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Thermal analysis for convective transport of nanoparticles with effective phenomenon of damped shear-thermal flux: A fractional model

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Partial Differential Equations in applied mathematics 2024年 12卷

作者： Ali, Qasim Khan, Sami Ullah Adnan Garalleh, Hakim AL Waqas, M. Zamri, Nurnadiah Abduvalieva, Dilsora Gupta, Manish Department of Mathematics University of Chakwal Chakwal 48800 Pakistan Department of Mathematics Namal University Mianwali 42250 Pakistan Department of Mathematics Mohi-ud-Din Islamic University Nerian Sharif AJ&K 12080 Pakistan Department of Mathematical Science College of Engineering University of Business and Technology Jeddah 21361 Saudi Arabia NUTECH School of Applied Sciences and Humanities National University of Technology Islamabad 44000 Pakistan Department of Computer Science and Mathematics Lebanese American University Beirut Lebanon Faculty of Informatics and Computing Universiti Sultan Zainal Abidin Besut Campus Terengganu Besut 22200 Malaysia Department of Mathematics and Information Technologies Tashkent State Pedagogical University Bunyodkor avenue 27 Tashkent 100070 Uzbekistan Division of Research and Development Lovely Professional University Phagwara India

The researchers are interested to enhance the temperature characteristics of convection heat transportation investigation. The studies based on nanofluids are accomplished because these phenomena exhibit an abnormal elevation in thermal transportation. This analysis captures historical impacts on heat and momentum transfer that traditional models ignore by using the Caputo fractional derivative in to model damped shear-thermal flux in nanofluid convection. In this manuscript, the natural convection flow, as well as heat transference of nanofluids, is studied. The classical expressions are fractionalized with the help of constitutive shearing stress expression along with Fourier relation. The Caputo kernel (power-law and non-local) engenders the damping on gradients of momentum and temperature;consequently, transportation approaches are affected by the histories entirely of the previous and current time. The fractional differential equations of velocity as well as temperature are solved analytically by invoking Laplace and the finite Sine-Fourier transform method. In a particular case, the solution to the classical model is also found. Moreover, these solutions are described in respect of the Lorenzo-Hartley G-function together with the Mittag-Leffler function. This investigation exposes that rising nanoparticle volume fraction improves the heat transfer rate, however the skin friction coefficient is affected by time and fractional parameters. The influences of diverse parameters are debated graphically. This study has numerous operations in thermal engineering. © 2024

关键词： Caputo time-fractional derivative Fourier law Free convection Heat transfer Laplace transform Nanofluid

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Digital Quantum Simulation of Cavity Quantum Electrodynamics: Insights from Superconducting and Trapped Ion Quantum Testbeds

arXiv

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arXiv 2024年

作者： Rubin, Alex H. Marinelli, Brian Norman, Victoria A. Rizvi, Zainab Burch, Ashlyn D. Naik, Ravi K. Kreikebaum, John Mark Chow, Matthew N.H. Lobser, Daniel S. Revelle, Melissa C. Yale, Christopher G. Ivory, Megan Santiago, David I. Spitzer, Christopher Krstic-Marinkovic, Marina Clark, Susan M. Siddiqi, Irfan Radulaski, Marina Department of Electrical and Computer Engineering University of California DavisCA95616 United States Department of Physics University of California DavisCA95616 United States Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley BerkeleyCA94720 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Department of Computer Science University of California DavisCA95616 United States Sandia National Laboratories AlbuquerqueNM87123 United States Materials Science Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Institute for Theoretical Physics ETH Zurich Zurich8093 Switzerland

We explore the potential for hybrid development of quantum hardware where currently available quantum computers simulate open Cavity Quantum Electrodynamical (CQED) systems for applications in optical quantum communication, simulation and computing. Our simulations make use of a recent quantum algorithm that maps the dynamics of a singly excited open Tavis-Cummings model containing N atoms coupled to a lossy cavity. We report the results of executing this algorithm on two noisy intermediate-scale quantum computers: a superconducting processor and a trapped ion processor, to simulate the population dynamics of an open CQED system featuring N = 3 atoms. By applying technology-specific transpilation and error mitigation techniques, we minimize the impact of gate errors, noise, and decoherence in each hardware platform, obtaining results which agree closely with the exact solution of the system. These results can be used as a recipe for efficient and platform-specific quantum simulation of cavity-emitter systems on contemporary and future quantum computers. Copyright © 2024, The Authors. All rights reserved.

