Scale Transformation Research Articles

Non-trivial solutions for the fractional Schrödinger–Poisson system with p-Laplacian

In this paper, we study a fractional Schrödinger–Poisson system with p-Laplacian. By using some scaling transformation and cut-off technique, the boundedness of the Palais–Smale sequences at the mountain pass level is gotten. As a result, the existence of non-trivial solutions for the system is obtained.

Well-separated soliton-antisoliton pairs with an adjoint Higgs field in 4D space

We present single soliton states and soliton-antisoliton states with an adjoint Higgs field in 4D flat space. The action of a single soliton state diverges, while the action of soliton-antisoliton states converges. The interaction in a soliton-antisoliton state takes a logarithmic dependence on separation. Such soliton-antisoliton states exhibit stability under a scaling transformation.

Sequential time scaling transformation technique for time-delay optimal control problem

The time-scaling transformation technique used within the computational framework of control parameterization serves as an effective method for the optimization of control switching time as well as the control value for time-delay optimal control problems. However, the conventional time-scaling transformation stipulates that the switching times for all control components must be identical, which may not be feasible in real-world scenarios. To address this limitation, we introduce the sequential time-scaling transformation technique for solving time-delay optimal control problems. By sequentially applying control parameterization and time-scaling transformation to each of the control variable, the new technique enables the configuration of a varying number of segments for the control, and the switching time for each control component can be adaptively selected. Numerical results demonstrate that our approach not only achieves superior cost performance but also offers enhanced flexibility in control strategy.

MHD peristaltic two-phase Williamson fluid flow, heat and mass transfer through a ureteral tube with microliths: Electromagnetic therapy simulation

The ureter typically experiences a frequency of one to five peristaltic contractions per minute. However, it is important to note that these contractions can be disrupted by various physical and mechanical irritants. Ionic contents in the urine make it electrically conducting and responsive to electromagnetic body forces. MHD can be deployed in bio magnetic therapy to control or mitigate symptoms associated with peristaltic pumping in the urinary system. This article therefore focuses on the hydromagnetic effects on flow patterns of urine with debris (monoliths). The mechanism of urine flow is largely coordinated by the kidneys. The flow inside the ureter is interrupted by microliths, which are generated by the sedimentation of excretory products. To simulate this, a two-phase formulation is adopted, comprising the electromagnetic urological viscous fluid phase and the particulate phase for solid grains. The peristaltic propulsion of two-phase liquid in the ureter is simulated as a sinusoidal wave propagation of incompressible non-Newtonian fluid. The Williamson viscoelastic model is deployed for the rheology. Heat transfer is also included with Soret thermo-diffusion and viscous heating effects. Long wave and low Reynolds number approximations are employed based on lubrication theory. The mass, momentum, energy and concentration conservation equations with associated boundary conditions are rendered non-dimensional via appropriate scaling transformations. A numerical solution is achieved via BVP4C MATLAB quadrature. Graphical visualizations of the velocity, temperature and concentration (solid grains) are given for the influence of suspension parameter ( ζ ), Hartmann number (M), Prandtl number (Pr), Weissenburg number (We), particle volume fraction (C), Eckert number (Ec), Soret number (Sr), Schmidt number (Sc). The novelty of the present work is therefore the simultaneous consideration of a generalized two-phase model, wall slip, non-Newtonian characteristics, cross diffusion, viscous dissipation, mass diffusion, magnetic body force and curvature effects in peristaltic urological transport, which has not been undertaken previously. The detailed simulations reveal that the flow velocity is reduced due to the presence of solid particles and the channel curvature, in comparison to the flow in an unobstructed channel devoid of solid particles. Enhancing the hydrodynamic slip parameter speeds up the movement of particles and fluid near the channel walls, boosts wall skin friction, raises pressure difference in the pumping area, and amplifies bolus magnitudes.The rise in peristaltic pumping results in a reduction in solid particle concentration, which is significant phenomena.This theoretical approach may aid in treating conditions such as Urinary Tract Infections (UTIs). The computations effectively demonstrate that significant manipulation of urological pumping characteristics can be achieved with an electromagnetic field. Some new features of two-phase ureteral dynamics are highlighted as relevant to magnetic therapy techniques, which may be beneficial to clinicians.

