Heat diffusion in a two-dimensional thermal fuse model

We present numerical studies of electrical breakdown in disordered materials using a two-dimensional thermal fuse model with heat diffusion. A conducting fuse is heated locally by a Joule heating term. Heat diffuses to neighbouring fuses by a diffusion term. When the temperature reaches a given threshold, the fuse breaks and turns into an insulator. The time dynamics is governed by the time scales related to the two terms, in the presence of quenched disorder in the conductances of the fuses. For the two limiting domains, when one time scale is much smaller than the other, we find that the global breakdown time $t_r$ follows $t_r\sim I^2$ and $t_r\sim L^2$, where $I$ is the applied current, and $L$ is the system size. However, such power law does not apply in the intermediate domain where the competition between the two terms produces a subtle behaviour.Comment: Physical Review E 81, 066111 (2010

Anomalous Scaling and Solitary Waves in Systems with Non-Linear Diffusion

We study a non-linear convective-diffusive equation, local in space and time, which has its background in the dynamics of the thickness of a wetting film. The presence of a non-linear diffusion predicts the existence of fronts as well as shock fronts. Despite the absence of memory effects, solutions in the case of pure non-linear diffusion exhibit an anomalous sub-diffusive scaling. Due to a balance between non-linear diffusion and convection we, in particular, show that solitary waves appear. For large times they merge into a single solitary wave exhibiting a topological stability. Even though our results concern a specific equation, numerical simulations supports the view that anomalous diffusion and the solitary waves disclosed will be general features in such non-linear convective-diffusive dynamics.Comment: Corrected typos, added 3 references and 2 figure

Design and model test of a soft-connected lattice-structured floating solar photovoltaic concept for harsh offshore conditions

Various types of floating solar photovoltaic (FPV) devices have been previously proposed, designed and constructed with applications primarily limited to onshore water bodies or nearshore regions with benign environmental conditions. This paper proposes a novel FPV concept which can survive harsh environmental conditions with extreme wave heights above 10 m. This concept uses standardised lightweight semi-submersible floats made of circular materials as individual modules. The floating modules are soft connected with ropes to form an FPV array. We first present the conceptual design of the floats and the connection systems, including hydrostatic, hydrodynamic, and structural assessments of the floats. To verify the motion response performance, we carried out 1:60 scaled model tests for a 2 by 3 array under regular and irregular wave conditions. From the time series and response spectra, the motion characteristics of the array and the mooring responses are analysed in detail. The proposed concept exhibits excellent performances in terms of modular motions with limited wave overtopping and no contact is observed between adjacent modules under the extreme wave conditions. The findings of this study can serve as a valuable reference to developing reliable and cost-effective FPV technologies for offshore conditions.publishedVersio