Proceedings of the Royal Society A-Mathematical Physical and Engineeri

Article	Citations
Stability of an inhomogeneous ferrofluid in a channel, subject to a normal field	134
The potential impact of intensified community hand hygiene interventions on respiratory tract infections: a modelling study	100
Wave spectroscopy in a driven granular material	72
Frequency tunable electromagnetic vibration energy harvester using piecewise linear nonlinearity	69
Riemannian geometry and molecular similarity I: spectrum of the Laplacian	50
Linear analysis of ice-shelf topography response to basal melting and freezing	44
Pushing coarse-grained models beyond the continuum limit using equation learning	43
Anisotropy distorts the spreading of a fixed volume porous gravity current	43
Self-similar solutions for high-energy density radiative transfer with separate ion and electron temperatures	41
Influence of the growth gradient on surface wrinkling and pattern transition in growing tubular tissues	40
Unstable cores are the source of instability in chemical reaction networks	38
Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics	37
Unconditionally secure relativistic multi-party biased coin flipping and die rolling	36
Exploring the role of crystal habit in the Ostwald rule of stages	34
Confined helium, density dependence of the inelastic electron and photon scattering cross-sections and the optical oscillator strength	33
Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework	33
A review on semi-analytical methods for aggregation and coupled aggregation–breakage equations	30
Bursty switching dynamics promotes the collapse of network topologies	30
Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend	29
Modelling the dynamics of product adoption and abandonment	28
Superconductivity and nucleation from fractal anisotropy and product-like fractal measure	27
Detecting damage in composites using volume decomposition analysis of tomographic data	25
Whitham shocks and resonant dispersive shock waves governed by the higher order Korteweg–de Vries equation	25
Extraction of the mass density using only the p-parts of the elastic fields generated by injected highly dense small inclusions	25
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from monodisperse prolate and oblate spheroidal particles	24

Modelling of stress transfer in root-reinforced soils informed by four-dimensional X-ray computed tomography and digital volume correlation data	23
Bifurcations of an elastic disc coated with an elastic inextensible rod	23
Chirality and curvature determine the meandering of spirals in multilayer excitable media	23
Allowing Wigner’s friend to sequentially measure incompatible observables	23
Quantifying the preventive effect of wearing face masks	23
Unsteady solute dispersion in the presence of reversible and irreversible reactions	22
Symplectic decomposition from submatrix determinants	22
The formation of cave scallops	22
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part I	22
Evolution of quantum non-equilibrium for coupled harmonic oscillators	21
Application of thrust layout optimization to masonry structures	21
Non-hyperbolicity at large scales of a high-dimensional chaotic system	21
Causal lifting and link prediction	21
Critical rates of climate warming and abrupt collapse of ecosystems	21
Edge resonance: exact results and fresh insights	20
Development and analysis of moments preserving finite volume schemes for multi-variate nonlinear breakage model	20
Heteroclinic bifurcation analysis of the tippedisk through the use of Melnikov theory	19
Efficient set-theoretic algorithms for computing high-order Forman-Ricci curvature on abstract simplicial complexes	19
Matrix factorizations and pentagon maps	19
Time-varying Bose–Einstein condensates	19
Point-like defect on Schrödinger particles under flux field with harmonic oscillator plus Mie-type potential: application to molecular potentials	18
Physics-informed Dyna-style model-based deep reinforcement learning for dynamic control	17
Prediction of general high-order lump solutions in the Davey–Stewartson II equation	17
Shear dynamics around self-organized viscosity-stratified autocatalytic fronts in channel flows	17
Correction: Continent-scale Hiatus Maps for the Atlantic Realm and Australia since the Upper Jurassic and links to mantle flow-induced dynamic topography	16
Electro-osmotic and viscous effects upon pressure to drive a droplet through a capillary	16
Phase tipping: how cyclic ecosystems respond to contemporary climate	16
An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow	16
The impact of time delays on mutant fixation in pairwise social dilemma games	16
Harmonic wave scattered by an inclusion in an elastic plane: The complete Gurtin-Murdoch model	16
On reduced inertial PDE models for Cucker–Smale flocking dynamics	16
Data-driven two-dimensional stationary quantum droplets and wave propagations in the amended Gross–Pitaevskii equation with two potentials via deep neural networks learning	15
On the identification of power-law creep parameters from conical indentation	15
Multimode multiple wave scattering in suspensions of solid particles in viscous liquids: part 2: numerical validation	15
