Showing papers in "Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences in 2020"
TL;DR: It is concluded that facemask use by the public, when used in combination with physical distancing or periods of lock-down, may provide an acceptable way of managing the COVID-19 pandemic and re-opening economic activity.
Abstract: COVID-19 is characterized by an infectious pre-symptomatic period, when newly infected individuals can unwittingly infect others. We are interested in what benefits facemasks could offer as a non-p...
239 citations
TL;DR: The aim of this paper is to review and analyse the latest available evidence to provide a greater clarity and understanding of the environmental impacts of different liquid biofuels and investigates the key methodological aspects and sources of uncertainty in the LCA ofBiofuels.
Abstract: Biofuels are being promoted as a low-carbon alternative to fossil fuels as they could help to reduce greenhouse gas (GHG) emissions and the related climate change impact from transport. However, there are also concerns that their wider deployment could lead to unintended environmental consequences. Numerous life cycle assessment (LCA) studies have considered the climate change and other environmental impacts of biofuels. However, their findings are often conflicting, with a wide variation in the estimates. Thus, the aim of this paper is to review and analyse the latest available evidence to provide a greater clarity and understanding of the environmental impacts of different liquid biofuels. It is evident from the review that the outcomes of LCA studies are highly situational and dependent on many factors, including the type of feedstock, production routes, data variations and methodological choices. Despite this, the existing evidence suggests that, if no land-use change (LUC) is involved, first-generation biofuels can-on average-have lower GHG emissions than fossil fuels, but the reductions for most feedstocks are insufficient to meet the GHG savings required by the EU Renewable Energy Directive (RED). However, second-generation biofuels have, in general, a greater potential to reduce the emissions, provided there is no LUC. Third-generation biofuels do not represent a feasible option at present state of development as their GHG emissions are higher than those from fossil fuels. As also discussed in the paper, several studies show that reductions in GHG emissions from biofuels are achieved at the expense of other impacts, such as acidification, eutrophication, water footprint and biodiversity loss. The paper also investigates the key methodological aspects and sources of uncertainty in the LCA of biofuels and provides recommendations to address these issues.
183 citations
TL;DR: It is proved that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposedmethod is not achievable by base methods with any (adaptive) learning rates.
Abstract: We propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing a scalable parameter in each layer (layer-wise) and for every neuron (neuron-wise) separately, and then optimizing it using a variant of stochastic gradient descent algorithm. In order to further increase the training speed, an activation slope-based slope recovery term is added in the loss function, which further accelerates convergence, thereby reducing the training cost. On the theoretical side, we prove that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposed method is not achievable by base methods with any (adaptive) learning rates. We further show that the adaptive activation methods accelerate the convergence by implicitly multiplying conditioning matrices to the gradient of the base method without any explicit computation of the conditioning matrix and the matrix-vector product. The different adaptive activation functions are shown to induce different implicit conditioning matrices. Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.
159 citations
TL;DR: This review provides a concise and comprehensive summary of the progress made in the development of VO-FC analytical and computational methods with application to the simulation of complex physical systems.
Abstract: Variable-order fractional operators were conceived and mathematically formalized only in recent years. The possibility of formulating evolutionary governing equations has led to the successful application of these operators to the modelling of complex real-world problems ranging from mechanics, to transport processes, to control theory, to biology. Variable-order fractional calculus (VO-FC) is a relatively less known branch of calculus that offers remarkable opportunities to simulate interdisciplinary processes. Recognizing this untapped potential, the scientific community has been intensively exploring applications of VO-FC to the modelling of engineering and physical systems. This review is intended to serve as a starting point for the reader interested in approaching this fascinating field. We provide a concise and comprehensive summary of the progress made in the development of VO-FC analytical and computational methods with application to the simulation of complex physical systems. More specifically, following a short introduction of the fundamental mathematical concepts, we present the topic of VO-FC from the point of view of practical applications in the context of scientific modelling.
