Expansion Method Research Articles

A comprehensive study on geometric shape optical soliton solutions to the time-factional nonlinear Schrödinger-Hirota equation

In this study, we investigate the analytical soliton solutions of a fundamental model, namely the nonlinear Schrödinger-Hirota equation, in the context of beta time-fractional derivative. We adopt the (ω′/ω, 1/ω)-expansion method, which is a reliable and straightforward approach to extract fresh and general soliton solutions in terms of hyperbolic, trigonometric, and rational functions. The solitons include anti-kink, anti-bell-shaped, bell-shaped, and periodic solitons. These solitons have significant applications in various scientific fields, such as optical fiber communications, signal processing, plasma physics, and trans-oceanic data transfer. This study demonstrates the significance of fractional-order differentiation in revealing new solitons. We also provide a comprehensive comparison with existing literature in normal and anomalous dispersion regions, highlighting the uniqueness of the solutions. Moreover, the graphical representations are used to illustrate the properties and potential applications of these solitons. This research might contribute to the advancement of nonlinear optical research and technology.

Residual Symmetry and Interaction Solutions of the (2+1)-Dimensional Generalized Calogero–Bogoyavlenskii–Schiff Equation

In this paper, we investigate the (2+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff (gCBS) equation by using the residual symmetry analysis and consistent Riccati expansion (CRE) method, respectively. The residual symmetry of the gCBS equation is localized into a Lie point symmetry in a prolonged system and a new Bäcklund transformation of this equation is obtained. By applying the standard Lie symmetry method to the prolonged gCBS system, new symmetry reduction solutions of the gCBS equation are obtained. The gCBS equation is proved to be CRE integrable and new Bäcklund transformations of it are obtained, from which interaction solutions between solitons and periodic waves are generated and analyzed.

Soliton solutions of cubic quintic septimal nonlinear Schrödinger wave equation with conformable derivative by two distinct algorithms

This paper investigates the cubic-quintic-septimal nonlinear Schrödinger wave equation with a conformable derivative, which governs the evolution of light beams in a weak nonlocal medium. The analysis utilizes the Kudryashov method and the enhanced modified tanh expansion method. By utilizing these analytical integration schemes, various optical wave solutions are derived within the present conformable model. The paper demonstrates the significance of these optical soliton solutions by illustrating different soliton solutions, including kink-type, bell-shaped, singular, dark, and wave soliton solutions, depicted via contour, three-dimensional, and two-dimensional representations. Moreover, it is crucial to emphasize the importance of analyzing the cubic-quintic-septimal nonlinear Schrödinger wave equation, which finds utility across a spectrum of fields including optics, quantum mechanics, and the study of nonlinear wave propagation. Moving forward, these approaches hold promise for investigating diverse sets of differential equations within multiple domains of applied sciences. This governing equation also has numerous applications in nonlinear optics, such as describing the propagation of laser beams through materials with nonlinear optical properties. The inclusion of these nonlinearities illustrates the interaction and behavior of light beams in weakly non-local media.

Wave resonances and the time-dependent capillary gravity wave motion

The interconnection of time and frequency domains for capillary gravity wave motion in the presence of current is discussed in this article. The general time-dependent problem is solved using Green’s function technique, and the asymptotic solution is derived using the method of stationary phase for large time and space. Also, the frequency domain solution is derived as a special case using the Cauchy Residue theorem. Different types of wave resonances like Trapping, Blocking and Bragg resonances are discussed. The existence of the trapped mode below the cutoff frequency is justified theoretically, and numerical results are obtained using the multipole expansion method. The blocking and Bragg resonances are analyzed above the cutoff frequency. It is found that in the presence of current, when the ripple wavenumber of the bottom undulation equals twice the cosine angle of incidence of wave times the wavenumber of the wave, Bragg resonance occurs. It is found that three propagating modes exist in the case of wave blocking, and the trapped modes exist only for the first propagating mode. Furthermore, because of the negative group velocity inside the blocking zone, the Bragg reflection increases while decreasing outside. The effect of current on the wave energy propagation in the form of group velocity is analyzed and the same is verified in the case of time-dependent problem.

