Journal of Engineering Mathematics最新文献

Immersed boundary (IB) methods have been successfully implemented for different applications. This paper focuses on the immersed boundary implementation for two different governing equations, namely the diffusion equation and Euler equations, using a bi-linear interpolation for the implementation of the boundary condition. The concept of implicit interpolation is introduced which eradicates the problems faced with the explicit interpolation in which it is required to move away from the boundary in the fluid domain in order to complete the interpolation stencil.

The total evaporation rate due to a volatile capillarity-dominated droplet diffusively evaporating into the surrounding gas is a critically important quantity in industrial and engineering applications such as Q/OLED screen manufacturing. However, the analytical expression in terms of integrals in toroidal coordinates can be unwieldy in applications, as well as expensive to compute. Therefore, simple yet highly accurate approximate solutions are frequently used in practical settings. Herein we present a new approximate form that is both accurate and fast to compute, but also retains the correct asymptotic behaviour in the key physical regimes, namely hydrophilic and superhydrophobic substrates, and a hemispherical droplet. We illustrate this by comparison to several previous approximations and, in particular, illustrate its use in calculating droplet lifetimes, as well as approximating the local evaporative flux.

Two-dimensional (2-D) direct numerical simulations of a compound droplet (a non-magnetizable droplet wrapped in a ferrofluid droplet) suspended in a non-magnetizable ambient fluid under a rotating uniform magnetic field are carried out. The motion and deformation of the compound droplet are studied. The numerical results show that there are two stable states (the concentric and the eccentric states) for the compound droplet at the stable stage, dependent on the frequency of the rotating magnetic field and the magnetic Bond number. The feature of the concentric state for the compound droplet at the stable stage is studied in detail. We find that the inner and outer parts of the compound droplet rotate with the magnetic field, while there is hysteresis between the inner (or outer) droplet and the external magnetic field. The hysteresis effect for the inner droplet is weaker than that of the outer droplet, mainly due to the viscous sweeping effect of the outer droplet on the inner droplet. Increasing the frequency of the external magnetic field, both the phase angle between the inner and outer droplets and the time required for the compound droplet to shift from the stable eccentric state to the stable concentric one will increase. For the eccentric state at the stable stage, the eccentricity decreases with the frequency of the rotating magnetic field increasing, but has a peak with the magnetic Bond number increasing. It is hoped that this paper would lay a solid foundation for some potential applications in magnetic biodevices.

In this work, an extended Euler–Bernoulli beam equation is addressed, where numerous phenomena are covered including damping, time-delay, and nonlinear source effects. A generalized fractional derivative is used to model dissipation of order less than one, which offers more flexibility for modeling tasks. Through a diffusive representation, the problem well-posedness is tackled and the exponential decay of the energy associated to global solutions is proved under some conditions. In order to validate our theoretical findings, we implement a finite difference scheme and we elucidate that the boundedness of the local propagation matrix may be inaccurate for the convergence evaluation in some situations. Furthermore, we show that deep neural networks are efficient alternatives to deal with computational and stability burdens resulting from the mesh refinement in standard numerical schemes.

Spaceborne SAR Interferometry techniques namely Differential SAR Interferometry (DInSAR) and Persistent Scatterer Interferometry (PSI) are remote sensing-based techniques used to measure and monitor terrain deformations. In the present study, advances in PSI since its inception, considering three important parameters (pixel selection criteria, baseline configuration, and deformation model) is discussed in detail. Further, in view of the research heading towards the pixel selection criteria and phase optimization of Distributed Scatterers (DSs) pixels, detailed discussion is made over its advancement also. In addition, the statistical homogenous pixel (SHP) and the similar time-series interferometric phase (STIP) pixel-based PSCs selection are the latest development. In view of this, the connection and difference of major and latest SHP and STIP pixel-based PSCs selection methods in term of the mathematic model of phase optimization for conventional DS and DS with multiple scattering mechanism (DS-MSM), types of pixel selection capability, computational efficiency are characterized. Further, in this study, a novel Bayesian methodology and its details are proposed for the phase optimization of DS pixels, which will provide a much better idea of the characteristics of the parameter of interest than latest one based on complex least square mathematic model for phase optimization of DS pixels.