关键词： Quantum computers

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Derivative-free optimization of a rapid-cycling synchrotron

arXiv

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arXiv 2021年

作者： Eldred, Jeffrey S. Larson, Jeffrey Padidar, Misha Stern, Eric Wild, Stefan M. Fermi National Accelerator Laboratory BataviaIL United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL United States Center for Applied Mathematics Cornell University IthacaNY United States

We develop and solve a constrained optimization model to identify an integrable optics rapid-cycling synchrotron lattice design that performs well in several capacities. Our model encodes the design criteria into 78 linear and nonlinear constraints, as well as a single nonsmooth objective, where the objective and some constraints are defined from the output of Synergia, an accelerator simulator. We detail the difficulties of the 23-dimensional simulation-constrained decision space and establish that the space is nonempty. We use a derivative-free manifold sampling algorithm to account for structured nondifierentiability in the objective function. Our numerical results quantify the dependence of solutions on constraint parameters and the effect of the form of objective function. Copyright © 2021, The Authors. All rights reserved.

关键词： Constrained optimization

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Incorporating Prior Knowledge into Neural Networks through an Implicit Composite Kernel

arXiv

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arXiv 2022年

作者： Jiang, Ziyang Zheng, Tongshu Liu, Yiling Carlson, David Department of Civil and Environmental Engineering Duke University United States Division of Natural and Applied Science Duke Kunshan University China Program in Computational Biology and Bioinformatics Duke University School of Medicine United States Department of Civil and Environmental Engineering Department of Biostatistics and Bioinformatics Department of Computer Science Duke University United States

It is challenging to guide neural network (NN) learning with prior knowledge. In contrast, many known properties, such as spatial smoothness or seasonality, are straightforward to model by choosing an appropriate kernel in a Gaussian process (GP). Many deep learning applications could be enhanced by modeling such known properties. For example, convolutional neural networks (CNNs) are frequently used in remote sensing, which is subject to strong seasonal effects. We propose to blend the strengths of NNs and the clear modeling capabilities of GPs by using a composite kernel that combines a kernel implicitly defined by a neural network with a second kernel function chosen to model known properties (e.g., seasonality). We implement this idea by combining a deep network and an efficient mapping function based on either Nyström approximation or random Fourier features, which we call Implicit Composite Kernel (ICK). We then adopt a sample-then-optimize approach to approximate the full GP posterior distribution. We demonstrate that ICK has superior performance and flexibility on both synthetic and real-world datasets including a remote sensing dataset. The ICK framework can be used to include prior information into neural networks in many applications. © 2022, CC BY.

关键词： Remote sensing

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Enabling equation-free modeling via diffusion maps

arXiv

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arXiv 2021年

作者： Chin, Tracy Ruth, Jacob Sanford, Clayton Santorella, Rebecca Carter, Paul Sandstede, Björn Department of Mathematics University of Washington Seattle United States Department of Computer Science Columbia University New York City United States Division of Applied Mathematics Brown University Providence United States Department of Mathematics University of California Irvine United States

Equation-free modeling aims at extracting low-dimensional macroscopic dynamics from complex high-dimensional systems that govern the evolution of microscopic states. This algorithm relies on lifting and restriction operators that map macroscopic states to microscopic states and vice versa. Combined with simulations of the microscopic state, this algorithm can be used to apply Newton solvers to the implicitly defined low-dimensional macroscopic system or solve it more efficiently using direct numerical simulations. The key challenge is the construction of the lifting and restrictions operators that usually require a priori insight into the underlying application. In this paper, we design an application-independent algorithm that uses diffusion maps to construct these operators from simulation data. Code is available at https://***/10.5281/zenodo.5793299. © 2021, CC BY.