127 citations
TL;DR: This work proposes a shallow neural network-based learning methodology for fluid flow reconstruction that learns an end-to-end mapping between the sensor measurements and the high-dimensional fluid flow field, without any heavy preprocessing on the raw data.
Abstract: In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data. In this work, we propose a shallow neural ...
117 citations
TL;DR: This work develops Sindy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities and demonstrates the ability of this algorithm to learn implicit ordinary and partial differential equations and conservation laws from limited and noisy data.
Abstract: Accurately 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 noise. In this work, we develop SINDy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities. The SINDy-PI framework includes multiple optimization algorithms and a principled approach to model selection. We demonstrate the ability of this algorithm to learn implicit ordinary and partial differential equations and conservation laws from limited and noisy data. In particular, we show that the proposed approach is several orders of magnitude more noise robust than previous approaches, and may be used to identify a class of ODE and PDE dynamics that were previously unattainable with SINDy, including for the double pendulum dynamics and simplified model for the Belousov-Zhabotinsky (BZ) reaction.
99 citations
TL;DR: A review of the progress of smoothed particle hydrodynamics towards high-order converged simulations as a mesh-free Lagrangian method suitable for complex flows with interfaces and multiple phases is presented.
Abstract: This paper presents a review of the progress of smoothed particle hydrodynamics (SPH) towards high-order converged simulations. As a mesh-free 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 method without emphasis on accuracy and convergence. The early method was of weakly compressible form resulting in noisy pressures due to spurious pressure waves. This was effectively removed in the incompressible (divergence-free) form which followed; since then the weakly compressible form has been advanced, reducing pressure noise. Now numerical convergence studies are standard. While the method is computationally demanding on conventional processors, it is well suited to parallel processing on massively parallel computing and graphics processing units. Applications are diverse and encompass wave-structure interaction, geophysical flows due to landslides, nuclear sludge flows, welding, gearbox flows and many others. In the state of the art, convergence is typically between the first- and second-order theoretical limits. Recent advances are improving convergence to fourth order (and higher) and these will also be outlined. This can be necessary to resolve multi-scale aspects of turbulent flow.
83 citations
TL;DR: Based on the Royal Society Inaugural Lecture, recent progress is reviewed and future directions in the fundamentals and applications of multiferroics are proposed, with a focus on initially unanticipated developments outside of the core activity of electric-field control of magnetism.
Abstract: Multiferroic materials, with their combined and coupled magnetism and ferroelectricity, provide a playground for studying new physics and chemistry as well as a platform for the development of novel devices and technologies. Based on my July 2017 Royal Society Inaugural Lecture, I review recent progress and propose future directions in the fundamentals and applications of multiferroics, with a focus on initially unanticipated developments outside of the core activity of electric-field control of magnetism.
80 citations
TL;DR: Recently, it has been found that JT gravity is dual to a matrix model as discussed by the authors, i.e., a random ensemble of quantum random ensembles of quantum objects.
Abstract: Recently, it has been found that Jackiw-Teitelboim (JT) gravity, which is a two-dimensional theory with bulk action −1/2∫d2xgϕ(R+2), is dual to a matrix model, that is, a random ensemble of quantum...
70 citations
TL;DR: For a long time it has been well-known that high-dimensional linear parabolic partial differential equations (PDEs) can be approximated by Monte Carlo methods with a computational effort which grows...
Abstract: For a long time it has been well-known that high-dimensional linear parabolic partial differential equations (PDEs) can be approximated by Monte Carlo methods with a computational effort which grow...
69 citations
TL;DR: In this article, the authors proved congruences on sums involving fourth powers of central q-binomial coefficients, where p⩾5 is a prime and r is a positive integer.
Abstract: We prove some congruences on sums involving fourth powers of central q-binomial coefficients. As a conclusion, we confirm the following supercongruence observed by Long [Pacific J. Math. 249 (2011), 405–418]: where p⩾5 is a prime and r is a positive integer. Our method is similar to but a little different from the WZ method used by Zudilin to prove Ramanujan-type supercongruences.
