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On the use of Artificial Neural Networks in Topology Optimisation

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arXiv 2022年

作者： Woldseth, Rebekka V. Aage, Niels Andreas Bærentzen, J. Sigmund, Ole Department of Mechanical Engineering Technical University of Denmark. Koppels Allé B.404 Kgs. Lyngby2800 Denmark Department of Applied Mathematics and Computer Science Technical University of Denmark. Richard Petersens Plads B.321 Kgs. Lyngby2800 Denmark

The question of how methods from the field of artificial intelligence can help improve the conventional frameworks for topology optimisation has received increasing attention over the last few years. Motivated by the capabilities of neural networks in image analysis, different model-variations aimed at obtaining iteration-free topology optimisation have been proposed with varying success. Other works focused on speed-up through replacing expensive optimisers and state solvers, or reducing the design-space have been attempted, but have not yet received the same attention. The portfolio of articles presenting different applications has as such become extensive, but few real breakthroughs have yet been celebrated. An overall trend in the literature is the strong faith in the "magic" of artificial intelligence and thus misunderstandings about the capabilities of such methods. The aim of this article is therefore to present a critical review of the current state of research in this field. To this end, an overview of the different model-applications is presented, and efforts are made to identify reasons for the overall lack of convincing success. A thorough analysis identifies and differentiates between problematic and promising aspects of existing models. The resulting findings are used to detail recommendations believed to encourage avenues of potential scientific progress for further research within the field. © 2022, CC BY.

关键词： Neural networks

Exploring Tidal Force Effects and Shadow Constraints for Schwarzschild-like Black Hole in Starobinsky-Bel-Robinson Gravity

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arXiv 2023年

作者： Arora, Dhruv Molla, Niyaz Uddin Chaudhary, Himanshu Debnath, Ujjal Atamurotov, Farruh Mustafa, G. Sagara Odisha Sambalpur768224 India Department of Mathematics Indian Institute of Engineering Science and Technology Shibpur Howrah711 103 India Department of Applied Mathematics Delhi Technological University Delhi110042 India Department of Mathematics Shyamlal College University of Delhi Delhi110032 India New Uzbekistan University Mustaqillik ave. 54 Tashkent100007 Uzbekistan Central Asian University Milliy Bog’ Street 264 Tashkent111221 Uzbekistan Faculty of Computer Engineering Tashkent University of Applied Sciences Gavhar Str. 1 Tashkent100149 Uzbekistan Institute of Theoretical Physics National University of Uzbekistan Tashkent100174 Uzbekistan Department of Physics Zhejiang Normal University Jinhua321004 China Zhejiang Institute of Photoelectronics Zhejiang Institute for Advanced Light Source Zhejiang Normal University Zhejiang Jinhua321004 China

The current manuscript deals with the tidal force effects, geodesic deviation, and shadow constraints of the Schwarzschild-like black hole theorised in Starobinsky-Bel-Robinson gravity exhibiting M-theory compactification. In the current analysis, we explore the radial and angular tidal force effects on a radially in-falling particle by the central black hole, which is located in this spacetime. We also numerically solve the geodesic deviation equation and study the variation of the geodesic separation vector with the radial coordinate for two nearby geodesics using suitable initial conditions. All the obtained results are tested for Sag A* and M87* by constraining the value of the stringy gravity parameter β using the shadow data from the event horizon telescope observations. All the results are compared with Schwarzschild black hole spacetime. In our study, we found that both the radial and angular tidal forces experienced by a particle switch their initial behaviour and turn compressive and stretching, respectively, before reaching the event horizon. The geodesic deviation shows an oscillating trend as well for the chosen initial condition. For the constrained value of β, we see that the spacetime geometry generated by Sag A* and M87* is effectively same for both Schwarzschild and Starobinsky-Bel-Robinson black hole. Furthermore, we also calculated the angular diameter of the shadow in Starobinsky-Bel-Robinson black hole and compared with the Schwarzschild black hole. It is observed that the angular diameter of shadow for M87* and Sgr A* in Starobinsky-Bel-Robinson black hole is smaller than the Schwarzschild black hole. The calculated results satisfy the event horizon telescope observational constraints. Copyright © 2023, The Authors. All rights reserved.

关键词： Black holes

A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

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applied mathematics and Mechanics(English Edition) 2019年第12期40卷 1695-1722页

作者： Lu LU Li ZHU Xingming GUO Jianzhong ZHAO Guanzhong LIU Shanghai Institute of Applied Mathematics and Mechanics Shanghai Key Laboratory of Mechanics in Energy Engineering School of Mechanics and Engineering ScienceShanghai UniversityShanghai 200072 China Department of Mechanical Engineering University of Alberta School of Mathematics and Computational Sciences Xiangtan UniversityXiangtan 411105 Hunan Province China

In this pap er, a novel size-dep endent functionally graded (FG) cylindrical shell model is develop ed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory . The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical typ es of size e ects simultaneously , which are the nonlocal stress ef- fect, the strain gradient e ect, and the surface energy e ects. With the help of Hamilton’s principle and rst-order shear deformation theory , the non-classical governing equations and related b oundary conditions are derived. By using the prop osed model, the free vibra- tion problem of FG cylindrical nanoshells with material prop erties varying continuously through the thickness according to a p ower-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various b oundary conditions are obtained. After verifying the reliability of the prop osed model and analytical method by comparing the degenerated results with those available in the literature, the in uences of nonlocal parameter, material length scale parameter, p ower-law index, radius-to-thickness ratio, length-to-radius ratio, and surface e ects on the vibration characteristic of func- tionally graded cylindrical nanoshells are examined in detail.

