Proceedings of the Royal Society A-Mathematical Physical and Engineeri

Article	Citations
Working with Mike	132
Fluid dynamics of droplet impact and splitting on superhydrophobic wedges	92
The deterministic core of stochastically perturbed nonlinear mechanical systems	71
Classification of bi-Hamiltonian pairs extended by isometries	65
Manifestation of the Berry curvature in geophysical ray tracing	48
Measuring the speed of quantum particles without a round-trip under non-synchronized quantum clocks	42
Integral equation methods for acoustic scattering by fractals	40
Michael J. Duff: a personal reminiscence	40
DDE-Find : learning delay differential equations from noisy, limited data	37
Representing the stress and strain energy of elastic solids with initial stress and transverse texture anisotropy	37
Exact evaluation and resummation of the divergent expansion for the Heisenberg–Euler Lagrangian	37
Bursty switching dynamics promotes the collapse of network topologies	35
A general solution for rotating lattices of identical point vortices	34
Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff–Love kinematicsand revealed by a three-dimensional computational framework	33
Wind-driven and buoyancy-driven circulation in the subtropical North Atlantic Ocean	31
Enhanced attraction between drops carrying fluctuating charge distributions	30
Stable coexistence in indefinitely large systems of competing species	30
Stability of state-dependent switched systems under hybrid delayed impulsive control	27
Muography as a new complementary tool in monitoring volcanic hazard: implications for early warning systems	27
The principle of compromise-in-competition: understanding mesoscale complexity of different levels	26
The microdynamics shaping the relationship between democracy and corruption	25
Structural engineering from an inverse problems perspective	25
Asymptotic analysis of subglacial plumes in stratified environments	24
Comment on: ‘A doubly anharmonic oscillator in an induced electric dipole system’	24
Exploring the role of crystal habit in the Ostwald rule of stages	24

Coupling-induced instability in a ring of thermoacoustic oscillators	23
Transverse spectral instability in generalized Kadomtsev–Petviashvili equation	22
Identification of subwavelength microstructural information from macroscopic boundary measurements in elastodynamics	22
Langevin dynamics for a heavy particle immersed within a flow of light particles	22
Introduction to the special issue dedicated to Michael J. Duff FRS on the occasion of his 70th birthday	21
The potential impact of intensified community hand hygiene interventions on respiratory tract infections: a modelling study	21
Rigid folding equations of degree-6 origami vertices	21
Modelling the anomalous shock response of titanium diboride	20
Selective and tunable excitation of topological non-Hermitian quasi-edge modes	20
Analysis of a model for surfactant transport around a foam meniscus	20
Wave spectroscopy in a driven granular material	20
Regolith flow on top-shaped asteroids	19
Revisiting causality using stochastics: 2. Applications	19
Quantum mechanics with spatial non-local effects and position-dependent mass	19
The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane	19
Confined helium, density dependence of the inelastic electron and photon scattering cross-sections and the optical oscillator strength	19
A sampling-based approach for information-theoretic inspection management	19
Continuum soft tissue models from upscaling of arrays of hyperelastic cells	18
Solving generalized eigenvalue problems by ordinary differential equations on a quantum computer	18
Clusters of Bloch waves in three-dimensional periodic media	18
Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework	17
Painlevé-type asymptotics for the defocusing Hirota equation in transition region	16
Kirigami tiled surfaces with multiple configurations	16
Gauß–Manin from scratch: theme, variations and fantasia	16
The Jones polynomial of collections of open curves in 3-space	16
Helicoids and vortices	16
Stability of an inhomogeneous ferrofluid in a channel, subject to a normal field	16
A digital-twin framework for genomic-based optimization of an agrophotovoltaic greenhouse system	16
Quenching for a semi-linear wave equation for micro-electro-mechanical systems	16
Whitham shocks and resonant dispersive shock waves governed by the higher order Korteweg–de Vries equation	15
Enhancing the performance of solenoidal spectrometers for inverse reactions	14
Uniform approximations and effective boundary conditions for a high-contrast elastic interface	14
Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology	14
Human decision-making in a non-ergodic additive environment	14
Equations for small amplitude shallow water waves over small bathymetric variations	14
Using a robotic platform to study the influence of relative tailbeat phase on the energetic costs of side-by-side swimming in fish	13
The Painlevé paradox in three dimensions: resolution with regularization	13
Bounds of the technical constants for two-dimensional anisotropic elasticity	13
Pushing coarse-grained models beyond the continuum limit using equation learning	13
