The solution of singular two-point boundary value problem is usually not sufficiently smooth at one or two endpoints of the interval, which leads to a great difficulty when the problem is solved numerically. In this paper, an algorithm is designed to recognize the singular behavior of the solution and then solve the equation efficiently. First, the singular problem is transformed to a Fredholm integral

The present paper aims to investigate the transport of suspended sediment in an open channel turbulent flow. The method of moments is used to solve the unsteady two-dimensional suspended sediment transport equation where the moment equations are evaluated using a standard finite difference implicit scheme. The distribution of concentration is obtained using the Hermite polynomial representation of

Water wave scattering by two asymmetric thin elastic plates with arbitrary inclinations is investigated using integral equations. The plates are submerged in finite depth water. The assumption of Euler–Bernoulli beam model for the plates, the use of the appropriate Euclidean transformations to handle the fifth-order plate conditions and the application of Green’s function technique allow us to obtain

Finite-amplitude free-surface flow in a wedge container is investigated analytically. We study a motionless standing wave of pure potential-flow acceleration with maximal amplitude where its right-angle surface peak falls from rest. The nonlinear free-surface conditions are satisfied by a family of flows where the chosen initial acceleration field is governed by one single dipole plus its three image

In this research paper, the diffraction of a Griffith crack, situated in an infinite strip of finite thickness, due to magnetoelastic shear wave propagation has been analyzed. The effect of magnetic field on the Griffith crack interaction has been studied. Fourier transform is used to reduce the mixed boundary value problem to the dual integral equations. Finally, with the help of Abel’s transform

We model shallow-water waves using a one-dimensional Korteweg–de Vries equation with the wave generation parameterized by random wave amplitudes for a predefined sea state. These wave amplitudes define the high-dimensional stochastic input vector for which we estimate the short-term wave crest exceedance probability at a reference point. For this high-dimensional and complex problem, most reliability

In the present study, the effects of different types of basic temperature and concentration gradients on a layer of reactive fluid under variable gravity field are analyzed using linear and non-linear analysis. Energy method is applied to obtain the non-linear energy threshold below which the solution is globally stable. It is found that the linear and non-linear analysis are not in agreement for the

In this paper, we investigate the limits of Riemann solutions to the Euler equations of compressible fluid flow with a source term as the adiabatic exponent tends to one. The source term can represent friction or gravity or both in Engineering. For instance, a concrete physical model is a model of gas dynamics in a gravitational field with entropy assumed to be a constant. The body force source term

It is a well-known fact that the onset of Rayleigh–Bénard convection occurs via a long-wavelength instability when the horizontal boundaries are thermally insulated. The aim of this paper is to quantify the exact dimensions of a cylinder of rectangular cross-section wherein stable three-dimensional Rayleigh–Bénard convection sets in via a long-wavelength instability from the motionless state at the

The purpose of this article is to construct a firm mathematical foundation for the boundary value problem associated with a generalized Emden equation that embraces Thomas–Fermi-like theories. Boundary value problems for the relativistic and non-relativistic Thomas–Fermi equations are included as special cases. Questions of existence and uniqueness of solutions to these boundary value problems form

In the present work, the band-pass filter characteristics of a coaxial waveguide with an impedance coated groove on the inner wall and perfectly conducting outer wall is analyzed rigorously through the Wiener–Hopf technique. By using the direct Fourier transform, the related boundary value problem is reduced to the Wiener–Hopf equation whose solution contains infinitely many constants satisfying an

Investigated in this paper is the coupled fluid–body motion of a thin solid body undergoing a skimming impact on a shallow-water layer. The underbody shape (the region that makes contact with the liquid layer) is described by a smooth polynomic curve for which the magnitude of underbody thickness is represented by the scale parameter C. The body undergoes an oblique impact (where the horizontal speed

