New connections between static elastic cloaking, low-frequency elastic wave scattering and neutral inclusions (NIs) are established in the context of two-dimensional elasticity. A cylindrical core surrounded by a cylindrical shell is embedded in a uniform elastic matrix. Given the core and matrix properties, we answer the questions of how to select the shell material such that (i) it acts as a static

R-symmetry gauged 6D (1, 0) supergravities free from all local anomalies, with gauge groups G × GR where GR is the R-symmetry group and G is semisimple with rank greater than one, and which have no hypermultiplet singlets, are extremely rare. There are three such models known in which the gauge symmetry group is G1 × G2 × U(1)R, where the first two factors are (E6/Z3)×E7, G2 × E7 and F4 × Sp(9). These

The semi-classical Korteweg–de Vries equation for step-like data is considered with a small parameter in front of the highest derivative. Using perturbation analysis, Whitham theory is constructed to the higher order. This allows the order one phase and the complete leading-order solution to be obtained; the results are confirmed by extensive numerical calculations.

The presented research focuses on masonry shells with dry (cohesionless) contacts. In the mechanical analysis of such structures, the material is often assumed to have zero resistance to tension. This simplification can be questioned in light of the fact that due to the frictional resistance between masonry layers compressed to each other, significant tension can be carried perpendicularly to the direction

In this manuscript, we introduce a method to measure entanglement of curves in 3-space that extends the notion of knot and link polynomials to open curves. We define the bracket polynomial of curves in 3-space and show that it has real coefficients and is a continuous function of the curve coordinates. This is used to define the Jones polynomial in a way that it is applicable to both open and closed

We identify a distinct two-phase flow invasion pattern in a mixed-wet porous medium. Time-resolved high-resolution synchrotron X-ray imaging is used to study the invasion of water through a small rock sample filled with oil, characterized by a wide non-uniform distribution of local contact angles both above and below 90°. The water advances in a connected front, but throats are not invaded in decreasing

Magnetic shape memory alloys (MSMAs) have drawn significant research attention as potential high actuation energy multi-functional materials. Such a dissipative material system can be considered as a solid continuum interacting with a magnetic field. A continuum-based phenomenological model provides a magneto-mechanical system of equations that simulates and predicts primary MSMA behaviours. In this

As is well known, the safe travel velocity of high-speed rail must remain below a well-defined limit commonly referred to as the critical speed. This upper bound depends, in turn, on the speed at which waves propagate in the ground. But as models for trains in motion have increased in complexity, over the years the concept of critical speed has grown in obscurity. It was not until late in the twentieth

We investigate the theoretical nonlinear response, Hessian stability, and possible wrinkling behaviour of a voltage-activated dielectric plate immersed in a tank filled with silicone oil. Fixed rigid electrodes are placed on the top and bottom of the tank, and an electric field is generated by a potential difference between the electrodes. We solve the associated incremental boundary value problem

Hyperbolic balance laws with uncertain (random) parameters and inputs are ubiquitous in science and engineering. Quantification of uncertainty in predictions derived from such laws, and reduction of predictive uncertainty via data assimilation, remain an open challenge. That is due to nonlinearity of governing equations, whose solutions are highly non-Gaussian and often discontinuous. To ameliorate

The bounded oscillations of rotating fluid-filled ellipsoids can provide physical insight into the flow dynamics of deformed planetary interiors. The inertial modes, sustained by the Coriolis force, are ubiquitous in rapidly rotating fluids and Vantieghem (2014, Proc. R. Soc. A, 470, 20140093. doi:10.1098/rspa.2014.0093) pioneered a method to compute them in incompressible fluid ellipsoids. Yet, taking

The rise of global value chains (GCVs) has seen the transfer of carbon emissions embodied in every step of international trade. Building a coordinated, inclusive and green GCV can be an effective and efficient way to achieve carbon emissions mitigation targets for countries that participate highly in GCVs. In this paper, we first describe the energy consumption as well as the territorial and consumption-based

Theory and observation suggest that Earth and Earth-like planets can undergo runaway low-latitude glaciation when changes in solar heating or in the carbon cycle exceed a critical threshold. Here, we use a simple dynamical-system representation of the ice–albedo feedback and the carbonate–silicate cycle to show that glaciation is also triggered when solar heating changes faster than a critical rate