Zb states as the mixture of the molecular and diquark-anti-diquark components within the effective field theory

In this study, we reconsider the states Zb(10610) and Zb(10650) by investigating the presence of diquark-anti-diquark components as well as the hadronic molecule components in the framework of effective field theory. The different masses of pseudoscalar mesons such as π0, η8, and η0, as well as vector mesons like ρ0 and ω violate the Okubo-Zweig-Iizuka (OZI) rule that is well depicted under the [U(3)L⊗U(3)R]global⊗[U(3)V]local symmetry. To account for the contribution of intermediate bosons of heavy masses within the one-boson-exchange model, we introduce an exponential form factor instead of the commonly used monopole form factor in the past. By solving the coupled-channel Schrödinger equation with the Gaussian expansion method, our numerical results indicate that the Zb(10610) and Zb(10650) states can be explained as hadronic molecules slightly mixing with diquark-anti-diquark states. Published by the American Physical Society 2024

Collision dynamics between breather and lump-type localized waves in the (3+1)-dimensional shallow water wave equation

In this paper, the collision dynamics of breather and lump-type localized waves in the (3+1)-dimensional shallow water wave equation are investigated in detail. Firstly, the auto-Bäcklund transformation and the linear representation of the (3+1)-dimensional shallow water wave equation are derived in virtue of the truncated Painlevé expansion method, which provide convenience in solving the (3+1)-dimensional shallow water wave equation. Secondly, based on the linear representation and the principle of linear superposition, the rational solutions in the exponential and polynomial forms are constructed. Tuning the free parameters of the rational solutions, localized waves of various patterns are obtained such as breather, lump-type localized waves and their hybrid structure. The anomalous inelastic interaction phenomenons of breather and lump-type localized waves are exhibited. Thirdly, combining the large-time behaviors of solution with the velocity relationship of localized waves, the dynamical properties and the classification of localized wave solutions are discussed in detail. Finally, we discuss the bound state of breather and lump-type localized waves under the velocity resonance condition, three different types of lump-breather molecules are displayed. The obtained results further enrich the structures and dynamical behaviors of localized waves. It is expected that the interaction phenomena taking place in the (3+1)-dimensional shallow water wave equation will be helpful in predicting or controlling some related shallow water wave phenomena.

Wind speed retrieval from X-Band marine radar based on the attenuation horizontal component and azimuth scale expansion method

ABSTRACT A method based on attenuation horizontal component and azimuth scale expansion is proposed to extract wind speed from X-band marine radar images. The attenuation horizontal component of each azimuth is first retrieved by ideal attenuation model, and the wind direction is extracted by the azimuthal dependence of the attenuation horizontal component. To overcome the influence of the occlusion area, the azimuth scale expansion method is used to extract the wind direction. Then the attenuation model in the upwind direction is determined according to the attenuation horizontal component. Finally, an empirical function model relationship between the full-range integral area of the attenuation function in the upwind direction and the reference wind speed is established. The radar data used to test the algorithm were collected from a ship in the Yellow China Sea. The real-time reference wind parameters were obtained by an anemometer installed on the main mast of the ship. The experimental results show that the algorithm improves the accuracy of wind speed retrieval, effectively reduces the error caused by outlier interference in radar images, and overcomes the interference of occlusion area by combining the azimuth scale expansion method.

