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	143
The potential impact of intensified community hand hygiene interventions on respiratory tract infections: a modelling study	108
Wave spectroscopy in a driven granular material	79
Riemannian geometry and molecular similarity I: spectrum of the Laplacian	72
Linear analysis of ice-shelf topography response to basal melting and freezing	52
Pushing coarse-grained models beyond the continuum limit using equation learning	48
Anisotropy distorts the spreading of a fixed volume porous gravity current	47
Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics	46
Confined helium, density dependence of the inelastic electron and photon scattering cross-sections and the optical oscillator strength	41
Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework	41
Bursty switching dynamics promotes the collapse of network topologies	40
Whitham shocks and resonant dispersive shock waves governed by the higher order Korteweg–de Vries equation	39
Modelling the dynamics of product adoption and abandonment	37
Extraction of the mass density using only the p-parts of the elastic fields generated by injected highly dense small inclusions	36
Unconditionally secure relativistic multi-party biased coin flipping and die rolling	33
Exploring the role of crystal habit in the Ostwald rule of stages	33
Influence of the growth gradient on surface wrinkling and pattern transition in growing tubular tissues	31
A review on semi-analytical methods for aggregation and coupled aggregation–breakage equations	31
Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend	30
Rediscovery of Cooper pair factor	28
Frequency tunable electromagnetic vibration energy harvester using piecewise linear nonlinearity	27
Unstable cores are the source of instability in chemical reaction networks	26
Modelling of stress transfer in root-reinforced soils informed by four-dimensional X-ray computed tomography and digital volume correlation data	25
Allowing Wigner’s friend to sequentially measure incompatible observables	25
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from monodisperse prolate and oblate spheroidal particles	25

Quantifying the preventive effect of wearing face masks	25
Detecting damage in composites using volume decomposition analysis of tomographic data	25
Chirality and curvature determine the meandering of spirals in multilayer excitable media	24
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part I	24
Bifurcations of an elastic disc coated with an elastic inextensible rod	24
Symplectic decomposition from submatrix determinants	23
Unsteady solute dispersion in the presence of reversible and irreversible reactions	23
Evolution of quantum non-equilibrium for coupled harmonic oscillators	22
The formation of cave scallops	22
Application of thrust layout optimization to masonry structures	22
Edge resonance: exact results and fresh insights	21
Heteroclinic bifurcation analysis of the tippedisk through the use of Melnikov theory	21
Critical rates of climate warming and abrupt collapse of ecosystems	21
Efficient set-theoretic algorithms for computing high-order Forman-Ricci curvature on abstract simplicial complexes	21
Causal lifting and link prediction	20
Point-like defect on Schrödinger particles under flux field with harmonic oscillator plus Mie-type potential: application to molecular potentials	20
Non-hyperbolicity at large scales of a high-dimensional chaotic system	20
Matrix factorizations and pentagon maps	19
Time-varying Bose–Einstein condensates	19
Development and analysis of moments preserving finite volume schemes for multi-variate nonlinear breakage model	19
Phase tipping: how cyclic ecosystems respond to contemporary climate	18
Shear dynamics around self-organized viscosity-stratified autocatalytic fronts in channel flows	18
On reduced inertial PDE models for Cucker–Smale flocking dynamics	18
Controlling moving interfaces in solid-state batteries	18
Data-driven two-dimensional stationary quantum droplets and wave propagations in the amended Gross–Pitaevskii equation with two potentials via deep neural networks learning	17
Multimode multiple wave scattering in suspensions of solid particles in viscous liquids: part 2: numerical validation	17
An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow	17
Electro-osmotic and viscous effects upon pressure to drive a droplet through a capillary	17
Harmonic wave scattered by an inclusion in an elastic plane: The complete Gurtin-Murdoch model	17
Correction: Continent-scale Hiatus Maps for the Atlantic Realm and Australia since the Upper Jurassic and links to mantle flow-induced dynamic topography	17
Unbiased estimation of the Hessian for partially observed diffusions	17
Measure of overlap between two arbitrary ellipses on a sphere	16
Prediction of general high-order lump solutions in the Davey–Stewartson II equation	15
Optimal regularity and Uhlenbeck compactness for general relativity and Yang–Mills theory	15
The impact of time delays on mutant fixation in pairwise social dilemma games	15
Revisiting causality using stochastics on atmospheric temperature and CO 2 concentration	15
