显示样式： 排序： IF:  GO 导出

Short branch cut approximation in twodimensional hydrodynamics with free surface Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210505
A. I. Dyachenko, S. A. Dyachenko, P. M. Lushnikov, V. E. ZakharovA potential motion of ideal incompressible fluid with a free surface and infinite depth is considered in twodimensional geometry. A timedependent conformal mapping of the lower complex halfplane of the auxiliary complex variable w into the area filled with fluid is performed with the real line of w mapped into the free fluid’s surface. The fluid dynamics can be fully characterized by the motion

Hybrid integral transform analysis of supercooled droplets solidification Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210428
Igor S. Carvalho, Renato M. Cotta, Carolina P. NaveiraCotta, Manish K. TiwariThe freezing phenomena in supercooled liquid droplets are important for many engineering applications. For instance, a theoretical model of this phenomenon can offer insights for tailoring surface coatings and for achieving icephobicity to reduce ice adhesion and accretion. In this work, a mathematical model and hybrid numerical–analytical solutions are developed for the freezing of a supercooled droplet

On the stability and instability of linear potential systems subjected to infinitesimal circulatory forces Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210428
Ranislav M. Bulatovic, Firdaus E. UdwadiaThe stability of linear multidegreeoffreedom stable potential systems with multiple natural frequencies under the action of infinitesimal circulatory forces is considered. Contrary to the received view that such systems are inherently unstable, a careful study shows that such systems have a much more complex behaviour than previously recognized and could exhibit an alternation of stability and instability

Implementing parallel arithmetic via acetylation and its application to chemical image processing Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210428
Amanda Dombroski, Kady Oakley, Christopher Arcadia, Farnaz Nouraei, Shui Ling Chen, Christopher Rose, Brenda Rubenstein, Jacob Rosenstein, Sherief Reda, Eunsuk KimChemical mixtures can be leveraged to store large amounts of data in a highly compact form and have the potential for massive scalability owing to the use of largescale molecular libraries. With the parallelism that comes from having many species available, chemicalbased memory can also provide the physical substrate for computation with increased throughput. Here, we represent nonbinary matrices

Graphite phases in chemical vapour deposited grown ZrC/graphite layers Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210428
Jan A. Pretorius, Johan B. MalherbeThe graphitic phases detected in chemical vapour deposited (CVD) ZrC layers were characterized by glancing angle Xray diffraction. The layers were deposited at different temperatures ranging from 1250 to 1450°C in steps of 50°C. The precursors used were ZrCl4 and CH4 in the presence of hydrogen and argon. A total of seven graphitic phases were detected, five of which have been reported in the literature

An axisymmetric problem for a pennyshaped crack under the influence of the SteigmannOgden surface energy Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210421
Anna Y. ZemlyanovaA problem for a nanosized pennyshaped fracture in an infinite homogeneous isotropic elastic medium is considered. The fracture is opened by applying an axisymmetric normal traction to its surface. The surface energy in the Steigmann–Ogden form is acting on the boundary of the fracture. The problem is solved by using the Boussinesq potentials represented by the Hankel transforms of certain unknown

A Fanobased acoustic metamaterial for ultrabroadband sound barriers Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210401
H. Q. Nguyen, Q. Wu, H. Chen, J. J. Chen, Y. K. Yu, S. Tracy, G. L. HuangUltrabroadband sound reduction schemes covering living and working noise spectra are of high scientific and industrial significance. Here, we report, both theoretically and experimentally, on an ultrabroadband acoustic barrier assembled from spacecoiling metamaterials (SCMs) supporting two Fano resonances. Moreover, acoustic hyperdamping is introduced by integrating additional thin viscous foam

The role of sliding in ice stream formation Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210401
Christian Schoof, Elisa MantelliIce streams are bands of fastflowing ice in ice sheets. We investigate their formation as an example of spontaneous pattern formation, based on positive feedbacks between dissipation and basal sliding. Our focus is on temperaturedependent subtemperate sliding, where faster sliding leads to enhanced dissipation and hence warmer temperatures, weak ening the bed further, and on a similar feedback driven

