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On an integrable multicomponent CamassaHolm system arising from Mbius geometry Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210728
Jing Kang, Xiaochuan Liu, Changzheng QuIn this paper, we mainly study the geometric background, integrability and peaked solutions of a (1+n)component Camassa–Holm (CH) system and some related multicomponent integrable systems. Firstly, we show this system arises from the invariant curve flows in the Möbius geometry and serves as the dual integrable counterpart of a geometrical (1+n)component Korteweg–de Vries system in the sense of

Classification of biHamiltonian pairs extended by isometries Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210728
Maxim V. Pavlov, Pierandrea Vergallo, Raffaele VitoloThe aim of this article is to classify pairs of the firstorder Hamiltonian operators of Dubrovin–Novikov type such that one of them has a nonlocal part defined by an isometry of its leading coefficient. An example of such a biHamiltonian pair was recently found for the constant astigmatism equation. We obtain a classification in the case of two dependent variables, and a significant new example

Deviations from classical droplet evaporation theory Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210721
Joshua Finneran, Colin P. Garner, François NadalIn this article, we show that significant deviations from the classical quasisteady models of droplet evaporation can arise solely due to transient effects in the gas phase. The problem of fully transient evaporation of a single droplet in an infinite atmosphere is solved in a generalized, dimensionless framework with explicitly stated assumptions. The differences between the classical quasisteady

Understanding targeted energy transfer from a symmetry breaking perspective Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210721
Dongxiao Hong, Thomas L. Hill, Simon A. NeildTargeted energy transfer (TET) represents the phenomenon where energy in a primary system is irreversibly transferred to a nonlinear energy sink (NES). This only occurs when the initial energy in the primary system is above a critical level. There is a natural asymmetry in the system due to the desire for the NES to be much smaller than the primary structure it is protecting. This asymmetry is also

Secondary instability in thin film flows under an inclined plane: growth of lenses on spatially developing rivulets Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210721
Pier Giuseppe Ledda, Franois GallaireThe response of a thin film flowing under an inclined plane, modelled using the lubrication equation, is studied. The flow at the inlet is perturbed by the superimposition of a spanwiseperiodic steady modulation and a decoupled temporally periodic but spatially homogeneous perturbation. As the consequence of the spanwise inlet forcing, the socalled rivulets grow downstream and eventually reach a

Wavenumberspace band clipping in nonlinear periodic structures Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210721
Weijian Jiao, Stefano GonellaIn weakly nonlinear systems, the main effect of cubic nonlinearity on wave propagation is an amplitudedependent correction of the dispersion relation. This phenomenon can manifest either as a frequency shift or as a wavenumber shift depending on whether the excitation is prescribed as an initial condition or as a boundary condition, respectively. Several models have been proposed to capture the frequency

Dimensionreduction of dynamics on realworld networks with symmetry Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210721
Jonathan A. WardWe derive explicit formulae to quantify the Markov chain statespace compression, or lumping, that can be achieved in a broad range of dynamical processes on realworld networks, including models of epidemics and voting behaviour, by exploiting redundancies due to symmetries. These formulae are applied in a largescale study of such symmetryinduced lumping in realworld networks, from which we identify

Efficient quantum gate teleportation in higher dimensions Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210721
Nadish de SilvaThe Clifford hierarchy is a nested sequence of sets of quantum gates critical to achieving faulttolerant quantum computation. Diagonal gates of the Clifford hierarchy and ‘nearly diagonal’ semiClifford gates are particularly important: they admit efficient gate teleportation protocols that implement these gates with fewer ancillary quantum resources such as magic states. Despite the practical importance

Electric field control of magnetism Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210714
Ramamoorthy Ramesh, Sasikanth ManipatruniElectric field control of magnetism is an extremely exciting area of research, from both a fundamental science and an applications perspective and has the potential to revolutionize the world of computing. To realize this will require numerous further innovations, both in the fundamental science arena as well as translating these scientific discoveries into real applications. Thus, this article will

Indentation mapping of stretched adhesive membranes Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210714
Ivan I. ArgatovUnilateral adhesive contact between a rigid indenter and a uniformly stretched membrane of arbitrary shape is considered. The generalized Johnson–Kendall–Roberts (JKR)type and Derjaguin– Muller–Toporov (DMT)type models of nonaxisymmetric adhesive contact are presented for short and longrange adhesion, respectively, and the JKR–DMT transition is established in the framework of the generalized Maugis–Dugdale

