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	159
Riemannian geometry and molecular similarity I: spectrum of the Laplacian	117
Stability of an inhomogeneous ferrofluid in a channel, subject to a normal field	111
Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend	75
Rediscovery of Cooper pair factor	66
Extraction of the mass density using only the p-parts of the elastic fields generated by injected highly dense small inclusions	62
Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework	46
Wave spectroscopy in a driven granular material	44
Confined helium, density dependence of the inelastic electron and photon scattering cross-sections and the optical oscillator strength	37
A review on semi-analytical methods for aggregation and coupled aggregation–breakage equations	36
Flexural wave interaction with compressive floating ice over undulating porous bed	36
Bursty switching dynamics promotes the collapse of network topologies	35
Stochastic calculus of run-and-tumble motion: an applied perspective	34
Unstable cores are the source of instability in chemical reaction networks	31
A high-resolution discourse on seismic tomography	30
Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics	30
Frequency tunable electromagnetic vibration energy harvester using piecewise linear nonlinearity	28
Predictions of asthenosphere flow from Couette/Poiseuille models compared to seismic anisotropy and mantle circulation models	27
Whitham shocks and resonant dispersive shock waves governed by the higher order Korteweg–de Vries equation	27
Pushing coarse-grained models beyond the continuum limit using equation learning	27
The potential impact of intensified community hand hygiene interventions on respiratory tract infections: a modelling study	25
Anisotropy distorts the spreading of a fixed volume porous gravity current	25
(3+1)-dimensional-modified Kadomtsev–Petviashvili equation and its ∂¯-formalism	25
Linear analysis of ice-shelf topography response to basal melting and freezing	24
Edge resonance: exact results and fresh insights	23

The formation of cave scallops	23
Detecting damage in composites using volume decomposition analysis of tomographic data	23
Modelling the dynamics of product adoption and abandonment	23
Learning the governing partial differential equation of solid diffusion from atomistic simulations	22
Transient and periodic shear wave propagation in a solid–fluid coupled system	22
Evolution of quantum non-equilibrium for coupled harmonic oscillators	20
Point-like defect on Schrödinger particles under flux field with harmonic oscillator plus Mie-type potential: application to molecular potentials	19
Homogenized phase transition model for perforated ferromagnetic media	19
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from monodisperse prolate and oblate spheroidal particles	18
Bifurcations of an elastic disc coated with an elastic inextensible rod	18
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part I	18
Heteroclinic bifurcation analysis of the tippedisk through the use of Melnikov theory	18
A framework for the use of generative modelling in non-equilibrium statistical mechanics	18
Non-hyperbolicity at large scales of a high-dimensional chaotic system	17
Application of thrust layout optimization to masonry structures	17
Chirality and curvature determine the meandering of spirals in multilayer excitable media	17
Causal lifting and link prediction	17
Development and analysis of moments preserving finite volume schemes for multi-variate nonlinear breakage model	17
Time-varying resonators in acoustic waveguides: a transfer matrix formalism for space–time-modulated metamaterials	17
Efficient set-theoretic algorithms for computing high-order Forman-Ricci curvature on abstract simplicial complexes	17
Exploring natural variation in tendon constitutive parameters via Bayesian data selection and mixed effects models	17
Rolling and lifting thresholds of sediment entrainment: effects of bed particle arrangement, particle exposure and slip-spinning motion	16
Unsteady solute dispersion in the presence of reversible and irreversible reactions	16
Matrix factorizations and pentagon maps	16
Allowing Wigner’s friend to sequentially measure incompatible observables	16
In continua with ‘active’ microstructure stability competes with multi-field destabilizing effects	16
An all-topology two-fluid model for two-phase flows derived through Hamilton’s stationary action principle	16
The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions	15
Amorphous bicontinuous minimal surface models and the superior Gaussian curvature uniformity of diamond, primitive and gyroid surfaces	15
Critical rates of climate warming and abrupt collapse of ecosystems	15
A design-space minimum sampling strategy based on proper-orthogonal-decomposition projection	15
Unbiased estimation of the Hessian for partially observed diffusions	15
On reduced inertial PDE models for Cucker–Smale flocking dynamics	15
Controlling moving interfaces in solid-state batteries	14
Capillary adhesion between solid surfaces: small-volume liquid rings and bridges	14
Can porous vertical penetrative convection become linearly unstable?	14
