Multiscale variety in complex systems

The Law of Requisite Variety is a mathematical theorem relating the number of control states of a system to the number of variations in control that is necessary for effective response. The Law of Requisite Variety does not consider the components of a system and how they must act together to respond effectively. Here we consider the additional requirement of scale of response and the effect of coordinated versus uncoordinated response as a key attribute of complex systems. The components of a system perform a task, with a number of such components needed to act in concert to perform subtasks. We apply the resulting generalization—a Multiscale Law of Requisite Variety—to understanding effective function of complex biological and social systems. This allows us to formalize an understanding of the limitations of hierarchical control structures and the inadequacy of central control and planning in the solution of many complex social problems and the functioning of complex social organizations, e.g., the military, healthcare, and education systems. © 2004 Wiley Periodicals, Inc. Complexity 9: 37–45, 2004     

Femtosecond dynamics of secondary radiation formation from quantum well excitons

The time-resolved secondary emission of resonantly created excitons in GaAs quantum wells is studied using femtosecond up-conversion spectroscopy. The behaviour of the rise and decay of the secondary emission and reflectivity in quantum wells is strongly dependent upon the disorder at the interfaces, the exciton density and the temperature. In the case of low densities and temperatures the emission is independent of the exciton density and rises quadratically in time, in excellent agreement with recent theory for Rayleigh scattering from two-dimensional excitons subjected to disorder. These rise times are compared directly with times measured by time-integrated four-wave mixing (FWM). The comparison of the dynamics displayed in time-resolved secondary radiation and time-integrated FWM provide a clear understanding of the coherence properties of QW excitons in the first few picoseconds after excitation. High-contrast oscillations that are due to quantum beats between the heavy- and light-hole 1s-states are seen. The visibility decay at very low densities is long ps and is related to the action of potential fluctuations on the scattering of heavy-hole and light-hole excitons.     

High-frequency (140-GHz) time domain EPR and ENDOR spectroscopy: the tyrosyl radical-diiron cofactor in ribonucleotide reductase from yeast

High-frequency pulsed EPR and ENDOR have been employed to characterize the tyrosyl radical (Y*)-diiron cofactor in the Y2-containing R2 subunit of ribonucleotide reductase (RNR) from yeast. The present work represents the first use of 140-GHz time domain EPR and ENDOR to examine this system and demonstrates the capabilities of the method to elucidate the electronic structure and the chemical environment of protein radicals. Low-temperature spin-echo-detected EPR spectra of yeast Y* reveal an EPR line shape typical of a tyrosyl radical; however, when compared with the EPR spectra of Y* from E. coli RNR, a substantial upfield shift of the g(1)-value is observed. The origin of the shift in g(1) was investigated by 140-GHz (1)H and (2)H pulsed ENDOR experiments of the Y2-containing subunit in protonated and D(2)O-exchanged buffer. (2)H ENDOR spectra and simulations provide unambiguous evidence for one strongly coupled (2)H arising from a bond between the radical and an exchangeable proton of an adjacent residue or a water molecule. Orientation-selective 140-GHz ENDOR spectra indicate the direction of the hydrogen bond with respect to the molecular symmetry axes and the bond length (1.81 A). Finally, we have performed saturation recovery experiments and observed enhanced spin lattice relaxation rates of the Y* above 10 K. At temperatures higher than 20 K, the relaxation rates are isotropic across the EPR line, a phenomenon that we attribute to isotropic exchange interaction between Y* and the first excited paramagnetic state of the diiron cluster adjacent to it. From the activation energy of the rates, we determine the exchange interaction between the two irons of the cluster, J(exc) = -85 cm(-)(1). The relaxation mechanism and the presence of the hydrogen bond are discussed in terms of the differences in the structure of the Y*-diiron cofactor in yeast Y2 and other class I R2s.     

S)-(+)-2-(p-tolylsulfinyl)-2-buten-4-olide: an enantiomerically pure Michael acceptor for asymmetric synthesis of 3-substituted 4-butanolides. (—)-podorhizon.

A short, reliable, and practical synthesis of ($\text{S}$)-(+)-2-($\text{p}$-tolylsulfinyl)-2-buten-4-olide has been developed, and the utility of this Michael acceptor for highly enantiocontrolled synthesis of 3-substituted 4-butanolides has been demonstrated.     

Crystallization kinetic studies: A means to evaluate time-temperature-transformation curves. Application to metallic glasses

It is shown that the study of the kinetics of crystallization of an amorphous alloy may be used to obtain the correct form of the low temperature part of the time-temperature-transformation (T-T-T) curves. A unified review of the current kinetics of crystallization studies is presented and the general kinetic equation which gives the reaction rate as a function of temperature and crystalline fraction is shown to contain information related to theT-T-T-curves. Finally examples of application to two metallic glasses, Nd₃Fe₇₇B₂₀ and Fe_67.5Co₁₅Nb_1.5B₁₆, obtained by rapid solidification techniques are presented. The comparison between theory and experiment is satisfactory.

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Zusammenfassung Es wird gezeigt, daß die Untersuchung der Kristallisationskinetik von amorphen Legierungen genutzt werden kann, die korrekte Form des Niedertemperaturbereiches der Zeit-Temperatur-Transformation (T-T-T) Kurven zu erhalten. Es wird ein einheitlicher Überblick über die jüngsten Untersuchungen von Kristallisationskinetiken gegeben und an der allgemeinen Gleichung der Reaktionsgeschwindigkeit als eine Funktion von Temperatur und Kristallanteil wird gezeigt, daß sie Informationen bezüglich der T-T-T-Kurven beinhaltet. Letztlich wird eine Anwendung an zwei, durch schnelles Erstarren gewonnenen metallischen Gläsern Nd₃Fe₇₇B₂₀ und Fe_67.5Co₁₅Nb_1.5B₁₆ dargelegt. Zwischen Theorie und Praxis konnte eine ausreichende Übereinstimmung festgestellt werden.