Because of geometric or material discontinuities, stress singularities can occur around the vertex of a V-notch. The singular order is an important parameter for characterizing the degree of the stress singularity. The present paper focuses on the calculation of the singular order for the anti-plane propagating V-notch in a composite material structure. Starting from the governing equation of elastodynamics

A ferrofluid saturated porous layer convection problem is studied in the variable gravitational field for a local thermal nonequilibrium (LTNE) model. Internal heating and variation (increasing or decreasing) in gravity with distance through the layer affected the stability of the convective system. The Darcy model is employed for the momentum equation and the LTNE model for the energy equation. The

A third-order highly non-linear ODE that arises in applications of non-Newtonian boundary-layer fluid flow, governed by a power-law Ostwald–de Waele rheology, is considered. The model appears in many disciplines related to applied and engineering mathematics, in addition to engineering and industrial applications. The aim is to use a new set of variables, defined via the first and second-order derivatives

For a pulsating free surface source in a three-dimensional finite depth fluid domain, the Green function of the source presented by John [Communs. Pure Appl. Math. 3:45–101, 1950] is superposed as the Rankine source potential, an image source potential and a wave integral in the infinite domain \((0, \infty )\). When the source point together with a field point is on the free surface, John’s integral

An effective-medium theory for the electrical conductivity of Ohmic dispersions taking explicit account of particle shape and spatial distribution independently is available from the work of Ponte Castañeda and Willis [J Mech Phys Solids 43:1919–1951, 1996]. When both shape and distribution take particular “ellipsoidal” forms, the theory provides analytically explicit estimates. The purpose of the

A recent asymptotic model for the operation of a vanadium redox flow battery (VRFB) is extended to include the dissociation of sulphuric acid—a bulk chemical reaction that occurs in the battery’s porous flow-through electrodes, but which is often omitted from VRFB models. Using asymptotic methods and time-dependent two-dimensional numerical simulations, we show that the charge–discharge curve for the

As an extension of the discrete Sommerfeld problems on lattices, the scattering of a time-harmonic wave is considered on an infinite square lattice when there exists a pair of semi-infinite cracks or rigid constraints. Due to the presence of stagger, also called offset, in the alignment of the defect edges the asymmetry in the problem leads to a matrix Wiener–Hopf kernel that cannot be reduced to scalar

The algebraic and semi-algebraic formulations of a new multiscale elliptic solver based on a non-overlapping domain decomposition method are presented. By algebraic we mean that all information needed to implement the proposed procedure can be extracted from the underlying fine grid finite volume linear system. In addition to the entries of this linear system, the proposed semi-algebraic procedure

Hyperbolic towers are towers in the shape of a single-sheet hyperboloid, and they are interesting in architecture. In this paper, we deal with the infinitesimal bending of a curve on a hyperboloid of one sheet; that is, we study the flexibility of the net-like structures used to make a hyperbolic tower. Visualization of infinitesimal bending has been carried out using Mathematica, and some examples

We find a general method to obtain the radially symmetric solutions of Dirichlet problem for Pennes bioheat equation in the exterior domain of a circle through the computation of Green’s function of a naturally related operator. We apply this technique to solve a problem in radio-frequency ablation.

The radiative–conductive transfer equation in the \(S_N\) approximation for spherical geometry is solved using a modified decomposition method. The focus of this work is to show how to distribute the source terms in the recursive equation system in order to guarantee arithmetic stability and thus numerical convergence of the obtained solution, guided by a condition number criterion. Some examples are

In geo-engineering, mechanical problems of surcharge loads acting on ground surface and shallow tunnel excavation are often encountered. When the complex variable method is applied, such problems turn to non-zero resultant issues and generally result in infinite displacement singularity in geomaterial at infinity, which violates the fact that displacement components at infinity should be zero in field

The problem of oblique scattering of surface waves by a thick partially immersed rectangular barrier or a thick submerged rectangular barrier extending infinitely downwards in deep water is studied here to obtain the reflection and transmission coefficients semi-analytically. Use of Havelock’s expansion of water wave potential function reduces each problem to an integral equation of first kind on the