An exact analysis of scalar transport in hydromagnetic flow between two parallel plates: a multiscale approach Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210401
Nanda Poddar, Subham Dhar, Bijoy Singha Mazumder, Kajal Kumar MondalThe present paper explores an analytical solution to study the twodimensional concentration distribution of a solute in a conducting fluid flowing between two parallel plates in the presence of a transverse magnetic field. Mei’s homogenization technique is used to acquire the mean concentration distributions up to the secondorder approximation and the transverse concentration distributions up to

Quantum relaxation in a system of harmonic oscillators with timedependent coupling Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210401
Francisco Bento Lustosa, Samuel Colin, Santiago E. Perez BergliaffaIn the context of the de Broglie–Bohm pilotwave theory, numerical simulations for simple systems have shown that states that are initially out of quantum equilibrium—thus violating the Born rule—usually relax over time to the expected ψ2 distribution on a coarsegrained level. We analyse the relaxation of nonequilibrium initial distributions for a system of coupled onedimensional harmonic oscillators

Variational principles of liquidporous material interactions with applications to approximate solutions and finiteelement modelling Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210401
Jing Tang Xing, Hongling QinFor liquid–porous material interactions (LPMI), three variational principles are developed in Biot's theory of porous materials in association with Darcy's Law. First one takes solid acceleration, and fluid velocity, acceleration, pressure with time derivative as five variables, while second and third, respectively, have three and two variables when Darcy's Law used as variational constraint reducing

Inverse differential quadrature method: mathematical formulation and error analysis Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210401
Saheed O. Ojo, Luan C. Trinh, Hasan M. Khalid, Paul M. WeaverEngineering systems are typically governed by systems of highorder differential equations which require efficient numerical methods to provide reliable solutions, subject to imposed constraints. The conventional approach by direct approximation of system variables can potentially incur considerable error due to high sensitivity of highorder numerical differentiation to noise, thus necessitating improved

Manifestation of the Berry curvature in geophysical ray tracing Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210401
N. Perez, P. Delplace, A. VenailleGeometrical phases, such as the Berry phase, have proven to be powerful concepts to understand numerous physical phenomena, from the precession of the Foucault pendulum to the quantum Hall effect and the existence of topological insulators. The Berry phase is generated by a quantity named the Berry curvature, which describes the local geometry of wave polarization relations and is known to appear in

Adding potentials to superintegrable systems with symmetry Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210401
Allan P. Fordy, Qing HuangIn previous work, we have considered Hamiltonians associated with threedimensional conformally flat spaces, possessing two, three and fourdimensional isometry algebras. Previously, our Hamiltonians have represented free motion, but here we consider the problem of adding potential functions in the presence of symmetry. Separable potentials in the threedimensional space reduce to 3 or 4 parameter

Asymptotic solution to convolution integral equations on large and small intervals Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210401
Dmitry PonomarevWe consider convolution integral equations on a finite interval with a realvalued kernel of even parity, a problem equivalent to finding a Wiener–Hopf factorization of a notoriously difficult class of 2 × 2 matrices. The kernel function is assumed to be sufficiently smooth and decaying for large values of the argument. Without loss of generality, we focus on a homogeneous equation and we propose methods

Puckering and wrinkling in a growing composite ring Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210414
T. C. T. Michaels, R. Kusters, L. MahadevanPattern formation driven by differential strain in constrained elastic systems is a common motif in many technological and biological systems. Here we introduce a biologically motivated case of elastic patterning that allows us to explore the conditions for the existence of local puckering and global wrinkling patterns: a soft growing composite ring adhered elastically to a constraining rigid ring

Better strategies for containing COVID19 pandemic: a study of 25 countries via a vSIADR model Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210407
Han Yan, Yuru Zhu, Jia Gu, Yaxuan Huang, Haoxuan Sun, Xinyu Zhang, Yuqing Wang, Yumou Qiu, Song Xi ChenWe study epidemiological characteristics of 25 early COVID19 outbreak countries, which emphasizes on the reproduction of infection and effects of government control measures. The study is based on a vSIADR model which allows asymptomatic and prediagnosis infections to reflect COVID19 clinical realities, and a linear mixedeffect model to analyse the association between each country’s control measures

The onset time of Fermis golden rule Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210407
V. Debierre, E. LassalleFermi’s golden rule describes the decay dynamics of unstable quantum systems coupled to a reservoir, and predicts a linear decay in time. Although it arises at relatively short times, the Fermi regime does not take hold in the earliest stages of the quantum dynamics. The standard criterion in the literature for the onset time of the Fermi regime is tF ∼ 1/Δω, with Δω the frequency interval around the

On a mixed energeticdissipative constitutive law for nonproportional loading, with focus on smallscale plasticity Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210407
Lorenzo BardellaWe analyse the mixed energetic–dissipative potential (MP) recently proposed by our group to predict, within higherorder strain gradient plasticity (SGP), reliable sizedependent responses under general loading histories. Such an MP follows former proposals by Chaboche, Ohno and coworkers for nonlinear kinematic hardening in the context of sizeindependent metal plasticity. The MP is given by M quadratic

Machine learningbased securityaware spatial modulation for heterogeneous radiooptical networks Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210407
Monette H. Khadr, Hany Elgala, Michael Rahaim, Abdallah Khreishah, Moussa Ayyash, Thomas LittleIn this article, we propose a physical layer security (PLS) technique, namely securityaware spatial modulation (SASM), in a multipleinput multipleoutputbased heterogeneous network, wherein both optical wireless communications and radiofrequency (RF) technologies coexist. In SASM, the timedomain signal is altered prior to transmission using a key at the physical layer for combating eavesdropping

On habit and habitat Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210331
Peter Vadasz, Alisa S. VadaszScientific theories based on mathematical models are frequently used in sciences to reveal natural behaviour of systems and eventually to be able in predicting such behaviour once the system's parameters and relevant conditions are known and can be specified. The integration of accumulated theoretical as well as experimental knowledge allows us to present such a unifying theory underlying the equivalence

Dimension reduction for thin films prestrained by shallow curvature Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210324
Silvia Jimnez Bolaos, Marta LewickaWe are concerned with the dimension reduction analysis for thin threedimensional elastic films, prestrained via Riemannian metrics with weak curvatures. For the prestrain inducing the incompatible version of the Föppl–von Kármán equations, we find the Γlimits of the rescaled energies, identify the optimal energy scaling laws, and display the equivalent conditions for optimality in terms of both the

Design of an acoustic energy distributor using thin resonant slits Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210324
Lucas Chesnel, Sergei A. NazarovWe consider the propagation of timeharmonic acoustic waves in a device made of three unbounded channels connected by thin slits. The wavenumber is chosen such that only one mode can propagate. The main goal of this work is to present a device which can serve as an energy distributor. More precisely, the geometry is first designed so that for an incident wave coming from one channel, the energy is

Fate of a bulge in an inflated hyperelastic tube: theory and experiment Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210324
Masoud Hejazi, York Hsiang, A. Srikantha PhaniMechanical instability in a pretensioned finite hyperelastic tube subjected to a slowly increasing internal pressure produces a spatially localized bulge at a critical pressure. This instability is studied in controlled experiments on inflated latex rubber tubes, from the perspective of buckling observed in aneurysms and their rupture risk. The fate of the bulge under continued inflation is governed

Thermal oscillations, second sound and thermal resonance in phonon hydrodynamics Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210324
Mingtian XuRecent observation of second sound in graphite at a temperature above 100 K has aroused a great interest in the study of thermal waves in nonmetallic solid materials. In this article, based on the Guyer–Krumhansl model, we investigate the second sound and thermal resonance phenomena in phonon hydrodynamics. The occurrence condition for the second sound is derived. It shows that the smaller the relaxation

A theory of pattern formation for reactiondiffusion systems on temporal networks Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210324
Robert A. Van GorderNetworks have become ubiquitous in the modern scientific literature, with recent work directed at understanding ‘temporal networks’—those networks having structure or topology which evolves over time. One area of active interest is pattern formation from reaction–diffusion systems, which themselves evolve over temporal networks. We derive analytical conditions for the onset of diffusive spatial and

The ventilation of buildings and other mitigating measures for COVID19: a focus on wintertime Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210317
Henry C. Burridge, Rajesh K. Bhagat, Marc E. J. Stettler, Prashant Kumar, Ishanki De Mel, Panagiotis Demis, Allen Hart, Yyanis JohnsonLlambias, MarcoFelipe King, Oleksiy Klymenko, Alison McMillan, Piotr Morawiecki, Thomas Pennington, Michael Short, David Sykes, Philippe H. Trinh, Stephen K. Wilson, Clint Wong, Hayley Wragg, Megan S. Davies Wykes, Chris Iddon, Andrew W. Woods, Nicola Mingotti, NeerajaThe year 2020 has seen the emergence of a global pandemic as a result of the disease COVID19. This report reviews knowledge of the transmission of COVID19 indoors, examines the evidence for mitigating measures, and considers the implications for wintertime with a focus on ventilation.

A closed form for Jacobian reconstruction from time series and its application as an early warning signal in network dynamics Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210317
Edmund Barter, Andreas Brechtel, Barbara Drossel, Thilo GrossThe Jacobian matrix of a dynamical system describes its response to perturbations. Conversely, one can estimate the Jacobian matrix by carefully monitoring how the system responds to environmental noise. We present a closedform analytical solution for the calculation of a system’s Jacobian from a time series. Being able to access the Jacobian enables a broad range of mathematical analyses by which

Semimartingale driven variational principles Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210310
O. D. Street, D. CrisanSpearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models, we present a general framework for introducing stochasticity into variational principles through the concept of a semimartingale driven variational principle and constraining the component variables to be compatible with the driving semimartingale. Within this framework and the corresponding choice of constraints

Indentation and bifurcation of inflated membranes Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210310
Tianshu Liu, Maurizio Chiaramonte, Amirhossein Amini, Yigit Menguc, G. M. HomsyWe study pneumatically inflated membranes indented by rigid indenters of different sizes and shapes. When the volume of the inflated membrane is beyond a critical value, a symmetric deformation mode becomes unstable and the system follows a path of asymmetric deformation. This bifurcation is analysed analytically for a twodimensional membrane with either a line or plane indenter for which the stable

Shock wave propagation through air: a reactive molecular dynamics study Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210310
S. Pal, N. MitraShock compression of air is observed in numerous situations ranging from explosions to hypersonic vehicle entry into atmosphere. In an effort to develop continuumbased equation of state for air subjected to shock compression, it is necessary to understand the dynamics of the shock compression process with regards to formation of new chemical species in air at the molecular level. With this in perspective

A novel contactless technique to measure water waves using a single photon avalanche diode detector array Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210310
R. Zhang, S. Draycott, I. Gyongy, D. M. Ingram, I. UnderwoodCommonly deployed measurement systems for water waves are intrusive and measure a limited number of parameters. This results in difficulties in inferring detailed sea state information while additionally subjecting the system to environmental loading. Optical techniques offer a nonintrusive alternative, yet documented systems suffer a range of problems related to usability and performance. Here, we

Marine iodine emissions in a changing world Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210303
Lucy J. Carpenter, Rosie J. Chance, Toms Sherwen, Thomas J. Adams, Stephen M. Ball, Mat J. Evans, Helmke Hepach, Lloyd D. J. Hollis, Claire Hughes, Timothy D. Jickells, Anoop Mahajan, David P. Stevens, Liselotte Tinel, Martin R. WadleyIodine is a critical trace element involved in many diverse and important processes in the Earth system. The importance of iodine for human health has been known for over a century, with low iodine in the diet being linked to goitre, cretinism and neonatal death. Research over the last few decades has shown that iodine has significant impacts on tropospheric photochemistry, ultimately impacting climate

Probability and consequences of living inside a computer simulation Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210303
Alexandre BibeauDelisle, Gilles Brassard FRSIt is shown that under reasonable assumptions a Drakestyle equation can be obtained for the probability that our universe is the result of a deliberate simulation. Evaluating loose bounds for certain terms in the equation shows that the probability is unlikely to be as high as previously reported in the literature, especially in a scenario where the simulations are recursive. Furthermore, we investigate

A focusing and defocusing semidiscrete complex shortpulse equation and its various soliton solutions Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210303
BaoFeng Feng, Liming Ling, Zuonong ZhuIn this paper, we are concerned with a semidiscrete complex shortpulse (sdCSP) equation of both focusing and defocusing types, which can be viewed as an analogue to the Ablowitz–Ladik lattice in the ultrashortpulse regime. By using a generalized Darboux transformation method, various soliton solutions to this newly integrable semidiscrete equation are studied with both zero and nonzero boundary

Sparsity induced by covariance transformation: some deterministic and probabilistic results Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210303
Jakub Rybak, Heather S. BatteyMotivated by statistical challenges arising in modern scientific fields, notably genomics, this paper seeks embeddings in which relevant covariance models are sparse. The work exploits a bijective mapping between a strictly positive definite matrix and its orthonormal eigendecomposition, and between an orthonormal eigenvector matrix and its principle matrix logarithm. This leads to a representation

Multispike solutions of a hybrid reactiontransport model Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210303
P. C. BressloffSimulations of classical patternforming reaction–diffusion systems indicate that they often operate in the strongly nonlinear regime, with the final steady state consisting of a spatially repeating pattern of localized spikes. In activator–inhibitor systems such as the twocomponent Gierer–Meinhardt (GM) model, one can consider the singular limit Da ≪ Dh, where Da and Dh are the diffusivities of the

Statics of fan vaulting: current state of knowledge and open issues Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210224
Katalin BagiFan vaults, the most spectacular structural form of the English Gothic architecture, has been admired by architect lovers for many centuries. The mechanics of fan vaulting raises several interesting questions, most of which are still unanswered, even though the maintenance and restoration of historic buildings would require the deep understanding how these fascinating structures work, how they respond

The cost of quantum locality Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210224
C. A. BdardIt has been more than 20 years since Deutsch and Hayden demonstrated that quantum systems can be completely described locally—notwithstanding Bell’s theorem. More recently, RaymondRobichaud proposed two other approaches to the same conclusion. In this paper, all these means of describing quantum systems locally are proved formally equivalent. The cost of such descriptions is then quantified by the

Rods coiling about a rigid constraint: helices and perversions Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210224
D. Riccobelli, G. Noselli, A. DeSimoneMechanical instabilities can be exploited to design innovative structures, able to change their shape in the presence of external stimuli. In this work, we derive a mathematical model of an elastic beam subjected to an axial force and constrained to smoothly slide along a rigid support, where the distance between the rod midline and the constraint is fixed and finite. Using both theoretical and computational

Prandtls extended mixing length model applied to the twodimensional turbulent classical far wake Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210224
Ashleigh J. Hutchinson, Nicholas Hale, Kendall Born, David P. MasonDespite its limitations, Prandtl’s mixing length model is widely applied in modelling turbulent free shear flows. Prandtl’s extended model addresses many of the shortfalls of the original model, but is not so widely used, in part due to additional mathematical complexities that arise in its derivation and implementation. Furthermore, in both models, Prandtl neglects the kinematic viscosity on the basis

Exact closedform and asymptotic expressions for the electrostatic force between two conducting spheres Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210224
Shubho Banerjee, Thomas Peters, Nolan Brown, Yi SongWe present exact closedform expressions and complete asymptotic expansions for the electrostatic force between two charged conducting spheres of arbitrary sizes. Using asymptotic expansions of the force, we confirm that even likecharged spheres attract each other at sufficiently small separation unless their voltages/charges are the same as they would be at contact. We show that for sufficiently

Bulky auxeticity, tensile buckling and deckofcards kinematics emerging from structured continua Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210224
S. Palumbo, A. R. Carotenuto, A. Cutolo, D. R. Owen, L. Deseri, M. FraldiComplex mechanical behaviours are generally met in macroscopically homogeneous media as effects of inelastic responses or as results of unconventional material properties, which are postulated or due to structural systems at the meso/microscale. Examples are strain localization due to plasticity or damage and metamaterials exhibiting negative Poisson’s ratios resulting from special porous, eventually

