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High-Impact Research from The Quarterly Journal of Mechanics & Applied Mathematics

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Explore a collection of the most read and most cited articles making an impact in the Quarterly Journal of Mechanics and Applied Mathematics published within the past two years. This collection will be continuously updated with the journal's leading articles so be sure to revisit periodically to see what is being read and cited.

Also discover the articles being discussed the most on digital media by exploring this Altmetric report pulling the most discussed articles from the past year.

Most cited

Diffraction by a Right-Angled No-Contrast Penetrable Wedge: Analytical Continuation of Spectral Functions
V D Kunz and R C Assier
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 76, Issue 2, May 2023, Pages 211–241, https://doi.org/10.1093/qjmam/hbad002
We study the problem of diffraction by a right-angled no-contrast penetrable wedge by means of a two-complex-variable Wiener–Hopf approach. Specifically, the analyticity properties of the unknown (spectral) functions of the two-complex-variable Wiener–Hopf equation are studied. We show that these spectral functions can be ...
Theory of Perturbation of Electrostatic Field By A Coated Anisotropic Dielectric Sphere
Nikolaos L Tsitsas and others
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 76, Issue 3, August 2023, Pages 297–314, https://doi.org/10.1093/qjmam/hbad005
A boundary-value problem was formulated for perturbation of an electrostatic field by a coated dielectric sphere made of two distinct linear anisotropic dielectric (LAD) materials. Specific affine transformations were employed to represent the electric potential inside the core and the coating in terms of the solutions of ...
Homogenisation of Nonlinear Heterogeneous Thin Plate When the Plate Thickness and In-Plane Heterogeneities are of the Same Order of Magnitude
E Pruchnicki
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 76, Issue 2, May 2023, Pages 277–295, https://doi.org/10.1093/qjmam/hbad004
In this work, we propose a new two-scale finite-strain thin plate theory for highly heterogeneous plates described by a repetitive periodic microstructure. For this type of theory, two scales exist, the macroscopic one is linked to the entire plate and the microscopic one is linked to the size of the heterogeneity. We ...
Linear stability of a compressible flow in a channel
M Deka and others
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 76, Issue 4, November 2023, Pages 405–434, https://doi.org/10.1093/qjmam/hbad010
Modal instabilities in a compressible flow through a channel at high Reynolds numbers are studied for three-dimensional (3D) perturbations. In addition to the Tollmien–Schlichting (TS) mode, there exist compressible modes in a channel flow that do not have a counterpart in the incompressible limit. The stability ...
A contribution to the mathematical theory of diffraction. Part II: Recovering the far-field asymptotics of the quarter-plane problem
R C Assier and others
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 77, Issue 1-2, February-May 2024, hbae005, https://doi.org/10.1093/qjmam/hbae005
We apply the stationary phase method developed in Assier, Shanin and Korolkov, QJMAM , 76 (2022) to the problem of wave diffraction by a quarter-plane subjected to Dirichlet boundary conditions. The wave field is written as a double Fourier transform of an unknown spectral function. We make use of the analytical ...
Analytical insights into semi-infinite plate scattering: the wiener–hopf technique and two-sided linear boundary conditions
A D G Hales and L J Ayton
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 77, Issue 1-2, February-May 2024, hbae003, https://doi.org/10.1093/qjmam/hbae003
The Wiener–Hopf Technique is popular throughout applied mathematics, particularly for wave scattering problems. One such problem is the scattering of an incident wave impinging upon a semi-infinite surface. For scattering problems in which one applies separate boundary conditions on each side of the diffraction medium, we ...
Dynamic problem of a power-law graded half-plane and an associated carleman problem for two functions
Y A Antipov
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 77, Issue 4, November 2024, hbae013, https://doi.org/10.1093/qjmam/hbae013
A steady state plane problem of an inhomogeneous half-plane subjected to a load running along the boundary at subsonic speed is analyzed. The Lame coefficients and the density of the half-plane are assumed to be power functions of depth. The model is different from the standard static model have been used in contact ...
Harmonic And Neutral Spherical Elastic Inhomogeneities with A Functionally Graded Interphase Layer
Xu Wang and Peter Schiavone
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 76, Issue 3, August 2023, Pages 315–327, https://doi.org/10.1093/qjmam/hbad006
We study the elastic field in a three-phase composite composed of an internal spherical homogeneous elastic inhomogeneity, an intermediate functionally graded interphase layer and an outer unbounded homogeneous elastic matrix subjected to an arbitrary uniform remote loading. The shear modulus of the interphase layer obeys ...