Structural transformation behavior of oxide scale during coiling of 0.9 wt% Cr-containing high-strength steel

The phase transformation mechanism of oxide scale on the surfaces of chromium (Cr)-free carbon steel and 0.9 wt% Cr-containing steel at different coiling temperatures and cooling rates was studied using thermal simulation and electron backscattering diffraction experiments. The results showed that the eutectoid transformation of both the steel followed the “C” curve relationship. The Cr-containing steel had a larger eutectoid transformation area fraction than the Cr-free carbon steel. The nose tip temperature of the eutectoid transformation of the oxide scale on the surfaces of Cr-free carbon steel and 0.9 wt% Cr-containing steel were 420∼510 °C and 420–480 °C, respectively. For the 0.9 wt% Cr-containing steel, the proportion of Σ3 and Σ13b grain boundaries in cubic Fe3O4 increased, followed by a decrease, when the coiling temperature decreased from 610 to 410 °C. The Σ3 and Σ13b grain boundaries of the Fe3O4 low-dimensional coincident site lattice had the highest proportion for 510 °C coiling temperature. The low-dimensional coincident site lattice grain boundaries could be used to enhance crack resistance and improve the oxide scale on the steel plate surface.

Research on Dynamic Quaternion Ship Domain Model in Open Water Based on AIS Data and Navigator State

During the process of establishing the analytical quaternion ship domain model, the impact of ship traffic conditions and navigator state was not taken into consideration. However, the significance of these factors in the ship domain cannot be ignored. To create a more realistic representation of changes in the ship domain in real navigation environments, this study further considers the influence of ship encounter course, waterway traffic intensity, relative ship velocity, and the navigator state based on the quaternion ship domain model. As a result, a new dynamic quaternion ship domain model is proposed. To assess the changes in the size and shape of the ship domain under various navigation environments, ship domain scaling and shape transformation functions are introduced. Specifically, this study focuses on analyzing the ship traffic near the Lao Tie Shan Waterway, simulating the size and shape changes of the ship domain during the navigation process in this area. The findings indicate that the size of the ship domain dynamically adjusts to the traffic conditions. Additionally, when the navigator state is excellent, the ship domain takes on an irregular diamond shape with the smallest area, whereas when the navigator state is poor, the shape approximates a rectangle with the largest area. Furthermore, the dynamic quaternion ship domain model proposed in this study is compared to the ship domain models put forth by Goodwin, Davis, and co-authors. The results demonstrate that the dynamic quaternion ship domain model is more compatible and suitable for open waters compared to the static quaternion ship domain model.

Energy and self-adaption in a memristive map neuron

Both capacitor and charge-controlled memristor (CCM) can regulate the inner energy levels during the release and accumulation of charges in these electronic components. Combination of inductive and capacitive components is crucial to build an oscillatory circuit, and incorporation of a nonlinear resistor is helpful to support nonlinear oscillation under continuous energy exchange between magnetic field and electric field. Relation between physical variables in neural circuits can be described by some equivalent nonlinear oscillators by applying scale transformation on the variables and parameters for the neural circuit, and the energy function becomes available from theoretical approach. In this work, a simple neural circuit coupled with a CCM is designed to obtain a memristive neuron model, and then linear transformation is applied to the sampled variables involved with time scale for time step, a new memristive map is obtained to discuss its energy characteristic and self-controllability under energy flow. The result provides guidance to measure the reliability of maps, and the new derived maps with reliable physical evidences can be further used in digital signal processing.

