Proceedings of the Royal Society A-Mathematical Physical and Engineeri

Article	Citations
Environmental sustainability of biofuels: a review	189
A modelling framework to assess the likely effectiveness of facemasks in combination with ‘lock-down’ in managing the COVID-19 pandemic	162
Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks	109
Shallow neural networks for fluid flow reconstruction with limited sensors	94
SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics	85
Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling	75
Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control	65
Evolution of spray and aerosol from respiratory releases: theoretical estimates for insight on viral transmission	63
Observation and modelling of solar jets	59
Contactless acoustic micro/nano manipulation: a paradigm for next generation applications in life sciences	53
Inductive biases for deep learning of higher-level cognition	45
The ventilation of buildings and other mitigating measures for COVID-19: a focus on wintertime	45
A unified approach for topology optimization with local stress constraints considering various failure criteria: von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, Bresler– Pister and Willam–Warnke	45
Marine iodine emissions in a changing world	44
Polaritons and excitons: Hamiltonian design for enhanced coherence	38
Contributions of modern network science to the cognitive sciences: revisiting research spirals of representation and process	36
Oscillatory dynamics in the dilemma of social distancing	36
Structure and function in human and primate social networks: implications for diffusion, network stability and health	35
Epidemics on multilayer simplicial complexes	35
The relationship between viscoelasticity and elasticity	31
Complex evolutionary dynamics due to punishment and free space in ecological multigames	31
Laguerre polynomial-based operational matrix of integration for solving fractional differential equations with non-singular kernel	31
Microfluidic devices for the detection of viruses: aspects of emergency fabrication during the COVID-19 pandemic and other outbreaks	31
Physics-informed dynamic mode decomposition	30
The impacts of ocean acidification on marine trace gases and the implications for atmospheric chemistry and climate	30

A symmetry-preserving difference scheme and analytical solutions of a generalized higher-order beam equation	30
Pear-shaped atomic nuclei	29
Dilation of subglacial sediment governs incipient surge motion in glaciers with deformable beds	29
Bits and pieces: understanding information decomposition from part-whole relationships and formal logic	29
Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations	29
Matrix models and deformations of JT gravity	28
Cost efficiency of institutional incentives for promoting cooperation in finite populations	27
Vigorous convection in porous media	27
A review of the UK and British Channel Islands practical tidal stream energy resource	26
Contact geometry for simple thermodynamical systems with friction	26
Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems	26
Dynamics of fluid displacement in mixed-wet porous media	25
An agent-based model of the interrelation between the COVID-19 outbreak and economic activities	24
A revisit of the tonal noise of small rotors	24
Bayesian mechanics for stationary processes	24
Network comparison and the within-ensemble graph distance	23
A generalized fractional-order elastodynamic theory for non-local attenuating media	23
Heterogeneity in evolutionary games: an analysis of the risk perception	23
Electric field control of magnetism	22
Big influence of small random imperfections in origami-based metamaterials	22
Using a robotic platform to study the influence of relative tailbeat phase on the energetic costs of side-by-side swimming in fish	21
Contemporary sea-level changes from global to local scales: a review	21
Electrocharged facepiece respirator fabrics using common materials	20
Certain implementations in fractional calculus operators involving Mittag-Leffler-confluent hypergeometric functions	20
Localized structures on librational and rotational travelling waves in the sine-Gordon equation	19
Indirect reduced-order modelling: using nonlinear manifolds to conserve kinetic energy	19
Kernel learning for robust dynamic mode decomposition: linear and nonlinear disambiguation optimization	19
Turing and Benjamin–Feir instability mechanisms in non-autonomous systems	19
Validity of Winkler’s mattress model for thin elastomeric layers: beyond Poisson’s ratio	19
Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states	18
The mechanics of brittle granular materials with coevolving grain size and shape	18
Core–periphery structure in directed networks	18
Three-dimensional magnetic reconnection in astrophysical plasmas	18
Short- and long-term predictions of chaotic flows and extreme events: a physics-constrained reservoir computing approach	17
Neural closure models for dynamical systems	17
Superconductivity and nucleation from fractal anisotropy and product-like fractal measure	17
Terahertz-range plasmon and whispering gallery mode resonances in the plane wave scattering from thin microsize dielectric disk with graphene covers	17
Discovering governing equations from partial measurements with deep delay autoencoders	17