Localized buckling modes in the axially compressed strut on a distributed-spring elastic foundation with a softening quadratic nonlinearity are numerically calculated based on a modified Petviashvili method in the spatial frequency domain. As the load decreases (increases), the maximum displacement of the corresponding localized buckling mode increases (decreases) and its width decreases (increases)

In the point-particle model of disperse multiphase flow, the particles, assumed to be very small compared with all the scales of the flow, are represented by singular forces acting on the fluid. The hydrodynamic forces are found from standard correlations by interpolating the velocity field from the grid nodes to the particle positions, with the implicit assumption that the computational cells are

For stability analysis of shallow shield tunnels in cohesive-frictional (clayey–sandy) soils, an analytical method of continuous upper bound limit analysis is developed to determine the most critical slip line position and the minimum required tunnel support pressure. The ground displacement field due to composite volume loss is calculated using a complex variable solution, and the optimization problem

The paper presents analytical and numerical results of radiation phenomena at the far field and solution of the acoustic wave equation with boundary conditions imposed by the pipe wall. A semi-infinite pipe with partial lining and interior perforated screen is considered. The study is important because of its applications in noise reduction in exhausts of automobile engines, in modern aircraft jet

In the hot end of a 3-D printer, polymer feedstock flows through a heated cylinder in order to become pliable. This setup determines a natural upper limit to the speed at which the polymer may be extruded. The case of polymers which undergo the crystalline-melt transition is considered; the resulting mathematical model is a Stefan-like moving boundary-value problem for the polymer temperature. Using

Multi-parameter sensitivity algorithms can be used to construct a Hessian matrix and second-degree Taylor expansion. In terms of an asymmetric dynamic system, two multi-parameter sensitivity algorithms are proposed in this paper. The modal method with its consistence proof is firstly derived to compute the first- and second-order sensitivities of the eigenpair, and the algebraic method with its stability

Thermal electrochemical models for porous electrode batteries (such as lithium ion batteries) are widely used. Due to the multiple scales involved, solving the model accounting for the porous microstructure is computationally expensive; therefore, effective models at the macroscale are preferable. However, these effective models are usually postulated ad hoc rather than systematically upscaled from

The stability of some simple density profiles in a vertically orientated two-dimensional porous medium is considered. The quasi-steady-state approximation is made so that the stability of the system can be approximated. As the profiles diffuse in time, the instantaneous growth rates evolve in time. For an initial step function density profile, the instantaneous growth rate was numerically found to

A novel nonlinear delayed susceptible–vaccinated–infected–recovered–susceptible (SVIRS) epidemic model with a Holling type II incidence rate for fully susceptible and vaccinated classes, a saturated treatment rate, and an imperfect vaccine given to susceptibles is proposed herein. Analysis of the model shows that it exhibits two equilibria, namely disease-free and endemic. The basic reproduction number

The purpose of this study is to theoretically probe how the joint effects of near-field source and surface topography impact the seismic wavefields. A simplified canyon model, which couples a semicircular model with a model for minor segments, is used to predict characteristic changes in ground motions due to line-source excitation. Based on a semi-analytical procedure using the region-matching technique

The redraw process is a method employed for the manufacture of glass sheets required for example special optical filters, bendable displays, or wearable devices. During this process, a glass block is fed into a heater zone and drawn off to reduce its thickness. Fluctuations in the feed speed, the draw speed or the ambient temperature can all lead to irregularities in the final thickness profile. We

The \(3\omega \) method may be used to estimate the thermal conductivity of an electrically conducting wire. In this method, an alternating voltage with an angular frequency \(\omega \) is applied to the wire. The resulting low electrical tension \(U_{3\omega }\) of angular frequency \(3\omega \) that appears in the total electrical tension is extracted by a lock-in amplifier. The amplitude of \(U_{3\omega

