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	148
Confined helium, density dependence of the inelastic electron and photon scattering cross-sections and the optical oscillator strength	116
Riemannian geometry and molecular similarity I: spectrum of the Laplacian	81
Stability of an inhomogeneous ferrofluid in a channel, subject to a normal field	74
Anisotropy distorts the spreading of a fixed volume porous gravity current	53
Linear analysis of ice-shelf topography response to basal melting and freezing	53
A review on semi-analytical methods for aggregation and coupled aggregation–breakage equations	50
Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend	43
Whitham shocks and resonant dispersive shock waves governed by the higher order Korteweg–de Vries equation	41
Influence of the growth gradient on surface wrinkling and pattern transition in growing tubular tissues	40
The potential impact of intensified community hand hygiene interventions on respiratory tract infections: a modelling study	38
Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework	36
Frequency tunable electromagnetic vibration energy harvester using piecewise linear nonlinearity	34
Wave spectroscopy in a driven granular material	34
Unconditionally secure relativistic multi-party biased coin flipping and die rolling	33
Rediscovery of Cooper pair factor	32
Extraction of the mass density using only the p-parts of the elastic fields generated by injected highly dense small inclusions	31
Exploring the role of crystal habit in the Ostwald rule of stages	29
Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics	28
Pushing coarse-grained models beyond the continuum limit using equation learning	28
Unstable cores are the source of instability in chemical reaction networks	27
Modelling the dynamics of product adoption and abandonment	27
Matrix factorizations and pentagon maps	26
Bursty switching dynamics promotes the collapse of network topologies	26
Efficient set-theoretic algorithms for computing high-order Forman-Ricci curvature on abstract simplicial complexes	26

Edge resonance: exact results and fresh insights	25
Detecting damage in composites using volume decomposition analysis of tomographic data	25
Time-varying Bose–Einstein condensates	24
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part I	24
The formation of cave scallops	23
Critical rates of climate warming and abrupt collapse of ecosystems	23
Symplectic decomposition from submatrix determinants	23
Allowing Wigner’s friend to sequentially measure incompatible observables	22
Application of thrust layout optimization to masonry structures	22
Causal lifting and link prediction	22
Unsteady solute dispersion in the presence of reversible and irreversible reactions	22
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from monodisperse prolate and oblate spheroidal particles	21
Heteroclinic bifurcation analysis of the tippedisk through the use of Melnikov theory	21
Modelling of stress transfer in root-reinforced soils informed by four-dimensional X-ray computed tomography and digital volume correlation data	21
Development and analysis of moments preserving finite volume schemes for multi-variate nonlinear breakage model	21
Chirality and curvature determine the meandering of spirals in multilayer excitable media	20
Point-like defect on Schrödinger particles under flux field with harmonic oscillator plus Mie-type potential: application to molecular potentials	19
Bifurcations of an elastic disc coated with an elastic inextensible rod	19
Non-hyperbolicity at large scales of a high-dimensional chaotic system	18
An exact integral-to-sum relation for products of Bessel functions	18
Multimode multiple wave scattering in suspensions of solid particles in viscous liquids: part 2: numerical validation	18
Evolution of quantum non-equilibrium for coupled harmonic oscillators	18
A design-space minimum sampling strategy based on proper-orthogonal-decomposition projection	18
On the propagation of nonlinear waves in the atmosphere	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
Measure of overlap between two arbitrary ellipses on a sphere	17
Shear dynamics around self-organized viscosity-stratified autocatalytic fronts in channel flows	17
Electro-osmotic and viscous effects upon pressure to drive a droplet through a capillary	17
On the identification of power-law creep parameters from conical indentation	17
Prediction of general high-order lump solutions in the Davey–Stewartson II equation	16
The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions	16
Harmonic wave scattered by an inclusion in an elastic plane: The complete Gurtin-Murdoch model	16
Optimal regularity and Uhlenbeck compactness for general relativity and Yang–Mills theory	15
Unbiased estimation of the Hessian for partially observed diffusions	15
An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow	15
