Proceedings of the Royal Society A-Mathematical Physical and Engineeri

Article	Citations
Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend	162
Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics	120
Whitham shocks and resonant dispersive shock waves governed by the higher order Korteweg–de Vries equation	68
Stability of an inhomogeneous ferrofluid in a channel, subject to a normal field	63
Modelling the dynamics of product adoption and abandonment	46
Bursty switching dynamics promotes the collapse of network topologies	45
A high-resolution discourse on seismic tomography	38
Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework	37
Pushing coarse-grained models beyond the continuum limit using equation learning	37
Unstable cores are the source of instability in chemical reaction networks	37
A review on semi-analytical methods for aggregation and coupled aggregation–breakage equations	36
(3+1)-dimensional-modified Kadomtsev–Petviashvili equation and its ∂¯-formalism	30
Linear analysis of ice-shelf topography response to basal melting and freezing	30
Flexural wave interaction with compressive floating ice over undulating porous bed	30
Rediscovery of Cooper pair factor	28
On the stability of solutions to Schrödinger’s equation short of the adiabatic limit	28
Predictions of asthenosphere flow from Couette/Poiseuille models compared to seismic anisotropy and mantle circulation models	27
Frequency tunable electromagnetic vibration energy harvester using piecewise linear nonlinearity	25
Confined helium, density dependence of the inelastic electron and photon scattering cross-sections and the optical oscillator strength	25
Anisotropy distorts the spreading of a fixed volume porous gravity current	25
Wave spectroscopy in a driven granular material	25
Active over-relaxation and stress memory of living tissues after osmotic shock	24
Stochastic calculus of run-and-tumble motion: an applied perspective	24
Riemannian geometry and molecular similarity I: spectrum of the Laplacian	24
In continua with ‘active’ microstructure stability competes with multi-field destabilizing effects	23

Extraction of the mass density using only the p-parts of the elastic fields generated by injected highly dense small inclusions	23
A framework for the use of generative modelling in non-equilibrium statistical mechanics	22
Transient and periodic shear wave propagation in a solid–fluid coupled system	21
Bifurcations of an elastic disc coated with an elastic inextensible rod	20
An all-topology two-fluid model for two-phase flows derived through Hamilton’s stationary action principle	20
Exploring natural variation in tendon constitutive parameters via Bayesian data selection and mixed effects models	19
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from monodisperse prolate and oblate spheroidal particles	19
Homogenized phase transition model for perforated ferromagnetic media	19
Matrix factorizations and pentagon maps	19
Rolling and lifting thresholds of sediment entrainment: effects of bed particle arrangement, particle exposure and slip-spinning motion	18
The formation of cave scallops	18
Point-like defect on Schrödinger particles under flux field with harmonic oscillator plus Mie-type potential: application to molecular potentials	18
Causal lifting and link prediction	17
Evolution of quantum non-equilibrium for coupled harmonic oscillators	17
Chirality and curvature determine the meandering of spirals in multilayer excitable media	17
Learning the governing partial differential equation of solid diffusion from atomistic simulations	17
Heteroclinic bifurcation analysis of the tippedisk through the use of Melnikov theory	17
Edge resonance: exact results and fresh insights	17
Application of thrust layout optimization to masonry structures	17
Development and analysis of moments preserving finite volume schemes for multi-variate nonlinear breakage model	16
Critical rates of climate warming and abrupt collapse of ecosystems	16
Detecting damage in composites using volume decomposition analysis of tomographic data	16
Allowing Wigner’s friend to sequentially measure incompatible observables	16
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part I	16
Efficient set-theoretic algorithms for computing high-order Forman-Ricci curvature on abstract simplicial complexes	16
Unsteady solute dispersion in the presence of reversible and irreversible reactions	16
Time-varying resonators in acoustic waveguides: a transfer matrix formalism for space–time-modulated metamaterials	16
Dislocation analysis in CrCoNi medium-entropy alloy using nanoindentation and molecular dynamics simulations	15
Revisiting causality using stochastics on atmospheric temperature and CO 2 concentration	15
Amorphous bicontinuous minimal surface models and the superior Gaussian curvature uniformity of diamond, primitive and gyroid surfaces	15
A constitutive model for hydrogels with coupled volumetric and entanglement effects	15
Sustainable material for filter fabric manufacturing: properties and feasibility	15
On reduced inertial PDE models for Cucker–Smale flocking dynamics	15