TL;DR: The current state, developments, and some of the emerging advances in transportation technologies and how these advances in smart roads will prepare the society towards the realization of future smart cities are discussed.
Abstract: Various countries throughout the world have started their efforts in designing and implementing smart cities. China alone has over 300 smart city projects, with strong participation by industries a...
TL;DR: It is shown that the ANN methodology outperforms previous denoising methods, including finite differences and both local and global polynomial regression splines, in the ability to accurately approximate partial derivatives and learn the correct PDE model.
Abstract: We investigate methods for learning partial differential equation (PDE) models from spatio-temporal data under biologically realistic levels and forms of noise. Recent progress in learning PDEs from data have used sparse regression to select candidate terms from a denoised set of data, including approximated partial derivatives. We analyse the performance in using previous methods to denoise data for the task of discovering the governing system of PDEs. We also develop a novel methodology that uses artificial neural networks (ANNs) to denoise data and approximate partial derivatives. We test the methodology on three PDE models for biological transport, i.e. the advection-diffusion, classical Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) and nonlinear Fisher-KPP equations. We show that the ANN methodology outperforms previous denoising methods, including finite differences and both local and global polynomial regression splines, in the ability to accurately approximate partial derivatives and learn the correct PDE model.
TL;DR: In this article, a new generalized uncertainty relation is constructed based on Li-Ostoja-Starzewski fractional gradient operator of order 0 < 1, which is motivated from dimensional r...
Abstract: A new generalized uncertainty relation is constructed based on Li-Ostoja-Starzewski fractional gradient operator of order 0<1 introduced recently in literature which is motivated from dimensional r...
TL;DR: An overview of how network science has been applied to the cognitive sciences is provided, with a specific focus on the two research ‘spirals’ of cognitive sciences related to the representation and processes of the human mind.
Abstract: Modelling the structure of cognitive systems is a central goal of the cognitive sciencesa goal that has greatly benefitted from the application of network science approaches. This paper provides an...
TL;DR: In this article, the authors considered the nonlinear Choquard equation where 0 < μ < N, N ⩾ 3, g(u) is of critical growth due to the Hardy-Littlewood-Sobolev inequality and showed the existence of high energy solution by using a nonlocal version of global compactness lemma.
Abstract: In this paper, we consider the nonlinear Choquard equation where 0 < μ < N, N ⩾ 3, g(u) is of critical growth due to the Hardy–Littlewood–Sobolev inequality and . Firstly, by assuming that the potential V(x) might be sign-changing, we study the existence of Mountain-Pass solution via a nonlocal version of the second concentration- compactness principle. Secondly, under the conditions introduced by Benci and Cerami , we also study the existence of high energy solution by using a nonlocal version of global compactness lemma.
TL;DR: The human social world is orders of magnitude smaller than the authors' highly urbanized world might lead us to suppose, and human social networks have a very distinct fractal structure similar to that observed in other primates.
Abstract: The human social world is orders of magnitude smaller than our highly urbanized world might lead us to suppose. In addition, human social networks have a very distinct fractal structure similar to ...
TL;DR: A unified yield function that is able to represent several classical failure criteria including von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, Bresler–Pister and Willam–Warnke is introduced and used to solve topology optimization problems with local stress constraints.
Abstract: An interesting, yet challenging problem in topology optimization consists of finding the lightest structure that is able to withstand a given set of applied loads without experiencing local material failure. Most studies consider material failure via the von Mises criterion, which is designed for ductile materials. To extend the range of applications to structures made of a variety of different materials, we introduce a unified yield function that is able to represent several classical failure criteria including von Mises, Drucker-Prager, Tresca, Mohr-Coulomb, Bresler-Pister and Willam-Warnke, and use it to solve topology optimization problems with local stress constraints. The unified yield function not only represents the classical criteria, but also provides a smooth representation of the Tresca and the Mohr-Coulomb criteria-an attribute that is desired when using gradient-based optimization algorithms. The present framework has been built so that it can be extended to failure criteria other than the ones addressed in this investigation. We present numerical examples to illustrate how the unified yield function can be used to obtain different designs, under prescribed loading or design-dependent loading (e.g. self-weight), depending on the chosen failure criterion.