Puckering and wrinkling in a growing composite ring	13
Modification of Turing patterns through the use of time-varying anisotropic diffusion	13
An axisymmetric problem for a penny-shaped crack under the influence of the Steigmann–Ogden surface energy	13
Determinants of successful mitigation in coupled social-climate dynamics	13
Short branch cut approximation in two-dimensional hydrodynamics with free surface	12
A constitutive model for transversely isotropic dispersive materials	12
Superconductivity and nucleation from fractal anisotropy and product-like fractal measure	12
Variational principles of liquid–porous material interactions with applications to approximate solutions and finite-element modelling	12
Asymptotic solution to convolution integral equations on large and small intervals	12
An Eulerian hyperbolic model for heat transfer derived via Hamilton’s principle: analytical and numerical study	12
Flutter instability in solids and structures, with a view on biomechanics and metamaterials	12

Self-similar solutions for high-energy density radiative transfer with separate ion and electron temperatures	12
Paraxial Dirac equation	12
Variational construction of tubular and toroidal streamsurfaces for flow visualization	11
Elastic cloaking for a periodic distribution of parallel finite cracks	11
Generating new gravitational solutions by matrix multiplication	11
Classification of first strain-gradient elasticity tensors by symmetry planes	11
Kinematic dynamos in triaxial ellipsoids	11
Unconditionally secure relativistic multi-party biased coin flipping and die rolling	11
Solution landscapes of the simplified Ericksen–Leslie model and its comparisonwith the reduced Landau–deGennes model	11
Anisotropic stress softening of residually stressed solids	11
Unstable cores are the source of instability in chemical reaction networks	11
Graphite phases in chemical vapour deposited grown ZrC/graphite layers	11
Improved estimations of stochastic chemical kinetics by finite-state expansion	11
Semiclassical approach for excitonic spectrum of Coulomb coupling between two Dirac particles	11
On the degeneracy of spin ice graphs, and its estimate via the Bethe permanent	11
Correction to ‘Exact solution to a Liouville equation with Stuart vortex distribution on the surface of a torus’	11
Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom	11
Melting of wall-mounted ice in shear flow	11
Zig-zag dynamics in a Stern–Gerlach spin measurement	11
Explorations of certain nonlinear waves of the Boussinesq and Camassa–Holm equations using physics-informed neural networks	11
Riemannian geometry and molecular similarity I: spectrum of the Laplacian	11
Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics	11
A mathematical model of thermoplastic elastomers for analysing the topology of microstructures and mechanical properties during elongation	11
Modelling the dynamics of product adoption and abandonment	11
Cluster-based Bayesian approach for noisy and sparse data: application to flow-state estimation	11
Thermal convection with a Cattaneo heat flux model	11
Snap-through and indirect reduced-order modelling	10
PT-symmetry and supersymmetry: interconnection of broken and unbroken phases	10
Discrete scattering and meta-arrest of locally resonant elastic wave metamaterials with a semi-infinite crack	10
Recovering multiple fractional orders in time-fractional diffusion in an unknown medium	10
Bi-Hamiltonian structures of WDVV-type	10
A discrete shear lag model of the mechanics of hitchhiker plants, and its prospective application to tendon-to-bone repair	10
Higher-order degenerations of Fay’s identities and applications to integrable equations	10
Mean and variance of the Eulerian and Lagrangian horizontal velocities induced by nonlinear multi-directional irregular water waves	10
Laguerre polynomial-based operational matrix of integration for solving fractional differential equations with non-singular kernel	10
Influence of the growth gradient on surface wrinkling and pattern transition in growing tubular tissues	10
Metamaterial applications of Tmatsolver, an easy-to-use software for simulating multiple wave scattering in two dimensions	10
Manifestations of inertia on light dragging revealed in plasmas	10
Mean-field theory for double-well systems on degree-heterogeneous networks	10
Explosive rigidity percolation in kirigami	10
Persistent currents, revival time and effects of rotation on an attractive inverse-square-type potential in a magnetic quadrupole moment system	10
Modelling and simulation of the cholesteric Landau-de Gennes model	10
Vassiliev measures of complexity of open and closed curves in 3-space	10
How norms shape the evolution of prosocial behaviour–compassion, universalizability, reciprocity and equity: a C.U.R.E for social dilemmas	10
Topological effects of a global monopole on a spherical quantum dot	10
Adaptive Bayesian inference of Markov transition rates	10
Universal dynamics of biological pattern formation in spatio-temporal morphogen variations	10
Data-driven reduction and decomposition with time-axis clustering	10
