Singular Parameter Research Articles

Sunspot number-based neural network model for global solar radiation estimation in Ghardaïa

In this investigation, the estimation of global solar radiation was meticulously carried out within Ghardaïa city, a region situated in Southern Algeria, utilizing a sophisticated multilayer perceptron (MLP) neural network architecture. This research primarily concentrated on developing a predictive model based on a singular input parameter, specifically, the sunspot numbers, to forecast global solar radiation levels. The model's formulation was rooted in empirical data collected over an extensive period from 1984 to 2000, which was used for training the neural network. To assess the model's predictive accuracy and robustness, data from the years 2001 to 2004 were employed for validation purposes. The outcomes of this study were highly satisfactory, indicating that the MLP-based model possesses a significant predictive capability for Diffuse Global Solar Radiation (DGSR). This is substantiated by robust statistical metrics, including a normalized Root Mean Square Error (nRMSE) of 0.076, reflecting the model's accuracy in prediction, and a correlation coefficient (R) of 93.16%, denoting a strong correlation between the predicted and observed values. These results underscore the model's efficacy and potential application in accurately estimating global solar radiation in the specified region.

Theoretical study on 3D elastic response and first layer failure strength of composite cylinders subjected to axisymmetric loadings

The traditional Lekhnitskii 3D elastic theory can obtain the exact stress and strain response of the composite cylinder under the axially symmetric loadings. However, when the cylinder contains 0° winding layers or isotropic layers, some calculation parameters corresponding to the two kinds of special layers will become singular. By analyzing the continuity of singular parameters and calculating their limits, the problem of singular parameters can be effectively solved and the Lekhnitskii theory can be extended to composite thick-walled cylinders with arbitrary winding angles. Furthermore, based on the Chang-Chang strength criterion of composite layers and the ideal elastic-plastic assumption of isotropic metal layers, the theoretical calculation method of first layer failure strength and the corresponding failure modes of the composite cylinders subjected to axisymmetric loadings was proposed. Then, the composite cylinder with metal liner was fabricated by fiber winding process. The experimental blasting pressure of the cylinder was 52.8 MPa with a major failure mode of fiber tensile fracture. Based on the proposed theoretical method, the cylinder's first layer failure strength of internal pressure was 44.1 MPa, and the initial failure mode was also fiber tensile fracture. The predicted result of the first layer failure strength was lower than the experimental results. The result proved the safety and economy of the proposed theoretical method for the initial design of the composite cylinder.

Enhancement of Mosquito Collection for Ultraviolet Light-Emitting Diodes Trapping System Using Cavity Reflectors

This research explores novel avenues for optimizing mosquito-catching efficiency using a multifaceted approach. While previous studies have primarily focused on singular parameters, such as light intensity or wind speed, this study delves into the intricate interplay between various factors. Experiment 1 challenges conventional wisdom by revealing a wider light divergence angle. When the reflective plate combined with the airflow board was set to 0 cm in length, the effectiveness of capturing mosquitoes was lower than that of the 3 cm unit, suggesting overlooked variables at play. Experiment 2 introduces a novel perspective by demonstrating the superior efficiency of the 5 cm unit, even with reduced wind speed and luminous area under optimized conditions, showcasing the significance of a holistic approach. Moreover, Experiment 3 uncovers nuanced insights, showcasing the differential performance of units in capturing small insects versus mosquitoes and moths, highlighting the need for tailored strategies. By integrating these findings, the study pioneers the development of two distinct mosquito collection units, emphasizing the critical importance of balancing diverse parameters for optimal results. The innovation lies in the thorough investigation of multifaceted optimization strategies, providing valuable insights to propel advancements in mosquito control technologies.