High‐efficiency electrothermal and electromagnetic interference shielding performance of expanded graphite/silicone film

AbstractExpanded graphite (EG) is a desired filler for electrothermal and electromagnetic interference (EMI) shielding because of its easy access, low‐cost, lightweight, high conductivity, and heat sensitivity. Herein, fluffy EG was prepared from natural flake graphite (NFG) by a simple expansive technology and subsequently heat treatment at 800°C for 2.0 h in 5% Ar/H2 atmosphere. EG/silicone films with a filling ratio of 15 wt% were obtained via hot‐pressing, which exhibited sensitive electrothermal and excellent EMI shielding performances. When the applied voltages were 5.0, 10.0, and 15.0 V, the steady‐state temperatures were 54.0, 136.5, and 237.8°C in the 30s, respectively. Meanwhile, their average EMI shielding efficiency was greater than 20 dB in 2–18 GHz at 0.84 mm, which was 6.3 times as much as NFG/silicone film. Therefore, this study offers a simple and effective strategy for preparing excellent electrothermal‐EMI shielding materials.Highlights Fluffy EG is prepared by a simple expansive method and treatment at 800°C. EG/silicone films exhibit good electrothermal and EMI shielding performances. Steady temperatures of 55.0/136.5/237.8°C are gotten at 5/10/15 V in 30 s. The EMI shielding efficiency is greater than 20 dB at 0.84 mm. Good properties are due to the EG with high conductivity and fluffy structure.

Wave-Current Interaction Effects on the OC4 DeepCwind Semi-Submersible Floating Offshore Wind Turbine

In order to investigate the hydrodynamic performances of semi-submersible type floating offshore wind turbines (FOWTs), particularly the effect of body-wave-current interaction, the OC4 FOWT is considered in the presence of co-existing regular wave and uniform current fields. The wind loads are not considered at this stage. The problem is treated in the framework of potential-flow theory in the frequency domain, assuming waves of small steepness, and the solution is obtained by using a perturbation expansion method for the diffraction potential with respect to the normalized current speed. Analytical and numerical formulations have been used to treat the inhomogeneous free-surface boundary condition involved in the hydrodynamic problem formulation for the derivation of the associated perturbation potential. The hydrodynamic loads were obtained after evaluating the pressure field around the multi-body configuration using three different computer codes. The results from the three computer codes compare very well with each other and with the numerical predictions of other investigators. Finally, the mean second-order drift forces are calculated by superposing their zero-current values with the corresponding current-dependent first-order corrections, with the latter being evaluated using a ‘heuristic’ approach.

Wave excited motion of a body floating on water confined between a semi-infinite ice sheet and a side wall

In this paper, we investigate the diffraction and radiation coupling problem of a floating body confined between a fixed wall and a semi-infinite ice sheet under the action of incident waves. Based on the linear water wave theory and Kirchhoff Love elastic thin plate assumption, the ice sheet is considered as an elastic beam, and the boundary conditions of fluid boundaries covered by the ice sheet are obtained. Dividing flow domains with different upper surfaces, the eigenfunction expansion method was used to obtain the velocity potential expansion equations for each sub-domain. Then, through the matching conditions at the interface of sub-domains, a system of equations was constructed to solve the unknown coefficients of the expansion equations. The influence of the existence of the ice sheet on the diffraction and radiation motion of the floating body is analyzed. The effects of changes in the draft and open water width of the floating body on the wave excitation force and hydrodynamic coefficient of the floating body are discussed. The influence of the reflection effect of the ice sheet on the added mass and damping coefficient of the floating body has been discovered, especially the changes and oscillation rules of their extreme points. This research achievement provides theoretical support for the safety design of floating structures in frozen harbors.

