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Lagrangian particle model for 3D simulation of pellets and SPI fragments in tokamaks

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arXiv 2020年

作者： Samulyak, Roman Yuan, S. Naitlho, N. Parks, P.B. Department of Applied Mathematics and Statistics Stony Brook University Stony BrookNY United States Computational Science Initiative Brookhaven National Laboratory UptownNY United States General Atomics San DiegoCA United States

A 3D numerical model for the ablation of pellets and shattered pellet injection (SPI) fragments in tokamaks in the plasma disruption mitigation and fueling parameter space has been developed based on the Lagrangian particle code [R. Samulyak, X. Wang, H.-S. Chen, Lagrangian Particle Method for Compressible Fluid Dynamics, J. Comput. Phys., 362 (2018), 1-19]. The pellet code implements the low magnetic Reynolds number MHD equations, kinetic models for the electronic heating, a pellet surface ablation model, an equation of state that supports multiple ionization states, radiation, and a model for grad-B drift of the ablated material across the magnetic field. The Lagrangian particle algorithm is highly adaptive, capable of simulating a large number of fragments in 3D while eliminating numerical difficulties of dealing with the tokamak background plasma. The code has achieved good agreement with theory for spherically symmetric ablation flows. Axisymmetric simulations of neon and deuterium pellets in magnetic fields ranging from 1 to 6 Tesla have been compared with previous simulations using the FronTier code, and very good agreement has also been obtained. The main physics contribution of the paper is a detailed study of the influence of 3D effects, in particular grad-B drift, on pellet ablation rates and properties of ablation clouds. Smaller reductions of ablation rates in magnetic fields compared to axially symmetric simulations have been demonstrated because the ablated material is not confined to narrowing channels in the presence of grad-B drift. Contribution of various factors in the grad-B drift model has also been quantified. © 2020, CC BY.

关键词： Pelletizing

On the Ψ−Second Level Fractional Derivative

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SSRN

SSRN 2024年

作者： Bany-Ahmad, Rami Mohammad Ibrahim, Alawiah Noorani, Mohd Salmi Md. Abdeljawad, Thabet Department of Mathematical Sciences Faculty of Science and Technology University Kebangsaan Malaysia Selangor Bangi43600 Malaysia University Preparatory Program Dar Al Uloom University Riyadh Saudi Arabia Department of Mathematics and Sciences Prince Sultan University Riyadh Saudi Arabia Department of Medical Research China Medical University Taichung40402 Taiwan Department of Mathematics and Applied Mathematics Sefako Makgatho Health Sciences University Medusa Garankuwa0204 South Africa Department of Mathematics Kyung Hee University 26 Kyungheedae-ro Dongdaemun-gu Seoul02447 Korea Republic of

In this article, we create another novel parametrization for the ψ−Hilfer fractional derivative, which can be easier to apply in some cases and cover the gaps between these concepts. Additionally, we unveil the most comprehensive variant of the second-level fractional derivative with respect to another function, so-called ψ−second level fractional derivative. Furthermore, we establish a comprehensive generalization termed as ψ−mth level FDs for the mth compositions of the nth−order derivative. Moreover, we obtain the remarkable derivatives that are widely studied, like ψ−Riemann Liouville, ψ−Caputo, and ψ−Hilfer fractional derivatives, which emerge as special cases of the transformative ψ−second level fractional derivative. Finally, the intricate interconnections between these derivatives across various parameter values and spaces are thoroughly explored, shedding light on some of their fundamental properties. © 2024, The Authors. All rights reserved.

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On Cyclic Finite-State Approximation of Data-Driven Systems

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arXiv 2019年

作者： Vides, Fredy Scientific Computing Innovation Center Department of Applied Mathematics Universidad Nacional Autónoma de Honduras UNAH Honduras Graduate Program in Structural Engineering Universidad Tecnológica Centroamericana UNITEC Honduras

In this document, some novel theoretical and computational techniques for constrained approximation of data-driven systems, are presented. The motivation for the development of these techniques came from structure-preserving matrix approximation problems that appear in the fields of system identification and model predictive control, for data-driven systems and processes. The research reported in this document is focused on finite-state approximation of data-driven systems. Some numerical implementations of the aforementioned techniques in the simulation and model predictive control of some generic data-driven systems, that are related to electrical signal transmission models, are outlined.93B28, 47N70 (primary) and 93C57, 93B40 (secondary) Copyright © 2019, The Authors. All rights reserved.

