Expansion Scheme Research Articles

Soliton solutions to the (3+1)-dimensional KP and BA models using advanced exp⁡(-ϕ(ξ))-expansion scheme in mathematical physics

Soliton solutions to the (3+1)-dimensional KP and BA models using advanced exp⁡(-ϕ(ξ))-expansion scheme in mathematical physics

Analysis of the wave solutions of the nonlinear evolution equations help of advanced exp⁡(-φ(ξ))-expansion scheme

With the assistance of emblematic calculation programming, the current paper explores the specific voyaging wave arrangements from the general (2+1)- layered nonlinear development conditions by utilizing the advanced exp⁡(-φ(ξ))-expansion with time-partial boundaries. As a result, the used technique is effectively utilized and recently created some precise voyaging wave arrangements. The recently created arrangements have been communicated regarding mathematical and exaggerated capabilities. The created arrangements have been inquired into their comparing condition with the guide of the emblematic calculation programming Maple. The elements of nonlinear wave arrangements are analyzed and shown by maple18 in 3D, and 2D plots, and form plots with explicit upsides of the mind boggling boundaries are plotted. The advanced exp⁡(-φ(ξ))-expansion strategy is a solid treatment for looking through fundamental nonlinear waves that enhance an assortment of water waves in the long-frequency system that emerges in designing fields.

New dynamics performances to the established dark solitons in Polariton Condensate

Abstract New diverse enormous soliton solutions to the Gross–Pitaevskii Equation, which describes the dynamics of two dark solitons in a polarization condensate under non-resonant pumping, have been constructed for the first time by using two various Schemes. The two utilized Schemes are the Generalized Kudryashov Scheme, the (G'/G)-Expansion Scheme. Throughout these two suggested schemata we construct new diverse forms solutions that include dark, bright-shaped soliton solutions, combined bright-shaped, dark-shaped soliton solutions, hyperbolic function soliton solution, singular shaped soliton solution and other rational soliton solutions. The two 2D and 3D figures designs have been configured by using the Mathematica-program. In addition, the Haar Wavelet Numerical Scheme has been applied to construct the identical numerical behavior for all soliton solutions achieved by the two suggested Schemes to show existing similarity between the soliton solutions and numerical solutions.

Solitons in magneto-optic waveguides with generalized Kudryashov’s form of self-phase modulation structure

AbstractThe current paper recovers soliton solutions in magneto-optic waveguides having generalized form of Kudryashov’s self-phase modulation structure. The retrieval of soliton solutions is achieved by the well-known and primitive $$G^{\prime }/G$$ G ′ / G -expansion scheme. The intermediary functions that made this retrieval possible are Jacobi’s elliptic functions and Weierstrass’ elliptic functions. The parameter constraints for the solitons to exist are also presented.

A Progressive Planning Scheme for Dynamic Expansion of Electric Vehicle Charging Resources

A Progressive Planning Scheme for Dynamic Expansion of Electric Vehicle Charging Resources

Data-driven visual model development and 3D visual analytics framework for underground mining

Data visualisation is broadly utilised to aid in presenting complex information, facilitating decision-making, and enhancing operational efficiency in the mining sector. However, due to the extensive utilisation of CAD files and the complexity and difficulty of converting 2D drawings into 3D models, it is challenging to realise (near) real-time 3D data visualisation in mining applications. The difficulties are including site drawing complexity, lack of standardisation, time-consuming cleaning, and imperative manual intervention. This paper addresses these challenges by focusing on an automatic, data-driven approach for 3D visual model development in mining, with an emphasis on lifetime support and sustainability. Therefore, we introduce standardised visual model data diagram and proposed conversion workflows to leverage digitised 2D drawings in automatic 3D visual model development. Moreover, to improve visualisation efficiency and facilitate visual analytics construction in mining, this paper also proposes a 3D tile index methodology for efficient visual model reconstruction and generic production data integration. To ensure lifetime support and sustainable development in visualisation, we propose two model expansion schemes: one based on dxf file-driven model development, and the other one is interaction-oriented 3D model design and development, which the two schemes share the same data exchange and conversion workflows. Furthermore, to facilitate data fusion among various datasets, we also provide insights into revealing spatial–temporal patterns among multimodality data by real-time visualisation. These advancements aim to propel the field of underground mining visualisation, offering significant insights into enhancing the efficiency and safety of mining operations.