Most read

Research Article
A Neutral Isotropic Elastic Ellipsoidal Inhomogeneity with a Spring-Type Imperfect Interface
Xu Wang and Peter Schiavone
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 77, Issue 4, November 2024, hbae012, https://doi.org/10.1093/qjmam/hbae012
We study the design of an imperfectly bonded neutral isotropic elastic ellipsoidal inhomogeneity that does not disturb the prescribed uniform normal stresses in an isotropic elastic matrix. The imperfect inhomogeneity-matrix interface is modeled by a spring-type imperfect interface characterized by a single imperfect ...
Research Article
Internal Structure of Decaying Solitary Waves: Comparison of Analytic and Numerical Results
Dane Grundy and P W Hammerton
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 78, Issue 1, February 2025, hbae014, https://doi.org/10.1093/qjmam/hbae014
The evolution of solitary waves governed by perturbations of the Korteweg-de Vries (KdV) equation is considered, focussing in particular on the Burgers-Korteweg-de Vries (BKdV) equation. Using matched asymptotic expansions the structure of the wave is determined for all timescales. A tail appears behind the main waveform, ...
Research Article
Exact and asymptotic solutions of Burgers’ equation on half-line
Pintu Samanta and Srinivasa Rao Chidella
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 78, Issue 1, February 2025, hbaf001, https://doi.org/10.1093/qjmam/hbaf001
In this article, we solve exactly an initial boundary value problem (IBVP) posed for Burgers’ equation on the quarter plane. Asymptotic behaviors of the solution of Burgers’ equation in different regions of the quarter plane are obtained from the exact solution. The special solutions of the Burgers’ equation, such as ...
Research Article
On the T-matrix for thermo-visco-elastic scattering
P A Martin
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 78, Issue 1, February 2025, hbaf002, https://doi.org/10.1093/qjmam/hbaf002
Waves in a thermo-visco-elastic medium interact with a bounded penetrable obstacle of arbitrary shape. The T -matrix for such a scattering problem connects the expansion of the incident wave in terms of regular vector spherical wavefunctions to the expansion of the scattered waves in terms of outgoing vector spherical ...
Research Article
Theory of Perturbation of Electrostatic Field By A Coated Anisotropic Dielectric Sphere
Nikolaos L Tsitsas and others
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 76, Issue 3, August 2023, Pages 297–314, https://doi.org/10.1093/qjmam/hbad005
A boundary-value problem was formulated for perturbation of an electrostatic field by a coated dielectric sphere made of two distinct linear anisotropic dielectric (LAD) materials. Specific affine transformations were employed to represent the electric potential inside the core and the coating in terms of the solutions of ...
Research Article
A contribution to the mathematical theory of diffraction. Part II: Recovering the far-field asymptotics of the quarter-plane problem
R C Assier and others
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 77, Issue 1-2, February-May 2024, hbae005, https://doi.org/10.1093/qjmam/hbae005
We apply the stationary phase method developed in Assier, Shanin and Korolkov, QJMAM , 76 (2022) to the problem of wave diffraction by a quarter-plane subjected to Dirichlet boundary conditions. The wave field is written as a double Fourier transform of an unknown spectral function. We make use of the analytical ...
Research Article
Linear stability of a compressible flow in a channel
M Deka and others
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 76, Issue 4, November 2023, Pages 405–434, https://doi.org/10.1093/qjmam/hbad010
Modal instabilities in a compressible flow through a channel at high Reynolds numbers are studied for three-dimensional (3D) perturbations. In addition to the Tollmien–Schlichting (TS) mode, there exist compressible modes in a channel flow that do not have a counterpart in the incompressible limit. The stability ...
Research Article
A numerical investigation on the vibration of a two-deck euler–bernoulli beam flooded by a potential flow
Zihua Liu and others
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 76, Issue 4, November 2023, Pages 531–550, https://doi.org/10.1093/qjmam/hbae006
This work concerns the structural vibration of a bladeless wind turbine, modelled by a two-deck Euler–Bernoulli beam, due to a surrounding potential flow. The deflection is governed by the Euler–Bernoulli equation which is studied first by a linear theory and then computed numerically by a finite difference method in space ...
Research Article
The behaviour of a forced spherical pendulum operating in a weightless environment
R E Grundy
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 76, Issue 3, August 2023, Pages 349–369, https://doi.org/10.1093/qjmam/hbad008
In this article, we show that by subjecting the pivot of a simple inextensible pendulum to small amplitude high frequency rectilinear oscillations it is possible to make it operate in a weightless environment. The axis of vibration of the pivot defines a preferred direction in space and a consequential dynamical structure ...
Research Article
Analytical insights into semi-infinite plate scattering: the wiener–hopf technique and two-sided linear boundary conditions
A D G Hales and L J Ayton
The Quarterly Journal of Mechanics and Applied Mathematics, Volume 77, Issue 1-2, February-May 2024, hbae003, https://doi.org/10.1093/qjmam/hbae003
The Wiener–Hopf Technique is popular throughout applied mathematics, particularly for wave scattering problems. One such problem is the scattering of an incident wave impinging upon a semi-infinite surface. For scattering problems in which one applies separate boundary conditions on each side of the diffraction medium, we ...
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