The impact of time delays on mutant fixation in pairwise social dilemma games	15
Prediction of general high-order lump solutions in the Davey–Stewartson II equation	15
Harmonic wave scattered by an inclusion in an elastic plane: The complete Gurtin-Murdoch model	14
A design-space minimum sampling strategy based on proper-orthogonal-decomposition projection	14
Hybridization theory for plasmon resonance in metallic nanostructures	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
Nonlinear estimators for the observation and stabilization of falling liquid films	14
The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions	14
Can porous vertical penetrative convection become linearly unstable?	14
Controlling moving interfaces in solid-state batteries	14
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
Unbiased estimation of the Hessian for partially observed diffusions	13
Capillary adhesion between solid surfaces: small-volume liquid rings and bridges	13
Optimal regularity and Uhlenbeck compactness for general relativity and Yang–Mills theory	13
Rheomergy : collective behaviour mediated by active flow-based recruitment	12

Shear dynamics around self-organized viscosity-stratified autocatalytic fronts in channel flows	12
Wide-angle multimodal parabolic equations: modelling of directional sound propagation in stratified range-dependent fluid waveguides	12
Tailored acoustic metamaterials. Part I. Thin- and thick-walled Helmholtz resonator arrays	12
Modelling cerebrovascular pathology and the spread of amyloid beta in Alzheimer’s disease	12
Inertia-gravity waves in geophysical vortices	12
The θ-formulation of the two-dimensional elastica: buckling and boundary layer theory	12
A predictive model of UV-A-riboflavin crosslinking treatment on porcine corneas	12
Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability	12
A Comment on: ‘Message passing methods on complex networks’ (2023), by M. E. J. Newman	12
Contact-line bending energy controls phospholipid vesicle adhesion	12
Classically bound and quantum quasi-bound states of an electron on a plane adjacent to a magnetic monopole	11
Hierarchical meta-porous materials as sound absorbers	11
Integrable nonlinear evolution equations in three spatial dimensions	11
Model for deformation-induced martensitic transformation in irradiated materials	11
Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology	11
Molecular dynamics simulation on oxidation process and interfacial performance of foamed asphalt binders based on ReaxFF force field	11
Representative microstructures for two-dimensional computational studies of ultrasonic wave propagation in titanium alloys	11
Scattering of elastic waves by a sphere with cubic anisotropy with application to attenuation in polycrystalline materials	11
A tunable electromagnetic metagrating	11
Analytical and numerical steady states for thermal convection in an inclined, slender, two-dimensional enclosure	10
Density functional theory calculations on the solvatochromism of covalent organic framework Py-TT cluster compounds	10
Cross-property connections involving thermal diffusivity and thermal expansion, and their extension to transversely isotropic constituents	10
Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media	10
Shaping network structures in evolutionary games for stronger cooperation	10
Stability evolution in triangular fractals: an algebraic dynamical system approach	10
A rigorous mathematical theory for topological phases and edge modes in spring-mass mechanical systems	10
Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations	10
Hamel’s equations and geometric mechanics of constrained and floating multibody and space systems	10
Hamilton–Jacobi as model reduction, extension to Newtonian particle mechanics, and a wave mechanical curiosity	10
Free propagation of resonant waves in nonlinear dissipative metamaterials	10
Judgment on the evolution state of asymmetric games	10
Mechanics of size effect on plane stress fracture toughness and R-curve development in thin sheet materials and consequent scaling laws	10
Instability bands for periodic travelling waves in the modified Korteweg–de Vries equation	9
Bayesian parameter identification in the Landau–de Gennes theory for nematic liquid crystals	9
Averaging plus learning models and their asymptotics	9
Klein–Gordon equation for electrically charged particles with new energy-momentum operator	9
Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces	9
Dispersive effective medium for anti-plane dynamics of piezo-magneto-elastic multiphase composites with generalized periodicity	9
Investigation of the influence of macrozones in titanium alloys on the propagation and scattering of ultrasound	9
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, II: characterization	9
Plane strain wedge indentation revisited	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
Movement bias in asymmetric landscapes and its impact on population distribution and critical habitat size	9
Parameter-free higher-order Schrödinger systems with weak dissipation and forcing	9