Estimates on the convergence of expansions at finite baryon chemical potentials

Convergence of three different expansion schemes at finite baryon chemical potentials, including the conventional Taylor expansion, the Padé approximants, and the T′ expansion proposed recently in lattice QCD simulations, have been investigated in a low energy effective theory within the functional renormalization group approach. It is found that the convergence of the T′ expansion and the Padé approximants is consistent with the conventional Taylor expansion, within the expansion orders considered in this work. Furthermore, we find that the consistent regions of the three different expansions are in agreement with the convergence radius of the Lee-Yang edge singularities. Published by the American Physical Society 2024

Analysis of potential niche shifts in alien pairs of mantis species (Insecta, Mantodea) with comments on the current taxonomic and ecological knowledge

Due to the pet and goods trade, several animals are now present in regions outside of their traditional native ranges. A peculiar situation has arisen in mantises, insects that are becoming more popular as pets: two genera (Hierodula and Tenodera) have begun to spread around the world, with two Hierodula species overlapping in Europe and two Tenodera species doing the same in North America. Such an event can lead to possible competition with both local taxa and alien congeneric sister species; the latter may reduce the impact of one of the invaders. Additionally, the situation allows the comparisons of niche shifts in displaced mantises, allowing us to understand whether such animals respect general patterns shown in terrestrial ectothermic invasive species. To do this, I adapted scripts from previous publications for analyzing niche overlap (Schoener’s D), niche expansion (E), and unfilling (U) through the centroid shift, overlap, unfilling, and expansion (COUE) scheme using presence records from GBIF and iNaturalist Research-Grade observations and bioclimatic variables available in BIOCLIM, selected according to variance inflation factor (VIF) values. I also evaluated the overlap between the sister species in the non-native range with D. Overall, there was relatively high niche expansion and unfilling patterns shared among the taxa, although species tended to have low abiotic overlap between native and alien ranges, and a relatively high niche overlap was present among congeneric species in the shared non-native area. However, such analyses may be biased due to chosen variables, taxonomic uncertainty, and lack of information on mantises’ ecology; particularly, the situation regarding H. tenuidentata/transcaucasica should be monitored and clarified, given the higher potential invasion risk of these species compared to other mantises and the uncertainties regarding which populations have reached Europe. Additionally, the biology of alien mantises should be studied in more detail in both native and non-native environments given the current critical lack of information.

Novel dynamics of the Fokas-Lenells model in Birefringent fibers applying different integration algorithms

Abstract The Fokas-Lenells model has the broad applications in nonlinear physics to study various soliton phenomena. Employing the direct algebraic scheme, the modified rational sine-cosine technique, and the (1/G′) expansion scheme, the analytical solutions to this model are derived. Double periodic waves, bright soliton, dark soliton, single and multiple breather waves, and periodic breather waves are extracted from this model using symbolic computation. The dynamic behaviors of the acquired outcomes are vividly illustrated through density, two-dimensional (2D), and three-dimensional (3D) graphical representations. These discoveries are strategically positioned to significantly contribute to the advancement of exploring nonlinear models, standing as a fundamental pillar for forthcoming research endeavors.

3‐5: Distinguished Paper: Full‐color, Wide FoV Single‐layer Waveguide for AR Displays

We analyze the field‐of‐view (FoV) limitations in a single‐layer, full‐color waveguide‐based augmented reality display, revealing key influences from the waveguide's refractive index, exit pupil expansion (EPE) scheme, and combiner's angular response. Based on these analyses, we propose an optimized butterfly EPE scheme with gradient‐pitch polarization volume gratings (PVGs), achieving a theoretical diagonal FoV of 54.06° with a 16:10 aspect ratio.

PENGEMBANGAN BAHAN PELATIHAN DESAIN SISTEM PEMBELAJARAN BAGI GURU BAHASA INDONESIA SMA

Purpose of this research is produce "Training Material of Study System Design for Senior High School Indonesia Language Teacher" as according (1) requirement of teacher; (2) condition of expansion; (3) effectif, (4) can increase teacher interest; and (5) earns for teacher training. This research adopts expansion models Dick and Carey (2009). The sequence: determination of general purpose, study analysis, identification of initial ability, writing of purpose of special, assessment expansion of directive reference, strategy expansion, election and matter expansion, scheme and expansion of formative evaluation, revision, and scheme and expansion of evaluation sumatif. Result of this research, in general shows product " Training Material", very good. Suggestion, that product exploited by Senior High School Indonesia Language Teacher and exploited for further education expansion. Keyword: Development, training materials, design, learning systems

