Proceedings of the Royal Society A-Mathematical Physical and Engineeri

Article	Citations
Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend	176
Active over-relaxation and stress memory of living tissues after osmotic shock	130
Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics	75
Whitham shocks and resonant dispersive shock waves governed by the higher order Korteweg–de Vries equation	70
Stability of an inhomogeneous ferrofluid in a channel, subject to a normal field	47
Modelling the dynamics of product adoption and abandonment	40
Pushing coarse-grained models beyond the continuum limit using equation learning	39
A high-resolution discourse on seismic tomography	39
A review on semi-analytical methods for aggregation and coupled aggregation–breakage equations	39
(3+1)-dimensional-modified Kadomtsev–Petviashvili equation and its ∂¯-formalism	36
Rediscovery of Cooper pair factor	32
On the stability of solutions to Schrödinger’s equation short of the adiabatic limit	32
Anisotropy distorts the spreading of a fixed volume porous gravity current	29
Extraction of the mass density using only the p-parts of the elastic fields generated by injected highly dense small inclusions	28
Flexural wave interaction with compressive floating ice over undulating porous bed	28
Riemannian geometry and molecular similarity I: spectrum of the Laplacian	28
Predictions of asthenosphere flow from Couette/Poiseuille models compared to seismic anisotropy and mantle circulation models	27
Stochastic calculus of run-and-tumble motion: an applied perspective	26
Unstable cores are the source of instability in chemical reaction networks	26
Existence, structure and properties of quantum-like states	25
Bursty switching dynamics promotes the collapse of network topologies	25
Linear analysis of ice-shelf topography response to basal melting and freezing	25
Frequency tunable electromagnetic vibration energy harvester using piecewise linear nonlinearity	24
Transient and periodic shear wave propagation in a solid–fluid coupled system	22
In continua with ‘active’ microstructure stability competes with multi-field destabilizing effects	22

Bifurcations of an elastic disc coated with an elastic inextensible rod	22
Exploring natural variation in tendon constitutive parameters via Bayesian data selection and mixed effects models	21
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from monodisperse prolate and oblate spheroidal particles	21
Homogenized phase transition model for perforated ferromagnetic media	21
Chirality and curvature determine the meandering of spirals in multilayer excitable media	20
The formation of cave scallops	20
Edge resonance: exact results and fresh insights	20
Learning the governing partial differential equation of solid diffusion from atomistic simulations	19
Detecting damage in composites using volume decomposition analysis of tomographic data	18
Unsteady solute dispersion in the presence of reversible and irreversible reactions	18
Evolution of quantum non-equilibrium for coupled harmonic oscillators	18
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part I	18
Allowing Wigner’s friend to sequentially measure incompatible observables	18
Efficient set-theoretic algorithms for computing high-order Forman-Ricci curvature on abstract simplicial complexes	18
Heteroclinic bifurcation analysis of the tippedisk through the use of Melnikov theory	18
Rolling and lifting thresholds of sediment entrainment: effects of bed particle arrangement, particle exposure and slip-spinning motion	18
Tipping resonance in a chaotically forced ice age model	17
Matrix factorizations and pentagon maps	17
Time-varying resonators in acoustic waveguides: a transfer matrix formalism for space–time-modulated metamaterials	17
Point-like defect on Schrödinger particles under flux field with harmonic oscillator plus Mie-type potential: application to molecular potentials	17
An all-topology two-fluid model for two-phase flows derived through Hamilton’s stationary action principle	17
Development and analysis of moments preserving finite volume schemes for multi-variate nonlinear breakage model	17
A framework for the use of generative modelling in non-equilibrium statistical mechanics	16
Critical rates of climate warming and abrupt collapse of ecosystems	16
On reduced inertial PDE models for Cucker–Smale flocking dynamics	16
Causal lifting and link prediction	16
The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions	16
Application of thrust layout optimization to masonry structures	16
Effect of the range of interaction on the time evolution of failure cascades	16
Revisiting causality using stochastics on atmospheric temperature and CO 2 concentration	15
Dislocation analysis in CrCoNi medium-entropy alloy using nanoindentation and molecular dynamics simulations	15
The impact of time delays on mutant fixation in pairwise social dilemma games	15
A viscoelastic model for multivalent cation-doped polyelectrolyte complexes: from doping levels to ion-responsive shape memory behaviour	15
A constitutive model for hydrogels with coupled volumetric and entanglement effects	15