Physics-informed Dyna-style model-based deep reinforcement learning for dynamic control	15
Inertia-gravity waves in geophysical vortices	15
On reduced inertial PDE models for Cucker–Smale flocking dynamics	15
Controlling moving interfaces in solid-state batteries	15
Revisiting causality using stochastics on atmospheric temperature and CO 2 concentration	14
Scattering of elastic waves by a sphere with cubic anisotropy with application to attenuation in polycrystalline materials	14
Phase tipping: how cyclic ecosystems respond to contemporary climate	14
Robust imaging using electrical impedance tomography: review of current tools	14
A tunable electromagnetic metagrating	14
The impact of time delays on mutant fixation in pairwise social dilemma games	14
Molecular dynamics simulation on oxidation process and interfacial performance of foamed asphalt binders based on ReaxFF force field	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
Rheomergy : collective behaviour mediated by active flow-based recruitment	13
Hierarchical meta-porous materials as sound absorbers	13
Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology	13

A generic approach to the quantum mechanical transition probability	13
Strategies for guided acoustic wave inspection using mobile robots	13
Contact-line bending energy controls phospholipid vesicle adhesion	13
The θ-formulation of the two-dimensional elastica: buckling and boundary layer theory	13
Hamel’s equations and geometric mechanics of constrained and floating multibody and space systems	13
Integrable nonlinear evolution equations in three spatial dimensions	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
Modelling cerebrovascular pathology and the spread of amyloid beta in Alzheimer’s disease	12
A theoretical model of Surtseyan bomb fragmentation	12
Parameter-free higher-order Schrödinger systems with weak dissipation and forcing	12
Challenges in computational fluid dynamics applications for bone tissue engineering	12
Judgment on the evolution state of asymmetric games	12
Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media	12
Free propagation of resonant waves in nonlinear dissipative metamaterials	12
Riemann–Hilbert problem on a hyperelliptic surface and uniformly stressed inclusions embedded into a half-plane subjected to antiplane strain	12
Finite-horizon, energy-efficient trajectories in unsteady flows	12
Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations	12
Dispersive effective medium for anti-plane dynamics of piezo-magneto-elastic multiphase composites with generalized periodicity	12
Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces	12
Movement bias in asymmetric landscapes and its impact on population distribution and critical habitat size	12
A predictive model of UV-A-riboflavin crosslinking treatment on porcine corneas	12
Generalization of Duhamel's integral to multi-degree-of-freedom systems	12
The contribution of plastic sink-in to the static friction of single asperity microscopic contacts	12
Inductive biases for deep learning of higher-level cognition	12
Improving surrogate model robustness to perturbations for dynamical systems through machine learning and data assimilation	12
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, II: characterization	12
Model for deformation-induced martensitic transformation in irradiated materials	12
Plane strain wedge indentation revisited	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
Soft wetting with (a)symmetric Shuttleworth effect	11
Averaging plus learning models and their asymptotics	11
The plausibility of origins scenarios requiring two impactors	11
Investigation of the influence of macrozones in titanium alloys on the propagation and scattering of ultrasound	11
A solvable two-dimensional swarmalator model	11
The interplay between Fano and Fabry–Pérot resonances in dual-period metagratings	11
A rigorous mathematical theory for topological phases and edge modes in spring-mass mechanical systems	11
Indirect exclusion can promote cooperation in repeated group interactions	11
Quantum measurement and colour perception: theory and applications	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
High-temperature and high-pressure plastic phase of ice at the boundary of liquid water and ice VII	11
Pace in concert with phase: rate-induced phase-tipping in birhythmic oscillators	11
Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results	10
Fracture modelling of plain concrete using non-local fracture mechanics and a graph-based computational framework	10
Cost efficiency of institutional incentives for promoting cooperation in finite populations	10
A Bose–Einstein condensate is a Bose condensate in the laboratory ground state	10
Tree search in DAG space with model-based reinforcement learning for causal discovery	10
Scattering from time-modulated subwavelength resonators	10
