Solution Domain Research Articles

Examining the soliton solutions and characteristics analysis of fractional coupled nonlinear Shrödinger equations

The [Formula: see text]-dimensional fractional coupled nonlinear Schrödinger equations (FCNLSEs) are investigated in this work. This model is important as it involves applications in allowing soliton wavelength division multiplexing and pulse propagation in two-mode optical fibers. This means it is important for the study of the dynamics of solitons in dispersive, inhomogeneous, nonlinear media, and, therefore, it is a tool of prime value for the development of advanced optical communication technologies. Beta space-time fractional derivative, which is important in dielectric polarization and electromagnetic systems, is used to evaluate the FCNLSE. We capitalize a modified version of the Sardar sub-equation method for the purpose of getting different soliton solutions. Solutions take the form of optical solitons, including dark, bright, periodic, peakons, compactons, and kink soliton solutions, formulated using exponential, trigonometric, and hyperbolic functions. To make our understanding of the physical meaning of these solutions richer, we apply advanced plotting techniques, examples of which are the three-dimensional (3D), two-dimensional (2D), contour, and density plots. Such plots provide a colorful overview of the dynamic behavior of the solutions obtained. The solutions do not only pinpoint the fact that the result is an effective and accurate method application, but they also set a high standard in further probing meaning in the numerous physical phenomena. These new solutions go beyond earlier studies in the literature by incorporating beta derivatives as a modeling tool for FCNLSE. The methodology applied here functions seamlessly and can be extended to address numerous advanced models in contemporary areas of science and engineering. The anticipated usefulness of the derived solutions in various scientific domains, particularly optics, is expected to make a valuable contribution to the fiber communication system in future research endeavors.

Experimental Analysis of Tribological Properties of Aluminium 6061-Al2O3- TiO2 MMC

Composite materials have gained significant prominence in modern engineering due to their superior properties such as high strength-to-weight ratio, wear resistance, and adaptability in design. This research paper focuses on the development and application of aluminum matrix composites (AMCs) reinforced with Al2O3 and TiO2 particulates, which offer enhanced mechanical, thermal, and tribological properties. The study investigates the historical evolution, material characteristics, and manufacturing techniques of metal matrix composites (MMCs) while emphasizing their increasing use in automotive, aerospace, and other industrial applications. Particular attention is given to the role of Al2O3 and TiO2 reinforcements in improving wear resistance and other tribological properties of aluminum alloys. This work underscores the necessity of integrating innovative materials and processes to meet the demands of lightweight, high-performance, and cost-effective solutions in the engineering domain.

A CRITICAL METAPHOR ANALYSIS OF ENVIRONMENTAL DISCOURSES IN THE PHILIPPINE SETTING

This research employed Critical Metaphor Analysis to examine the inaccuracies embedded in metaphors within the environmental discourses in the Philippines from a corpus of 30 documentary films. The study involved interviews with 5 science teachers and 5 senior high school students in the metaphor analyses. The pre-metaphor analysis level encompassed the discussions on pollution, climate change, biodiversity loss, and nature conservation. During the metaphor identification level, 35 conceptual metaphors containing inaccuracies were identified such as paradise, festival, treasure, refuge, landscape, society, patient, lungs, psychological disorder, sinking ship, waterworld, victims, battle, karma, last forest, symbols of freedom, burning, and simple solution domains. These are grouped into 12 conceptual keys such as ideal place, home, threat, interconnected system, living organism, monster, war, cause and effect, unrestricted movement, combustion, and simple solution source domains. At the metaphor interpretation phase, topics comprised conservation, preservation, and natural value; resource value and commodification of nature; waste and pollution; climate change and environmental degradation; and human influence and environmental ethics. The identified metaphors were characterized by orientational (5), ontological (17), and structural (13) mappings, with 23 metaphors conveying alarmist tones and 12 relational and hopeful tones. Purposes were found as ideological (9), empathetic (10), heuristic (7), and aesthetic (9). At the metaphor explanation level, ideologies such as human dominance, commodification, environmental ethics, sanctity of nature, and overwhelming burden were revealed reflecting modify (2), adapt (1), and depend (2) power dynamics. This study highlighted the cultural, ideological, and motivational underpinnings of metaphor usage in public media that can significantly shape public perception and environmental action. KEYWORDS: environmental discourses; documentary films; critical metaphor analysis; applied linguistics; Philippines