Delaydependent attractivity on a tick population dynamics model incorporating two distinctive timevarying delays Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210714
Chuangxia Huang, Jian Zhang, Jinde CaoIn this paper, we aim to investigate the influence of delay on the global attractivity of a tick population dynamics model incorporating two distinctive timevarying delays. By exploiting some differential inequality techniques and with the aid of the fluctuation lemma, we first prove the persistence and positiveness for all solutions of the addressed equation. Consequently, a delaydependent criterion

Optimization of a type of elastic metamaterial for broadband wave suppression Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210714
Kun Wu, Haiyan Hu, Lifeng WangThe optimal design is studied for a type of onedimensional dissipative metamaterial to achieve broadband wave attenuation at lowfrequency ranges. The complex dispersion analysis is made on a supercell consisting of multiple massinmass unit cells. An optimization algorithm based on the sequential quadratic programming method is used to design the wave suppression of target frequencies by coupling

Highresolution achromatic Xray optical systems for broadband imaging and for focusing attosecond pulses Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210714
H. N. Chapman, S. BajtAchromatic focusing systems for hard Xrays are examined which consist of a refractive lens paired with a diffractive lens. Compared with previous analyses, we take into account the behaviour of thick refractive lenses, such as compound refractive lenses and waveguide gradient index refractive lenses, in which both the focal length and the position of the principal planes vary with wavelength. Achromatic

Electrocharging face masks with corona discharge treatment Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210714
M. M. Bandi, N. Ishizu, H.B. KangWe detail an experimental method to electrocharge N95 facepiece respirators and face masks (FMs) made from a variety of fabrics (including nonwoven polymer and knitted cloth) using corona discharge treatment (CDT). We present practical designs to construct a CDT system from commonly available parts and detail calibrations performed on different fabrics to study their electrocharging characteristics

An extensive review of computational dance automation techniques and applications Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210707
Manish Joshi, Sangeeta ChakrabartyDance is an art and when technology meets this kind of art, it is a novel attempt in itself. Many researchers have attempted to automate several aspects of dance, right from dance notation to choreography; from dance capturing to dance generation. We define and illustrate the concept of ‘Dance Automation’ in this paper. Furthermore, we have encountered several applications of dance automation like

Creation of discontinuities in circle maps Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210707
G. Derks, P. A. Glendinning, A. C. SkeldonCircle maps frequently arise in mathematical models of physical or biological systems. Motivated by Cherry flows and ‘threshold’ systems such as integrate and fire neuronal models, models of cardiac arrhythmias, and models of sleep/wake regulation, we consider how structural transitions in circle maps occur. In particular, we describe how maps evolve near the creation of a discontinuity. We show that

Bits and pieces: understanding information decomposition from partwhole relationships and formal logic Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210707
A. J. Gutknecht, M. Wibral, A. MakkehPartial information decomposition (PID) seeks to decompose the multivariate mutual information that a set of source variables contains about a target variable into basic pieces, the socalled ‘atoms of information’. Each atom describes a distinct way in which the sources may contain information about the target. For instance, some information may be contained uniquely in a particular source, some information

Beyond periodic revivals for linear dispersive PDEs Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210707
Lyonell Boulton, George Farmakis, Beatrice PelloniWe study the phenomenon of revivals for the linear Schrödinger and Airy equations over a finite interval, by considering several types of nonperiodic boundary conditions. In contrast to the case of the linear Schrödinger equation examined recently (which we develop further), we prove that, remarkably, the Airy equation does not generally exhibit revivals even for boundary conditions very close to

Improved estimations of stochastic chemical kinetics by finitestate expansion Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210707
Tabea Waizmann, Luca Bortolussi, Andrea Vandin, Mirco TribastoneStochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed

The eigenbuckling analysis of hexagonal lattices: closedform solutions Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210707
S. AdhikariElastic instability such as the buckling of cellular materials plays a pivotal role in their analysis and design. Despite extensive research, the quantifi cation of critical stresses leading to elastic instabi lities remains challenging due to the inherent nonlinearities. We develop an analytical approach considering the spectral decomposition of the elasticity matrix of twodimensional hexagonal

Nearly constant Q dissipative models and wave equations for general viscoelastic anisotropy Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210707
Qi Hao, Stewart GreenhalghThe quality factor (Q) links seismic wave energy dissipation to physical properties of the Earth’s interior, such as temperature, stress and composition. Frequency independence of Q, also called constant Q for brevity, is a common assumption in practice for seismic Q inversions. Although exactly and nearly constant Q dissipative models are proposed in the literature, it is inconvenient to obtain constant