Numerical and artificial intelligence analysis of squeezing flow between parallel disks under complex physical fields

This study presents the time-dependent squeezing flow between parallel discs under the influence of various physical processes such as magnetohydrodynamics, micropolarity, thermophysics, homogeneous-heterogeneous chemical reactions, and bioconvection. The slip and permeability effects are considered at the boundaries. The nonlinear system is simplified through scaling transformations and subsequently solved numerically. Besides, an artificial neural network (ANN) model is developed to predict the values of skin-friction coefficients, heat transfer rates, and mass transfer rates at both discs. The performance of the ANN model is validated against the computational results, demonstrating robustness with correlation coefficients being almost close to 1. The ANN model performs more robustly for instance, skin-friction coefficient model revealed correlation (R) equaling 0.99775 and 0.99537 for the test data of the lower and upper discs, respectively. The values for heat and mass transfer observe as 0.99999, 0.99938, and 0.99839, 0.99167 for the test data of lower and upper discs. Parametric and sensitivity analyses produce results that are comparable to the numerical findings. Graphical and tabular representations are provided for various dimensionless parameters. Results indicate that the developed model is reliable and capable of accurately predicting multiple physical processes.

Investigating Nonlinear Dynamics in Atmospheric Aerosols during the Transition from Laminar to Turbulent Flow

This paper investigates the nonlinear dynamics of atmospheric aerosols during the transition from laminar to turbulent flows using the framework of Scale Relativity Theory. It is proposed that the transition from multifractal to non-multifractal scales (in the dynamics of the atmospheric aerosols) can be assimilated to the transition between laminar and turbulent states. These transitions are determined by the multifractal diffusion and deposition processes. The methodology used involves the application of the principle of scale covariance, which states that the laws of atmospheric physics remain invariant with respect to spatial and temporal transformations as well as scale transformations. Based on this principle, several conservation laws are constructed. In such context, the conservation law of the density of states associated with the multifractal-non-multifractal scale transition in a one-dimensional case is then considered. The model describes the non-linear behaviour of atmospheric aerosols undergoing diffusion and deposition processes. The theoretical approach was correlated using experimental data from a ceilometer and radar reflectivity factor data.

Anisotropic Morphing in Bistable Kirigami through Symmetry Breaking and Geometric Frustration.

Shape morphing in bistable kirigami enables remarkable functionalities appealing to a diverse range of applications across the spectrum of length scale. At the core of their shape shifting lies the architecture of their repeating unit, where highly deformable slits and quasi-rigid rotating units often exhibit multiple symmetries that confer isotropic deployment obeying uniform scaling transformation. In this work, symmetry breaking in bistable kirigami is investigated to access geometric frustration and anisotropic morphing, enabling arbitrarily scaled deployment in planar and spatial bistable domains. With an analysis on their symmetry properties complemented by a systematic investigation integrating semi-analytical derivations, numerical simulations, and experiments on elastic kirigami sheets, this work unveils the fundamental relations between slit symmetry, geometric frustration, and anisotropic bistable deployment. Furthermore, asymmetric kirigami units are leveraged in planar and flat-to-3D demonstrations to showcase the pivotal role of shear deformation in achieving target shapes and functions so far unattainable with uniformly stretchable kirigami. The insights provided in this work unveil the role of slit symmetry breaking in controlling the anisotropic bistable deployment of soft kirigami metamaterials, enriching the range of achievable functionalities for applications spanning deployable space structures, wearable technologies, and soft machines.

Кореляційний аналіз залежності здоров’я населення України від паління як чинника виникнення розвитку цукрового діабету

