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. In the low-speed limit of a static spin lattice, we find purely conductive spreading, reminiscent of heat transfer. Swarm motility and heterogeneity can break reciprocity and spin conservation. But what seems more consequential for the swarm response is that the dispersion relation acquires a significant convective contribution along the leader's direction of motion.

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. A growing delay time initially facilitates but ultimately impedes collective ordering and turns the dynamical scaling from diffusive to ballistic. It provides an alternative explanation of swarm traits previously attributed to inertia.

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. In contrast, 1Me[B(Ar(F))4] adopts a "rigid" structure in solution due to the higher energy required for the interconversion of the "σ-bonded" isomer into a putative NHC-stabilized disilamethonium ion. Addition of alkali metal borates to 1 afforded the alkali metal disilicon(0) borates 1M[BAr4] (M = Li, Ar = C6F5; M = Na, Ar = Ar(F)) as brown, air-sensitive solids. Single-crystal X-ray diffraction analyses and NMR spectroscopic studies of 1M[BAr4] suggest in concert with quantum chemical calculations that encapsulation of the alkali metal cations in the cavity of 1 predominantly occurs via electrostatic cation-π interactions with the Si═Si π-bond and the peripheral NHC aryl rings. Displacement of the [Si(NHC)] fragments by the isolobal fragments [PR] and [SiR](-) interrelates the cations [(NHC)(R)Si═Si(NHC)](+) to a series of familiar, multiply bonded Si and P compounds as verified by analyses of their electronic structures.

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 2.1188(7)Å and acute bonding angles at Si (96.90(6)°) and P (95.38(6)°). The bonding parameters indicate the presence of a Si=P bond with a lone electron pair of high s-character at Si and P, in agreement with natural bond orbital (NBO) analysis. Comparative cyclic voltammetric and UV/Vis spectroscopic experiments of this compound, the disilicon(0) compound (IDipp)Si=Si(IDipp), and the diphosphene Mes*P=PMes* reveal, in combination with quantum chemical calculations, the isolobal relationship of the three double-bond systems.

Silicon(i) chemistry: the NHC-stabilised silicon(i) halides Si2X2(Idipp)2 (X = Br, I) and the disilicon(i)-iodido cation [Si2(I)(Idipp)2].

An efficient method for the synthesis of the NHC-stabilised Si(i) halides Si2X2(Idipp)2 (2-X, X = Cl, Br, I; Idipp = C[N(C6H3-2,6-iPr2)CH]2) was developed, which involves the oxidation of Si2(Idipp)2 (1) with 1,2-dihaloethanes. Halogenation of 1 is a diastereoselective reaction leading exclusively to a racemic mixture of the RR and SS enantiomers of 2-X. Compounds 2-Br and 2-I were characterised by single-crystal X-ray crystallography and multinuclear NMR spectroscopy, and their electronic structures were analysed by quantum chemical methods. Dynamic NMR spectroscopy unraveled a fluxional process of 2-Br and 2-I in solution, which involved a hindered rotation of the NHC groups about the Si-CNHC bonds. Iodide abstraction from 2-I by [Li(Et2O)2.5][B(C6F5)4] selectively afforded the disilicon(i) salt [Si2(I)(Idipp)2][B(C6F5)4] (3). X-ray crystallography and variable-temperature NMR spectroscopy of 3 in combination with quantum chemical calculations shed light on the ground-state geometric and electronic structure of the [Si2(I)(Idipp)2]+ ion, which features a Si[double bond, length as m-dash]Si bond between a trigonal planar coordinated SiII atom with a Si-I bond and a two-coordinate Si0 center carrying a lone pair of electrons. The dynamics of the [Si2(I)(Idipp)2]+ ion were studied in solution by variable-temperature NMR spectroscopy and they involve a topomerisation, which proceeds according to quantum theory via a disilaiodonium intermediate ("π-bonded" isomer) and exchanges the two heterotopic Si sites.