Showing papers in "Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences in 2021"
TL;DR: In this paper, an elliptic operator obtained as the superposition of a classical second-order differential operator and a nonlocal operator of fractional type is considered, and the symmetry properties of the solutions are investigated.
Abstract: In this paper, we consider an elliptic operator obtained as the superposition of a classical second-order differential operator and a nonlocal operator of fractional type. Though the methods that we develop are quite general, for concreteness we focus on the case in which the operator takes the form − Δ + ( − Δ)s, with s ∈ (0, 1). We focus here on symmetry properties of the solutions and we prove a radial symmetry result, based on the moving plane method, and a one-dimensional symmetry result, related to a classical conjecture by G.W. Gibbons.
60 citations
TL;DR: By modeling the evaporation and settling of droplets emitted during respiratory releases and using previous measurements of droplet size distributions and SARS-CoV-2 viral load, estimates of the e...
Abstract: By modelling the evaporation and settling of droplets emitted during respiratory releases and using previous measurements of droplet size distributions and SARS-CoV-2 viral load, estimates of the e...
60 citations
TL;DR: The solar atmosphere is full of complicated transients manifesting the reconfiguration of the solar magnetic field and plasma as discussed by the authors, and the solar jets represent collimated, beam-like plasma ejections.
Abstract: The solar atmosphere is full of complicated transients manifesting the reconfiguration of the solar magnetic field and plasma. Solar jets represent collimated, beam-like plasma ejections; they are ...
47 citations
Imperial College London1, University of Cambridge2, University of Surrey3, Engineering and Physical Sciences Research Council4, University of Leeds5, University of Strathclyde6, University of Oxford7, Chartered Institution of Building Services Engineers8, Leeds Beckett University9, Royal School of Mines10
TL;DR: In this article, the authors reviewed knowledge of the transmission of COVID-19 indoors, examined the evidence for mitigating measures, and considered the implications for wintertime with a focus on ventilation.
Abstract: The year 2020 has seen the emergence of a global pandemic as a result of the disease COVID-19. This report reviews knowledge of the transmission of COVID-19 indoors, examines the evidence for mitigating measures, and considers the implications for wintertime with a focus on ventilation.
41 citations
TL;DR: In this paper, the global existence for a class of Keller-Segel models with signal-dependent motility and general logistic term under homogeneous Neumann boundary conditions in a higher-dimensional smoothly bounded domain is studied.
Abstract: This paper deals with the global existence for a class of Keller–Segel model with signal-dependent motility and general logistic term under homogeneous Neumann boundary conditions in a higher-dimensional smoothly bounded domain, which can be written as
It is shown that whenever ρ ∈ ℝ, μ > 0 and
then the considered system possesses a global classical solution for all sufficiently smooth initial data. Furthermore, the solution converges to the equilibrium
as t → ∞ under some extra hypotheses, where ρ+ = max{ρ, 0}.
33 citations
TL;DR: In this article, the existence and concentration of positive solutions for the following class of fractional p-Kirchhoff type problems were studied: where ǫ is a small positive parameter, a and b are positive constants, s ∈ (0, 1) and p ∈(1, ∞) are such that is the fractional k-Laplacian operator, f: ℝ → ∄� is a superlinear continuous function with subcritical growth, and V: ∞ → ∞ is a continuous potential having a local minimum.
Abstract: We study the existence and concentration of positive solutions for the following class of fractional p-Kirchhoff type problems: where ɛ is a small positive parameter, a and b are positive constants, s ∈ (0, 1) and p ∈ (1, ∞) are such that is the fractional p-Laplacian operator, f: ℝ → ℝ is a superlinear continuous function with subcritical growth and V: ℝ3 → ℝ is a continuous potential having a local minimum. We also prove a multiplicity result and relate the number of positive solutions with the topology of the set where the potential V attains its minimum values. Finally, we obtain an existence result when f(u) = uq−1 + γur−1, where γ > 0 is sufficiently small, and the powers q and r satisfy 2p < q < p*s ⩽ r. The main results are obtained by using some appropriate variational arguments.
31 citations
TL;DR: In this paper, the authors study eco-evolutionary dynamics by adopting two paradigma, i.e., the concurrence of ecological and evolutionary processes often arises as an integral part of various biological and social systems.
Abstract: The concurrence of ecological and evolutionary processes often arises as an integral part of various biological and social systems. We here study eco-evolutionary dynamics by adopting two paradigma...
28 citations
TL;DR: Iodine is a critical trace element involved in many diverse and important processes in the Earth system as mentioned in this paper, and the importance of iodine for human health has been known for over a century, with low iodine levels.
Abstract: Iodine 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...
28 citations
TL;DR: The AtanganaBaleanu derivative and the Laguerre polynomial were used in this paper to define a new computational technique for solving fractional differential equations, which is a new technique for fractional equation analysis.