The impact of time delays on mutant fixation in pairwise social dilemma games	14
Harmonic wave scattered by an inclusion in an elastic plane: The complete Gurtin-Murdoch model	14
Inertia-gravity waves in geophysical vortices	14
Measure of overlap between two arbitrary ellipses on a sphere	14
Optimal regularity and Uhlenbeck compactness for general relativity and Yang–Mills theory	13
Shear dynamics around self-organized viscosity-stratified autocatalytic fronts in channel flows	13
Nonlinear estimators for the observation and stabilization of falling liquid films	13
Revisiting causality using stochastics on atmospheric temperature and CO 2 concentration	13
A constitutive model for hydrogels with coupled volumetric and entanglement effects	13
Data-driven two-dimensional stationary quantum droplets and wave propagations in the amended Gross–Pitaevskii equation with two potentials via deep neural networks learning	13
An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow	13
Multimode multiple wave scattering in suspensions of solid particles in viscous liquids: part 2: numerical validation	13
Dislocation analysis in CrCoNi medium-entropy alloy using nanoindentation and molecular dynamics simulations	12
A tunable electromagnetic metagrating	12

Sustainable material for filter fabric manufacturing: properties and feasibility	12
Weber’s Law of perception is a consequence of resolving the intensity of natural scintillating light and sound with the least possible error	12
Density functional theory calculations on the solvatochromism of covalent organic framework Py-TT cluster compounds	12
Prediction of general high-order lump solutions in the Davey–Stewartson II equation	12
Hybridization theory for plasmon resonance in metallic nanostructures	12
Analytical and numerical steady states for thermal convection in an inclined, slender, two-dimensional enclosure	12
Model for deformation-induced martensitic transformation in irradiated materials	12
A Comment on: ‘Message passing methods on complex networks’ (2023), by M. E. J. Newman	12
Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability	11
Free propagation of resonant waves in nonlinear dissipative metamaterials	11
The θ-formulation of the two-dimensional elastica: buckling and boundary layer theory	11
Classically bound and quantum quasi-bound states of an electron on a plane adjacent to a magnetic monopole	11
Representative microstructures for two-dimensional computational studies of ultrasonic wave propagation in titanium alloys	11
Rheomergy : collective behaviour mediated by active flow-based recruitment	11
Molecular dynamics simulation on oxidation process and interfacial performance of foamed asphalt binders based on ReaxFF force field	11
Contact-line bending energy controls phospholipid vesicle adhesion	11
Hierarchical meta-porous materials as sound absorbers	11
Scattering of elastic waves by a sphere with cubic anisotropy with application to attenuation in polycrystalline materials	11
A predictive model of UV-A-riboflavin crosslinking treatment on porcine corneas	10
Shaping network structures in evolutionary games for stronger cooperation	10
Modelling cerebrovascular pathology and the spread of amyloid beta in Alzheimer’s disease	10
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, II: characterization	10
A rigorous mathematical theory for topological phases and edge modes in spring-mass mechanical systems	10
Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology	10
Integrable nonlinear evolution equations in three spatial dimensions	10
Averaging plus learning models and their asymptotics	10
Klein–Gordon equation for electrically charged particles with new energy-momentum operator	10
Hamel’s equations and geometric mechanics of constrained and floating multibody and space systems	10
Tailored acoustic metamaterials. Part I. Thin- and thick-walled Helmholtz resonator arrays	10
Dispersive effective medium for anti-plane dynamics of piezo-magneto-elastic multiphase composites with generalized periodicity	10
Plane strain wedge indentation revisited	10
Chevron patterns in an active nematic liquid crystal film in contact with smectic A	9
Improving surrogate model robustness to perturbations for dynamical systems through machine learning and data assimilation	9
Bayesian parameter identification in the Landau–de Gennes theory for nematic liquid crystals	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
Soft wetting with (a)symmetric Shuttleworth effect	9
A solvable two-dimensional swarmalator model	9
Parameter-free higher-order Schrödinger systems with weak dissipation and forcing	9
Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations	9
Unified wavefront singularity characterization of three-dimensional elastodynamic time-domain half-space Green's function under impulsive boundary and internal loads	9
Indirect exclusion can promote cooperation in repeated group interactions	9
Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media	9
Cross-property connections involving thermal diffusivity and thermal expansion, and their extension to transversely isotropic constituents	9
