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Fast microjets can emerge out of liquid pools from the rebounding of drop-impact craters, or when a bubble bursts at its surface. The fastest jets are the narrowest and are a source of aerosols both from the ocean and from a glass of champagne, of importance to climate and the olfactory senses. The most singular jets, which we observe experimentally at a maximum velocity of 
$137\pm 4\ {\rm m}\ {\rm s}^{-1}$ and a diameter of 
$12\ \mathrm {\mu }{\rm m}$, under reduced ambient pressure, are produced when a small dimple forms at the crater bottom and rebounds without pinching off a small bubble. The radial collapse and rebounding of this dimple is purely inertial, but highly sensitive to initial conditions. High-resolution numerical simulations reveal a new focusing mechanism, which drives the fastest jet within a converging conical channel, where an entrained air sheet provides effective slip at the outer boundary of the conically converging flow into the jet. This configuration bypasses any viscous cutoff of the jetting speed and explains the extreme sensitivity to initial conditions observed in detailed experiments of the phenomenon.
$\mathbb {Z}^{d}$-actions
Let 
$k\geq 2$ and 
$(X_{i}, \mathcal {T}_{i}), i=1,\ldots ,k$, be 
$\mathbb {Z}^{d}$-actions topological dynamical systems with 
$\mathcal {T}_i:=\{T_i^{\textbf {g}}:X_i{\rightarrow } X_i\}_{\textbf {g}\in \mathbb {Z}^{d}}$, where 
$d\in \mathbb {N}$ and 
$f\in C(X_{1})$. Assume that for each 
$1\leq i\leq k-1$, 
$(X_{i+1}, \mathcal {T}_{i+1})$ is a factor of 
$(X_{i}, \mathcal {T}_{i})$. In this paper, we introduce the weighted topological pressure 
$P^{\textbf {a}}(\mathcal {T}_{1},f)$ and weighted measure-theoretic entropy 
$h_{\mu }^{\textbf {a}}(\mathcal {T}_{1})$ for 
$\mathbb {Z}^{d}$-actions, and establish a weighted variational principle as 
$$ \begin{align*} P^{\textbf{a}}(\mathcal{T}_{1},f)=\sup\bigg\{h_{\mu}^{\textbf{a}}(\mathcal{T}_{1})+\int_{X_{1}}f\,d\mu:\mu\in\mathcal{M}(X_{1}, \mathcal{T}_{1})\bigg\}. \end{align*} $$
This result not only generalizes some well-known variational principles about topological pressure for compact or non-compact sets, but also improves the variational principle for weighted topological pressure in [16] from 
$\mathbb {Z}_{+}$-action topological dynamical systems to 
$\mathbb {Z}^{d}$-actions topological dynamical systems.
Thermal convection of fluid is a more efficient way than diffusion to carry heat from hot sources to cold places. Here, we experimentally study the Rayleigh–Bénard convection of aqueous glycerol solution in a cubic cell with suspensions of rod-like particles made of polydimethylsiloxane. The particles are inertial due to their large thermal expansion coefficient and finite sizes. The thermal expansion coefficient of the particles is three times larger than that of the background fluid. This contrast makes the suspended particles lighter than the local fluid in hot regions and heavier in cold regions. The heat transport is enhanced at relatively large Rayleigh number (
$\textit {Ra}$) but reduced at small 
$\textit {Ra}$. We demonstrate that the increase of Nusselt number arises from the particle–boundary layer interactions: the particles act as ‘active’ mixers of the flow and temperature fields across the boundary layers.
We study singular jets from the collapse of drop-impact craters, when the drop and pool are of different immiscible liquids. The fastest jets emerge from a dimple at the bottom of the rebounding crater, when no bubble is pinched off. The parameter space is considerably more complex than for identical liquids, revealing intricate compound-dimple shapes. In contrast to the universal capillary–inertial drop pinch-off regime, where the neck radius scales as 
$R\sim t^{2/3}$, for a purely inertial air dimple the collapse has 
$R \sim t^{1/2}$. The bottom dimple dynamics is not self-similar but possesses memory effects, being sensitive to initial and boundary conditions. Sequence of capillary waves can therefore mould the air dimple into different collapse shapes, such as bamboo-like and telescopic forms. The finest jets are only 
$12\ \mathrm {\mu }\textrm {m}$ in diameter and the normalized jetting speeds are up to one order of magnitude larger than for jets from bursting bubbles. We study the cross-over between the two power laws approaching the singularity. The singular jets show the earliest cross-over into the inertial regime. The fastest jets can pinch off a toroidal micro-bubble from the cusp at the base of the jet.
Laser pulses of 200 ps with extremely high intensities and high energies are sufficient to satisfy the demand of shock ignition, which is an alternative path to ignition in inertial confinement fusion (ICF). This paper reports a type of Brillouin scheme to obtain high-intensity 200-ps laser pulses, where the pulse durations are a challenge for conventional pulsed laser amplification systems. In the amplification process, excited Brillouin acoustic waves fulfill the nonlinear optical effect through which the high energy of a long pump pulse is entirely transferred to a 200-ps laser pulse. This method was introduced and achieved within the SG-III prototype system in China. Compared favorably with the intensity of 
$2~\text{GW}/\text{cm}^{2}$ in existing ICF laser drivers, a 6.96-
$\text{GW}/\text{cm}^{2}$ pulse with a width of 170 ps was obtained in our experiment. The practical scalability of the results to larger ICF laser drivers is discussed.