Fractal contours: Order, chaos, and art

Over the recent decades, a variety of indices, such as the fractal dimension, Hurst exponent, or Betti numbers, have been used to characterize structural or topological properties of art via a singular parameter, which could then help to classify artworks. A single fractal dimension, in particular, has been commonly interpreted as characteristic of the entire image, such as an abstract painting, whether binary, gray-scale, or in color, and whether self-similar or not. There is now ample evidence, however, that fractal exponents obtained using the standard box-counting are strongly dependent on the details of the method adopted, and on fitting straight lines to the entire scaling plots, which are typically nonlinear. Here, we propose a more discriminating approach with the aim of obtaining robust scaling plots and extracting relevant information encoded in them without any fitting routines. To this goal, we carefully average over all possible grid locations at each scale, rendering scaling plots independent of any particular choice of grids and, crucially, of the orientation of images. We then calculate the derivatives of the scaling plots, so that an image is described by a continuous function, its fractal contour, rather than a single scaling exponent valid over a limited range of scales. We test this method on synthetic examples, ordered and random, then on images of algorithmically defined fractals, and finally, examine selected abstract paintings and prints by acknowledged masters of modern art.

Multi-pulse thermoreflectance imaging with structure function analyses for measuring thermophysical properties of microscale heterostructures

The thermophysical properties of nano/microscale heterostructures play a crucial role in the performance and reliability of electronics. However, existing measurements encounter several challenges, including detecting multiple parameters synchronously and reliance on reference samples etc. In this study, we propose a multi-pulse thermoreflectance thermal imaging (TTI) combining with structure function algorithm, achieving simultaneous measurement of the thermal conductivities, specific heat capacities, and thermal boundary resistances (TBRs) of microscale heterostructures. A non-iterative methodology is established and the singular model parameter is evaluated through transient heat conduction modeling. We delineate criteria for thermal transient testing and achieve high-precision measurements over a broad time range by employing a multi-pulse strategy with a TTI system with a 50 ns temporal resolution. Our experimental measurements on a microscale Silicon-on-Insulator (SOI) sample validate the method's effectiveness. The measured thermophysical properties, including thermal conductivities of the device layer and handle wafer, TBR, and specific heat capacity of the device layer, exhibit a relative error of <10% compared to prior studies. Our approach presents an effective solution for precise thermal characterization within modern electronic devices.

Effect of volumetric deformation on saturation of unsaturated soils under constant suction

The soil–water retention curve (SWRC) represents a fundamental relationship in the study of unsaturated soils, where volumetric deformation plays a crucial role in shaping the water retention characteristics by impacting the pore size distribution. This study conducted a thermodynamic analysis to derive a relationship between the effective stress parameter and the water retention properties of unsaturated soils. Consequently, a streamlined formula was introduced to forecast the impact of volumetric deformation on saturation at constant suction. This formula, incorporating a singular parameter from the effective stress parameters equations, can be seamlessly integrated with any prevailing SWRC model to characterize the influence of volume deformation on the SWRC. The effectiveness of the proposed model was corroborated through seven sets of experimental data spanning various soils, affirming its capability to precisely describe the water retention behavior of deformable soils under deformation.

Slow passage through a transcritical bifurcation in piecewise linear differential systems: Canard explosion and enhanced delay

In this paper we analyse the phenomenon of the slow passage through a transcritical bifurcation with special emphasis in the maximal delay zd(λ,ɛ) as a function of the bifurcation parameter λ and the singular parameter ɛ. We quantify the maximal delay by constructing a piecewise linear (PWL) transcritical minimal model and studying the dynamics near the slow-manifolds. Our findings encompass all potential maximum delay behaviours within the range of parameters, allowing us to identify: (i) the trivial scenario where the maximal delay tends to zero with the singular parameter; (ii) the singular scenario where zd(λ,ɛ) is not bounded, and also (iii) the transitional scenario where the maximal delay tends to a positive finite value as the singular parameter goes to zero. Moreover, building upon the concepts by Vidal and Françoise (2012), we construct a PWL system combining symmetrically two transcritical minimal models in such a way it shows periodic behaviour. As the parameter λ changes, the system presents a non-bounded canard explosion leading to an enhanced delay phenomenon at the critical value. Our understanding of the maximal delay zd(λ,ɛ) of a single normal form, allows us to determine both, the amplitude of the canard cycles and, in the enhanced delay case, the increase of the amplitude for each passage.

