Dynamical control on the Adomian decomposition method for solving shallow water wave equation

The aim of this study is to apply a novel technique to control the accuracy and error of the Adomian decomposition method (ADM) for solving nonlinear shallow water wave equation. The ADM is among semi-analytical and powerful methods for solving many mathematical and engineering problems. We apply the Controle et Estimation Stochastique des Arrondis de Calculs (CESTAC) method which is based on stochastic arithmetic (SA). Also instead of applying mathematical packages we use the Control of Accuracy and Debugging for Numerical Applications (CADNA) library. In this library we will write all codes using C++ programming codes. Applying the method we can find the optimal numerical results, error and step of the ADM and they are the main novelties of this research. The numerical results show the accuracy and efficiency of the novel scheme.

Dissolved Organic Matter in the Global Ocean: A Primer

Marine dissolved organic matter (DOM) holds ~660 billion metric tons of carbon, making it one of Earth’s major carbon reservoirs that is exchangeable with the atmosphere on annual to millennial time scales. The global ocean scale dynamics of the pool have become better illuminated over the past few decades, and those are very briefly described here. What is still far from understood is the dynamical control on this pool at the molecular level; in the case of this Special Issue, the role of microgels is poorly known. This manuscript provides the global context of a large pool of marine DOM upon which those missing insights can be built.

Reconfigurable artificial microswimmers with internal feedback

Self-propelling microparticles are often proposed as synthetic models for biological microswimmers, yet they lack the internally regulated adaptation of their biological counterparts. Conversely, adaptation can be encoded in larger-scale soft-robotic devices but remains elusive to transfer to the colloidal scale. Here, we create responsive microswimmers, powered by electro-hydrodynamic flows, which can adapt their motility via internal reconfiguration. Using sequential capillary assembly, we fabricate deterministic colloidal clusters comprising soft thermo-responsive microgels and light-absorbing particles. Light absorption induces preferential local heating and triggers the volume phase transition of the microgels, leading to an adaptation of the clusters’ motility, which is orthogonal to their propulsion scheme. We rationalize this response via the coupling between self-propulsion and variations of particle shape and dielectric properties upon heating. Harnessing such coupling allows for strategies to achieve local dynamical control with simple illumination patterns, revealing exciting opportunities for developing tactic active materials.

Maxwell Points of Dynamical Control Systems Based on Vertical Rolling Disc—Numerical Solutions

We study two nilpotent affine control systems derived from the dynamic and control of a vertical rolling disc that is a simplification of a differential drive wheeled mobile robot. For both systems, their controllable Lie algebras are calculated and optimal control problems are formulated, and their Hamiltonian systems of ODEs are derived using the Pontryagin maximum principle. These optimal control problems completely determine the energetically optimal trajectories between two states. Then, a novel numerical algorithm based on optimisation for finding the Maxwell points is presented and tested on these control systems. The results show that the use of such numerical methods can be beneficial in cases where common analytical approaches fail or are impractical.

Dynamic control of Purcell enhanced emission of erbium ions in nanoparticles

The interaction of single quantum emitters with an optical cavity enables the realization of efficient spin-photon interfaces, an essential resource for quantum networks. The dynamical control of the spontaneous emission rate of quantum emitters in cavities has important implications in quantum technologies, e.g., for shaping the emitted photons’ waveform or for driving coherently the optical transition while preventing photon emission. Here we demonstrate the dynamical control of the Purcell enhanced emission of a small ensemble of erbium ions doped into a nanoparticle. By embedding the nanoparticles into a fully tunable high finesse fiber based optical microcavity, we demonstrate a median Purcell factor of 15 for the ensemble of ions. We also show that we can dynamically control the Purcell enhanced emission by tuning the cavity on and out of resonance, by controlling its length with sub-nanometer precision on a time scale more than two orders of magnitude faster than the natural lifetime of the erbium ions. This capability opens prospects for the realization of efficient nanoscale quantum interfaces between solid-state spins and single telecom photons with controllable waveform, for non-destructive detection of photonic qubits, and for the realization of quantum gates between rare-earth ion qubits coupled to an optical cavity.