On the identification of power-law creep parameters from conical indentation	15
Weber’s Law of perception is a consequence of resolving the intensity of natural scintillating light and sound with the least possible error	15
A design-space minimum sampling strategy based on proper-orthogonal-decomposition projection	15
On the propagation of nonlinear waves in the atmosphere	14
An exact integral-to-sum relation for products of Bessel functions	14
Inertia-gravity waves in geophysical vortices	14
Physics-informed Dyna-style model-based deep reinforcement learning for dynamic control	14
Molecular dynamics simulation on oxidation process and interfacial performance of foamed asphalt binders based on ReaxFF force field	14
The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions	14
Hamel’s equations and geometric mechanics of constrained and floating multibody and space systems	14
Riemann–Hilbert problem on a hyperelliptic surface and uniformly stressed inclusions embedded into a half-plane subjected to antiplane strain	13
Correction to ‘Ice sheet flow with thermally activated sliding. Part 2: the stability of subtemperate regions’	13
A tunable electromagnetic metagrating	13
Tailored acoustic metamaterials. Part I. Thin- and thick-walled Helmholtz resonator arrays	13

Contact-line bending energy controls phospholipid vesicle adhesion	13
Model for deformation-induced martensitic transformation in irradiated materials	13
A predictive model of UV-A-riboflavin crosslinking treatment on porcine corneas	13
Generalization of Duhamel's integral to multi-degree-of-freedom systems	13
Rheomergy : collective behaviour mediated by active flow-based recruitment	13
The contribution of plastic sink-in to the static friction of single asperity microscopic contacts	13
The θ-formulation of the two-dimensional elastica: buckling and boundary layer theory	13
A generic approach to the quantum mechanical transition probability	13
Modelling cerebrovascular pathology and the spread of amyloid beta in Alzheimer’s disease	13
Integrable nonlinear evolution equations in three spatial dimensions	13
Density functional theory calculations on the solvatochromism of covalent organic framework Py-TT cluster compounds	13
Free propagation of resonant waves in nonlinear dissipative metamaterials	12
Robust imaging using electrical impedance tomography: review of current tools	12
Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology	12
Plane strain wedge indentation revisited	12
Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media	12
The interplay between Fano and Fabry–Pérot resonances in dual-period metagratings	12
Strategies for guided acoustic wave inspection using mobile robots	12
Finite-horizon, energy-efficient trajectories in unsteady flows	12
Hierarchical meta-porous materials as sound absorbers	12
Unified wavefront singularity characterization of three-dimensional elastodynamic time-domain half-space Green's function under impulsive boundary and internal loads	12
Movement bias in asymmetric landscapes and its impact on population distribution and critical habitat size	12
High-temperature and high-pressure plastic phase of ice at the boundary of liquid water and ice VII	12
Scattering of elastic waves by a sphere with cubic anisotropy with application to attenuation in polycrystalline materials	12
Electric field control of magnetism	12
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, II: characterization	12
A theoretical model of Surtseyan bomb fragmentation	12
Judgment on the evolution state of asymmetric games	11
A solvable two-dimensional swarmalator model	11
The plausibility of origins scenarios requiring two impactors	11
Evidence for active upper mantle flow in the Atlantic and Indo-Australian realms since the Upper Jurassic from hiatus maps and spreading rate changes	11
Indirect exclusion can promote cooperation in repeated group interactions	11
Soft wetting with (a)symmetric Shuttleworth effect	11
Averaging plus learning models and their asymptotics	11
Klein–Gordon equation for electrically charged particles with new energy-momentum operator	11
Improving surrogate model robustness to perturbations for dynamical systems through machine learning and data assimilation	11
Dispersive effective medium for anti-plane dynamics of piezo-magneto-elastic multiphase composites with generalized periodicity	11
Dynamic multi-dose vaccination with initial immunity on higher-order networks	11
A rigorous mathematical theory for topological phases and edge modes in spring-mass mechanical systems	11
Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces	11
Pace in concert with phase: rate-induced phase-tipping in birhythmic oscillators	11
Investigation of the influence of macrozones in titanium alloys on the propagation and scattering of ultrasound	11
Challenges in computational fluid dynamics applications for bone tissue engineering	11
Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations	11
The Madelung constant in N dimensions	10
Ultrasensitivity and bistability in covalent-modification cycles with positive autoregulation	10
