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	169
(3+1)-dimensional-modified Kadomtsev–Petviashvili equation and its ∂¯-formalism	137
Exploring the role of crystal habit in the Ostwald rule of stages	94
Stability of an inhomogeneous ferrofluid in a channel, subject to a normal field	86
Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics	61
Linear analysis of ice-shelf topography response to basal melting and freezing	61
Unstable cores are the source of instability in chemical reaction networks	56
Rediscovery of Cooper pair factor	48
Extraction of the mass density using only the p-parts of the elastic fields generated by injected highly dense small inclusions	46
Anisotropy distorts the spreading of a fixed volume porous gravity current	40
A review on semi-analytical methods for aggregation and coupled aggregation–breakage equations	37
Canonical scattering problem in topological metamaterials: Valley-Hall modes through a bend	36
The potential impact of intensified community hand hygiene interventions on respiratory tract infections: a modelling study	35
Whitham shocks and resonant dispersive shock waves governed by the higher order Korteweg–de Vries equation	35
Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework	31
Wave spectroscopy in a driven granular material	31
Confined helium, density dependence of the inelastic electron and photon scattering cross-sections and the optical oscillator strength	29
Bursty switching dynamics promotes the collapse of network topologies	29
A high-resolution discourse on seismic tomography	28
Riemannian geometry and molecular similarity I: spectrum of the Laplacian	27
Pushing coarse-grained models beyond the continuum limit using equation learning	27
Frequency tunable electromagnetic vibration energy harvester using piecewise linear nonlinearity	27
Flexural wave interaction with compressive floating ice over undulating porous bed	25
Stochastic calculus of run-and-tumble motion: an applied perspective	25
Modelling the dynamics of product adoption and abandonment	24

Predictions of asthenosphere flow from Couette/Poiseuille models compared to seismic anisotropy and mantle circulation models	24
The formation of cave scallops	24
Efficient set-theoretic algorithms for computing high-order Forman-Ricci curvature on abstract simplicial complexes	22
Edge resonance: exact results and fresh insights	22
Matrix factorizations and pentagon maps	22
Detecting damage in composites using volume decomposition analysis of tomographic data	22
Evolution of quantum non-equilibrium for coupled harmonic oscillators	21
Non-hyperbolicity at large scales of a high-dimensional chaotic system	21
Learning the governing partial differential equation of solid diffusion from atomistic simulations	21
Allowing Wigner’s friend to sequentially measure incompatible observables	20
Point-like defect on Schrödinger particles under flux field with harmonic oscillator plus Mie-type potential: application to molecular potentials	20
Symplectic decomposition from submatrix determinants	20
Bifurcations of an elastic disc coated with an elastic inextensible rod	20
Homogenized phase transition model for perforated ferromagnetic media	20
Rolling and lifting thresholds of sediment entrainment: effects of bed particle arrangement, particle exposure and slip-spinning motion	19
Application of thrust layout optimization to masonry structures	19
Development and analysis of moments preserving finite volume schemes for multi-variate nonlinear breakage model	19
Critical rates of climate warming and abrupt collapse of ecosystems	19
Heteroclinic bifurcation analysis of the tippedisk through the use of Melnikov theory	18
Unsteady solute dispersion in the presence of reversible and irreversible reactions	17
Time-varying resonators in acoustic waveguides: a transfer matrix formalism for space–time-modulated metamaterials	17
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from monodisperse prolate and oblate spheroidal particles	17
Modelling of stress transfer in root-reinforced soils informed by four-dimensional X-ray computed tomography and digital volume correlation data	17
Exploring natural variation in tendon constitutive parameters via Bayesian data selection and mixed effects models	17
Causal lifting and link prediction	16
Chirality and curvature determine the meandering of spirals in multilayer excitable media	16
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part I	16
Revisiting causality using stochastics on atmospheric temperature and CO 2 concentration	15
The multipolar elastic fields of ellipsoidal and polytopal plastic inclusions	15
Optimal regularity and Uhlenbeck compactness for general relativity and Yang–Mills theory	15
Unbiased estimation of the Hessian for partially observed diffusions	15
On reduced inertial PDE models for Cucker–Smale flocking dynamics	15
An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow	15
Harmonic wave scattered by an inclusion in an elastic plane: The complete Gurtin-Murdoch model	15