Numerically solving a nonlinear integral equation when the reciprocal of the solution lies in the integrand	9
Integrating neural operators with diffusion models improves spectral representation in turbulence modelling	9
Wind tunnel evaluation of novel drafting formations for an elite marathon runner	9
Self-similarity of spectral response functions for fractional quantum Hall states	9
On the problem of comparing graded metamaterials	9
Equivalent in-plane elastic moduli of honeycomb materials under hypergravity conditions	9
Self-dual electromagnetic fields	9
Triple-spherical Bessel function integrals with exponential and Gaussian damping: towards an analytic N-point correlation function covariance model	9
Stress relaxation after low- and high-rate deformation of polyurethanes	9
Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta	9
Anisotropy distorts the spreading of a fixed volume porous gravity current	9
Shear and flexural deformations in flextegrity segmental beams inspired by Leonardo’s triangular masonry construction	9
Linear analysis of ice-shelf topography response to basal melting and freezing	9
Extending the analysis on the best solar activity proxy for long-term ionospheric investigations	9
How time-discretization can break the asymptotics of inverse scattering	9
Frequency tunable electromagnetic vibration energy harvester using piecewise linear nonlinearity	9
Debunking revolutionary paradigm shifts: evidence of cumulative scientific progress across science	8
∂¯-problem for the focusing nonlinear Schrödinger equation and soliton shielding	8
Towards an information-theoretic framework for multiple sequence alignment sub-sampling	8
Active nematodynamics on deformable surfaces	8
Another perspective on elastic and plastic anisotropy of textured metals	8
Travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion	8
Homotopy perturbation method and its convergence analysis for nonlinear collisional fragmentation equations	8
A novel multiscale model for micro-structured electromagnetic media	8
Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend	8
The topological origin of the Peierls–Nabarro barrier	8
A generalized Dean–Kawasaki equation for an interacting Brownian gas in a partially absorbing medium	8
Growth and morphogenesis of an everted tubular biological tissue	8
The seismic wavefield as seen by distributed acoustic sensing arrays: local, regional and teleseismic sources	8
Better strategies for containing COVID-19 pandemic: a study of 25 countries via a vSIADR model	8
Turing patterns on discrete topologies: from networks to higher-order structures	8
A review on semi-analytical methods for aggregation and coupled aggregation–breakage equations	8

A system model of three-body interactions in complex networks: consensus and conservation	8
Contemporary sea-level changes from global to local scales: a review	8
Deeply subwavelength giant monopole elastodynamic metacluster resonators	8
Evolution of quantum non-equilibrium for coupled harmonic oscillators	7
On quantum states over time	7
Guided wave tomography for quantitative thickness mapping using non-dispersive SH0 mode through geometrical full waveform inversion (GFWI)	7
Efficient set-theoretic algorithms for computing high-order Forman-Ricci curvature on abstract simplicial complexes	7
The theory of fifth-order Stokes waves in a linear shear current	7
Trapping of an active Brownian particle at a partially absorbing wall	7
The linear viscoelastic fracture theory applies to soft solids better when they are…viscoelastic	7
Special issue: advances in Wiener–Hopf type techniques: theory and applications	7
Structural function from sequential, interacting elastic instabilities	7
Comments on effective use of numerical modelling and extended classical shell buckling theory	7
Fractional-order viscoelastic model of musculoskeletal tissues: correlation with fractals	7
Exact hydrodynamics and onset of phase separation for an active exclusion process	7
Atomistic mechanisms of phase nucleation and propagation in a model two-dimensional system	7
Nematic liquid crystalline elastomers are aeolotropic materials	7
Signature of transition to supershear rupture speed in the coseismic off-fault damage zone	7
Of fiery sparks and glittering spots: melting-resolidification and spherical particle formation in abrasion	7
Stability of penetrative convective currents in local thermal non-equilibrium	7
Local supersymmetry: variations on a theme by Volkov and Soroka	7
Extraction of the mass density using only the p-parts of the elastic fields generated by injected highly dense small inclusions	7
Sensitivity analysis of large body of control parameters in machine learning control of a square-back Ahmed body	7
Flextegrity simple cubic lattices	7
Symmetries in transmission electron microscopy imaging of crystals with strain	7
Torque-driven superhydrophobic cylinders swim in circles	7
A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem	7
Enabling novel dispersion and topological characteristics in mechanical lattices via stable negative inertial coupling	7
Generalized higher-order Freud weights	7
Τhe role of surface energy in the apparent solubility of two different calcite crystal habits	7