Fault diagnosis of lithium-ion batteries based on wavelet packet decomposition and Manhattan average distance

ABSTRACT As lithium-ion batteries are widely used in electric vehicles, safety accidents caused by battery failures emerge one after another. Nevertheless, failures caused by changes in the internal structure or characteristics of the battery, such as sudden and progressive failures, are still a serious problem for electric vehicles, challenging existing fault diagnosis methods. This paper first performs wavelet packet decomposition on the battery’s raw voltage signal to obtain high-quality low-frequency and high-frequency characteristic signal components. Then performs singular value decomposition on the characteristic signal components to extract the corresponding singular value characteristic parameters, and introduces the Manhattan average distance algorithm to battery faults. Diagnosing and locating faulty battery units using the Laida criterion (3-σ criterion) outlier detection method. Finally, actual vehicle data were used to verify the reliability, stability, accuracy of the method, and compared with the traditional Manhattan distance, correlation coefficient, information entropy methods. The method in this paper has good fault detection effects on vehicles with sudden and progressive faults vehicles.

Effective splitting of invariant measures for a stochastic reaction diffusion equation with multiplicative noise

This work is concerned with the effective dynamics for the stochastic reaction diffusion equations with cubic nonlinearity driven by a multiplicative noise. By splitting the solution into the finite dimension kernel space and its complement space with some appropriate multi-scale, it derives the dominant solution and the effective invariant measure in the sense of the Wasserstein distance, which capture the complex dynamical behaviors of the original system as a singular parameter is enough small. Furthermore, the effective invariant measure is decomposed to a product of two invariant measures.

Enhanced Crowd Dynamics Simulation with Deep Learning and Improved Social Force Model

The traditional social force model (SFM) in crowd simulation experiences difficulty coping with the complexity of the crowd, limited by singular physical formulas and parameters. Recent attempts to combine deep learning with these models focus more on simulating specific states of crowds. This paper introduces an advanced deep social force model, influenced by crowd states. It utilizes deep neural networks to accurately fit crowd trajectory features, enhancing behavior simulation capabilities. Geometrical constraints within the model provide control over varied crowd behaviors, adjustable to simulate different crowd types. Before training, we use the SFM to refine behaviors in real trajectories with excessively small distances, aiming to enhance the general applicability of the model. Comparative experiments affirm the effectiveness of the model, showing comparable performance to both classic physical models and modern learning-based hybrid models in pedestrian simulations, with reduced collisions. In addition, the model has a certain ability to simulate crowds with high density and diverse behaviors.

Instability of a Kerr-type naked singularity due to light and matter accretion and its shadow

We study null and timelike constant radii geodesics in the environment of an over-spinning putative Kerr-type naked singularity. We are particularly interested in two topics: first, the differences of the shadows of the naked rotating singularity and the Kerr black hole; and second, the spinning down effect of the particles falling from the accretion disk. Around the naked singularity, the non-equatorial prograde orbits in the Kerr black hole remain intact up to a critical rotation parameter ( α=63−9 ) and cease to exist above this value (Charbulák and Stuchlík 2018 Eur. Phys. J. C 78 879). This has an important consequence in the shadow of the naked singularity if the shadow is registered by an observer on the polar plane or close to it as the shadow cannot be distinguished from that of a Kerr black hole viewed from the same angle considering only the light emanating from the unstable photon orbits. We show that the timelike retrograde orbits in the equatorial plane immediately (after about an 8% increase in mass for the case of initial α = 1.5) reduce the spin parameter of the naked singularity from larger values to α = 1 at which an event horizon appears. This happens because the retrograde orbits have a larger capture cross-section than the prograde ones. So if a naked singularity happens to have an accretion disk, it will not remain naked for long, an event horizon forms.