Cohen’s first model is a model of Zermelo–Fraenkel set theory in which there is a Dedekind-finite set of real numbers, and it is perhaps the most famous model where the Axiom of Choice fails. We force over this model to add a function from this Dedekind-finite set to some infinite ordinal κ. In the case that we force the function to be injective, it turns out that the resulting model is the same as

An operational definition for the ductility of failure is given. Many examples illustrate the procedure for specific applications. The ductile/brittle transition is an integral part of the formalism. Further applications are made to the solids forming elements in the Periodic Table. The cases of graphene and diamond are used to verify the procedure. Bond bending and bond stretching are shown to provide

Shock response spectrum (SRS) is a widely accepted method for shock testing specification. However, SRS, as a supremum, is over-conservative and cannot fully describe the relative severity for various shock environments. This study introduces shock response matrix, from which shock severity infimum (SSI) can be extracted using singular value decomposition method. Based on SRS and SSI, dual spectra

Plants and photovoltaics share the same purpose as harvesting sunlight. Therefore, botanical studies could lead to new breakthroughs in photovoltaics. However, the basic mechanism of photosynthesis is different to semiconductor-based photovoltaics and the gap between photosynthesis and solar cells must be bridged before we can apply the botanical principles to photovoltaics. In this study, we analysed

We address the teleportation of single- and two-qubit quantum states, parametrized by weight θ and phase ϕ parameters, in the presence of the Unruh effect experienced by a mode of a free Dirac field. We investigate the effects of the partial measurement (PM) and partial measurement reversal (PMR) on the quantum resources and quantum Fisher information (QFI) of the teleported states. In particular,

Vaccinating decisions can be influenced by imitation as well as self-evaluation or aspiration. This work analyses vaccinating behaviours by coupling both imitation and aspiration update rules, adopting an existing set-up of the mean-field vaccination game. We incorporate the imitation mechanism with several variants of the aspiration protocol, encompassing constant and adaptive aspirations. Equations

The Stroh formalism was adapted for Rayleigh-wave propagation guided by the planar traction-free surface of a continuously twisted structurally chiral material (CTSCM), which is an anisotropic solid that is periodically non-homogeneous in the direction normal to the planar surface. Numerical studies reveal that this surface can support either one or two Rayleigh waves at a fixed frequency, depending

Recent experiments show that quasi-one-dimensional lattices of self-propelled droplets exhibit collective instabilities in the form of out-of-phase oscillations and solitary-like waves. This hydrodynamic lattice is driven by the external forcing of a vertically vibrating fluid bath, which invokes a field of subcritical Faraday waves on the bath surface, mediating the spatio-temporal droplet coupling

Every autumn rail networks across the world suffer delays, accidents and schedule changes due to low friction problems caused by leaves landing on the rails. These leaves form a layer that can reduce the friction between the wheel and the rail to a similar level as that between ice and an ice-skate (μ=0.01–0.05). Previous works have generated several hypotheses for the chemical reactions and low friction

Cadmium telluride (CdTe) solar cells are deposited in current production using evaporation-based tech- niques. Fabricating CdTe solar cells using magnetron sputtering would have the advantage of being more cost-efficient. Here, we show that such deposition results in the incorporation of the magnetron working gas Ar, within the films. Post deposition processing with CdCl2 improves cell efficiency and

A non-constructive existence theory for certain operator equationsLu=Du,using the substitution u=B12ξ with B = L−1, is developed, where L is a linear operator (in a suitable Banach space) and D is a homogeneous nonlinear operator such that Dλu = λαD u for all λ ≥ 0 and some α∈R, α ≠ ~1. This theory is based on the positive-operator approach of Krasnosel’skii. The method has the advantage of being able

We obtain solution representation formulae for some linear initial boundary value problems posed on the half space that involve mixed spatial derivative terms via the unified transform method (UTM), also known as the Fokas method. We first implement the method on the second-order parabolic PDEs; in this case one can alternatively eliminate the mixed derivatives by a linear change of variables. Then

We consider the n-component transversely isotropic unidirectional elastic composites, the longitudinal axis of which is parallel to those of the transversely isotropic components as well as the generators of the cylindrical phase boundaries between them. From the minimum energy and complementary energy principles, with appropriate constant strain and piece-wise constant stress trial fields, optimization

Knowledge is a network of interconnected concepts. Yet, precisely how the topological structure of knowledge constrains its acquisition remains unknown, hampering the development of learning enhancement strategies. Here, we study the topological structure of semantic networks reflecting mathematical concepts and their relations in college-level linear algebra texts. We hypothesize that these networks