Abstract: The AtanganaBaleanu derivative and the Laguerre polynomial are used in this analysis to define a new computational technique for solving fractional differential equations. To serve this purpose, we...
25 citations
TL;DR: Adami et al. as discussed by the authors considered the mass-critical non-linear Schrodinger equation on non-compact metric graphs and proved that the existence and properties of ground states depend in a crucial way on both the value of the mass and the topological properties of the underlying graph.
Abstract: We consider the mass-critical non-linear Schrodinger equation on non-compact metric graphs. A quite complete description of the structure of the ground states, which correspond to global minimizers of the energy functional under a mass constraint, is provided by Adami, Serra and Tilli in [R. Adami, E. Serra and P. Tilli. Negative energy ground states for the L2-critical NLSE on metric graphs. Comm. Math. Phys. 352 (2017), 387–406.] , where it is proved that existence and properties of ground states depend in a crucial way on both the value of the mass, and the topological properties of the underlying graph. In this paper we address cases when ground states do not exist and show that, under suitable assumptions, constrained local minimizers of the energy do exist. This result paves the way to the existence of stable solutions in the time-dependent equation in cases where the ground state energy level is not achieved.
22 citations
TL;DR: In this paper, the controllability of second-order nonlinear stochastic delay systems driven by the Rosenblatt distributions in finite dimensional spaces is studied and sufficient conditions are established for controllable delay systems using fixed point theory, delayed sine and cosine matrices and delayed Grammian matrices.
Abstract: In this paper, we study the controllability of second-order nonlinear stochastic delay systems driven by the Rosenblatt distributions in finite dimensional spaces. A set of sufficient conditions are established for controllability of nonlinear stochastic delay systems using fixed point theory, delayed sine and cosine matrices and delayed Grammian matrices. Furthermore, controllability results for second-order stochastic delay systems driven by Rosenblatt distributions via the representation of solution by delayed sine and cosine functions are presented. Finally, our theoretical results are illustrated through numerical simulation.
TL;DR: In this paper, an abstract agent-based model of the COVID-19 outbreak that accounts for economic activities is proposed to summarize the trade-off between the health and economic damage associated with voluntary restraint measures.
Abstract: As of July 2020, COVID-19 caused by SARS-COV-2 is spreading worldwide, causing severe economic damage. While minimizing human contact is effective in managing outbreaks, it causes severe economic losses. Strategies to solve this dilemma by considering the interrelation between the spread of the virus and economic activities are urgently needed to mitigate the health and economic damage. Here, we propose an abstract agent-based model of the COVID-19 outbreak that accounts for economic activities. The computational simulation of the model recapitulates the trade-off between the health and economic damage associated with voluntary restraint measures. Based on the simulation results, we discuss how the macroscopic dynamics of infection and economics emerge from individuals' behaviours. We believe our model can serve as a platform for discussing solutions to the above-mentioned dilemma.
TL;DR: In this article, a mathematical epidemiological model named SUIHTER was proposed to solve the COVID-19 pandemic, which is the latest in a long list of pandemics that have affected humankind in the last century.
Abstract: The COVID-19 epidemic is the latest in a long list of pandemics that have affected humankind in the last century. In this paper, we propose a novel mathematical epidemiological model named SUIHTER ...
TL;DR: In this paper, the Gibbs measure was constructed in the range 0 < β 2 < 4π via the variational approach due to Barashkov-Gubinelli (2018) for the hyperbolic stochastic damped sine-Gordon equation (SdSG).
Abstract: In this note, we study the hyperbolic stochastic damped sine-Gordon equation (SdSG), with a parameter β2 > 0, and its associated Gibbs dynamics on the two-dimensional torus. After introducing a suitable renormalization, we first construct the Gibbs measure in the range 0 < β2 < 4π via the variational approach due to Barashkov-Gubinelli (2018). We then prove almost sure global well-posedness and invariance of the Gibbs measure under the hyperbolic SdSG dynamics in the range 0 < β2 < 2π. Our construction of the Gibbs measure also yields almost sure global well-posedness and invariance of the Gibbs measure for the parabolic sine-Gordon model in the range 0 < β2 < 4π.
TL;DR: In this paper, it was shown that viscosity solutions to fully nonlinear elliptic equations with degeneracy of double phase type are locally C1, γ-regular.
Abstract: We prove that viscosity solutions to fully nonlinear elliptic equations with degeneracy of double phase type are locally C1, γ-regular.
TL;DR: In this article, the authors provide incentives to enhance cooperation in a population where this behaviour is infrequent, and thus it is important to optimize the overall spending of the overall budget.
Abstract: Institutions can provide incentives to enhance cooperation in a population where this behaviour is infrequent. This process is costly, and it is thus important to optimize the overall spending. Thi...