Transient dispersion of settling gyrotactic microorganisms in an open channel flow

Dispersion of microorganisms is a key issue in bio-physics and has many applications in the fields of algae cultivation, biomass energy, and wetland ecology. However, there has been limited exploration of the effects of settling behavior and initial release conditions on the transient dispersion of gyrotactic microorganisms. This paper explores the transient dispersion of settling gyrotactic microorganisms in an open channel flow. The moment equations derived from the Smoluchowski equation are solved by the biorthogonal expansion method, and the results are compared with random walk simulations, showing good agreement. The time variations of concentration distribution, drift velocity, and dispersivity of settling gyrotactic microorganism suspension are explored in detail under typical initial release conditions. As illustrated and characterized, settlement weakens the gravitactic focusing of microorganisms near the free surface, leads to accumulation at the bottom, and increases the dispersivity; from a line source release, the relaxation time is shortest, and the microorganisms scatter fastest in the longitudinal direction, while the point source at the water surface leads to the most concentrated longitudinal distribution and the highest drift velocity; furthermore, the initial release condition assumes an important role in shaping the concentration distribution and drift velocity.

Hydrodynamic analysis of an oscillating water column array in presence of variable bathymetry

In this study, hydrodynamic analysis of an oscillating water column (OWC) array in the presence of the variable bathymetry (seafloor depth) is performed by using a semi-analytical potential-flow solver. Within the framework of linear theory, the boundary-value problem associated with wave diffraction and radiation by an OWC array with variable bathymetry is formulated and the semi-analytical hydrodynamic model is developed using the matched eigenfunction expansion method. The fluid domain above variable bathymetry is mathematically discretized into multiple subdomains using the boundary approximation method. The Haskind relation and the energy flux conservation law are used to verify the semi-analytical model. The hydrodynamic performance of the OWC array in the presence of the ripple and coral reef bathymetries are investigated in further. Pronounced oscillations are observed for the curve of reflection coefficient Cr and hydrodynamic efficiency η for cases with ripple and coral reef bathymetries. Bragg resonance is identified as the triggering of the strong oscillations in Cr and η for case of ripple bathymetry. The primary frequency of Bragg resonance and the peaked value of Cr converge as the ripple number increases (i.e., Ns > 3). Particularly, for cases with coral reef bathymetry, the wave resonance modal in open-ended basins results in a significant wave amplification at the weather side of the OWC array.

Viscous effects on the hydrodynamic performance of a two-body wave energy converter with a damping plate

In this study, the hydrodynamic forces and power absorption performance of an autonomous underwater vehicle (AUV)-based two-body wave energy converter (2BWEC) are investigated. A theoretical model is developed within the framework of linear potential flow to solve for added mass, radiation damping, and wave excitation force using the matched eigenfunction expansion method (MEEM). A computational fluid dynamics (CFD) model is employed to account for vortex-shedding effects of the floater and inner cylinder with a damping plate under various excitation conditions. Empirical formulas for supplementary added mass and drag coefficients caused by flow separation are proposed based on curve-fitting the differences between CFD results and MEEM calculations. These formulas are integrated into motion equations to enhance accuracy in evaluating the power absorption of the 2BWEC. It has been found that in the context of viscous flow, both the added mass and damping coefficients are increased, particularly for the inner cylinder with a damping plate. In addition, the viscous hydrodynamic coefficients exhibit strong dependence on the Keulegan–Carpenter number, while showing insensitivity to changes in the frequency parameter β. The supplementary (viscous) added mass provides additional inertia for the AUV with a limited mass itself, which is advantageous for the power absorption of the AUV-based 2BWEC. Conversely, the presence of viscous damping from the damping plate impedes wave energy capture.

Constructing novel metal-free HCOF-Ph@g-C3N4 heterojunctions through molecular expansion to enhance photogenerated carrier involved molecular oxygen activation and photocatalytic hydrogen evolution

