Proceedings of the Royal Society A-Mathematical Physical and Engineeri

Article	Citations
On the stability of solutions to Schrödinger’s equation short of the adiabatic limit	157
The potential impact of intensified community hand hygiene interventions on respiratory tract infections: a modelling study	127
Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework	86
Wave spectroscopy in a driven granular material	78
Confined helium, density dependence of the inelastic electron and photon scattering cross-sections and the optical oscillator strength	57
Riemannian geometry and molecular similarity I: spectrum of the Laplacian	53
A review on semi-analytical methods for aggregation and coupled aggregation–breakage equations	52
Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics	43
Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend	40
Whitham shocks and resonant dispersive shock waves governed by the higher order Korteweg–de Vries equation	38
Influence of the growth gradient on surface wrinkling and pattern transition in growing tubular tissues	38
Modelling the dynamics of product adoption and abandonment	36
Anisotropy distorts the spreading of a fixed volume porous gravity current	35
Pushing coarse-grained models beyond the continuum limit using equation learning	34
Rediscovery of Cooper pair factor	34
Extraction of the mass density using only the p-parts of the elastic fields generated by injected highly dense small inclusions	34
Exploring the role of crystal habit in the Ostwald rule of stages	30
Unstable cores are the source of instability in chemical reaction networks	29
Bursty switching dynamics promotes the collapse of network topologies	29
(3+1)-dimensional-modified Kadomtsev–Petviashvili equation and its ∂¯-formalism	28
Stability of an inhomogeneous ferrofluid in a channel, subject to a normal field	27
A high-resolution discourse on seismic tomography	27
Linear analysis of ice-shelf topography response to basal melting and freezing	26
Modelling of stress transfer in root-reinforced soils informed by four-dimensional X-ray computed tomography and digital volume correlation data	25
Evolution of quantum non-equilibrium for coupled harmonic oscillators	25

Development and analysis of moments preserving finite volume schemes for multi-variate nonlinear breakage model	25
Frequency tunable electromagnetic vibration energy harvester using piecewise linear nonlinearity	25
Matrix factorizations and pentagon maps	24
Detecting damage in composites using volume decomposition analysis of tomographic data	24
Non-hyperbolicity at large scales of a high-dimensional chaotic system	24
Efficient set-theoretic algorithms for computing high-order Forman-Ricci curvature on abstract simplicial complexes	24
Edge resonance: exact results and fresh insights	23
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part I	23
Critical rates of climate warming and abrupt collapse of ecosystems	22
The formation of cave scallops	22
Causal lifting and link prediction	22
Unsteady solute dispersion in the presence of reversible and irreversible reactions	22
Heteroclinic bifurcation analysis of the tippedisk through the use of Melnikov theory	21
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from monodisperse prolate and oblate spheroidal particles	21
Application of thrust layout optimization to masonry structures	21
Bifurcations of an elastic disc coated with an elastic inextensible rod	20
Homogenized phase transition model for perforated ferromagnetic media	19
Point-like defect on Schrödinger particles under flux field with harmonic oscillator plus Mie-type potential: application to molecular potentials	18
Chirality and curvature determine the meandering of spirals in multilayer excitable media	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	18
Symplectic decomposition from submatrix determinants	18
An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow	18
Allowing Wigner’s friend to sequentially measure incompatible observables	18
Time-varying Bose–Einstein condensates	18
Unbiased estimation of the Hessian for partially observed diffusions	17
Multimode multiple wave scattering in suspensions of solid particles in viscous liquids: part 2: numerical validation	17
On the propagation of nonlinear waves in the atmosphere	17
The impact of time delays on mutant fixation in pairwise social dilemma games	17
Inertia-gravity waves in geophysical vortices	17
Revisiting causality using stochastics on atmospheric temperature and CO 2 concentration	16
On reduced inertial PDE models for Cucker–Smale flocking dynamics	15
Electro-osmotic and viscous effects upon pressure to drive a droplet through a capillary	15
Optimal regularity and Uhlenbeck compactness for general relativity and Yang–Mills theory	15
Measure of overlap between two arbitrary ellipses on a sphere	15
Controlling moving interfaces in solid-state batteries	15
A design-space minimum sampling strategy based on proper-orthogonal-decomposition projection	15
Shear dynamics around self-organized viscosity-stratified autocatalytic fronts in channel flows	15