TL;DR: In this paper, the authors predict the motion of vessels in extreme sea states by computing complex nonlinear wave-body interactions, hence taxonomies of the wave body interactions. But predicting the motions of vessels is a challenging problem in naval hydrodynamics.
Abstract: Predicting motions of vessels in extreme sea states represents one of the most challenging problems in naval hydrodynamics. It involves computing complex nonlinear wave-body interactions, hence tax...
TL;DR: In this paper, two independent data analysis methodologies were applied to locate stable climate states in an intermediate complexity climate model and analyse their interplay, drawing from the theory of quasi-quasi-analysis.
Abstract: We 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 quasi...
TL;DR: In this article, a generalized higher-order beam equation is proposed to describe the vibrations of a rod by considering Lie symmetry analysis, and it is shown that the model can be expressed as a beam equation.
Abstract: Under investigation in this work is a generalized higher-order beam equation, which is an important physical model and describes the vibrations of a rod. By considering Lie symmetry analysis, and u...
TL;DR: In this article, the leading-order equations governing the unsteady dynamics of large-scale atmospheric motions are derived via a systematic asymptotic approach based on the thin-shell approximation applied to the...
Abstract: The leading-order equations governing the unsteady dynamics of large-scale atmospheric motions are derived, via a systematic asymptotic approach based on the thin-shell approximation applied to the...
Abstract: This review provides a critical, multi-faceted assessment of the practical contribution tidal stream energy can make to the UK and British Channel Islands future energy mix. Evidence is presented t...
TL;DR: In this article, the authors studied a class of one-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter, where the drift term is locally Lipschitz and unbounded in the neighbourhood of the origin.
Abstract: In this paper, we study a class of one-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter . The drift term of the equation is locally Lipschitz and unbounded in the neighbourhood of the origin. We show the existence, uniqueness and positivity of the solutions. The estimates of moments, including the negative power moments, are given. We also develop the implicit Euler scheme, proved that the scheme is positivity preserving and strong convergent, and obtain rate of convergence. Furthermore, by using Lamperti transformation, we show that our results can be applied to stochastic interest rate models such as mean-reverting stochastic volatility model and strongly nonlinear Ait-Sahalia type model.
TL;DR: In this article, a general framework for introducing stochasticity into variational principles through the concep- tation of the variational framework is presented, which is based on the work of the authors of this paper.
Abstract: Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models, we present a general framework for introducing stochasticity into variational principles through the concep...
TL;DR: In this paper, the authors studied the homotopy theory of gauge groups over higher dimensional manifolds with mild restrictions on the structure groups of principal bundles of bundles over closed closed closed $2n$-manifolds, the classification of which was determined by Wall and Freedman.
Abstract: The homotopy theory of gauge groups received considerable attentions in the recent decades, in the theme of which, the works mainly focus on bundles over $4$-dimensional manifolds and vary the structure groups case by case In this work, we study the homotopy theory of gauge groups over higher dimensional manifolds with mild restrictions on the structure groups of principal bundles In particular, we study gauge groups of bundles over $(n-1)$-connected closed $2n$-manifolds, the classification of which was determined by Wall and Freedman We also investigate the gauge groups of the total spaces of sphere bundles based on the classical work of James and Whitehead Furthermore, other types of $2n$-manifolds are also considered In all the cases, we show various homotopy decompositions of gauge groups The methods are of combinations of manifold topology and various techniques in homotopy theory
TL;DR: In this article, superconductivity is analyzed based on the product-like fractal measure approach with fractal dimension α introduced by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal elas...
Abstract: Superconductivity is analysed based on the product-like fractal measure approach with fractal dimension α introduced by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal elas...
TL;DR: In this article, the authors report both theoretically and experimentally on an ultra-broadband sound reduction scheme covering living and working noise spectra, both in terms of both theoretical and experimental results.
Abstract: Ultra-broadband 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 u...
TL;DR: In this paper, epidemiological characteristics of 25 early COVID-19 outbreak countries were studied, which emphasizes on the reproduction of infection and effects of government control measures, based on epidemiological data.
Abstract: We study epidemiological characteristics of 25 early COVID-19 outbreak countries, which emphasizes on the reproduction of infection and effects of government control measures The study is based on
TL;DR: The electric 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 magnetic field control as discussed by the authors.
Abstract: Electric 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 co...
TL;DR: In this article, a general version of Grobman-Hartman's theorem for one-sided and continuous time dynamics is shown to be invertible and a converse result is also true.
Abstract: Let is invertible we prove that a converse result is also true. Furthermore, we get similar results for one-sided and continuous time dynamics. As applications of our results, we study the Hyers–Ulam stability for certain difference equations and we obtain a very general version of the Grobman–Hartman's theorem for nonautonomous dynamics.