Technological University 21 Nanyang Link Singapore637371 Singapore NUS Environmental Research Institute National University of Singapore T-Lab Building 5A Engineering Drive 1 Singapore117411 Singapore Graduate Institute of Applied Science and Technology National Taiwan University of Science and Technology Taipei106335 Taiwan

Transient rod-climbing in an Oldroyd-B fluid

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arXiv 2025年

作者： Ruangkriengsin, Tachin Brandão, Rodolfo Wu, Katie Hwang, Jonghyun Boyko, Evgeniy Stone, Howard A. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Mathematics University of Bristol Fry Building Woodland Road BristolBS8 1UG United Kingdom Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ08544 United States Faculty of Mechanical Engineering Technion – Israel Institute of Technology Haifa3200003 Israel

The Weissenberg effect, or rod-climbing phenomenon, occurs in non-Newtonian fluids where the fluid interface ascends along a rotating rod. Despite its prominence, theoretical insights into this phenomenon remain limited. In earlier work, Joseph & Fosdick (Arch. Rat. Mech. Anal., vol. 49, 1973, pp. 321–380) employed domain perturbation methods for second-order fluids to determine the equilibrium interface height by expanding solutions based on the rotation speed. In this work, we investigate the time-dependent interface height through asymptotic analysis with dimensionless variables and equations using the Oldroyd-B model. We begin by neglecting surface tension and inertia to focus on the interaction between gravity and viscoelasticity. In the small-deformation scenario, the governing equations indicate the presence of a boundary layer in time, where the interface rises rapidly over a short time scale before gradually approaching a steady state. By employing a stretched time variable, we derive the transient velocity field and corresponding interface profile on this short time scale and recover the steady-state profile on a longer time scale. Subsequently, we reintroduce small but finite inertial effects to investigate their interplay with viscoelasticity and propose a criterion for determining the conditions under which rod-climbing occurs. © 2025, CC BY.

关键词： Non Newtonian liquids

Modelling and Economic Optimal Control for a Laboratory-scale Continuous Stirred Tank Reactor for Single-cell Protein Production

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arXiv 2022年

作者： Nielsen, Marcus Krogh Dynesen, Jens Dragheim, Jess Christensen, Ib Jørgensen, Sten Bay Huusom, Jakob Kjøbsted Gernaey, Krist V. Jørgensen, John Bagterp Department of Applied Mathematics and Computer Science Denmark Department of Chemical and Biochemical Engineering the Technical University of Denmark Kgs. Lyngby Denmark Unibio A/S Roskilde Denmark

In this paper, we present a novel kinetic growth model for the micro-organism Methylococcus capsulatus (Bath) that couples growth and pH. We apply growth kinetics in a model for single-cell protein production in a laboratory-scale continuous stirred tank reactor inspired by a physical laboratory fermentor. The model contains a set of differential algebraic equations describing growth and pH-dynamics in the system. We present a method of simulation that ensures non-negativity in the state and algebraic variables. Additionally, we introduce linear scaling of the algebraic equations and variables for numerical stability in Newton’s method. Finally, we conduct a numerical experiment of economic optimal control for single-cell protein production in the laboratory-scale reactor. The numerical experiment shows non-trivial input profiles for biomass growth and pH tracking. Copyright © 2022, The Authors. All rights reserved.

关键词： Laboratories

Recent progress in all-inorganic metal halide nanostructured perovskites:Materials design,optical properties,and application

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Frontiers of physics 2021年第3期16卷 65-84页

作者： Lianzhen Cao Xia Liu Yingde Li Xiusheng Li Lena Du Shengyao Chen Shenlong Zhao Cong Wang Department of Physics and Optoelectronic Engineering Weifang UniversityWeifang261061China Division of Physics and Applied Physics School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore637371Singapore CAS Center for Excellence in Nanoscience National Center for Nanoscience and Technology Beijing100190China School of Chemical and Biomolecular Engineering The University of SydneySydneyNew South Wales2006Australia College of Mathematics and Physics Beijing University of Chemical TechnologyBeijing100029China

Low-dimensional all-inorganic metal halide perovskite(AIMHP)materials,as a new class of nanomaterials,hold great promise for various optoelectronic *** the past few years,tremendous progress has been achieved in the development of efficient and stable AIMHP nanomaterials for optical property studies and related ***,we offer a critical overview on the unique merits and the state-of-the-art design of AIMHP using different composition ***,the effects of material compositions,dimensionality,morphologies and structures on optical properties are *** also comprehensively present recent advances in the development AIMHP nanomaterials for practical applications including solar cells,light-emitting diodes,lasers and ***,the critical challenges and future opportunities in this emerging field are highlighted.

关键词： inorganic perovskite nano-structure materials design optical properties applications

Multi-hump Collapsing Solutions in the Nonlinear Schrödinger Problem: Existence, Stability and Dynamics

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arXiv 2025年

作者： Chapman, S. Jon Kavousanakis, Mihalis Charalampidis, Efstathios G. Kevrekidis, Ioannis G. Kevrekidis, Panayotis G. Mathematical Institute University of Oxford AWB ROQ Woodstock Road OxfordOX2 6GG United Kingdom School of Chemical Engineering National Technical University of Athens Athens15780 Greece Department of Mathematics and Statistics Computational Science Research Center San Diego State University San DiegoCA92182-7720 United States Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD21218 United States Department of Mathematics and Statistics University of Massachusetts AmherstMA01003-4515 United States Department of Physics University of Massachusetts AmherstMA01003 United States

In the present work we examine multi-hump solutions of the nonlinear Schrödinger equation in the blowup regime of the one-dimensional model with power law nonlinearity, bearing a suitable exponent of σ > 2. We find that families of such solutions exist for arbitrary pulse numbers, with all of them bifurcating from the critical case of σ = 2. Remarkably, all of them involve "bifurcations from infinity", i.e., the pulses come inward from an infinite distance as the exponent σ increases past the critical point. The position of the pulses is quantified and the stability of the waveforms is also systematically examined in the so-called "co-exploding frame". Both the equilibrium distance between the pulse peaks and the point spectrum eigenvalues associated with the multi-hump configurations are obtained as a function of the blowup rate G theoretically, and these findings are supported by detailed numerical computations. Finally, some prototypical dynamical scenarios are explored, and an outlook towards such multi-hump solutions in higher dimensions is provided. Copyright © 2025, The Authors. All rights reserved.

关键词： Schrodinger equation

Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior

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Gaussian Process Port-Hamiltonian Systems: Bayesian Learning...

IEEE Conference on Decision and Control

作者： Thomas Beckers Jacob Seidman Paris Perdikaris George J. Pappas Department of Electrical and Systems Engineering University of Pennsylvania Philadelphia PA USA graduate program in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia PA USA Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia PA USA

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

Data-driven approaches achieve remarkable results for the modeling of complex dynamics based on collected data. However, these models often neglect basic physical principles which determine the behavior of any real-world system. This omission is unfavorable in two ways: The models are not as data-efficient as they could be by incorporating physical prior knowledge, and the model itself might not be physically correct. We propose Gaussian Process Port-Hamiltonian systems (GPPHS) as a physics-informed Bayesian learning approach with uncertainty quantification. The Bayesian nature of GP-PHS uses collected data to form a distribution over all possible Hamiltonians instead of a single point estimate. Due to the underlying physics model, a GP-PHS generates passive systems with respect to designated inputs and outputs. Further, the proposed approach preserves the compositional nature of Port-Hamiltonian systems.

关键词： Uncertainty Gaussian processes Probabilistic logic Data models Bayes methods Behavioral sciences Kernel