Prediction of general high-order lump solutions in the Davey–Stewartson II equation	14
An exact integral-to-sum relation for products of Bessel functions	14
Capillary adhesion between solid surfaces: small-volume liquid rings and bridges	14
Harmonic wave scattered by an inclusion in an elastic plane: The complete Gurtin-Murdoch model	14
Phase tipping: how cyclic ecosystems respond to contemporary climate	14
Weber’s Law of perception is a consequence of resolving the intensity of natural scintillating light and sound with the least possible error	14
The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions	14
Physics-informed Dyna-style model-based deep reinforcement learning for dynamic control	14
The θ-formulation of the two-dimensional elastica: buckling and boundary layer theory	13
Finite-horizon, energy-efficient trajectories in unsteady flows	13
Model for deformation-induced martensitic transformation in irradiated materials	13
A tunable electromagnetic metagrating	13
The contribution of plastic sink-in to the static friction of single asperity microscopic contacts	13

Modelling cerebrovascular pathology and the spread of amyloid beta in Alzheimer’s disease	13
Generalization of Duhamel's integral to multi-degree-of-freedom systems	13
Rheomergy : collective behaviour mediated by active flow-based recruitment	13
Scattering of elastic waves by a sphere with cubic anisotropy with application to attenuation in polycrystalline materials	13
Free propagation of resonant waves in nonlinear dissipative metamaterials	13
Tailored acoustic metamaterials. Part I. Thin- and thick-walled Helmholtz resonator arrays	13
Density functional theory calculations on the solvatochromism of covalent organic framework Py-TT cluster compounds	13
A predictive model of UV-A-riboflavin crosslinking treatment on porcine corneas	13
Hamel’s equations and geometric mechanics of constrained and floating multibody and space systems	13
Molecular dynamics simulation on oxidation process and interfacial performance of foamed asphalt binders based on ReaxFF force field	13
High-temperature and high-pressure plastic phase of ice at the boundary of liquid water and ice VII	12
Unified wavefront singularity characterization of three-dimensional elastodynamic time-domain half-space Green's function under impulsive boundary and internal loads	12
Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology	12
Contact-line bending energy controls phospholipid vesicle adhesion	12
Investigation of the influence of macrozones in titanium alloys on the propagation and scattering of ultrasound	12
Dispersive effective medium for anti-plane dynamics of piezo-magneto-elastic multiphase composites with generalized periodicity	12
The plausibility of origins scenarios requiring two impactors	12
Robust imaging using electrical impedance tomography: review of current tools	12
Strategies for guided acoustic wave inspection using mobile robots	12
Integrable nonlinear evolution equations in three spatial dimensions	12
The interplay between Fano and Fabry–Pérot resonances in dual-period metagratings	12
Klein–Gordon equation for electrically charged particles with new energy-momentum operator	12
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, II: characterization	12
Hierarchical meta-porous materials as sound absorbers	12
A generic approach to the quantum mechanical transition probability	12
A theoretical model of Surtseyan bomb fragmentation	12
A rigorous mathematical theory for topological phases and edge modes in spring-mass mechanical systems	11
Improving surrogate model robustness to perturbations for dynamical systems through machine learning and data assimilation	11
Movement bias in asymmetric landscapes and its impact on population distribution and critical habitat size	11
Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations	11
Instability bands for periodic travelling waves in the modified Korteweg–de Vries equation	11
Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media	11
Averaging plus learning models and their asymptotics	11
Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces	11
Soft wetting with (a)symmetric Shuttleworth effect	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
Plane strain wedge indentation revisited	11
Judgment on the evolution state of asymmetric games	11
Parameter-free higher-order Schrödinger systems with weak dissipation and forcing	11
Challenges in computational fluid dynamics applications for bone tissue engineering	11
Inductive biases for deep learning of higher-level cognition	11
Dynamic multi-dose vaccination with initial immunity on higher-order networks	10
A probabilistic model of diffusion through a semi-permeable barrier	10
Semiclassical theory predicts stochastic ghosts scaling	10
A solvable two-dimensional swarmalator model	10
Indirect exclusion can promote cooperation in repeated group interactions	10
Spectral theory of diffusion in partially absorbing media	10
Quantum measurement and colour perception: theory and applications	10
Chevron patterns in an active nematic liquid crystal film in contact with smectic A	10
Active nematic fluids on Riemannian two-manifolds	10