We present the results of a theoretical investigation of a dynamical system consisting of a particle self-propelling through a resonant interaction with its own quasi-monochromatic pilot-wave field. We rationalize two distinct mechanisms, arising in different regions of parameter space, that may lead to a wavelike statistical signature with the pilot-wavelength. First, resonant speed oscillations with

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

This review presents the current status of experimental evidence for the occurrence of reflection-asymmetric or ‘pear’ shapes in atomic nuclei, which arises from the presence of strong octupole correlations in the nucleon–nucleon interactions. The behaviour of energy levels and electric octupole transition moments is reviewed, with particular emphasis on recent measurements. The relevance of nuclear

A linear stability analysis of a viscous liquid on a vertically oscillating porous plane is performed for infinitesimal disturbances of arbitrary wavenumbers. A time-dependent boundary value problem is derived and solved based on the Floquet theory along with the complex Fourier series expansion. Numerical results show that the Faraday instability is dominated by the subharmonic solution at high forcing

Accurate and efficient aeroelastic models are critically important for enabling the optimization and control of highly flexible aerospace structures, which are expected to become pervasive in future transportation and energy systems. Advanced materials and morphing wing technologies are resulting in next-generation aeroelastic systems that are characterized by highly coupled and nonlinear interactions

Topological insulators are frequently also one of the best-known thermoelectric materials. It has been recently discovered that in three-dimensional (3D) topological insulators each skew dislocation can host a pair of one-dimensional (1D) topological states—a helical Tomonaga–Luttinger liquid (TLL). We derive exact analytical formulae for thermoelectric Seebeck coefficient in TLL and investigate up

An alternative approach for the analysis of flexible structure is presented. Instead of following theories of finite deformation, classical models with infinitesimal strain and engineering stress are assumed as the basis of formulation. A compatible description concept is developed to handle the large geometrical change due to load. Basic concepts are discussed in an accompanied article: ‘Analysis

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

If the vorticity field of an ideal fluid is tangent to a foliation, additional conservation laws arise. For a class of zero-helicity vorticity fields, the Godbillon-Vey (GV) invariant of foliations is defined and is shown to be an invariant purely of the vorticity, becoming a higher-order helicity-type invariant of the flow. GV ≠ 0 gives both a global topological obstruction to steady flow and, in

Slow-roll inflation may simultaneously solve the horizon problem and generate a near scale-free fluctuation spectrum P(k). These two processes are intimately connected via the initiation and duration of the inflationary phase. But a recent study based on the latest Planck release suggests that P(k) has a hard cut-off, kmin≠0, inconsistent with this conventional picture. Here, we demonstrate quantitatively

We present a new method of establishing the finite-dimensionality of limit dynamics (in terms of bi-Lipschitz Mané projectors) for semilinear parabolic systems with cross diffusion terms and illustrate it on the model example of three-dimensional complex Ginzburg-Landau equation with periodic boundary conditions. The method combines the so-called spatial-averaging principle invented by Sell and Mallet–Paret

We present an efficient high-precision numerical approach for Davey–Stewartson (DS) II type equa- tions, treating initial data from the Schwartz class of smooth, rapidly decreasing functions. As with previous approaches, the presented code uses discrete Fourier transforms for the spatial dependence and Driscoll’s composite Runge–Kutta method for the time dependence. Since DS equations are non-local

Landscapes evolve towards surfaces with complex networks of channels and ridges in response to climatic and tectonic forcing. Here, we analyse variational principles giving rise to minimalist models of landscape evolution as a system of partial differential equations that capture the essential dynamics of sediment and water balances. Our results show that in the absence of diffusive soil transport

As humans, we are uniquely competent at incorporating ourselves into groups that scale up from a few members to millions of individuals to engage in joint activities in social circles of varying sizes. Yet, the question of how a group's survival depends on its social structure is not well understood. In an analysis of more than 10 122 real-life online communities (with a total of 134 147 members) hosted

Co-morbidity between medical and psychiatric conditions is commonly considered between individual pairs of conditions. However, an important alternative is to consider all conditions as part of a co-morbidity network, which encompasses all interactions between patients and a healthcare system. Analysis of co-morbidity networks could detect and quantify general tendencies not observed by smaller-scale