Solution Of Model Research Articles

Travelling waves for a fast reaction limit of a discrete coagulation-fragmentation model with diffusion and proliferation.

We study traveling wave solutions for a reaction-diffusion model, introduced in the article Calvez et al. (Regime switching on the propagation speed of travelling waves of some size-structured myxobacteriapopulation models, 2023), describing the spread of the social bacterium Myxococcus xanthus. This model describes the spatial dynamics of two different cluster sizes: isolated bacteria and paired bacteria. Two isolated bacteria can coagulate to form a cluster of two bacteria and conversely, a pair of bacteria can fragment into two isolated bacteria. Coagulation and fragmentation are assumed to occur at a certain rate denoted by k. In this article we study theoretically the limit of fast coagulation fragmentation corresponding mathematically to the limit when the value of the parameter k tends to . For this regime, we demonstrate the existence and uniqueness of a transition between pulled and pushed fronts for a certain critical ratio between the diffusion coefficient of isolated bacteria and the diffusion coefficient of paired bacteria. When the ratio is below , the critical front speed is constant and corresponds to the linear speed. Conversely, when the ratio is above the critical threshold, the critical spreading speed becomes strictly greater than the linear speed.

Dynamics of propagation patterns: An analytical investigation into fractional systems

Recent years have seen a growing interest in fractional differential equations, particularly the fractional Chaffee-Infante ([Formula: see text]) equation, pivotal for understanding dynamics governed by fractional orders in specific physical systems. Exploring solitary wave solutions, this study employs the extended Khater method and truncated Mittag-Leffler function properties to formulate tailored solutions for the ([Formula: see text]) model. Through a traveling wave ansatz, the equation transforms into a nonlinear ordinary differential equation, revealing intricate propagation patterns of solitary waves. Visual representations aid comprehension, while rigorous validation ensures solution precision, ultimately providing a comprehensive understanding of system responses to external stimuli. This study effectively integrates analytical and numerical methodologies to derive precise solitary wave solutions, with significant implications for advancing comprehension of complex phenomena in various disciplines governed by fractional-order dynamics.

Mathematical modelling of impurity deposition during evaporation of dirty liquid in a porous material

When a contaminated liquid evaporates from within a porous material, the impurities or dirt accumulate and deposit within the pore space. This occurs during the cleaning of filters and fouling of textiles, and is related to the ‘coffee-ring’ problem. To investigate how and where dirt is deposited in the pore space, we present a model for the motion of an evaporation front through a porous material, and the related accumulation, transport, and deposition of dirt, assuming that the liquid remains stationary. For physically relevant parameters, vapour transport out of the porous material is quasi-steady and we derive a single ordinary differential equation describing the motion of the evaporation front in time. Model solutions exhibit spatially non-uniform profiles of the deposited dirt-layer thickness through the porous material. The dirt accumulation and evaporation problems are coupled: deposited dirt hinders vapour transport through the porous material, slowing the evaporation. We identify two scenarios in which the porous material becomes clogged with dirt. Accumulation of suspended dirt at the evaporating interface along with slow dirt diffusion results in the deposited dirt layers clogging the pores at the evaporating interface, halting the drying and trapping liquid in the porous material. Alternatively, slow dirt deposition results in the suspended dirt being pushed far into the porous material by the evaporation, eventually leaving only dirt (with no liquid) in the pore space. We investigate the dynamics of both clogging scenarios, characterising the parameter regimes for which each occurs. Both clogging scenarios must be avoided in practice since they may be detrimental to future filter efficacy or textile breathability.

Analytical Solutions of the 3-DOF Gyroscope Model

The motion of a rigid body (a gyroscope) is one of the key issues in classical mechanics. It remains a significant challenge, as evidenced by its extensive practical implementations in various scientific disciplines and engineering operations. It is important to obtain analytical solutions, as they provide solutions that depend directly on the system’s parameters, which can be definitively interpreted. The coupling of numerical and analytical solutions allows for a more precise representation of the real phenomenon. The main objective of the article was to formulate analytical solutions for the motion of a Cardan suspension gyroscope subjected to controlling torque moments. Analytical solutions for the proposed mathematical model were developed using the Laplace transform and Green’s function. Subsequently, they were validated by numerical tests. The obtained analytical solutions are universally applicable, regardless of the type of controlling moments.