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Dedicated to Professor Dr. H. J. Seifert on the occasion of his 60^th birthday

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This work was supported by the Comision Interdepartamental de Cienca y Tecnologia, CICYT (project No. MAT88-0439) which are acknowledged.     

Real-time measurement and control of particle-number density and size of the detonation products of lead azide

Time-resolved measurement and modeling of the number density and size of lead particles produced following the detonation of Lead Azide (LA) are presented. Particles expanding freely into vacuum through a supersonic nozzle or interacting with a barrier placed above the LA sample are monitored via attenuation of laser beams at 0.67, 1.3 and 10.6 µm. The attenuation depends on the conditions of expansion, but is always much more pronounced at 0.67 µm and 1.3 µm. From the ratio between the attenuations at 0.67 µm and 10.6 µm, the radius and number density of the particles are calculated applying Beer's law and Mie's theory. It is found that 20–90 µs following the detonation the attenuation at 32–36 mm above the LA sample is due to particles with radii of 0.9, 0.7 and 0.1 µm for free expansion into vacuum through the nozzle or near the barrier, respectively. Also, the expansion through the nozzle results in a transparent medium above the nozzle exit for the first few µs following the detonation. The effect of the nozzle is attributed to the fact that the velocity of the expanding detonation products is supersonic, which leads to compression and heating in the throat region, in contrast to the more familiar phenomenon of cooling at subsonic velocities. The dynamics of particles expanding under the different conditions and the mechanism of size reduction and elimination of particles is discussed.     

An anion-dependent switch in selectivity results from a change of C-H activation mechanism in the reaction of an imidazolium salt with IrH5(PPh3)2

Changing the counteranion along the series Br, BF4, PF6, SbF6 in their ion-paired 2-pyridylmethyl imidazolium salts causes the kinetic reaction products with IrH5(PPh3)2 to switch from chelating N-heterocyclic carbenes (NHCs) having normal C2 (N path) to abnormal C5 binding (AN path). Computational work (DFT) suggests that the AN path involves C-H oxidative addition to Ir(III) to give Ir(V) with little anion dependence. The N path, in contrast, goes by heterolytic C-H activation with proton transfer to the adjacent hydride. The proton that is transferred is accompanied by the counteranion in an anion-coupled proton transfer, leading to an anion dependence of the N path, and therefore of the N/AN selectivity. The N path goes via Ir(III), not Ir(V), because the normal NHC is a much less strong donor ligand than the abnormal NHC. PGSE NMR experiments support the formation of ion-pair in both the reactants and the products. 19F,1H-HOESY NMR experiments indicate an ion-pair structure for the products that is consistent with the computational prediction (ONIOM(B3PW91/UFF)).     

Synthesis of unstrained Criegee intermediates: inverse α-effect and other protective stereoelectronic forces can stop Baeyer–Villiger rearrangement of γ-hydroperoxy-γ-peroxylactones

How far can we push the limits in removing stereoelectronic protection from an unstable intermediate? We address this question by exploring the interplay between the primary and secondary stereoelectronic effects in the Baeyer–Villiger (BV) rearrangement by experimental and computational studies of γ-OR-substituted γ-peroxylactones, the previously elusive non-strained Criegee intermediates (CI). These new cyclic peroxides were synthesized by the peroxidation of γ-ketoesters followed by in situ cyclization using a BF₃·Et₂O/H₂O₂ system. Although the primary effect (alignment of the migrating C–R_m bond with the breaking O–O bond) is active in the 6-membered ring, weakening of the secondary effect (donation from the OR lone pair to the breaking C–R_m bond) provides sufficient kinetic stabilization to allow the formation and isolation of stable γ-hydroperoxy-γ-peroxylactones with a methyl-substituent in the C6-position. Furthermore, supplementary protection is also provided by reactant stabilization originating from two new stereoelectronic factors, both identified and quantified for the first time in the present work. First, an unexpected boat preference in the γ-hydroperoxy-γ-peroxylactones weakens the primary stereoelectronic effects and introduces a ∼2 kcal mol⁻¹ Curtin–Hammett penalty for reacquiring the more reactive chair conformation. Second, activation of the secondary stereoelectronic effect in the TS comes with a ∼2–3 kcal mol⁻¹ penalty for giving up the exo-anomeric stabilization in the 6-membered Criegee intermediate. Together, the three new stereoelectronic factors (inverse α-effect, misalignment of reacting bonds in the boat conformation, and the exo-anomeric effect) illustrate the richness of stereoelectronic patterns in peroxide chemistry and provide experimentally significant kinetic stabilization to this new class of bisperoxides. Furthermore, mild reduction of γ-hydroperoxy-γ-peroxylactone with Ph₃P produced an isolable γ-hydroxy-γ-peroxylactone, the first example of a structurally unencumbered CI where neither the primary nor the secondary stereoelectronic effect are impeded. Although this compound is relatively unstable, it does not undergo the BV reaction and instead follows a new mode of reactivity for the CI – a ring-opening process.

Protecting stereoelectronic effects prevent Baeyer–Villiger rearrangement and stabilize γ-OX-γ-peroxylactones (X = H, OH), the previously elusive non-strained Criegee intermediates.