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Topology optimization including a model of the layer-by-layer additive manufacturing process

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arXiv 2022年

作者： Haveroth, Geovane A. Thore, C.-J. Correa, M.R. Ausas, R.F. Jakobsson, S. Cuminato, J.A. Klarbring, A. Department of Applied Mathematics and Statistics Institute of Mathematics and Computer Sciences University of São Paulo SP São Carlos Brazil Division of Solid Mechanics Department of Management and Engineering Institute of Technology Linköping University Linköping581 83 Sweden Arcam EBM Mölndal Sweden Department of Applied Mathematics Institute of Mathematics Statistics and Scientific Computing University of Campinas Campinas-SP Brazil

A topology optimization formulation including a model of the layer-by-layer additive manufacturing (AM) process is considered. Defined as a multi-objective minimization problem, the formulation accounts for the performance and cost of both the final and partially manufactured designs and allows for considering AM-related issues such as overhang and residual stresses in the optimization. The formulation is exemplified by stiffness optimization in which the overhang is limited by adding mechanical or thermal compliance as a measure of the cost of partially manufactured designs. Convergence of the model as the approximate layer-by-layer model is refined is shown theoretically, and an extensive numerical study indicates that this convergence can be fast, thus making it a computationally viable approach useful for including AM-related issues into topology optimization. The examples also show that drips and sharp corners associated with some geometry-based formulations for overhang limitation can be avoided. The codes used in this article are written in Python using only open sources libraries and are available for reference. Copyright © 2022, The Authors. All rights reserved.

关键词： Stiffness

Linear Combination of Hamiltonian Simulation for Nonunitary Dynamics with Optimal State Preparation Cost

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Physical Review Letters 2023年第15期131卷 150603-150603页

作者： Dong An Jin-Peng Liu Lin Lin Joint Center for Quantum Information and Computer Science University of Maryland College Park Maryland 20742 USA Department of Mathematics University of California Berkeley California 94720 USA Simons Institute for the Theory of Computing University of California Berkeley California 94720 USA Center for Theoretical Physics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Lawrence Berkeley National Laboratory Applied Mathematics and Computational Research Division Berkeley California 94720 USA Challenge Institute for Quantum Computation University of California Berkeley California 94720 USA

We propose a simple method for simulating a general class of nonunitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving nonunitary processes, such as the quantum singular value transformation. The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters.

关键词： Open quantum systems Quantum algorithms Quantum algorithms & computation Quantum simulation Differential equations

On the relevance of lift force modelling in turbulent wall flows with small inertial particles

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arXiv 2024年

作者： Gao, Wei Shi, Pengyu Parsani, Matteo Costa, Pedro Mechanical Engineering Physical Science and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Applied Mathematics and Computational Science Computer Electrical and Mathematical Science and Engineering Division Extreme Computing Research Center King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Université de Toulouse CNRS Toulouse France Helmholtz-Zentrum Dresden – Rossendorf Institute of Fluid Dynamics Dresden01328 Germany Process & Energy Department TU Delft Leeghwaterstraat 39 Delft2628 CB Netherlands

In particle-laden turbulent wall flows, lift forces can influence the near-wall turbulence. This has been recently observed in particle-resolved simulations, which, however, are too expensive to be used in upscaled models. Instead, point-particle simulations have been the method of choice to simulate the dynamics of these flows during the last decades. While this approach is simpler, cheaper, and physically sound for small inertial particles in turbulence, some issues remain. In the present work, we address challenges associated with lift force modelling in turbulent wall flows and the impact of lift forces in the near-wall flow. We performed direct numerical simulations (DNS) of small inertial point particles in turbulent channel flow for fixed Stokes number and mass loading while varying the particle size. Our results show that the particle dynamics in the buffer region, causing the apparent particle-to-fluid slip velocity to vanish, raises major challenges for accurately modelling lift forces. While our results confirm that lift forces have little influence on particle dynamics for sufficiently small particle sizes, for inner-scaled diameters of order one and beyond, lift forces become quite important near the wall. The different particle dynamics under lift forces results in the modulation of streamwise momentum transport in the near-wall region. We analyze this lift-induced turbulence modulation for different lift force models, and the results indicate that realistic models are critical for particle-modelled simulations to correctly predict turbulence modulation by particles in the near-wall region. © 2024, CC BY.

关键词： Wall flow

Operator Learning Enhanced Physics-informed Neural Networks for Solving Partial Differential Equations Characterized by Sharp Solutions

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arXiv 2023年

作者： Lin, Bin Mao, Zhiping Wang, Zhicheng Karniadakis, George Em School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University Xiamen361005 China Laboratory of Ocean Energy Utilization Ministry of Education School of Energy and Power Engineering Dalian University of Technology Dalian China Division of Applied Mathematics Brown University ProvidenceRI02906 United States

Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep Operator Network (DeepONet) and Fourier neural operator (FNO), has been introduced and extensively employed in approximating solution of PDEs. Nevertheless, to solve problems consisting of sharp solutions poses a significant challenge when employing these two approaches. To address this issue, we propose in this work a novel framework termed Operator Learning Enhanced Physics-informed Neural Networks (OL-PINN). Initially, we utilize DeepONet to learn the solution operator for a set of smooth problems relevant to the PDEs characterized by sharp solutions. Subsequently, we integrate the pre-trained DeepONet with PINN to resolve the target sharp solution problem. We showcase the efficacy of OL-PINN by successfully addressing various problems, such as the nonlinear diffusion-reaction equation, the Burgers equation and the incompressible Navier-Stokes equation at high Reynolds number. Compared with the vanilla PINN, the proposed method requires only a small number of residual points to achieve a strong generalization capability. Moreover, it substantially enhances accuracy, while also ensuring a robust training process. Furthermore, OL-PINN inherits the advantage of PINN for solving inverse problems. To this end, we apply the OL-PINN approach for solving problems with only partial boundary conditions, which usually cannot be solved by the classical numerical methods, showing its capacity in solving ill-posed problems and consequently more complex inverse problems. Copyright © 2023, The Authors. All rights reserved.