On the construction of various soliton solutions of two space-time fractional nonlinear models

Abstract In this article, we investigate a couple of nonlinear fractional models of eminent interests subsequently the conformable derivative sense is used to designate the fractional order derivatives. The given structures are transformed into nonlinear ordinary differential equations of integer order, and the extended simple equation technique is then employed to solve the resulting equations. Initially, the nonlinear space time fractional Klein–Gordon equation is considered emerging from quantum and classical relativistic mechanics, which have application in plasma physics, dispersive wave phenomena, quantum field theory, and optical fibres. Later, the (2 + 1)-dimensional time fractional Zoomeron equation is analysed which is convenient to explore the innovative phenomena related to boomerons and trappons. As a result, various new soliton solutions are successfully established. The reported results offer a key implementation for analysing the soliton solutions of nonlinear fractional models which are extremely encouraging arising in the recent era of science and engineering. The 3D simulations have been carried out to demonstrate dynamics of the various soliton solutions for a given set of parameters.

How is photon-blockade breakdown different from optical bistability? A neoclassical story

The photon-blockade breakdown bistability can be intuitively explained invoking the energy spectrum of the interacting qubit-mode system. Yet, the neoclassical solution of the driven-dissipative Jaynes-Cummings model has been shown to capture several key aspects of the phenomenon. In this paper, we set out to compare a fully quantum solution with the neo- and semiclassical solutions. Although the neoclassical theory is founded on the assumption of a pure partial state for the qubit, it is not simply the γ→0 limit of the semiclassical theory, the semi- versus neoclassical duality being a case of non-commutativity of limits. Furthermore, we show that the neoclassical predictions still hold in the case of a small qubit decay. Tracing the bistable behavior for different detunings, we show that it is robust over a significant range of Δ values. We demonstrate that the aptitude of the neoclassical description is founded on the high quantum purity of the bright state of the photon-blockade breakdown bistability, which sharply differentiates this phenomenology from conventional optical bistability. It is thereby demonstrated that driven-dissipative dynamics can produce closely separable pure steady states in an interacting bipartite.

Efficient recovery and recycling/upcycling of precious metals using hydrazide-functionalized star-shaped polymers

There is a growing demand for adsorption technologies for recovering and recycling precious metals (PMs) in various industries. Unfortunately, amine-functionalized polymers widely used as metal adsorbents are ineffective at recovering PMs owing to their unsatisfactory PM adsorption performance. Herein, a star-shaped, hydrazide-functionalized polymer (S-PAcH) is proposed as a readily recoverable standalone adsorbent with high PM adsorption performance. The compact chain structure of S-PAcH containing numerous hydrazide groups with strong reducibility promotes PM adsorption by enhancing PM reduction while forming large, collectable precipitates. Compared with previously reported PM adsorbents, commercial amine polymers, and reducing agents, S-PAcH exhibited significantly higher adsorption capacity, selectivity, and kinetics toward three PMs (gold, palladium, and platinum) with model, simulated, and real-world feed solutions. The superior PM recovery performance of S-PAcH was attributed to its strong reduction capability combined with its chemisorption mechanism. Moreover, PM-adsorbed S-PAcH could be refined into high-purity PMs via calcination, directly utilized (upcycled) as catalysts for dye reduction, or regenerated for reuse, demonstrating its high practical feasibility. Our proposed PM adsorbents would have a tremendous impact on various industrial sectors from the perspectives of environmental protection and sustainable development.

The solitary solutions for the stochastic fractional Chen Lee Liu model perturbed by multiplicative noise in optical fibers and plasma physics

In this paper, we consider the stochastic fractional Chen Lee Liu model (SFCLLM). We apply the mapping method in order to get hyperbolic, elliptic, rational and trigonometric stochastic fractional solutions. These solutions are important for understanding some fundamentally complicated phenomena. The acquired solutions will be very helpful for applications such as fiber optics and plasma physics. Finally, we show how the conformable derivative order and stochastic term affect the exact solution of the SFCLLM.

