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	140
The potential impact of intensified community hand hygiene interventions on respiratory tract infections: a modelling study	102
Wave spectroscopy in a driven granular material	76
Riemannian geometry and molecular similarity I: spectrum of the Laplacian	71
Linear analysis of ice-shelf topography response to basal melting and freezing	52
Pushing coarse-grained models beyond the continuum limit using equation learning	46
Anisotropy distorts the spreading of a fixed volume porous gravity current	44
Influence of the growth gradient on surface wrinkling and pattern transition in growing tubular tissues	43
Exploring the role of crystal habit in the Ostwald rule of stages	41
Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics	41
Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework	39
Confined helium, density dependence of the inelastic electron and photon scattering cross-sections and the optical oscillator strength	38
Bursty switching dynamics promotes the collapse of network topologies	36
Modelling the dynamics of product adoption and abandonment	36
Extraction of the mass density using only the p-parts of the elastic fields generated by injected highly dense small inclusions	33
Whitham shocks and resonant dispersive shock waves governed by the higher order Korteweg–de Vries equation	33
Unstable cores are the source of instability in chemical reaction networks	30
Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend	28
A review on semi-analytical methods for aggregation and coupled aggregation–breakage equations	28
Unconditionally secure relativistic multi-party biased coin flipping and die rolling	28
Rediscovery of Cooper pair factor	27
Frequency tunable electromagnetic vibration energy harvester using piecewise linear nonlinearity	25
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from monodisperse prolate and oblate spheroidal particles	25
Detecting damage in composites using volume decomposition analysis of tomographic data	25
Modelling of stress transfer in root-reinforced soils informed by four-dimensional X-ray computed tomography and digital volume correlation data	24

Quantifying the preventive effect of wearing face masks	24
Chirality and curvature determine the meandering of spirals in multilayer excitable media	23
Allowing Wigner’s friend to sequentially measure incompatible observables	23
Symplectic decomposition from submatrix determinants	22
Bifurcations of an elastic disc coated with an elastic inextensible rod	22
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part I	22
Unsteady solute dispersion in the presence of reversible and irreversible reactions	22
Non-hyperbolicity at large scales of a high-dimensional chaotic system	21
Point-like defect on Schrödinger particles under flux field with harmonic oscillator plus Mie-type potential: application to molecular potentials	21
Application of thrust layout optimization to masonry structures	21
The formation of cave scallops	21
Causal lifting and link prediction	21
Development and analysis of moments preserving finite volume schemes for multi-variate nonlinear breakage model	20
Evolution of quantum non-equilibrium for coupled harmonic oscillators	20
Edge resonance: exact results and fresh insights	20
Matrix factorizations and pentagon maps	19
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	18
Critical rates of climate warming and abrupt collapse of ecosystems	18
Time-varying Bose–Einstein condensates	18
Phase tipping: how cyclic ecosystems respond to contemporary climate	17
Shear dynamics around self-organized viscosity-stratified autocatalytic fronts in channel flows	17
On reduced inertial PDE models for Cucker–Smale flocking dynamics	17
Physics-informed Dyna-style model-based deep reinforcement learning for dynamic control	17
On the identification of power-law creep parameters from conical indentation	16
Harmonic wave scattered by an inclusion in an elastic plane: The complete Gurtin-Murdoch model	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	16
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
Inertia-gravity waves in geophysical vortices	16
An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow	16
Unbiased estimation of the Hessian for partially observed diffusions	15
Multimode multiple wave scattering in suspensions of solid particles in viscous liquids: part 2: numerical validation	15
An exact integral-to-sum relation for products of Bessel functions	15
Optimal regularity and Uhlenbeck compactness for general relativity and Yang–Mills theory	14
Measure of overlap between two arbitrary ellipses on a sphere	14
Revisiting causality using stochastics on atmospheric temperature and CO 2 concentration	14
The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions	14
A design-space minimum sampling strategy based on proper-orthogonal-decomposition projection	14
A predictive model of UV-A-riboflavin crosslinking treatment on porcine corneas	13
A tunable electromagnetic metagrating	13
The impact of time delays on mutant fixation in pairwise social dilemma games	13
Molecular dynamics simulation on oxidation process and interfacial performance of foamed asphalt binders based on ReaxFF force field	13
Riemann–Hilbert problem on a hyperelliptic surface and uniformly stressed inclusions embedded into a half-plane subjected to antiplane strain	13
Contact-line bending energy controls phospholipid vesicle adhesion	13
The θ-formulation of the two-dimensional elastica: buckling and boundary layer theory	13
Prediction of general high-order lump solutions in the Davey–Stewartson II equation	13
Hamel’s equations and geometric mechanics of constrained and floating multibody and space systems	13
Correction to ‘Ice sheet flow with thermally activated sliding. Part 2: the stability of subtemperate regions’	13
A generic approach to the quantum mechanical transition probability	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
On the propagation of nonlinear waves in the atmosphere	13
Model for deformation-induced martensitic transformation in irradiated materials	13
Scattering of elastic waves by a sphere with cubic anisotropy with application to attenuation in polycrystalline materials	12