Inertia-gravity waves in geophysical vortices	15
An exact integral-to-sum relation for products of Bessel functions	15
Revisiting causality using stochastics on atmospheric temperature and CO 2 concentration	14
Unbiased estimation of the Hessian for partially observed diffusions	14
A design-space minimum sampling strategy based on proper-orthogonal-decomposition projection	14
Optimal regularity and Uhlenbeck compactness for general relativity and Yang–Mills theory	14
Measure of overlap between two arbitrary ellipses on a sphere	14
Molecular dynamics simulation on oxidation process and interfacial performance of foamed asphalt binders based on ReaxFF force field	13
Correction to ‘Ice sheet flow with thermally activated sliding. Part 2: the stability of subtemperate regions’	13
On the propagation of nonlinear waves in the atmosphere	13
Model for deformation-induced martensitic transformation in irradiated materials	13
Riemann–Hilbert problem on a hyperelliptic surface and uniformly stressed inclusions embedded into a half-plane subjected to antiplane strain	13
The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions	13
Hamel’s equations and geometric mechanics of constrained and floating multibody and space systems	13
The θ-formulation of the two-dimensional elastica: buckling and boundary layer theory	13
Weber’s Law of perception is a consequence of resolving the intensity of natural scintillating light and sound with the least possible error	13

A tunable electromagnetic metagrating	12
Generalization of Duhamel's integral to multi-degree-of-freedom systems	12
Electric field control of magnetism	12
Density functional theory calculations on the solvatochromism of covalent organic framework Py-TT cluster compounds	12
A predictive model of UV-A-riboflavin crosslinking treatment on porcine corneas	12
Free propagation of resonant waves in nonlinear dissipative metamaterials	12
A generic approach to the quantum mechanical transition probability	12
Robust imaging using electrical impedance tomography: review of current tools	12
Contact-line bending energy controls phospholipid vesicle adhesion	12
Hierarchical meta-porous materials as sound absorbers	12
Modelling cerebrovascular pathology and the spread of amyloid beta in Alzheimer’s disease	12
Integrable nonlinear evolution equations in three spatial dimensions	12
The contribution of plastic sink-in to the static friction of single asperity microscopic contacts	11
Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media	11
Dynamic multi-dose vaccination with initial immunity on higher-order networks	11
Unified wavefront singularity characterization of three-dimensional elastodynamic time-domain half-space Green's function under impulsive boundary and internal loads	11
Rheomergy : collective behaviour mediated by active flow-based recruitment	11
Tailored acoustic metamaterials. Part I. Thin- and thick-walled Helmholtz resonator arrays	11
Finite-horizon, energy-efficient trajectories in unsteady flows	11
A theoretical model of Surtseyan bomb fragmentation	11
Movement bias in asymmetric landscapes and its impact on population distribution and critical habitat size	11
A rigorous mathematical theory for topological phases and edge modes in spring-mass mechanical systems	11
Plane strain wedge indentation revisited	11
Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology	11
Strategies for guided acoustic wave inspection using mobile robots	11
Indirect exclusion can promote cooperation in repeated group interactions	11
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, II: characterization	11
The interplay between Fano and Fabry–Pérot resonances in dual-period metagratings	11
Judgment on the evolution state of asymmetric games	11
High-temperature and high-pressure plastic phase of ice at the boundary of liquid water and ice VII	11
Scattering of elastic waves by a sphere with cubic anisotropy with application to attenuation in polycrystalline materials	11
Quantum measurement and colour perception: theory and applications	11
Soft wetting with (a)symmetric Shuttleworth effect	10
Three-dimensional magnetic reconnection in astrophysical plasmas	10
Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces	10
Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations	10
Elastic waves in particulate glass-rubber mixtures	10
Ultrasensitivity and bistability in covalent-modification cycles with positive autoregulation	10
Quantitative mapping of thickness variations along a ray path using geometrical full waveform inversion and guided wave mode conversion	10
Evidence for active upper mantle flow in the Atlantic and Indo-Australian realms since the Upper Jurassic from hiatus maps and spreading rate changes	10
Challenges in computational fluid dynamics applications for bone tissue engineering	10
Pace in concert with phase: rate-induced phase-tipping in birhythmic oscillators	10
A solvable two-dimensional swarmalator model	10
Inductive biases for deep learning of higher-level cognition	10
Fracture modelling of plain concrete using non-local fracture mechanics and a graph-based computational framework	10
