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Radiation of waves by a thin cap submerged in ice-covered ocean Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2020-09-19 Arijit Das; Soumen De; B N Mandal
The present article is concerned with the radiation of flexural gravity waves due to a thin cap submerged in the ice-covered ocean. The problem is reduced to a system of hypersingular integral equations using the boundary perturbation method. The first-order approximation has only been considered. The effects of the rigidity of the ice sheet and depth of submergence on the added mass and damping coefficient
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Four solutions of a two-cylinder electrostatic problem, and identities resulting from their equivalence Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2020-08-04 Lekner J.
SummaryFour distinct solutions exist for the potential distribution around two equal circular parallel conducting cylinders, charged to the same potential. Their equivalence is demonstrated, and the resulting analytical identities are discussed. The identities relate the Jacobi elliptic function $sn$, the Jacobi theta functions $\theta _1 ,~\theta _2 $ and infinite series over trigonometric and hyperbolic
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Capillary-gravity waves on the interface of two dielectric fluid layers under normal electric fields Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2020-06-05 A Doak; T Gao; J -M Vanden-Broeck; J J S Kandola
In this article, we consider capillary-gravity waves propagating on the interface of two dielectric fluids under the influence of normal electric fields. The density of the upper fluid is assumed to be much smaller than the lower one. Linear and weakly nonlinear theories are studied. The connection to the results in other limit configurations is discussed. Fully nonlinear computations for travelling
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A Singular Nonlinear History-Dependent Cohesive Zone Model: Is it Possible? Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2020-05-20 I I Argatov
A history-dependent cohesive zone model is considered in the linear elasticity framework with the cohesive stresses governed by the fracture condition formulated in terms of a nonlinear Abel-type integral operator. A possibility for the cohesive stresses to possess a weak singularity has been examined by utilizing asymptotic modeling approach. It has been shown that the balance of the leading-term
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Regularity of Desingularized Models for Vortex Filaments in Incompressible Viscous Flows: A Geometrical Approach Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2020-05-20 Siran Li
We establish the regularity of weak solutions for the vorticity equation associated to a family of desingularized models for vortex filament dynamics in 3D incompressible viscous flows. These generalize the classical model ‘of an allowance for the thickness of the vortices’ due to Louis Rosenhead in 1930. Our approach is based on an interplay between the geometry of vorticity and analytic inequalities
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Some Universal Solutions for a Class of Incompressible Elastic Body that is Not Green Elastic: The Case of Large Elastic Deformations Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2020-04-04 R Bustamante
Some universal solutions are studied for a new class of elastic bodies, wherein the Hencky strain tensor is assumed to be a function of the Kirchhoff stress tensor, considering in particular the case of assuming the bodies to be isotropic and incompressible. It is shown that the families of universal solutions found in the classical theory of nonlinear elasticity, are also universal solutions for this
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‘Killing Mie Softly’: Analytic Integrals for Complex Resonant States Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2020-03-20 R C Mcphedran; B Stout
We consider integrals of products of Bessel functions and of spherical Bessel functions, combined with a Gaussian factor guaranteeing convergence at infinity. These integrals arise in wave and quantum mechanical scattering problems of open systems containing cylindrical or spherical scatterers, particularly when those problems are considered in the framework of complex resonant modes. Explicit representations
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Image Conditions for Elliptical-Coordinate Separation-of-Variables Acoustic Multiple Scattering Models with Perfectly Reflecting Flat Boundaries: Application to in Situ Tunable Noise Barriers Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2020-03-02 Ho-Chul Shin
Two-dimensional time-harmonic multiple scattering problems are addressed for a finite number of elliptical objects placed in wedge-shaped acoustic domains including half-plane and right-angled corners. The method of separation of variables in conjunction with the addition theorems is employed in the elliptical coordinates. The wavefunctions are represented in terms of radial and angular Mathieu functions