Multimode multiple wave scattering in suspensions of solid particles in viscous liquids: part 2: numerical validation	14
A design-space minimum sampling strategy based on proper-orthogonal-decomposition projection	14
The impact of time delays on mutant fixation in pairwise social dilemma games	14
Controlling moving interfaces in solid-state batteries	14
Electro-osmotic and viscous effects upon pressure to drive a droplet through a capillary	14
Measure of overlap between two arbitrary ellipses on a sphere	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	14
Shear dynamics around self-organized viscosity-stratified autocatalytic fronts in channel flows	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
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
Capillary adhesion between solid surfaces: small-volume liquid rings and bridges	13
Inertia-gravity waves in geophysical vortices	13
Shaping network structures in evolutionary games for stronger cooperation	13
The contribution of plastic sink-in to the static friction of single asperity microscopic contacts	13

Prediction of general high-order lump solutions in the Davey–Stewartson II equation	13
Physics-informed Dyna-style model-based deep reinforcement learning for dynamic control	13
Analytical and numerical steady states for thermal convection in an inclined, slender, two-dimensional enclosure	13
Scattering of elastic waves by a sphere with cubic anisotropy with application to attenuation in polycrystalline materials	12
Modelling cerebrovascular pathology and the spread of amyloid beta in Alzheimer’s disease	12
Density functional theory calculations on the solvatochromism of covalent organic framework Py-TT cluster compounds	12
A tunable electromagnetic metagrating	12
A generic approach to the quantum mechanical transition probability	12
A predictive model of UV-A-riboflavin crosslinking treatment on porcine corneas	12
Rheomergy : collective behaviour mediated by active flow-based recruitment	12
Molecular dynamics simulation on oxidation process and interfacial performance of foamed asphalt binders based on ReaxFF force field	12
The θ-formulation of the two-dimensional elastica: buckling and boundary layer theory	12
Generalization of Duhamel's integral to multi-degree-of-freedom systems	12
Representative microstructures for two-dimensional computational studies of ultrasonic wave propagation in titanium alloys	12
Hamel’s equations and geometric mechanics of constrained and floating multibody and space systems	12
Integrable nonlinear evolution equations in three spatial dimensions	12
Finite-horizon, energy-efficient trajectories in unsteady flows	12
Contact-line bending energy controls phospholipid vesicle adhesion	11
Hierarchical meta-porous materials as sound absorbers	11
A rigorous mathematical theory for topological phases and edge modes in spring-mass mechanical systems	11
Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology	11
Robust imaging using electrical impedance tomography: review of current tools	11
Strategies for guided acoustic wave inspection using mobile robots	11
Model for deformation-induced martensitic transformation in irradiated materials	11
Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability	11
Judgment on the evolution state of asymmetric games	11
Klein–Gordon equation for electrically charged particles with new energy-momentum operator	10
Dispersive effective medium for anti-plane dynamics of piezo-magneto-elastic multiphase composites with generalized periodicity	10
Unified wavefront singularity characterization of three-dimensional elastodynamic time-domain half-space Green's function under impulsive boundary and internal loads	10
Movement bias in asymmetric landscapes and its impact on population distribution and critical habitat size	10
Averaging plus learning models and their asymptotics	10
Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, II: characterization	10
The interplay between Fano and Fabry–Pérot resonances in dual-period metagratings	10
High-temperature and high-pressure plastic phase of ice at the boundary of liquid water and ice VII	10
Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces	10
Plane strain wedge indentation revisited	10
The plausibility of origins scenarios requiring two impactors	10
Inductive biases for deep learning of higher-level cognition	9
Parameter-free higher-order Schrödinger systems with weak dissipation and forcing	9
Soft wetting with (a)symmetric Shuttleworth effect	9
Challenges in computational fluid dynamics applications for bone tissue engineering	9
Investigation of the influence of macrozones in titanium alloys on the propagation and scattering of ultrasound	9
A solvable two-dimensional swarmalator model	9
Active nematic fluids on Riemannian two-manifolds	9
Scattering of surface waves by a vertical truncated structured cylinder	9
Quantum measurement and colour perception: theory and applications	9
Improving surrogate model robustness to perturbations for dynamical systems through machine learning and data assimilation	9
Dynamic multi-dose vaccination with initial immunity on higher-order networks	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
Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media	9
Indirect exclusion can promote cooperation in repeated group interactions	9
Energy allocation theory for bacterial growth control in and out of steady state	9
Instability bands for periodic travelling waves in the modified Korteweg–de Vries equation	9
New actuation modes of composite dielectric elastomers	9
Chevron patterns in an active nematic liquid crystal film in contact with smectic A	9
Bayesian parameter identification in the Landau–de Gennes theory for nematic liquid crystals	9
Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations	9
Pace in concert with phase: rate-induced phase-tipping in birhythmic oscillators	9
Chiral mode transfer of symmetry-broken states in anti-parity-time-symmetric mechanical system	9
Semiclassical theory predicts stochastic ghosts scaling	9
A micromechanical model for phase-change composites	8
The obstacle problem in no-tension structures and cable nets	8
Weyl almost automorphic solutions in distribution sense of Clifford-valued stochastic neural networks with time-varying delays	8
Spectral theory of diffusion in partially absorbing media	8
Robustness of subwavelength devices: a case study of cochlea-inspired rainbow sensors	8
Multi-mode multiple wave scattering in suspensions of solid particles in viscous liquids: part 1 asymptotic results	8
The generalized Hashin–Shtrikman approach to Al/nano-TiC composite	8
Effect of pulsating solidification on the surface properties of conductive materials	8
Axisymmetric vibration and stability of dielectric-elastic tubular bilayer system	8
A probabilistic model of diffusion through a semi-permeable barrier	8
Unifying temperature definition in atomistic and field representations of conservation laws	8
Zig-zag dynamics in a Stern–Gerlach spin measurement	8
Uncertainty in Manning’s roughness coefficient in multilevel simulations of future tsunamis in Sumatra	8
Effect of stacking order on the vibration properties of bilayer black phosphorus	8
Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics	8
The Madelung constant in N dimensions	8
Kinematics and dynamics of disclination lines in three-dimensional nematics	8
Quantitative mapping of thickness variations along a ray path using geometrical full waveform inversion and guided wave mode conversion	8
Scattering from time-modulated subwavelength resonators	8
Supply chain loss from easing COVID-19 restrictions: an evolutionary economic-epidemiological modelling study	8

Mechanics of tension-induced film wrinkling and restabilization: a review	8
Tree search in DAG space with model-based reinforcement learning for causal discovery	8
Transformations, symmetries and Noether theorems for differential-difference equations	8
On the association of kinematics, spanwise instability and growth of secondary vortex structures in the wake of oscillating foils	8
Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom	7
Mean and variance of the Eulerian and Lagrangian horizontal velocities induced by nonlinear multi-directional irregular water waves	7
Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology	7
Explorations of certain nonlinear waves of the Boussinesq and Camassa–Holm equations using physics-informed neural networks	7
Human decision-making in a non-ergodic additive environment	7
A general solution for rotating lattices of identical point vortices	7
Mori–Zwanzig latent space Koopman closure for nonlinear autoencoder	7
The linear viscoelastic fracture theory applies to soft solids better when they are…viscoelastic	7
Integral equation methods for acoustic scattering by fractals	7
Gauß–Manin from scratch: theme, variations and fantasia	7
Stability of a material interface in a two-phase system with a free surface	7
Regolith flow on top-shaped asteroids	7
Full-field mechanics imaging by direct inversion of electrical data	7
Computational modelling distinguishes diverse contributors to aneurysmal progression in the Marfan aorta	7
An alternative approach to the phonon theory of liquids: the evolution of the energy of diffusion	7
Stochastic reduced-order Koopman model for turbulent flows	7
Generating new gravitational solutions by matrix multiplication	7
A data-driven analysis of the impact of non-compliant individuals on epidemic diffusion in urban settings	7
Introduction to the special issue dedicated to Michael J. Duff FRS on the occasion of his 70th birthday	7
Determinants of successful mitigation in coupled social-climate dynamics	7
Modification of Turing patterns through the use of time-varying anisotropic diffusion	7
Analysis of a model for surfactant transport around a foam meniscus	7
Biomembranes undergo complex, non-axisymmetric deformations governed by Kirchhoff–Love kinematicsand revealed by a three-dimensional computational framework	7
Variational derivation and compatible discretizations of the Maxwell-GLM system	7
Travelling-wave analysis of a model of tumour invasion with degenerate, cross-dependent diffusion	7