Strategies for guided acoustic wave inspection using mobile robots	12
Hierarchical meta-porous materials as sound absorbers	12
Robust imaging using electrical impedance tomography: review of current tools	12
Modelling cerebrovascular pathology and the spread of amyloid beta in Alzheimer’s disease	12
Generalization of Duhamel's integral to multi-degree-of-freedom systems	12
Finite-horizon, energy-efficient trajectories in unsteady flows	12
Free propagation of resonant waves in nonlinear dissipative metamaterials	12
Tailored acoustic metamaterials. Part I. Thin- and thick-walled Helmholtz resonator arrays	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	12
Rheomergy : collective behaviour mediated by active flow-based recruitment	12
Electric field control of magnetism	12
Density functional theory calculations on the solvatochromism of covalent organic framework Py-TT cluster compounds	12
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, II: characterization	11
Quantum measurement and colour perception: theory and applications	11
Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media	11
The interplay between Fano and Fabry–Pérot resonances in dual-period metagratings	11
Judgment on the evolution state of asymmetric games	11
A solvable two-dimensional swarmalator model	11
A theoretical model of Surtseyan bomb fragmentation	11
Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology	11
Plane strain wedge indentation revisited	11
Dynamic multi-dose vaccination with initial immunity on higher-order networks	11
Averaging plus learning models and their asymptotics	11
Klein–Gordon equation for electrically charged particles with new energy-momentum operator	11
Unified wavefront singularity characterization of three-dimensional elastodynamic time-domain half-space Green's function under impulsive boundary and internal loads	11
High-temperature and high-pressure plastic phase of ice at the boundary of liquid water and ice VII	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
Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces	11
Challenges in computational fluid dynamics applications for bone tissue engineering	10
Effect of pulsating solidification on the surface properties of conductive materials	10
The original Wigner’s friend paradox within a realist toy model	10
Quantitative mapping of thickness variations along a ray path using geometrical full waveform inversion and guided wave mode conversion	10
Pace in concert with phase: rate-induced phase-tipping in birhythmic oscillators	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
Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations	10
Dimension-reduction of dynamics on real-world networks with symmetry	10
Fracture modelling of plain concrete using non-local fracture mechanics and a graph-based computational framework	10
Robustness of subwavelength devices: a case study of cochlea-inspired rainbow sensors	10
Inductive biases for deep learning of higher-level cognition	10
The plausibility of origins scenarios requiring two impactors	10
Investigation of the influence of macrozones in titanium alloys on the propagation and scattering of ultrasound	10
The Madelung constant in N dimensions	10
Ultrasensitivity and bistability in covalent-modification cycles with positive autoregulation	10
Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results	10
Axisymmetric vibration and stability of dielectric-elastic tubular bilayer system	10
Soft wetting with (a)symmetric Shuttleworth effect	10
Indirect exclusion can promote cooperation in repeated group interactions	10
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
Cost efficiency of institutional incentives for promoting cooperation in finite populations	9
A probabilistic model of diffusion through a semi-permeable barrier	9
Scattering from time-modulated subwavelength resonators	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
New actuation modes of composite dielectric elastomers	9
Energy allocation theory for bacterial growth control in and out of steady state	9
A Bose–Einstein condensate is a Bose condensate in the laboratory ground state	9
Semiclassical theory predicts stochastic ghosts scaling	9
Transformations, symmetries and Noether theorems for differential-difference equations	9
Effect of stacking order on the vibration properties of bilayer black phosphorus	9
Unifying temperature definition in atomistic and field representations of conservation laws	9
A sampling-based approach for information-theoretic inspection management	8
Enhancing the performance of solenoidal spectrometers for inverse reactions	8
Travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion	8
A general solution for rotating lattices of identical point vortices	8
Gauß–Manin from scratch: theme, variations and fantasia	8
Chiral mode transfer of symmetry-broken states in anti-parity-time-symmetric mechanical system	8
A micromechanical model for phase-change composites	8
The principle of compromise-in-competition: understanding mesoscale complexity of different levels	8
Determinants of successful mitigation in coupled social-climate dynamics	8
Modification of Turing patterns through the use of time-varying anisotropic diffusion	8
Analysis of a model for surfactant transport around a foam meniscus	8
Solving generalized eigenvalue problems by ordinary differential equations on a quantum computer	8
Tree search in DAG space with model-based reinforcement learning for causal discovery	8

Kinematics and dynamics of disclination lines in three-dimensional nematics	8
Active nematic fluids on Riemannian two-manifolds	8
Mechanics of tension-induced film wrinkling and restabilization: a review	8
Semiclassical approach for excitonic spectrum of Coulomb coupling between two Dirac particles	8
Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta	8
Regolith flow on top-shaped asteroids	8
Weyl almost automorphic solutions in distribution sense of Clifford-valued stochastic neural networks with time-varying delays	8
The obstacle problem in no-tension structures and cable nets	8
Spectral theory of diffusion in partially absorbing media	8
Supply chain loss from easing COVID-19 restrictions: an evolutionary economic-epidemiological modelling study	8
