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	179
Exploring the role of crystal habit in the Ostwald rule of stages	140
Riemannian geometry and molecular similarity I: spectrum of the Laplacian	99
Predictions of asthenosphere flow from Couette/Poiseuille models compared to seismic anisotropy and mantle circulation models	98
Stability of an inhomogeneous ferrofluid in a channel, subject to a normal field	65
Rediscovery of Cooper pair factor	56
Extraction of the mass density using only the p-parts of the elastic fields generated by injected highly dense small inclusions	51
A review on semi-analytical methods for aggregation and coupled aggregation–breakage equations	43
Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend	41
Whitham shocks and resonant dispersive shock waves governed by the higher order Korteweg–de Vries equation	36
Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework	35
Wave spectroscopy in a driven granular material	35
Confined helium, density dependence of the inelastic electron and photon scattering cross-sections and the optical oscillator strength	32
Unstable cores are the source of instability in chemical reaction networks	31
Stochastic calculus of run-and-tumble motion: an applied perspective	31
The potential impact of intensified community hand hygiene interventions on respiratory tract infections: a modelling study	29
Frequency tunable electromagnetic vibration energy harvester using piecewise linear nonlinearity	28
Anisotropy distorts the spreading of a fixed volume porous gravity current	28
Pushing coarse-grained models beyond the continuum limit using equation learning	28
Flexural wave interaction with compressive floating ice over undulating porous bed	27
A high-resolution discourse on seismic tomography	27
Modelling the dynamics of product adoption and abandonment	26
Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics	26
Linear analysis of ice-shelf topography response to basal melting and freezing	25
Bursty switching dynamics promotes the collapse of network topologies	24

(3+1)-dimensional-modified Kadomtsev–Petviashvili equation and its ∂¯-formalism	24
Matrix factorizations and pentagon maps	23
The formation of cave scallops	23
Efficient set-theoretic algorithms for computing high-order Forman-Ricci curvature on abstract simplicial complexes	22
Edge resonance: exact results and fresh insights	22
Detecting damage in composites using volume decomposition analysis of tomographic data	22
Non-hyperbolicity at large scales of a high-dimensional chaotic system	21
Evolution of quantum non-equilibrium for coupled harmonic oscillators	21
Critical rates of climate warming and abrupt collapse of ecosystems	21
Learning the governing partial differential equation of solid diffusion from atomistic simulations	21
Application of thrust layout optimization to masonry structures	20
Time-varying resonators in acoustic waveguides: a transfer matrix formalism for space–time-modulated metamaterials	20
Allowing Wigner’s friend to sequentially measure incompatible observables	20
Heteroclinic bifurcation analysis of the tippedisk through the use of Melnikov theory	20
Homogenized phase transition model for perforated ferromagnetic media	20
Causal lifting and link prediction	19
Exploring natural variation in tendon constitutive parameters via Bayesian data selection and mixed effects models	18
Rolling and lifting thresholds of sediment entrainment: effects of bed particle arrangement, particle exposure and slip-spinning motion	18
Chirality and curvature determine the meandering of spirals in multilayer excitable media	17
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part I	17
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from monodisperse prolate and oblate spheroidal particles	17
Unsteady solute dispersion in the presence of reversible and irreversible reactions	16
Bifurcations of an elastic disc coated with an elastic inextensible rod	16
Development and analysis of moments preserving finite volume schemes for multi-variate nonlinear breakage model	16
Point-like defect on Schrödinger particles under flux field with harmonic oscillator plus Mie-type potential: application to molecular potentials	16
Modelling of stress transfer in root-reinforced soils informed by four-dimensional X-ray computed tomography and digital volume correlation data	16
The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions	16
On reduced inertial PDE models for Cucker–Smale flocking dynamics	15
Unbiased estimation of the Hessian for partially observed diffusions	15
Controlling moving interfaces in solid-state batteries	15
Harmonic wave scattered by an inclusion in an elastic plane: The complete Gurtin-Murdoch model	15
Data-driven two-dimensional stationary quantum droplets and wave propagations in the amended Gross–Pitaevskii equation with two potentials via deep neural networks learning	14
Capillary adhesion between solid surfaces: small-volume liquid rings and bridges	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
Revisiting causality using stochastics on atmospheric temperature and CO 2 concentration	14
