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.     

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.     

Electrochemistry of uranium in ionic organic media: Ethylammonium nitrate and acetamide-KSCN eutectic

The electrochemical reduction of hexavalent and tetravalent uranium is investigated in ethylammonium nitrate at 298 K and in the acetamide-KSCN eutectic at 400 K. The transient techniques describe a two-step reduction of UO ₂ ²⁺ in acetamide-KSCN while only one step is observed in ethylammonium nitrate. The reduction of tetravalent uranium proceeds in one step giving trivalent uranium in the two media. In any cases, additional kinetic phenomena are the source of difficulties for the understanding of the reactions. In controlled potential electrolysis, side-reactions between the reduced species and the solvent impede completely the mechanism foreseen by transient methods.     

Living ring-opening metathesis polymerization of norbornenes bay-functionalized perylene diimides

Ring-opening metathesis polymerization (ROMP)-derived poly(oxanorbornene imide)s bearing bay-linked mono - alkoxy -M1 and 1,7-di-alkoxy M2 functionalized perylene diimides (PDIs) were synthesized using Grubb's third ( G3 ) and Hoveyda-Grubbs second generation ( HG2 ) ruthenium-alkylidene metathesis initiators. The mono-alkoxy-derived PDI-based non-ladderphane polymer poly M1 displayed 67% to 77% of the trans olefin content in the polymer chain depending on the initiator used for the polymerization. When using the symmetrical 1,7-di-alkoxy-derived PDI-based polymer poly M2 having the ladderphane type-structure, this displayed a significant amount of cis and trans olefin contents in the polymer chains, irrespective of the type of initiators used for the polymerization. ROMP of both monomers M1 and M2 proceeded in a well-controlled manner with a linear dependence of molecular weight on the monomer/initiator ratio using G3 as initiator. Optical properties of the ladderphane-based poly M2 and non-ladderphane-based poly M1 were characterized in both solution and the film state. X-ray diffraction (XRD) analysis for all the polymers showed significant π-stacking in the thin film state with ordered molecular packing and closer values of d-spacing for both poly M1 and poly M2 . Film morphology examined by AFM elucidated homogenous smooth polymer surface for both polymers in general, but with some irregularities observed for poly M1 . In addition, CV analysis revealed both polymers could be good candidates as electron-accepting materials, with excellent film-forming ability, and thermal stability.     

Three‐Component Self‐Assembly of a Series of Triply Interlocked Pd12 Coordination Prisms and Their Non‐Interlocked Pd6 Analogues

Template‐assisted formation of multicomponent Pd₆ coordination prisms and formation of their self‐templated triply interlocked Pd₁₂ analogues in the absence of an external template have been established in a single step through Pd? N/Pd? O coordination. Treatment of cis‐[Pd(en)(NO₃)₂] with K₃tma and linear pillar 4,4′‐bpy (en=ethylenediamine, H₃tma=benzene‐1,3,5‐tricarboxylic acid, 4,4′‐bpy=4,4′‐bipyridine) gave intercalated coordination cage [{Pd(en)}₆(bpy)₃(tma)₂]₂[NO₃]₁₂ ( 1 ) exclusively, whereas the same reaction in the presence of H₃tma as an aromatic guest gave a H₃tma‐encapsulating non‐interlocked discrete Pd₆ molecular prism [{Pd(en)}₆(bpy)₃(tma)₂(H₃tma)₂][NO₃]₆ ( 2 ). Though the same reaction using cis‐[Pd(NO₃)₂(pn)] (pn=propane‐1,2‐diamine) instead of cis‐[Pd(en)(NO₃)₂] gave triply interlocked coordination cage [{Pd(pn)}₆(bpy)₃(tma)₂]₂[NO₃]₁₂ ( 3 ) along with non‐interlocked Pd₆ analogue [{Pd(pn)}₆(bpy)₃(tma)₂](NO₃)₆ ( 3′ ), and the presence of H₃tma as a guest gave H₃tma‐encapsulating molecular prism [{Pd(pn)}₆(bpy)₃(tma)₂(H₃tma)₂][NO₃]₆ ( 4 ) exclusively. In solution, the amount of 3′ decreases as the temperature is decreased, and in the solid state 3 is the sole product. Notably, an analogous reaction using the relatively short pillar pz (pz=pyrazine) instead of 4,4′‐bpy gave triply interlocked coordination cage [{Pd(pn)}₆(pz)₃(tma)₂]₂[NO₃]₁₂ ( 5 ) as the single product. Interestingly, the same reaction using slightly more bulky cis‐[Pd(NO₃)₂(tmen)] (tmen=N,N,N′,N′‐tetramethylethylene diamine) instead of cis‐[Pd(NO₃)₂(pn)] gave non‐interlocked [{Pd(tmen)}₆(pz)₃(tma)₂][NO₃]₆ ( 6 ) exclusively. Complexes 1 , 3 , and 5 represent the first examples of template‐free triply interlocked molecular prisms obtained through multicomponent self‐assembly. Formation of the complexes was supported by IR and multinuclear NMR (¹H and ¹³C) spectroscopy. Formation of guest‐encapsulating complexes ( 2 and 4 ) was confirmed by 2D DOSY and ROESY NMR spectroscopic analyses, whereas for complexes 1 , 3 , 5 , and 6 single‐crystal X‐ray diffraction techniques unambiguously confirmed their formation. The gross geometries of H₃tma‐encapsulating complexes 2 and 4 were obtained by universal force field (UFF) simulations.