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Exponentially Convergent multiscale Finite Element method

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Communications on Applied mathematics and Computation 2024年第2期6卷 862-878页

作者： yifan Chen Thomas y.Hou yixuan wang Applied and Computational mathematics CaltechPasadena 91106USA

We provide a concise review of the exponentially convergent multiscale finite element method(ExpmsFEm)for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave *** ExpmsFEm is built on the non-overlapped domain decomposition in the classical msFEm while enriching the approximation space systematically to achieve a nearly exponential convergence rate regarding the number of basis *** most generalizations of the msFEm in the literature,the ExpmsFEm does not rely on any partition of unity *** general,it is necessary to use function representations dependent on the right-hand side to break the algebraic Kolmogorov n-width barrier to achieve exponential ***,there are online and offline parts in the function representation provided by the *** online part depends on the right-hand side locally and can be computed in parallel *** offline part contains basis functions that are used in the Galerkin method to assemble the stiffness matrix;they are all independent of the right-hand side,so the stiffness matrix can be used repeatedly in multi-query scenarios.

关键词： multiscale method Exponential convergence Helmholtz's equation Domain decomposition Nonlinear model reduction

Tomographic reconstruction of the Earth’s magnetosheath from multiple spacecraft:a theoretical study

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Earth and Planetary Physics 2024年第1期8卷 204-214页

作者： A.m.Jorgensen TianRan Sun y.Huang L.Li R.Xu L.Dai Chi wang New mexico Institute of mining and Technology SocorroNMUSA National Space Science Center Chinese Academy of SciencesBeijing 100190China Tsinghua University Beijing 100084China

Following our earlier work on tomographic reconstruction of the magnetosheath soft X-ray emissions with superposed epoch analysis of many images recorded from a single spacecraft we now explore the instantaneous reconstruction of the magnetosheath and magnetopause using a few images recorded simultaneously from a few *** work is motivated by the prospect of possibly having two or three soft X-ray imagers in space in the coming years,and that many phenomena which occur at the magnetopause boundary,such as reconnection events and pressure pulse responses,do not lend themselves as well to superposed epoch *** the reconstruction is successful-which we demonstrate in this paper that it can be-this collection of imagers can be used to reconstruct the magnetosheath and magnetopause from a single image from each spacecraft,allowing for high time resolution *** this paper we explore the reconstruction using,two,three,and four *** show that the location of the subsolar point of the magnetopause can be determined with just two satellites,and that volume emissions of soft X-rays,and the shape of the boundary,can be reconstructed using three or more satellites.

关键词： magnetosheath tomography soft X-ray imaging SmILE

multi-layer perceptron-based data-driven multiscale modelling of granular materials with a novel Frobenius norm-based internal variable

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Journal of Rock mechanics and Geotechnical Engineering 2024年第6期16卷 2198-2218页

作者： mengqi wang y.T.Feng Shaoheng Guan Tongming Qu Zienkiewicz Centre for Computational Engineering Faculty of Science and EngineeringSwansea UniversitySwanseaWalesSA18EPUK Institute of Theoretical and Computational Physics Graz University of TechnologyGraz8010Austria Department of Civil and Environmental Engineering Hong Kong University of Science and TechnologyClearwater BayKowloonHong KongChina

One objective of developing machine learning(mL)-based material models is to integrate them with well-established numerical methods to solve boundary value problems(BVPs).In the family of mL models,recurrent neural networks(RNNs)have been extensively applied to capture history-dependent constitutive responses of granular materials,but these multiple-step-based neural networks are neither sufficiently efficient nor aligned with the standard finite element method(FEm).Single-step-based neural networks like the multi-layer perceptron(mLP)are an alternative to bypass the above issues but have to introduce some internal variables to encode complex loading *** this work,one novel Frobenius norm-based internal variable,together with the Fourier layer and residual architectureenhanced mLP model,is crafted to replicate the history-dependent constitutive features of representative volume element(RVE)for granular *** obtained mL models are then seamlessly embedded into the FEm to solve the BVP of a biaxial compression case and a rigid strip footing *** obtained solutions are comparable to results from the FEm-DEm multiscale modelling but achieve significantly improved *** results demonstrate the applicability of the proposed internal variable in enabling mLP to capture highly nonlinear constitutive responses of granular materials.