Effective hydrogen supply chain management framework considering nonlinear multi-stage process uncertainties

The large amount of carbon emitted due to industrial development is posing serious climate change. Under these circumstances, hydrogen energy is being used as a major energy source and is attracting attention as an alternative energy to fossil fuels, characterized by high carbon emissions. While the use of hydrogen has the obvious benefit of a low carbon footprint, the hydrogen production process possesses a high carbon footprint difference depending on the source of utilized electricity. This study considers several situations arising in an electrolysis-based hydrogen supply chain network (HSCN). A multi-stage stochastic programming (SP) is modeled to consider the uncertainty of demand and transportation capacity generated in HSCN. Moreover, a typical stochastic model has a chain rule between the decision variables resulting from nonlinearity and uncertainty, and these features make it difficult to derive an effective solution. Thus, in this study, a new methodology, Weighted Scenario Sample Average Approximation (WSSAA), is proposed to derive an effective solution for the multistage SP model considering various scenarios under the hydrogen supply chain. While a general stochastic programming approach fails to generate feasible solutions with volatile HSCN uncertainties, the proposed WSSAA framework provides feasible decisions considering multiple scenarios. The effectiveness of the proposed model applied with WSSAA is demonstrated through comparative experiments over the models used in existing studies.

Dynamical behavior of fractal-fractional order monkeypox virus model

A virus that infects both humans and animals, monkeypox is common in many West African countries and has sporadically spread to other parts of the world. There are serious public health concerns around the globe as a result of the recent spike in cases of monkeypox among both endemic and non-endemic populations. This paper proposes to use the Caputo sense of fractal fractional-order derivatives to examine the dynamics of monkeypox transmission. The study uses Schauder’s fixed point theorem to evaluate the solutions qualitatively and establish their uniqueness inside the model. The next generation matrix technique is used to compute the essential reproduction number. The stability of equilibrium points is further investigated in the research, and a sensitivity analysis of model parameters is carried out. When the basic reproduction number R0 is less than 1, the equilibrium without infections is locally stable. Also, when R0 exceeds 1, this equilibrium becomes unstable. The proposed model incorporates Ulam–Hyers stability through nonlinear functional analysis. To estimate solutions for the fractal-fractional order monkeypox model, the Lagrange’s interpolation method is utilized. In addition, numerical simulations are carried out to examine the influence of some parameters on the overall dynamics of the model. Numerical simulations are performed using MATLAB software to exemplify the model behavior in the context of the Nigerian case study. The graphical representations suggest that the fractal fractional order affects the dynamics of the monkeypox. The findings indicate that isolation of infected individuals in the human population helps to reduce disease transmission.

An Effective Arbitrary Lagrangian-Eulerian-Lattice Boltzmann Flux Solver Integrated with the Mode Superposition Method for Flutter Prediction

An arbitrary Lagrangian-Eulerian lattice Boltzmann flux solver (ALE-LBFS) coupled with the mode superposition method is proposed in this work and applied to study two- and three-dimensional flutter phenomenon on dynamic unstructured meshes. The ALE-LBFS is applied to predict the flow field by using the vertex-centered finite volume method with an implicit dual time-stepping method. The convective fluxes are evaluated by using lattice Boltzmann solutions of the non-free D1Q4 lattice model and the viscous fluxes are obtained directly. Additional fluxes due to mesh motion are calculated directly by using local conservative variables and mesh velocity. The mode superposition method is used to solve for the dynamic response of solid structures. The exchange of aerodynamic forces and structural motions is achieved through interpolation with the radial basis function. The flow solver and the structural solver are tightly coupled so that the restriction on the physical time step can be removed. In addition, geometric conservation law (GCL) is also applied to guarantee conservation laws. The proposed method is tested through a series of simulations about moving boundaries and fluid–structure interaction problems in 2D and 3D. The present results show good consistency against the experiments and numerical simulations obtained from the literature. It is also shown that the proposed method not only can effectively predict the flutter boundaries in both 2D and 3D cases but can also accurately capture the transonic dip phenomenon. The tight coupling of the ALE-LBFS and the mode superposition method presents an effective and powerful tool for flutter prediction and can be applied to many essential aeronautical problems.