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PHYSICS INFORMED MACHINE LEARNING WITH SMOOTHED PARTICLE HYDRODYNAMICS: HIERARCHY OF REDUCED LAGRANGIAN MODELS OF TURBULENCE

arXiv

引用

arXiv 2021年

作者： Woodward, Michael Tian, Yifeng Hyett, Criston Fryer, Chris Stepanov, Mikhail Livescu, Daniel Chertkov, Michael Graduate Interdisciplinary Program in Applied Mathematics UArizona TucsonAZ85721 United States Department of Mathematics UArizona TucsonAZ85721 United States Computer Computational and Statistical Sciences Division LANL Los AlamosNM87544 United States

Building efficient, accurate and generalizable reduced order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for turbulent flows, and investigates the effects of enforcing physical structure through Smoothed Particle Hydrodynamics (SPH) versus relying on neural networks (NN)s as universal function approximators. Starting from Neural Network (NN) parameterizations of a Lagrangian acceleration operator, this hierarchy of models gradually incorporates a weakly compressible and parameterized SPH framework, which enforces physical symmetries, such as Galilean, rotational and translational invariances. Within this hierarchy, two new parameterized smoothing kernels are developed in order to increase the flexibility of the learn-able SPH simulators. For each model we experiment with different loss functions which are minimized using gradient based optimization, where efficient computations of gradients are obtained by using Automatic Differentiation (AD) and Sensitivity Analysis (SA). Each model within the hierarchy is trained on two data sets associated with weekly compressible Homogeneous Isotropic Turbulence (HIT): (1) a validation set using weakly compressible SPH;and (2) a high fidelity set from Direct Numerical Simulations (DNS). Numerical evidence shows that encoding more SPH structure improves generalizability to different turbulent Mach numbers and time shifts, and that including the novel parameterized smoothing kernels improves the accuracy of SPH at the resolved scales. Copyright © 2021, The Authors. All rights reserved.

关键词： Parameterization

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Correction: Feynman checkers: lattice quantum field theory with real time

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Analysis and Mathematical Physics 2024年第3期14卷 1-1页

作者： Skopenkov, M. Ustinov, A. King Abdullah University of Science and Technology Thuwal Saudi Arabia Faculty of Computer Science HSE University Khabarovsk Division of the Institute for Applied Mathematics Far-Eastern Branch Russian Academy of Sciences Moscow Russia

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Quantum Computing: Vision and Challenges

arXiv

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arXiv 2024年

作者： Gill, Sukhpal Singh Cetinkaya, Oktay Marrone, Stefano Claudino, Daniel Haunschild, David Schlote, Leon Wu, Huaming Ottaviani, Carlo Liu, Xiaoyuan Machupalli, Sree Pragna Kaur, Kamalpreet Arora, Priyansh Liu, Ji Farouk, Ahmed Song, Houbing Herbert Uhlig, Steve Ramamohanarao, Kotagiri School of Electronic Engineering and Computer Science Queen Mary University of London London United Kingdom Department of Engineering Science University of Oxford Oxford United Kingdom Dipartimento di Matematica e Fisica Università della Campania "Luigi Vanvitelli" Italy Quantum Information Science Section Oak Ridge National Laboratory Oak RidgeTN United States Detecon International GmbH Munich Germany DB Cargo Berlin Germany Center for Applied Mathematics Tianjin University Tianjin China Department of Computer Science York Centre for Quantum Technologies University of York York United Kingdom Fujitsu Research of America Inc. Santa ClaraCA United States Information Networking Institute Carnegie Mellon University United States Cymax Group Technologies BC Canada Microsoft Schiphol Netherlands Mathematics and Computational Research Division Argonne National Laboratory IL United States Department of Computer Science Faculty of Computers and Artificial Intelligence South Valley University Hurghada Egypt Baltimore United States The University of Melbourne VIC Australia