TL;DR: A universal perspective of the known acoustic micromanipulation technologies in terms of their applications and governing physics is provided and these manipulation methods are surveyed with regards to passive and active manipulation of agents.
Abstract: Acoustic actuation techniques offer a promising tool for contactless manipulation of both synthetic and biological micro/nano agents that encompass different length scales. The traditional usage of sound waves has steadily progressed from mid-air manipulation of salt grains to sophisticated techniques that employ nanoparticle flow in microfluidic networks. State-of-the-art in microfabrication and instrumentation have further expanded the outreach of these actuation techniques to autonomous propulsion of micro-agents. In this review article, we provide a universal perspective of the known acoustic micromanipulation technologies in terms of their applications and governing physics. Hereby, we survey these technologies and classify them with regards to passive and active manipulation of agents. These manipulation methods account for both intelligent devices adept at dexterous non-contact handling of micro-agents, and acoustically induced mechanisms for self-propulsion of micro-robots. Moreover, owing to the clinical compliance of ultrasound, we provide future considerations of acoustic manipulation techniques to be fruitfully employed in biological applications that range from label-free drug testing to minimally invasive clinical interventions.
TL;DR: Progress towards achieving a quantitative understanding of the exchanges of water between Earth's main water reservoirs is reviewed with emphasis on advances accrued from the latest advances in Earth Observation from space.
Abstract: Progress towards achieving a quantitative understanding of the exchanges of water between Earth's main water reservoirs is reviewed with emphasis on advances accrued from the latest advances in Earth Observation from space. These exchanges of water between the reservoirs are a result of processes that are at the core of important physical Earth-system feedbacks, which fundamentally control the response of Earth's climate to the greenhouse gas forcing it is now experiencing, and are therefore vital to understanding the future evolution of Earth's climate. The changing nature of global mean sea level (GMSL) is the context for discussion of these exchanges. Different sources of satellite observations that are used to quantify ice mass loss and water storage over continents, how water can be tracked to its source using water isotope information and how the waters in different reservoirs influence the fluxes of water between reservoirs are described. The profound influence of Earth's hydrological cycle, including human influences on it, on the rate of GMSL rise is emphasized. The many intricate ways water cycle processes influence water exchanges between reservoirs and thus sea-level rise, including disproportionate influences by the tiniest water reservoirs, are emphasized.
TL;DR: A generalized elastodynamic theory, based on fractional-order operators, capable of modelling the propagation of elastic waves in non-local attenuating solids and across complex non- local interfaces and of Snell's Law of refraction and of the corresponding Fresnel’s coefficients is presented.
Abstract: This study presents a generalized elastodynamic theory, based on fractional-order operators, capable of modelling the propagation of elastic waves in non-local attenuating solids and across complex
TL;DR: The critical SPSED is hypothesized to be a material property and sufficient to predict the fatigue life, and the lognormal mean lives at each strain range are in good agreement with the experimental evidence.
Abstract: In the present work, we postulate that a critical value of the stored plastic strain energy density (SPSED) is associated with fatigue failure in metals and is independent of the applied load. Unlike the classical approach of estimating the (homogenized) SPSED as the cumulative area enclosed within the macroscopic stress-strain hysteresis loops, we use crystal plasticity finite element simulations to compute the (local) SPSED at each material point within polycrystalline aggregates of a nickel-based superalloy. A Bayesian inference method is used to calibrate the critical SPSED, which is subsequently used to predict fatigue lives at nine different strain ranges, including strain ratios of 0.05 and -1, using nine statistically equivalent microstructures. For each strain range, the predicted lives from all simulated microstructures follow a lognormal distribution. Moreover, for a given strain ratio, the predicted scatter is seen to be increasing with decreasing strain amplitude; this is indicative of the scatter observed in the fatigue experiments. Finally, the lognormal mean lives at each strain range are in good agreement with the experimental evidence. Since the critical SPSED captures the experimental data with reasonable accuracy across various loading regimes, it is hypothesized to be a material property and sufficient to predict the fatigue life.