Full‐color, wide field‐of‐view single‐layer waveguide for augmented reality displays

AbstractIn the quest for more compact and efficient augmented reality (AR) displays, the standard approach often necessitates the use of multiple layers to facilitate a large full‐color field of view (FoV). Here, we delve into the constraints of FoV in single‐layer, full‐color waveguide‐based AR displays, uncovering the critical roles played by the waveguide's refractive index, the exit pupil expansion (EPE) scheme, and the combiner's angular response in dictating these limitations. Through detailed analysis, we introduce an innovative approach, featuring an optimized butterfly EPE scheme coupled with gradient‐pitch polarization volume gratings (PVGs). This novel configuration successfully achieves a theoretical diagonal FoV of 54.06° while maintaining a 16:10 aspect ratio.

Bifurcation, phase plane analysis and exact soliton solutions in the nonlinear Schrodinger equation with Atangana's conformable derivative

The nonlinear Schrodinger equation (NLSE) with Atangana's conformable fractional derivative (ACFD) is an equation that describes how the quantum state of a physical system changes in time. This present study examines the exact soliton results (ESRs) and analyze their bifurcations and phase plane (PP) of the NLSE with ACFD through the modified (G′/G)-expansion scheme (MG′/GES). Firstly, ACFD and its properties are included and then by MG′/GES, the exact soliton results and analyze their bifurcations and phase plane of NLSE, displayed with the ACFD, are classified. These obtained ESRs include periodic wave pulse, bright-dark periodic wave pulse, multiple bright-dark soliton pulse, and so many types. We provide 2-D, 3-D and contour diagrams, Hamiltonian function (HF) for phase plane dynamics analysis and bifurcation analysis diagrams to examine the nonlinear effects and the impact of fractional and time parameters on these obtained ESRs. The obtained ESRs illustration the novelty and prominence of the dynamical construction and promulgation performance of the resultant equation and also have practical effects for real world problems. The ESRs obtained with MG′/GES show that this scheme is very humble, well-organized and can be implemented to other the NLSE with ACFD.

Elastoplastic Solution of Cylindrical Cavity Expansion in Unsaturated Offshore Island Soil Considering Anisotropy

An elastoplastic analysis scheme for the cylindrical cavity expansion in offshore islands unsaturated soils considering anisotropy is established. The hydraulic properties and anisotropy caused by stress of unsaturated soils are coupled in an elastoplastic constitutive matrix for unsaturated soil to obtain the governing equations for the cylindrical cavity expansion problem, with an analytical solution that utilizes the original hydro-mechanical state of the soil as the initial conditions. Through a comparative analysis with other analytical solutions, the effectiveness of the new solution is verified. Moreover, the swelling response of the cylindrical cavity expansion in unsaturated soils is examined by systematically analyzing different parameters of the surrounding soil. The findings reveal that the development and rate of anisotropy in normal consolidated soil and over-consolidated soil exert a significant impact on the soil’s mechanical characteristics. Nevertheless, the alteration in the model constant h has little effect on the soil’s mechanical characteristics. The analytical solution introduces anisotropy and broadens the expansion theory of unsaturated soils to yield a more comprehensive theoretical framework for the comprehensive analysis of offshore islands’ unsaturated soils.

Various wave solutions to the nonlinear fractional Korteweg-de Vries Zakharov-Kuznetsov equation by a new approach to the two-variable expansion scheme

Solving nonlinear differential equations is crucial for the design, optimization, and characterization of engineering systems. However, investigating such equations poses significant challenges and requires the development of new mathematical and computational techniques. In this article, we extend the two-variable (G′/G,1/G) -expansion approach and establish scores of general analytical solutions, consisting of different functions and arbitrary parameters, to the time-fractional Korteweg–de Vries Zakharov-Kuznetsov (KdV-ZK) equation. The KdV-ZK equation provides a powerful model for modulating nonlinear waves in an assortment of physical systems, including plasma physics, atmospheric science, fluid dynamics, soliton theory, and optical fibers. The proposed technique allows extracting several novel solutions to the KdV-ZK equation, which is essential for gaining new insights into physical problems. In addition, the suggested extension shortens the calculation process and enhances computational efficiency. The obtained solitons have potential applications in several scientific and technological fields. The beta fractional derivative and the consistent wave variable are considered to restructure the stated fractional nonlinear equation. This study investigates the merits and demerits of the fractional-order derivative β on the dynamics of the system through the representation of two-dimensional graphs, which vary according to different values of β. The enhanced computational efficiency might assist the researchers in exploring a wider range of phenomena, facilitating further extensive investigations, and contributing to overall progress in the fields of science and engineering.

