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Analogue neuromemristive convolutional dropout nets Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201014
O. Krestinskaya; A. P. JamesRandomly switching neurons ON/OFF while training and inference process is an interesting characteristic of biological neural networks, that potentially results in inherent adaptability and creativity expressed by human mind. Dropouts inspire from this random switching behaviour and in the artificial neural network they are used as a regularization techniques to reduce the impact of overfitting during

RayleighBnard magnetoconvection with temperature modulation Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201014
Suparna Hazra; Krishna Kumar; Saheli MitraFloquet analysis of modulated magnetoconvection in Rayleigh–Bénard geometry is performed. A sinusoidally varying temperature is imposed on the lower plate. As Rayleigh number Ra is increased above a critical value Rao, the oscillatory magnetoconvection begins. The flow at the onset of magnetoconvection may oscillate either subhar monically or harmonically with the external modulation. The critical

Stability and memoryloss go handinhand: three results in dynamics and computation Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201014
G. ManjunathThe search for universal laws that help establish a relationship between dynamics and computation is driven by recent expansionist initiatives in biologically inspired computing. A general setting to understand both such dynamics and computation is a driven dynamical system that responds to a temporal input. Surprisingly, we find memoryloss a feature of driven systems to forget their internal states

Target competition for resources under multiple searchandcapture events with stochastic resetting Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201014
P. C. BressloffWe develop a general framework for analysing the distribution of resources in a population of targets under multiple independent searchandcapture events. Each event involves a single particle executing a stochastic search that resets to a fixed location xr at a random sequence of times. Whenever the particle is captured by a target, it delivers a packet of resources and then returns to xr, where

A fully coupled hybrid lattice Boltzmann and finite difference methodbased study of transient electrokinetic flows Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201014
Himadri Sekhar Basu; Supreet Singh Bahga; Sasidhar KondarajuTransient electrokinetic (EK) flows involve the transport of conductivity gradients developed as a result of mixing of ionic species in the fluid, which in turn is affected by the electric field applied across the channel. The presence of three different coupled equations with corresponding different time scales makes it difficult to model the problem using the lattice Boltzmann method (LBM). The present

Optimizing Global Navigation Satellite Systems network realtime kinematic infrastructure for homogeneous positioning performance from the perspective of tropospheric effects Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201014
Chen Yu; Nigel T. Penna; Zhenhong LiRealtime centimetrelevel precise positioning from Global Navigation Satellite Systems (GNSS) is critical for activities including landslide, glacier and coastal erosion monitoring, flood modelling, precision agriculture, intelligent transport systems, autonomous vehicles and the Internet of Things. This may be achieved via the realtime kinematic (RTK) GNSS approach, which uses a single receiver

Hydrodynamics of a bordered collar as a countermeasure against pier scouring Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201014
Domenico Ferraro; Andrea Fenocchi; Roberto GaudioAn experimental campaign on longterm clearwater scour at bridge piers with different configurations was performed in a laboratory to investigate the effects of different countermeasures. Tests were performed in a flume with a movable sediment bed for an unprotected cylindrical pier, a cylindrical pier with a standard collar and a cylindrical pier with a bordered collar. The scoured beds at the equilibrium

Quotation errors in general science journals Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201014
SmithNeal Jr; Aaron CumberledgeDue to the incremental nature of scientific discovery, scientific writing requires extensive referencing to the writings of others. The accuracy of this referencing is vital, yet errors do occur. These errors are called ‘quotation errors’. This paper presents the first assessment of quotation errors in highimpact general science journals. A total of 250 random citations were examined. The propositions

Magnetic winding: what is it and what is it good for? Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201014
Christopher Prior; David MacTaggartMagnetic winding is a fundamental topological quantity that underpins magnetic helicity and measures the entanglement of magnetic field lines. Like magnetic helicity, magnetic winding is also an invariant of ideal magnetohydrodynamics. In this article, we give a detailed description of what magnetic winding describes, how to calculate it and how to interpret it in relation to helicity. We show how