The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane	7
Integral equation methods for acoustic scattering by fractals	7
Explorations of certain nonlinear waves of the Boussinesq and Camassa–Holm equations using physics-informed neural networks	7
Self-folding of two-dimensional thin templates into pyramidal microstructures by a liquid drop: a numerical model	7
Mean and variance of the Eulerian and Lagrangian horizontal velocities induced by nonlinear multi-directional irregular water waves	7
Controlling the dispersion of metamaterials in three dimensions	7
Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom	7
Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology	7
Normal form for maps with nilpotent linear part	7
Transient processes in a gas/plate structure in the case of light loading	7
Classification of bi-Hamiltonian pairs extended by isometries	7
Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff–Love kinematicsand revealed by a three-dimensional computational framework	7
Generating new gravitational solutions by matrix multiplication	7
Nonlinear acoustics of an aperture under grazing flow	7
Numerically solving a nonlinear integral equation when the reciprocal of the solution lies in the integrand	7
Human decision-making in a non-ergodic additive environment	7
Characterization of near-miss connectivity-invariant homogeneous convex polyhedral cages	7
Zig-zag dynamics in a Stern–Gerlach spin measurement	7
Effects of an impermeable layer on pore pressure response to tsunami-like inundation	7
Finite time blowup of incompressible flows surrounding compressible bubbles evolving under soft equations of state	7
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
Manifestations of inertia on light dragging revealed in plasmas	7
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part II	7
Mori–Zwanzig latent space Koopman closure for nonlinear autoencoder	7
Structural dynamic characteristics of vertical axis wind and tidal current turbines	7
Rheology of three-phase suspensions determined via dam-break experiments	7
Multistability, symmetry and geometric conservation in eightfold waterbomb origami	7
Aberration-corrected transmission electron microscopy of a non-graphitizing carbon	6
Shape reconfiguration through origami folding sets an upper limit on drag	6
Computation of Burgers vectors from elastic strain and lattice rotation data	6
A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem	6
Nonlinear realization approach to topologically massive supergravity	6
Diffusion-induced elastic cavitation	6
A novel matrix technique for multi-order pantograph differential equations of fractional order	6
On the origin of shear-band network patterns in ductile shear zones	6
Goal-directed graph construction using reinforcement learning	6
Wallpaper group kirigami	6
The Robin boundary condition for modelling heat transfer	6
Modelling sediment compaction beneath ice lenses during frost heave	6
A model to validate effective waves in random particulate media: spherical symmetry	6
Young and Young–Laplace equations for a static ridge of nematic liquid crystal, and transitions between equilibrium states	6
A new integrable model of long wave–short wave interaction and linear stability spectra	6
Curved schemes for stochastic differential equations on, or near, manifolds	6
Computational synthesis of wheeled vehicles via multi-layer topology optimization	6
A theory of stochastic fluvial landscape evolution	6
State-space systems as dynamic generative models	6
Mechanism for turbulence proliferation in subcritical flows	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
Inertial wave attractors in rapidly rotating tilted cuboids	6
An ion trap design for a space-deployable strontium-ion optical clock	6
Conical Kresling origami and its applications to curvature and energy programming	6
Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators	6
Geometric mechanics of ordered and disordered kirigami	6
Symmetries in transmission electron microscopy imaging of crystals with strain	6
Numerical direct scattering transform for breathers	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
Unidirectional edge modes in time-modulated metamaterials	6
The motion of a bubble in a non-uniform Hele-Shaw flow	6
An experimental study of tie transparency and individual perception in social networks	6
Shear wave transmissivity and wave-induced vorticity diffusion through conversion scattering to slow-shear diffusion wave	6
A dynamic trap well model of hydrothermal shape-memory effect in amorphous polymers undergoing tailorable shape recovery behaviour	6
Utilization of the ExactMPF package for solving a discrete analogue of the nonlinear Schrödinger equation by the inverse scattering transform method	6
Steklov eigenvalues of nearly hyperspherical domains	6
Analysis of the superdeterministic Invariant-set theory in a hidden-variable setting	5
Neural closure models for dynamical systems	5
The theory of scaled electromagnetism	5
Enhanced wave transmission in random media with mirror symmetry	5
Symmetry-breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials	5
Memory effects in friction: the role of sliding heterogeneities	5
Epidemics on multilayer simplicial complexes	5
Coexistence times in the Moran process with environmental heterogeneity	5
Analytic mode-matching for accurate handling of exceptional points in a lined acoustic waveguide	5
Tensor networks for quantum machine learning	5
Biological efficiency in processing information in green plants	5
Mechanics of structural size effect in impact brittle fracture of steels and consequent scaling laws for fracture	5
Direct method to determine singular point of enveloped surface and its application to worm wheel tooth surface	5
Rogue waves in the three-level defocusing coupled Maxwell–Bloch equations	5
The wave function as a true ensemble	5
Geometric mechanics of hybrid origami assemblies combining developable and non-developable patterns	5
Topology optimization with local stress constraints and continuously varying load direction and magnitude: towards practical applications	5
Two-layer gravity currents of generalized Newtonian fluids	5
SINDy for delay-differential equations: application to model bacterial zinc response	5