Spectral Methods For Hamiltonian Systems And Their Applications

Hamiltonian systems typically arise as models of conservative physical systems and have many applications. Our main emphasis is using spectral methods to preserve both symplectic structure and energy up to machine error in long time. An engery error estimation is given for a type of Hamiltonian systems with polynomial nonlinear part, which is numerical verified by solving a Henon-Heiles systems. Three interesting applications are presented : the first one is the N-body problems. The second one is approximation for Weyl\u27s Law and the third one is simulating quantum cooling in an optomechanical system to study the dissipative dynamics. Moreover, nonsmooth Hamiltonian systems problems are discussed for the limitation of this method which motivates our future work

Two-parameter localization and related phase transition for a Schr\"{o}dinger operator in balls and spherical shells

Here we investigate the two-parameter high-frequency localization for the eigenfunctions of a Schr\"{o}dinger operator with a singular inverse square potential in high-dimensional balls and spherical shells as the azimuthal quantum number $l$ and the principal quantum number $k$ tend to infinity simultaneously, while keeping their ratio as a constant, generalizing the classical one-parameter localization for Laplacian eigenfunctions [SIAM J. Appl. Math. 73:780-803, 2013]. We prove that the eigenfunctions in balls are localized around an intermediate sphere whose radius is increasing with respect to the $l$-$k$ ratio. The eigenfunctions decay exponentially inside the localized sphere and decay polynomially outside. Furthermore, we discover a novel second-order phase transition for the eigenfunctions in spherical shells as the $l$-$k$ ratio crosses a critical value. In the supercritical case, the eigenfunctions are localized around a sphere between the inner and outer boundaries of the spherical shell. In the critical case, the eigenfunctions are localized around the inner boundary. In the subcritical case, no localization could be observed, giving rise to localization breaking.Comment: 24 pages, 5 figure

Value Creation of E-commerce Platform Firms in Competitive Dynamics: From a Resource Orchestration Perspective

This study examines the rules of resource combination for e-commerce platform firms value creation in competitive dynamics. Based on the resource orchestration view and competitive dynamics theory, we suggest a configurational analytic framework that departs from the standard linear paradigm to examine how configurations of digital strategic action formed by digital resources creates value through the effect that competitors hard to respond to. In line with this approach, we use fuzzy-set qualitative comparative analysis (fsQCA) to news data from Chinese online tourism industry. Our findings suggest equifinal pathways to gain the effect that is hard to be responded and the specific boundary conditions of our propositions that determine what way digital technologies and partnership resources orchestrate in e-commerce platform firms’ creating value. We discuss implications for theory and practice

A YOLOv7 incorporating the Adan optimizer based corn pests identification method

Major pests of corn insects include corn borer, armyworm, bollworm, aphid, and corn leaf mites. Timely and accurate detection of these pests is crucial for effective pests control and scientific decision making. However, existing methods for identification based on traditional machine learning and neural networks are limited by high model training costs and low recognition accuracy. To address these problems, we proposed a YOLOv7 maize pests identification method incorporating the Adan optimizer. First, we selected three major corn pests, corn borer, armyworm and bollworm as research objects. Then, we collected and constructed a corn pests dataset by using data augmentation to address the problem of scarce corn pests data. Second, we chose the YOLOv7 network as the detection model, and we proposed to replace the original optimizer of YOLOv7 with the Adan optimizer for its high computational cost. The Adan optimizer can efficiently sense the surrounding gradient information in advance, allowing the model to escape sharp local minima. Thus, the robustness and accuracy of the model can be improved while significantly reducing the computing power. Finally, we did ablation experiments and compared the experiments with traditional methods and other common object detection networks. Theoretical analysis and experimental result show that the model incorporating with Adan optimizer only requires 1/2-2/3 of the computing power of the original network to obtain performance beyond that of the original network. The mAP@[.5:.95] (mean Average Precision) of the improved network reaches 96.69% and the precision reaches 99.95%. Meanwhile, the mAP@[.5:.95] was improved by 2.79%-11.83% compared to the original YOLOv7 and 41.98%-60.61% compared to other common object detection models. In complex natural scenes, our proposed method is not only time-efficient and has higher recognition accuracy, reaching the level of SOTA

A State-similarity-based fast reliability assessment for power systems with variations of generation and load

