Based on the direct linearization framework of the discrete Kadomtsev–Petviashvili-type equations presented in the work of Fu & Nijhoff (Fu W, Nijhoff FW. 2017 Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations. Proc. R. Soc. A473, 20160915 (doi:10.1098/rspa.2016.0915)), six novel non-autonomous differential-difference equations are

The storage of granular materials is a critical process in industry, which has driven research into flow in silos. Varying material properties, such as particle size, can cause segregation of mixtures. This work seeks to elucidate the effects of size differences and determine how using a flow-correcting insert mitigates segregation during silo discharge. A rotating table was used to collect mustard

We study a prototypical system describing instability effects due to geometric constraints in the framework of nonlinear elasticity. By considering the equilibrium configurations of an elastic ring constrained inside a rigid circle with smaller radius, we analytically determine different possible shapes, reproducing well-known physical phenomena. As we show, both single- (with different complexity)

Arteries are exposed to relentless pulsatile haemodynamic loads, but via mechanical homeostasis they tend to maintain near optimal structure, properties and function over long periods in maturity in health. Numerous insults can compromise such homeostatic tendencies, however, resulting in maladaptations or disease. Chronic inflammation can be counted among the detrimental insults experienced by arteries

The pressure-driven growth model has been employed to study a propagating foam front in the foam-improved oil recovery process. A first-order solution of the model proves the existence of a concave corner on the front, which initially migrates downwards at a well defined speed that differs from the speed of front material points. At later times, however, it remains unclear how the concave corner moves

In this investigation, the non-reciprocal transmission in a nonlinear elastic metamaterial with imperfect interfaces is studied. Based on the Bloch theorem and stiffness matrix method, the band gaps and transmission coefficients with imperfect interfaces are obtained for the fundamental and double frequency cases. The interfacial influences on the transmission behaviour are discussed for both the nonlinear

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 evolution of the liquid mass and the number of viral copies suspended were performed as a function of time from the release. The settling times of a droplet cloud and its suspended viral dose are significantly

The next generations of wireless networks will work in frequency bands ranging from sub-6 GHz up to 100 GHz. Radio signal propagation differs here in several critical aspects from the behaviour in the microwave frequencies currently used. With wavelengths in the millimetre range (mmWave), both penetration loss and free-space path loss increase, while specular reflection will dominate over diffraction

Cities are complex systems whose characteristics impact the health of people who live in them. Nonetheless, urban determinants of health often vary within spatial scales smaller than the resolution of epidemiological datasets. Thus, as cities expand and their inequalities grow, the development of theoretical frameworks that explain health at the neighbourhood level is becoming increasingly critical

We study the interaction of in-plane elastic waves with imperfect interfaces composed of a periodic array of voids or cracks. An effective model is derived from high-order asymptotic analysis based on two-scale homogenization and matched asymptotic technique. In two-dimensional elasticity, we obtain jump conditions set on the in-plane displacements and normal stresses; the jumps involve in addition

Quantifying corrosion damage is vital for the petrochemical industry, and guided wave tomography can provide thickness maps of such regions by transmitting guided waves through these areas and capturing the scattering information using arrays. The dispersive nature of the guided waves enables a reconstruction of wave velocity to be converted into thickness. However, existing approaches have been shown

In this paper, we study the N-periodic wave solutions of coupled Korteweg–de Vries (KdV)–Toda-type equations. We present a numerical process to calculate the N-periodic waves based on the direct method of calculating periodic wave solutions proposed by Akira Nakamura. Particularly, in the case of N = 3, we give some detailed examples to show the N-periodic wave solutions to the coupled Ramani equation

A central tool of nonlinear anelasticity is the multiplicative decomposition of the deformation tensor that assumes that the deformation gradient can be decomposed as a product of an elastic and an anelastic tensor. It is usually justified by the existence of an intermediate configuration. Yet, this configuration cannot exist in Euclidean space, in general, and the mathematical basis for this assumption

Dynamical PDEs that have a spatial divergence form possess conservation laws that involve an arbitrary function of time. In one spatial dimension, such conservation laws are shown to describe the presence of an x-independent source/sink; in two and more spatial dimensions, they are shown to produce a topological charge. Two applications are demonstrated. First, a topological charge gives rise to an