Parameterized neural ordinary differential equations: applications to computational physics problems	17
SUIHTER : a new mathematical model for COVID-19. Application to the analysis of the second epidemic outbreak in Italy	17
Discovery of nonlinear dynamical systems using a Runge–Kutta inspired dictionary-based sparse regression approach	16
Knot polynomials of open and closed curves	16
Epidemics on hypergraphs: spectral thresholds for extinction	16
Structured time-delay models for dynamical systems with connections to Frenet–Serret frame	16
A mathematical analysis for constructal design of tree flow networks under unsteady flow	16
Quotation errors in general science journals	16
Terahertz range resonances of metasurface formed by double-layer grating of microsize graphene strips inside dielectric slab	16
Semi-martingale driven variational principles	16
High endemic levels of typhoid fever in rural areas of Ghana may stem from optimal voluntary vaccination behaviour	16
Data-driven nonlinear aeroelastic models of morphing wings for control	15

Rogue waves in the three-level defocusing coupled Maxwell–Bloch equations	15
A Fano-based acoustic metamaterial for ultra-broadband sound barriers	15
A novel matrix technique for multi-order pantograph differential equations of fractional order	15
The accumulative law and its probability model: an extension of the Pareto distribution and the log-normal distribution	15
Robust imaging using electrical impedance tomography: review of current tools	15
Phase tipping: how cyclic ecosystems respond to contemporary climate	15
Non-standard magnetohydrodynamics equations and their implications in sunspots	15
Bayesian differential programming for robust systems identification under uncertainty	15
Liquid crystals on deformable surfaces	15
On the propagation of nonlinear waves in the atmosphere	15
Speed oscillations in classical pilot-wave dynamics	14
The mathematical foundations of anelasticity: existence of smooth global intermediate configurations	14
On the Wiener–Hopf solution of water-wave interaction with a submerged elastic or poroelastic plate	14
Fixed-time synchronization of quaternion-valued neural networks with time-varying delay	14
Addressing the curse of dimensionality in stochastic dynamics: a Wiener path integral variational formulation with free boundaries	14
Crosswise tensile resistance of masonry patterns due to contact friction	14
Fusion of multi-view ultrasonic data for increased detection performance in non-destructive evaluation	14
Conical Kresling origami and its applications to curvature and energy programming	14
Observing the Mpemba effect with minimal bias and the value of the Mpemba effect to scientific outreach and engagement	14
Searching for a source without gradients: how good is infotaxis and how to beat it	14
A theory of pattern formation for reaction–diffusion systems on temporal networks	14
Extreme dissipation and intermittency in turbulence at very high Reynolds numbers	14
How rare are power-law networks really?	14
Spectral theory of diffusion in partially absorbing media	13
Population dynamics with spatial structure and an Allee effect	13
The Wiener–Hopf technique, its generalizations and applications: constructive and approximate methods	13
A new method to generate superoscillating functions and supershifts	13
Influence of temperature on Turing pattern formation	13
A refined dynamic finite-strain shell theory for incompressible hyperelastic materials: equations and two-dimensional shell virtual work principle	13
Architecture and evolution of semantic networks in mathematics texts	13
Improved phase-field models of melting and dissolution in multi-component flows	13
A one-dimensional model for elasto-capillary necking	13
Analytical model for electrohydrodynamic thrust	12
Variational analysis of landscape elevation and drainage networks	12
Magnetic winding: what is it and what is it good for?	12
Weyl almost automorphic solutions in distribution sense of Clifford-valued stochastic neural networks with time-varying delays	12
Asymptotic analysis of extended two-dimensional narrow capture problems	12
Radio-frequency chain selection for energy and spectral efficiency maximization in hybrid beamforming under hardware imperfections	12
Routes to global glaciation	12
Ultrasensitivity and bistability in covalent-modification cycles with positive autoregulation	12
High-resolution thickness maps of corrosion using SH1 guided wave tomography	12
Delayed Leidenfrost phenomenon during impact of elastic fluid droplets	11
Stochastic compartmental models of the COVID-19 pandemic must have temporally correlated uncertainties	11
A new type of constitutive equation for nonlinear elastic bodies. Fitting with experimental data for rubber-like materials	11
Placing limits on long-term variations in quiet-Sun irradiance and their contribution to total solar irradiance and solar radiative forcing of climate	11
Nematic liquid crystalline elastomers are aeolotropic materials	11
Better strategies for containing COVID-19 pandemic: a study of 25 countries via a vSIADR model	11
Polarization whorls from M87* at the event horizon telescope	11
Exponential stability in Mindlin’s Form II gradient thermoelasticity with microtemperatures of type III	11
Physics-informed Dyna-style model-based deep reinforcement learning for dynamic control	11
