We consider the heat equation for monolayer two-dimensional materials in the presence of heat flow into a substrate and Joule heating due to electrical current. We compare devices including a nanowire of constant width and a bow tie (or wedge) constriction of varying width, and we derive approximate one-dimensional heat equations for them; a bow tie constriction is described by the modified Bessel equation of zero order. We compare steady state analytic solutions of the approximate equations with numerical results obtained by a finite element method solution of the two-dimensional equation. Using these solutions, we describe the role of thermal conductivity, thermal boundary resistance with the substrate and device geometry. The temperature in a device at fixed potential difference will remain finite as the width shrinks, but will diverge for fixed current, logarithmically with width for the bow tie as compared to an inverse square dependence in a nanowire.

The absorption and emission properties of a series of 44 aromatic molecules have been investigated in Time Dependent Density Functional Theory (TDDFT) using different exchange‐correlation functionals. Solvent effects have been included within linear response (LR) and state specific (SS) polarisable continuum model (PCM). The comparison with experimental UV‐Vis data showed reasonable agreement for all the aromatic molecules when ωB97XD with SS‐PCM is used. In particular, we found an accurate linear correlation between experimental and theoretical results which is revealed in an equation for absorption and another equation for emission derived from a linear fitting between theoretical and experimental data. Through these linear equations we propose a simple, pragmatic and effective approach able to describe and predict the absorption and the emission of aromatic molecules with a reasonable computational cost.