Imitation and aspiration dynamics bring different evolutionary outcomes in feedbackevolving games Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210707
Md. Rajib Arefin, Jun TanimotoFeedbackevolving games characterize the interplay between the evolution of strategies and environments. Rich dynamics have been derived for such games under the premise of the replicator equation, which unveils persistent oscillations between cooperation and defection. Besides replicator dynamics, here we have employed aspiration dynamics, in which individuals, instead of comparing payoffs with opposite

Semiclassical approach for excitonic spectrum of Coulomb coupling between two Dirac particles Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210707
Victor V. Zalipaev, Vladislav V. KuidinThe properties of the energy spectrum of excitons in monolayer transition metal dichalcogenides are investigated using a multiband model. In the multiband model, we use the excitonic Hamiltonian in the product base of the Dirac singleparticle states at the conduction and valence band edges. Following the separation of variables, we decouple the corresponding energy eigenvalue system of the firstorder

Quantifying the preventive effect of wearing face masks Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210707
Tom BrittonAn important task in combating the current Covid19 pandemic lies in estimating the effect of different preventive measures. Here, we focus on the preventive effect of enforcing the use of face masks. Several publications study this effect, however, often using different measures such as: the relative attack rate in casecontrol studies, the effect on incidence growth/decline in a specific time frame

Selfrotating 3D chiral mechanical metamaterials Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210707
K. K. Dudek, A. Drzewiski, M. KadicIn this work, we demonstrate that threedimensional chiral mechanical metamaterials are able to selftwist and control their global rotation. We also discuss the possibility of adjusting the extent of the global rotation manifested by the system in a programmable manner. In addition, we show that the effect of the global rotation can be observed both for small systems composed of a single structural

Classification of first straingradient elasticity tensors by symmetry planes Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210707
Hung Le Quang, QiChang He, Nicolas AuffrayFirst straingradient elasticity is a generalized continuum theory capable of modelling size effects in materials. This extended capability comes from the inclusion in the mechanical energy density of terms related to the straingradient. In its linear formulation, the constitutive law is defined by three elasticity tensors whose orders range from four to six. In the present contribution, the symmetry

Operads for complex system design specification, analysis and synthesis Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210623
John D. Foley, Spencer Breiner, Eswaran Subrahmanian, John M. DuselAs the complexity and heterogeneity of a system grows, the challenge of specifying, documenting and synthesizing correct, machinereadable designs increases dramatically. Separation of the system into manageable parts is needed to support analysis at various levels of granularity so that the system is maintainable and adaptable over its life cycle. In this paper, we argue that operads provide an effective

Differential invariant method for seeking nonlocally related systems and nonlocal symmetries. I: General theory and examples Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210623
George W. Bluman, Rafael de la Rosa, Mara Santos Bruzn, Mara Luz GandariasNonlocally related systems, obtained through conservation law and symmetrybased methods, have proved to be useful for determining nonlocal symmetries, nonlocal conservation laws, noninvertible mappings and new exact solutions of a given partial differential equation (PDE) system. In this paper, it is shown that the symmetrybased method is a differential invariantbased method. It is shown that this

Differential invariant method for seeking nonlocally related systems and nonlocal symmetries. II: Connections with the conservation law method Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210623
George W. Bluman, Rafael de la Rosa, Mara Santos Bruzn, Mara Luz GandariasIn this paper, we show direct connections between the conservation law (CL)based method and the differential invariant (DI)based method for obtaining nonlocally related systems and nonlocal symmetries for a given partial differential equation (PDE) system. For a PDE system with two independent variables, we show that the CL method is a special case for the DI method. For a PDE system with at least

Buckling between soft walls: sequential stabilization through contact Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210623
Zhenkui Wang, Gert H. M. van der HeijdenMotivated by applications of softcontact problems such as guidewires used in medical and engineering applications, we consider a compressed rod deforming between two parallel elastic walls. Free elastica buckling modes other than the first are known to be unstable. We find the soft constraining walls to have the effect of sequentially stabilizing higher modes in multiple contacts by a series of bifurcations