关键词： Singular value decomposition

Affine approximation of parametrized kernels and model order reduction for nonlocal and fractional laplace models

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arXiv 2019年

作者： Burkovska, Olena Gunzburger, Max Computational and Applied Mathematics Oak Ridge National Laboratory Oak RidgeTN37831 United States Department of Scientific Computing Florida State University 400 Dirac Science Library TallahasseeFL32306-4120 United States

We consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius δ 0 and fractional Laplace ker-nels, parametrized by the fractional power s ϵ (0;1), are studied. In order to provide an efficient and reliable approximation of the solution for different values of the parameters, we develop the reduced basis method as a paramet-ric model order reduction approach. Major diffculties arise since the kernels are not affine in the parameters, singular, and discontinuous. Moreover, the spatial regularity of the solutions depends on the varying fractional power s. To address this, we derive regularity and differentiability results with respect to δ;and s, which are of independent interest for other applications such as optimization and parameter identification. We then use these results to con-struct affine approximations of the kernels by local polynomials. Finally, we certify the method by providing reliable a posteriori error estimators, which account for all approximation errors, and support the theoretical findings by numerical experiments. Copyright © 2019, The Authors. All rights reserved.

关键词： Laplace transforms

Semiclassical inverse spectral problem for elastic love waves in isotropic media

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arXiv 2019年

作者： de Hoop, Maarten V. Iantchenko, Alexei van der Hilst, Robert D. Zhai, Jian Simons Chair in Computational and Applied Mathematics and Earth Science Rice University HoustonTX77005 United States Department of Materials Science and Applied Mathematics Faculty of Technology and Society Malmö University MalmöSE-205 06 Sweden Department of Earth Atmospheric and Planetary Sciences Massachusetts Institute of Technology CambridgeMA02139 United States Institute for Advanced Study Hong Kong University of Science and Technology Kowloon Hong Kong

We analyze the inverse spectral problem on the half line associated with elastic surface waves. Here, we focus on Love waves. Under certain generic conditions, we establish uniqueness and present a reconstruction scheme for the S-wavespeed with multiple wells from the semiclassical spectrum of these waves. Copyright © 2019, The Authors. All rights reserved.

关键词： Surface waves

Interacting models for twisted bilayer graphene: A quantum chemistry approach

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Physical Review B 2023年第23期107卷 235123-235123页

作者： Fabian M. Faulstich Kevin D. Stubbs Qinyi Zhu Tomohiro Soejima Rohit Dilip Huanchen Zhai Raehyun Kim Michael P. Zaletel Garnet Kin-Lic Chan Lin Lin Department of Mathematics University of California Berkeley California 94720 USA Department of Physics University of California Berkeley California 94720 USA Division of Engineering and Applied Science California Institute of Technology Pasadena California 91125 United States Division of Chemistry and Chemical Engineering California Institute of Technology Pasadena California 91125 USA Materials Science Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA

The nature of correlated states in twisted bilayer graphene (TBG) at the magic angle has received intense attention in recent years. We present a numerical study of an interacting Bistritzer-MacDonald (IBM) model of TBG using a suite of methods in quantum chemistry, including Hartree-Fock, coupled cluster singles, doubles (CCSD), and perturbative triples [CCSD(T)], as well as a quantum chemistry formulation of the density matrix renormalization group method (DMRG). Our treatment of TBG is agnostic to gauge choices, and hence we present a new gauge-invariant formulation to detect the spontaneous symmetry breaking in interacting models. To benchmark our approach, we focus on a simplified spinless, valleyless IBM model. At integer filling (ν=0), all numerical methods agree in terms of energy and C2zT symmetry breaking. Additionally, as part of our benchmarking, we explore the impact of different schemes for removing “double-counting” in the IBM model. Our results at integer filling suggest that cross validation of different IBM models may be needed for future studies of the TBG system. After benchmarking our approach at integer filling, we perform the first systematic study of the IBM model near integer filling (for |ν|<0.2). In this regime, we find that the ground state can be in a metallic and C2zT symmetry breaking phase. The ground state appears to have low entropy, and therefore can be relatively well approximated by a single Slater determinant. Furthermore, we observe many low entropy states with energies very close to the ground-state energy in the near integer filling regime.