Dynamic multi-dose vaccination with initial immunity on higher-order networks	9
The plausibility of origins scenarios requiring two impactors	9
Judgment on the evolution state of asymmetric games	9
Instability bands for periodic travelling waves in the modified Korteweg–de Vries equation	9
Movement bias in asymmetric landscapes and its impact on population distribution and critical habitat size	9
Mechanics of size effect on plane stress fracture toughness and R-curve development in thin sheet materials and consequent scaling laws	9
Pace in concert with phase: rate-induced phase-tipping in birhythmic oscillators	9
Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces	9
Semiclassical theory predicts stochastic ghosts scaling	8
New actuation modes of composite dielectric elastomers	8
Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results	8
Supply chain loss from easing COVID-19 restrictions: an evolutionary economic-epidemiological modelling study	8
Spectral theory of diffusion in partially absorbing media	8
The Madelung constant in N dimensions	8
Inductive biases for deep learning of higher-level cognition	8
Investigation of the influence of macrozones in titanium alloys on the propagation and scattering of ultrasound	8
A probabilistic model of diffusion through a semi-permeable barrier	8
On the association of kinematics, spanwise instability and growth of secondary vortex structures in the wake of oscillating foils	8
Unifying temperature definition in atomistic and field representations of conservation laws	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
Robustness of subwavelength devices: a case study of cochlea-inspired rainbow sensors	8
The obstacle problem in no-tension structures and cable nets	8
Effect of pulsating solidification on the surface properties of conductive materials	8
Effect of stacking order on the vibration properties of bilayer black phosphorus	8
Axisymmetric vibration and stability of dielectric-elastic tubular bilayer system	8
Integration of the Fokker–Planck equation on quantum computers: a new path to modelling nonlinear dynamics	8
Scattering from time-modulated subwavelength resonators	8
Macroscopic emitters on origami structures: a group theoretic approach	8
A micromechanical model for phase-change composites	8
Solving generalized eigenvalue problems by ordinary differential equations on a quantum computer	7
Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics	7
Active nematic fluids on Riemannian two-manifolds	7
Tree search in DAG space with model-based reinforcement learning for causal discovery	7
Mechanics of tension-induced film wrinkling and restabilization: a review	7
Variational derivation and compatible discretizations of the Maxwell-GLM system	7
The linear viscoelastic fracture theory applies to soft solids better when they are…viscoelastic	7

A data-driven analysis of the impact of non-compliant individuals on epidemic diffusion in urban settings	7
Numerically solving a nonlinear integral equation when the reciprocal of the solution lies in the integrand	7
Zig-zag dynamics in a Stern–Gerlach spin measurement	7
Individual-based foundation of SIR-type epidemic models: mean-field limit and large-time behaviour	7
Elucidating effects of magnesium sulfate on chemical properties, enzyme activity and microbial community in rare earth ores extraction	7
Energy allocation theory for bacterial growth control in and out of steady state	7
Integral equation methods for acoustic scattering by fractals	7
Regolith flow on top-shaped asteroids	7
Stochastic reduced-order Koopman model for turbulent flows	7
Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom	7
Uncertainty in Manning’s roughness coefficient in multilevel simulations of future tsunamis in Sumatra	7
Kinematics and dynamics of disclination lines in three-dimensional nematics	7
Modification of Turing patterns through the use of time-varying anisotropic diffusion	7
Gauß–Manin from scratch: theme, variations and fantasia	7
Analysis of a model for surfactant transport around a foam meniscus	7
Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology	7
Mori–Zwanzig latent space Koopman closure for nonlinear autoencoder	7
Generating new gravitational solutions by matrix multiplication	7
Functionally graded energy-absorbing metamaterials with negative stiffness curved beams: sequentially-adaptive modal multi-stability encoding	6
Symmetries in transmission electron microscopy imaging of crystals with strain	6
Structural dynamic characteristics of vertical axis wind and tidal current turbines	6
Manifestations of inertia on light dragging revealed in plasmas	6
Explorations of certain nonlinear waves of the Boussinesq and Camassa–Holm equations using physics-informed neural networks	6
A general solution for rotating lattices of identical point vortices	6
A sampling-based approach for information-theoretic inspection management	6
Normal form for maps with nilpotent linear part	6
Subwavelength localization in disordered systems	6
A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem	6
Curved schemes for stochastic differential equations on, or near, manifolds	6
A computational-based kinetostatic synthesis method for realization of nonlinear translational stiffness	6