Collective vibrations of a hydrodynamic active lattice	11
From a discrete model of chemotaxis with volume-filling to a generalized Patlak–Keller–Segel model	11
The seismic wavefield as seen by distributed acoustic sensing arrays: local, regional and teleseismic sources	11
Effects of Lorentz symmetry breaking by a tensor field subject to Coulomb-type potential on relativistic quantum oscillator	11
Extensive layer clouds in the global electric circuit: their effects on vertical charge distribution and storage	11
A comprehensive analysis of different 7T SRAM topologies to design a 1R1 W bit interleaving enabled and half select free cell for 32 nm technology node	11
Rheology of three-phase suspensions determined via dam-break experiments	11
Structural engineering from an inverse problems perspective	11
A system model of three-body interactions in complex networks: consensus and conservation	11
Unsteady Reynolds-averaged Navier–Stokes investigation of free surface wave impact on tidal turbine wake	10
Highly coordinated nationwide massive travel restrictions are central to effective mitigation and control of COVID-19 outbreaks in China	10
Folding arrays of uniform-thickness panels to compact bundles with a single degree of freedom	10
Three-phase flow displacement dynamics and Haines jumps in a hydrophobic porous medium	10
A data-centric approach to generative modelling for 3D-printed steel	10
Review of the exponential and Cayley map on SE(3) as relevant for Lie group integration of the generalized Poisson equation and flexible multibody systems	10
Learning on dynamic statistical manifolds	10
Tunable mechanical diode of nonlinear elastic metamaterials induced by imperfect interface	10
Inflationary routes to Gaussian curved topography	10
Continent-scale Hiatus Maps for the Atlantic Realm and Australia since the Upper Jurassic and links to mantle flow induced dynamic topography	10
Mechanisms and measures for the ductility of materials failure	10
An exact analysis of scalar transport in hydromagnetic flow between two parallel plates: a multi-scale approach	10
Direct and inverse scattering problems of the modified Sawada–Kotera equation: Riemann–Hilbert approach	10
Effects of partial measurements on quantum resources and quantum Fisher information of a teleported state in a relativistic scenario	10
Simple, low-cost and accurate data-driven geophysical forecasting with learned kernels	10
Wallpaper group kirigami	10
Deviations from classical droplet evaporation theory	10
Active thermal cloaking and mimicking	10
Nonlinear self-dual network equations: modulation instability, interactions of higher-order discrete vector rational solitons and dynamical behaviours	10
An extensive review of computational dance automation techniques and applications	10
Multi-breather solutions to the Sasa–Satsuma equation	10

Predicting the spatio-temporal infection risk in indoor spaces using an efficient airborne transmission model	10
Fractional-order viscoelastic model of musculoskeletal tissues: correlation with fractals	10
Finite-horizon, energy-efficient trajectories in unsteady flows	9
Addendum 2020 to ‘Measurement of the Earth’s rotation: 720 BC to AD 2015’	9
Fokas method for linear boundary value problems involving mixed spatial derivatives	9
Recovering multiple fractional orders in time-fractional diffusion in an unknown medium	9
A study on resonant collision in the two-dimensional multi-component long-wave–short-wave resonance system	9
Using spectral submanifolds for optimal mode selection in nonlinear model reduction	9
Plasmonic modes in cylindrical nanoparticles and dimers	9
The changing nature of Earth's reflected sunlight	9
Inert gas bubble formation in magnetron sputtered thin-film CdTe solar cells	9
Non-reciprocal acoustics in a viscous environment	9
Shape analysis via inconsistent surface registration	9
Chiral triclinic metamaterial crystals supporting isotropic acoustical activity and isotropic chiral phonons	9
Vaccinating behaviour guided by imitation and aspiration	9
Post-bifurcation behaviour of elasto-capillary necking and bulging in soft tubes	9
Nonlinear system of PT-symmetric excitations and Toda vibrations integrable by the Darboux–Bäcklund dressing method	9
Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics	9
The effect of an exterior electric field on the instability of dielectric plates	9
Mega riverbed-patterns: linear and weakly nonlinear perspectives	9
Whitham equations and phase shifts for the Korteweg–de Vries equation	9
A pseudo-anelastic model for stress softening in liquid crystal elastomers	9
Mechanisms of root reinforcement in soils: an experimental methodology using four-dimensional X-ray computed tomography and digital volume correlation	9
Biomechanical modelling of spinal tumour anisotropic growth	9
Understanding the role of urban design in disease spreading	9
Inverse differential quadrature method: mathematical formulation and error analysis	9
Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations	9
Viability of slow-roll inflation in light of the non-zero k min measured in the cosmic microwave background power spectrum	9
An improved statistical approach for reconstructing past climates from biotic assemblages	9
Fate of a bulge in an inflated hyperelastic tube: theory and experiment	9