The impact of time delays on mutant fixation in pairwise social dilemma games	14
Electro-osmotic and viscous effects upon pressure to drive a droplet through a capillary	14
A design-space minimum sampling strategy based on proper-orthogonal-decomposition projection	14
Shear dynamics around self-organized viscosity-stratified autocatalytic fronts in channel flows	14
Prediction of general high-order lump solutions in the Davey–Stewartson II equation	14
Hybridization theory for plasmon resonance in metallic nanostructures	14
An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow	14
Can porous vertical penetrative convection become linearly unstable?	14
Inertia-gravity waves in geophysical vortices	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
Classically bound and quantum quasi-bound states of an electron on a plane adjacent to a magnetic monopole	13
On the propagation of nonlinear waves in the atmosphere	13
Free propagation of resonant waves in nonlinear dissipative metamaterials	13
Tailored acoustic metamaterials. Part I. Thin- and thick-walled Helmholtz resonator arrays	13

Multimode multiple wave scattering in suspensions of solid particles in viscous liquids: part 2: numerical validation	13
A tunable electromagnetic metagrating	13
Analytical and numerical steady states for thermal convection in an inclined, slender, two-dimensional enclosure	13
Density functional theory calculations on the solvatochromism of covalent organic framework Py-TT cluster compounds	12
Rheomergy : collective behaviour mediated by active flow-based recruitment	12
Model for deformation-induced martensitic transformation in irradiated materials	12
Contact-line bending energy controls phospholipid vesicle adhesion	12
A generic approach to the quantum mechanical transition probability	12
Strategies for guided acoustic wave inspection using mobile robots	12
Integrable nonlinear evolution equations in three spatial dimensions	12
Generalization of Duhamel's integral to multi-degree-of-freedom systems	12
Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability	12
Representative microstructures for two-dimensional computational studies of ultrasonic wave propagation in titanium alloys	12
Hierarchical meta-porous materials as sound absorbers	11
Modelling cerebrovascular pathology and the spread of amyloid beta in Alzheimer’s disease	11
Shaping network structures in evolutionary games for stronger cooperation	11
Averaging plus learning models and their asymptotics	11
Klein–Gordon equation for electrically charged particles with new energy-momentum operator	11
Hamel’s equations and geometric mechanics of constrained and floating multibody and space systems	11
The θ-formulation of the two-dimensional elastica: buckling and boundary layer theory	11
Molecular dynamics simulation on oxidation process and interfacial performance of foamed asphalt binders based on ReaxFF force field	11
Robust imaging using electrical impedance tomography: review of current tools	11
Dispersive effective medium for anti-plane dynamics of piezo-magneto-elastic multiphase composites with generalized periodicity	11
A predictive model of UV-A-riboflavin crosslinking treatment on porcine corneas	11
Finite-horizon, energy-efficient trajectories in unsteady flows	11
Scattering of elastic waves by a sphere with cubic anisotropy with application to attenuation in polycrystalline materials	11
Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology	11
A rigorous mathematical theory for topological phases and edge modes in spring-mass mechanical systems	11
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, II: characterization	11
Investigation of the influence of macrozones in titanium alloys on the propagation and scattering of ultrasound	10
Quantum measurement and colour perception: theory and applications	10
Judgment on the evolution state of asymmetric games	10
Plane strain wedge indentation revisited	10
Movement bias in asymmetric landscapes and its impact on population distribution and critical habitat size	10
Improving surrogate model robustness to perturbations for dynamical systems through machine learning and data assimilation	10
Challenges in computational fluid dynamics applications for bone tissue engineering	10
High-temperature and high-pressure plastic phase of ice at the boundary of liquid water and ice VII	10
Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media	10
A solvable two-dimensional swarmalator model	10
Indirect exclusion can promote cooperation in repeated group interactions	10
Unified wavefront singularity characterization of three-dimensional elastodynamic time-domain half-space Green's function under impulsive boundary and internal loads	10
Pace in concert with phase: rate-induced phase-tipping in birhythmic oscillators	9
Instability bands for periodic travelling waves in the modified Korteweg–de Vries equation	9
Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations	9
Inductive biases for deep learning of higher-level cognition	9
Quantitative mapping of thickness variations along a ray path using geometrical full waveform inversion and guided wave mode conversion	9
Chevron patterns in an active nematic liquid crystal film in contact with smectic A	9