Higher-mode filtering: optimum attenuation in a continuum of exceptional points	15
Prediction of general high-order lump solutions in the Davey–Stewartson II equation	14
Nonlinear estimators for the observation and stabilization of falling liquid films	14
Hybridization theory for plasmon resonance in metallic nanostructures	13
A design-space minimum sampling strategy based on proper-orthogonal-decomposition projection	13
Harmonic wave scattered by an inclusion in an elastic plane: The complete Gurtin-Murdoch model	13
Controlling moving interfaces in solid-state batteries	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
A Comment on: ‘Message passing methods on complex networks’ (2023), by M. E. J. Newman	13
Can porous vertical penetrative convection become linearly unstable?	13
Capillary adhesion between solid surfaces: small-volume liquid rings and bridges	13
Shear dynamics around self-organized viscosity-stratified autocatalytic fronts in channel flows	12
Multimode multiple wave scattering in suspensions of solid particles in viscous liquids: part 2: numerical validation	12
Optimal regularity and Uhlenbeck compactness for general relativity and Yang–Mills theory	12
Inertia-gravity waves in geophysical vortices	12
Amorphous bicontinuous minimal surface models and the superior Gaussian curvature uniformity of diamond, primitive and gyroid surfaces	12

An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow	12
Sustainable material for filter fabric manufacturing: properties and feasibility	12
A predictive model of UV-A-riboflavin crosslinking treatment on porcine corneas	11
Weber’s Law of perception is a consequence of resolving the intensity of natural scintillating light and sound with the least possible error	11
A tunable electromagnetic metagrating	11
Classically bound and quantum quasi-bound states of an electron on a plane adjacent to a magnetic monopole	11
Density functional theory calculations on the solvatochromism of covalent organic framework Py-TT cluster compounds	11
Rheomergy : collective behaviour mediated by active flow-based recruitment	11
Hamilton–Jacobi as model reduction, extension to Newtonian particle mechanics, and a wave mechanical curiosity	11
Model for deformation-induced martensitic transformation in irradiated materials	11
Analytical and numerical steady states for thermal convection in an inclined, slender, two-dimensional enclosure	11
Stability evolution in triangular fractals: an algebraic dynamical system approach	11
The θ-formulation of the two-dimensional elastica: buckling and boundary layer theory	11
Scattering of elastic waves by a sphere with cubic anisotropy with application to attenuation in polycrystalline materials	11
Molecular dynamics simulation on oxidation process and interfacial performance of foamed asphalt binders based on ReaxFF force field	11
Wide-angle multimodal parabolic equations: modelling of directional sound propagation in stratified range-dependent fluid waveguides	10
Hamel’s equations and geometric mechanics of constrained and floating multibody and space systems	10
Shaping network structures in evolutionary games for stronger cooperation	10
Free propagation of resonant waves in nonlinear dissipative metamaterials	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
On finitely deforming elastic–plastic materials	10
Contact-line bending energy controls phospholipid vesicle adhesion	10
Mechanics of size effect on plane stress fracture toughness and R-curve development in thin sheet materials and consequent scaling laws	10
Judgment on the evolution state of asymmetric games	10
Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability	10
Hierarchical meta-porous materials as sound absorbers	10
Representative microstructures for two-dimensional computational studies of ultrasonic wave propagation in titanium alloys	10
Cross-property connections involving thermal diffusivity and thermal expansion, and their extension to transversely isotropic constituents	10
Modelling cerebrovascular pathology and the spread of amyloid beta in Alzheimer’s disease	10
Chevron patterns in an active nematic liquid crystal film in contact with smectic A	9
Movement bias in asymmetric landscapes and its impact on population distribution and critical habitat size	9
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
Klein–Gordon equation for electrically charged particles with new energy-momentum operator	9
Unified wavefront singularity characterization of three-dimensional elastodynamic time-domain half-space Green's function under impulsive boundary and internal loads	9
Correction: ‘Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology’ (2024), by Browning  et al.	9
Parameter-free higher-order Schrödinger systems with weak dissipation and forcing	9
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, II: characterization	9
On conditions of potentialness for geometrically exact shearable beams	9
Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media	9
Averaging plus learning models and their asymptotics	9
The plausibility of origins scenarios requiring two impactors	9
