Strong and weak interactions of rational vector rogue waves and solitons to any n -component nonlinear Schrödinger system with higher-order effects

The higher-order effects play an important role in the wave propagations of ultrashort (e.g. subpicosecond or femtosecond) light pulses in optical fibres. In this paper, we investigate any n -component fourth-order nonlinear Schrödinger ( n -FONLS) system with non-zero backgrounds containing the n -Hirota equation and the n -Lakshmanan–Porsezian–Daniel equation. Based on the loop group theory, we find the multi-parameter family of novel rational vector rogue waves (RVRWs) of the n -FONLS equation starting from the plane-wave solutions. Moreover, we exhibit the weak and strong interactions of some representative RVRW structures. In particular, we also find that the W-shaped rational vector dark and bright solitons of the n -FONLS equation as the second- and fourth-order dispersion coefficients satisfy some relation. Furthermore, we find the higher-order RVRWs of the n -FONLS equation. These obtained rational solutions will be useful in the study of RVRW phenomena of multi-component nonlinear wave models in nonlinear optics, deep ocean and Bose–Einstein condensates.

Quantitative mapping of thickness variations along a ray path using geometrical full waveform inversion and guided wave mode conversion

Quantitative guided wave thickness mapping in plate-like structures and pipelines is of significant importance for the petrochemical industry to accurately estimate the minimum remaining wall thickness in the presence of corrosion, as guided waves can inspect a large area without needing direct access. Although a number of inverse algorithms have been studied and implemented in guided wave reconstruction, a primary assumption is widely used: the three-dimensional guided wave inversion of thickness is simplified as a two-dimensional acoustic wave inversion of velocity, with the dispersive nature of the waves linking thickness to velocity. This assumption considerably simplifies the inversion procedure; however, it makes it impossible to account for mode conversion. In reality, mode conversion is quite common in guided wave scattering with asymmetric wall loss, and compared with non-converted guided wave modes, converted modes may provide greater access to valuable information about the thickness variation, which, if exploited, could lead to improved performance. Geometrical full waveform inversion (GFWI) is an ideal tool for this, since it can account for mode conversion. In this paper, quantitative thickness reconstruction based on GFWI is developed in a plate cross-section and applied to study the performance of thickness reconstruction using mode conversion.

Conical Kresling origami and its applications to curvature and energy programming

Kresling origami has recently been widely used to design mechanical metamaterials, soft robots and smart devices, benefiting from its bistability and compression-twist coupling deformation. However, previous studies mostly focus on the traditional parallelogram Kresling patterns which can only be folded to cylindrical configurations. In this paper, we generalize the Kresling patterns by introducing free-form quadrilateral unit cells, leading to diverse conical folded configurations. The conical Kresling origami is modelled with a truss system, by which the stable states and energy landscapes are derived analytically. We find that the generalization preserves the bistable nature of parallelogram Kresling patterns, while enabling an enlarged design space of geometric parameters for structural and mechanical applications. To demonstrate this, we develop inverse design frameworks to employ conical Kresling origami to approximate arbitrary target surfaces of revolution and achieve prescribed energy landscapes. Various numerical examples obtained from our framework are presented, which agree well with the paper models and the finite-element simulations. We envision that the proposed conical Kresling pattern and inverse design framework can provide a new perspective for applications in deployable structures, shape-morphing devices, multi-modal robots and multistable metamaterials.

Constant stress arches and their design space

It is generally accepted that an optimal arch has a funicular (moment-less) form and least weight. However, the feature of least weight restricts the design options and raises the question of durability of such structures. This study, building on the analytical form-finding approach presented in Lewis (2016. Proc. R. Soc. A 472 , 20160019. ( doi:10.1098/rspa.2016.0019 )), proposes constant axial stress as a design criterion for smooth, two-pin arches that are moment-less under permanent (statistically prevalent) load. This approach ensures that no part of the structure becomes over-stressed under variable load (wind, snow and/or moving objects), relative to its other parts—a phenomenon observed in natural structures, such as trees, bones, shells. The theory considers a general case of an asymmetric arch, deriving the equation of its centre-line profile, horizontal reactions and varying cross-section area. The analysis of symmetric arches follows, and includes a solution for structures of least weight by supplying an equation for a volume-minimizing, span/rise ratio. The paper proposes a new concept, that of a design space controlled by two non-dimensional input parameters; their theoretical and practical limits define the existence of constant axial stress arches. It is shown that, for stand-alone arches, the design space reduces to a constraint relationship between constant stress and span/rise ratio.

The microdynamics shaping the relationship between democracy and corruption

Physics has a long tradition of laying rigorous quantitative foundations for social phenomena. Here, we up the ante for physics' forays into the territory of social sciences by (i) empirically documenting a tipping point in the relationship between democratic norms and corruption suppression, and then (ii) demonstrating how such a tipping point emerges from a micro-scale mechanistic model of spin dynamics in a complex network. Specifically, the tipping point in the relationship between democratic norms and corruption suppression is such that democratization has little effect on suppressing corruption below a critical threshold, but a large effect above the threshold. The micro-scale model of spin dynamics underpins this phenomenon by reinterpreting spins in terms of unbiased (i.e. altruistic) and biased (i.e. parochial) other-regarding behaviour, as well as the corresponding voting preferences. Under weak democratic norms, dense social connections of parochialists enable coercing enough opportunist voters to vote in favour of perpetuating parochial in-group bias. Society may, however, strengthen democratic norms in a rapid turn of events during which opportunists adopt altruism and vote to subdue bias. The emerging model outcome at the societal scale thus mirrors the data, implying that democracy either perpetuates or suppresses corruption depending on the prevailing democratic norms.

