A Riemann-Liouville fractional Robin boundary-value problem is proposed to describe the fast heat transfer law both within isotropic materials and through the boundary of the materials in high temperature environment. The variational formulation of the fractional model is given, and further the energy estimation of the weak solution is deduced. The uniqueness theorem of weak solution is proved. A valid finite difference scheme is developed for the fractional model and numerical experiment is implemented. Numerical results indicate that the fractional model is applicable to discover the thermal superdiffusion in the thermal protective clothing(TPC) system and numerical algorithms are effective to improve the intelligence of TPC design.

In this work, we extend the direct method in [26] to identify the marine sources and scatterers simultaneously from the far-field pattern in a stratified ocean waveguide. The proposed approach is essentially direct and does not involve any optimizations, solution procedures or matrix inversions, thus computationally rather efficient and simple. Some numerical simulations are carried out to exhibit the robustness and effectiveness of the proposed method in the reconstruction procedure. The extended direct method can not only identify the sources in different locations but also can reconstruct the scatterers in different shapes and positions, therefore it can be considered as an efficient numerical approach for providing reliable estimates of the marine inhomogeneities in the marine acoustics.