Unsteady Reynoldsaveraged NavierStokes investigation of free surface wave impact on tidal turbine wake Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210224
Zhisong Li, Kirti Ghia, Ye Li, Zhun Fan, Lian ShenTidal current is a promising renewable energy source. Previous studies have investigated the influence of surface waves on tidal turbines in many aspects. However, the turbine wake development in a surface wave environment, which is crucial for power extraction in a turbine array, remains elusive. In this study, we focus on the wake evolution behind a single turbine and its interaction with surface

f distance of knotoids and protein structure Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210217
Agnese barbensi, Dimos GoundaroulisRecent studies classify the topology of proteins by analysing the distribution of their projections using knotoids. The approximation of this distribution depends on the number of projection directions that are sampled. Here, we investigate the relation between knotoids differing only by small perturbations of the direction of projection. Since such knotoids are connected by at most a single forbidden

A delay equation model for the Atlantic Multidecadal Oscillation Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210217
Swinda K. J. Falkena, Courtney Quinn, Jan Sieber, Henk A. DijkstraA new technique to derive delay models from systems of partial differential equations, based on the Mori–Zwanzig (MZ) formalism, is used to derive a delaydifference equation model for the Atlantic Multidecadal Oscillation (AMO). The MZ formalism gives a rewriting of the original system of equations, which contains a memory term. This memory term can be related to a delay term in a resulting delay

Addendum 2020 to Measurement of the Earths rotation: 720 BC to AD 2015 Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210217
L. V. Morrison, F. R. Stephenson, C. Y. Hohenkerk, M. ZawilskiHistorical reports of solar eclipses are added to our previous dataset (Stephenson et al. 2016 Proc. R. Soc. A472, 20160404 (doi:10.1098/rspa.2016.0404)) in order to refine our determination of centennial and longerterm changes since 720 BC in the rate of rotation of the Earth. The revised observed deceleration is −4.59 ± 0.08 × 10−22 rad s−2. By comparison the predicted tidal deceleration based on

Using spectral submanifolds for optimal mode selection in nonlinear model reduction Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210217
Gergely Buza, Shobhit Jain, George HallerModel reduction of large nonlinear systems often involves the projection of the governing equations onto linear subspaces spanned by carefully selected modes. The criteria to select the modes relevant for reduction are usually problemspecific and heuristic. In this work, we propose a rigorous modeselection criterion based on the recent theory of spectral submanifolds (SSMs), which facilitates a reliable

Interaction between surface waves on wire lines Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210217
Daniel Molnar, Tobias Schaich, Anas AlRawi, Mike PayneThis paper investigates coupling between electromagnetic surface waves on parallel wires. Finiteelement method (FEM)based and analytic models are developed for single and doublewire Sommerfeld and Goubau lines. Models are validated via measurements for Goubau lines and a comparison between the analytic and the FEMbased computations for coupled Sommerfeld and Goubautype lines is carried out.

Rogue waves of ultrahigh peak amplitude: a mechanism for reaching up to a thousand times the background level Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210217
WenRong Sun, Lei Liu, P. G. KevrekidisWe unveil a mechanism enabling a fundamental rogue wave, expressed by a rational function of fourth degree, to reach a peak amplitude as high as a thousand times the background level in a system of coupled nonlinear Schrödinger equations involving both incoherent and coherent coupling terms with suitable coefficients. We obtain the exact explicit vector rational solutions using a Darbouxdressing transformation

Construction of exact minimal parking garages: nonlinear helical motifs in optimally packed lamellar structures Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210217
Luiz C. B. da Silva, Efi EfratiMinimal surfaces arise as energy minimizers for fluid membranes and are thus found in a variety of biological systems. The tight lamellar structures of the endoplasmic reticulum and plant thylakoids are comprised of such minimal surfaces in which right and lefthanded helical motifs are embedded in stoichiometry suggesting global pitch balance. So far, the analytical treatment of helical motifs in