Modification of covalent organic frameworks (COFs) have exceptional stability as well as tunable structures is the key to efficient photocatalysts. In this study, hyper-crosslinked COF-Ph was constructed with g-C3N4 to obtain a novel HCOF-Ph@g-C3N4 heterojunction, and the lamellar mesoporous of g-C3N4 was successfully embedded into the pores of 3D HCOF-Ph. The synthetic strategy greatly enhanced the photocatalytic properties and molecular oxygen activation capability of the catalyst. 10 mg of HCOF-Ph@g-C3N4 heterojunction could completely degrade 30 mg/L of tetracycline (TC) within 14 min, and the rate of hydrogen generation reached 9214.69 μmol g−1 h−1. The active species in this process of photocatalysis were verified through tests with free radical trapping and ESR spectra. In addition, the molecular oxygen activation capacity of heterojunction interface and the yield of superoxide radicals were examined by 3,3′,5,5′-tetramethylbenzidine (TMB) oxidation and degradation of nitrotetrazolium nlue chloride (NBT) experiments, respectively. We found that the molecular expansion strategy can change molecule energy band structure to improve absorption of sunlight, and the efficient segregation of the photogenerated charge were ensured by the complementary energy band structure between g-C3N4 and HCOF-Ph. This study created an efficient molecular expansion method for the synthesis of COF-based catalysts with potential uses in the energy and environmental fields.

Theoretical investigation on vibration reduction characteristics of a novel foundation metaconcrete beam

The issue of low-frequency vibration problems in foundation beams is becoming increasingly serious. Therefore, it is imperative to find new methods for effectively reducing and controlling these low-frequency vibrations. This study proposes a novel foundation metaconcrete beam to address the challenge of low-frequency vibrations based on locally resonance theory. Additionally, an improved transfer matrix method (ITMM) is proposed to quickly and effectively calculate the bandgap of foundation metaconcrete beam. The validity of the ITMM is verified through the plane wave expansion method (PWEM), and transmission characteristics are fully analyzed using the spectral element method (SEM). Furthermore, the influences of geometric and material parameters of the foundation metaconcrete beam on band structures and transmission functions are investigated in detail. The results show that the proposed foundation metaconcrete beam exhibits multiple bandgaps, and can effectively attenuate low-frequency vibrations. These bandgaps can be tailored by appropriately adjusting relevant parameters. The foundation properties determine the formation of the first bandgap, the damping ratio of the resonator has double effects on band structures, the mass ratio of the resonator is crucial in adjusting these bandgaps, and the axial force can adjust the attenuation capability of the first bandgap.

Fetus descent simulation with the active uterine contraction during the vaginal delivery: MRI-based evaluation and uncertainty quantification

Finite element models ranging from single to multiscale models have been widely used to gain valuable insights into the physiological delivery process and associated complication scenarios. However, the fetus descent simulation with the active uterine contraction is still challenging for validation and uncertainty quantification issues. The present study performed a fetus descent simulation using the active uterine contraction. Then, simulation outcomes were evaluated using theoretical and in vivo MRI childbirth data. Moreover, parameter uncertainty and propagation were also performed. A maternal pelvis model was developed. The active uterine contraction was modeled using a transversely isotropic Mooney–Rivlin material. Displacement trajectories were compared between simulation, theoretical and in vivo MRI childbirth data. Monte Carlo (M.C) and Polynomial Chaos Expansion (PCE) methods were applied to quantify uncertain parameters and their propagations. Obtained results showed that fetal descent behavior is consistent with the MRI-based observation as well as the theoretical trajectory (curve of Carus). The head downward vertical displacement ranges from 0 to approximately 47 mm. A reduction of 50% in uterine size was observed during the simulation. Three high-sensitive parameters ( C 1 , C 2 , Ca 0 ) were also identified. Our study suggested that the use of the active uterine contraction is essential for simulating vaginal delivery but the global parameter sensitivity, parameter uncertainty, and outcome evaluation should be carefully performed. As a perspective, the developed approach could be extrapolated for patient-specific modeling and associated delivery complication simulations to identify risks and potential therapeutic solutions.