关键词： Granular materials History-dependence multi-layer perceptron(mLP) Discrete element method FEm-DEm machine learning

Effect of Al_(2)O_(3)on the mechanical Properties of(B_(4)C+Al_(2)O_(3))/Al Neutron Absorbing materials

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Acta metallurgica Sinica(English Letters) 2024年第8期37卷 1411-1420页

作者： J.X.Cai B.m.Shi N.Li y.Liu Z.G.Zhang y.N.Zan Q.Z.wang B.L.Xiao Z.y.m. Shi‑Changxu Innovation Center for Advanced materials Institute of Metal ResearchChinese Academy of SciencesShenyang 110016China Key Laboratory of Nuclear materials and Safety Assessment Institute of Metal ResearchChinese Academy of SciencesShenyang 110016China Nuclear Equipment Division Beijing Institute of Nuclear EngineeringChina Nuclear Power Engineering Co.Ltd.Beijing 100840China Department of materials Science School of Mechanical EngineeringShenyang UniversityShenyang 110044China

B_(4)C/Al composites are widely utilized as neutron absorbing materials for the storage and transportation of spent nuclear *** order to improve the high-temperature mechanical properties of B_(4)C/Al composites,in-situ nano-Al_(2)O_(3)was introduced utilizing oxide on Al powder *** this study,the Al_(2)O_(3)content was adjusted by utilizing spheroid Al powder with varying diameters,thereby investigating the impact of Al_(2)O_(3)content on the tensile properties of(B_(4)C+Al_(2)O_(3))/Al *** was found that the pinning effect of Al_(2)O_(3)on the grain boundaries could hinder the recovery of dislocations and lead to dislocation accumulation at high *** the result,with the increase in Al_(2)O_(3)content and the decrease in grain size,the high-temperature strength of the composites increased *** finest Al powder used in this investigation had a diameter of 1.4μm,whereas the resultant composite exhibited a maximum strength of 251 mPa at room temperature and 133 mPa at 350℃,surpassing that of traditional B_(4)C/Al composites.

关键词： Al matrix composites Neutron absorbing materials (B_(4)C+Al_(2)O_(3))/Al composites High-temperature strength

Grain refinement of mg-Ca alloys by native mgO particles

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Journal of magnesium and Alloys 2024年第3期12卷 980-996页

作者： Shihao wang yun wang Quentin m.Ramasse Zhongyun Fan Super STEm Laboratory SciTech Daresbury CampusDaresbury WA44ADUK School of Chemical and Process Engineering University of LeedsLeeds LS29JTUK BCAST Brunel University LondonUxbridgeMiddlesex UB83PHUK

In mg-Ca alloys the grain refining mechanism,in particular regarding the role of nucleant substrates,remains the object of *** native mgO is being recognised as a nucleating substrate accounting for grain refinement of mg alloys,the possible interactions of mgO with alloying elements that may alter the nucleation potency have not been elucidated ***,we design casting experiments of mg-xCa alloys varied qualitatively in number density of native mgO,which are then comprehensively studied by advanced electron *** results show that grain refinement is enhanced as the particle number density of mgO *** native mgO particles are modified by interfacial layers due to the co-segregation of Ca and N solute atoms at the mgO/mg *** aberration-corrected scanning transmission electron microscopy and electron energy loss spectroscopy,we reveal the nature of these Ca/N interfacial layers at the atomic *** of the crystallographic termination of mgO,Ca and N co-segregate at the mgO/mg interface and occupy.m. and O sites,respectively,forming an interfacial structure of a few atomic *** interfacial structure is slightly expanded,less ordered and defective compared to the mgO matrix due to compositional deviations,whereby the mgO substrate is altered as a poorer template to nucleate mg *** solidification in a TP-1 mould,the impotent mgO particles account for the grain refining mechanism,where they are suggested to participate into nucleation and grain initiation processes in an explosive *** work not only reveals the atomic engineering of a substrate through interfacial segregation but also demonstrates the effectiveness of a strategy whereby native mgO particles can be harnessed for grain refinement in mg-Ca alloys.

关键词： mg-Ca alloy Grain refinement mgO Interfacial segregation STEm/EELS Solidification.

Growth of RB Population in the Conversion Phase of Chlamydia Life Cycle

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Communications on Applied mathematics and Computation 2024年第1期6卷 90-112页

作者： Frederic y.m.Wan Department of mathematics University of CaliforniaIrvineCA92697-3875USA

Upon infecting a host cell,the reticulate body(RB)form of the Chlamydia bacteria simply proliferates by binary fission for an extended *** data show only RB units in the infected cells 20 hours post infection(hpi),spanning nearly half way through the development *** data collected every 4 hpi,conversion to the elementary body(EB)form begins abruptly at a rapid rate sometime around 24 *** modeling proliferation and conversion as simple birth and death processes,it has been shown that the optimal strategy for maximizing the total(mean)EB population at host cell lysis time is a bang-bang control qualitatively replicating the observed conversion ***,the simple birth and death model for the RB proliferation and conversion to EB deviates in a significant way from the available data on the evolution of the RB population after the onset of RB-to-EB *** working with a more refined model that takes into account a small size threshold eligibility requirement for conversion noted in the available data,we succeed in removing the deficiency of the previous models on the evolution of the RB population without affecting the optimal bang-bang conversion strategy.