Dislocation dynamics modelling of the creep behaviour of particlestrengthened materials Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210616
F. X. liu, A. C. F Cocks, E. TarletonPlastic deformation in crystalline materials occurs through dislocation slip and strengthening is achieved with obstacles that hinder the motion of dislocations. At relatively low temperatures, dislocations bypass the particles by Orowan looping, particle shearing, crossslip or a combination of these mechanisms. At elevated temperatures, atomic diffusivity becomes appreciable, so that dislocations

Fractionally integrated Bessel process Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210616
Georgiy Shevchenko, Dmytro ZatulaWe consider a fractionally integrated Bessel process defined by Ysδ,H=∫0∞(uH−(1/2)−(u−s)+H−(1/2))dXuδ, where Xδ is the Bessel process of dimension δ > 2. We discuss the relation of this process to the fractional Brownian motion at its maximum, study the basic properties of the process and prove its Hölder continuity.

Statistical analysis of thermal conductivity experimentally measured in waterbased nanofluids Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210616
J. Tielke, M. Maas, M. Castillo, K. Rezwan, M. AvilaNanofluids are suspensions of nanoparticles in a base heattransfer liquid. They have been widely investigated to boost heat transfer since they were proposed in the 1990s. We present a statistical correlation analysis of experimentally measured thermal conductivity of waterbased nanofluids available in the literature. The influences of particle concentration, particle size, temperature and surfactants

Detecting internal resonances during model reduction Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210616
Evangelia Nicolaidou, Thomas L. Hill, Simon A. NeildModel order reduction of geometrically nonlinear dynamic structures is often achieved via a static condensation procedure, whereby highfrequency modes are assumed to be quasistatically coupled to a small set of lower frequency modes, which form the reduction basis. This approach is mathematically justifiable for structures characterized by slow/fast dynamics, such as thin plates and slender beams

Accurate artificial boundary conditions for semidiscretized onedimensional peridynamics Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210616
Songsong Ji, Gang Pang, Jiwei Zhang, Yibo Yang, Paris PerdikarisThe peridynamic theory reformulates the equations of continuum mechanics in terms of integrodifferential equations instead of partial differential equations. In this paper, we consider the construction of artificial boundary conditions (ABCs) for semidiscretized peridynamics using Green functions. Especially, the Green functions that represent the response to the single wave source are used to construct

Hardy inequalities on metric measure spaces, II: the case p>q Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210609
Michael Ruzhansky, Daulti VermaIn this paper, we continue our investigations giving the characterization of weights for twoweight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the inequalities are given in the integral form in the spirit of Hardy’s original inequality. This is a continuation of our paper (Ruzhansky & Verma

Perspectives on the formation of peakons in the stochastic CamassaHolm equation Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210609
Thomas M. Bendall, Colin J. Cotter, Darryl D. HolmA famous feature of the Camassa–Holm equation is its admission of peaked soliton solutions known as peakons. We investigate this equation under the influence of stochastic transport. Noting that peakons are weak solutions of the equation, we present a finiteelement discretization for it, which we use to explore the formation of peakons. Our simulations using this discretization reveal that peakons

A Wronskian method for elastic waves propagating along a tube Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210609
C. J. Chapman, S. V. SorokinA technique involving the higher Wronskians of a differential equation is presented for analysing the dispersion relation in a class of wave propagation problems. The technique shows that the complicated transcendentalfunction expressions which occur in series expansions of the dispersion function can, remarkably, be simplified to loworder polynomials exactly, with explicit coefficients which we

Dynamics of onedimensional spin models under the linegraph operator Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210609
Marco Alberto Javarone, Josh A. OConnorWe investigate the application of the linegraph operator to onedimensional spin models with periodic boundary conditions. The spins (or interactions) in the original spin structure become the interactions (or spins) in the resulting spin structure. We identify conditions which ensure that each new spin structure is stable, that is, its spin configuration minimizes its internal energy. Then, making

More views of a onesided surface: mechanical models and stereo vision techniques for Mbius strips Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210609
Arun Kumar, Poornakanta Handral, Darshan Bhandari, Ramsharan RangarajanMöbius strips are prototypical examples of ribbonlike structures. Inspecting their shapes and features provides useful insights into the rich mechanics of elastic ribbons. Despite their ubiquity and ease of construction, quantitative experimental measurements of the threedimensional shapes of Möbius strips are surprisingly nonexistent in the literature. We propose two novel stereo visionbased techniques