In this paper, we derive fully implementable first-order time-stepping schemes for McKean–Vlasov stochastic differential equations, allowing for a drift term with super-linear growth in the state component. We propose Milstein schemes for a time-discretized interacting particle system associated with the McKean–Vlasov equation and prove strong convergence of order 1 and moment stability, taming the

We propose a new approach for the solution of initial value problems for integrable evolution equations in the periodic setting based on the unified transform. Using the nonlinear Schrödinger equation as a model example, we show that the solution of the initial value problem on the circle can be expressed in terms of the solution of a Riemann–Hilbert problem whose formulation involves quantities which

Gradient-based optimization is used to reliably and optimally induce ignition in three examples of laminar non-premixed mixture configurations. Using time-integrated heat release as a cost functional, the non-convex optimization problem identified optimal energy source locations that coincide with the stoichiometric local mixture fraction surface for short optimization horizons, while for longer horizons

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

The moon illusion is a visual deception when people perceive the angular diameter of the Moon/Sun near the horizon larger than that of the one higher in the sky. Some theories have been proposed to explain this illusion, but not any is generally accepted. Although several psychophysical experiments have been performed to study different aspects of the moon illusion, their results have sometimes contradicted

This paper is dedicated to Michael J. Duff on the occasion of his 70th birthday. I discuss some issues of M-theory/string theory/supergravity closely related to Mike’s interests. I describe a relation between STU black hole entropy, the Cayley hyperdeterminant, the Bhargava cube and a three-qubit Alice–Bob–Charlie triality symmetry. I shortly describe my recent work with Gunaydin, Linde and Yamada

Wave fields obeying the two-dimensional Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied. Such surfaces appear naturally as a result of applying the reflection method to diffraction problems with straight scatterers bearing ideal boundary conditions. This is for example the case for the classical canonical problems of diffraction by a half-line or a segment. In the present

Pillai & Meng (Pillai & Meng 2016 Ann. Stat.44, 2089–2097; p. 2091) speculated that ‘the dependence among [random variables, rvs] can be overwhelmed by the heaviness of their marginal tails ·· ·’. We give examples of statistical models that support this speculation. While under natural conditions the sample correlation of regularly varying (RV) rvs converges to a generally random limit, this limit

The proposed theory defines a relative index of epidemic lethality that compares any two configurations in different observation periods, preferably one in the acute and the other in a mild epidemic phase. Raw mortality data represent the input, with no need to recognize the cause of death. Data are categorized according to the victims’ age, which must be renormalized because older people have a greater

We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions. All systems are nudged towards the common centre of mass. We derive Kramers–Kronig relations and sum rules for the linear susceptibilities obtained through mean field Fokker–Planck equations and then propose

We use synchrotron X-ray micro-tomography to investigate the displacement dynamics during three-phase—oil, water and gas—flow in a hydrophobic porous medium. We observe a distinct gas invasion pattern, where gas progresses through the pore space in the form of disconnected clusters mediated by double and multiple displacement events. Gas advances in a process we name three-phase Haines jumps, during

Spontaneous violations of the Clausius–Duhem (CD) inequality in Couette-type collisional flows of model granular media are studied. Planar systems of monosized circular discs (with disc numbers from 10 to 204, and disc diameters from 0.001 m to 1 m) with frictional-Hookean contacts are simulated under periodic boundary conditions by a molecular dynamics. The scale-dependent homogenization of micropolar

The quasi-harmonic model proposes that a crystal can be modelled as atoms connected by springs. We demonstrate how this viewpoint can be misleading: a simple application of Gauss’s law shows that the ion–ion potential for a cubic Coulomb system can have no diagonal harmonic contribution and so cannot necessarily be modelled by springs. We investigate the repercussions of this observation by examining

The problem of capillary transport in fibrous porous materials at low levels of liquid saturation has been addressed. It has been demonstrated that the process of liquid spreading in this type of porous material at low saturation can be described macroscopically by a similar super-fast, nonlinear diffusion model to that which had been previously identified in experiments and simulations in particulate

We revisit the classical problem of diffusion of a scalar (or heat) released in a two-dimensional medium with an embedded periodic array of impermeable obstacles such as perforations. Homogenization theory provides a coarse-grained description of the scalar at large times and predicts that it diffuses with a certain effective diffusivity, so the concentration is approximately Gaussian. We improve on

The next-generation wireless communications require reduced energy consumption, increased data rates and better signal coverage. The millimetre-wave frequency spectrum above 30 GHz can help fulfil the performance requirements of the next-generation mobile broadband systems. Multiple-input multiple-output technology can provide performance gains to help mitigate the increased path loss experienced at

