Search Results (9)

In this work, some dynamical properties of Hill’s system are studied under the effect of continued fraction perturbation. The locations and kinds of equilibrium points are identified, and it is demonstrated that these points are saddle points and the general motion in their proximity is unstable. Furthermore, the curves of zero velocity and the regions of possible motion are defined at different Jacobian constant values. It is shown that the regions of forbidden motion increase with increasing Jacobian constant values and there is a noticeable decrease in the permissible regions of motion, leading to the possibility that the body takes a path far away from the primary body and escapes to take an unknown trajectory. Furthermore, the stability of perturbed motion is analyzed from the perspective of a linear sense, and it is observed that the linear motion is also unstable. Full article

In the deep-sea environment, the volume available for an in-situ gene sequencer is severely limited. In addition, optical imaging systems are subject to real-time, large-scale defocusing problems caused by ambient temperature fluctuations and vibrational perturbations. To address these challenges, we propose an edge detection algorithm for defocused images based on grayscale gradients and establish a defocus state detection model with nanometer resolution capabilities by relying on the inherent critical illumination light field. The model has been applied to a prototype deep-sea gene sequencing microscope with a 20× objective. It has demonstrated the ability to focus within a dynamic range of ±40 μm with an accuracy of 200 nm by a single iteration within 160 ms. By increasing the number of iterations and exposures, the focusing accuracy can be refined to 78 nm within a dynamic range of ±100 μm within 1.2 s. Notably, unlike conventional photoelectric hill-climbing, this method requires no additional hardware and meets the wide dynamic range, speed, and high-accuracy autofocusing requirements of deep-sea gene sequencing in a compact form factor. Full article

Ecosystems are undergoing continuous degradation due to the dual perturbation of global climate change and human activities, posing unprecedented threats and challenges to the ecosystem services they provide. To gain a deeper understanding of the spatio-temporal evolution of ecosystem service value (ESV), it is essential to accurately capture the characteristics of its spatial and temporal changes and its influencing factors. However, traditional spatio-temporal statistical methods are limited to analyzing the heterogeneity of ESV in a single temporal or spatial dimension, which fails to meet the comprehensive analysis needs for spatio-temporal heterogeneity over an extended continuum. Therefore, this paper constructs a Bayesian spatio-temporal hierarchical model to analyze the ESV heterogeneity in both temporal and spatial dimensions in Northeast China from 2000 to 2020 to accurately identify the regions with unstable fluctuations in ESV and analyze the influencing factors behind them. It aims to comprehensively and systematically reveal the intrinsic laws of spatio-temporal evolution of ESV, and provide a scientific basis for relevant decision-making. The study found a continuous fluctuating downward trend of ESV in Northeast China from 2000 to 2020, with significant spatial and temporal heterogeneity. Notably, the distribution of hot and cold spots is regularly concentrated, especially in the transition zone from low hills to plains, which forms an “unstable zone” of spatial and temporal fluctuations of ESV. Natural factors such as NDVI and NPP exhibit a significant positive correlation with ESV, while social factors like population density and GDP show a strong negative correlation. Compared to traditional statistical methods, the Bayesian spatio-temporal hierarchical model, with its outstanding flexibility and accuracy, provides a new perspective and way of thinking for analyzing classical spatio-temporal problems. Firstly, the model examines time and space as a whole and fully accounts for the influence of spatio-temporal interactions on ESV. Secondly, the Bayesian spatio-temporal hierarchical model meets the needs of long-term continuous ESV outcome detection, which provides us with solid support for a deeper understanding of the evolution of ESV. Full article

The stability properties of the Hill equation are discussed, especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu-Hill equation for a trapped ion are characterized by employing the Floquet theory and Hill’s method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters a and q that are real. Characteristic curves are introduced naturally by the Sturm–Liouville problem for the well-known even and odd Mathieu equations $c{e}_m(z,q)$ and $s{e}_m(z,q)$. In the case of a Paul trap, the stable solution corresponds to a superposition of harmonic motions. The maximum amplitude of stable oscillations for ideal conditions (taken into consideration) is derived. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for both axial and radial motion, where the former is described by the canonical Mathieu equation. Anharmonic corrections for nonlinear Paul traps are discussed within the frame of perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter and we demonstrate they are shifted towards negative values of the a parameter. The applications of the results include but are not restricted to 2D and 3D ion traps used for different applications such as mass spectrometry (including nanoparticles), high resolution atomic spectroscopy and quantum engineering applications, among which we mention optical atomic clocks and quantum frequency metrology. Full article