Unitary unfoldings of a BoseHubbard exceptional point with and without particle number conservation Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201014
Miloslav ZnojilThe conventional nonHermitian but PTsymmetric threeparametric Bose–Hubbard Hamiltonian H(γ, v, c) represents a quantum system of N bosons, unitary only for parameters γ, v and c in a domain D. Its boundary ∂D contains an exceptional point of order K (EPK; K = N + 1) at c = 0 and γ = v, but even at the smallest nonvanishing parameter c ≠ ~0 the spectrum of H(v, v, c) ceases to be real, i.e. the

On the asymptotic properties of a canonical diffraction integral Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201014
Raphal C. Assier; I. David AbrahamsWe introduce and study a new canonical integral, denoted I+−ε, depending on two complex parameters α1 and α2. It arises from the problem of wave diffraction by a quarterplane and is heuristically constructed to capture the complex field near the tip and edges. We establish some region of analyticity of this integral in C2, and derive its rich asymptotic behaviour as α1  and α2  tend to infinity

Shape analysis via inconsistent surface registration Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201007
Gary P. T. Choi; Di Qiu; Lok Ming LuiIn this work, we develop a framework for shape analysis using inconsistent surface mapping. Traditional landmarkbased geometric morphometr ics methods suffer from the limited degrees of freedom, while most of the more advanced nonrigid surface mapping methods rely on a strong assumption of the global consistency of two surfaces. From a practical point of view, given two anatomical surfaces with

Geodesic Loewner paths with varying boundary conditions Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201007
Robb McDonaldEquations of the Loewner class subject to nonconstant boundary conditions along the real axis are formulated and solved giving the geodesic paths of slits growing in the upper half complex plane. The problem is motivated by Laplacian growth in which the slits represent thin fingers growing in a diffusion field. A single finger follows a curved path determined by the forcing function appearing in Loewner’s

Continentscale Hiatus Maps for the Atlantic Realm and Australia since the Upper Jurassic and links to mantle flow induced dynamic topography Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201007
Jorge Nicolas Hayek; Berta Vilacs; HansPeter Bunge; Anke M. Friedrich; Sara Carena; Yulia VibeInterregional geological maps hold important information for geodynamic models. Here, we use such maps to visualize major conformable and unconformable contacts at interregional scales and at the level of geologic series from the Upper Jurassic onward across North and South America, Europe, Africa and Australia. We extract hiatus information from these paleogeological maps, which we plot in a paleogeographical

Hyperspace fermions, Mbius transformations, Krein space, fermion doubling, dark matter Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201007
George JaroszkiewiczWe develop an approach to classical and quantum mechanics where continuous time is extended by an infinitesimal parameter T and equations of motion converted into difference equations. These equations are solved and the physical limit T → 0 then taken. In principle, this strategy should recover all standard solutions to the original continuous time differential equations. We find this is valid for

SINDyPI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201007
Kadierdan Kaheman; J. Nathan Kutz; Steven L. BruntonAccurately modelling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data. Although extensions have been developed to identify implicit dynamics, or dynamics described by rational functions, these extensions are extremely sensitive to

Novel statistical emulator construction for volcanic ash transport model Ash3d with physically motivated measures Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201007
Qingyuan Yang; E. Bruce Pitman; Elaine Spiller; Marcus Bursik; Andrea BevilacquaStatistical emulators are a key tool for rapidly producing probabilistic hazard analysis of geophysical processes. Given output data computed for a relatively small number of parameter inputs, an emulator interpolates the data, providing the expected value of the output at untried inputs and an estimate of error at that point. In this work, we propose to fit Gaussian Process emulators to the output

Deterministic normal contact of rough surfaces with adhesion using a surface integral method Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201007
Ali Ghanbarzadeh; Mostafa Faraji; Anne NevilleThe fundamental problem of adhesion in the presence of surface roughness and its effect on the prediction of friction has been a hot topic for decades in numerous areas of science and engineering, attracting even more attention in recent years in areas such as geotechnics and tectonics, nanotechnology, highvalue manufacturing and biomechanics. In this paper a new model for deterministic calculation