Riemannian geometry and molecular similarity II: Kähler quantization	6
Full-field mechanics imaging by direct inversion of electrical data	6
Determinants of successful mitigation in coupled social-climate dynamics	6
Human decision-making in a non-ergodic additive environment	6
An alternative approach to the phonon theory of liquids: the evolution of the energy of diffusion	6
Enhancing the performance of solenoidal spectrometers for inverse reactions	6
Controlling the dispersion of metamaterials in three dimensions	6
Self-folding of two-dimensional thin templates into pyramidal microstructures by a liquid drop: a numerical model	6
Constructive quantum logics	6
Numerical direct scattering transform for breathers	6
Computation of Burgers vectors from elastic strain and lattice rotation data	6
Finite time blowup of incompressible flows surrounding compressible bubbles evolving under soft equations of state	6
The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane	6
First-order global stress patterns inferred from upper mantle flow models	6
A new generalized potential with exchangeable functions of octahedral cross sections for modelling yielding or failure of frictional materials	6
Nonlinear acoustics of an aperture under grazing flow	6
Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta	6
The principle of compromise-in-competition: understanding mesoscale complexity of different levels	6
Geometric mechanics of ordered and disordered kirigami	6
Stability of a material interface in a two-phase system with a free surface	6
Theta neuron subject to delayed feedback: a prototypical model for self-sustained pulsing	6
Shape reconfiguration through origami folding sets an upper limit on drag	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
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part II	6
Multistability, symmetry and geometric conservation in eightfold waterbomb origami	6
Global branching of solutions to ordinary differential equations and integrability	5
A model to validate effective waves in random particulate media: spherical symmetry	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
Enhanced wave transmission in random media with mirror symmetry	5
The wave function as a true ensemble	5
Eshelby’s inclusion and inhomogeneity problems under harmonic heat transfer	5
A cluster of N -bubbles driven along a channel at high imposed driving pressure: film orientations and bubble pressures	5
Analytic representation of the polarization tensor: application to the plasmon resonance of nanoparticles	5
Symmetry-breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials	5
Non-existence of propagating Rayleigh waves in extremal materials	5
An asymmetric graded indexed helical structured optical fibre for enhanced optical delays	5
The role of vascular smooth muscle cell plasticity in arterial remodelling and biomechanical failure: a numerical approach	5
High-degree cubature on Wiener space through unshuffle expansions	5
Modelling sediment compaction beneath ice lenses during frost heave	5
Numerical schemes for a fully nonlinear coagulation–fragmentation model coming from wave kinetic theory	5
Direct method to determine singular point of enveloped surface and its application to worm wheel tooth surface	5
Extending Q -learning to continuous and mixed strategy games based on spatial reciprocity	5
Tiered social distancing policies and epidemic control	5
A generalized method for the reliability assessment of safety–critical inspection	5
Harmonic-measure distribution functions of multiply connected domains with various geometries	5
A novel computational approach combined with deep learning for dynamic analysis of sandwich plates featuring inversely designed auxetic core	5
State-space systems as dynamic generative models	5
Biological efficiency in processing information in green plants	5
Inertial wave attractors in rapidly rotating tilted cuboids	5
Reviewers in 2024	5
Growing neural networks: dynamic evolution through gradient descent	5
A dynamic trap well model of hydrothermal shape-memory effect in amorphous polymers undergoing tailorable shape recovery behaviour	5
Linking deep-time subduction history to modern day expressions of dynamic topography	5
Mechanics of structural size effect in impact brittle fracture of steels and consequent scaling laws for fracture	5
A generalized Coleman–Noll procedure and the balance laws of hyper-anelasticity	5
A multi-agent system to dynamically devise an LCA framework weighting system taking into account socio-technical and environmental consideration	5
Exact solutions to fall of particle to singular potential: classical versus quantum cases	5
Thermodynamics of decoherence	5
The viscoelastic rheology of transient diffusion creep	5
Two-layer gravity currents of generalized Newtonian fluids	5
Computational synthesis of wheeled vehicles via multi-layer topology optimization	5
Experimental dynamical encircling of an exceptional point in coupled pendulums	5
Unidirectional edge modes in time-modulated metamaterials	5
The classical microcanonical ensemble: covariant reformulation and application to small systems	5