New actuation modes of composite dielectric elastomers	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
A micromechanical model for phase-change composites	10
Dynamic multi-dose vaccination with initial immunity on higher-order networks	10
Mechanics of tension-induced film wrinkling and restabilization: a review	10
Uncertainty in Manning’s roughness coefficient in multilevel simulations of future tsunamis in Sumatra	10
Scattering of surface waves by a vertical truncated structured cylinder	10
Semiclassical theory predicts stochastic ghosts scaling	9
Effect of pulsating solidification on the surface properties of conductive materials	9
Ultrasensitivity and bistability in covalent-modification cycles with positive autoregulation	9
Chiral mode transfer of symmetry-broken states in anti-parity-time-symmetric mechanical system	9
The Madelung constant in N dimensions	9
Energy allocation theory for bacterial growth control in and out of steady state	9
The obstacle problem in no-tension structures and cable nets	9
Axisymmetric vibration and stability of dielectric-elastic tubular bilayer system	9
A probabilistic model of diffusion through a semi-permeable barrier	9
Weyl almost automorphic solutions in distribution sense of Clifford-valued stochastic neural networks with time-varying delays	9
Kinematics and dynamics of disclination lines in three-dimensional nematics	9
Spectral theory of diffusion in partially absorbing media	9
Supply chain loss from easing COVID-19 restrictions: an evolutionary economic-epidemiological modelling study	9
Effect of stacking order on the vibration properties of bilayer black phosphorus	9
The generalized Hashin–Shtrikman approach to Al/nano-TiC composite	9
Transformations, symmetries and Noether theorems for differential-difference equations	9
Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology	8
Numerically solving a nonlinear integral equation when the reciprocal of the solution lies in the integrand	8
Regolith flow on top-shaped asteroids	8
Generating new gravitational solutions by matrix multiplication	8
Gauß–Manin from scratch: theme, variations and fantasia	8
Manifestations of inertia on light dragging revealed in plasmas	8
Modification of Turing patterns through the use of time-varying anisotropic diffusion	8

Active nematic fluids on Riemannian two-manifolds	8
Unifying temperature definition in atomistic and field representations of conservation laws	8
Travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion	8
Analysis of a model for surfactant transport around a foam meniscus	8
The linear viscoelastic fracture theory applies to soft solids better when they are…viscoelastic	8
Enhancing the performance of solenoidal spectrometers for inverse reactions	8
Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta	8
Solving generalized eigenvalue problems by ordinary differential equations on a quantum computer	8
Mean and variance of the Eulerian and Lagrangian horizontal velocities induced by nonlinear multi-directional irregular water waves	8
Integral equation methods for acoustic scattering by fractals	8
Quantitative mapping of thickness variations along a ray path using geometrical full waveform inversion and guided wave mode conversion	8
Zig-zag dynamics in a Stern–Gerlach spin measurement	8
On the association of kinematics, spanwise instability and growth of secondary vortex structures in the wake of oscillating foils	8
A sampling-based approach for information-theoretic inspection management	8
Mori–Zwanzig latent space Koopman closure for nonlinear autoencoder	8
Introduction to the special issue dedicated to Michael J. Duff FRS on the occasion of his 70th birthday	8
Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom	8
A general solution for rotating lattices of identical point vortices	8
The principle of compromise-in-competition: understanding mesoscale complexity of different levels	8
The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane	8
Human decision-making in a non-ergodic additive environment	8
Determinants of successful mitigation in coupled social-climate dynamics	8
Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics	8
Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff–Love kinematicsand revealed by a three-dimensional computational framework	8
Young and Young–Laplace equations for a static ridge of nematic liquid crystal, and transitions between equilibrium states	7
Rheology of three-phase suspensions determined via dam-break experiments	7
Shape reconfiguration through origami folding sets an upper limit on drag	7
Conical Kresling origami and its applications to curvature and energy programming	7
Explorations of certain nonlinear waves of the Boussinesq and Camassa–Holm equations using physics-informed neural networks	7
Normal form for maps with nilpotent linear part	7