TL;DR: The key result of this report is that, for some classes of Hamiltonian matrix structure, coherent delocalization is not easily defeated by energy disorder, even when the electronic coupling is small compared to disorder.
Abstract: The primary questions motivating this report are: Are there ways to increase coherence and delocalization of excitation among many molecules at moderate electronic coupling strength? Coherent delocalization of excitation in disordered molecular systems is studied using numerical calculations. The results are relevant to molecular excitons, polaritons, and make connections to classical phase oscillator synchronization. In particular, it is hypothesized that it is not only the magnitude of electronic coupling relative to the standard deviation of energetic disorder that decides the limits of coherence, but that the structure of the Hamiltonian-connections between sites (or molecules) made by electronic coupling-is a significant design parameter. Inspired by synchronization phenomena in analogous systems of phase oscillators, some properties of graphs that define the structure of different Hamiltonian matrices are explored. The report focuses on eigenvalues and ensemble density matrices of various structured, random matrices. Some reasons for the special delocalization properties and robustness of polaritons in the single-excitation subspace (the star graph) are discussed. The key result of this report is that, for some classes of Hamiltonian matrix structure, coherent delocalization is not easily defeated by energy disorder, even when the electronic coupling is small compared to disorder.
TL;DR: By means of the Jacobi structure associated with a contact structure, this article used the so-called evolution vector field to propose a new characterization of isolated thermodynamic systems with friction.
Abstract: By means of the Jacobi structure associated with a contact structure, we use the so-called evolution vector field to propose a new characterization of isolated thermodynamical systems with friction...
TL;DR: The problem of convection in a fluid-saturated porous medium is reviewed with a focus on ‘vigorous’ convective flow, when the driving buoyancy forces are large relative to any dissipative forces in the system.
Abstract: The problem of convection in a fluid-saturated porous medium is reviewed with a focus on 'vigorous' convective flow, when the driving buoyancy forces are large relative to any dissipative forces in the system This limit of strong convection is applicable in numerous settings in geophysics and beyond, including geothermal circulation, thermohaline mixing in the subsurface and heat transport through the lithosphere Its manifestations range from 'black smoker' chimneys at mid-ocean ridges to salt-desert patterns to astrological plumes, and it has received a great deal of recent attention because of its important role in the long-term stability of geologically sequestered CO2 In this review, the basic mathematical framework for convection in porous media governed by Darcy's Law is outlined, and its validity and limitations discussed The main focus of the review is split between 'two-sided' and 'one-sided' systems: the former mimics the classical Rayleigh-Benard set-up of a cell heated from below and cooled from above, allowing for detailed examination of convective dynamics and fluxes; the latter involves convection from one boundary only, which evolves in time through a series of regimes Both set-ups are reviewed, accounting for theoretical, numerical and experimental studies in each case, and studies that incorporate additional physical effects are discussed Future research in this area and various associated modelling challenges are also discussed
TL;DR: A new model of incipient surge motion for glaciers underlain by sediments is developed to explore how surges may arise from slip instabilities within a thin layer of saturated, deforming subglacial till.
Abstract: Glacier surges are quasi-periodic episodes of rapid ice flow that arise from increases in slip rate at the icebed interface. The mechanisms that trigger and sustain surges are not well understood. ...
Plymouth Marine Laboratory1, University of East Anglia2, University of Bristol3, Bigelow Laboratory For Ocean Sciences4, École Normale Supérieure5, École Polytechnique6, University of Toulouse7, Texas A&M University8, Bjerknes Centre for Climate Research9, University of Malaya10, University of Otago11, National Institute of Water and Atmospheric Research12, Pohang University of Science and Technology13, Laval University14, National Institute of Oceanography, India15
TL;DR: Future ocean observations of trace gases should be routinely accompanied by measurements of two components of the carbonate system to improve the understanding of how in situ carbonate chemistry influences trace gas production, which will lead to improvements in current process model capabilities and more reliable predictions of future global marine trace gas fluxes.