关键词： nonlocal strain gradient theory surface elasticity theory rst-order shear deformation theory vibration functionally graded (FG) cylindrical nanoshell

Synergistic Interface Effects in Composite Dielectrics: Insights into Charge Trapping Regulation through Multiscale Modeling

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arXiv 2024年

作者： Zhao, Haoxiang An, Lixuan Zhang, Daning Yang, Xiong Yao, Huanmin Zhang, Guanjun Mu, Haibao Baumeier, Björn State Key Laboratory of Electrical Insulation and Power Equipment School of Electrical Engineering Xi'an Jiaotong University Xi'An710049 China Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven5600MB Netherlands Department of Applied Physics Eindhoven University of Technology Eindhoven5600MB Netherlands KERMIT Department of Data Analysis and Mathematical Modelling Ghent University Ghent9000 Belgium Institute for Complex Molecular Systems Eindhoven University of Technology Eindhoven5600MB Netherlands

The rapid development of modern energy applications drives an urgent need to enhance the dielectric strength of energy storage dielectrics for higher power density. Interface design is a promising strategy to regulate the crucial charge transport process determining dielectric strength. However, the targeted exploitation of interface effects on charge transport is limited due to a lack of fundamental understanding of the underlying mechanisms involving elementary electronic processes and details of the intricate interplay of characteristics of molecular building blocks and the interfacial morphology - details that cannot fully be resolved with experimental methods. Here we employ a multiscale modeling approach linking the quantum properties of the charge carriers with nano- and mesoscale structural details of complex interfaces. applied to a prototypical application-proven cellulose-oil composite with interfaces formed between oil, disordered, and crystalline cellulose regions, this approach demonstrates that charges are trapped in the disordered region. Specifically, it unveils this trapping as a synergistic effect of two transport-regulating interface mechanisms: back-transfer to the oil region is suppressed by energetic factors, while forward-transfer to the crystalline cellulose is suppressed by low electronic coupling. The insight into the molecular origins of interface effects via dual-interface regulation offers new development paths for advanced energy materials. © 2024, CC BY.

关键词： Nanocrystals

Transforming Dental Education in Poland: Exploring User Acceptance of Immersive Vr Training with Haptic Simulators

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SSRN

SSRN 2024年

作者： Zadrożny, Lukasz Ponto-Wolska, Malgorzata Ćwirzeń, Waldemar Orlańska, Aleksandra Bąk, Iwona Polster, Anuradha Sulikowski, Piotr Department of Dental Propaedeutics and Prophylaxis Faculty of Dental Medicine Medical University of Warsaw Warsaw02-006 Poland Department of Applied Mathematics in Economics Faculty of Economics West Pomeranian University of Technology Szczecin Poland Restorative Dentistry Dentistry & Oral Health La Trobe Rural Health School La Trobe University PO Box 199 BendigoVIC3552 Australia Department of Information Systems Engineering Faculty of Computer Science and Information Technology West Pomeranian University of Technology Szczecin Poland

Background: The evolution of digital technologies, teaching techniques as well as changes in the recent students generations requires adaptation and transformations to provide effective knowledge and practical, manual skills to dental students. Recent development in the implementing of the virtual reality (VR) to the simulation based training in medicine revealed promising outcome. Much part of dental students education is based on the practice on simulators and development of different simulators is crucial to the quality of education. Objective: The goal of this study was analyze students’ experience and further expectations regarding training with VR based, haptic technology simulators for dentistry. Methods: The qualitative group survey study was addressed to the 143 students in 2020/2021. Data analysis was done in Microsoft Forms and further Multiple Correspondence Analysis (MCA) was performed. The survey was contains: Part one - 9 questions covering demographics and general information regarding using the digital technologies and learning preferences. And Part two – Simodont experience, with 18 statements formed to fit response type of a five-point Likert scale and 5 single choice questions. Results: 90 (62,9%) replies were obtained. Simulator training was easy (82%), realistic (62.2%), had a positive impact on the learning process (80%) and helped improve manual dexterity (70%). Feedback provided by Simodont was clear, (60%). Over 51% of respondents would like to continue using Simodont. 50% claims that students in the preclinical stage should practice on Simodont rather than on phantom heads. Conclusions: VR training with Simodont is well-accepted. © 2024, The Authors. All rights reserved.