In accord with the analysis by Emanuel [J Eng Math, 117:79–105, 2019], the upstream and downstream vorticities are provided for an unsteady, three-dimensional shock, where the upstream flow may be non-uniform. The transformation for the upstream velocity Taylor series coefficients, \(e_{ij}^{*}\rightarrow e_{ij}\), is also provided. The analytic approach is illustrated for the vorticity with a simplified

In a recent paper, Al-Housseiny and Stone (J Fluid Mech 706:597–606, 2012) considered the dynamics of a stretching surface and how this interacts with the boundary-layer flow it generates. These authors discussed the cases \(c= -3\) for an elastic sheet and \(c= -1\) for the viscous fluid, c being representative for the stretching velocity of the sheet. The aim of the present paper is to extend the

The influence of dispersion or equivalently of the Péclet number (Pe) on miscible viscous fingering in a homogeneous porous medium is examined. The linear optimal perturbations maximizing finite-time energy gain is demonstrated with the help of the propagator matrix approach based non-modal analysis (NMA). We show that onset of instability is a monotonically decreasing function of Pe and the onset

A theoretical approach is taken into consideration to investigate the propagation behaviour of shear acoustic waves in a piezoelectric cylindrical layered structure composed of a piezoelectric material cylinder imperfectly bonded to a concentric functionally graded piezoelectric material (FGPM) cylindrical layer of finite width. The functional gradient in the FGPM cylindrical layer is considered to

We study the shear-driven instability, of Kelvin–Helmholtz type, that forms at the interface between a cylindrical jet of flowing fluid and its surroundings. The results of an infinitesimal-amplitude theory based on linearising the system about the undisturbed jet are given. A novel numerical model based on the Galerkin spectral method is developed and employed to simulate the non-linear development

Recent work highlighting an anomaly in the modelling of rotary electromagnetic stirring (EMS) in the continuous casting of round steel billets is extended to the case of longitudinal stirring for rectangular blooms. An earlier, still often-cited, model forms the basis of the current analysis, which uses asymptotic methods on the three-dimensional (3D) Maxwell equations and demonstrates how the earlier

We consider the diffusion-limited evaporation of thin two-dimensional sessile droplets either singly or in a pair. A conformal-mapping technique is used to calculate the vapour concentrations in the surrounding atmosphere, and thus to obtain closed-form solutions for the evolution and the lifetimes of the droplets in various modes of evaporation. These solutions demonstrate that, in contrast to in

A model is presented for the dewatering of a saturated two-phase medium in a screw press. The model accounts for the detailed two-phase rheological behaviour of the pressed material and splits the press into two zones, an initial well-mixed constant-pressure region followed by an axial transport region in which the total pressure steadily increases. In this latter region, a slowly varying helical coordinate

The present article gives an analysis of the impact of Darcy–Forchheimer flow and partial slip along with heat transfer in single-wall carbon nanotube/multi-wall carbon nanotube (SWCNT/MWCNT)-water nanofluid flow over a stretching/shrinking rotating disk. The study considers the heat transfer in nanofluids, using both static and dynamic models, namely the Xue and Buongiorno models, respectively. The

A mathematical model for thermosolutal convection flow in an open two-dimensional vertical channel containing a porous medium saturated with reactive Newtonian fluid is developed and studied. Robin boundary conditions are prescribed, and a first-order homogenous chemical reaction is considered. The Darcy–Forchheimer model is used to simulate both the first- and second-order porous mediums’ drag effects

The study of the oscillation periods of suspended wires has an engineering background in the oscillation of electric transmission lines. However, the oscillation periods of suspended wires have not yet been thoroughly studied, especially in terms of comparative analysis of their oscillation periods with and without the effect of bending deformation energy. Herein, mathematical expressions for the oscillation