Pace in concert with phase: rate-induced phase-tipping in birhythmic oscillators	10
The generalized Hashin–Shtrikman approach to Al/nano-TiC composite	9
Energy allocation theory for bacterial growth control in and out of steady state	9
Effect of stacking order on the vibration properties of bilayer black phosphorus	9
Supply chain loss from easing COVID-19 restrictions: an evolutionary economic-epidemiological modelling study	9
Transformations, symmetries and Noether theorems for differential-difference equations	9
Kinematics and dynamics of disclination lines in three-dimensional nematics	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
Axisymmetric vibration and stability of dielectric-elastic tubular bilayer system	9
Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results	9
Unifying temperature definition in atomistic and field representations of conservation laws	9
Weyl almost automorphic solutions in distribution sense of Clifford-valued stochastic neural networks with time-varying delays	9
On the association of kinematics, spanwise instability and growth of secondary vortex structures in the wake of oscillating foils	9
The Madelung constant in N dimensions	9
Human decision-making in a non-ergodic additive environment	8
Mean and variance of the Eulerian and Lagrangian horizontal velocities induced by nonlinear multi-directional irregular water waves	8
A sampling-based approach for information-theoretic inspection management	8
The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane	8
Manifestations of inertia on light dragging revealed in plasmas	8
Mechanics of tension-induced film wrinkling and restabilization: a review	8
Quantitative mapping of thickness variations along a ray path using geometrical full waveform inversion and guided wave mode conversion	8
Robustness of subwavelength devices: a case study of cochlea-inspired rainbow sensors	8
Uncertainty in Manning’s roughness coefficient in multilevel simulations of future tsunamis in Sumatra	8
Effect of pulsating solidification on the surface properties of conductive materials	8
The principle of compromise-in-competition: understanding mesoscale complexity of different levels	8
A general solution for rotating lattices of identical point vortices	8
Regolith flow on top-shaped asteroids	8
Introduction to the special issue dedicated to Michael J. Duff FRS on the occasion of his 70th birthday	8
Gauß–Manin from scratch: theme, variations and fantasia	8

Modification of Turing patterns through the use of time-varying anisotropic diffusion	8
Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics	8
New actuation modes of composite dielectric elastomers	8
A micromechanical model for phase-change composites	8
Cost efficiency of institutional incentives for promoting cooperation in finite populations	8
Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology	8
Scattering of surface waves by a vertical truncated structured cylinder	8
Solving generalized eigenvalue problems by ordinary differential equations on a quantum computer	8
Enhancing the performance of solenoidal spectrometers for inverse reactions	8
Integral equation methods for acoustic scattering by fractals	8
Travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion	8
Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom	8
Analysis of a model for surfactant transport around a foam meniscus	8
Explorations of certain nonlinear waves of the Boussinesq and Camassa–Holm equations using physics-informed neural networks	8
Scattering from time-modulated subwavelength resonators	8
The original Wigner’s friend paradox within a realist toy model	8
A Bose–Einstein condensate is a Bose condensate in the laboratory ground state	8
Tree search in DAG space with model-based reinforcement learning for causal discovery	8
Zig-zag dynamics in a Stern–Gerlach spin measurement	8
Full-field mechanics imaging by direct inversion of electrical data	7
Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff–Love kinematicsand revealed by a three-dimensional computational framework	7
Numerically solving a nonlinear integral equation when the reciprocal of the solution lies in the integrand	7
Rheology of three-phase suspensions determined via dam-break experiments	7
Symmetries in transmission electron microscopy imaging of crystals with strain	7
First-order global stress patterns inferred from upper mantle flow models	7
Geometric mechanics of ordered and disordered kirigami	7
Self-folding of two-dimensional thin templates into pyramidal microstructures by a liquid drop: a numerical model	7
Finite time blowup of incompressible flows surrounding compressible bubbles evolving under soft equations of state	7
Stability of a material interface in a two-phase system with a free surface	7
Subwavelength localization in disordered systems	7
Determinants of successful mitigation in coupled social-climate dynamics	7
Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta	7
The linear viscoelastic fracture theory applies to soft solids better when they are…viscoelastic	7
Normal form for maps with nilpotent linear part	7