The plausibility of origins scenarios requiring two impactors	9
Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces	9
A micromechanical model for phase-change composites	9
Semiclassical theory predicts stochastic ghosts scaling	9
Soft wetting with (a)symmetric Shuttleworth effect	9
Parameter-free higher-order Schrödinger systems with weak dissipation and forcing	9
Bayesian parameter identification in the Landau–de Gennes theory for nematic liquid crystals	9
Dynamic multi-dose vaccination with initial immunity on higher-order networks	9
A probabilistic model of diffusion through a semi-permeable barrier	9
Evidence for active upper mantle flow in the Atlantic and Indo-Australian realms since the Upper Jurassic from hiatus maps and spreading rate changes	9
Energy allocation theory for bacterial growth control in and out of steady state	8
Weyl almost automorphic solutions in distribution sense of Clifford-valued stochastic neural networks with time-varying delays	8
Active nematic fluids on Riemannian two-manifolds	8
The obstacle problem in no-tension structures and cable nets	8
Integration of the Fokker–Planck equation on quantum computers: a new path to modelling nonlinear dynamics	8
Effect of stacking order on the vibration properties of bilayer black phosphorus	8
Tree search in DAG space with model-based reinforcement learning for causal discovery	8
On the association of kinematics, spanwise instability and growth of secondary vortex structures in the wake of oscillating foils	8
Uncertainty in Manning’s roughness coefficient in multilevel simulations of future tsunamis in Sumatra	8
Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results	8
Zig-zag dynamics in a Stern–Gerlach spin measurement	8
Kinematics and dynamics of disclination lines in three-dimensional nematics	8
Mechanics of tension-induced film wrinkling and restabilization: a review	8
Spectral theory of diffusion in partially absorbing media	8
New actuation modes of composite dielectric elastomers	8
Robustness of subwavelength devices: a case study of cochlea-inspired rainbow sensors	8
Transformations, symmetries and Noether theorems for differential-difference equations	8
Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics	8
Axisymmetric vibration and stability of dielectric-elastic tubular bilayer system	8
Modification of Turing patterns through the use of time-varying anisotropic diffusion	8
Unifying temperature definition in atomistic and field representations of conservation laws	8
Solving generalized eigenvalue problems by ordinary differential equations on a quantum computer	8
Scattering from time-modulated subwavelength resonators	8

The Madelung constant in N dimensions	8
Effect of pulsating solidification on the surface properties of conductive materials	8
A self-consistent Schrödinger–Laplace theory of a sub-nanometer-radius field emitter	8
The generalized Hashin–Shtrikman approach to Al/nano-TiC composite	8
Scattering of surface waves by a vertical truncated structured cylinder	8
Supply chain loss from easing COVID-19 restrictions: an evolutionary economic-epidemiological modelling study	8
Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom	7
Introduction to the special issue dedicated to Michael J. Duff FRS on the occasion of his 70th birthday	7
Numerically solving a nonlinear integral equation when the reciprocal of the solution lies in the integrand	7
Explorations of certain nonlinear waves of the Boussinesq and Camassa–Holm equations using physics-informed neural networks	7
Integral equation methods for acoustic scattering by fractals	7
Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology	7
A data-driven analysis of the impact of non-compliant individuals on epidemic diffusion in urban settings	7
The principle of compromise-in-competition: understanding mesoscale complexity of different levels	7
Manifestations of inertia on light dragging revealed in plasmas	7
Regolith flow on top-shaped asteroids	7
Generating new gravitational solutions by matrix multiplication	7
An alternative approach to the phonon theory of liquids: the evolution of the energy of diffusion	7
The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane	7
Enhancing the performance of solenoidal spectrometers for inverse reactions	7
Stochastic reduced-order Koopman model for turbulent flows	7
A general solution for rotating lattices of identical point vortices	7
Determinants of successful mitigation in coupled social-climate dynamics	7
The linear viscoelastic fracture theory applies to soft solids better when they are…viscoelastic	7
Variational derivation and compatible discretizations of the Maxwell-GLM system	7
Analysis of a model for surfactant transport around a foam meniscus	7
A sampling-based approach for information-theoretic inspection management	7
Gauß–Manin from scratch: theme, variations and fantasia	7
Mori–Zwanzig latent space Koopman closure for nonlinear autoencoder	7
Stability of a material interface in a two-phase system with a free surface	7
Finite time blowup of incompressible flows surrounding compressible bubbles evolving under soft equations of state	6