Rapid indirect solar responses observed in the lower atmosphere	8
How old are dense-core vesicles residing in en passant boutons: simulation of the mean age of dense-core vesicles in axonal arbours accounting for resident and transitin	8
Bayesian uncertainty quantification for data-driven equation learning	8
Capillary imbibition of non-Newtonian fluids in a microfluidic channel: analysis and experiments	8
Flexural tensegrity of segmental beams	8
Target competition for resources under multiple search-and-capture events with stochastic resetting	8
Optimization of a type of elastic metamaterial for broadband wave suppression	8
How surface stress transforms surface profiles and adhesion of rough elastic bodies	8
Mechanics of tension-induced film wrinkling and restabilization: a review	8
The generalized Wiener–Hopf equations for wave motion in angular regions: electromagnetic application	8
SINDy for delay-differential equations: application to model bacterial zinc response	8
The wave function as a true ensemble	8
Acceleration waves and oscillating gas bubbles modelled by rational extended thermodynamics	8
Nonlinear viscoelasticity of strain rate type: an overview	8
Universal deformations in inhomogeneous isotropic nonlinear elastic solids	8
Vassiliev measures of complexity of open and closed curves in 3-space	8
Modelling song popularity as a contagious process	8
Scattering of surface waves by a vertical truncated structured cylinder	8
Rational solutions of the defocusing non-local nonlinear Schrödinger equation: asymptotic analysis and soliton interactions	8
Magic state distillation with the ternary Golay code	8
Optical wireless communications for cyber-secure ubiquitous wireless networks	8
A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with applications to metamaterials and acoustics	8
First-order convergence of Milstein schemes for McKean–Vlasov equations and interacting particle systems	8
Enhanced models for the nonlinear bending of planar rods: localization phenomena and multistability	8
USP: an independence test that improves on Pearson’s chi-squared and the G -test	8
Topological mode switching in modulated structures with dynamic encircling of an exceptional point	8
Message passing methods on complex networks	8
Analogue neuro-memristive convolutional dropout nets	8
Elastic waves in particulate glass-rubber mixtures	8
Self-rotating 3D chiral mechanical metamaterials	8
Thermal oscillations, second sound and thermal resonance in phonon hydrodynamics	8
f -distance of knotoids and protein structure	7
Swell-induced flexural vibrations of a thickening ice shelf over a shoaling seabed	7
Everettian relative states in the Heisenberg picture	7
On blockage coefficients: flow past a body in a pipe	7
Mean-field theory for double-well systems on degree-heterogeneous networks	7
Pair approximation model for the vaccination game: predicting the dynamic process of epidemic spread and individual actions against contagion	7
Fracture modelling of plain concrete using non-local fracture mechanics and a graph-based computational framework	7
A probabilistic model of diffusion through a semi-permeable barrier	7
Soft wetting with (a)symmetric Shuttleworth effect	7
Plesio-geostrophy for Earth’s core: I. Basic equations, inertial modes and induction	7
Design of arbitrarily shaped acoustic cloaks through partial differential equation-constrained optimization satisfying sonic-metamaterial design requirements	7
Brachistochrone on a velodrome	7
Functional difference equations and eigenfunctions of a Schrödinger operator with δ ′ −interaction on a circular conical surface	7
A new integrable model of long wave–short wave interaction and linear stability spectra	7
Novel statistical emulator construction for volcanic ash transport model Ash3d with physically motivated measures	7
Short branch cut approximation in two-dimensional hydrodynamics with free surface	7
Interaction between surface waves on wire lines	7
Fast active thermal cloaking through PDE-constrained optimization and reduced-order modelling	7
Editorial: citation malpractice	7
Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis	7
A new approach to integrable evolution equations on the circle	7
On explicit Wiener–Hopf factorization of 2 × 2 matrices in a vicinity of a given matrix	7
Superdeterministic hidden-variables models I: non-equilibrium and signalling	7
Covid-19: predictive mathematical formulae for the number of deaths during lockdown and possible scenarios for the post-lockdown period	7
Enhanced attraction between drops carrying fluctuating charge distributions	7
A focusing and defocusing semi-discrete complex short-pulse equation and its various soliton solutions	7
Sensitivity analysis of Wasserstein distributionally robust optimization problems	7
A new class of mass dimension one fermions	7
Low-carbon development via greening global value chains: a case study of Belarus	6
Coupling-induced instability in a ring of thermoacoustic oscillators	6
Violations of the Clausius–Duhem inequality in Couette flows of granular media	6
Wald’s martingale and the conditional distributions of absorption time in the Moran process	6
Interpreting how nonlinear diffusion affects the fate of bistable populations using a discrete modelling framework	6
Perturbation theory for Bose–Einstein condensates on bounded space domains	6