Inductive biases for deep learning of higher-level cognition	10
Semiclassical theory predicts stochastic ghosts scaling	10
Quantitative mapping of thickness variations along a ray path using geometrical full waveform inversion and guided wave mode conversion	10
A Bose–Einstein condensate is a Bose condensate in the laboratory ground state	10
Effect of pulsating solidification on the surface properties of conductive materials	10
Axisymmetric vibration and stability of dielectric-elastic tubular bilayer system	10
The original Wigner’s friend paradox within a realist toy model	10
Robustness of subwavelength devices: a case study of cochlea-inspired rainbow sensors	10
Fracture modelling of plain concrete using non-local fracture mechanics and a graph-based computational framework	10
A probabilistic model of diffusion through a semi-permeable barrier	10
Transformations, symmetries and Noether theorems for differential-difference equations	10
Quantum measurement and colour perception: theory and applications	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
On the association of kinematics, spanwise instability and growth of secondary vortex structures in the wake of oscillating foils	10
Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics	10
The generalized Hashin–Shtrikman approach to Al/nano-TiC composite	10
Spectral theory of diffusion in partially absorbing media	10
Scattering from time-modulated subwavelength resonators	9
Tree search in DAG space with model-based reinforcement learning for causal discovery	9
Supply chain loss from easing COVID-19 restrictions: an evolutionary economic-epidemiological modelling study	9
Uncertainty in Manning’s roughness coefficient in multilevel simulations of future tsunamis in Sumatra	9
Effect of stacking order on the vibration properties of bilayer black phosphorus	9
Chiral mode transfer of symmetry-broken states in anti-parity-time-symmetric mechanical system	9
The obstacle problem in no-tension structures and cable nets	9
Unifying temperature definition in atomistic and field representations of conservation laws	9
Mechanics of tension-induced film wrinkling and restabilization: a review	9
Kinematics and dynamics of disclination lines in three-dimensional nematics	9
Analysis of a model for surfactant transport around a foam meniscus	8
Gauß–Manin from scratch: theme, variations and fantasia	8
Active nematic fluids on Riemannian two-manifolds	8
A general solution for rotating lattices of identical point vortices	8
Enhancing the performance of solenoidal spectrometers for inverse reactions	8
Zig-zag dynamics in a Stern–Gerlach spin measurement	8

Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff–Love kinematicsand revealed by a three-dimensional computational framework	8
Generating new gravitational solutions by matrix multiplication	8
Numerically solving a nonlinear integral equation when the reciprocal of the solution lies in the integrand	8
A sampling-based approach for information-theoretic inspection management	8
New actuation modes of composite dielectric elastomers	8
A micromechanical model for phase-change composites	8
Weyl almost automorphic solutions in distribution sense of Clifford-valued stochastic neural networks with time-varying delays	8
Regolith flow on top-shaped asteroids	8
Classification of bi-Hamiltonian pairs extended by isometries	8
Introduction to the special issue dedicated to Michael J. Duff FRS on the occasion of his 70th birthday	8
Manifestations of inertia on light dragging revealed in plasmas	8
Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom	8
Solving generalized eigenvalue problems by ordinary differential equations on a quantum computer	8
Energy allocation theory for bacterial growth control in and out of steady state	8
Scattering of surface waves by a vertical truncated structured cylinder	8
Cost efficiency of institutional incentives for promoting cooperation in finite populations	8
Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta	8
Semiclassical approach for excitonic spectrum of Coulomb coupling between two Dirac particles	8
Integral equation methods for acoustic scattering by fractals	8
Mean and variance of the Eulerian and Lagrangian horizontal velocities induced by nonlinear multi-directional irregular water waves	8
Normal form for maps with nilpotent linear part	7
Travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion	7
Human decision-making in a non-ergodic additive environment	7
Determinants of successful mitigation in coupled social-climate dynamics	7
Finite time blowup of incompressible flows surrounding compressible bubbles evolving under soft equations of state	7
Curved schemes for stochastic differential equations on, or near, manifolds	7
Rheology of three-phase suspensions determined via dam-break experiments	7
Geometric mechanics of ordered and disordered kirigami	7
Characterization of near-miss connectivity-invariant homogeneous convex polyhedral cages	7
A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem	7
Effects of an impermeable layer on pore pressure response to tsunami-like inundation	7