关键词： Chlamydia Life cycle Optimal control maximal infectious spread Specie competitive survival

mindfulness Facets and Psychological Well-Being among meditators:Serenity as a mediating Process

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International Journal of mental Health Promotion 2024年第3期26卷 177-187页

作者： Rebecca y.m.Cheung Iris yili wang Elsa Ngar-Sze Lau School of Psychology and Clinical Language Sciences University of ReadingReadingUK Department of Special Education and Counselling The Education University of Hong KongHong KongChina Department of Educational Administration and Policy The Chinese University of Hong KongHong KongChina

Guided by the theoretical processes of mindfulness and psychological well-being,this study examined serenity as a mediator between mindfulness facets and psychological well-being,as indexed by depressive symptoms and life *** were 133 mindfulness practitioners who took part in a 3-day transnational meditation event in Hong *** informed consent,participants completed a self-report *** findings from structural equation modeling showed that serenity.m.diated the relation between two facets of mindfulness,including describing and nonreacting to inner experience,and life *** also mediated the relation between the mindfulness facet of describing and depressive *** associations were indicated between two mindfulness facets,including observing and nonjudging of inner experience,and depressive *** together,the findings revealed mindfulness facets as major correlates of serenity and psychological outcomes among Chinese meditation *** foster psychological well-being,researchers,educators,and practitioners should pay attention to the role of serenity,describing,and nonreacting to inner experience in mental health.

关键词： Depressive symptoms mindfulness mindfulness practitioners satisfaction with life serenity

A Collocation Technique via Pell-Lucas Polynomials to Solve Fractional Differential Equationmodel for HIV/AIDS with Treatment Compartment

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Computer modeling in Engineering & Sciences 2024年第10期141卷 281-310页

作者： Gamze yıldırım Suayip yüzbası Department of mathematics Faculty of ScienceAkdeniz UniversityAntalya07058Turkey Department of mathematics Faculty of Basic ScienceGebze Technical UniversityKocaeli41400Turkey Department of mathematics Faculty of ScienceBartın UniversityBartın74100Turkey

In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment *** HIV/AIDS mathematical model with a treatment compartment is divided into five classes,namely,susceptible patients(S),HIV-positive individuals(I),individuals with full-blown AIDS but not receiving ARV treatment(A),individuals being treated(T),and individuals who have changed their sexual habits sufficiently(R).According to the method,by utilizing the PLPs and the collocation points,we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into a nonlinear system of the algebraic ***,the error analysis is presented for the Pell-Lucas approximation *** aim of this study is to observe the behavior of five populations after 200 days when drug treatment is applied to HIV-infectious and full-blown AIDS *** demonstrate the usefulness of this method,the applications are made on the numerical example with the help of *** addition,four cases of the fractional order derivative(p=1,p=0.95,p=0.9,p=0.85)are examined in the range[0,200].Owing to applications,we figured out that the outcomes have quite decent ***,we understand that the errors decrease when the value of N *** figures in this study are created in *** outcomes indicate that the presented method is reasonably sufficient and correct.

关键词： Collocation method fractional differential equations HIV/AIDS epidemic model Pell-Lucas polynomials

Quantum correlations and entanglement in coupled optomechanical resonators with photon hopping via Gaussian interferometric power analysis

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Chinese Physics B 2024年第5期33卷 204-211页

作者： y.Lahlou B.maroufi m.Daoud LPHE-mS Department of PhysicsFaculty of SciencesMohammed V UniversityRabatMorocco LPmS Department of PhysicsFaculty of SciencesIbn Tofail UniversityKénitraMorocco

Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum ***,for quantum systems prepared in pure states,it is difficult to differentiate between quantum entanglement and quantum ***,this indistinguishability is no longer holds for mixed *** contribute to a better understanding of this differentiation,we have explored a simple model for both generating and measuring these quantum *** study concerns two macroscopic mechanical resonators placed in separate Fabry–Pérot cavities,coupled through the photon hopping *** system offers a comprehensively way to investigate and quantify quantum correlations beyond entanglement between these mechanical *** key ingredient in analyzing quantum correlation in this system is the global covariance *** forms the basis for computing two essential metrics:the logarithmic negativity(E_(N)^(m))and the Gaussian interferometric power(P_(G)^(m)).These metrics provide the tools to measure the degree of quantum entanglement and quantum correlations,*** study reveals that the Gaussian interferometric power(P_(G)^(m))proves to be a more suitable metric for characterizing quantum correlations among the mechanical modes in an optomechanical quantum system,particularly in scenarios featuring resilient photon hopping.

关键词： quantum correlations entanglement Gaussian interferometric power logarithmic negativity optomechanics photon hopping