Normal form for maps with nilpotent linear part	6
Controlling the dispersion of metamaterials in three dimensions	6
Young and Young–Laplace equations for a static ridge of nematic liquid crystal, and transitions between equilibrium states	6
Human decision-making in a non-ergodic additive environment	6
Symmetries in transmission electron microscopy imaging of crystals with strain	6
Unidirectional edge modes in time-modulated metamaterials	6
Conical Kresling origami and its applications to curvature and energy programming	6
Multistability, symmetry and geometric conservation in eightfold waterbomb origami	6
Waves generated at the lateral surfaces of an elastic block due to a time-varying homogeneous external pressure applied to its frontal surface	6
Geometric mechanics of ordered and disordered kirigami	6
Effects of an impermeable layer on pore pressure response to tsunami-like inundation	6
Characterization of near-miss connectivity-invariant homogeneous convex polyhedral cages	6
Curved schemes for stochastic differential equations on, or near, manifolds	6
A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem	6
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part II	6
Nonlinear acoustics of an aperture under grazing flow	6
Shape reconfiguration through origami folding sets an upper limit on drag	6
Numerical direct scattering transform for breathers	6
Growing neural networks: dynamic evolution through gradient descent	6
A computational-based kinetostatic synthesis method for realization of nonlinear translational stiffness	6
A new generalized potential with exchangeable functions of octahedral cross sections for modelling yielding or failure of frictional materials	6
First-order global stress patterns inferred from upper mantle flow models	6
Self-folding of two-dimensional thin templates into pyramidal microstructures by a liquid drop: a numerical model	6
Full-field mechanics imaging by direct inversion of electrical data	6
Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta	6
Computation of Burgers vectors from elastic strain and lattice rotation data	6
Riemannian geometry and molecular similarity II: Kähler quantization	6
Theta neuron subject to delayed feedback: a prototypical model for self-sustained pulsing	6
Subwavelength localization in disordered systems	6
Structural dynamic characteristics of vertical axis wind and tidal current turbines	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	5
On the origin of shear-band network patterns in ductile shear zones	5
Analytic representation of the polarization tensor: application to the plasmon resonance of nanoparticles	5
On the force of vertical winds in the upper atmosphere: consequences for small biological particles	5
Exact solutions to fall of particle to singular potential: classical versus quantum cases	5
Analysis of the superdeterministic Invariant-set theory in a hidden-variable setting	5
Experimental dynamical encircling of an exceptional point in coupled pendulums	5
Evolutionary dynamics of voluntary vaccination for imperfect multi-efficacy vaccines	5
Thermodynamics of decoherence	5
Homotopy classification of knotted defects in ordered media	5
Biological efficiency in processing information in green plants	5
Rheology and electro-magnetism stimulated non-trivial deformation dynamics of viscoelastic compound droplets	5
Shear wave transmissivity and wave-induced vorticity diffusion through conversion scattering to slow-shear diffusion wave	5
A model to validate effective waves in random particulate media: spherical symmetry	5
A dynamic trap well model of hydrothermal shape-memory effect in amorphous polymers undergoing tailorable shape recovery behaviour	5
The classical microcanonical ensemble: covariant reformulation and application to small systems	5
Reviewers in 2024	5
Symmetry-breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials	5
Enhanced wave transmission in random media with mirror symmetry	5
Predicting the spatio-temporal infection risk in indoor spaces using an efficient airborne transmission model	5
Analytic mode-matching for accurate handling of exceptional points in a lined acoustic waveguide	5
A low-rank ensemble Kalman filter for elliptic observations	5
Existence and location of internal resonance of two-mode nonlinear conservative oscillators	5
Inertial wave attractors in rapidly rotating tilted cuboids	5
A theory of stochastic fluvial landscape evolution	5
Smooth stable manifolds for the non-instantaneous impulsive equations with applications to Duffing oscillators	5
Geometric mechanics of hybrid origami assemblies combining developable and non-developable patterns	5
Variational analysis of inextensible elastic curves	5
An asymmetric graded indexed helical structured optical fibre for enhanced optical delays	5
Two-layer gravity currents of generalized Newtonian fluids	5
A novel computational approach combined with deep learning for dynamic analysis of sandwich plates featuring inversely designed auxetic core	5
Snap-through eversion of axisymmetric shells under contact indentation	5
A generalized Coleman–Noll procedure and the balance laws of hyper-anelasticity	5