Fractional power series and the method of dominant balances Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210217
C. J. Chapman, H. P. WynnThis paper derives an explicit formula for a type of fractional power series, known as a Puiseux series, arising in a wide class of applied problems in the physical sciences and engineering. Detailed consideration is given to the gaps which occur in these series (lacunae); they are shown to be determined by a numbertheoretic argument involving the greatest common divisor of a set of exponents appearing

Generalized tessellations of superellipitcal voids in low porosity architected materials for stress mitigation Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210217
Jiazhen Leng, Hang Xu, Megan Schaenzer, Minh Quan Pham, Genevieve Bourgeois, Ali Shanian, Damiano PasiniStress concentration is a crucial source of mechanical failure in structural elements, especially those embedding voids. This paper examines periodic porous materials with porosity lower than 5%. We investigate their stress distribution under planar multiaxial loading, and presents a family of geometrically optimized void shapes for stress mitigation. We adopt a generalized description for both void

Fay meets van der Pauw: the trisecant identity and the resistivity of holey samples Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210217
Hiroyuki Miyoshi, Darren G. Crowdy, Rhodri NelsonThe van der Pauw method is commonly used in the applied sciences to find the resistivity of a simply connected, twodimensional conducting laminate. Given the usefulness of this ‘4point probe’ method there has been much recent interest in trying to extend it to holey, that is, multiply connected, samples. This paper introduces two new mathematical tools to this area of investigation—the prime function

Everettian relative states in the Heisenberg picture Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210217
Samuel Kuypers, David DeutschEverett's relativestate construction in quantum theory has never been satisfactorily expressed in the Heisenberg picture. What one might have expected to be a straightforward process was impeded by conceptual and technical problems that we solve here. The result is a construction which, unlike Everett's one in the Schrödinger picture, makes manifest the locality of Everettian multiplicity, its inherently

Onset of energy equipartition among surface and body waves Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210210
L. Borcea, J. Garnier, K. SlnaWe derive a radiative transfer equation that accounts for coupling from surface waves to body waves and the other way around. The model is the acoustic wave equation in a twodimensional waveguide with reflecting boundary. The waveguide has a thin, weakly randomly heterogeneous layer near the top surface, and a thick homogeneous layer beneath it. There are two types of modes that propagate along the

Bridging the gap between rectifying developables and tangent developables: a family of developable surfaces associated with a space curve Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210210
Brian Seguin, Yichao Chen, Eliot FriedThere are two familiar constructions of a developable surface from a space curve. The tangent developable is a ruled surface for which the rulings are tangent to the curve at each point and relative to this surface the absolute value of the geodesic curvature κg of the curve equals the curvature κ. The alternative construction is the rectifying developable. The geodesic curvature of the curve relative

Observation and modelling of solar jets Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210203
Yuandeng ShenThe solar atmosphere is full of complicated transients manifesting the reconfiguration of the solar magnetic field and plasma. Solar jets represent collimated, beamlike plasma ejections; they are ubiquitous in the solar atmosphere and important for our understanding of solar activities at different scales, the magnetic reconnection process, particle acceleration, coronal heating, solar wind acceleration

Shapes of large, static soap bubbles Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210203
Nicholas D. BrubakerStandard predictions induced by the balance of surface tension and pressure dictate that static soap bubbles must be spherical. However, definite nonspherical shapes appear in large bubbles, where noticeable oblate or prolate deformations occur. Gravity is the principal cause of such deformations, and multiple approaches for including its influence appear in recent literature. This paper derives a

Homogenization of an elastic material reinforced by very strong fibres arranged along a periodic lattice Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.741) Pub Date : 20210203
Houssam AbdoulAnziz, Luk Jakabin, Pierre SeppecherWe provide in this paper homogenization results for the L2topology leading to complete straingradient models and generalized continua. Actually, we extend to the L2topology the results obtained in (AbdoulAnziz & Seppecher, 2018 Homogenization of periodic graphbased elastic structures. Journal de l’Ecole polytechnique–Mathématiques5, 259–288) using a topology adapted to minimization problems set