The coupled motion of shallow-water sloshing in a horizontally translating upright annular vessel is considered. The vessel’s motion is restricted to a single space dimension, such as for Tuned Liquid Damper systems. For particular parameters, the system is shown to support an internal 1 : 1 resonance, where the frequency of coupled sloshing mode which generates the vessel’s motion is equal to the

A mathematical framework for the coupling of gas networks to electric grids is presented to describe in particular the transition from gas to power. The dynamics of the gas flow are given by the isentropic Euler equations, while the power flow equations are used to model the power grid. We derive pressure laws for the gas flow that allow for the well-posedness of the coupling and a rigorous treatment

We consider the inverse problem of reconstructing the interior boundary curve of a doubly connected bounded domain from the knowledge of the temperature and the thermal flux on the exterior boundary curve. The use of the Laguerre transform in time leads to a sequence of stationary inverse problems. Then, the application of the modified single-layer ansatz reduces the problem to a sequence of systems

Since dispersion is one of the key parameters in solute transport, its accurate modeling is essential to avoid wrong predictions of flow and transport behavior. In this research, we derive new effective dispersion models which are valid also in evolving geometries. To this end, we consider reactive ion transport under dominate flow conditions (i.e. for high Peclet number) in a thin, potentially evolving

New analytical representations of the Stokes flows due to periodic arrays of point singularities in a two-dimensional no-slip channel and in the half-plane near a no-slip wall are derived. The analysis makes use of a conformal mapping from a concentric annulus (or a disc) to a rectangle and a complex variable formulation of Stokes flow to derive the solutions. The form of the solutions is amenable

This paper presents a conservative finite difference scheme for solving the N -component Cahn–Hilliard (CH) system on curved surfaces in three-dimensional (3D) space. Inspired by the closest point method (Macdonald and Ruuth, SIAM J Sci Comput 31(6):4330–4350, 2019), we use the standard seven-point finite difference discretization for the Laplacian operator instead of the Laplacian–Beltrami operator

This study addresses the sloshing characteristics of a liquid contained in a tank with a vertical baffle mounted at the bottom of the tank. Liquid sloshing characteristics are studied through an analytical solution procedure based on the linear velocity potential theory. The tank is forced to sway horizontally and periodically, while the baffle is fixed to the tank or rolling around a hinged point

An arterial dissection is a longitudinal tear in the vessel wall, which can create a false lumen for blood flow and may propagate quickly, leading to death. We employ a computational model for a dissection using the extended finite element method with a cohesive traction-separation law for the tear faces. The arterial wall is described by the anisotropic hyperelastic Holzapfel-Gasser-Ogden material

The unsteady viscous flow induced by streamwise-travelling waves of spanwise wall velocity in an incompressible laminar channel flow is investigated. Wall waves belonging to this category have found important practical applications, such as microfluidic flow manipulation via electro-osmosis and surface acoustic forcing and reduction of wall friction in turbulent wall-bounded flows. An analytical solution

A meshless method is proposed to simulate fully nonlinear wave–wave and wave–current interactions in the time domain. The fully nonlinear free surface motion is simulated using the local radial point interpolation collocation method (LRPICM), material node approach, and fourth-order Runge–Kutta method (RK4). LRPICM is a truly meshless method and efficient for moving-boundary problems. Potential theory

Fins are surface extensions used to increase the rate of heat transfer from a heated surface to the surrounding cooler fluid or from a heated fluid to the surface. In this article, we describe new families of straight and pin fins for which the temperature distribution along the fin as well as fin effectiveness and efficiency can be computed in closed form. The profile of the new straight fin is a

The numerical simulations of the dynamics of high Reynolds number (\(Re>100{,}000\)) swirling flows in pipes with varying geometries of engineering applications continues to be a challenging computational problem, specifically when vortex-breakdown zones or wall-separation regions naturally evolve in the flows. To tackle this challenge, the present paper describes a simulation scheme of the evolution