Physics

We introduce the "leaking elastic capacitor" (LEC) model, a nonconservative dynamical system that combines simple electrical and mechanical degrees of freedom. We show that an LEC connected to an external voltage source can be destabilized (Hopf bifurcation) due to positive feedback between the mechanical separation of the plates and their electrical charging. Numerical simulation finds regimes in which the LEC exhibits a limit cycle (regular self-oscillation) or strange attractors (chaos). The LEC acts as an autonomous engine, cyclically performing work at the expense of the constant voltage source. We show that this mechanical work can be used to pump current, generating an electromotive force without any time-varying magnetic flux and in a thermodynamically irreversible way. We consider how this mechanism can sustain electromechanical waves propagating along flexible plates. We argue that the LEC model can offer a qualitatively new and more realistic description of important properties of active systems with electrical double layers in condensed-matter physics, chemistry, and biology.

The cavitation of solid elastic spheres is a classical problem of continuum mechanics. Here, we study this problem within the context of "stochastic elasticity" where the constitutive parameters are characterised by probability density functions. We consider homogeneous spheres of stochastic neo-Hookean material, composites with two concentric stochastic neo-Hookean phases, and inhomogeneous spheres of locally neo-Hookean material with a radially varying parameter. In all cases, we show that the material at the centre determines the critical load at which a spherical cavity forms there. However, while under dead-load traction, a supercritical bifurcation, with stable cavitation, is obtained in a static sphere of stochastic neo-Hookean material, for the composite and radially inhomogeneous spheres, a subcritical bifurcation, with snap cavitation, is also possible. For the dynamic spheres, oscillatory motions are produced under suitable dead-load traction, such that a cavity forms and expands to a maximum radius, then collapses again to zero periodically, but not under impulse traction. Under a surface impulse, a subcritical bifurcation is found in a static sphere of stochastic neo-Hookean material and also in an inhomogeneous sphere, whereas in composite spheres, supercritical bifurcations can occur as well. Given the non-deterministic material parameters, the results can be characterised in terms of probability distributions.

Stochastic homogeneous hyperelastic solids are characterised by strain-energy densities where the parameters are random variables defined by probability density functions. These models allow for the propagation of uncertainties from input data to output quantities of interest. To investigate the effect of probabilistic parameters on predicted mechanical responses, we study radial oscillations of cylindrical and spherical shells of stochastic incompressible isotropic hyperelastic material, formulated as quasi-equilibrated motions where the system is in equilibrium at every time instant. Additionally, we study finite shear oscillations of a cuboid, which are not quasi-equilibrated. We find that, for hyperelastic bodies of stochastic neo-Hookean or Mooney-Rivlin material, the amplitude and period of the oscillations follow probability distributions that can be characterised. Further, for cylindrical tubes and spherical shells, when an impulse surface traction is applied, there is a parameter interval where the oscillatory and non-oscillatory motions compete, in the sense that both have a chance to occur with a given probability. We refer to the dynamic evolution of these elastic systems, which exhibit inherent uncertainties due to the material properties, as `likely oscillatory motions'.

In this paper, we consider an imperfect finite beam lying on a nonlinear foundation, whose dimensionless stiffness is reduced from 1 to k as the beam deflection increases. Periodic equilibrium solutions are found analytically and are in good agreement with a numerical resolution, suggesting that localized buckling does not appear for a finite beam. The equilibrium paths may exhibit a limit point whose existence is related to the imperfection size and the stiffness parameter k through an explicit condition. The limit point decreases with the imperfection size while it increases with the stiffness parameter. We show that the decay/growth rate is sensitive to the restoring force model. The analytical results on the limit load may be of particular interest for engineers in structural mechanics

In the present article the linear mass Density for vertically suspended heavy springs is calculated for two different cases. First for a spring of invariable length suspended at the top and fixed at the bottom of the spring, then for a hanging heavy spring with an additional load. Both cases are solved by minimizing the total energy which is a sum of potential energy and energy due to the deformation.

In the present paper, the relationship between localised flexural waves in wedges of power-law profile and flexural wave reflection from acoustic black holes is examined. The geometrical acoustics theory of localised flexural waves in wedges of power-law profile is briefly discussed. It is noted that, for wedge profiles with power-law exponents equal or larger than two, the velocities of all localised modes take zero values, unless there is a wedge truncation. It is demonstrated that this effect of zero velocities of localised flexural waves in ideal wedges is closely related to the phenomenon of zero reflection of flexural waves from ideally sharp one-dimensional acoustic black holes. A possible influence of localised wedge modes on flexural wave reflection from one-dimensional acoustic black holes having rough edges is discussed. With regard to two-dimensional acoustic black holes, the role of localised flexural waves propagating along wedge edges that are curved in their middle plane is considered. Such waves can propagate along edges of inner holes in two-dimensional acoustic black holes formed by circular indentations in plates of constant thickness. A possible impact of such localised waves on the processes of scattering of flexural waves by edge imperfections of inner holes in two-dimensional acoustic black holes is discussed, including their influence on the efficiency of two-dimensional acoustic black holes as vibration dampers.

In the present article we consider the problem of wave interaction with a partially immersed, but floating body. We assume that the motion of the body is prescribed. The general mathematical formulation for this problem is presented in the framework of a hierarchy of mathematical models. Namely, in this first part we formulate the problem at every hierarchical level. The special attention is payed to fully nonlinear and weakly dispersive models since they are most likely to be used in practice. For this model we have to consider separately the inner (under the body) and outer domains. Various approached to the gluing of solutions at the boundary is discussed as well. We propose several strategies which ensure the global conservation or continuity of some important physical quantities.

In this short paper, it is shown that Lorenz gauge condition leads to disappearance of long-range longitudinal electric wave emitted by an arbitrary electrical system. In any other gauge, longitudinal electric wave would be non-negligible. Implications of the obtained results are discussed.

In view of extremely challenging requirements on design and optimization of future mobile communication systems, researchers are considering possibilities of creation intelligent radio environments by using reconfigurable and smart metasurfaces integrated into walls, ceilings, or facades. In this novel communication paradigm, tunable metasurfaces redirect incident waves into the desired directions. In order to design and characterize such smart radio environments in any realistic scenario, it is necessary to know how these metasurfaces behave when illuminated from other directions and how scattering from finite-sized anomalous reflectors can be estimated. We study the angular response of anomalous reflectors for arbitrary illumination angles. Using the surface-impedance model, we explain the dependence of the reflection coefficients of phase-gradient metasurfaces on the illumination angle and present numerical examples for typical structures. We also consider scattering from finite-size metasurfaces and define a route toward including the full-angle response of anomalous reflections into the ray-tracing models of the propagation channel. The developed models apply to other diffraction gratings of finite size.

We report a detailed theoretical model of recently-demonstrated magnetic trap system based on a pair of magnetic tips. The model takes into account key parameters such as tip diameter, facet angle and gap separation. It yields quantitative descriptions consistent with experiments such as the vertical and radial frequency, equilibrium position and the optimum facet angle that produces the strongest confinement. We arrive at striking conclusions that a maximum confinement enhancement can be achieved at an optimum facet angle θ max =arccos 2/3 − − − √ and a critical gap exists beyond which this enhancement effect no longer applies. This magnetic trap and its theoretical model serves as a new and interesting example of a simple and elementary magnetic trap in physics.