Response time analysis of adaptive variable-rate tasks (AVR tasks) is a challenging problem in automotive real-time systems. While in periodic event-triggered systems, the worst-case response time is easy to determine, the analysis of AVR tasks has to deal with an exponentially growing number of combinations of execution paths. Each execution path has a specific dynamic behavior. In this paper, we present a new approach for reducing the number of potential worst-case combinations by introducing an intuitive view on the relation of start and end speeds given by speed-phase diagram. Here we propose a minimal inter-arrival time algorithm (MIAT) which is built on time constant lines (isochrones) in a speed-phase diagram first introduced in this work. Compared with previous work, the MIAT algorithm is more accurate and shows a significant improvement in runtime.

We study the evolution of a cold single BaRb+ molecule while it continuously collides with ultracold Rb atoms. The initially weakly bound molecule can undergo a sequence of elastic, inelastic, reactive, and radiative processes. We investigate these processes by developing methods for discriminating between different ion species, electronic states, and kinetic ion energy ranges. By analyzing the experimental data while taking into account theoretical insights, we obtain a consistent description of the typical trajectory through the manifold of available atomic and molecular states. Monte Carlo simulations describe the measured dynamics well. As a further result, we determine rates for collisional and radiative relaxation as well as photodissociation, spin-flip collisions, and chemical reactions.

Collisions with cold particles can dissipate a hot particle’s energy and therefore can be exploited as a cooling mechanism. Kinetics teach us that cooling a particle down by several orders of magnitude typically takes many elastic collisions as each one only carries away a fraction of the collision energy. Recently, for a system comprising hot ions and cold atoms, a very fast cooling process has been suggested (Ravi et al 2012 Nat. Commun. 3 1126) where cooling over several orders of magnitude can occur in a single step. Namely, in a homo-nuclear atom–ion collision, an electron can resonantly hop from an ultracold atom onto the hot ion, converting the cold atom into a cold ion. Here, we demonstrate such swap cooling in a direct way as we experimentally observe how a single energetic ion loses energy in a cold atom cloud. In order to contrast swap cooling with sympathetic cooling, we perform the same measurements with a hetero-nuclear atom–ion system, for which swap cooling cannot take place, and indeed observe very different cooling dynamics. Ab initio numerical model calculations agree well with our measured data and corroborate our interpretations.

Collisions with cold particles can dissipate the energy of a hot particle and therefore be exploited as a cooling mechanism. Kinetics teaches us that for a particle to be cooled down by several orders of magnitude, it will typically take many elastic collisions as each one only carries away a certain fraction of the collision energy. Recently, for a system consisting of hot ions and cold atoms, a much faster cooling process has been suggested where cooling over several orders of magnitude can occur in a single step. Namely, in a homo-nuclear atom-ion collision, an electron can resonantly hop from an ultracold atom onto the hot ion, converting the cold atom into a cold ion. Here, we demonstrate such swap cooling in a direct way as we experimentally observe how a single energetic ion loses energy in a cold atom cloud. In order to contrast swap cooling with standard sympathetic cooling, we perform the same measurements with a hetero-nuclear atom-ion system, for which swap cooling cannot take place, and indeed observe much different cooling dynamics. Ab initio numerical model calculations agree well with our measured data and corroborate our interpretations. We expect swap cooling to occur quite universally in any homo-nuclear atom-ion collision. It should therefore be a ubiquitous process in mixed atom-ion gases and plasmas. Furthermore, it offers interesting prospects for fast cooling applications.