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 systems rather than a specific quantum mechanical system. In this article, we argue that a deformation of JT gravity with bulk action −1/2∫d2xg(ϕR+W(ϕ)) is likewise dual to a matrix model. With a specific

The pressure-driven growth model that describes the two-dimensional (2-D) propagation of a foam through an oil reservoir is considered as a model for surfactant-alternating-gas improved oil recovery. The model assumes a region of low mobility, finely textured foam at the foam front where injected gas meets liquid. The net pressure driving the foam is assumed to reduce suddenly at a specific time. Parts

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 polynomially both in the dimension and in the reciprocal of the prescribed accuracy. In other words, linear PDEs do not suffer from the curse of dimensionality. For general semilinear PDEs with Lipschitz

We deduce the Born rule from a purely statistical take on quantum theory within minimalistic math-setup. No use is required of quantum postulates. One exploits only rudimentary quantum mathematics—a linear, not Hilbert’, vector space—and empirical notion of the Statistical Length of a state. Its statistical nature comes from the lab micro-events (detector-clicks) being formalized into the C-coefficients

In this work, the concept of high-frequency homogenization is extended to the case of one-dimensional periodic media with imperfect interfaces of the spring-mass type. In other words, when considering the propagation of elastic waves in such media, displacement and stress discontinuities are allowed across the borders of the periodic cell. As is customary in high-frequency homogenization, the homogenization

How can we manipulate the topological connectivity of a three-dimensional prismatic assembly to control the number of internal degrees of freedom and the number of connected components in it? To answer this question in a deterministic setting, we use ideas from elementary number theory to provide a hierarchical deterministic protocol for the control of rigidity and connectivity. We then show that it

We present analytical expressions for the resonance frequencies of the plasmonic modes hosted in a cylindrical nanoparticle within the quasi-static approximation. Our theoretical model gives us access to both the longitudinally and transversally polarized dipolar modes for a metallic cylinder with an arbitrary aspect ratio, which allows us to capture the physics of both plasmonic nanodisks and nanowires

In this work, we adopt a new approach to the construction of a global theory of algebras of generalized functions on manifolds based on the concept of smoothing operators. This produces a generalization of previous theories in a form which is suitable for applications to differential geometry. The generalized Lie derivative is introduced and shown to extend the Lie derivative of Schwartz distributions

This paper builds on the theory of nonlinear generalized functions begun in Nigsch & Vickers (Nigsch, Vickers 2021 Proc. R. Soc. A 20200640 (doi:10.1098/rspa.2020.0640)) and extends this to a diffeomorphism-invariant nonlinear theory of generalized tensor fields with the sheaf property. The generalized Lie derivative is introduced and shown to commute with the embedding of distributional tensor fields

Several biological materials are fibre networks infused with fluid, often referred to as fibrous gels. An important feature of these gels is that the fibres buckle under compression, causing a densification of the network that is accompanied by a reduction in volume and release of fluid. Displacement-controlled compression of fibrous gels has shown that the network can exist in a rarefied and a densified

In this paper, we develop a conceptually unified approach for characterizing and determining scattering poles and interior eigenvalues for a given scattering problem. Our approach explores a duality stemming from interchanging the roles of incident and scattered fields in our analysis. Both sets are related to the kernel of the relative scattering operator mapping incident fields to scattered fields

The presence of macropores and fractures significantly affects the effective transport properties of porous solids such as concrete and rocks. The dimensions of the fractures are generally large behind that of the initial porosity, so that the problem contains two porosities. The influence of the macroporosity is studied in the homogenization framework by solving at the intermediate scale, that of

A study of dynamics of a waveboard is presented. The equations of motion are derived and analysed to understand the intriguing propulsion mechanism. A reduced order model is obtained, and the contributions of different terms are clearly brought out. The geometry of the castor wheels is found to play a key role in the conversion of the twisting oscillatory motion of the rider to the forward translational

In this study, asymptotic analysis of the frequency-domain formulation to compute the tonal noise of the small rotors in the now ubiquitously multi-rotor powered drones is conducted. Simple scaling laws are proposed to evaluate the impacts of the influential parameters such as blade number, flow speed, rotation speed, unsteady motion, thrust and observer angle on the tonal noise. The rate of noise