Numerous clinical studies have established that smoking has a harmful effect on human health including diabetes mellitus. The aim is to assess the peculiarities of health changes among citizens of Ukraine under the influence of a harmful factor, thanks to a simultaneous questionnaire and in-depth medical examination for further improvement of diagnostics and stratification of the degree of risk of developing various diseases and timely appointment of adequate therapy. Materials and methods. Among the laboratory tests, the following were determined: blood glucose level, IR marker – Нoma index, which were determined on an empty stomach, in the morning, the last meal was 12 hours before blood donation. Determination of the results of indicators was carried out using chemiluminescence analysis. Reagents: Roche Diagnostics (Switzerland). Analyzer Cobas 8000 | ProCobas 6000 |Cobas 411 (Switzerland). Statistical data processing was carried out using a software package. The relationship between quantitative indicators was carried out using Pearson’s correlation analysis (r ). Statistical probability was estimated by the parametric Student’s t-test. The difference was considered probable at p<0.05. The relationship between quantitative and rank indicators was carried out using variance analysis, the Fisher coefficient (F). Results. A register of respondents was created - adults (men and women) who were under the influence of a modified factor that is a trigger for the prevalence of such conditions as insulin resistance and hyperglycemia; prediabetes, diabetes, cardiovascular diseases (CVD), etc. Answers related to smoking were converted from rank indicators into quantitative indicators. Through prospective observations, during the research, it was established that 47.5% consumed tobacco products in one form or another (not often - 15%, moderately - 12.5%, quite often - 7.5%, extremely often - 12.5%). A reliable relationship between quantitative indicators was also confirmed using Pearson’s correlation analysis (rs) between the level of glucose and the IR Нoma index (r=0.444, p=0.004), which once again confirms that the IR Нoma index increases due to the increase in glucose, and the prerequisite for this can be serve: age-related changes in the body’s hormonal balance, a passive lifestyle, weight gain and the presence of a bad habit, namely smoking. For the first time, the relationship between quantitative and rank indicators was established using variance analysis: between the level of glucose and smoking (F=2.757; p=0.043), between the level of IR Нoma index and smoking. Conclusions. As a result of the implementation of the pilot project, it was established that 47.5% of respondents smoke, of which 7.5% very often, 12.5% extremely often. In the course of the implementation of the pilot project, a register of respondents participating in the study was created. The relationship between quantitative indicators was also confirmed, one of which is the relationship between health status and smoking (rs=0.428; p=0.005). For the first time, the relationship between quantitative and rank indicators was investigated using variance analysis: between glucose level and smoking (F=2.757; p=0.043). Thanks to the transformation of the measurement scale, the dependence of the IR level on the Нoma annealing index was established for the first time.

Urban agglomeration, glocalisation, and the governance of scalar transformation in the global south: a case study from Cape Town, South Africa

AbstractIn theorising the rapid expansion of urban agglomeration across the world, a significant body of work has examined the transformation of scale from the perspective of geographical size and the regulatory facets of devolved power. A further literature has examined what are seen as the relational dimensions in the transformation and constitution of space and the extent to which these are socially constructed. In this conceptualisation, scale is constituted and reconstituted by capitalist relations of production, social production, and consumption. The influence of capitalist relations on scale has most explicitly been illustrated by the impact of globalisation and the way it has served to weaken the regulatory powers of nation states and is simultaneously reordering the hierarchy of government power within them. Metropolitan governments have been exposed to global markets and to the influence of transnational corporations and, in a process of glocalisation, increasingly endeavour to create an entrepreneurial environment conducive to attract and retain foreign investment. Hitherto the interpenetration of the global and local has largely been studied in the context of urban agglomeration and scalar transformation in the global North. In an attempt to address this lacuna this article examines the manifestation of the process of glocalisation in metropolitan Cape Town in South Africa in the global South. It posits that the municipal government’s ambition to transform the city into a modern digitally based economy linked to global markets manifests many of the characteristics of glocalisation. Furthermore, it argues, far from promoting greater social inclusion in a highly unequal post-apartheid city, the economic model which has been adopted is exacerbating social inequality and poverty.

Cauchy-Stieltjes Kernel families: Some properties

In the setting of the theory of Cauchy-Stieltjes Kernel (CSK) families, we present in this article some properties related to the Marchenko–Pastur and Semicircle laws. Let K+(μ)={Qmμ(dx);m∈(m1μ,m+μ)} be the CSK family generated by a non degenerate probability measure μ with support bounded from above. Firstly, for 0<t≠1 such that Qmμ⊞t is well defined, we prove that if Qmμ⊞t∈K+(μ) then the measure μ is a scale transformation of the Marchenko–Pastur law. Secondly, consider Tβ:x⟼x+β, for β∈R∖{0}. We prove that if Tβ(Qmμ)∈K+(μ), then the measure μ is an affine transformation of the Semicircle law.