In this work, we derived a new type model for spatial Hill’s system considering the created perturbation by the parameter effect of the continuation fractional potential. The new model is considered a reduced system from the restricted three-body problem under the same effect for describing Hill’s problem. We identified the associated Lagrangian and Hamiltonian functions of the new system, and used them to verify the existence of the new equations of motion. We also proved that the new model has different six valid solutions under different six symmetries transformations as well as the original solution, where the new model is an invariant under these transformations. The several symmetries of Hill’s model can extremely simplify the calculation and analysis of preparatory studies for the dynamical behavior of the system. Finally, we confirm that these symmetries also authorize us to explore the similarities and differences among many classes of paths that otherwise differ from the obtained trajectories by restricted three-body problem. Full article

Photovoltaic (PV) arrays have a considerably lower output when exposed to partial shadowing (PS). Whilst adding bypass diodes to the output reduces PS’s impact, this adjustment causes many output power peaks. Because of their tendency to converge to local maxima, traditional algorithms like perturb and observe and hill-climbing should not be used to track the optimal peak. The tracking of the optimal peak is achieved by employing a range of artificial intelligence methodologies, such as utilizing an artificial neural network and implementing control based on fuzzy logic principles. These algorithms perform satisfactorily under PS conditions but their training method necessitates a sizable quantity of data which result in placing an unnecessary demand on CPU memory. In order to achieve maximum power point tracking (MPPT) with fast convergence, minimal power fluctuations, and excellent stability, this paper introduces a novel optimization algorithm named PSO-AWDV (particle swarm optimization–adaptive weighted delay velocity). This algorithm employs a stochastic search approach, which involves the random exploration of the search space, to accomplish these goals. The efficacy of the proposed algorithm is demonstrated by conducting experiments on a series-connected configuration of four modules, under different levels of solar radiation. The algorithm successfully gets rid of the problems brought on by current traditional and AI-based methods. The PSO-AWDV algorithm stands out for its simplicity and reduced computational complexity when compared to traditional PSO and its variant PSO-VC, while excelling in locating the maximum power point (MPP) even in intricate shading scenarios, encompassing partial shading conditions and notable insolation fluctuations. Furthermore, its tracking efficiency surpasses that of both conventional PSO and PSO-VC. To further validate our results, we conducted a real-time hardware-in-the-loop (HIL) emulation, which confirmed the superiority of the PSO-AWDV algorithm over traditional and AI-based methods. Overall, the proposed algorithm offers a practical solution to the challenges of MPPT under PS conditions, with promising outcomes for real-world PV applications. Full article

Accurate turbulent inflow conditions are needed to broaden the application of the large-eddy simulation technique to predict winds around arbitrarily complex terrain. We investigate the concept of buoyancy perturbations with colored noise to trigger turbulence in upstream flows approaching complex terrain regions. Random perturbations are imposed on the source term in the pseudo-temperature transport equation. These perturbations are effective within three-dimensional boxes and scaled using a bulk Richardson number defined for each box. We apply the turbulent inflow generation technique to predict winds around the Askervein and Bolund Hills under neutrally stratified conditions. We find that a common value for the bulk Richardson number works well for a variety of flow problems. Additionally, we show that the height of the perturbation box plays an important role in the accuracy of the predictions around complex terrain. We consistently obtained good results for both simulation cases when the perturbation box height was made a fraction of the Obukhov length scale. Full article

In this work, the quantized Hill problem is considered in order for us to study the existence and stability of equilibrium points. In particular, we have studied three different cases which give all whole possible locations in which two points are emerging from the first case and four points from the second case, while the third case does not provide a realistic locations. Hence, we have obtained four new equilibrium points related to the quantum perturbations. Furthermore, the allowed and forbidden regions of motion of the first case are investigated numerically. We demonstrate that the obtained result in the first case is a generalization to the classical one and it can be reduced to the classical result in the absence of quantum perturbation, while the four new points will disappear. The regions of allowed motions decrease as the value of the Jacobian constant increases, and these regions will form three separate areas. Thus, the infinitesimal body can never move from one allowed region to another, and it will be trapped inside one of the possible regions of motion with the relative large values of the Jacobian constant. Full article

In this work, we investigated the differences and similarities among some perturbation approaches, such as the classical perturbation theory, Poincaré–Lindstedt technique, multiple scales method, the KB averaging method, and averaging theory. The necessary conditions to construct the periodic solutions for the spatial quantized Hill problem—in this context, the periodic solutions emerging from the equilibrium points for the spatial Hill problem—were evaluated by using the averaging theory, under the perturbation effect of quantum corrections. This model can be used to develop a Lunar theory and the families of periodic orbits in the frame work for the spatial quantized Hill problem. Thereby, these applications serve to reinforce the obtained results on these periodic solutions and gain its own significance. Full article