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This paper presents a framework for incorporating arbitrary implicit multistep schemes into the lattice Boltzmann method. While the temporal discretization of the lattice Boltzmann equation is usually derived using a second-order trapezoidal rule, it appears natural to augment the time discretization by using multistep methods. The effect of incorporating multistep methods into the lattice Boltzmann method is studied in terms of accuracy and stability. Numerical tests for the third-order accurate Adams-Moulton method and the second-order backward differentiation formula show that the temporal order of the method can be increased when the stability properties of multistep methods are considered in accordance with the second Dahlquist barrier.     

Semi-active stabilisation of a pipe conveying fluid using eddy-current dampers: state-feedback control design,experimental validation

An application of electromagnetic devices of the motional type (i.e. eddy-current dampers) to improve the dynamic stability of a cantilever pipe discharging fluid is proposed. When the flow velocity reaches a critical value, this system loses stability through the flutter. A contactless damping device is used. This actuator is made of a conducting plate attached to the pipe that moves together with it within the perpendicular magnetic field that is generated by the controlled electromagnets. During the motion the eddy currents in the plate and a resultant drag force of a viscous character are generated. First, an optimal control problem that aims to stabilise the system with the optimal rate of decrease of the system’s energy is posed and solved. Then a state-feedback parametrization of the obtained optimal control, which can be used in a closed-loop scheme is proposed. The effectiveness of the designed optimal controller is validated by making a comparison with the corresponding passive solutions on the specially designed and constructed experimental test stand of a pipe conveying air.

     

Singlet Fission in Carbene-Derived Diradicaloids

Herein, we present a new class of singlet fission (SF) materials based on diradicaloids of carbene scaffolds, namely cyclic (alkyl)(amino)carbenes (CAACs). Our modular approach allows the tuning of two key SF criteria: the steric factor and the diradical character. In turn, we modified the energy landscapes of excited states in a systematic manner to accommodate the needs for SF. We report the first example of intermolecular SF in solution by dimer self-assembly at cryogenic temperatures.     

Synthesis of Polymers Containing Potassium Acyltrifluoroborates (KATs) and Post-polymerization Ligation and Conjugation

We report the synthesis of monomers for atom-transfer radical polymerization (ATRP) and a reversible addition-fragmentation chain transfer (RAFT) agent bearing trifluoroborate iminiums (TIMs), which are quantitatively converted into potassium acyltrifluoroborates (KATs) after polymerization. The resulting KAT-containing polymers are suitable for rapid amide-forming ligations for both post-polymerization modification and polymer conjugation. The polymer conjugation occurs rapidly, even under dilute (micromolar) aqueous conditions at ambient temperatures, thereby enabling the synthesis of a variety of linear and star-shaped block copolymers. In addition, we applied post-polymerization modification to the covalent linking of a photocaged cyclic antibiotic (gramicidin S) to the side chains of the KAT-containing copolymer. Cellular assays revealed that the polymer–antibiotic conjugate is biocompatible and provides efficient light-controlled release of the antibiotic on demand.     

Generating Excess Protons in Microsolvated Acid Clusters under Ambient Conditions: An Issue of Configurational Entropy versus Internal Energy

Acid dissociation, and thus liberation of excess protons in small water droplets, impacts on diverse fields such as interstellar, atmospheric or environmental chemistry. At cryogenic temperatures below 1 K, it is now well established that as few as four water molecules suffice to dissociate the generic strong acid HCl, yet temperature-driven recombination sets in simply upon heating that cluster. Here, the fundamental question is posed of how many more water molecules are required to stabilize a hydrated excess proton at room temperature. Ab initio path integral simulations disclose that not five, but six water molecules are needed at 300 K to allow for HCl dissociation independently from nuclear quantum effects. In order to provide the molecular underpinnings of these observations, the classical and quantum free energy profiles were decomposed along the dissociation coordinate in terms of the corresponding internal energy and entropy profiles. What decides in the end about acid dissociation, and thus ion pair formation, in a specific microsolvated water cluster at room temperature is found to be a fierce competition between classical configurational entropy and internal energy, where the former stabilizes the undissociated state whereas the latter favors dissociation. It is expected that these are generic findings with broad implications on acid–base chemistry depending on temperature in small water assemblies.     

Localizing Binding Sites on Bioconjugated Hydrogen-Bonded Organic Semiconductors at the Nanoscale

Hydrogen-bonded organic semiconductors are extraordinarily stable organic solids forming stable, large crystallites with the ability to preserve favorable electrical properties upon bioconjugation. Lately, tremendous efforts have been made to use these bioconjugated semiconductors as platforms for stable multifunctional bioelectronics devices, yet the detailed characterization of bio-active binding sites (orientation, density, etc.) at the nanoscale has not been achieved yet. The presented work investigates the bioconjugation of epindolidione and quinacridone, two representative semiconductors, with respect to their exposed amine-functionalities. Relying on the biotin-avidin lock-and-key system and applying the atomic force microscopy (AFM) derivative topography and recognition (TREC) imaging, we used activated biotin to flag crystal-faces with exposed amine functional groups. Contrary to previous studies, biotin bonds were found to be stable towards removal by autolysis. The resolution strength and clear recognition capability makes TREC-AFM a valuable tool in the investigation of bio-conjugated, hydrogen-bonded semiconductors.     

Jordan generalized derivations on triangular algebras

Let 𝒜 be a unital algebra and let ? be a unitary 𝒜-bimodule. We consider Jordan generalized derivations mapping from 𝒜 into ?. Our results on unitary algebras are applied to triangular algebras. In particular, we prove that any Jordan generalized derivation of a triangular algebra is a generalized derivation.     

Generalized skew derivations on triangular algebras determined by action on zero products

For a triangular algebra 𝒜 and an automorphism σ of 𝒜, we describe linear maps F,G:𝒜→𝒜 satisfying F(x)y+σ(x)G(y) = 0 whenever x,y∈𝒜 are such that xy = 0. In particular, when 𝒜 is a zero product determined triangular algebra, maps F and G satisfying the above condition are generalized skew derivations of the form F(x) = F(1)x+D(x) and G(x) = σ(x)G(1)+D(x) for all x∈𝒜, where D:𝒜→𝒜 is a skew derivation. When 𝒜 is not zero product determined, we show that there are also nonstandard solutions for maps F and G.