This article introduces a proficient method for solving both linear and nonlinear second-order singular value differential equations within the framework of Fibonacci wavelets and the collocation technique. Two key theorems are presented to facilitate a discussion on the convergence analysis of the method. The efficacy, ease of application, and computational speed of this approach are demonstrated through its application to diverse problem scenarios. The resulting solutions are compared with existing numerical solutions, further affirming the correctness and effectiveness of the proposed method. Notably, the method consistently yields solutions that align with the exact answers for a multitude of issues. Graphs and figures are employed to visually demonstrate the higher accuracy achieved by the Fibonacci wavelet approach for specific problems. All calculations and data processing are conducted using MATLAB software.

Abstract

The present study examines the impact of effective viscosity and suction/injection on the two-dimensional boundary layer flow and heat transfer across a wedge immersed in a porous medium. In this study, we analyze the mechanisms associated with porous media and the fluid, focusing specifically on the viscosity ratio(effective viscosity to the dynamic viscosity) effects. The movement or progression of the fluid outside the boundary layer is acquired in the form of a concept of fluid distance. The governing nonlinear ordinary differential equations are derived from the boundary layer equations with suitable similarity transformations. Two approaches are utilized in this study: comprehensive numerical simulations that solve the nonlinear fully coupled fluid-wedge interaction issue and asymptotic approaches that solve the linearized equation-acquired at a significant distance away from the wedge and a small Prandtl number. A high level of concordance exists between the two methodologies in their predictive capabilities. The velocity and temperature distributions for different favorable pressure gradient and suction parameters are to reduce both momentum and thermal boundary layer thickness, while an opposite scenario is noticed for injection parameters. These results are shown to be a continuation of classical Falkner-Skan flows. The viscosity ratio plays a role in reducing the thickness of the boundary layer, leading to the fluid exhibiting adhesion to the surface of the wedge. Moreover, the effect of permeability-the presence of a porous medium, reduces the thickness of the boundary layer. A comprehensive examination of the outcomes and their associated hydrodynamics concerning the physical parameters is conducted and made in some detail.

This study employs the two-dimensional nonlinear Stokes ice sheet model and a Galerkin least-squares (GLS) finite element method to investigate iceberg calving at the terminus of tidewater glaciers. We propose an approach based on pressure and normal stress solutions to adjust the grounding line position and present effective principal stress contours and profiles for grounded and notch glaciers with basal crevasses at the grounding line. Our results indicate that the openings of these basal crevasses are significantly affected by water pressure. In addition, stress profiles in ungrounded tidewater glaciers vary from those in fully grounded tidewater glaciers, which could affect iceberg calving. We also conduct numerical experiments to analyze the effects of slip length, notch length, and surface slope and examine the effectiveness of the GLS method in numerical solutions. Our results are in agreement with prior findings in the literature that basal crevasses are significantly affected by water pressure, and stress profiles are significantly different in grounded and ungrounded tidewater glaciers.

Abstract

Natural icicles have an overall conical shape modulated by surface ripples. It has been noted from many observations of icicles formed in nature and in the laboratory that the wavelength of the ripples has a very narrow spectrum between about 8 and 12 mm and that, as time evolves, the phase of the ripples migrates upwards. In this pedagogical review, I explore some of the physical mechanisms that can cause and mediate the formation and migration of ripples on icicles using simple mathematical models. To keep the mathematics more straightforward and transparent, I confine attention to two dimensions. A key physical parameter is the surface tension between the film of water that coats an icicle and the air that surrounds it, which causes a phase shift between the film–air interface and the ice–film interface. I show that the wavelength of ripples is dominantly proportional to the cube root of the square of the gravity-capillary length times the thickness of the water film. At high film-flow rates, advection-dominated heat transfer coupled with the interfacial phase shift becomes the dominant driver of instability. Gibbs–Thomson undercooling provides an unexpectedly large stabilisation of small wavelengths at these large flow rates, sufficient to maintain wavelength selection at millimetre scales.