Axisymmetric vibration and stability of dielectric-elastic tubular bilayer system	10
The original Wigner’s friend paradox within a realist toy model	10
A micromechanical model for phase-change composites	10
The plausibility of origins scenarios requiring two impactors	10
Klein–Gordon equation for electrically charged particles with new energy-momentum operator	10
Investigation of the influence of macrozones in titanium alloys on the propagation and scattering of ultrasound	10
Averaging plus learning models and their asymptotics	10
The Madelung constant in N dimensions	10
Dimension-reduction of dynamics on real-world networks with symmetry	10
Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results	10
Effect of pulsating solidification on the surface properties of conductive materials	10
Robustness of subwavelength devices: a case study of cochlea-inspired rainbow sensors	9
Semiclassical theory predicts stochastic ghosts scaling	9
Transformations, symmetries and Noether theorems for differential-difference equations	9
A probabilistic model of diffusion through a semi-permeable barrier	9
Unifying temperature definition in atomistic and field representations of conservation laws	9
Scattering of surface waves by a vertical truncated structured cylinder	9
Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics	9
Active nematic fluids on Riemannian two-manifolds	9
Energy allocation theory for bacterial growth control in and out of steady state	9
Weyl almost automorphic solutions in distribution sense of Clifford-valued stochastic neural networks with time-varying delays	9
A Bose–Einstein condensate is a Bose condensate in the laboratory ground state	9
The generalized Hashin–Shtrikman approach to Al/nano-TiC composite	9
On the association of kinematics, spanwise instability and growth of secondary vortex structures in the wake of oscillating foils	9
Spectral theory of diffusion in partially absorbing media	9
Cost efficiency of institutional incentives for promoting cooperation in finite populations	9
Effect of stacking order on the vibration properties of bilayer black phosphorus	9
Regolith flow on top-shaped asteroids	8
Numerically solving a nonlinear integral equation when the reciprocal of the solution lies in the integrand	8
Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta	8
Modification of Turing patterns through the use of time-varying anisotropic diffusion	8
Enhancing the performance of solenoidal spectrometers for inverse reactions	8
Solving generalized eigenvalue problems by ordinary differential equations on a quantum computer	8
Scattering from time-modulated subwavelength resonators	8
Kinematics and dynamics of disclination lines in three-dimensional nematics	8

Tree search in DAG space with model-based reinforcement learning for causal discovery	8
Supply chain loss from easing COVID-19 restrictions: an evolutionary economic-epidemiological modelling study	8
Human decision-making in a non-ergodic additive environment	8
Semiclassical approach for excitonic spectrum of Coulomb coupling between two Dirac particles	8
A general solution for rotating lattices of identical point vortices	8
The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane	8
The principle of compromise-in-competition: understanding mesoscale complexity of different levels	8
New actuation modes of composite dielectric elastomers	8
Chiral mode transfer of symmetry-broken states in anti-parity-time-symmetric mechanical system	8
Mechanics of tension-induced film wrinkling and restabilization: a review	8
Analysis of a model for surfactant transport around a foam meniscus	8
Determinants of successful mitigation in coupled social-climate dynamics	8
Short branch cut approximation in two-dimensional hydrodynamics with free surface	8
Travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion	8
Gauß–Manin from scratch: theme, variations and fantasia	8
The obstacle problem in no-tension structures and cable nets	8
A sampling-based approach for information-theoretic inspection management	8
The linear viscoelastic fracture theory applies to soft solids better when they are…viscoelastic	7
Introduction to the special issue dedicated to Michael J. Duff FRS on the occasion of his 70th birthday	7
Explorations of certain nonlinear waves of the Boussinesq and Camassa–Holm equations using physics-informed neural networks	7
Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology	7
Multistability, symmetry and geometric conservation in eightfold waterbomb origami	7
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part II	7
Normal form for maps with nilpotent linear part	7
Characterization of near-miss connectivity-invariant homogeneous convex polyhedral cages	7
Integral equation methods for acoustic scattering by fractals	7
Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom	7
Mean and variance of the Eulerian and Lagrangian horizontal velocities induced by nonlinear multi-directional irregular water waves	7
Generating new gravitational solutions by matrix multiplication	7
Wallpaper group kirigami	7
Covid-19: predictive mathematical formulae for the number of deaths during lockdown and possible scenarios for the post-lockdown period	7