3D Gaussian Geometric Moment Invariants

ABSTRACT 3D moment invariants are important tools for 3D image feature representation. In this paper, we introduced a novel approach for constructing 3D moment invariants using Gaussian geometric moments. Our proposed method demonstrated invariance under translation, rotation, and scale transformations. The numerical experiments validate the invariance and robustness of the proposed method, comparing it with traditional 3D geometric moments and revealing superior performance in the presence of noise and transformations. Additionally, the method is applied to content-based 3D image retrieval, exhibiting promising results through Minkowski distance-based retrieval on the Princeton Shape Benchmark (PSB) database.

CytoPipeline and CytoPipelineGUI: a Bioconductor R package suite for building and visualizing automated pre-processing pipelines for flow cytometry data

BackgroundWith the increase of the dimensionality in flow cytometry data over the past years, there is a growing need to replace or complement traditional manual analysis (i.e. iterative 2D gating) with automated data analysis pipelines. A crucial part of these pipelines consists of pre-processing and applying quality control filtering to the raw data, in order to use high quality events in the downstream analyses. This part can in turn be split into a number of elementary steps: signal compensation or unmixing, scale transformation, debris, doublets and dead cells removal, batch effect correction, etc. However, assembling and assessing the pre-processing part can be challenging for a number of reasons. First, each of the involved elementary steps can be implemented using various methods and R packages. Second, the order of the steps can have an impact on the downstream analysis results. Finally, each method typically comes with its specific, non standardized diagnostic and visualizations, making objective comparison difficult for the end user.ResultsHere, we present CytoPipeline and CytoPipelineGUI, two R packages to build, compare and assess pre-processing pipelines for flow cytometry data. To exemplify these new tools, we present the steps involved in designing a pre-processing pipeline on a real life dataset and demonstrate different visual assessment use cases. We also set up a benchmarking comparing two pre-processing pipelines differing by their quality control methods, and show how the package visualization utilities can provide crucial user insight into the obtained benchmark metrics.ConclusionCytoPipeline and CytoPipelineGUI are two Bioconductor R packages that help building, visualizing and assessing pre-processing pipelines for flow cytometry data. They increase productivity during pipeline development and testing, and complement benchmarking tools, by providing user intuitive insight into benchmarking results.

Real and virtual environments have comparable spatial memory distortions after scale and geometric transformations

ABSTRACT Boundaries define space, impacting spatial memory and neural representations. Unlike rodents, impact in humans is often tested using desktop virtual-reality (VR). This lacks self-motion cues, diminishing path-integration input. We replicated a desktop-VR study testing boundary impact on spatial memory for object locations using a physical, desktop-VR, and head-mounted-display-VR environment. Performance was measured by comparing participant responses to seven spatial distribution models using geometric or walking-path metrics. A weighted-linear combination of geometric models and a “place-cell-firing” model performed best, with identical fits across environments. Spatial representation appears differentially influenced by different boundary changes, but similarly across virtual and physical environments.

A method for evaluation of the probability density function of white noise filtered non-Gaussian stochastic process

Passing non-Gaussian white noises through a pre-designed linear filter can generate non-Gaussian stochastic processes with desired probabilistic and spectral properties. This linear filtering methodology has been extensively employed in non-Gaussian signal processing and simulation. At present, the investigation of probability properties for the output non-Gaussian processes is primarily concentrated on the higher-order statistics, spectra, and correlation functions. However, evaluating the probability density function (PDF) of the output process remains a challenging task. In order to address this issue, this short communication commences with the theoretical derivation of the PDF formula for the white noise filtered non-Gaussian stochastic process. The derived PDF is the result of a convolution of multiple PDFs, each obtained by applying a scaling transformation to the input white noise PDF. Subsequently, a discretized numerical calculation method is proposed to overcome the analytical difficulties associated with the computation of multiple convolutions. Finally, the accuracy and efficiency of the proposed method are demonstrated through several numerical examples.

Nanophotosensitizing through Space Charge Transfer Assemblies of Pentacenequinone Derivative for 'Metal-free' Photoamidation Reactions.