关键词： Partial differential equations

EXPLICIT RUNGE–KUTTA METHODS THAT ALLEVIATE ORDER REDUCTION

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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

Spatiotemporal PET reconstruction with attenuation and motion correction

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Spatiotemporal PET reconstruction with attenuation and motio...

IEEE Symposium on Nuclear Science (NSS/MIC)

作者： E. Cece P. V.F.J. Meyrat O. Verdier E. Torino M. Colarieti-Tosti Division of Biomedical Imaging KTH Royal Institute of Technology Stockholm Sweden Department of Chemical Engineering Materials and Production University of Naples Federico II Naples Italy Department of Computing Mathematics and Physics HVL Western Norway University of Applied Sciences Bergen Norway Centro Interdipartimentale di Ricerca sui Biomateriali (CRIB) University of Naples Federico II Naples Italy

The diagnostic power of Positron Emission Tomography for early stage lung cancer is challenging since the lesion dimensions are comparable with the spatial resolution of modern clinical scanners and their contrast is decreased by respiratory motion. Moreover, strong artifacts in reconstructed images are introduced by attenuation, resulting in depression of activity in the middle of the image. In this paper we propose a modified version of Maximum Likelihood Activity and Attenuation (MLAA) algorithm, the Morphed-MLAA (M-MLAA), which, given gated data, jointly corrects for patient motion during the acquisition by composing the forward and backward operators with the registration fields between the different gates. The registration fields are evaluated with the deep-learning model Synthmorph. The main advantage of the proposed algorithm is that it makes use of the entire projection data set, thus improving the lesion signal-to-noise ratio, compared to the case in which images are reconstructed from a subset of the data. Our proposed algorithm has been tested on the XCAT phantom with some added lung lesions and shows improved performance for the detection and reconstruction of some of them; this improved performance is corroborated by the evaluation of two figures of merit (PSNR and RC). Our results show the potential of M-MLAA algorithm, but, at the same time, also that there is still space for improvements, since some lesions are better detected by the other more classical approaches, as MLAA single or total gates reconstructions.

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Mathematical modeling and simulation of magnetized bioconvective nanoliquid flow capturing Brownian motion, multiple slip, thermophoresis and gyrotactic microorganisms configured by rotating disk

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Partial Differential Equations in applied mathematics 2024年 12卷

作者： Garalleh, Hakim AL Khan, Sami Ullah Waqas, M. Zamri, Nurnadiah Abdullaeva, Barno Gupta, Manish Department of Mathematical Science College of Engineering University of Business and Technology Jeddah 21361 Saudi Arabia Department of Mathematics Namal University Mianwali 42250 Pakistan 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 University Sultan Zainal Abidin Besut Campus Terengganu Besut 22200 Malaysia Department of Mathematics and Information Technologies Vice-Rector for Scientific Affairs Tashkent State Pedagogical University Tashkent Uzbekistan Division of Research and Development Lovely Professional University Phagwara India

This analysis describes the bioconvective flow of nanofluid due to rotation of disk. A uniform suspension of nanofluid between microorganisms is considered to analyze the applications of bioconvection. The nanofluid assumed to be electrically conducting with amplification of magnetic force. The problem is entertained in presence of different slip features including velocity, temperature, concentration and microorganisms. The formulation of problem in simplified form is attained via dimensionless variables. Shooting numerical scheme is used to compute the simulations. Physical interpretation and visualization of results is observed in view of parameters. The observations concluded that interaction of slip effects reduces the velocity profile but enhances nanofluid temperature and concentration profiles. The temperature profile increases with thermophoresis parameter. Current results comprise applications in cooling of electronics devices, thin film coating, gas turbines engine, energy systems etc. © 2024

关键词： Bioconvection Multiple slip effects Nanoparticles Numerical computations Rotating disks

Quantum Entanglement Based on Two-Photon Joint Subtraction from Two-Mode Squeezed Vacuum States

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Quantum Entanglement Based on Two-Photon Joint Subtraction f...

OptoElectronics and Communications Conference, OECC

作者： Hongbin Song Heyu Huang Hao Liu Ai Zhou Guofeng Zhang Hidehiro Yonezawa The General Education Division and Guangdong Key Laboratory of Optoelectronic Materials and Chips and Shenzhen Key Lab of Semiconductor Lasers The Chinese University of Hong Kong Shenzhen Shenzhen China School of Materials Science and Engineering and National Engineering Research Center of Fiber Optic Sensing Technology and Networks Wuhan University of Technology Wuhan China National Engineering Research Center of Fiber Optic Sensing Technology and Networks Wuhan University of Technology Wuhan China Department of Applied Mathematics The Hong Kong Polytechnic University Hongkong China Optical Quantum Control Research Team RIKEN Center for Quantum Computing Saitama Japan

We present and analyze the quantum entanglement generated from two-photon joint subtraction from two-mode squeezed vacuum states (TMSV). Larger entanglement negativity than single-photon jointly subtracted TMSV, photo... 详细信息

ISBN: (数字)9798350308396

ISBN: (纸本)9798350308402

关键词： Protocols Correlation Quantum entanglement Simulation Elementary particle vacuum Quantum networks Photonics

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