In this article, we show that significant deviations from the classical quasi-steady 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 quasi-steady

Targeted 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

The 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 spanwise-periodic steady modulation and a decoupled temporally periodic but spatially homogeneous perturbation. As the consequence of the spanwise inlet forcing, the so-called rivulets grow downstream and eventually reach a

In weakly nonlinear systems, the main effect of cubic nonlinearity on wave propagation is an amplitude-dependent 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

We derive explicit formulae to quantify the Markov chain state-space compression, or lumping, that can be achieved in a broad range of dynamical processes on real-world networks, including models of epidemics and voting behaviour, by exploiting redundancies due to symmetries. These formulae are applied in a large-scale study of such symmetry-induced lumping in real-world networks, from which we identify

The Clifford hierarchy is a nested sequence of sets of quantum gates critical to achieving fault-tolerant quantum computation. Diagonal gates of the Clifford hierarchy and ‘nearly diagonal’ semi-Clifford 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 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

Unilateral 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 non-axisymmetric adhesive contact are presented for short- and long-range adhesion, respectively, and the JKR–DMT transition is established in the framework of the generalized Maugis–Dugdale

In this paper, we aim to investigate the influence of delay on the global attractivity of a tick population dynamics model incorporating two distinctive time-varying 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 delay-dependent criterion

The optimal design is studied for a type of one-dimensional dissipative metamaterial to achieve broadband wave attenuation at low-frequency ranges. The complex dispersion analysis is made on a super-cell consisting of multiple mass-in-mass unit cells. An optimization algorithm based on the sequential quadratic programming method is used to design the wave suppression of target frequencies by coupling

Achromatic focusing systems for hard X-rays 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

We detail an experimental method to electrocharge N95 facepiece respirators and face masks (FMs) made from a variety of fabrics (including non-woven 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

Dance 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

Circle 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

Partial 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 so-called ‘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

We study the phenomenon of revivals for the linear Schrödinger and Airy equations over a finite interval, by considering several types of non-periodic 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

Stochastic 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

Elastic 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 two-dimensional hexagonal

The 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

Feedback-evolving 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

The 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 single-particle states at the conduction and valence band edges. Following the separation of variables, we decouple the corresponding energy eigenvalue system of the first-order

An important task in combating the current Covid-19 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 case-control studies, the effect on incidence growth/decline in a specific time frame

In this work, we demonstrate that three-dimensional chiral mechanical metamaterials are able to self-twist 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

First strain-gradient 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 strain-gradient. 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

As the complexity and heterogeneity of a system grows, the challenge of specifying, documenting and synthesizing correct, machine-readable 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

Nonlocally related systems, obtained through conservation law and symmetry-based methods, have proved to be useful for determining nonlocal symmetries, nonlocal conservation laws, non-invertible mappings and new exact solutions of a given partial differential equation (PDE) system. In this paper, it is shown that the symmetry-based method is a differential invariant-based method. It is shown that this

In 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

Motivated by applications of soft-contact 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

Plastic 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, cross-slip or a combination of these mechanisms. At elevated temperatures, atomic diffusivity becomes appreciable, so that dislocations

We 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.

Nanofluids are suspensions of nanoparticles in a base heat-transfer 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 water-based nanofluids available in the literature. The influences of particle concentration, particle size, temperature and surfactants

Model order reduction of geometrically nonlinear dynamic structures is often achieved via a static condensation procedure, whereby high-frequency modes are assumed to be quasi-statically 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

The peridynamic theory reformulates the equations of continuum mechanics in terms of integro-differential equations instead of partial differential equations. In this paper, we consider the construction of artificial boundary conditions (ABCs) for semi-discretized peridynamics using Green functions. Especially, the Green functions that represent the response to the single wave source are used to construct

In this paper, we continue our investigations giving the characterization of weights for two-weight 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

A 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 finite-element discretization for it, which we use to explore the formation of peakons. Our simulations using this discretization reveal that peakons

A 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 transcendental-function expressions which occur in series expansions of the dispersion function can, remarkably, be simplified to low-order polynomials exactly, with explicit coefficients which we

We investigate the application of the line-graph operator to one-dimensional 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

Möbius strips are prototypical examples of ribbon-like 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 three-dimensional shapes of Möbius strips are surprisingly non-existent in the literature. We propose two novel stereo vision-based techniques

In this paper, statistical emulation is shown to be an essential tool for the end-to-end 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

We 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 one-dimensional 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

Using 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’.

Glassy 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

Theoretical studies indicating the presence of long-lived 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 long-lived electron spin coherence is unlikely in a multinuclear

In 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 one-dimensional optimal system for TFNSE in Riemann–Liouville sense are obtained. Then, based on the admitted symmetries and optimal system, we reduce these equations to one-dimensional equations or (1 + 1)-dimensional

Recent research has shown an association between monthly law enforcement drug seizure events and accidental drug overdose deaths using cross-sectional data in a single state, whereby increased seizures correlated with more deaths. In this study, we conduct statistical analysis of street-level data on law enforcement drug seizures, along with street-level data on fatal and non-fatal overdose events

In conventional industrial computed tomography, the source–detector system rotates in equiangular steps in-plane 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

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-potentials, 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

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 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

We revisit the arguments underlying two well-known arrival-time 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

We 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 local-realistic model for quantum theory.

Many 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

We 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

We 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 (Yeoh-type elastic skeleton, and saturating fluid). In this case, the linear dispersive waves governed by Biot’s theory are either of compression or shear-wave type, and

Self-similar fractals are widely obtained from biomaterials within the human musculoskeletal system, and their viscoelastic behaviours can be described by fractional-order derivatives. However, existing viscoelastic models neglect the internal correlation between the fractal structure of biomaterials and their fractional-order temporal responses. We further expanded the fractal hyper-cell (FHC) viscoelasticity

Motivated by the increased interest in modelling non-dissipative materials by constitutive relations more general than those from Cauchy elasticity, we initiate the study of a class of stretch-limited 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 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 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

This 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 three-dimensional 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

In 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 texture-induced reorganizations, still, is in a position

We propose a dynamical model for state symmetrization of two identical particles produced in spacelike-separated events by independent sources. We adopt the hypothesis that the pair of non-interacting particles can initially be described by a tensor product state since they are in principle distinguishable due to their spacelike separation. As the particles approach each other, a quantum jump takes

We classify integrable Hamiltonian equations of the form ut=∂x(δHδu),H=∫h(u,w) dxdy, where the Hamiltonian density h(u, w) is a function of two variables: dependent variable u and the non-locality w=∂x−1∂yu. Based on the method of hydrodynamic reductions, the integrability conditions are derived (in the form of an involutive PDE system for the Hamiltonian density h). We show that the generic integrable