The present study demonstrates the influence of small portion (20 %) of organic co-solvent (DMSO/THF/ACN/MeOH) in mixed aqueous media (80 % water) in controlling the size, quantum yield and life time of the through space charge transfer assemblies (TSCT) of pentacenequinone derivative (TPy-PCQ-TPy). Among various solvent systems [H2 O : DMSO (8 : 2), H2 O : THF (8 : 2), H2 O : ACN (8 : 2) and H2 O : MeOH (8 : 2)] examined, highly emissive (Φf =12 %) and nano-sized assemblies having long life time (3.11 ns) were formed in H2 O : DMSO (8 : 2) solvent system. The solvent dependent differences in the size and excited state properties of TPy-PCQ-TPy assemblies are reflected in their photosensitizing behaviour in different solvent systems. Backed by excellent photosensitizing properties, TPy-PCQ-TPy assemblies smoothly catalyse the photoamidation reactions between unactivated/activated aldehydes and secondary amine under mild reaction conditions (visible light irradiation, aerial atmosphere, room temperature) in H2 O : DMSO (8 : 2) solvent mixture. The as prepared assemblies of TPy-PCQ-TPy also exhibit high potential to catalyse the oxidation of benzyl alcohols to aromatic aldehydes, thus, generating a possibility to use aromatic alcohols as the starting material in photoamidation reactions. The real time application of TSCT assemblies has also been demonstrated in gram scale transformation of aromatic aldehydes to aromatic amides and photooxidation of benzyl alcohol to aromatic aldehyde.

Remote sensing monitoring of rice growth under Cnaphalocrocis medinalis (Guenée) damage by integrating satellite and UAV remote sensing data

ABSTRACT Satellite remote sensing is commonly used for large-scale agricultural monitoring, but the low spatial resolution of its imagery does not allow it to present details of crop growth. Combining satellite remote sensing and unmanned aerial vehicle (UAV) remote sensing to complement each other’s advantages may be a way to realize large-scale and precision agricultural monitoring. Therefore, to explore the effect of the fusion method of UAV remote sensing data and satellite remote sensing data on improving satellite monitoring of the growth of damaged rice and to achieve large-scale accurate monitoring of the growth characteristics of damaged rice, in this study, the research object was rice infested by Cnaphalocrocis medinalis Guenee. We selected SuperDove satellite imagery on 14 August 2022 and UAV multispectral imagery on 15 August 2022 for vegetation index calculation and fused the two by a scale transformation method. We constructed LAI monitoring models using multiple linear regression (MLR), back-propagation neural network (BPNN) and support vector machine regression (SVR) to evaluate the effect of satellite data on LAI inversion for affected rice before and after fusion. The results showed that (1) the learning ability of the machine learning model represented by BPNN and SVR was better than that of the traditional regression model represented by MLR. The SVR model had the best inversion effect on the LAI. (2) The satellite data after fusion with UAV data significantly improved the inversion accuracy of the LAI of damaged rice. Compared with the original satellite data, with the combined data, R2 increased by approximately 0.3, RMSE and MAE decreased by approximately 0.1. Moreover, the spatial details of remote sensing images were clearer, and the spatial matching degree with the UAV image inversion results was higher. This study can provide theoretical and technical support for large-scale and high-precision monitoring of affected rice.

Promoting Learning Health System Cycles by Optimizing EHR Data Clinical Concept Encoding Processes.

Electronic health records (EHRs) and other real-world data (RWD) are critical to accelerating and scaling care improvement and transformation. To efficiently leverage it for secondary uses, EHR/RWD should be optimally managed and mapped to industry standard concepts (ISCs). Inherent challenges in concept encoding usually result in inefficient and costly workflows and resultant metadata representation structures outside the EHR. Using three related projects to map data to ISCs, we describe the development of standard, repeatable processes for precisely and unambiguously representing EHR data using appropriate ISCs within the EHR platform lifecycle and mappings specific to SNOMED-CT for Demographics, Specialty and Services. Mappings in these 3 areas resulted in ISC mappings of 779 data elements requiring 90 new concept requests to SNOMED-CT and 738 new ISCs mapped into the workflow within an accessible, enterprise-wide EHR resource with supporting processes.