Advancing Fixed-Source Reactor Analysis Through OpenNode Implementation

OpenNode, a new open-source Fortran code, enables the simulation of fixed-source reactors. Powered by the nodal expansion method (NEM) and seamless Python integration, OpenNode competes with existing nuclear reactor simulation tools. The fixed-source problem plays a crucial role in radioprotection, providing flux calculations and detailed insights into heating effects and dose rates. Users can define and configure reactor models via a JSON input file, specifying critical parameters like geometry, materials, cross-section data, boundary conditions, and fixed sources. OpenNode further empowers users with a Python interface for preprocessing and postprocessing, streamlining result analysis. Distinguishing itself from conventional NEM codes, OpenNode supports three-dimensional (3D) Cartesian geometries, facilitating intricate reactor design simulations. Customization options, including mesh sizes, polynomial orders, and calculation modes, enhance precision and efficiency. In our comprehensive study, we verified OpenNode’s fixed-source mode using the 3D-IAEA reactor, comparing it with the SANM code KOMODO. The results underscore OpenNode’s exceptional accuracy in computing critical parameters, like the effective multiplication factor, power distribution, and nodal flux, within fixed-source reactors. OpenNode stands as a reliable, user-friendly tool poised to advance nuclear reactor simulations.

Wave Pressure and Wave Height Distribution around Seawall Structure Constructed by an Array of TSP Circular Piles

An analytic solution for the interaction between an array of circular piles made by joining trapezoid steel pipes (TSP) and waves was obtained using an eigenfunction expansion method. First, an analytic model for the wave scattering of multiple piles fixed at arbitrary positions was derived, and then a simplified model was obtained assuming that an infinite array of identical piles were deployed perpendicular to the propagating direction of incident waves. A regular wave experiment was conducted using an experimental model with a scale ratio of 1/100 in a two-dimensional wave tank to verify the analytic solutions. The analytic results and experimental results were qualitatively consistent with each other. Using a developed analytic model, we examined the wave force on the multiple piles and the wave deformation in front of the arrayed piles. The period for the installation is greatly reduced as the TSP pile can be prefabricated in a factory. In particular, it is possible to install at the soft seabed. A seawall structure using arrayed TSP piles will be an ideal complement for a concrete seawall in future.

A new study on fractional Schamel Korteweg–De Vries equation and modified Liouville equation

Traveling wave solutions of fractional partial differential equations have great importance in the literature. The diversity of solutions plays an important role in understanding the physical structure of the model it represents. For this reason, two important differential equations with the fractional order, which have a significant role in applied sciences and can model real-life problems most accurately, have been solved by the generalized (G′G)-expansion method in this study. This method is a generalization of the classical (G′G)-expansion method. With this developed method, the non-linear fractional Schmael Korteweg–De Vries equation and fractional modified Liouville differential equations are discussed to find their exact solutions. In this way, new exact solutions of these equations that were not previously included in the literature have been found. The presented method has been applied to these two equations for the first time, and various new traveling wave solutions have been obtained. Thus, the study goes beyond other studies. To understand the physical behavior of these new exact solutions, three-dimensional graphs have been drawn according to different parameter values.

CELL: a Python package for cluster expansion with a focus on complex alloys

We present the Python package CELL, which provides a modular approach to the cluster expansion (CE) method. CELL can treat a wide variety of substitutional systems, including one-, two-, and three-dimensional alloys, in a general multi-component and multi-sublattice framework. It is capable of dealing with complex materials comprising several atoms in their parent lattice. CELL uses state-of-the-art techniques for the construction of training data sets, model selection, and finite-temperature simulations. The user interface consists of well-documented Python classes and modules (http://sol.physik.hu-berlin.de/cell/). CELL also provides visualization utilities and can be interfaced with virtually any ab initio package, total-energy codes based on interatomic potentials, and more. The usage and capabilities of CELL are illustrated by a number of examples, comprising a Cu-Pt surface alloy with oxygen adsorption, featuring two coupled binary sublattices, and the thermodynamic analysis of its order-disorder transition; the demixing transition and lattice-constant bowing of the Si-Ge alloy; and an iterative CE approach for a complex clathrate compound with a parent lattice consisting of 54 atoms.