The recent development of quantum computing, which uses entanglement, superposition, and other quantum fundamental concepts, can provide substantial processing advantages over traditional computing. These quantum features help solve many complex problems that cannot be solved otherwise with conventional computing methods. These problems include modeling quantum mechanics, logistics, chemical-based advances, drug design, statistical science, sustainable energy, banking, reliable communication, and quantum chemical engineering. The last few years have witnessed remarkable progress in quantum software and algorithm creation and quantum hardware research, which has significantly advanced the prospect of realizing quantum computers. It would be helpful to have comprehensive literature research on this area to grasp the current status and find outstanding problems that require considerable attention from the research community working in the quantum computing industry. To better understand quantum computing, this paper examines the foundations and vision based on current research in this area. We discuss cutting-edge developments in quantum computer hardware advancement and subsequent advances in quantum cryptography, quantum software, and high-scalability quantum computers. Many potential challenges and exciting new trends for quantum technology research and development are highlighted in this paper for a broader debate. Copyright © 2024, The Authors. All rights reserved.

关键词： Quantum computers

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EXPLICIT RUNGE–KUTTA METHODS THAT ALLEVIATE ORDER REDUCTION

arXiv

引用

arXiv 2023年

作者： Biswas, Abhijit Ketcheson, David I. Roberts, Steven Seibold, Benjamin Shirokoff, David Computer Electrical and Mathematical Sciences & Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia Center for Applied Scientific Computing Lawrence Livermore National Laboratory LivermoreCA94550 United States Department of Mathematics Temple University PhiladelphiaPA19122 United States Department of Mathematical Sciences New Jersey Institute of Technology NewarkNJ07102 United States

Explicit Runge–Kutta (RK) methods are susceptible to a reduction in the observed order of convergence when applied to initial-boundary value problem with time-dependent boundary conditions. We study conditions on explicit RK methods that guarantee high-order convergence for linear problems;we refer to these conditions as weak stage order conditions. We prove a general relationship between the method’s order, weak stage order, and number of stages. We derive explicit RK methods with high weak stage order and demonstrate, through numerical tests, that they avoid the order reduction phenomenon up to any order for linear problems and up to order three for nonlinear *** Codes 65L04, 65L20, 65M12 Copyright © 2023, The Authors. All rights reserved.

关键词： Runge Kutta methods

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Importance of Kernel Bandwidth in Quantum Machine Learning

arXiv

引用

arXiv 2021年

作者： Shaydulin, Ruslan Wild, Stefan M. Global Technology Applied Research JPMorgan Chase New YorkNY10017 United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL60439 United States

Quantum kernel methods are considered a promising avenue for applying quantum computers to machine learning problems. Identifying hyperparameters controlling the inductive bias of quantum machine learning models is expected to be crucial given the central role hyperparameters play in determining the performance of classical machine learning methods. In this work we introduce the hyperparameter controlling the bandwidth of a quantum kernel and show that it controls the ex-pressivity of the resulting model. We use extensive numerical experiments with multiple quantum kernels and classical datasets to show consistent change in the model behavior from underfitting (bandwidth too large) to overfitting (bandwidth too small), with optimal generalization in between. We draw a connection between the bandwidth of classical and quantum kernels and show analogous behavior in both cases. Furthermore, we show that optimizing the bandwidth can help mitigate the exponential decay of kernel values with qubit count, which is the cause behind recent observations that the performance of quantum kernel methods decreases with qubit count. We reproduce these negative results and show that if the kernel bandwidth is optimized, the performance instead improves with growing qubit count and becomes competitive with the best classical methods. Copyright © 2021, The Authors. All rights reserved.

关键词： Bandwidth

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