Dielectric Properties of Textile Materials: Analytical Approximations and Experimental Measurements—A Review

Deciphering how the dielectric properties of textile materials are orchestrated by their internal components has far-reaching implications. For the development of textile-based electronics, which have gained ever-increasing attention for their uniquely combined features of electronics and traditional fabrics, both performance and form factor are critically dependent on the dielectric properties. The knowledge of the dielectric properties of textile materials is thus crucial in successful design and operation of textile-based electronics. While the dielectric properties of textile materials could be estimated to some extent from the compositional profiles, recent studies have identified various additional factors that have also substantial influence. From the viewpoint of materials characterization, such dependence of the dielectric properties of textile materials have given rise to a new possibility—information on various internal components could be, upon successful correlation, extracted by measuring the dielectric properties. In view of these considerable implications, this invited review paper summarizes various fundamental theories and principles related to the dielectric properties of textile materials. In order to provide an imperative basis for uncovering various factors that intricately influence the dielectric properties of textile materials, the foundations of the dielectrics and polarization mechanisms are first recapitulated, followed by an overview on the concept of homogenization and the dielectric mixture theory. The principal advantages, challenges and opportunities in the analytical approximations of the dielectric properties of textile materials are then discussed based on the findings from the recent literature, and finally a variety of characterization methods suitable for measuring the dielectric properties of textile materials are described. It is among the objectives of this paper to build a practical signpost for scientists and engineers in this rapidly evolving, cross-disciplinary field.

Stability of Fixed Points in an Approximate Solution of the Spring-Mass Running Model

We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on our previous results concerning asymptotic solutions for large spring constant (or small angle of attack), we construct analytical approximations of solutions in the considered model. The model itself consists of two sets of differential equations - one set describes the motion of the centre of mass of a runner in contact with the ground (support phase), and the second set describes the phase of no contact with the ground (flight phase). By appropriately concatenating asymptotic solutions for the two phases we are able to reduce the dynamics to a onedimensional apex to apex return map. We find sufficient conditions for this map to have a unique stable fixed point. By numerical continuation of fixed points with respect to energy, we find a transcritical bifurcation in our model system.MSC 2020 Classification: 34C20, 34D05, 37N25, 70K20, 70K42, 70K50, 70K60

Spatial effects in parasite induced marine diseases of immobile hosts

Marine infectious diseases are more prevalent in recent times due to climate change and other anthropogenic pressures, posing a substantial threat to marine ecosystems and the conservation of their biodiversity. An important subset of marine organisms are sessile, for which the most common mechanism for disease transmission is direct contact with waterborne parasites. Only recently, some deterministic compartmental models have been proposed to describe this kind of epidemics, being these models based on non-spatial descriptions where space is homogenised and parasite mobility is not explicitly accounted for. However, in realistic situations, epidemic transmission is conditioned by the spatial distribution of hosts and the parasites mobility patterns. Thus, the interplay between these factors is expected to have a crucial effect in the evolution of the epidemic, so calling for a explicit description of space. In this work we develop a spatially-explicit individual-based model to study disease transmission by waterborne parasites in sessile marine populations. We investigate the impact of spatial disease transmission, performing extensive numerical simulations and analytical approximations. Specifically, the effects of parasite mobility into the epidemic threshold and the temporal evolution of the epidemic are assessed. We show that larger values of pathogen mobility have two main implications: more severe epidemics, as the number of infections increases, and shorter time-scales to extinction. Moreover, an analytical expression for the basic reproduction number of the spatial model, is derived as function of the non-spatial counterpart, which characterises a transition between a disease-free and a propagation phase, in which the disease propagates over a large fraction of the system. This allows to determine a phase diagram for the epidemic model as function of the parasite mobility and the basic reproduction number of the non-spatial model.

Optimal Design Approach for One-dimensional Rubber-Concrete Periodic Foundations based on Analytical Approximations of Band Gaps

This research investigates band gaps and frequency responses of one-dimensional periodic structures and further presents an optimal design approach for one-dimensional rubber-concrete periodic foundations based on the proposed analytical formulas for approximating the first few band gaps. The presented design approach is optimal for being able of globally searching the best solution which effectively cooperates the band gaps with the superstructure’s resonance frequencies. Firstly, frequency responses of one-dimensional periodic structures and the corresponding approximation method are studied. Furthermore, analytical approximation formulas for the first few band gaps, localization factor, attenuation coefficient, and frequency responses of one-dimensional rubber-concrete periodic foundations are proposed and verified. Lastly, inspired by the proposed analytical approximation for computing band gaps, an optimal design approach for one-dimensional rubber-concrete periodic foundations is presented and applied to a practical example, whose optimality is verified theoretically and numerically.