Improving surrogate model robustness to perturbations for dynamical systems through machine learning and data assimilation	9
The plausibility of origins scenarios requiring two impactors	9
Dynamic multi-dose vaccination with initial immunity on higher-order networks	9
Indirect exclusion can promote cooperation in repeated group interactions	9
Kinematics and dynamics of disclination lines in three-dimensional nematics	8
Macroscopic emitters on origami structures: a group theoretic approach	8
Pace in concert with phase: rate-induced phase-tipping in birhythmic oscillators	8
On conditions of potentialness for geometrically exact shearable beams	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
Semiclassical theory predicts stochastic ghosts scaling	8
Scattering from time-modulated subwavelength resonators	8
Individual-based foundation of SIR-type epidemic models: mean-field limit and large-time behaviour	8
A solvable two-dimensional swarmalator model	8
Inductive biases for deep learning of higher-level cognition	8
Soft wetting with (a)symmetric Shuttleworth effect	8
Supply chain loss from easing COVID-19 restrictions: an evolutionary economic-epidemiological modelling study	8
Robustness of subwavelength devices: a case study of cochlea-inspired rainbow sensors	8
The Madelung constant in N dimensions	8
A probabilistic model of diffusion through a semi-permeable barrier	8
Elucidating effects of magnesium sulfate on chemical properties, enzyme activity and microbial community in rare earth ores extraction	8
Chevron patterns in an active nematic liquid crystal film in contact with smectic A	8
Unified wavefront singularity characterization of three-dimensional elastodynamic time-domain half-space Green's function under impulsive boundary and internal loads	8
On the association of kinematics, spanwise instability and growth of secondary vortex structures in the wake of oscillating foils	8
Tree search in DAG space with model-based reinforcement learning for causal discovery	8
New actuation modes of composite dielectric elastomers	8
A self-consistent Schrödinger–Laplace theory of a sub-nanometer-radius field emitter	8
Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results	8
Gauß–Manin from scratch: theme, variations and fantasia	7
Zig-zag dynamics in a Stern–Gerlach spin measurement	7
Energy allocation theory for bacterial growth control in and out of steady state	7
Mechanics of tension-induced film wrinkling and restabilization: a review	7
Unifying temperature definition in atomistic and field representations of conservation laws	7
Integration of the Fokker–Planck equation on quantum computers: a new path to modelling nonlinear dynamics	7
Analysis of a model for surfactant transport around a foam meniscus	7
Generating new gravitational solutions by matrix multiplication	7

Enhancing the performance of solenoidal spectrometers for inverse reactions	7
Uncertainty in Manning’s roughness coefficient in multilevel simulations of future tsunamis in Sumatra	7
Spectral theory of diffusion in partially absorbing media	7
The generalized Hashin–Shtrikman approach to Al/nano-TiC composite	7
Spherical image analysis of origami and kirigami	7
Human decision-making in a non-ergodic additive environment	7
Regolith flow on top-shaped asteroids	7
A general solution for rotating lattices of identical point vortices	7
Integral equation methods for acoustic scattering by fractals	7
Active nematic fluids on Riemannian two-manifolds	7
Effect of stacking order on the vibration properties of bilayer black phosphorus	7
The obstacle problem in no-tension structures and cable nets	7
Numerically solving a nonlinear integral equation when the reciprocal of the solution lies in the integrand	7
Solving generalized eigenvalue problems by ordinary differential equations on a quantum computer	7
Stability of a material interface in a two-phase system with a free surface	6
Geometric mechanics of ordered and disordered kirigami	6
The viscoelastic rheology of transient diffusion creep	6
Riemannian geometry and molecular similarity II: Kähler quantization	6
Curved schemes for stochastic differential equations on, or near, manifolds	6
Computation of Burgers vectors from elastic strain and lattice rotation data	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
Constructive quantum logics	6
A computational-based kinetostatic synthesis method for realization of nonlinear translational stiffness	6
Structural dynamic characteristics of vertical axis wind and tidal current turbines	6
The principle of compromise-in-competition: understanding mesoscale complexity of different levels	6
Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology	6
Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom	6
Explorations of certain nonlinear waves of the Boussinesq and Camassa–Holm equations using physics-informed neural networks	6
A sampling-based approach for information-theoretic inspection management	6
Nonlinear acoustics of an aperture under grazing flow	6
Numerical direct scattering transform for breathers	6