The field of values of Jones matrices: classification and special cases Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201007
Julio C. GutirrezVegaThe concept of field of values (FoV), also known as the numerical range, is applied to the 2 × 2 Jones matrices used in polarization optics. We discover the relevant interplay between the geometric properties of the FoV, the algebraic properties of the Jones matrices and the representation of polarization states on the Poincaré sphere. The properties of the FoV reveal hidden symmetries in the relationships

Optical wireless communications for cybersecure ubiquitous wireless networks Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201007
Hanaa Abumarshoud; Cheng Chen; Mohamed Sufyan Islim; Harald HaasWireless connectivity is no longer limited to facilitating communications between individuals, but is also required to support diverse and heterogeneous applications, services and infrastructures. Internet of things (IoT) systems will dominate future technologies, allowing any and all devices to create, share and process data. If artificial intelligence resembles the brain of IoT, then highspeed connectivity

Linear angular momentum multiplexingconceptualization and experimental evaluation with antenna arrays Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201007
Tim W. C. Brown; Ben H. Allen; Timothy D. Drysdale; Upasana K. DagiaLinear angular momentum multiplexing is a new method for providing highly spectrally efficient shortrange communication between a transmitter and receiver, where one may move at speed transverse to the propagation. Such applications include rail, vehicle and hyperloop transport systems communicating with fixed infrastructure on the ground. This paper describes how the scientific concept of linear

Spontaneous divergence of disease status in an economic epidemiological game Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20201007
Ewan Colman; Nick Hanley; Rowland R. KaoWe introduce a game inspired by the challenges of disease management in livestock farming and the transmission of endemic disease through a trade network. Success in this game comes from balancing the cost of buying new stock with the risk that it will be carrying some disease. When players follow a simple memorybased strategy we observe a spontaneous separation into two groups corresponding to players

Axisymmetric bending analysis of functionally graded onedimensional hexagonal piezoelectric quasicrystal circular plate Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200930
Yang Li; Yuan Li; Qinghua Qin; Lianzhi Yang; Liangliang Zhang; Yang GaoWithin a framework of the state space method, an axisymmetric solution for functionally graded onedimensional hexagonal piezoelectric quasicrystal circular plate is presented in this paper. Applying the finite Hankel transform onto the state space vector, an ordinary differential equation with constant coefficients is obtained for the circular plate provided that the free boundary terms are zero

EulerMaclaurin expansions without analytic derivatives Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200930
Bengt FornbergThe Euler–Maclaurin (EM) formulae relate sums and integrals. Discovered nearly 300 years ago, they have lost none of their importance over the years, and are nowadays routinely taught in scientific computing and numerical analysis courses. The two common versions can be viewed as providing error expansions for the trapezoidal rule and for the midpoint rule, respectively. More importantly, they provide

How old are densecore vesicles residing in en passant boutons: simulation of the mean age of densecore vesicles in axonal arbours accounting for resident and transiting vesicle populations Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200930
Ivan A. Kuznetsov; Andrey V. KuznetsovIn neurons, neuropeptides are synthesized in the soma and are then transported along the axon in densecore vesicles (DCVs). DCVs are captured in varicosities located along the axon terminal called en passant boutons, which are active terminal sites that accumulate and release neurotransmitters. Recently developed experimental techniques allow for the estimation of the age of DCVs in various locations

The convective instability of a MaxwellCattaneo fluid in the presence of a vertical magnetic field Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200930
I. A. Eltayeb; D. W. Hughes; M. R. E. ProctorWe study the instability of a Bénard layer subject to a vertical uniform magnetic field, in which the fluid obeys the Maxwell–Cattaneo (MC) heat flux–temperature relation. We extend the work of Bissell (Proc. R. Soc. A 472, 20160649 (doi:10.1098/rspa.2016.0649)) to nonzero values of the magnetic Prandtl number pm. With nonzero pm, the order of the dispersion relation is increased, leading to considerably

Equilibria and stability of four point vortices on a sphere Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200930
David G. DritschelThis paper discusses the problem of finding the equilibrium positions of four point vortices, of generally unequal circulations, on the surface of a sphere. A random search method is developed which uses a modification of the linearized equations to converge on distinct equilibria. Many equilibria (47 and possibly more) may exist for prescribed circulations and angular impulse. A linear stability analysis

Captive diffusions and their applications to orderpreserving dynamics Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200930
Levent Ali Mengtrk; Murat Cahit MengtrkWe propose a class of stochastic processes that we call captive diffusions, which evolve within measurable pairs of càdlàg bounded functions that admit bounded rightderivatives at points where they are continuous. In full generality, such processes allow reflection and absorption dynamics at their boundaries—possibly in a hybrid manner over nonoverlapping time periods—and if they are martingales

Measuring friction at an interface using ultrasonic response Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200930
X. Li; R. S. DwyerJoyceFriction between sliding surfaces is a fundamental phenomenon prevalent in many aspects of engineering. There are many sliding contact tribometers that measure friction force in a laboratory environment. However, the transfer of laboratory data to real machine elements is unreliable. Results depend on the specimen configuration, surface condition and environment. In this work, a method has been developed

A regularized phasefield model for faceting in a kinetically controlled crystal growth Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200930
T. Philippe; H. Henry; M. PlappAt equilibrium, the shape of a strongly anisotropic crystal exhibits corners when for some orientations the surface stiffness is negative. In the sharpinterface problem, the surface free energy is traditionally augmented with a curvaturedependent term in order to round the corners and regularize the dynamic equations that describe the motion of such interfaces. In this paper, we adopt a diffuse interface

Faraday waves in soft elastic solids Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200930
Giulia Bevilacqua; Xingchen Shao; John R. Saylor; Joshua B. Bostwick; Pasquale CiarlettaRecent experiments have observed the emergence of standing waves at the free surface of elastic bodies attached to a rigid oscillating substrate and subjected to critical values of forcing frequency and amplitude. This phenomenon, known as Faraday instability, is now well understood for viscous fluids but surprisingly eluded any theoretical explanation for soft solids. Here, we characterize Faraday

Analytical model for electrohydrodynamic thrust Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200930
Ravi Sankar Vaddi; Yifei Guan; Alexander Mamishev; Igor NovosselovElectrohydrodynamic (EHD) thrust is produced when ionized fluid is accelerated in an electric field due to the momentum transfer between the charged species and neutral molecules. We extend the previously reported analytical model that couples space charge, electric field and momentum transfer to derive thrust force in onedimensional planar coordinates. The electric current density in the model can

Rapid indirect solar responses observed in the lower atmosphere Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200930
R. Giles Harrison; Michael LockwoodEstablishing clear evidence of solarinduced lower atmosphere effects is hampered by the small 11year solar cycle responses, typically swamped by meteorological variability. Strong 27day cyclic changes are exploited here instead. During the 2007/8 minimum in solar activity, regular 27day lighthouselike sweeps of energetic particles crossed the heliosphere and Earth, followed by a burst of solar

Exact solutions of the harmonic oscillator plus nonpolynomial interaction Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200923
Qian Dong; H. Ivn Garca Hernndez; GuoHua Sun; Mohamad Toutounji; ShiHai DongThe exact solutions to a onedimensional harmonic oscillator plus a nonpolynomial interaction a x2 + b x2/(1 + c x2) (a > 0, c > 0) are given by the confluent Heun functions Hc(α, β, γ, δ, η;z). The minimum value of the potential well is calculated as Vmin(x)=−(a+b−2a b)/c at x=±[(b/a−1)/c]1/2 (b > a) for the doublewell case (b < 0). We illustrate the wave functions through varying the potential