Modelling of stress transfer in root-reinforced soils informed by four-dimensional X-ray computed tomography and digital volume correlation data

Vegetation enhances soil shearing resistance through water uptake and root reinforcement. Analytical models for soils reinforced with roots rely on input parameters that are difficult to measure, leading to widely varying predictions of behaviour. The opaque heterogeneous nature of rooted soils results in complex soil–root interaction mechanisms that cannot easily be quantified. The authors measured, for the first time, the shear resistance and deformations of fallow, willow-rooted and gorse-rooted soils during direct shear using X-ray computed tomography and digital volume correlation. Both species caused an increase in shear zone thickness, both initially and as shear progressed. Shear zone thickness peaked at up to 35 mm, often close to the thickest roots and towards the centre of the column. Root extension during shear was 10–30% less than the tri-linear root profile assumed in a Waldron-type model, owing to root curvature. Root analogues used to explore the root–soil interface behaviour suggested that root lateral branches play an important role in anchoring the roots. The Waldron-type model was modified to incorporate non-uniform shear zone thickness and growth, and accurately predicted the observed, up to sevenfold, increase in shear resistance of root-reinforced soil.

Effects of an impermeable layer on pore pressure response to tsunami-like inundation

Tsunami hazards have been observed to cause soil instability resulting in substantial damage to coastal infrastructure. Studying this problem is difficult owing to tsunamis’ transient, non-uniform and large loading characteristics. To create realistic tsunami conditions in a laboratory environment, we control the body force using a centrifuge facility. With an apparatus specifically designed to mimic tsunami inundation in a scaled-down model, we examine the effects of an embedded impermeable layer on soil instability: the impermeable layer represents a man-made pavement, a building foundation, a clay layer and alike. The results reveal that the effective vertical soil stress is substantially reduced at the underside of the impermeable layer. During the sudden runup flow, this instability is caused by a combination of temporal dislocation of soil grains and an increase in pore pressure under the impermeable layer. The instability during the drawdown phase is caused by the development of excess pore-pressure gradients, and the presence of the impermeable layer substantially enhances the pressure gradients leading to greater soil instability. The laboratory results demonstrate that the presence of an impermeable layer plays an important role in weakening the soil resistance under tsunami-like rapid runup and drawdown processes.

The generalized Wiener–Hopf equations for the elastic wave motion in angular regions

In this work, we introduce a general method to deduce spectral functional equations in elasticity and thus, the generalized Wiener–Hopf equations (GWHEs), for the wave motion in angular regions filled by arbitrary linear homogeneous media and illuminated by sources localized at infinity. The work extends the methodology used in electromagnetic applications and proposes for the first time a complete theory to get the GWHEs in elasticity. In particular, we introduce a vector differential equation of first-order characterized by a matrix that depends on the medium filling the angular region. The functional equations are easily obtained by a projection of the reciprocal vectors of this matrix on the elastic field present on the faces of the angular region. The application of the boundary conditions to the functional equations yields GWHEs for practical problems. This paper extends and applies the general theory to the challenging canonical problem of elastic scattering in angular regions.

On the force of vertical winds in the upper atmosphere: consequences for small biological particles

For many decades, vertical winds have been observed at high altitudes of the Earth’s atmosphere, in the mesosphere and thermosphere layers. These observations have been used with a simple one-dimensional model to make estimates of possible altitude climbs by biologically sized particles deeper into the thermosphere, in the rare occurrence where such a particle has been propelled to these altitudes. A particle transport mechanism is suggested from the literature on auroral arcs, indicating that an altitude of 120 km could be reached by a nanometre-sized particle, which is higher than the measured 77 km limit on the biosphere. Vertical wind observations in the upper mesophere and lower thermosphere are challenging to make and so we suggest that particles could reach altitudes greater than 120 km, depending on the magnitude of the vertical wind. Applications of the larger vertical winds in the upper atmosphere to astrobiology and climate science are explored.

Wind-driven and buoyancy-driven circulation in the subtropical North Atlantic Ocean

Continuous observations of ocean circulation at 26°N in the subtropical Atlantic Ocean have been made since April 2004 to quantify the strength and variability in the Atlantic Meridional overturning circulation (AMOC), in which warm, upper waters flow northward and colder deep waters below 1100 m depth return southward. The principal components of the AMOC are northward western boundary current transport in the Gulf Stream and Antilles Current, northward surface Ekman transport and southward thermocline recirculation, all of which are generally considered to be part of the wind-driven circulation. Southward flowing deep waters below 1100 m depth are usually considered to represent the buoyancy-driven circulation. We argue that the Gulf Stream is partially wind-driven but also partially buoyancy-driven as it returns upper waters upwelled in the global ocean back to water mass formation regions in the northern Atlantic. Seasonal to interannual variations in the circulation at 26°N are principally wind-driven. Variability in the buoyancy-driven circulation occurred in a sharp reduction in 2009 in the southward flow of Lower North Atlantic Deep Water when its transport decreased by 30% from pre-2009 values. Over the 14-year observational period from 2004 to 2018, the AMOC declined by 2.4 Sv from 18.3 to 15.9 Sv.