Improving surrogate model robustness to perturbations for dynamical systems through machine learning and data assimilation	9
Dispersive effective medium for anti-plane dynamics of piezo-magneto-elastic multiphase composites with generalized periodicity	9
Macroscopic emitters on origami structures: a group theoretic approach	8
Inductive biases for deep learning of higher-level cognition	8
A solvable two-dimensional swarmalator model	8
Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces	8
Kinematics and dynamics of disclination lines in three-dimensional nematics	8
Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results	8
New actuation modes of composite dielectric elastomers	8
On the association of kinematics, spanwise instability and growth of secondary vortex structures in the wake of oscillating foils	8
Elucidating effects of magnesium sulfate on chemical properties, enzyme activity and microbial community in rare earth ores extraction	8
Dynamic multi-dose vaccination with initial immunity on higher-order networks	8
Pace in concert with phase: rate-induced phase-tipping in birhythmic oscillators	8
Spectral theory of diffusion in partially absorbing media	8
Energy allocation theory for bacterial growth control in and out of steady state	8
A self-consistent Schrödinger–Laplace theory of a sub-nanometer-radius field emitter	8
Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics	8
Supply chain loss from easing COVID-19 restrictions: an evolutionary economic-epidemiological modelling study	8
Soft wetting with (a)symmetric Shuttleworth effect	8
Investigation of the influence of macrozones in titanium alloys on the propagation and scattering of ultrasound	8
Spherical image analysis of origami and kirigami	8
Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations	8
Semiclassical theory predicts stochastic ghosts scaling	8
Scattering from time-modulated subwavelength resonators	8
Tree search in DAG space with model-based reinforcement learning for causal discovery	8
Generating new gravitational solutions by matrix multiplication	7
Numerically solving a nonlinear integral equation when the reciprocal of the solution lies in the integrand	7
Uncertainty in Manning’s roughness coefficient in multilevel simulations of future tsunamis in Sumatra	7
Self-stress and the nonlinear response of the Kresling origami and tensegrity frustums: a unified outlook	7
Zig-zag dynamics in a Stern–Gerlach spin measurement	7
Enhancing the performance of solenoidal spectrometers for inverse reactions	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
Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta	7
Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology	7
Mori–Zwanzig latent space Koopman closure for nonlinear autoencoder	7
Human decision-making in a non-ergodic additive environment	7

The obstacle problem in no-tension structures and cable nets	7
Individual-based foundation of SIR-type epidemic models: mean-field limit and large-time behaviour	7
Integration of the Fokker–Planck equation on quantum computers: a new path to modelling nonlinear dynamics	7
Axisymmetric vibration and stability of dielectric-elastic tubular bilayer system	7
Explorations of certain nonlinear waves of the Boussinesq and Camassa–Holm equations using physics-informed neural networks	7
An alternative approach to the phonon theory of liquids: the evolution of the energy of diffusion	7
Variational derivation and compatible discretizations of the Maxwell-GLM system	7
Determinants of successful mitigation in coupled social-climate dynamics	7
Modification of Turing patterns through the use of time-varying anisotropic diffusion	7
The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane	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
The Madelung constant in N dimensions	7
Unifying temperature definition in atomistic and field representations of conservation laws	7
A probabilistic model of diffusion through a semi-permeable barrier	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
Manifestations of inertia on light dragging revealed in plasmas	7
Waves in the Earth’s core. V. inertial modes modified by magnetic effects	7
Stability of a material interface in a two-phase system with a free surface	7
Global branching of solutions to ordinary differential equations and integrability	6
A nonlinear spectral core–periphery detection method for multiplex networks	6
Analytic representation of the polarization tensor: application to the plasmon resonance of nanoparticles	6
A computational-based kinetostatic synthesis method for realization of nonlinear translational stiffness	6
On the origin of shear-band network patterns in ductile shear zones	6
Constructive quantum logics	6
Do irrotational water waves remain irrotational in the limit of a vanishing viscosity?	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
A low-rank ensemble Kalman filter for elliptic observations	6
Shape reconfiguration through origami folding sets an upper limit on drag	6
Riemannian geometry and molecular similarity II: Kähler quantization	6
Functionally graded energy-absorbing metamaterials with negative stiffness curved beams: sequentially-adaptive modal multi-stability encoding	6
