Erratum: Information conduction and convection in noiseless Vicsek flocks [Phys. Rev. E 106, 014609 (2022)].

This corrects the article DOI: 10.1103/PhysRevE.106.

Signal propagation and linear response in the delay Vicsek model.

Retardation between sensation and action is an inherent biological trait. Here we study its effect in the Vicsek model, which is a paradigmatic swarm model. We find that (1) a discrete time delay in the orientational interactions diminishes the ability of strongly aligned swarms to follow a leader and, in return, increases their stability against random orientation fluctuations; (2) both longer delays and higher speeds favor ballistic over diffusive spreading of information (orientation) through the swarm; (3) for short delays, the mean change in the total orientation (the order parameter) scales linearly in a small orientational bias of the leaders and inversely in the delay time, while its variance first increases and then saturates with increasing delays; and (4) the linear response breaks down when orientation conservation is broken.

Information conduction and convection in noiseless Vicsek flocks.

Physical interactions generally respect certain symmetries, such as reciprocity and energy conservation, which survive in coarse-grained isothermal descriptions. Active many-body systems usually break such symmetries intrinsically, on the particle level, so that their collective behavior is often more naturally interpreted as a result of information exchange. Here we study numerically how information spreads from a "leader" particle through an initially aligned flock, described by the Vicsek model without noise.

Finite-Size Scaling at the Edge of Disorder in a Time-Delay Vicsek Model.

Living many-body systems often exhibit scale-free collective behavior reminiscent of thermal critical phenomena. But their mutual interactions are inevitably retarded due to information processing and delayed actuation. We numerically investigate the consequences for the finite-size scaling in the Vicsek model of motile active matter.

Addition of Small Electrophiles to N-Heterocyclic-Carbene-Stabilized Disilicon(0): A Revisit of the Isolobal Concept in Low-Valent Silicon Chemistry.

Protonation and alkylation of (Idipp)Si═Si(Idipp) (1) afforded the mixed-valent disilicon(I)-borates [(Idipp)(R)Si(II)═Si(0)(Idipp)][B(Ar(F))4] (1R[B(Ar(F))4]; R = H, Me, Et; Ar(F) = C6H3-3,5-(CF3)2; Idipp = C[N(C6H3-2,6-iPr2)CH]2) as red to orange colored, highly air-sensitive solids, which were characterized by single-crystal X-ray diffraction, IR spectroscopy and multinuclear NMR spectroscopy. Dynamic NMR studies in solution revealed a degenerate isomerization (topomerization) of the "σ-bonded" tautomers of 1H[B(Ar(F))4], which proceeds according to quantum chemical calculations via a NHC-stabilized (NHC = N-heterocyclic carbene) disilahydronium ion ("π-bonded" isomer) and is reminiscent of the degenerate rearrangement of carbenium ions formed upon protonation of olefins. The topomerization of 1H[B(Ar(F))4] provides the first example of a reversible 1,2-H migration along a Si═Si bond observed in a molecular system.

Silicon(i) chemistry: the NHC-stabilised silicon(i) halides SiX(Idipp) (X = Br, I) and the disilicon(i)-iodido cation [Si(I)(Idipp)].

An efficient method for the synthesis of the NHC-stabilised Si(i) halides SiX(Idipp) (, X = Cl, Br, I; Idipp = C[N(CH-2,6-Pr)CH]) was developed, which involves the oxidation of Si(Idipp) () with 1,2-dihaloethanes. Halogenation of is a diastereoselective reaction leading exclusively to a racemic mixture of the and enantiomers of . Compounds and were characterised by single-crystal X-ray crystallography and multinuclear NMR spectroscopy, and their electronic structures were analysed by quantum chemical methods.

Si=P double bonds: experimental and theoretical study of an NHC-stabilized phosphasilenylidene.

An experimental and theoretical study of the first compound featuring a Si=P bond to a two-coordinate silicon atom is reported. The NHC-stabilized phosphasilenylidene (IDipp)Si=PMes* (IDipp=1,3-bis(2,6-diisopropylphenyl)imidazolin-2-ylidene, Mes*=2,4,6-tBu3 C6 H2 ) was prepared by SiMe3 Cl elimination from SiCl2 (IDipp) and LiP(Mes*)SiMe3 and characterized by X-ray crystallography, NMR spectroscopy, cyclic voltammetry, and UV/Vis spectroscopy. It has a planar trans-bent geometry with a short Si=P distance of 2.