Maxwell tipping points: the hidden mechanics of an axially compressed cylindrical shell Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200923
G. W. Hunt; R. M. J. Groh; T. J. DodwellNumerical results for the axially compressed cylindrical shell demonstrate the postbuckling response snaking in both the applied load and corresponding endshortening. Fluctuations in load, associated with progressive axial formation of circumferential rings of dimples, are well known. Snaking in endshortening, describing the evolution from a single dimple into the first complete ring of dimples

Exponential stability in Mindlins Form II gradient thermoelasticity with microtemperatures of type III Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200923
M. Aouadi; F. Passarella; V. TibulloIn this paper, we derive a nonlinear strain gradient theory of thermoelastic materials with microtemperatures taking into account microinertia effects as well. The elastic behaviour is assumed to be consistent with Mindlin’s Form II gradient elasticity theory, while the thermal behaviour is based on the entropy balance of type III postulated by Green and Naghdi for both temperature and microtemperatures

A Mathieu function boundary spectral method for scattering by multiple variable poroelastic plates, with applications to metamaterials and acoustics Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200923
Matthew J. Colbrook; Anastasia V. KisilMany problems in fluid mechanics and acoustics can be modelled by Helmholtz scattering off poroelastic plates. We develop a boundary spectral method, based on collocation of local Mathieu function expansions, for Helmholtz scattering off multiple variable poroelastic plates in two dimensions. Such boundary conditions, namely the varying physical parameters and coupled thinplate equation, present

How to smooth a crinkled map of space–time: Uhlenbeck compactness for L∞ connections and optimal regularity for general relativistic shock waves by the Reintjes–Temple equations Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200916
Moritz Reintjes; Blake TempleWe present the authors’ new theory of the RTequations (‘regularity transformation’ or ‘Reintjes–Temple’ equations), nonlinear elliptic partial differential equations which determine the coordinate transformations which smooth connections Γ to optimal regularity, one derivative smoother than the Riemann curvature tensor Riem(Γ). As one application we extend Uhlenbeck compactness from Riemannian to

Nonstandard magnetohydrodynamics equations and their implications in sunspots Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200916
Rami Ahmad ElNabulsiIn this work, we study the physics of plasma waves and magnetohydrodynamic (MHD) equilibrium of sunspots based on the concept of nonstandard Lagrangians which play an important role in several branches of science. We derived the modified fluid equations from the Maxwell–Vlasov equation using the moment conventional procedure. Several new interaction terms between physical quantities arise in the nonstandard

Predictive modelling of drop ejection from damped, dampened wings by machine learning Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200916
MD Erfanul Alam; Dazhong Wu; Andrew K. DickersonThe high frequency, low amplitude wing motion that mosquitoes employ to dry their wings inspires the study of drop release from millimetric, forced cantilevers. Our mimicking system, a 10mm polytetrafluoroethylene cantilever driven through ±1 mm base amplitude at 85 Hz, displaces drops via three principal ejection modes: normaltocantilever ejection, sliding and pinchoff. The selection of system

Kernel representation of longwave dynamics on a uniform slope Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200916
T. ShimozonoLongwave propagation on a uniformly sloping beach is formulated as a transientresponse problem, with initially stationary water subjected to an incident wave. Both the water surface elevation and the horizontal flow velocity on the slope can be represented as convolutions of the rate of displacement of the water surface at the toe of the slope with a singular kernel function of time and space. The

Nonlinear MHD Rossby wave interactions and persistent geomagnetic field structures Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200916
Breno Raphaldini; Carlos F. M. RauppThe geomagnetic field presents several stationary features that are thought to be linked to inhomogeneities at the core–mantle boundary. Particularly important stationary structures of the geomagnetic field are the flux lobes, which appear in pairs in mid to high mid to high latitudes. A recently discovered stratified layer at the top of the Earth’s core poses important constraints on the dynamics

Debonding waves in gel thin films Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200916
Xianmin Xu; M. Carme Calderer; Masao Doi; Duvan HenaoWe develop a mathematical model for the sliding of a gel sheet adhered to a moving substrate. The sliding takes place by the motion of detached region between the gel sheet and the substrates, i.e. the propagation of a Schallamach wave. Efficient numerical methods are developed to solve the problem. Numerical examples illustrate that the model can describe the Schallamach wave and are consistent with