Modulation instability and comparative observation of the effect of fractional parameters on new optical soliton solutions of the paraxial wave model

This work focuses on the study of the paraxial wave model with a space–time fractional form. This model has more importance for describing light propagation in nonlinear optical fibers and telecommunication lines. The main aim of this work is to observe the effect of the fractional parameters and compare the truncated M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M$$\\end{document}-fraction with the beta-fraction, conformable fraction form, and classical form of the PW model. For this observation, we applied the Simplest equation technique to acquire analytical solutions to the space–time (spatiotemporal) M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M$$\\end{document}-fractional paraxial wave model. We are able to acquire several new optical soliton solutions, including periodic waves, kink-type waves, rogue-type waves, and several novel periodic waves, by providing the appropriate fractional parametric values. These solutions have significance for shedding light on a number of physical phenomena in the realms of optical fiber and communication sciences. The diverse values of fractional parameters and the three-dimensional and contour plot graphs of certain chosen solutions are depicted, which are the most accurate physical characterizations of the outcomes. We also sketch the comparative graph of diverse fractional forms and the classical form of the paraxial wave equation in two-dimensional plots. Consequently, our findings represent an important breakthrough in this complex area and help further develop our comprehension of the behavior of solitons.

New solitary wave solutions of space-time fractional dynamical models

New solitary wave solutions of space-time fractional dynamical models

Multiwaves, breathers, lump and other solutions for the Heimburg model in biomembranes and nerves

In this manuscript, a mathematical model known as the Heimburg model is investigated analytically to get the soliton solutions. Both biomembranes and nerves can be studied using this model. The cell membrane’s lipid bilayer is regarded by the model as a substance that experiences phase transitions. It implies that the membrane responds to electrical disruptions in a nonlinear way. The importance of ionic conductance in nerve impulse propagation is shown by Heimburg’s model. The dynamics of the electromechanical pulse in a nerve are analytically investigated using the Hirota Bilinear method. The various types of solitons are investigates, such as homoclinic breather waves, interaction via double exponents, lump waves, multi-wave, mixed type solutions, and periodic cross kink solutions. The electromechanical pulse’s ensuing three-dimensional and contour shapes offer crucial insight into how nerves function and may one day be used in medicine and the biological sciences. Our grasp of soliton dynamics is improved by this research, which also opens up new directions for biomedical investigation and medical developments. A few 3D and contour profiles have also been created for new solutions, and interaction behaviors have also been shown.

Simulation study of the Gilbert damping in Ni80Fe20/Nd bilayers: comparison with experiments

We present an experimental and computational investigation the Neodymium thickness dependence of the effective damping constant ( αeff ) in Ni 80 Fe 20/Neodymium (Py/Nd) bilayers. The computational results show that the magnetic damping is strongly dependent on the thickness of Nd, which is in agreement with experimental data. Self consistent solutions of the spin accumulation model and the local magnetisation were used in the simulations. It was not possible to obtain agreement with experiment under the assumption of an enhanced damping in a single Py monolayer. Instead, it was found that the enhanced damping due to spin pumping needed to be spread across two monolayers of Py. This is suggested to arise from interface mixing. Subsequently, the temperature dependence of the effective damping was investigated. It is found that, with increasing temperature, the influence of thermally-induced spin fluctuations on magnetic damping becomes stronger with increasing Nd thickness.

A new version of trial equation method for a complex nonlinear system arising in optical fibers

In this study, the dissipation problem of nonlinear pulse in mono mode optical fibers which is governed by the Fokas system (FS) is considered. The solutions of this system have an important role in comprehending the different wave structures in physical settings. Therefore, a new version of the trial equation method (NVTEM) is employed to present the new exact wave solutions of the FS. The advantage of the NVTEM is to use different root possibilities of a polynomial which shape the solutions of the related model. Primarily this system is converted to a nonlinear ordinary differential equation (NODE) via the traveling wave transform to apply the proposed method. Various exact wave solutions to the FS are obtained such as rational function, exponential function, hyperbolic function, and Jacobi elliptic function solutions. Thus, we have revealed solutions featly which are unlike the wave solutions previously found by other analytical methods. The present results depict the formation and development of such waves and their interactions. The exhibition of the solutions is given by 3D plots together with the corresponding 2D plots. The outcomes have shown that the proposed technique is abundant in achieving different wave solutions of many nonlinear differential equations in the field of optics.