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Asymptotic Field Near the Tip of a Debonded Anticrack in an Anisotropic Elastic Material Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2020-02-20 Xu Wang; Peter Schiavone
We use the sextic Stroh formalism to study the asymptotic elastic field near the tip of a debonded anticrack in a generally anisotropic elastic material under generalised plane strain deformations. The stresses near the tip of the debonded anticrack exhibit the oscillatory singularities |$r^{-3/4\pm i\varepsilon }$| and |$r^{-1/4\pm i\varepsilon }$| (where |$\varepsilon $| is the oscillatory index)
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Converging shock waves in a Van der Waals gas of variable density Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2020-02-15 Antim Chauhan; Rajan Arora; Amit Tomar
The converging problem of cylindrically or spherically symmetric strong shock wave collapsing at the axis/centre of symmetry, is studied in a non-ideal inhomogeneous gaseous medium. Here, we assume that the undisturbed medium is spatially variable and the density of a gas is decreasing towards the axis/centre according to a power law. In the present work, we have used the perturbation technique to
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Asymptotic Approximant for the Falkner–Skan Boundary Layer Equation Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2020-02-10 E R Belden; Z A Dickman; S J Weinstein; A D Archibee; E Burroughs; N S Barlow
We demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., Q. J. Mech. Appl. Math. 70 (2017) 21–48.) yields accurate analytic closed-form solutions to the Falkner–Skan boundary layer equation for flow over a wedge having angle |$\beta\pi/2$| to the horizontal. A wide range of wedge angles satisfying |$\beta\in[-0.198837735, 1]$| are considered
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On the Connection Between Step Approximations and Depth-Averaged Models for Wave Scattering by Variable Bathymetry Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2020-02-03 R Porter
Two popular and computationally inexpensive class of methods for approximating the propagation of surface waves over two-dimensional variable bathymetry are ‘step approximations’ and ‘depth-averaged models’. In the former, the bathymetry is discretised into short sections of constant depth connected by vertical steps. Scattering across the bathymetry is calculated from the product of |$2 \times 2$|
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Hypersingular Integral Equations Arising in the Boundary Value Problems of the Elasticity Theory Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2020-01-24 S M Mkhitaryan; M S Mkrtchyan; E G Kanetsyan
The exact solutions of a class of hypersingular integral equations with kernels |$\left( {s-x} \right)^{-2}$|, |$\left( {\sin \frac{s-x}{2}} \right)^{-2}$|, |$\left( {\sinh \frac{s-x}{2}} \right)^{-2},\cos \frac{s-x}{2}\left( {\sin \frac{s-x}{2}} \right)^{-2}$|, |$\cosh \frac{s-x}{2}\left( {\sinh \frac{s-x}{2}} \right)^{-2}$| are obtained where the integrals must be interpreted as Hadamard finite-part
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Periodic Auxetics: Structure and Design. Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2018-06-26 Ciprian S Borcea,Ileana Streinu
Materials science has adopted the term of auxetic behavior for structural deformations where stretching in some direction entails lateral widening, rather than lateral shrinking. Most studies, in the last three decades, have explored repetitive or cellular structures and used the notion of negative Poisson's ratio as the hallmark of auxetic behavior. However, no general auxetic principle has been established
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A Note on Viscous Flow Induced by Half-Line Sources Bounded by Conical Surfaces Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2019-10-21 Prabakaran Rajamanickam; Adam D Weiss
In this article, axisymmetric solutions of the Navier–Stokes equations governing the flow induced by a half-line source when the fluid domain is bounded by a conical wall are discussed. Two types of boundary conditions are identified; one in which the radial velocity along the axis is prescribed, and the other in which the radial velocity along the axis is obtained as an eigenvalue of the problem.
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Time to Approach Similarity Q. J. Mech. Appl. Math. (IF 1.265) Pub Date : 2019-10-11 Joseph J Webber; Herbert E Huppert
In a recent article, Ball and Huppert (J. Fluid Mech., 874, 2019) introduced a novel method for ascertaining the characteristic timescale over which the similarity solution to a given time-dependent nonlinear differential equation converges to the actual solution, obtained by numerical integration, starting from given initial conditions. In this article, we apply this method to a range of different