Scale-Resolving Simulations of Turbulent Flow Retaining the Exact Blade Count With the Time-Inclined Method

Abstract Simulations of the T106 low-pressure turbine linear cascade with incoming wakes have been conducted to demonstrate the suitability of the time-inclined method for retaining the exact blade count in scale-resolving simulations. The time-inclined method has been implemented into a high-order unstructured time-marching code based on the flux reconstruction method. The pitch ratio between the upstream incoming wakes and the cascade is not a small integer, and the time-inclined method is used to reduce simulations to a single-passage computational domain. Three-way comparisons have been generated: the solution of the direct periodic full domain, spanning several blade passages, is compared to the single-passage time-inclined solution and to a single-passage solution that approximates the pitch ratio to the nearest integer. Two sets of virtual experiments, which differ in modeling of the incoming perturbations, are reported. First, the immersed boundary approach is used to introduce a cascade of moving bars that act as the trailing edges of the preceding row and generate incoming wakes. The second set of simulations introduces wake-like perturbations at the inlet section of the computational domain. The present work shows that the time-inclined method, retaining the exact blade count, can produce very accurate results for turbulence-resolving simulations. Moreover, the time-inclined method outperforms the standard single-passage methodology in most of the variables of interest and is equivalent in the rest.

Reduced order modeling of blood perfusion in parametric multipatch liver lobules

In this paper, we present a computationally efficient reduced order model for obtaining blood perfusion profiles within parametric functional units of the liver called ‘lobules’. We consider Darcy’s equation in two-dimensional hexagonal lobule domains with six flow inlets and one outlet, whose positions are parameterized to represent varying lobule geometries. To avoid the meshing effort for every new lobule domain, we map the parametric domain onto a single reference domain. By making use of the contra-variant Piola mapping, we represent solutions of the parametric domains in the reference domain. We then construct a reduced order model via proper orthogonal decomposition (POD). Additionally, we employ the discrete empirical interpolation method (DEIM) to treat the non-affine parameter dependence that appears due to the geometric mapping. For sampling random shapes and sizes of lobules, we generate Voronoi diagrams (VD) from Delaunay triangulations and use an energy minimization problem to control the packing of the lobule structures. To reduce the dimension of the parameterized problem, we exploit the mesh symmetry of the full lobule domain to split the full domain into six rotationally symmetric subdomains. We then use the same set of reduced order basis (ROB) functions within each subdomain for the construction of the reduced order model. We close our study by a thorough investigation of the accuracy and computational efficiency of the resulting reduced order model.

Nonlinear Dynamic Analysis Using Harmonic Balance Method

There is a high demand for nonlinear structural dynamics in implicit Finite Element Analysis (FEA). Although such methods are available, there are several obstacles to use them daily. One is their extreme and unpredictable computation time, which makes it often impossible to get results in time. Another point is the restriction of the methods to the time domain, which is often in contrary to the usual design rules based on frequency domain results. The Harmonic Balance Method (HBM) is a solution for an important sub-class of analysis cases, which resolves the two mentioned obstacles. As a starting point, we define HBM as a frequency response analysis with local nonlinearities. This allows to solve contact problems or mounting problems with nonlinear force-deflection curves. The primary results of HBM are in frequency domain. For all calculated frequencies, a solution in time domain is also available for a periodic response. A simplified radiator is used as industrial example. To prove the validity of HBM, a comparison with a linear frequency response analysis is performed, which shows same results. Then, rubber bushes and contact are added to the model as nonlinearities. Key results of stress and fatigue are presented, and the computation times are analysed to demonstrate the feasibility of the HBM implementation for applications in research and industry. All simulations are performed with the FEA software PERMAS, which contains the HBM among many other analysis methods in structural dynamics.