Probabilistic quantification of tsunami current hazard using statistical emulation Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210609
Devaraj Gopinathan, Mohammad Heidarzadeh, Serge GuillasIn this paper, statistical emulation is shown to be an essential tool for the endtoend physical and numerical modelling of local tsunami impact, i.e. from the earthquake source to tsunami velocities and heights. In order to surmount the prohibitive computational cost of running a large number of simulations, the emulator, constructed using 300 training simulations from a validated tsunami code, yields

Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210609
Matthew J. Simpson, Alexander P. Browning, Christopher Drovandi, Elliot J. Carr, Oliver J. Maclaren, Ruth E. BakerWe compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered onedimensional material, where each layer has a distinct particle hopping rate. Particles are released at some location, and the duration of time taken for each particle to reach an absorbing

Asperity level characterization of abrasive wear using atomic force microscopy Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210609
Jack Walker, Jamal Umer, Mahdi Mohammadpour, Stephanos Theodossiades, Stephen R. Bewsher, Guenter Offner, Hemant Bansal, Michael Leighton, Michael Braunstingl, HeinzGeorg FleschUsing an atomic force microscope, a nanoscale wear characterization method has been applied to a commercial steel substrate AISI 52100, a common bearing material. Two wear mechanisms were observed by the presented method: atom attrition and elastoplastic ploughing. It is shown that not only friction can be used to classify the difference between these two mechanisms, but also the ‘degree of wear’.

Diffusion of strontium implanted in glassy carbon Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210609
Johan B. Malherbe, Opeyemi S. Odutemowo, Chris C. Theron, Elke WendlerGlassy carbon has properties making it attractive as a containment material for radioactive waste. In this study, the diffusivity of the radiological important fission product, strontium, is measured. Two hundred kiloelectronvolt strontium ions were implanted at room temperature. The implanted samples were either annealed isochronally for 1 h up to 900°C or by increasing the temperature linearly up

The avian compass can be sensitive even without sustained electron spin coherence Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210609
Rakshit Jain, Vishvendra S. Poonia, Kasturi Saha, Dipankar Saha, Swaroop GangulyTheoretical studies indicating the presence of longlived coherence in the radical pair system have engendered questions about its utilitarian role in the avian compass. In this paper, we investigate the role of electron spin coherence in a multinuclear radical pair system including its impact on compass sensitivity. We find that sustenance of longlived electron spin coherence is unlikely in a multinuclear

Invariant analysis, exact solutions and conservation laws of (2+1)dimensional time fractional NavierStokes equations Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210602
Xiaoyu Cheng, Lizhen WangIn this paper, we investigate the exact solutions and conservation laws of (2 + 1)dimensional time fractional Navier–Stokes equations (TFNSE). Specifically, Lie symmetries and corresponding onedimensional optimal system for TFNSE in Riemann–Liouville sense are obtained. Then, based on the admitted symmetries and optimal system, we reduce these equations to onedimensional equations or (1 + 1)dimensional

A modified twoprocess Knox test for investigating the relationship between law enforcement opioid seizures and overdoses Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210602
G. Mohler, S. Mishra, B. Ray, L. Magee, P. Huynh, M. Canada, D. ODonnell, S. FlaxmanRecent research has shown an association between monthly law enforcement drug seizure events and accidental drug overdose deaths using crosssectional data in a single state, whereby increased seizures correlated with more deaths. In this study, we conduct statistical analysis of streetlevel data on law enforcement drug seizures, along with streetlevel data on fatal and nonfatal overdose events

Selection and evaluation of spherical acquisition trajectories for industrial computed tomography Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210602
Fabian Bauer, Matthias Goldammer, Christian U. GrosseIn conventional industrial computed tomography, the source–detector system rotates in equiangular steps inplane relative to the part of investigation. While being by far the most frequently used acquisition trajectory today, this method has several drawbacks like the formation of cone beam artefacts or limited usability in case of geometrical restrictions. In such cases, the usage of alternative spherical

Dynamical landscape and multistability of a climate model Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210602
Georgios Margazoglou, Tobias Grafke, Alessandro Laio, Valerio LucariniWe apply two independent data analysis methodologies to locate stable climate states in an intermediate complexity climate model and analyse their interplay. First, drawing from the theory of quasipotentials, and viewing the state space as an energy landscape with valleys and mountain ridges, we infer the relative likelihood of the identified multistable climate states and investigate the most likely

On the propagation of waves in the atmosphere Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210602
Adrian Constantin, Robin S. JohnsonThe leadingorder equations governing the unsteady dynamics of largescale atmospheric motions are derived, via a systematic asymptotic approach based on the thinshell approximation applied to the ellipsoidal model of the Earth’s geoid. We present some solutions of this single set of equations that capture properties of specific atmospheric flows, using field data to choose models for the heat sources