Modelling sediment compaction beneath ice lenses during frost heave	6
Full-field mechanics imaging by direct inversion of electrical data	6
Finite time blowup of incompressible flows surrounding compressible bubbles evolving under soft equations of state	6
Determinants of successful mitigation in coupled social-climate dynamics	6
Controlling the dispersion of metamaterials in three dimensions	6
A new generalized potential with exchangeable functions of octahedral cross sections for modelling yielding or failure of frictional materials	6
The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane	6
A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem	6
Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta	6
Mori–Zwanzig latent space Koopman closure for nonlinear autoencoder	6
A data-driven analysis of the impact of non-compliant individuals on epidemic diffusion in urban settings	6
Stochastic reduced-order Koopman model for turbulent flows	6
Self-folding of two-dimensional thin templates into pyramidal microstructures by a liquid drop: a numerical model	6
Modification of Turing patterns through the use of time-varying anisotropic diffusion	6
Diffusion-induced elastic cavitation	6
Subwavelength localization in disordered systems	6
Multistability, symmetry and geometric conservation in eightfold waterbomb origami	6
Shape reconfiguration through origami folding sets an upper limit on drag	6
Functionally graded energy-absorbing metamaterials with negative stiffness curved beams: sequentially-adaptive modal multi-stability encoding	6
First-order global stress patterns inferred from upper mantle flow models	6
Symmetries in transmission electron microscopy imaging of crystals with strain	6
Waves in the Earth’s core. V. inertial modes modified by magnetic effects	6
The linear viscoelastic fracture theory applies to soft solids better when they are…viscoelastic	6
Variational derivation and compatible discretizations of the Maxwell-GLM system	6
Manifestations of inertia on light dragging revealed in plasmas	6
An alternative approach to the phonon theory of liquids: the evolution of the energy of diffusion	6
Snap-through eversion of axisymmetric shells under contact indentation	5
Asymptotic analysis of three-dimensional boundary-value problems for three-layered high-contrast plates	5
Harmonic-measure distribution functions of multiply connected domains with various geometries	5
The motion of a bubble in a non-uniform Hele-Shaw flow	5
A generalized method for the reliability assessment of safety–critical inspection	5
State-space systems as dynamic generative models	5
Rate-induced tipping in savanna–forest ecosystems: effects of fast-varying fitness parameters in the framework of compactification	5
Coexistence times in the Moran process with environmental heterogeneity	5
A multi-agent system to dynamically devise an LCA framework weighting system taking into account socio-technical and environmental consideration	5
Geometric mechanics of hybrid origami assemblies combining developable and non-developable patterns	5
Tiered social distancing policies and epidemic control	5
The wave function as a true ensemble	5
Adhesion of elastic membranes. Part I: a generalized Tabor parameter	5
Time-domain scattering of acoustic spherical waves: an analytical method for the penetrable sphere	5
Nonlinear realization approach to topologically massive supergravity	5
Dispersion relations of generalized one-dimensional phononic crystals	5
Soft cells, Kelvin foam and the minimal surfaces of Schwarz	5
Analytic mode-matching for accurate handling of exceptional points in a lined acoustic waveguide	5
Global branching of solutions to ordinary differential equations and integrability	5
Tensor networks for quantum machine learning	5
Two-layer gravity currents of generalized Newtonian fluids	5
A cluster of N -bubbles driven along a channel at high imposed driving pressure: film orientations and bubble pressures	5
Biological efficiency in processing information in green plants	5
Eshelby’s inclusion and inhomogeneity problems under harmonic heat transfer	5
An asymmetric graded indexed helical structured optical fibre for enhanced optical delays	5
High-degree cubature on Wiener space through unshuffle expansions	5
Reviewers in 2024	5
Mechanism for turbulence proliferation in subcritical flows	5
The theory of scaled electromagnetism	5
A generalized Coleman–Noll procedure and the balance laws of hyper-anelasticity	5
Unidirectional edge modes in time-modulated metamaterials	5
The role of elastic anisotropy in active nematics	5
Symmetry-breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials	5
Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with time-dependent bases	5
Mechanics of structural size effect in impact brittle fracture of steels and consequent scaling laws for fracture	5
Topology optimization with local stress constraints and continuously varying load direction and magnitude: towards practical applications	5
Extending Q -learning to continuous and mixed strategy games based on spatial reciprocity	5