Structural dynamic characteristics of vertical axis wind and tidal current turbines	7
Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff–Love kinematicsand revealed by a three-dimensional computational framework	7
Manifestations of inertia on light dragging revealed in plasmas	7
Zig-zag dynamics in a Stern–Gerlach spin measurement	7
Classification of bi-Hamiltonian pairs extended by isometries	7
Controlling the dispersion of metamaterials in three dimensions	7
Effects of an impermeable layer on pore pressure response to tsunami-like inundation	7
Transient processes in a gas/plate structure in the case of light loading	7
Finite time blowup of incompressible flows surrounding compressible bubbles evolving under soft equations of state	7
A theory of stochastic fluvial landscape evolution	6
Conical Kresling origami and its applications to curvature and energy programming	6
Nonlinear realization approach to topologically massive supergravity	6
Fractional-order viscoelastic model of musculoskeletal tissues: correlation with fractals	6
Symmetries in transmission electron microscopy imaging of crystals with strain	6
Curved schemes for stochastic differential equations on, or near, manifolds	6
Rheology of three-phase suspensions determined via dam-break experiments	6
Shape reconfiguration through origami folding sets an upper limit on drag	6
Shear wave transmissivity and wave-induced vorticity diffusion through conversion scattering to slow-shear diffusion wave	6
Inertial wave attractors in rapidly rotating tilted cuboids	6
A dynamic trap well model of hydrothermal shape-memory effect in amorphous polymers undergoing tailorable shape recovery behaviour	6
An experimental study of tie transparency and individual perception in social networks	6
A nonlinear spectral core–periphery detection method for multiplex networks	6
A model to validate effective waves in random particulate media: spherical symmetry	6
A new integrable model of long wave–short wave interaction and linear stability spectra	6
Computational synthesis of wheeled vehicles via multi-layer topology optimization	6
Geometric mechanics of ordered and disordered kirigami	6
Numerical direct scattering transform for breathers	6
A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem	6
Nonlinear acoustics of an aperture under grazing flow	6
Utilization of the ExactMPF package for solving a discrete analogue of the nonlinear Schrödinger equation by the inverse scattering transform method	6
On the origin of shear-band network patterns in ductile shear zones	6
Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators	6
Homotopy classification of knotted defects in ordered media	6
Steklov eigenvalues of nearly hyperspherical domains	6
A new generalized potential with exchangeable functions of octahedral cross sections for modelling yielding or failure of frictional materials	6
Tunable morphing of electroactive dielectric-elastomer balloons	6
Young and Young–Laplace equations for a static ridge of nematic liquid crystal, and transitions between equilibrium states	6
An ion trap design for a space-deployable strontium-ion optical clock	6
Aberration-corrected transmission electron microscopy of a non-graphitizing carbon	6
Computation of Burgers vectors from elastic strain and lattice rotation data	6
Self-folding of two-dimensional thin templates into pyramidal microstructures by a liquid drop: a numerical model	6
Modelling sediment compaction beneath ice lenses during frost heave	6
Unidirectional edge modes in time-modulated metamaterials	6
A low-rank ensemble Kalman filter for elliptic observations	6
On the force of vertical winds in the upper atmosphere: consequences for small biological particles	6
The Robin boundary condition for modelling heat transfer	6
SINDy for delay-differential equations: application to model bacterial zinc response	5
Variational analysis of inextensible elastic curves	5
Direct method to determine singular point of enveloped surface and its application to worm wheel tooth surface	5
Biological efficiency in processing information in green plants	5
An asymmetric graded indexed helical structured optical fibre for enhanced optical delays	5
The wave function as a true ensemble	5
Topology optimization with local stress constraints and continuously varying load direction and magnitude: towards practical applications	5
The theory of scaled electromagnetism	5
Symmetry-breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials	5
Mechanics of structural size effect in impact brittle fracture of steels and consequent scaling laws for fracture	5
Exact solutions to fall of particle to singular potential: classical versus quantum cases	5
Snap-through eversion of axisymmetric shells under contact indentation	5
Coexistence times in the Moran process with environmental heterogeneity	5
Geometric mechanics of hybrid origami assemblies combining developable and non-developable patterns	5
Two-layer gravity currents of generalized Newtonian fluids	5
Analytic mode-matching for accurate handling of exceptional points in a lined acoustic waveguide	5
Tensor networks for quantum machine learning	5
Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with time-dependent bases	5