Development of a finite element program for acoustics

Acoustic is the study of mechanical waves in solids, liquid and gases. Altougth the differential equations describing these problems are well known, with analytical solutions for simple geometries and/or loads, there are no closed solution for general problems. Thus, it is common to sougth on numerical procedures to address such problems.This work addresses the simulation of mechanical waves in loseless air using the linear finite element method. Solution in both time and frequency domains are discussed and compared to theoretical results.

Logarithmic Bernstein functions for fractional Rosenau-Hyman equation with the Caputo-Hadamard derivative

In this study, the Caputo-Hadamard derivative is fittingly used to define a fractional form of the Rosenau-Hyman equation. To solve this equation, the orthonormal logarithmic Bernstein functions (BFs) are created as a suitable basis for handling this type of derivative. The primary benefit of these functions lies in the ease of computing their Hadamard fractional integral and derivative. These logarithmic functions, combined with the orthonormal Bernstein polynomials (BPs), are simultaneously employed to develop a hybrid strategy for solving the aforementioned equation. More precisely, the orthonormal logarithmic BFs are utilized to approximate the solution in the temporal domain and the orthonormal BPs are employed in the spatial domain. In addition, a matrix is extracted for the Hadamard integral of the orthonormal logarithmic BFs due to the implementation of the presented method. The effectiveness of the established scheme in finding accurate numerical solutions is evaluated through the resolution of three examples.

Piezothermoelastic interaction in piezoelectric rods induced by a timed laser pulse without energy dissipation

The main aim of this article is to study the piezo-thermoelastic interaction in piezoelectric rods without energy dissipation due to a laser heat source with a timed pulse. Laplace transforms are used to represent the analytical solutions in the transformations domain. The governing equations of piezo-thermoelasticity in the Green and Naghdi model (GNII model without energy dissipation) in the presence of a laser heat source with a timed pulse are solved exactly in the Laplace domain, calculating the temperature, the stress, the displacement, and the electric potential. Numerical Laplace inversion is then used to find the general solution of the variables under study, which are then graphically shown.

Exact solution to a class of problems for the Burgers’ equation on bounded intervals

In this study, we consider Burgers’ equation with fixed Dirichlet boundary conditions on generic bounded intervals. By employing the Hopf-Cole transformation and a recently established exact operational solution for linear reaction–diffusion equations, an exact solution in the time domain is derived through inverse Laplace transforms. In the event that analytic inverses do in fact exist, they can be obtained in closed form through the use of Mellin transforms. Nevertheless, highly efficient algorithms are available, and numerical inverses in the time domain are always feasible, regardless of the complexity of the Laplace domain expressions. Two illustrative tests demonstrate that the results align closely with those of classical exact solutions. In comparison to the solutions obtained with series expressions or by numerical methods, closed-form expressions, even in the Laplace domain, represent a novel alternative, offering new insights and perspectives. The exact solution via the inverse Laplace transform is shown to be more computationally efficient, providing a reference point for numerical and semi-analytical methods.

A Krylov eigenvalue solver based on filtered time domain solutions

This paper introduces a method for computing eigenvalues and eigenvectors of a generalized Hermitian, matrix eigenvalue problem. The work is focused on large scale eigenvalue problems, where the application of a direct inverse is out of reach. Instead, an explicit time-domain integrator for the corresponding wave problem is combined with a proper filtering and a Krylov iteration in order to solve for eigenvalues within a given region of interest. We report results of small scale model problems to confirm the reliability of the method, as well as the computation of acoustic resonances in a three dimensional model of a hunting horn to demonstrate the efficiency.

Decentralized Voting Application Using Blockchain

The emergence of blockchain technology has paved the way for innovative solutions in various domains, particularly in enhancing democratic processes. This research paper presents the design, development, and evaluation of a Web3 blockchain decentralized voting application (DAPP) built using React JS for frontend development and Solidity for smart contract implementation. The objective of this study is to explore the feasibility and effectiveness of employing blockchain technology to create a secure, transparent, and decentralized voting system. The proposed DAPP leverages the immutability and transparency features of blockchain technology to ensure the integrity of the voting process. Smart contracts coded in Solidity are utilized to execute the voting mechanism, ensuring tamper-proof recording and tallying of votes. React JS, a popular JavaScript library for building user interfaces, is employed to develop an intuitive and user-friendly frontend interface, enhancing accessibility and usability for voters. Key aspects addressed in this research include the architecture of the DAPP, the design of smart contracts for voting logic, integration of React JS components for frontend development, and security considerations to prevent vulnerabilities and attacks. Additionally, the paper discusses the implications of decentralized voting systems on democracy, including increased trust, transparency, and participation.