Effects of an impermeable layer on pore pressure response to tsunami-like inundation	7
Characterization of near-miss connectivity-invariant homogeneous convex polyhedral cages	7
Aberration-corrected transmission electron microscopy of a non-graphitizing carbon	7
Multistability, symmetry and geometric conservation in eightfold waterbomb origami	7
A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem	7
Nonlinear acoustics of an aperture under grazing flow	7
Controlling the dispersion of metamaterials in three dimensions	7
A new generalized potential with exchangeable functions of octahedral cross sections for modelling yielding or failure of frictional materials	7
Curved schemes for stochastic differential equations on, or near, manifolds	7
Symmetries in transmission electron microscopy imaging of crystals with strain	7
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part II	7
Computation of Burgers vectors from elastic strain and lattice rotation data	7
Structural dynamic characteristics of vertical axis wind and tidal current turbines	7
Geometric mechanics of ordered and disordered kirigami	7
A new integrable model of long wave–short wave interaction and linear stability spectra	7
Self-folding of two-dimensional thin templates into pyramidal microstructures by a liquid drop: a numerical model	7
Nonlinear realization approach to topologically massive supergravity	6
Numerical schemes for a fully nonlinear coagulation–fragmentation model coming from wave kinetic theory	6
A low-rank ensemble Kalman filter for elliptic observations	6
The Robin boundary condition for modelling heat transfer	6
Unidirectional edge modes in time-modulated metamaterials	6
Theta neuron subject to delayed feedback: a prototypical model for self-sustained pulsing	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
Wallpaper group kirigami	6
Finite time blowup of incompressible flows surrounding compressible bubbles evolving under soft equations of state	6
Transient processes in a gas/plate structure in the case of light loading	6
A nonlinear spectral core–periphery detection method for multiplex networks	6
A theory of stochastic fluvial landscape evolution	6
Goal-directed graph construction using reinforcement learning	6
Diffusion-induced elastic cavitation	6
An experimental study of tie transparency and individual perception in social networks	6
Modelling sediment compaction beneath ice lenses during frost heave	6
An ion trap design for a space-deployable strontium-ion optical clock	6
Utilization of the ExactMPF package for solving a discrete analogue of the nonlinear Schrödinger equation by the inverse scattering transform method	6
State-space systems as dynamic generative models	6
Predicting the spatio-temporal infection risk in indoor spaces using an efficient airborne transmission model	6
A novel matrix technique for multi-order pantograph differential equations of fractional order	6
Numerical direct scattering transform for breathers	6
Analytic representation of the polarization tensor: application to the plasmon resonance of nanoparticles	6
Homotopy classification of knotted defects in ordered media	6
A model to validate effective waves in random particulate media: spherical symmetry	6
Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators	6
Thermodynamics of decoherence	6
Universal scaling limits for spin networks via martingale methods	6
Tunable morphing of electroactive dielectric-elastomer balloons	6
Mechanism for turbulence proliferation in subcritical flows	6
Rheology and electro-magnetism stimulated non-trivial deformation dynamics of viscoelastic compound droplets	6
Non-existence of propagating Rayleigh waves in extremal materials	6
A computational-based kinetostatic synthesis method for realization of nonlinear translational stiffness	6
First-order global stress patterns inferred from upper mantle flow models	6
Growing neural networks: dynamic evolution through gradient descent	6
On the force of vertical winds in the upper atmosphere: consequences for small biological particles	6
Analytic mode-matching for accurate handling of exceptional points in a lined acoustic waveguide	5
Analysis of the superdeterministic Invariant-set theory in a hidden-variable setting	5
Simple circuit simulations of classical and quantum Turing machines	5
A cluster of N -bubbles driven along a channel at high imposed driving pressure: film orientations and bubble pressures	5
Variational analysis of inextensible elastic curves	5
The wave function as a true ensemble	5
Multiphysics modelling of light-actuated liquid crystal elastomers	5
Evolutionary dynamics of voluntary vaccination for imperfect multi-efficacy vaccines	5
Reviewers in 2024	5
The numerical unified transform method for the nonlinear Schrödinger equation on the half-line	5
The theory of scaled electromagnetism	5
Biological efficiency in processing information in green plants	5