The increasing penetration of intermittent renewable generators and the uncertainty of loads have brought significant challenges to the power system reliability assessment, as large numbers of optimal power flow (OPF) tasks need to be repetitively solved considering these uncertainties. To deal with that, this paper proposes a state-similarity-based (SS) approach to replace the computationally demanding AC OPF. It is observed that the active constraints related to the least load curtailment typically remain consistent across varying system states. Following this, the active constraints are used to represent the state similarity, and then nonlinear equations are derived to replace the original AC OPF problems. Thereafter, an alternating iterative approach is developed to obtain the minimal load curtailment instead of calculating the time-consuming optimization. An optimality criterion is developed to exclude the majority of mismatched solutions, thereby minimizing potential inaccuracies in the reliability assessment. Case studies conducted on the RTS-79, IEEE 118-bus, and Brazilian systems demonstrate that the proposed methods can significantly enhance computational efficiency with minimal errors. In some instances, these methods can outperform traditional reliability assessment methods by over 10 times

Particle arc therapy: Status and potential

There is a rising interest in developing and utilizing arc delivery techniques with charged particle beams, e.g., proton, carbon or other ions, for clinical implementation. In this work, perspectives from the European Society for Radiotherapy and Oncology (ESTRO) 2022 physics workshop on particle arc therapy are reported. This outlook provides an outline and prospective vision for the path forward to clinically deliverable proton, carbon, and other ion arc treatments. Through the collaboration among industry, academic, and clinical research and development, the scientific landscape and outlook for particle arc therapy are presented here to help our community understand the physics, radiobiology, and clinical principles. The work is presented in three main sections: (i) treatment planning, (ii) treatment delivery, and (iii) clinical outlook.</p

Lactation-promoting ingredients of Hemerocallis citrina Borani and the corresponding mechanisms

Hemerocallis citrina Borani is a traditional folk food used to promote the lactation of postpartum mothers in China; however, the active ingredients and corresponding mechanisms are still unknown. In this study, the lactogenic effect of alcoholic and aqueous extracts of H. citrina was primarily evaluated, and the aqueous extract (1,000 and 2,000 mg/kg) displayed significant lactation-promoting effects. Three eluates of the aqueous extract (0%, 30%, and 50%HCW) were further evaluated for their lactogenic effect, and 30% and 50% HCW showed significant lactation-promoting activity. Nineteen ingredients, including those with a high content of rutin and isoquercetin, were then identified from 30% and 50%HCW using the ultra-performance liquid chromatography-quadrupole-time-of-flight-mass spectrometry (UPLC-Q-TOF-MS) method. Finally, the lactogenic effect of rutin and isoquercetin was evaluated, and both compounds displayed significant lactation-promoting activity. The mechanisms relative to the lactation-promoting active ingredients for H. citrina extracts and compounds are to stimulate the release of prolactin (PRL) and progesterone (P), as well as to induce the expression of prolactin receptor (PRLR) and improve the morphology of mammary tissue. This study first clarified the lactation-promoting active ingredients of H. citrina and the corresponding mechanisms, which provide a new insight into the new lactation-promoting drug and promote the high-value utilization of H. citrina resources

Dynamic Modeling of a Flexible-Link Flexible-Joint System with Tip Mass Considering Stiffening Effect

This paper presents the dynamic model of a flexible-link, flexible-joint manipulator system with a considerable stiffening effect of the flexible link. A gripper, along with tip mass, is attached at one end of the flexible link. By employing the extended Hamilton&rsquo;s principle, a nonlinear governing equation of motion is derived along with several boundary constraints. Under the assumption of small deformation in free vibration, a simplified motion equation is deduced to determine the natural frequencies of the mechanical system. Four parameters of the system are selected to carry out the sensitivity study on frequency. The results show that the second frequency mainly depends on the mass of tip payload. Moreover, the third frequency is significantly affected by the moment inertia of tip payload. Regarding the constant angular motion, the finite element method is adopted to analyze the dynamic model by considering the stiffening effect. The frequency results are obtained which show a higher stiffness of the Single Flexible-link Flexible-joint (SFF) system with the angular velocity increasing. The influence of three factors (i.e., payload mass, length of the flexible link, and angular velocity) on the fundamental natural frequencies are discussed, which show instinct characteristics of the flexible manipulator system

Investigation of instability in ultrasonic welding under parametric excitation

This paper develops a time-varying model for battery tabs based on the parametric excitation of Euler-Bernoulli beams. The instability caused by combination resonance under a high-frequency longitudinal load is considered. A Galerkin procedure is used to discretize the time-dependent problem into the Mathieu equation. The critical axial load is obtained from the transition curve of combination resonance. The effectiveness of the stability analysis was verified by numerical simulations involving longitudinal and bending loads. </jats:p