Linear and nonlinear stability analyses were performed on a fluid layer with a concentration-based internal heat source. Clear bimodal behaviour in the neutral curve (with stationary and oscillatory modes) is observed in the region of the onset of oscillatory convection, which is a previously unobserved phenomenon in radiation-induced convection. The numerical results for the linear instability analysis suggest a critical value γ c of γ , a measure for the strength of the internal heat source, for which oscillatory convection is inhibited when γ > γ c . Linear instability analyses on the effect of varying the ratio of the salt concentrations at the upper and lower boundaries conclude that the ratio has a significant effect on the stability boundary. A nonlinear analysis using an energy approach confirms that the linear theory describes the stability boundary most accurately when γ is such that the linear theory predicts the onset of mostly stationary convection. Nevertheless, the agreement between the linear and nonlinear stability thresholds deteriorates for larger values of the solute Rayleigh number for any value of γ .

We present Monte-Carlo (MC) simulations of the crystallization transition of single-chain square-well homopolymers, with a continuous description of monomer positions. For long chains with short-ranged interactions this system shows a strong configurational bottleneck, which makes it difficult to explore the whole configuration space. To surmount this problem we combine parallel tempering with a nonstandard choice of tempering levels, a bespoke biasing strategy and a method to map results between different temperatures. We verify that our simulations mix well when simulating chains of 128 and 256 beads. Our simulation approach resolves issues with reproducibility of MC simulations reported in prior work, particularly for the transition region between the expanded coil and crystalline region. We obtain highly reproducible results for both the free energy landscape and the inverse temperature, with low statistical noise. We outline a method to extract the free energy barrier, at any temperature, for any choice of order parameter, illustrating this technique by computing the free energy landscape as a function of the Steinhardt-Nelson order parameter for a range of temperatures.