Disentangling CO Chemistry in a Protoplanetary Disk Using Explanatory Machine-learning Techniques

Molecular abundances in protoplanetary disks are highly sensitive to the local physical conditions, including gas temperature, gas density, radiation field, and dust properties. Often multiple factors are intertwined, impacting the abundances of both simple and complex species. We present a new approach to understanding these chemical and physical interdependencies using machine learning. Specifically, we explore the case of CO modeled under the conditions of a generic disk and build an explanatory regression model to study the dependence of CO spatial density on the gas density, gas temperature, cosmic-ray ionization rate, X-ray ionization rate, and UV flux. Our findings indicate that combinations of parameters play a surprisingly powerful role in regulating CO abundance compared to any singular physical parameter. Moreover, in general we find the conditions in the disk are destructive toward CO. CO depletion is further enhanced in an increased cosmic-ray environment and in disks with higher initial C/O ratios. These dependencies uncovered by our new approach are consistent with previous studies, which are more modeling intensive and computationally expensive. Our work thus shows that machine learning can be a powerful tool not only for creating efficient predictive models, but also for enabling a deeper understanding of complex chemical processes.

On homeomorphisms with integral constraints acting in a domain with Poincaré inequalities

We study homeomorphisms with one normalization condition that transform some domain of the Euclidean space onto a domain which is Ahlfors regular and supports Poincare inequality. We assume that, the homeomorphisms satisfy the weighted modulus Poletsky condition. If the majorant in this condition satisfies some relation written in terms of singular parameters, then the specified homeomorphisms satisfy the corresponding distortion estimate at the boundary points written in their terms. In more detail, the manuscript is written in the vein of research on mappings with bounded and finite distortion, which have been actively studied recently. Observe that, for mappings with direct and inverse Poletsky inequality, the estimates of the distortion under the mappings at the inner points of a domain may be considered known, since such estimates have been obtained by various authors over the last 10-15 years. We could, in particular, point to the results of V. Ryazanov, O. Martio, U. Srebro, E. Yakubov, M. Cristea, E. Sevost'yanov, S. Skvortsov, and O. Dovhopiatyi in this regard. It should be noted that, under certain additional assumptions, mappings with a direct Poletsky inequalities are included in the class of mappings with finite distortion by Iwaniec-Martin. At the same time, the above-mentioned estimates of distance distortion at the boundary points of the domain have not been sufficiently studied. Our manuscript is dedicated to obtaining such estimates. Of course, we require that the majorant in Poletsky's inequality satisfy certain requirements for obtaining them. The conditions written in terms of singular parameters are the most convenient and cover important partial cases. In particular, functions of finite and bounded mean oscillation by John-Nirenberg, as well as functions with the Lehto integral divergence condition can be described in terms of singular parameters, and this will be taken into account in our future research. In addition to singular parameters and the use of modulus techniques, the key point of our manuscript is spaces with Poincaré inequalities. Note that one of the characteristic features of such spaces is their fulfillment of Loewner-type inequalities, i.e., metric lower bounds of the modulus of families of curves through the diameter of the sets they join. This inequality is crucial for obtaining the result of the paper.

Stress discontinuity and singularity around the vertex of a triangular inhomogeneity

The stress field around a vertex of angular inhomogeneity has been investigated by Eshelby’s equivalent inclusion method (EIM). Different from Eshelby’s problem for ellipsoidal inhomogeneity with a uniform or polynomial eigenstrain, a singular eigenstrain field is derived by Airy’s stress function and asymptotic analysis, in which the singular elastic fields can be expressed in terms of the distance to the vertex. The discontinuity of Eshelby’s tensor along the boundary has been analytically derived and are used in the stress equivalence condition at the vertex, which can be converted into an eigenvalue problem with the integral of the Green’s function and singular eigenstrain over the inhomogeneity. To verify the solution, when the opening angle 2β at the vertex approaches zero, the triangular void reduces to a slit-like crack, and the paper reproduces the classic solution of 1/r singularity. When β increases from 0 to π/2, the singularity parameter λ around the vertex of the triangular void reduces at different pace under the symmetric and antisymmetric loading conditions. When a triangular inhomogeneity exhibits nonzero stiffness and different angles, λ changes with the stiffness ratio, β, and loading conditions, and the dominant stress singularity around the vertex and stress discontinuity across the boundary are analytically provided. Particularly, the stress singularity for an adhesive interface with varying stiffness provides insight for structure repair and integration.