Young and Young–Laplace equations for a static ridge of nematic liquid crystal, and transitions between equilibrium states	7
Computation of Burgers vectors from elastic strain and lattice rotation data	7
Transient processes in a gas/plate structure in the case of light loading	7
Controlling the dispersion of metamaterials in three dimensions	7
Structural dynamic characteristics of vertical axis wind and tidal current turbines	7
Mori–Zwanzig latent space Koopman closure for nonlinear autoencoder	7
Generating new gravitational solutions by matrix multiplication	7
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part II	7
A new generalized potential with exchangeable functions of octahedral cross sections for modelling yielding or failure of frictional materials	7
Effects of an impermeable layer on pore pressure response to tsunami-like inundation	7
Curved schemes for stochastic differential equations on, or near, manifolds	7
Characterization of near-miss connectivity-invariant homogeneous convex polyhedral cages	7
Nonlinear acoustics of an aperture under grazing flow	7
Universal scaling limits for spin networks via martingale methods	6
A novel matrix technique for multi-order pantograph differential equations of fractional order	6
Inertial wave attractors in rapidly rotating tilted cuboids	6
A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem	6
A computational-based kinetostatic synthesis method for realization of nonlinear translational stiffness	6
Multistability, symmetry and geometric conservation in eightfold waterbomb origami	6
On the force of vertical winds in the upper atmosphere: consequences for small biological particles	6
Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators	6
An experimental study of tie transparency and individual perception in social networks	6
Tunable morphing of electroactive dielectric-elastomer balloons	6
Utilization of the ExactMPF package for solving a discrete analogue of the nonlinear Schrödinger equation by the inverse scattering transform method	6
Theta neuron subject to delayed feedback: a prototypical model for self-sustained pulsing	6
Aberration-corrected transmission electron microscopy of a non-graphitizing carbon	6
Numerical direct scattering transform for breathers	6
A nonlinear spectral core–periphery detection method for multiplex networks	6
Goal-directed graph construction using reinforcement learning	6
Numerical schemes for a fully nonlinear coagulation–fragmentation model coming from wave kinetic theory	6
Diffusion-induced elastic cavitation	6
Shear wave transmissivity and wave-induced vorticity diffusion through conversion scattering to slow-shear diffusion wave	6
Rheology and electro-magnetism stimulated non-trivial deformation dynamics of viscoelastic compound droplets	6
Conical Kresling origami and its applications to curvature and energy programming	6
Shape reconfiguration through origami folding sets an upper limit on drag	6
Analytic representation of the polarization tensor: application to the plasmon resonance of nanoparticles	6
Modelling sediment compaction beneath ice lenses during frost heave	6
A low-rank ensemble Kalman filter for elliptic observations	6
State-space systems as dynamic generative models	6
The Robin boundary condition for modelling heat transfer	6
Extending Q -learning to continuous and mixed strategy games based on spatial reciprocity	5
Variational analysis of inextensible elastic curves	5
Evolutionary dynamics of voluntary vaccination for imperfect multi-efficacy vaccines	5
Coexistence times in the Moran process with environmental heterogeneity	5
The classical microcanonical ensemble: covariant reformulation and application to small systems	5
Existence and location of internal resonance of two-mode nonlinear conservative oscillators	5
Direct method to determine singular point of enveloped surface and its application to worm wheel tooth surface	5
Mechanics of structural size effect in impact brittle fracture of steels and consequent scaling laws for fracture	5
Snap-through eversion of axisymmetric shells under contact indentation	5
Enhanced wave transmission in random media with mirror symmetry	5
A cluster of N -bubbles driven along a channel at high imposed driving pressure: film orientations and bubble pressures	5
An asymmetric graded indexed helical structured optical fibre for enhanced optical delays	5
A novel computational approach combined with deep learning for dynamic analysis of sandwich plates featuring inversely designed auxetic core	5
Tiered social distancing policies and epidemic control	5
Rogue waves in the three-level defocusing coupled Maxwell–Bloch equations	5
Topology optimization with local stress constraints and continuously varying load direction and magnitude: towards practical applications	5
Tensor networks for quantum machine learning	5
Biological efficiency in processing information in green plants	5
Eshelby’s inclusion and inhomogeneity problems under harmonic heat transfer	5
Memory effects in friction: the role of sliding heterogeneities	5
A generalized method for the reliability assessment of safety–critical inspection	5