Times of arrival and gauge invariance Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210602
Siddhant Das, Markus NthWe revisit the arguments underlying two wellknown arrivaltime distributions in quantum mechanics, viz., the Aharonov–Bohm–Kijowski (ABK) distribution, applicable for freely moving particles, and the quantum flux (QF) distribution. An inconsistency in the original axiomatic derivation of Kijowski’s result is pointed out, along with an inescapable consequence of the ‘negative arrival times’ inherent

A localrealistic model for quantum theory Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210602
Paul RaymondRobichaudWe provide a rigorous definition of local realism. We show that the universal wave function cannot be a complete description of a local reality. Finally, we construct a localrealistic model for quantum theory.

Nonlinear stochastic modelling with Langevin regression Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210602
J. L. Callaham, J.C. Loiseau, G. Rigas, S. L. BruntonMany physical systems characterized by nonlinear multiscale interactions can be modelled by treating unresolved degrees of freedom as random fluctuations. However, even when the microscopic governing equations and qualitative macroscopic behaviour are known, it is often difficult to derive a stochastic model that is consistent with observations. This is especially true for systems such as turbulence

The reflection of a blast wave by a very intense explosion Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210602
Andrew W. Cook, Joseph D. Bauer, Gregory D. SpriggsWe demonstrate that the geometric similarity of Taylor’s blast wave persists beyond reflection from an ideal surface. Upon impacting the surface, the spherical symmetry of the blast wave is lost but its cylindrical symmetry endures. As the flow acquires dependence on a second spatial dimension, an analytic solution of the Euler equations becomes elusive. However, the preservation of axisymmetry, geometric

Nonlinear plane waves in saturated porous media with incompressible constituents Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210602
Harold BerjaminWe consider the propagation of nonlinear plane waves in porous media within the framework of the Biot–Coussy biphasic mixture theory. The tortuosity effect is included in the model, and both constituents are assumed incompressible (Yeohtype elastic skeleton, and saturating fluid). In this case, the linear dispersive waves governed by Biot’s theory are either of compression or shearwave type, and

Fractionalorder viscoelastic model of musculoskeletal tissues: correlation with fractals Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210526
Jianqiao Guo, Yajun Yin, Gang PengSelfsimilar fractals are widely obtained from biomaterials within the human musculoskeletal system, and their viscoelastic behaviours can be described by fractionalorder derivatives. However, existing viscoelastic models neglect the internal correlation between the fractal structure of biomaterials and their fractionalorder temporal responses. We further expanded the fractal hypercell (FHC) viscoelasticity

On stretchlimited elastic strings Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210526
Casey RodriguezMotivated by the increased interest in modelling nondissipative materials by constitutive relations more general than those from Cauchy elasticity, we initiate the study of a class of stretchlimited elastic strings: the string cannot be compressed smaller than a certain length less than its natural length nor elongated larger than a certain length greater than its natural length. In particular, we

Superconductivity and nucleation from fractal anisotropy and productlike fractal measure Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210526
Rami Ahmad ElNabulsiSuperconductivity is analysed based on the productlike fractal measure approach with fractal dimension α introduced by Li and OstojaStarzewski in their attempt to explore anisotropic fractal elastic media. Our study shows the emergence of a massless state at the boundary of the superconductor and the simultaneous occurrence of isothermal and adiabatic processes in the superconductor depending on

A novel modelling and simulation approach for the hindered mobility of charged particles in biological hydrogels Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210526
Maximilian J. Grill, Jonas F. Eichinger, Jonas Koban, Christoph Meier, Oliver Lieleg, Wolfgang A. WallThis article presents a novel computational model to study the selective filtering of biological hydrogels due to the surface charge and size of diffusing particles. It is the first model that includes the random threedimensional fibre orientation and connectivity of the biopolymer network and that accounts for elastic deformations of the fibres by means of beam theory. As a key component of the model

Another perspective on elastic and plastic anisotropy of textured metals Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 2.704) Pub Date : 20210526
Aleksander ZubelewiczIn textured metals, the elastic directionality reflects the crystallographic organization, while the plastic flow follows the preferential pathways of deformation beyond the elastic limit. In here, the elastic and plastic anisotropies are characterized by two observers. One of them is immersed into the material and, while there, is unaware of the textureinduced reorganizations, still, is in a position