A continuum model for the growth of dendritic actin networks Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200916
Rohan Abeyaratne; Prashant K. PurohitPolymerization of dendritic actin networks underlies important mechanical processes in cell biology such as the protrusion of lamellipodia, propulsion of growth cones in dendrites of neurons, intracellular transport of organelles and pathogens, among others. The forces required for these mechanical functions have been deduced from mechanochemical models of actin polymerization; most models are focused

Minimum wave speeds in monostable reactiondiffusion equations: sharp bounds by polynomial optimization Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200916
Jason J. Bramburger; David GoluskinMany monostable reaction–diffusion equations admit onedimensional travelling waves if and only if the wave speed is sufficiently high. The values of these minimum wave speeds are not known exactly, except in a few simple cases. We present methods for finding upper and lower bounds on minimum wave speed. They rely on constructing trapping boundaries for dynamical systems whose heteroclinic connections

Unpacking the Allee effect: determining individuallevel mechanisms that drive global population dynamics Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200916
Nabil T. Fadai; Stuart T. Johnston; Matthew J. SimpsonWe present a solid theoretical foundation for interpreting the origin of Allee effects by providing the missing link in understanding how local individualbased mechanisms translate to global population dynamics. Allee effects were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. However, standard methods often calibrate Allee effect

Fixedtime synchronization of quaternionvalued neural networks with timevarying delay Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200916
Umesh Kumar; Subir Das; Chuangxia Huang; Jinde CaoIn this article, sufficient conditions for fixedtime synchronization of timedelayed quaternionvalued neural networks (QVNNs) are derived. Firstly, QVNNs are decomposed into four realvalued systems. Then using the available lemmas and by constructing the Lyapunov function, the synchronization criterion for the neural networks is proposed. Activation functions satisfy the Lipschitz condition. A suitable

Contact geometry for simple thermodynamical systems with friction Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200916
Alexandre Anahory Simoes; Manuel de Len; Manuel Lainz Valczar; David Martn de DiegoBy means of the Jacobi structure associated with a contact structure, we use the socalled evolution vector field to propose a new characterization of isolated thermodynamical systems with friction, a simple but important class of thermodynamical systems which naturally satisfy the first and second laws of thermodynamics, i.e. total energy preservation of isolated systems and nondecreasing total entropy

Big influence of small random imperfections in origamibased metamaterials Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200916
Ke Liu; Larissa S. Novelino; Paolo Gardoni; Glaucio H. PaulinoOrigami structures demonstrate great theoretical potential for creating metamaterials with exotic properties. However, there is a lack of understanding of how imperfections influence the mechanical behaviour of origamibased metamaterials, which, in practice, are inevitable. For conventional materials, imperfection plays a profound role in shaping their behaviour. Thus, this paper investigates the

Functional difference equations and eigenfunctions of a Schrödinger operator with δ′ −interaction on a circular conical surface Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200916
Mikhail A. LyalinovEigenfunctions and their asymptotic behaviour at large distances for the Laplace operator with singular potential, the support of which is on a circular conical surface in threedimensional space, are studied. Within the framework of incomplete separation of variables an integral representation of the Kontorovich–Lebedev (KL) type for the eigenfunctions is obtained in terms of solution of an auxiliary

How rare are powerlaw networks really? Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200916
I. Artico; I. Smolyarenko; V. Vinciotti; E. C. WitThe putative scalefree nature of realworld networks has generated a lot of interest in the past 20 years: if networks from many different fields share a common structure, then perhaps this suggests some underlying ‘network law’. Testing the degree distribution of networks for powerlaw tails has been a topic of considerable discussion. Ad hoc statistical methodology has been used both to discredit

Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200909
Steven J. Lind; Benedict D. Rogers; Peter K. StansbyThis paper presents a review of the progress of smoothed particle hydrodynamics (SPH) towards highorder converged simulations. As a meshfree Lagrangian method suitable for complex flows with interfaces and multiple phases, SPH has developed considerably in the past decade. While original applications were in astrophysics, early engineering applications showed the versatility and robustness of the

Atmospheric composition of exoplanets based on the thermal escape of gases and implications for habitability Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200909
Samuel Konatham; Javier MartinTorres; MariaPaz ZorzanoThe detection of habitable exoplanets is an exciting scientific and technical challenge. Owing to the current and most likely longlasting impossibility of performing in situ exploration of exoplanets, their study and hypotheses regarding their capability to host life will be based on the restricted lowresolution spatial and spectral information of their atmospheres. On the other hand, with the advent

Novel cloaking lamellar structures for a screw dislocation dipole, a circular Eshelby inclusion and a concentrated couple Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200909
Xu Wang; Peter SchiavoneUsing conformal mapping techniques, we design novel lamellar structures which cloak the influence of any one of a screw dislocation dipole, a circular Eshelby inclusion or a concentrated couple. The lamellar structure is composed of two halfplanes bonded through a middle coating with a variable thickness within which is located either the dislocation dipole, the circular Eshelby inclusion or the concentrated

Coreperiphery structure in directed networks Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200909
Andrew Elliott; Angus Chiu; Marya Bazzi; Gesine Reinert; Mihai CucuringuEmpirical networks often exhibit different mesoscale structures, such as community and core–periphery structures. Core–periphery structure typically consists of a wellconnected core and a periphery that is well connected to the core but sparsely connected internally. Most core–periphery studies focus on undirected networks. We propose a generalization of core–periphery structure to directed networks

CycleRank, or there and back again: personalized relevance scores from cyclic paths on directed graphs Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200909
Cristian Consonni; David Laniado; Alberto MontresorSurfing the links between Wikipedia articles constitutes a valuable way to acquire new knowledge related to a topic by exploring its connections to other pages. In this sense, Personalized PageRank is a wellknown option to make sense of the graph of links between pages and identify the most relevant articles with respect to a given one; its performance, however, is hindered by pages with high indegree

Force reversal and energy dissipation in composite tubes through nonlinear viscoelasticity of component materials Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200902
Audrey Sedal; Alan WinemanFibrereinforced, fluidfilled structures are commonly found in nature and emulated in devices. Researchers in the field of soft robotics have used such structures to build lightweight, impactresistant and safe robots. The polymers and biological materials in many soft actuators have these advantageous characteristics because of viscoelastic energy dissipation. Yet, the gross effects of these underlying

Nucleation properties of isolated shear bands Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200902
Shwetabh Yadav; Dinakar SagapuramShear banding, or localization of intense strains along narrow bands, is a plastic instability in solids with important implications for material failure in a wide range of materials and across length scales. In this article, we report on a series of experiments on the nucleation of single isolated shear bands in three model alloys. Nucleation kinetics of isolated bands and characteristic stresses

High endemic levels of typhoid fever in rural areas of Ghana may stem from optimal voluntary vaccination behaviour Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200902
Carmen B. AcostaAlonzo; Igor V. Erovenko; Aaleah Lancaster; Hyunju Oh; Jan Rycht; Dewey TaylorTyphoid fever has long established itself endemically in rural Ghana despite the availability of cheap and effective vaccines. We used a gametheoretic model to investigate whether the low vaccination coverage in Ghana could be attributed to rational human behaviour. We adopted a version of an epidemiological model of typhoid fever dynamics, which accounted not only for chronic lifelong carriers but

Walds martingale and the conditional distributions of absorption time in the Moran process Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20200902
Travis Monk; Andr van SchaikMany models of evolution are stochastic processes, where some quantity of interest fluctuates randomly in time. One classic example is the Moranbirth–death process, where that quantity is the number of mutants in a population. In such processes, we are often interested in their absorption (i.e. fixation) probabilities and the conditional distributions of absorption time. Those conditional time distributions