关键词： Electronic structure First-principles calculations Bilayer graphene Twisted bilayer graphene Approximation methods for many-body systems Electron-correlation calculations Many-body techniques Mean field theory Quantum chemistry methods Second quantization Symmetries

An energy stable C0 finite element scheme for a phase-field model of vesicle motion and deformation

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arXiv 2020年

作者： Shen, Lingyue Xu, Zhiliang Lin, Ping Huang, Huaxiong Xu, Shixin Department of Mathematics University of Dundee DundeeDD1 4HN United Kingdom Duke Kunshan University 8 Duke Ave KunshanJiangsu China Research Centre for Mathematics Advanced Institute of Natural Sciences Beijing Normal University Zhuhai China BNU-HKBU United International College Zhuhai China Department of Mathematics University of California Riverside 900 University Avenue RiversideCA United States Department of Applied and Computational Mathematics and Statistics University of Notre Dame 102G Crowley Hall Notre DameIN46556 United States

A thermodynamically consistent phase-field model is introduced for simulating motion and shape transformation of vesicles under flow conditions. In particular, a general slip boundary condition is used to describe the interaction between vesicles and the wall of the fluid domain. A second-order accurate in both space and time C0 finite element method is proposed to solved the model governing equations. Various numerical tests confirm the convergence, energy stability, and conservation of mass and surface area of cells of the proposed scheme. Vesicles with different mechanical properties are also used to explain the pathological risk for patient with sickle cell *** Codes 76T06 92B05 35Q92 © 2020, CC BY.

关键词： Finite element method

A Quantum Computing View on Unitary Coupled Cluster Theory

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arXiv 2021年

作者： Anand, Abhinav Schleich, Philipp Alperin-Lea, Sumner Jensen, Phillip W. K. Sim, Sukin Díaz-Tinoco, Manuel Kottmann, Jakob S. Degroote, Matthias Izmaylov, Artur F. Aspuru-Guzik, Alán Chemical Physics Theory Group Department of Chemistry University of Toronto Canada Department of Computer Science University of Toronto Canada Applied and Computational Mathematics Department of Mathematics RWTH Aachen University Aachen Germany Vector Institute for Artificial Intelligence Toronto Canada Department of Chemistry and Chemical Biology Harvard University United States Department of Physical and Environmental Sciences University of Toronto Scarborough Canada Lebovic Fellow Toronto Canada

We present a review of the Unitary Coupled Cluster (UCC) ansatz and related ansätze which are used to variationally solve the electronic structure problem on quantum computers. A brief history of coupled cluster (CC) methods is provided, followed by a broad discussion of the formulation of CC theory. This includes touching on the merits and difficulties of the method and several variants, UCC among them, in the classical context, to motivate their applications on quantum computers. In the core of the text, the UCC ansatz and its implementation on a quantum computer are discussed at length, in addition to a discussion on several derived and related ansätze specific to quantum computing. The review concludes with a unified perspective on the discussed ansätze, attempting to bring them under a common framework, as well as with a reflection upon open problems within the field. © 2021, CC BY.

关键词： Cluster analysis

Swarm Intelligence Approach for Parametric Optimization of Railway Simply Supported Beam Bridges with a Single Dynamic Load and Vibration Mode

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Swarm Intelligence Approach for Parametric Optimization of R...

Computer Technologies (ICCTech), International Conference on

作者： Javier Sánchez-Haro Akemi Gálvez Guillermo Capellán Andrés Iglesias Department of Structural Engineering University of Cantabria Santander Spain Dept. of Applied Mathematics & Computational Sciences University of Cantabria Santander Spain Arenas y Asociados Ingenieria de Diseño S.L. Santander Spain

ISBN: (数字)9798350395419

ISBN: (纸本)9798350395426

Analyzing the structural response of bridges to dynamic loads is a crucial concern in bridge engineering, with the primary goal to ensure the bridge safety and stability under varying conditions. The application of artificial intelligence techniques to address this challenge represents a promising yet relatively unexplored area of research in the existing literature. In this context, this paper introduces a swarm intelligence approach known as the bat algorithm for the optimal determination of the geometric and mechanical parameters in railway simply supported beam bridges. This work focuses on the assumption of a single dynamic load and one vibration mode. Our results, validated through Sofistik, a renowned software package for civil engineering, demonstrate that our approach performs well as it yields satisfactory engineering solutions. This opens the door for further swarm intelligence-based developments in this field.

关键词： Bridges Vibrations Software packages Heuristic algorithms Software algorithms Rail transportation Stability analysis