Error analysis for a spectral element method for solving two-parameter singularly perturbed diffusion equation

In this paper, we study the two-parameter spectral element method based on weighted shifted orthogonal polynomials for solving singularly perturbed diffusion equation on an interval [0, 1] which are modeled with singular parameters. We continue our study to estimate the lower bound of the weighted orthogonal polynomial coefficient and the upper bound of a posteriori error estimates of the method through different weighted norms to minimize the computational cost. Numerical examples are implemented to study the applicability and efficiency of the technique. The obtained error bounds for the coefficient of orthogonal polynomials and the posteriori estimates fall within the bounds derived in the theoretical section. It is also observed that the two weighted norms decreases when the values of [Formula: see text] and [Formula: see text] increases for the three choices of [Formula: see text] and for different values of x and y. The quality and accuracy of the solution can be realized through figures and tables.

Prediction of Pathological Risk Stratification using Computed Tomography Features in Gastrointestinal Stromal Tumours: A Retrospective observational Study

Introduction: Gastrointestinal Stromal Tumours (GISTs) are the most common mesenchymal tumours of gastrointestinal tract. A high postsurgical recurrence and metastatic rate have created a need for a presurgical risk profile identification system. Aim: To assess the association between morphological Computed Tomography (CT) parameters with the pathological risk profile and analyse which CT features can predict the risk grading of GISTs. Materials and Methods: This was a retrospective cohort study based on imaging and histopathological data of 26 patients with pathologically proven GISTs presenting to the Department of Radiodiagnosis of a tertiary hospital in the northern Indian Himalayan foothills over a period of five years from July 2018 to June 2023. CT imaging features including size, growth pattern, margins, enhancement, calcifications, necrosis, intralesional haemorrhage, enlarged feeding vessels, direct organ invasion, and associations such as ascites and lymphadenopathy were studied. All lesions were classified as per Miettinen risk classification into no risk, very low-risk, low, moderate, and high-risk lesions. Analysis was done by the Chi-square test. Predictive analysis was carried out by computing the odds ratio and performing regression analysis on significantly associated imaging features. Results: Out of 26 patients, the study group comprised 16 males (61.54%) and 10 females (38.46%). The most common decade of presentation was the 6th decade with the mean age of presentation being 55.81±4.23 years. Twelve patients were grouped under intermediate to high-risk grading. Lesion size &gt;5 cm (p-value=0.0171, OR=19.12), ill-defined margins (p-value=0.0048, OR=18.33), intralesional necrosis (p-value=0.0053, OR=19.8), and enlarged feeding vessels (p-value=0.012, OR=21.27) were identified as imaging features with significant association and predictive ability for high-risk lesions. The strongest predictive ability for a high-risk profile was shown by ill-defined margins (R2 =0.381) and intralesional necrosis (R2 =0.3287). Conclusion: A preoperative Contrast Enhanced Computed Tomography (CECT) assessment provides a comprehensive imaging profile for GISTs as well as a fair accuracy of risk profile prediction via various singular and clustered morphological parameters.

Stratonovich–Khasminskii averaging principle for multiscale random Korteweg–de Vries-Burgers equation

In this paper, we consider the multiscale random Korteweg–de Vries-Burgers (KdVB) equation, namely, the KdVB equation perturbated by a fast time oscillating external force and a random oscillating noise, the random oscillating noise is made up of a family of strong mixing stationary processes with singular small parameters. A Stratonovich–Khasminskii type averaging principle for multiscale random KdVB equation is established, in physics, this averaging principle can describe the asymptotic behavior for the propagation of small-amplitude long waves in nonlinear dispersive and dissipative media with singular structure and the soliton propagation in the random weakly viscous media or in the random field.