It is demonstrated that acoustic transmission through a phononic crystal with anisotropic solid scatterers becomes non-reciprocal if the background fluid is viscous. In an ideal (inviscid) fluid, the transmission along the direction of broken P symmetry is asymmetric. This asymmetry is compatible with reciprocity since time-reversal symmetry (T symmetry) holds. Viscous losses break T symmetry, adding

The paper shows that for the case of an ideal gas in the equilibrium state there exists a method for splitting it into portions with different temperatures without energy transfer to or from the environment and without work being done. Compared with the thought experiment known as ‘Maxwell's demon’, in which such splitting is based on sorting specific molecules according to their energy levels, the

We prove that superdeterministic models of quantum mechanics are conspiratorial in a mathematically well-defined sense, by further development of the ideas presented in a previous article A. We consider a Bell scenario where, in each run and at each wing, the experimenter chooses one of N devices to determine the local measurement setting. We prove, without assuming any features of quantum statistics

Random walks have been proven to be useful for constructing various algorithms to gain information on networks. Algorithm node2vec employs biased random walks to realize embeddings of nodes into low-dimensional spaces, which can then be used for tasks such as multi-label classification and link prediction. The performance of the node2vec algorithm in these applications is considered to depend on properties

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

Social distancing as one of the main non-pharmaceutical interventions can help slow down the spread of diseases, like in the COVID-19 pandemic. Effective social distancing, unless enforced as drastic lockdowns and mandatory cordon sanitaire, requires consistent strict collective adherence. However, it remains unknown what the determinants for the resultant compliance of social distancing and their

Face masks in general, and N95 filtering facepiece respirators (FRs) that protect against SARS-Cov-2 virion in particular, have become scarce during the ongoing COVID-19 global pandemic. This work presents practical design principles for the fabrication of electrocharged filtration layers employed in N95 FRs using commonly available materials and easily replicable methods. The input polymer is polypropylene

Quantitative reconstructions of past climates are an important resource for evaluating how well climate models reproduce climate changes. One widely used statistical approach for making such reconstructions from fossil biotic assemblages is weighted averaging partial least-squares regression (WA-PLS). There is however a known tendency for WA-PLS to yield reconstructions compressed towards the centre

We consider a plane flexural wave incident on a semi-infinite rigid strip in a Mindlin plate. The boundary conditions on the strip lead to three Wiener–Hopf equations, one of which decouples, leaving a scalar problem and a 2 × 2 matrix problem. The latter is solved using a simple method based on quadrature. The far-field diffraction coefficient is calculated and some numerical results are presented

This paper presents an investigation and discussion of the accuracy and applicability of an implicit Taylor (IT) method versus the classical higher-order spectral (HOS) method when used to simulate two-dimensional regular waves. This comparison is relevant, because the HOS method is in fact an explicit perturbation solution of the IT formulation. First, we consider the Dirichlet–Neumann problem of

Double-precision floating-point arithmetic (FP64) has been the de facto standard for engineering and scientific simulations for several decades. Problem complexity and the sheer volume of data coming from various instruments and sensors motivate researchers to mix and match various approaches to optimize compute resources, including different levels of floating-point precision. In recent years, machine

There is a major restriction in the formulation of rigorous lower bound limit analysis by means of the finite-element method. Once the stress field has been discretized, the yield criterion and the equilibrium conditions must be applied at a finite number of points so that they are satisfied everywhere throughout the discretized structure. Until now, only the linear stress elements fulfil this requirement

A classical system of conservation laws descriptive of relativistic gasdynamics is examined. In the two-dimensional stationary case, the system is shown to be invariant under a novel multi-parameter class of reciprocal transformations. The class of invariant transformations originally obtained by Bateman in non-relativistic gasdynamics in connection with lift and drag phenomena is retrieved as a reduction

Semantic edge detection has recently gained a lot of attention as an image-processing task, mainly because of its wide range of real-world applications. This is based on the fact that edges in images contain most of the semantic information. Semantic edge detection involves two tasks, namely pure edge detection and edge classification. Those are in fact fundamentally distinct in terms of the level

This paper presents two approaches to mathematical modelling of a synthetic seismic pulse, and a comparison between them. First, a new analytical model is developed in two-dimensional Cartesian coordinates. Combined with an initial condition of sufficient symmetry, this provides a valuable check for the validity of the numerical method that follows. A particular initial condition is found which allows

This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters