A linear electrohydrodynamic Kelvin-Helmholtz instability of the interface between two viscoelastic Rivlin-Ericksen fluids enclosed by two concentric horizontal cylinders has been studied via the viscoelastic potential flow theory. The dispersion equation of complex coefficients for asymmetric disturbance has been obtained by using normal mode technique. the stability criteria are analyzed theoretically and illustrated graphically. The imaginary part of growth rate is plotted versus the wave number. The influences of dynamic viscoelastic, uniform velocities, Reynolds number, electric field, dynamic viscosity, density fluids ratio, dielectric constant ratio and inner fluid fraction on the stability of the system are discussed. The study finds its significance in Ocean pipelines to transfer oil or gas such as Eastern Siberia-Pacific Ocean oil pipeline.
Highlights
● The linear electrohydrodynamic Kelvin-Helmholtz instability analysis of two viscoelastic Rivlin-Ericksen fluids has been studied via the viscoelastic potential flow theory.
● The dispersion equation of complex coefficients has been obtaind by using normal mode technique.
● The effect of various parameters on the stability of the system are discussed.
● some limiting cases are considered and recovered previous works.
The primary objective of this research problem is to analyze the Rayleigh wave propagation in homogeneous isotropic half space with mass diffusion in Three Phase Lag (TPL) thermoelasticity at two temperature. The governing equations of thermodiffusive elastic half space have been solved using the normal mode analysis in order to obtain the Rayleigh wave frequency equation at relevant boundary conditions. The variation of various parameters like non-dimensional speed, attenuation coefficient, penetration depth and specific loss corresponding to thermodiffusion parameter, relaxation time, wave number and frequency has been obtained. The effect of these parameters on Rayleigh wave propagation in thermoelastic half space are graphically demonstrated and variations of all these parameters have been compared within Lord-Shulman (L-S), Green-Nagdhi (GN-III) and Three Phase Lag (TPL) theory of thermoelasticity.
Highlights
● Rayleigh wave propagation in homogeneous isotropic half space with mass diffusion in Three Phase Lag thermoelasticity at two temperature.
● Normal mode analysis is used to obtain the Rayleigh wave frequency equation at relevant boundary conditions.
● Relevant cobalt material parameter has been considered to demonstrate the variation of various parameters of Rayleigh wave propagation.
● Variation of non-dimensional speed, attenuation coefficient, penetration depth and specific loss has been demonstrated graphically.
● Variation of parameters have been compared within Lord-Shulman (L-S), Green-Nagdhi (GN-III) and Three phase lag theory of thermoelasticity.
This study looks at the mathematical model of internal atmospheric waves, often known as gravity waves, occurring inside a fluid rather than on the surface. Under the shallow-fluid assumption, internal atmospheric waves may be described by a nonlinear partial differential equation system. The shallow flow model's primary concept is that the waves are spread out across a large horizontal area before rising vertically. The Fractional Reduced Differential Transform Method(FRDTM) is applied to provide approximate solutions for any given model. This aids in the modelling of the global atmosphere, which has applications in weather and climate forecasting. For the integer-order value (α=1), the FRDTM solution is compared to the precise solution, EADM, and HAM to assess the correctness and efficacy of the proposed technique.
Highlights
● Under the shallow fluid assumption, the mathematical model of internal atmospheric waves is considered.
● In this model, waves are spread out across a large horizontal area before rising vertically.
● The fractional reduced differential transform method (FRDTM) is applied to find the approximate solution of time-fractional non-linear system of PDEs.
● The fractional solution provides a pragmatic look into the physical behaviour of internal waves, which can be helpful to refine climate and weather models.
● The obtained results have been compared with the numerical solution, EADM, and HAM for integer order to check the correctness and efficacy of the proposed technique.
The fundamental objective of this paper is to study the effectiveness of magnetic field and gravity on an isotropic homogeneous thermoelastic structure based on four theories of generalized thermoelasticity. In another meaning, the models of coupled dynamic theory (CDT), Lord-Shulman (LS), Green-Lindsay (GL) as well as Green-Naghdi (GN II) will be taken in the consideration. Then, applying the harmonic method (normal mode technique), the solution of the governing equations and the expressions for the components of the displacement, temperature and (Mechanical and Maxwell's) stresses is taken into account and calculated numerically. The impacts of the gravity and magnetic field are illustrated graphically which are pronounced on the different physical quantities. Finally, the results of some research that others have previously obtained may be found some or all of them as special cases from this study.
Highlights
Investigate conducting thermoelectric materials as a new class of applicable thermoelectric solids. The result provides a motivation to investigate conducting thermoelectric materials as a new class of applicable thermoelectric solids. The results presented in this paper should prove useful for researchers in material science, designers of new materials, physicists as well as for those working on the development of magneto-thermo-elasticity and in practical situations as in geophysics, optics, acoustics, geomagnetic and oil prospecting etc. The used methods in the present article are applicable to a wide range of problems in thermodynamics and thermoelasticity.
In this paper, the generalized dissipative Kawahara equation in the sense of conformable fractional derivative is presented and solved by applying the tanh-coth-expansion and sine-cosine function techniques. The quadratic-case and cubic-case are investigated for the proposed model. Expected solutions are obtained with highlighting to the effect of the presence of the alternative fractional-derivative and the effect of the added dissipation term to the generalized Kawahara equation. Some graphical analysis is presented to support the findings of the paper. Finally, we believe that the obtained results in this work will be important and valuable in nonlinear sciences and ocean engineering.
Highlights
● The conformable-time-fractional generalized dissipative Kawahara equation is presented and solved by using the tanh-coth-expansion and sine-cosine-function methods.
● The quadratic-case and cubic-case are investigated for the proposed model.
● The new solutions highlighted the effect of the presence of the alternative fractional-derivative and the effect of the added dissipation term to the generalized Kawahara equation.
● Some graphical analysis is presented to support the findings of the current work.
The Schrodinger equation type nonlinear coupled Maccari system is a significant equation that flourished with the wide-ranging arena concerning fluid flow and the theory of deep-water waves, physics of plasma, nonlinear optics, etc. We exploit the enhanced tanh approach and the rational (G′/G) -expansion process to retrieve the soliton and dissimilar soliton solutions to the Maccari system in this study. The suggested systems of nonlinear equations turn into a differential equation of single variable through executing some operations of wave variable alteration. Thereupon, with the successful implementation of the advised techniques, a lot of exact soliton solutions are regained. The obtained solutions are depicted in 2D, 3D, and contour traces by assigning appropriate values of the allied unknown constants. These diverse graphical appearances assist the researchers to understand the underlying processes of intricate phenomena of the leading equations. The individual performances of the employed methods are praiseworthy which justify further application to unravel many other nonlinear evolution equations ascending in various branches of science and engineering.
Highlights
● We have obtained new solitons for the coupled nonlinear Maccari's system describing the motion of isolated waves in fluid-flow.
● This model describes propagation of solitons in the theory of deep-water waves.
● Abundant closed form wave solutions are successfully generated in terms of rational, trigonometric and hyperbolic functions.
● The acquired solutions alongside particular values of involved free parameters are figured out in 3D, 2D and contour profiles to depict diverse soliton patterns.
In the field of maritime transport, motion and energy, the dynamics of deep-sea waves is one of the major problems in ocean science. A mathematical modeling of dynamics of solitary waves in deep sea under the two-layer stratification leads to NLS equation, and consequently, the interaction two of them can be formulated by coupled NLS equation. In this work, extended auxiliary equation and the exp(−Ï-(χ)) -expansion methods are employed to make the optical solutions of the Manakov model of coupled NLS equation. The methods used in this paper, in addition to providing the analysis of individual wave solutions, also provide general optical solutions. Some previously known solutions can be obtained by some special selections of parameters obtained by solving systems of algebraic equations. At this stage, it is more practical and convenient to apply methods with a symbolic calculation system.
Highlights
● Construction of optical soliton solutions Manakov model of coupled nonlinear Schrodinger equation.
● Applications of extended auxiliary equation methods.
● Hyperbolic, complex trigonometric, trigonometric and rational solutions.
● 3D, contour and 2D graphics for the solutions.
The Cahn-Hilliard system was proposed to the first time by Chan and Hilliard in 1958. This model (or system of equations) has intrinsic participation energy and materials sciences and depicts significant characteristics of two phase systems relating to the procedures of phase separation when the temperature is constant. For instance, it can be noticed when a binary alloy (“Aluminum + Zinc†or “Iron + Chromiumâ€) is cooled down adequately. In this case, partially or totally nucleation (nucleation means the appearance of nuclides in the material) is observed: the homogeneous material in the initial state gradually turns into inhomogeneous, giving rise to a very accurate dispersive microstructure. Next, when the time scale is slower the microstructure becomes coarse. In this work, to the first time, the unified method is presented to investigate some physical interpretations for the solutions of the Cahn-Hilliard system when its coefficients varying with time, and to show how phase separation of one or two components and their concentrations occurs dynamically in the system. Finally, 2D and 3D plots are introduced to add more comprehensive study which help to understand the physical phenomena of this model. The technique applied in this analysis is powerful and efficient, as evidenced by the computational work and results. This technique can also solve a large number of higher-order evolution equations.
Highlights
● Different wave structures for abundant solutions to the Chan–Hilliard system are investigated.
● Performance was done using the strategy of the unified method.
● Physical explanations are discussed for the obtained solutions.
Deep-sea submersibles are significant mobile platforms requiring multi-functional capabilities that are strongly determined by the constituent materials. Their cylindrical protective cover can be advanced by designing their sandwiched cellular materials whose physical properties can be readily parameterized and flexibly tuned. Porous honeycomb materials are capable of possessing tuned positive, negative, or zero Poisson's ratios (PPR, NPR, and ZPR), which is expected to produce distinct physical performance when utilized as a cellular core of cylindrical shells for the deep-sea submersibles. A novel cylindrical meta-structure sandwiched with the semi-re-entrant ZPR metamaterial has been designed as well as its similarly-shaped sandwich cylindrical shell structures with PPR and NPR honeycombs. The mechanical and vibroacoustic performance of sandwich cylindrical shells with cellular materials featuring a full characteristic range of Poisson's ratios are then compared systematically to explore their potential for engineering applications on submerged pressure-resistant structures. The respective unit cells are designed to feature an equivalent load-bearing capability. Physical properties of pressure resistance, buckling, and sound insulation are simulated, respectively, and the orders of each property are then generalized by systematic comparison. The results indicate that the PPR honeycomb core takes advantage of higher structural strength and stability while the ZPR one yields better energy absorption and sound insulation behavior. The NPR one yields moderate properties and has the potential for lower circumferential deformation. The work explores the application of cellular materials with varied Poisson's ratios and provides guidance for the multi-functional design of sandwich cylindrical meta-structures.
Highlights
● The properties of sandwich cylindrical shells with cellular materials with a full characteristic range of Poisson's ratios have been systematically compared.
● The PPR honeycomb core takes advantage of the highest structural strength and stability.
● The ZPR core yields the best energy absorption capability and sound insulation performance.
● The NPR honeycomb core yields moderate properties and has the potential for lower circumferential deformation.
Ensuring accurate parameter identification and diving motion prediction of marine crafts is essential for safe navigation, optimized operational efficiency, and the advancement of marine exploration. Addressing this, this paper proposes an instrumental variable-based least squares (IVLS) algorithm. Firstly, aiming to balance complexity with accuracy, a decoupled diving model is constructed, incorporating nonlinear actuator characteristics, inertia coefficients, and damping coefficients. Secondly, a discrete parameter identification matrix is designed based on this dedicated model, and then a IVLS algorithm is innovatively derived to reject measurement noise. Furthermore, the stability of the proposed algorithm is validated from a probabilistic point of view, providing a solid theoretical foundation. Finally, performance evaluation is conducted using four depth control datasets obtained from a piston-driven profiling float in Qiandao Lake, with desired depths of 30 m, 40 m, 50 m, and 60 m. Based on the diving dynamics identification results, the IVLS algorithm consistently shows superior performance when compared to recursive weighted least squares algorithm and least squares support vector machine algorithm across all depths, as evidenced by lower average absolute error (AVGAE), root mean square error (RMSE), and maximum absolute error values and higher determination coefficient (). Specifically, for desired depth of 60 m, the IVLS algorithm achieved an AVGAE of 0.553 m and RMSE of 0.655 m, significantly outperforming LS-SVM with AVGAE and RMSE values of 8.782 m and 11.117 m, respectively. Moreover, the IVLS algorithm demonstrates a remarkable generalization capability with values consistently above 0.95, indicating its robustness in handling varied diving dynamics.
Highlights
● Integration of measurement noise and nonlinear actuator traits refines dynamic environmental modeling.
● IVLS promotes noise-data independence, ensuring parameter convergence sans prior noise knowledge.
● Employing moderate depth data exemplifies successful marine craft motion modeling in real-world.
● Field data parameter identification and prediction are enhanced by superior IVLS over RWLS, LS-SVM.
This study establishes a common coupled fixed point for two pairs of compatible and sequentially continuous mappings in the intuitionistic fuzzy metric space that satisfy the Ï• -contractive conditions. Many basic definitions and theorems have been used from some recent scientific papers about the binary operator, t-norm, t-conorm, intuitionistic fuzzy metric space, and compatible mapping for reaching to the paper's purpose.
Highlights
● Coupled Fixed Point Theorems
● Contractive Condition
● Intuitionistic Fuzzy Metric Spaces.