The principle of compromise-in-competition: understanding mesoscale complexity of different levels	7
The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane	7
The linear viscoelastic fracture theory applies to soft solids better when they are…viscoelastic	7
Mori–Zwanzig latent space Koopman closure for nonlinear autoencoder	7
Nonlinear acoustics of an aperture under grazing flow	7
First-order global stress patterns inferred from upper mantle flow models	7
A new generalized potential with exchangeable functions of octahedral cross sections for modelling yielding or failure of frictional materials	7
Computation of Burgers vectors from elastic strain and lattice rotation data	7
Self-folding of two-dimensional thin templates into pyramidal microstructures by a liquid drop: a numerical model	7
Transient processes in a gas/plate structure in the case of light loading	7
Modification of Turing patterns through the use of time-varying anisotropic diffusion	7
Shape reconfiguration through origami folding sets an upper limit on drag	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
Controlling the dispersion of metamaterials in three dimensions	7
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part II	7
Young and Young–Laplace equations for a static ridge of nematic liquid crystal, and transitions between equilibrium states	7
Symmetries in transmission electron microscopy imaging of crystals with strain	7
Numerical direct scattering transform for breathers	7
A theory of stochastic fluvial landscape evolution	6
Nonlinear realization approach to topologically massive supergravity	6
Modelling sediment compaction beneath ice lenses during frost heave	6
A new integrable model of long wave–short wave interaction and linear stability spectra	6
The Robin boundary condition for modelling heat transfer	6
A low-rank ensemble Kalman filter for elliptic observations	6
Thermodynamics of decoherence	6
State-space systems as dynamic generative models	6
Mechanism for turbulence proliferation in subcritical flows	6
Analytic representation of the polarization tensor: application to the plasmon resonance of nanoparticles	6
Shear wave transmissivity and wave-induced vorticity diffusion through conversion scattering to slow-shear diffusion wave	6
An experimental study of tie transparency and individual perception in social networks	6
A model to validate effective waves in random particulate media: spherical symmetry	6
Inertial wave attractors in rapidly rotating tilted cuboids	6
Conical Kresling origami and its applications to curvature and energy programming	6
Aberration-corrected transmission electron microscopy of a non-graphitizing carbon	6
Utilization of the ExactMPF package for solving a discrete analogue of the nonlinear Schrödinger equation by the inverse scattering transform method	6
Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators	6
Universal scaling limits for spin networks via martingale methods	6
Goal-directed graph construction using reinforcement learning	6
Rheology and electro-magnetism stimulated non-trivial deformation dynamics of viscoelastic compound droplets	6
Unidirectional edge modes in time-modulated metamaterials	6
Steklov eigenvalues of nearly hyperspherical domains	6
The motion of a bubble in a non-uniform Hele-Shaw flow	6
Tunable morphing of electroactive dielectric-elastomer balloons	6
Wallpaper group kirigami	6
Multistability, symmetry and geometric conservation in eightfold waterbomb origami	6
Structural dynamic characteristics of vertical axis wind and tidal current turbines	6
A dynamic trap well model of hydrothermal shape-memory effect in amorphous polymers undergoing tailorable shape recovery behaviour	6
On the force of vertical winds in the upper atmosphere: consequences for small biological particles	6
Diffusion-induced elastic cavitation	6
A novel matrix technique for multi-order pantograph differential equations of fractional order	6
Numerical schemes for a fully nonlinear coagulation–fragmentation model coming from wave kinetic theory	6
An ion trap design for a space-deployable strontium-ion optical clock	6
On the origin of shear-band network patterns in ductile shear zones	6
Snap-through eversion of axisymmetric shells under contact indentation	5
An asymmetric graded indexed helical structured optical fibre for enhanced optical delays	5
Rogue waves in the three-level defocusing coupled Maxwell–Bloch equations	5
Coexistence times in the Moran process with environmental heterogeneity	5
Exact solutions to fall of particle to singular potential: classical versus quantum cases	5
Geometric mechanics of hybrid origami assemblies combining developable and non-developable patterns	5
Biological efficiency in processing information in green plants	5
Topology optimization with local stress constraints and continuously varying load direction and magnitude: towards practical applications	5
Mechanics of structural size effect in impact brittle fracture of steels and consequent scaling laws for fracture	5
Variational analysis of inextensible elastic curves	5