A numerical control machining tool path step error prediction method based on BP neural network

Step error calculation of numerical control (NC) machining tool path is a premise for generating high-quality tool path and promoting its application. At present, iterative methods are generally used to calculate step error, and the computation time increases when accuracy improves. Neural networks can be calculated on GPUs and cloud platforms, which is conducive to reducing computation time and improving accuracy through continuous learning. This article innovatively introduces a BP neural network model to predict step error values. Firstly, the core parameters required for step error calculation are taken as the data samples to construct the neural network model, and map to the same scale through Z-score normalization to eliminate the adverse effects of singular parameters on the calculation results. Then, considering only a small number of parameters determine theoretical values of step error, the Dropout technique can drop hidden layer neurons with a certain probability, which is helpful to avoid overfitting and used in the neural network model design. In the neural network model training, this paper adds the Stochastic Gradient Descent with Momentum (SGDM) optimizer to the back propagation of network training in order to improves the network’ stability and accuracy. The proposed neural network predicts step error of samples from three surface models, the results show that the prediction error decreases as sample training increases. After trained by 15% of the surface samples, the neural network predicts the step errors of the remaining samples. Compared with theoretical values, more than 99% of the predicted values have an absolute error less than 1 μm. Moreover, the cost time is only one-third of the geometric method, which verifies the effectiveness and efficiency of our method.

Analyzing the influence of Cerchar abrasiveness index on particle size distribution in ball milling based on multifractal theory

This study investigates the influence of cerchar abrasiveness index (CAI) on the multifractal parameters of particle size distribution (PSD) in the ball milling from both global and local perspectives. The results indicate that with increase of CAI, the generalized dimension spectrum parameters D(0) and D(1) exhibit three distinct stages, and the concentration of PSD gradually decreases. The variations in singular spectrum parameters Δα and Δf reveal that, for CAI below 1.0, the main variation in milling is dominated by large particle, and the local heterogeneity changes are not significant. As the CAI exceeds 1.0, variability of particle sizes approaches each other, and the local heterogeneity shows a trend of increasing and then decreasing. As CAI increases, the point of maximum heterogeneity in PSD becomes more concentrated towards the later stages of milling. Finally, the micro-mechanisms of differences in CAI and multifractal parameters were discussed by considering mineralogical composition and bond work index of individual minerals.

A bulk-edge correspondence between the second Chern number and the spectral flow

A one-parameter family of semi-quantum Hamiltonians admitting the time-reversal symmetry is defined on the product S2(r1)×S2(r2) of two-spheres of respective radii r1 and r2, and a corresponding one-parameter family of quantum Hamiltonians is defined in terms of the angular momentum operators associated with respective spheres. The second Chern number of the eigen-vector bundle associated with a positive eigenvalue of the semi-quantum Hamiltonian is a piecewise constant function of the parameter with jumps at singular parameter values leading to the emergence of total degeneracy points for the eigenvalues. Correspondingly, the quantum Hamiltonian has edge-state eigenvalues which, as functions of the parameter, pass the zero energy level at the singular parameter values and the bulk-state eigenvalues prove to correspond to eigenvalues of the semi-quantum Hamiltonian. It is shown that the second-Chern number c2(T) at a non-singular parameter value T is in one-to-one correspondence with the spectral flow as a function of the end point of the interval (−∞,T). The bulk-edge correspondence is also shown to hold between the linearized semi-quantum and quantum systems, where the semi-quantum Hamiltonian is linearized at each of the degeneracy points of the eigenvalues and quantized to define linear quantum Hamiltonians. On this level, the spectral flow of each linear quantum Hamiltonian with a parameter μ proves to coincide with the index of the linear quantum Hamiltonian with μ=0.