Geometric mechanics of ordered and disordered kirigami	6
Growing neural networks: dynamic evolution through gradient descent	6
Tunable morphing of electroactive dielectric-elastomer balloons	6
A model to validate effective waves in random particulate media: spherical symmetry	6
The motion of a bubble in a non-uniform Hele-Shaw flow	6
First-order global stress patterns inferred from upper mantle flow models	6
Soft cells, Kelvin foam and the minimal surfaces of Schwarz	6
Numerical direct scattering transform for breathers	6
Diffusion-induced elastic cavitation	6
Multistability, symmetry and geometric conservation in eightfold waterbomb origami	6
Utilization of the ExactMPF package for solving a discrete analogue of the nonlinear Schrödinger equation by the inverse scattering transform method	6
Structural dynamic characteristics of vertical axis wind and tidal current turbines	6
Symmetries in transmission electron microscopy imaging of crystals with strain	6
The principle of compromise-in-competition: understanding mesoscale complexity of different levels	6
A new generalized potential with exchangeable functions of octahedral cross sections for modelling yielding or failure of frictional materials	6
The Robin boundary condition for modelling heat transfer	6
Unidirectional edge modes in time-modulated metamaterials	6
A dynamic trap well model of hydrothermal shape-memory effect in amorphous polymers undergoing tailorable shape recovery behaviour	6
Universal scaling limits for spin networks via martingale methods	6
A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem	6
The viscoelastic rheology of transient diffusion creep	6
Nonlinear acoustics of an aperture under grazing flow	6
Modelling sediment compaction beneath ice lenses during frost heave	6
Subwavelength localization in disordered systems	6
Full-field mechanics imaging by direct inversion of electrical data	6
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part II	6
Modelling human activities in a system of cities	6
Self-folding of two-dimensional thin templates into pyramidal microstructures by a liquid drop: a numerical model	6
Multiphysics modelling of light-actuated liquid crystal elastomers	5
The classical microcanonical ensemble: covariant reformulation and application to small systems	5
Asymptotic analysis of three-dimensional boundary-value problems for three-layered high-contrast plates	5
Biological efficiency in processing information in green plants	5
Uncovering wall-shear stress dynamics from neural-network enhanced fluid flow measurements	5
Stress or strain?	5
Tensor networks for quantum machine learning	5
SINDy for delay-differential equations: application to model bacterial zinc response	5
Dispersion relations of generalized one-dimensional phononic crystals	5
Topology optimization with local stress constraints and continuously varying load direction and magnitude: towards practical applications	5
Symmetry-breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials	5
Direct method to determine singular point of enveloped surface and its application to worm wheel tooth surface	5
Simple circuit simulations of classical and quantum Turing machines	5
State-space systems as dynamic generative models	5
Time-domain scattering of acoustic spherical waves: an analytical method for the penetrable sphere	5
Oblique projection for scalable rank-adaptive reduced-order modelling of nonlinear stochastic partial differential equations with time-dependent bases	5
An updated quantum complementarity principle	5
Analytic mode-matching for accurate handling of exceptional points in a lined acoustic waveguide	5
The theory of scaled electromagnetism	5
Dispersion of reacting settling particles in ice-covered channels: transient behaviour and asymptotic analysis	5
Geometric mechanics of hybrid origami assemblies combining developable and non-developable patterns	5
Snap-through eversion of axisymmetric shells under contact indentation	5
Enhanced wave transmission in random media with mirror symmetry	5
Experimental dynamical encircling of an exceptional point in coupled pendulums	5
A novel computational approach combined with deep learning for dynamic analysis of sandwich plates featuring inversely designed auxetic core	5
A cluster of N -bubbles driven along a channel at high imposed driving pressure: film orientations and bubble pressures	5
Evolutionary dynamics of voluntary vaccination for imperfect multi-efficacy vaccines	5
A multi-agent system to dynamically devise an LCA framework weighting system taking into account socio-technical and environmental consideration	5
Time–frequency domain local spectral analysis of seismic signals with multiple windows	5
Two-layer gravity currents of generalized Newtonian fluids	5
Extending Q -learning to continuous and mixed strategy games based on spatial reciprocity	5
Mechanics of structural size effect in impact brittle fracture of steels and consequent scaling laws for fracture	5
Linking deep-time subduction history to modern day expressions of dynamic topography	5
Coexistence times in the Moran process with environmental heterogeneity	5