Distance functions between points in a domain are sometimes used to automatically plan a gradient-descent path towards a given target point in the domain, avoiding obstacles that may be present. A key requirement from such distance functions is the absence of spurious local minima, which may foil such an approach, and this has led to the common use of harmonic potential functions. Based on the ...

This work uses the dual-phase-lag (DPL) model of heat conduction to demonstrate the effect of temperature gradient relaxation time on the result of non-Fourier hyperbolic conduction in a finite slab subjected to a periodic thermal disturbance. DPL model combines the wave features of hyperbolic conduction with a diffusion-like feature of the evidence not captured by the hyperbolic case. For the ...

\begin{abstract} In this paper, we partly solve the generalized Khavinson conjecture in setting of hyperbolic harmonic mappings Hardy space. Assume that $u=\mathcal{P}_{\Omega}[\phi]$ and $\phi\in L^{p}(\partial\Omega, \mathbb{R})$, where $p\in[1,\infty]$, $\mathcal{P}_{\Omega}[\phi]$ denotes Poisson integral $\phi$ with respect to Laplacian operator $\Delta_{h}$ $\Omega$, $\Omega$ unit ball $\...

The detection and processing of information carried by evanescent field components are key elements for subwavelength optical microscopy as well as single molecule sensing applications. Here, we numerically demonstrate the potential of a hyperbolic medium in the design of an efficient metamaterial antenna enabling detection and tracking of a nonlinear object, with an otherwise hidden second-har...