Research and verification on parameter solution of mixed shock model for common cause failure based on particle swarm algorithm

AbstractMixed shock model is an explicit construction method of failure probability model based on component independent failure, system nonfatal shock, and fatal shock failure, which considers common cause failure (CCF) in redundant system. For aerospace systems, a modified mixed shock model is proposed, which considers several components may fail independently and simultaneously in operation. In order to solve the issue that the parameters of the mixed shock model cannot be solved directly based on the failure probability data, a parameter solving method based on particle swarm optimization (PSO) algorithm is proposed. Additionally, the relationship between the failure probability and the gradient of the parameter change is deduced, and the reduced‐order (RO) solution based on the gradient of the parameter change is proposed to improve the efficiency of the solution. A fitness function construction method based on the relative error of the solution probability and the true probability is proposed to improve the probability solution accuracy of multicomponent failure. The nonlinear inertia factor optimization method combined with fitness change is studied to improve the particle swarm dynamics. The accuracy of the results of different parameters solving sequence and different PSO methods are compared, and the effectiveness of the RO solution is verified. The results of the mixed shock model before and after modification are compared with the different CCF data, which verifies the effectiveness and wide applicability of the modified mixed shock model. The results show that the modified mixed shock model for CCF and its parameter solution method can significantly improve the probability solution accuracy of all components failure, and also provide a new theoretical basis and solution method for the quantitative analysis of multiredundant system failure.

An investigation on the torsional vibration of a FG strain gradient nanotube

AbstractIn this work, an attention is paid to the prediction of torsional vibration frequencies of functionally graded porous nanotubes based on the Lam strain gradient elasticity theory. The nanotubes are formed of functionally graded porous nanomaterials that vary in the radial direction. This study also aims to obtain the analytical solution of the strain gradient model presented by Lam for torsional vibration response, in a simple manner, for different rigid or restrained boundary conditions. The torsion angle of a functionally graded nanotube is defined by an infinite Fourier series. Then, the Stokes’ transformation is applied to force the boundary conditions to the desired state. An eigenvalue problem is established with the help of the two systems of equations obtained. This eigenvalue problem, which includes deformable springs at both ends of the nanotube, appears as a general analytical solution that can find torsional vibration frequencies. It is shown that the vibrational responses can be significantly influenced by the through‐radius gradings of material, material length scale parameters and deformable springs of the functionally graded nanotubes and consequently can be predicted by giving proper values to torsional spring parameters.

Qualitative analysis of solutions for a degenerate partial differential equations model of epidemic spread dynamics

Compartmental models are widely used in mathematical epidemiology to describe the dynamics of infectious diseases or in mathematical models of population genetics. In this study, we study a time-dependent Susceptible-Infectious-Susceptible (SIS) Partial Differential Equation (PDE) model that is based on a diffusion-drift approximation of a probability density from a well-known discrete-time Markov chain model. This SIS-PDE model is conservative due to the degeneracy of the diffusion term at the origin. The main results of this article are the qualitative behavior of weak solutions, the dependence of the local asymptotic property of these solutions on initial data, and the existence of Dirac delta function type solutions. Moreover, we study the long-term behavior of solutions and confirm our analysis with numerical computations.

Selection of Appropriate Criteria for Optimization of Ventilation Element for Protective Clothing Using a Numerical Approach

While there are multiple methods to ventilate protective clothing, there is still room for improvement. In our research, we are using ventilation elements that are positioned at the ventilation holes in the air space between the body and clothing. These ventilation elements allow air to flow freely while preventing sun radiation, rain drops, and insects from directly accessing the body. Therefore, the shape of the ventilation element is crucial. This led us to study the shape optimization of ventilation elements through the utilization of metamodels and numerical approaches. In order to accomplish the objective, it is crucial to thoroughly evaluate and choose suitable criteria for the optimization process. We know from prior research that the toroidal cut-out shape element provides better results. In a previous study, we optimized the shape of this element based on the minimum pressure difference as a criterion. In this study, we are using different criteria for the shape optimization of ventilation elements to determine which are most effective. This study involves a metamodeling strategy that utilizes local and global approximations with different order polynomials, as well as Kriging approximations, for the purpose of optimizing the geometry of ventilation elements. The goal was achieved by a sequential process. (1) Planning the position of control points of Non-Uniform Rational B-Splines (NURBS) in order to generate elements with a smooth shape. (2) Constructing geometric CAD models based on the design of experiments. (3) Compute detailed model solutions using SolidWorks Flow Simulation. (4) Developing metamodels for responses using computer experiments. (5) Optimization of element shape using metamodels. The procedure is repeated for six criteria, and subsequently, the results are compared to determine the most efficient criteria for optimizing the design of the ventilation element.