关键词： Students

Numerical investigation of gas hydrate dissociation in the porous medium of multiphase flow

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AIP Conference Proceedings 2023年第1期2872卷

作者： Ahmed K. Abu-Nab Alexander V. Koldoba Elena V. Koldoba Yury A. Poveshchenko Viktoriia O. Podryga Parvin I. Rahimly Ahmed E. Bakeer Department of Mathematics and Computer Science Faculty of Science Menoufia University Shebin El-Koom 32511 Egypt Phystech School of Applied Mathematics and Informatics Moscow Institute of Physics and Technology Dolgoprudny Moscow 141700 Russia Lomonosov Moscow State University Moscow 119991 Russia Keldysh Institute of Applied Mathematics Russian Academy of Sciences Moscow 125047 Russia Department of Mathematics Faculty of Science Damanhur University Damanhur 22516 Egypt

Understanding the mechanisms involved in the growth and decomposition of methane hydrates (MHs) is currently an urgent issue since they are essential in improving the global climate and future energy supplies. As a result, many scientists and researchers around the world are looking into and studying this critical topic. The objective of the presented work is to illustrate the thermo-physical processes of MHs decomposition in porous media based on a one-dimensional model throughout a multiphase flow. The thermodynamic equilibrium, which actually happens between temperature and pressure (P-T) in the hydrate stability region. The mathematical model was presented and solved by using the implicit finite differences technique under the initial and boundary conditions. After the Jacobin matrix was formed, the system of nonlinear algebraic equations was solved by using the Newton-Raphson methodology. Within the framework of this study, we take into consideration the Buckley-Leverett problem of incompressible fluid displacement. Our approach and computations are predicated on the assumption that there are constant heat conditions without hydrate formation anywhere in the whole computational domain.

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Sketch-and-solve approaches to k-means clustering by semidefinite programming

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arXiv 2022年

作者： Clum, Charles Mixon, Dustin G. Villar, Soledad Xie, Kaiying Department of Mathematics The Ohio State University ColumbusOH United States Translational Data Analytics Institute The Ohio State University ColumbusOH United States Department of Applied Mathematics & Statistics Johns Hopkins University BaltimoreMD United States Mathematical Institute for Data Science Johns Hopkins University BaltimoreMD United States Department of Electrical and Computer Engineering The Ohio State University ColumbusOH United States

We introduce a sketch-and-solve approach to speed up the Peng-Wei semidefinite relaxation of k-means clustering. When the data is appropriately separated we identify the k-means optimal clustering. Otherwise, our approach provides a high-confidence lower bound on the optimal k-means value. This lower bound is data-driven;it does not make any assumption on the data nor how it is generated. We provide code and an extensive set of numerical experiments where we use this approach to certify approximate optimality of clustering solutions obtained by k-means++. © 2022, CC BY.

关键词： Optimal systems

Symmetries of cross caps

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arXiv 2021年

作者： Honda, Atsufumi Naokawa, Kosuke Saji, Kentaro Umehara, Masaaki Yamada, Kotaro Department of Applied Mathematics Faculty of Engineering Yokohama National University 79-5 Tokiwadai Hodogaya Yokohama240-8501 Japan Department of Computer Science Faculty of Applied Information Science Hiroshima Institute of Technology 2-1-1 Miyake Saeki Hiroshima731-5193 Japan Department of Mathematics Faculty of Science Kobe University Rokko Kobe657-8501 Japan Department of Mathematical and Computing Sciences Tokyo Institute of Technology Tokyo152-8552 Japan Department of Mathematics Tokyo Institute of Technology Tokyo152-8551 Japan

It is well-known that cross caps on surfaces in the Euclidean 3-space can be expressed in Bruce-West's normal form, which is a special local coordinate system centered at the singular point. In this paper, we show a certain kind of uniqueness of such a coordinate system. In particular, the functions associated with this coordinate system produce new invariants on cross cap singular points. Using them, we characterize the possible symmetries on cross *** Codes 57R45, 53A05 Copyright © 2021, The Authors. All rights reserved.

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Mind the (Formula Presented.): Asymptotically Better, but Still Impractical, Quantum Distributed Algorithms

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Algorithms 2023年第7期16卷

作者： Kerger, Phillip Bernal Neira, David E. Gonzalez Izquierdo, Zoe Rieffel, Eleanor G. Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD21218 United States Quantum Artificial Intelligence Laboratory NASA Ames Research Center Moffett Field CA94035 United States Research Institute of Advanced Computer Science Universities Space Research Association Mountain ViewCA94043 United States Davidson School of Chemical Engineering Purdue University West LafayetteIN47907 United States

We present two algorithms in the quantum CONGEST-CLIQUE model of distributed computation that succeed with high probability: one for producing an approximately optimal Steiner tree, and one for producing an exact directed minimum spanning tree, each of which uses (Formula presented.) rounds of communication and (Formula presented.) messages, achieving a lower asymptotic round and message complexity than any known algorithms in the classical CONGEST-CLIQUE model. At a high level, we achieve these results by combining classical algorithmic frameworks with quantum subroutines. Additionally, we characterize the constants and logarithmic factors involved in our algorithms as well as related classical algorithms, otherwise obscured by (Formula presented.) notation, revealing that advances are needed to render both the quantum and classical algorithms practical. © 2023 by the authors.

关键词： Quantum computers