Development and analysis of moments preserving finite volume schemes for multi-variate nonlinear breakage model	7
Interfacial metric mechanics: stitching patterns of shape change in active sheets	7
Geometric mechanics of ordered and disordered kirigami	7
Imitation and aspiration dynamics bring different evolutionary outcomes in feedback-evolving games	6
The role of sliding in ice stream formation	6
Bifurcations of an elastic disc coated with an elastic inextensible rod	6
Stability of longitudinal sediment waves formed by turbidity currents: linear and weakly nonlinear perspectives	6
Strain, disfigurement and flexure tensors in continuum kinematics	6
Triggering of electro-elastic anti-superhydrophobicity during non-Newtonian droplet collision	6
Effective governing equations for dual porosity Darcy–Brinkman systems subjected to inhomogeneous body forces and their application to the lymph node	6
Effective statistical control strategies for complex turbulent dynamical systems	6
Compressed hydrogen atoms confined within generic boxes	6
Multistability, symmetry and geometric conservation in eightfold waterbomb origami	6
Critical rates of climate warming and abrupt collapse of ecosystems	6
Law of elasticity and fracture limit of magnetic forcelines under their gravitational deformation	6
Continuation of the Stieltjes series to the large regime by finite-part integration	6
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part II	6
Chirality and curvature determine the meandering of spirals in multilayer excitable media	6
Sturm–Liouville systems for the survival probability in first-passage time problems	6
A high-eigenfrequency differential stiffness probe for high-speed scanning probe microscopy	6
Elastic wave propagation in anisotropic polycrystals: inferring physical properties of glacier ice	6
The most predictable component of a linear stochastic model	6
Introduction to special feature dedicated to Prof. Allan Fordy on the occasion of his 70th birthday	6
The density and pressure of helium nano-bubbles encapsulated in silicon	6
Analysis of the energy transfer process for multiple scattering problems involving lossy media	6
Gravity, duality and conformal symmetry	6
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from monodisperse prolate and oblate spheroidal particles	6
Computation of Burgers vectors from elastic strain and lattice rotation data	6
Ranking with multiple types of pairwise comparisons	6
Quantum chaos in the Dicke model and its variants	6
Response of flexible structures to air-blast: nonlinear compressibility effects in fluid–structure interaction	6
Matrix factorizations and pentagon maps	6
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part I	6
Lévy flights as an emergent phenomenon in a spatially extended system	6
Edge resonance: exact results and fresh insights	6
An effective semilocal model for wave turbulence in two-dimensional nonlinear optics	6
Optimal intercellular competition in senescence and cancer	6
Symmetries and Casimirs of radial compressible fluid flow and gas dynamics inn > 1 dimensions	6
Curvature dependences of wave propagation in reaction–diffusion models	6
Unsteady solute dispersion in the presence of reversible and irreversible reactions	6
Can comets deliver prebiotic molecules to rocky exoplanets?	6
The onset time of Fermi’s golden rule	6
Symplectic decomposition from submatrix determinants	5
Time-varying Bose–Einstein condensates	5
Direct statistical simulation of low-order dynamosystems	5
Rheology of three-phase suspensions determined via dam-break experiments	5
Wallpaper group kirigami	5
Elastic bounds of the coupling tensor of anisotropic composite laminates: a polar approach	5
Post-buckling dynamics of spherical shells	5
Spectral stability of travelling waves in a thin-layer two-fluid Couette flow	5
Are the chemical families still there? Formal structure of similarity of elements and its thermochemical domain	5
On the well-posedness of Eringen’s non-local elasticity for harmonic plane wave problems	5
An optimal control strategy to design passive thermal cloaks of arbitrary shape	5
Numerical direct scattering transform for breathers	5
Border collision bifurcations of chaotic attractors in one-dimensional maps with multiple discontinuities	5
Critical transitions in spatial systems induced by Ornstein–Uhlenbeck noise: spatial mutual information as a precursor	5
The Wiener–Hopf technique, its generalizations and applications: constructive and approximate methods	5
Efficient computational modelling of smooth muscle orientation and function in the aorta	5
Wave-breaking phenomena and global existence for the weakly dissipative generalized Novikov equation	5
Non-reciprocal population dynamics in a quantum trimer	5
Transient processes in a gas/plate structure in the case of light loading	5
A new integrable model of long wave–short wave interaction and linear stability spectra	5
Efficient quantum gate teleportation in higher dimensions	5
Quantum simulation of discrete linear dynamical systems and simple iterative methods in linear algebra	5
A growth model for water distribution networks with loops	5