A sampling-based approach for information-theoretic inspection management	7
Enhancing the performance of solenoidal spectrometers for inverse reactions	7
The principle of compromise-in-competition: understanding mesoscale complexity of different levels	7
Manifestations of inertia on light dragging revealed in plasmas	7
Numerically solving a nonlinear integral equation when the reciprocal of the solution lies in the integrand	7
The Robin and Neumann problems for the nonlinear Schrödinger equation on the half-plane	7
Solving generalized eigenvalue problems by ordinary differential equations on a quantum computer	7
Geometric mechanics of ordered and disordered kirigami	6
Aberration-corrected transmission electron microscopy of a non-graphitizing carbon	6
Symmetries in transmission electron microscopy imaging of crystals with strain	6
Multistability, symmetry and geometric conservation in eightfold waterbomb origami	6
Growing neural networks: dynamic evolution through gradient descent	6
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
Shape reconfiguration through origami folding sets an upper limit on drag	6
Characterization of near-miss connectivity-invariant homogeneous convex polyhedral cages	6
Theta neuron subject to delayed feedback: a prototypical model for self-sustained pulsing	6
A new generalized potential with exchangeable functions of octahedral cross sections for modelling yielding or failure of frictional materials	6
A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem	6
Conical Kresling origami and its applications to curvature and energy programming	6
A computational-based kinetostatic synthesis method for realization of nonlinear translational stiffness	6
Numerical direct scattering transform for breathers	6
Young and Young–Laplace equations for a static ridge of nematic liquid crystal, and transitions between equilibrium states	6
Self-folding of two-dimensional thin templates into pyramidal microstructures by a liquid drop: a numerical model	6
Structural dynamic characteristics of vertical axis wind and tidal current turbines	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
Riemannian geometry and molecular similarity II: Kähler quantization	6
Subwavelength localization in disordered systems	6
Computation of Burgers vectors from elastic strain and lattice rotation data	6
Thermodynamics of decoherence	6
Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part II	6
First-order global stress patterns inferred from upper mantle flow models	6
Curved schemes for stochastic differential equations on, or near, manifolds	6
Effects of an impermeable layer on pore pressure response to tsunami-like inundation	6
Nonlinear acoustics of an aperture under grazing flow	6
Geometric mechanics of hybrid origami assemblies combining developable and non-developable patterns	5
Dispersion relations of generalized one-dimensional phononic crystals	5
Existence and location of internal resonance of two-mode nonlinear conservative oscillators	5
Universal scaling limits for spin networks via martingale methods	5
Homotopy classification of knotted defects in ordered media	5
Modelling sediment compaction beneath ice lenses during frost heave	5
Rheology and electro-magnetism stimulated non-trivial deformation dynamics of viscoelastic compound droplets	5
On the origin of shear-band network patterns in ductile shear zones	5
A nonlinear spectral core–periphery detection method for multiplex networks	5
On the force of vertical winds in the upper atmosphere: consequences for small biological particles	5
Enhanced wave transmission in random media with mirror symmetry	5
A generalized Coleman–Noll procedure and the balance laws of hyper-anelasticity	5
Memory effects in friction: the role of sliding heterogeneities	5
An ion trap design for a space-deployable strontium-ion optical clock	5
An experimental study of tie transparency and individual perception in social networks	5
A generalized method for the reliability assessment of safety–critical inspection	5
A theory of stochastic fluvial landscape evolution	5
Inertial wave attractors in rapidly rotating tilted cuboids	5
Unidirectional edge modes in time-modulated metamaterials	5
Analytic representation of the polarization tensor: application to the plasmon resonance of nanoparticles	5
A novel computational approach combined with deep learning for dynamic analysis of sandwich plates featuring inversely designed auxetic core	5
Biological efficiency in processing information in green plants	5
Analytic mode-matching for accurate handling of exceptional points in a lined acoustic waveguide	5
Snap-through eversion of axisymmetric shells under contact indentation	5
Predicting the spatio-temporal infection risk in indoor spaces using an efficient airborne transmission model	5
The Robin boundary condition for modelling heat transfer	5
Mechanism for turbulence proliferation in subcritical flows	5
The motion of a bubble in a non-uniform Hele-Shaw flow	5
Non-existence of propagating Rayleigh waves in extremal materials	5
Tunable morphing of electroactive dielectric-elastomer balloons	5