Numerical estimation of thermal ignition conditions for reactive medium with Gaussian distribution of activation energy

The article investigates the solutions of the one-dimensional stationary integro-differential heat equation. The source of heat release is determined through the Gaussian distribution function of the activation energy. In such a statement, the critical conditions for the existence of a bounded solution depend on the distribution variance. With the help of numerical methods, such dependences are obtained; for their explanation, the analytical approximations of the thermal explosion theory are used.

Thermopower, figure of merit and Fermi integrals

The thermoelectric efficiency accounting for the conversion of thermal energy into electricity is usually given by the figure of merit which involves three transport coefficients, with the thermopower, the electrical and the thermal conductivities. These coefficients can be defined at a semi-classical level as a function of Fermi integrals which only allow analytical approximations in either highly degenerate or strongly non-degenerate regimes. Otherwise, the intermediate regime which is of interest in order to describe high thermoelectric performance requires numerical calculations. It is shown that these Fermi integrals can actually be calculated and that the transport coefficients can be reformulated accordingly. This allows for a new definition of the figure of merit which covers all the regimes of interest without numerical calculations. This formulation of the Fermi integrals also provides a good starting point in order to perform a power expansion leading to a new approximation relevant for the intermediate regime. It turns out that the transport coefficients can then be expanded by revealing their high temperatures asymptotic behaviors. These results shed new light on the thermoelectric properties of the materials and point out that the analysis of their high temperatures behaviors allow to characterize experimentally the energy dependence in the transport integrals.

Speed Oscillations of a Vehicle Rolling on a Wavy Road

Every driver knows that his car is slowing down or accelerating when driving up or down, respectively. The same happens on uneven roads with plastic wave deformations, e.g., in front of traffic lights or on nonpaved desert roads. This paper investigates the resulting travel speed oscillations of a quarter car model rolling in contact on a sinusoidal and stochastic road surface. The nonlinear equations of motion of the vehicle road system leads to ill-conditioned differential–algebraic equations. They are solved introducing polar coordinates into the sinusoidal road model. Numerical simulations show the Sommerfeld effect, in which the vehicle becomes stuck before the resonance speed, exhibiting limit cycles of oscillating acceleration and speed, which bifurcate from one-periodic limit cycle to one that is double periodic. Analytical approximations are derived by means of nonlinear Fourier expansions. Extensions to more realistic road models by means of noise perturbation show limit flows as bundles of nonperiodic trajectories with periodic side limits. Vehicles with higher degrees of freedom become stuck before the first speed resonance, as well as in between further resonance speeds with strong vertical vibrations and longitudinal speed oscillations. They need more power supply in order to overcome the resonance peak. For small damping, the speeds after resonance are unstable. They migrate to lower or supercritical speeds of operation. Stability in mean is investigated.

Network processes on clique-networks with high average degree: the limited effect of higher-order structure

In this paper, we investigate the effect of local structures on network processes. We investigate a random graph model that incorporates local clique structures, and thus deviates from the locally tree-like behavior of most standard random graph models. For the process of bond percolation, we derive analytical approximations for large percolation probabilities and the critical percolation value. Interestingly, these derivations show that when the average degree of a vertex is large, the influence of the deviations from the locally tree-like structure is small. In our simulations, this insensitivity to local clique structures often already kicks in for networks with average degrees as low as 6. Furthermore, we show that the different behavior of bond percolation on clustered networks compared to tree-like networks that was found in previous works can be almost completely attributed to differences in degree sequences rather than differences in clustering structures. We finally show that these results also extend to completely different types of dynamics, by deriving similar conclusions and simulations for the Kuramoto model on the same types of clustered and non-clustered networks.

Exceptional points in composite structures consisting of two dielectric diffraction gratings with Lorentzian line shape

Using scattering matrix formalism we derive analytical expressions for the eigenmodes of a composite structure consisting of two dielectric diffraction gratings with Lorentzian profile in reflection. Analyzing these expressions we prove formation of two distinct pairs of exceptional points, provide analytical approximations for their coordinates and by rigorous simulation demonstrate eigenmodes interchange as a result of encircling said exceptional points.