Application of a boundary-type algorithm to the inverse problems of convective heat and mass transfer

The inverse problems of the convection-diffusion equation (ICDE) have received extensive attention in incomplete boundary conditions and uncertain source terms. They can be applied in thermally stratified pipe elbows and so on. Many algorithms need to combine with optimization algorithms to repeatedly calculate the direct problem in the solution process. To solve such problems, this paper employs a boundary-type algorithm named the half-boundary method (HBM). The HBM does not require additional repeated optimization of the direct problem. To test the performance of the method, the numerical simulations of some problems have been carried out, including the inverse problems of heat convection, river pollution and air pollution. The results show that the HBM has the desired accuracy by comparing with the exact solution. If there are errors in the measurement process, the solution doesn't generate a large deviation from the result. It is worth noting that the placement of internal measurement points minimally impacts the numerical results within the solution domain. And the method is also able to handle with discontinuous problems. Because the Gaussian plume model verifies the accuracy of HBM, the HBM can quickly calculate the atmospheric diffusion of the non-Gaussian plume model.

2025 Roadmap on 3D Nano-magnetism.

The transition from planar (2D) to three-dimensional (3D) magnetic nanostructures represents a significant advancement in both fundamental research and practical applications, offering vast potential for next-generation technologies like ultrahigh-density storage, memory, logic, and neuromorphic computing. Despite being a relatively new field, the emergence of 3D nanomagnetism presents numerous opportunities for innovation, prompting the creation of a comprehensive roadmap by leading international researchers. This roadmap aims to facilitate collaboration and interdisciplinary dialogue to address challenges in materials science, physics, engineering, and computing.
The roadmap comprises eighteen sections, roughly divided into three parts. The first section explores the fundamentals of 3D nanomagnetism, focusing on recent trends in fabrication techniques and imaging methods crucial for understanding complex spin textures, curved surfaces, and small-scale interactions. Techniques such as two-photon lithography and focused electron beam-induced deposition enable the creation of intricate 3D architectures, while advanced imaging methods like electron holography and Lorentz electron Ptychography provide sub-nanometer resolution for studying magnetization dynamics in three dimensions. Various 3D magnetic systems, including coupled multilayer systems, artificial spin ice, magneto-plasmonic systems, topological spin textures, and molecular magnets, are discussed.
The second section introduces analytical and numerical methods for investigating 3D nanomagnetic structures and curvilinear systems, highlighting geometrically curved architectures, interconnected nanowire systems, and other complex geometries. Finite element methods are emphasized for capturing complex geometries, along with direct frequency domain solutions for addressing magnonic problems.
The final section focuses on 3D magnonic crystals and networks, exploring their fundamental properties and potential applications in magnonic circuits, memory, and spintronics. Computational approaches using 3D nanomagnetic systems and complex topological textures in 3D spintronics are highlighted for their potential to enable faster and more energy-efficient computing.&#xD.

Generalized piezothermoelastic interactions in a piezoelectric rod subjected to pulse heat flux

Abstract This work investigates, using the Laplace transforms, the influence of thermal relaxation time in the piezo-thermoelastic rod under pulse heat flux. For the piezoelectric medium, the generalized piezothermoelastic fundamental equations are developed. The analytical solutions are expressed in the transformation domain using Laplace transforms. Laplace transforms are presented to solve the problem’s governing equations, removing the time impact and yielding analytical solutions for the temperature, electric field, displacement, and stresses in the Laplace domain. The time domain solutions of the variables under consideration are then found using numerical Laplace inversion and visually shown. The effects of the thermal time, pulse heating flux characteristic time, and constant heat flux are studied in a piezoelectric thermoelastic medium. The figures show that the thermal time, pulse heating flux characteristic time, and constant heat flux play significant roles in determining the values of all physical quantities.

Solving Fuzzy Delay Differential Equations using Fuzzy Elzaki Transform and Fuzzy Elzaki Decomposition Method

Objective: In this work, the fuzzy Elzaki transform and fuzzy Elzaki decomposition method are used to solve fuzzy delay differential equations. The fuzzy Elzaki decomposition method is a combination of the fuzzy Elzaki transform and Adomian decomposition method in a fuzzy environment. The use of transforms in solving differential equations makes the solution process simpler. Methodology: The fuzzy Elzaki transform is applied in the fuzzy delay differential equation. The nonlinear terms are decomposed using Adomian polynomials in a nonlinear fuzzy delay differential equation. In the transformed domain, the resulting algebraic equation is solved. The solution in the original time domain is obtained by applying the inverse Elzaki transform. Findings: The fuzzy Elzaki transform and fuzzy Elzaki decomposition method are useful for handling the complexities associated with fuzzy functions and delays in differential equations. The technique used to solve the fuzzy delay differential equation gives results with better accuracy compared to the exact solution. The applicability of the method is illustrated with numerical examples. Novelty: The Elzaki transform is a helpful tool for solving delay differential equations with discontinuities. For the resilient solution of complicated differential equations, especially those including nonlinearity and fuzzy logic, the fuzzy Elzaki decomposition approach is useful. It gives an organized way to find the solution to fuzzy delay differential equation by utilizing the advantages of both the Elzaki transform and the Adomian decomposition method in a fuzzy situation. Keywords: Triangular Fuzzy Number, Fuzzy Elzaki Transform, Adomian decomposition method, Fuzzy Elzaki decomposition method, Fuzzy Delay Differential Equations (FDDE)

A new fourth-order compact finite difference method for solving Lane-Emden-Fowler type singular boundary value problems

We develop a novel fourth-order compact finite difference scheme to solve nonlinear singular ordinary differential equations. Such problems occur in many fields of science and engineering, such as studying the equilibrium of an isothermal gas sphere, reaction–diffusion in a spherical permeable catalyst, etc. These problems are challenging to solve because of their singularity or nonlinearity. By our proposed method, we can easily solve these complex problems without removing or modifying the singularity. To construct the new fourth-order compact difference method, Initially, we created a uniform mesh within the solution domain and developed a compact finite difference scheme. This scheme approximates the derivatives at the boundary nodal points to handle the problem’s singularity effectively. Employing a matrix analysis approach, we discussed the convergence analysis of the methods. To demonstrate its efficacy, we apply our approach to solve various real-life problems from the literature. The new method offers high-order accuracy with minimal grid points and provides better numerical results than the nonstandard finite difference method and exponential compact finite difference method.

Lippmann-Schwinger equation representation of Green's function and its preconditioned generalized over-relaxation iterative solution in wavelet domain

The calculation of Green's function is the core of seismic forward and inverse methods based on integral operators. When the Lippmann-Schwinger (L-S) equation is used to calculate Green's function in strongly scattering media, both the Born scattering series and the numerical iterative method encounter issues of slow convergence or divergence. Although the renormalization method derived from quantum mechanics can effectively address the convergence problem of Born scattering series in strong scattering problems, it is acknowledgeed that the convergence conditions and rates of convergence of different reformulation series may vary, and no universal convergence reformulation scattering series exists. Numerical methods for solving integral equations tend to be more general and mathematically robust. In this work, we focus on the numerical solution method of L-S equations. By using a wavelet-domain preconditioner to a reformulated or equivalent Lippmann-Schwinger (L-S) equation, we present an iterative method for numerically solving the equivalent L-S equation aimed at improving the rate of convergence and iteration efficiency in strongly inhomogeneous media. Following Jakobsen et al. (2020), we first introduce a small imaginary component into the background wave number，then rewrite the L-S equation to derive the equivalent complex wave number L-S equation. This reformulation ensures that the coefficient matrix exhibits a banded structure after numerical discretization, allowing the wavelet coefficient matrix to maintain good sparsity. We employ a multi-level fill-in incomplete LU (ILU) factorization method along with a block ILU-based algebraic recursive multilevel solve (ARMS) method in the wavelet domain to generate sparse approximate inverses as preconditioning operators, thereby accelerating the convergence of the generalized successive over-relaxation (GSOR) iterative method. This method is applied to compute numerical Green's functions in strongly inhomogeneous media. Numerical results demonstrate that our method yields simulation outcomes consistent with those obtained from the direct method for solving the original real wave number L-S equation. By testing various preconditioners, we find that the ARMS preconditioner offers significant advantages in operator generation efficiency and non-zero element filling ratio, effectively accelerating the convergence of the GSOR iterative method while achieving higher computational efficiency.

