Some arboreal monocotyledons, such as the dragon trees (Dracaena sp.), can develop impressive trunks (>5 m perimeter) through a lateral meristem, but their ages are difficult to determine. We report here a series of calibrated radiocarbon (14C) dates obtained from a stem section of Dracaena draco (L.) L. subsp. draco growing on the island of Tenerife, Canary Islands, Spain. This radial section, about 40 cm long, was cut on October 18, 2023, from a large (∼60 cm diameter) branch that had fallen off the main stem of a privately owned dragon tree. In order to apply 14C calibration, and given the lack of clearly defined growth layers, we collected 33 sequential samples at ∼1-cm intervals along this radial section. A first attempt at wiggle-matching resulted in a calibrated dating of ∼1787 CE for the innermost sample. Because we only knew the spatial distance, but not the time interval, between 14C dates, we further applied calibration tools commonly used for sedimentary sequences. The Poisson-process deposition model in the software OxCal resulted in a calibrated age for the innermost sample of 1776–1798 CE (2σ). The classic and Bayesian age-depth deposition models available as R packages dated the innermost sample to, respectively, 1775–1862 and 1768–1813 CE. Because the branch was at a height of ∼3 m from the ground, and its section did not reach the pith, our results suggest that this dragon tree was ∼300 years old in 2023.

For any integer $t \geq 2$, we prove a local limit theorem (LLT) with an explicit convergence rate for the number of parts in a uniformly chosen t-regular partition. When $t = 2$, this recovers the LLT for partitions into distinct parts, as previously established in the work of Szekeres [‘Asymptotic distributions of the number and size of parts in unequal partitions’, Bull. Aust. Math. Soc. 36 (1987), 89–97].

Supersonic jets impinging on a ground plane produce a highly unsteady jet shear layer, often resulting in extremely high noise level. The widely accepted mechanism for this jet resonance involves a feedback loop consisting of downstream-travelling coherent structures and upstream-propagating acoustic waves. Despite the importance of coherent structures, often referred to as disturbances, that travel downstream, a comprehensive discussion on the disturbance convection velocity has been limited due to the challenges posed by non-intrusive measurement requirements. To determine the convection velocity of disturbances in the jet shear layer, a high-speed schlieren flow visualisation is carried out, and phase-averaged wave diagrams are constructed from the image sets. The experiments are conducted using a Mach 1.5 jet under various nozzle pressure ratios and across a range of impingement distances. A parametric analysis is performed to examine the influence of nozzle pressure ratio on the convection velocity and phase lead/lag at specific impingement distances. The results reveal that impingement tonal frequency is nearly independent of the disturbance convection velocity, except in cases of staging behaviour. They also demonstrated that slower downstream convection velocity of the disturbance corresponds to larger coherent structures, resulting in increased noise levels. Based on the observation of acoustic standing waves, an acoustic speed-based frequency model has been proposed. With the help of the allowable frequency range calculated from the vortex-sheet model, this model can provide a good approximation for the majority of axisymmetric impingement tonal frequencies.

The literature on internal commitment cites Adam Smith as a precursor because of his elaboration of diachronic control, and this has given rise to attempts to model his account. Some of these efforts stress the role he assigns to the “general rules of morality” by which the “bulk of mankind” ensure the constancy of their conduct, and interpret them as self-enforcing resolutions. But how could such internal tactics as adopted by weak agents be effective? How could the knowledge of general rules escape self-deception? We take a closer look at what Smith writes about beliefs and emotional dispositions regarding the important rules of morality.

One-degree-of-freedom flow-induced vibration (FIV) and energy harvesting through FIV of an elastically mounted circular cylinder with mechanically coupled rotation were investigated numerically for low Reynolds number 100, mass ratio 8 and a wide range of reduced velocities. The aims of this study are to investigate the effect of the flow direction angle $\beta$ on the vibration and energy harvesting through FIV. Two types of lock-in are found: vortex-induced vibration (VIV) and galloping. The response amplitude increases with the increase of $\beta$ in both regimes. Both VIV response and galloping regimes are found for $\beta$ = 45° to $\beta$ = 90°. For $\beta$ = −90° to $\beta$ = 0°, only VIV response regimes are found. The fluid force and fluid torque play different roles in exciting/damping the vibration. In the high-amplitude gallop regime, the fluid force excites the vibration, and the torque damps the vibration. Energy harvesting at flow direction angle 90° is investigated as this flow direction has the maximum galloping amplitude. The energy harvesting is achieved by a linear electric damping coefficient in the numerical model. The maximum harvestable power in the galloping regime is significantly greater than that in the VIV regime, and it increases with the increase of the reduced velocity. When the reduced velocity is 20, the harvested power is over 20 times that in the VIV regime, and can further increase if reduced velocity further increases. The maximum efficiency over all simulated parameters is 0.424, occurring when the reduced velocity is 20, and electric damping factor is 0.04.