Fault detection and identification in induction motor using weightless neural network.

This paper presents a novel multiclass, multiparameter real-valued weightless neural network-based classifier for fault detection and identification. In contrast to primitive variants of weightless neural nets, the proposed method is capable of multiclass identification with real-valued input features and has improved recognition and generalization capabilities. The major accomplishments of the proposed method include an improved input-to-address mapping strategy that is suitable for address assignment within discriminator units and an effective memory expansion scheme based on similarity metric-based membership value. The developed classifier is utilized for fault detection and identification in single-phase and three-phase induction motors. The sensitivity analysis of the method is investigated for design parameter variation and the fault diagnosis is performed for multiple faults of the motor. The proposed method achieves the highest accuracy of 99.6% and 89.25% for single-phase and three-phase induction motor fault identification, respectively.

A data center expansion scheme considering net-zero carbon operation: Optimization of geographical location, on-site renewable utilization and green certificate purchase

Recently, more and more global attention has been paid to data centers’ energy consumption and climate impact. Serving as the backbone of the digital world, the energy and carbon-intensive data centers have to find a green expansion way to fulfill their obligations in building a carbon-neutral society. Therefore, this paper proposes a net-zero carbon operation oriented data center expansion scheme for the central government to formulate incentive policies. The economic expansion model minimizes newly established data centers’ investment and electricity consumption costs. Geographical location, on-site renewable utilization, and green certificate purchase are integrated and considered to achieve net-zero carbon operation by reducing total electricity consumption, increasing green power consumption, and offsetting inevitable carbon emissions. A case study in China is conducted, and results under different geographical location scenarios, power supply mix scenarios, and green certificates market scenarios are analyzed and compared. It is found that the zero-carbon operation of new data centers mainly relies on clean main-grid power, but a more decentralized layout and a provincial green certificate market can increase the contribution of on-site renewable energy. Lastly, four detailed policy implications for stimulating China’s data center expansion are discussed.

The new soliton solution types to the Myrzakulov-Lakshmanan-XXXII-equation

<abstract> <p>Our attention concenters on deriving diverse forms of the soliton arising from the Myrzakulov-Lakshmanan XXXII (M-XXXII) that describes the generalized Heisenberg ferromagnetic equation. This model has been solved numerically only using the N-fold Darboux Transformation method, not solved analytically before. We will derive new types of the analytical soliton solutions that will be constructed for the first time in the framework of three impressive schemas that are prepared for this target. These three techniques are the Generalized Kudryashov scheme (GKS), the (G'/G)-expansion scheme and the extended direct algebraic scheme (EDAS). Moreover, we will establish the 2D, 3D graphical simulations that clear the new dynamic properties of our achieved solutions.</p> </abstract>

Adsorption kinetics of H2O on graphene surface based on a new potential energy surface

The interaction between water and graphene is important for understanding the thermodynamic and kinetic properties of water on hydrophobic surfaces. In this study, we constructed a high-dimensional potential energy surface (PES) for the water-graphene system using the many-body expansion scheme and neural network fitting. By analyzing the landscape of the PES, we found that the water molecule exhibits a weak physisorption behavior with a binding energy of about − 1000 cm−1 and a very low diffusion barrier. Furthermore, extensive molecular dynamics were performed to investigate the adsorption and diffusion dynamics of a single water on a graphene surface at temperatures ranging from 50 to 300 K. Potential-of-mean-forces were computed from the trajectories, providing a comprehensive and accurate description of the water-graphene interaction kinetics.

Stability of the vector-borne disease model with direct transmission using Boubaker polynomials approach

In this paper, we delve into the analysis of an epidemic model for a vector-borne disease. Our study focuses on utilizing a baseline version of the ordinary differential equations (ODE) model to capture the dynamics of the disease transmission. Specifically, we aim to study the long-term behavior and properties of the model's solutions using a novel analytical approach known as the Boubaker polynomial Expansion Scheme (BPES). Furthermore, to complement our theoretical analysis, we conduct numerical simulations to provide a more practical perspective on the epidemic.