Deciphering Electrocatalytic Hydrogen Production in Water Through a Bioinspired Water-Stable Copper(II) Complex Adorned with (N2S2)-Donor Sites.

Electrocatalytic hydrogen production stands as a pivotal cornerstone in ushering the revolutionary era of the hydrogen economy. With a keen focus on emulating the significance of hydrogenase-like active sites in sustainable H2 generation, a meticulously designed and water-stable copper(II) complex, [Cl-Cu-LN2S2]ClO4, featuring the N,S-type ligand, LN2S2 (2,2'-((butane-2,3-diylbis(sulfanediyl))bis(methylene))dipyridine), has been crafted and assessed for its prowess in electrocatalytic H2 production in water, leveraging acetic acid as a proton source. The molecular catalyst, adopting a square pyramidal coordination geometry, undergoes -Cl substitution by H2O during electrochemical conditions yielding [H2O-Cu-LN2S2]2+ as the true catalyst, showcases outstanding activity in electrochemical proton reduction in acidic water, achieving an impressive rate of 241.75 s-1 for hydrogen generation. Controlled potential electrolysis at -1.2 V vs. Ag/AgCl for 1.6 h reveals a high turnover number of 73.06 with a commendable Faradic efficiency of 94.2 %. A comprehensive analysis encompassing electrochemical, spectroscopic, and analytical methods reveals an insignificant degradation of the molecular catalyst. However, the post-CPE electrocatalyst, present in the solution domain, signifies the coveted stability and effective activity under the specified electrochemical conditions. The synergy of electrochemical, spectroscopic, and computational studies endorses the proton-electron coupling mediated catalytic pathways, affirming the viability of sustainable hydrogen production.

On the dual-phase-lag thermal response in the pulsed photoacoustic effect: A theoretical and experimental 1D-approach

In a recent work, assuming a Beer–Lambert optical absorption and a Gaussian laser time profile, it was shown that the exact solutions for a 1D photoacoustic (PA) boundary-value-problem predict a null pressure for optically strong absorbent materials. In order to overcome this inconsistency, a heuristic correction was introduced by assuming that heat flux travels a characteristic length during the duration of the laser pulse [M. Ruiz-Veloz et al., J. Appl. Phys. 130, 025104 (2021)] τp. In this work, we obtained exact analytical solutions in the frequency domain for a 1D boundary-value-problem for the Dual-Phase-Lag (DPL) heat equation coupled with a 1D PA-boundary-value-problem via the acoustic wave equation. Temperature and pressure solutions were studied by assuming that the sample and its surroundings have a similar characteristic thermal lag response time τT; therefore, the whole system is assumed to have a similar thermal relaxation. A second assumption for τT is that it is considered as a free parameter that can be adjusted to reproduce experimental results. Solutions for temperature and pressure were obtained for a one-layer 1D system. It was found that for τT<τp, the DPL temperature has a similar thermal profile of the Fourier heat equation; however, when τT≥τp, this profile is very different from the Fourier case. Additionally, via a numerical Fourier transform, the wave-like behavior of DPL temperature is explored, and it was found that as τT increases, thermal wave amplitude is increasingly attenuated. Exact solutions for pressure were compared with experimental PA signals, showing a close resemblance between both data sets, particularly in time domain, for an appropriated value of τT; the transference function was also calculated, which allowed us to find the maximum response in frequency for the considered experimental setup.