Abstract: Surface ocean biogeochemistry and photochemistry regulate ocean-atmosphere fluxes of trace gases critical for Earth's atmospheric chemistry and climate. The oceanic processes governing these fluxes are often sensitive to the changes in ocean pH (or pCO2) accompanying ocean acidification (OA), with potential for future climate feedbacks. Here, we review current understanding (from observational, experimental and model studies) on the impact of OA on marine sources of key climate-active trace gases, including dimethyl sulfide (DMS), nitrous oxide (N2O), ammonia and halocarbons. We focus on DMS, for which available information is considerably greater than for other trace gases. We highlight OA-sensitive regions such as polar oceans and upwelling systems, and discuss the combined effect of multiple climate stressors (ocean warming and deoxygenation) on trace gas fluxes. To unravel the biological mechanisms responsible for trace gas production, and to detect adaptation, we propose combining process rate measurements of trace gases with longer term experiments using both model organisms in the laboratory and natural planktonic communities in the field. Future ocean observations of trace gases should be routinely accompanied by measurements of two components of the carbonate system to improve our understanding of how in situ carbonate chemistry influences trace gas production. Together, this will lead to improvements in current process model capabilities and more reliable predictions of future global marine trace gas fluxes.
TL;DR: The existence, uniqueness, time-semi-uniform compactness and asymptotically autonomous robustness of pullback random attractors with dispersive and viscosity dissipative terms driven by operator-type noise defined on the entire space was proved in this paper.
Abstract: This paper is concerned with the asymptotic behaviour of solutions to a class of non-autonomous stochastic nonlinear wave equations with dispersive and viscosity dissipative terms driven by operator-type noise defined on the entire space $\\mathbb {R}^n$. The existence, uniqueness, time-semi-uniform compactness and asymptotically autonomous robustness of pullback random attractors are proved in $H^1(\\mathbb {R}^n)\\times H^1(\\mathbb {R}^n)$ when the growth rate of the nonlinearity has a subcritical range, the density of the noise is suitably controllable, and the time-dependent force converges to a time-independent function in some sense. The main difficulty to establish the time-semi-uniform pullback asymptotic compactness of the solutions in $H^1(\\mathbb {R}^n)\\times H^1(\\mathbb {R}^n)$ is caused by the lack of compact Sobolev embeddings on $\\mathbb {R}^n$, as well as the weak dissipativeness of the equations is surmounted at light of the idea of uniform tail-estimates and a spectral decomposition approach. The measurability of random attractors is proved by using an argument which considers two attracting universes developed by Wang and Li (Phys. D 382: 46–57, 2018).
TL;DR: In this work, the most recent publications on microfluidics devices for the detection of viruses are reviewed and approaches such as electrochemical analyses, field-effect transistors and resistive pulse sensors are considered.
Abstract: Extensive testing of populations against COVID-19 has been suggested as a game-changer quest to control the spread of this contagious disease and to avoid further disruption in our social, healthcare and economical systems. Nonetheless, testing millions of people for a new virus brings about quite a few challenges. The development of effective tests for the new coronavirus has become a worldwide task that relies on recent discoveries and lessons learned from past outbreaks. In this work, we review the most recent publications on microfluidics devices for the detection of viruses. The topics of discussion include different detection approaches, methods of signalling and fabrication techniques. Besides the miniaturization of traditional benchtop detection assays, approaches such as electrochemical analyses, field-effect transistors and resistive pulse sensors are considered. For emergency fabrication of quick test kits, the local capabilities must be evaluated, and the joint work of universities, industries, and governments seems to be an unequivocal necessity.
TL;DR: The elastic correspondence can offer an insightful tool for a broad class of problems; as an illustration, it is shown how the presence or absence of an elastic limit determines the fate of a elastic thread during capillary instability.
Abstract: Soft materials that are subjected to large deformations exhibit an extremely rich phenomenology, with properties lying in between those of simple fluids and those of elastic solids. In the continuu...