Extreme statistics of complex random and quantum chaotic states

Complex random states have the statistical properties of the Gaussian and circular unitary ensemble eigenstates of random matrix theory. Even though their components are correlated by the normalization constraint, it is nevertheless possible to derive compact analytic formulas for their extreme values' statistical properties for all dimensionalities. The maximum intensity result slowly approaches the Gumbel distribution even though the variables are bounded, whereas the minimum intensity result rapidly approaches the Weibull distribution. Since random matrix theory is conjectured to be applicable to chaotic quantum systems, we calculate the extreme eigenfunction statistics for the standard map with parameters at which its classical map is fully chaotic. The statistical behaviors are consistent with the finite-N formulas.     

meta-Nitration of Arenes Bearing ortho/para Directing Group(s) Using C−H Borylation

Herein, we report the meta-nitration of arenes bearing ortho/para directing group(s) using the iridium-catalyzed C−H borylation reaction followed by a newly developed copper(II)-catalyzed transformation of the crude aryl pinacol boronate esters into the corresponding nitroarenes in a one-pot fashion. This protocol allows the synthesis of meta-nitrated arenes that are tedious to prepare or require multistep synthesis using the existing methods. The reaction tolerates a wide array of ortho/para-directing groups, such as −F, −Cl, −Br, −CH₃, −Et, −iPr −OCH₃, and −OCF₃. It also provides regioselective access to the nitro derivatives of π-electron-deficient heterocycles, such as pyridine and quinoline derivatives. The application of this method is demonstrated in the late-stage modification of complex molecules and also in the gram-scale preparation of an intermediate en route to the FDA-approved drug Nilotinib. Finally, we have shown that the nitro product obtained by this strategy can also be directly converted to the aniline or hindered amine through Baran's amination protocol.     

Bis-4,4′-biphenyl Ring Embedded Octaphyrin with Three Distinct Conformational Structures

Three distinct conformational structures of carbaoctaphyrins were prepared by incorporating bis-4,4'-biphenyl units in the macrocyclic core. The free-base form adopts a figure-eight conformation, whereas the protonation triggers a conformational change with a pyrrole ring inversion and acquires an open-framework structure. The insertion of bis-Rh^I metal ion in the macrocyclic core affords a singly twisted conformational structure. Furthermore, the local aromaticity in the bis-4,4'-biphenyl ring dominates the overall macrocyclic aromaticity in all three forms, and thus adopts nonaromatic characteristics. These results are supported by spectral as well as theoretical studies, and they are unambiguously confirmed by X-ray crystal analyses.     

Temperature dependence of the ESR spectra of Mn2+ in iron pyrite (FeS2)

The first observation of the ESR spectra of Mn²⁺, entering substitutionally for Fe²⁺ in the Van Vleck paramagnet FeS₂ (polycrystals), is reported. The data from 5 to 295 K fits the spin-Hamiltonian $\text{h}{}_{\mathrm{s}}\text{= gβ}\text{H}\text{·}\text{S}$ + $\text{[S}{}^{\mathrm{<mtext>2</mtext>}}{}_{\mathrm{z}}\text{?}\text{1}\text{3}\text{S(S + 1)] + A}\text{S}\text{·}\text{I}$, with g = 2.000 ± 0.001, A/β = ?95.0 ± 0.5 Oe and D/β varying from 50 Oe (5K) to 59 Oe (295 K). The temperature dependence of D can be described in terms of a single phonon-mode with frequency ? 145 cm^?1.     

Elastic constants of sodium chlorate from 77 K to 350 K

The elastic constantsC ₁₁,C ₁₂ andC ₄₄ of sodium chlorate single crystal have been evaluated using 10 MHz ultrasonic pulse echo superposition technique. The values areC ₁₁=4.90,C ₁₂=1.39,C ₄₄=1.17 (× 10¹⁰ N/m ²) at 298 K and 6.15, 2.16, 1.32 (×10¹⁰ N/m ²) at 77 K. The data agree well with the values measured earlier up to 223 K. Brief mention is also made of the low temperature bonding problems in these soft crystals.     

The elastic constants of isomorphous sodium bromate and sodium chlorate from 77 to 350 K

The elastic constants of NaBrO₃ and NaClO₃ are evaluated from ultrasonic velocity measurements using pulse superposition techniques. The values of C₁₁, C₁₂ and C₄₄ for NaBrO₃ at 298°K are 5.57₈, 1.70₅, 1.51₀ (x 10¹⁰ N/m²) and for NaClO₃ the values are 4.89₇, 1.38₉, 1.17₄. The values at 77°K are respectively 6.35, 1.98 and 1.65 for NaBrO₃ and 6.15, 2.16 and 1.32 for NaClO₃.     

Reliability analysis of a three unit warm standby redundant system with repair

Two-unit warm standby redundant systems have been investigated extensively in the past. The most general model is the one in which both the lifetime and repair time distributions of the units are arbitrary. However the study of standby systems with more than two units, though very important, has received much less attention, possibly because of the built-in difficulties in analyzing them. Such systems have been studied only when either the lifetime or the repair time is exponentially distributed. When both these distributions are general, the problem appears to be intractable even in the case of cold standby systems. The present contribution is an improvement in the state of art in the sense that a three unit warm standby system is shown to be capable of comprehensive analysis. In particular we show that there are imbedded renewal points that render the analysis possible. Using these imbedded renewal points we obtain the reliability and availability functions. Emeritus Deceased 23rd December 2003.     

First direct kinetic measurement of i-C4H5 (CH2CHCCH2) + O2 reaction: Toward quantitative understanding of aromatic ring formation chemistry

The kinetics of the i-C₄H₅ (buta-1,3-dien-2-yl) radical reaction with molecular oxygen has been measured over a wide temperature range (275–852 K) at low pressures (0.8–3 Torr) in direct, time-resolved experiments. The measurements were performed using a laminar flow reactor coupled to photoionization mass spectrometer (PIMS), and laser photolysis of either chloroprene (2-chlorobuta-1,3-diene) or isoprene was used to produce the resonantly stabilized i-C₄H₅ radical. Under the experimental conditions, the measured bimolecular rate coefficient of i-C₄H₅ + O₂ reaction is independent of bath gas density and exhibits weak, negative temperature dependency, and can be described by the expression k₃ = (1.45 ± 0.05) × 10^?12 × (T/298 K)^{?(0.13±0.05)} cm³ s^?1. The measured bimolecular rate coefficient is surprisingly fast for a resonantly stabilized radical. Under combustion conditions, the reactions of i-C₄H₅ radical with ethylene and acetylene are believed to play an important role in forming the first aromatic ring. However, the current measurements show that i-C₄H₅ + O₂ reaction is significantly faster under combustion conditions than previous estimations suggest and, consequently, inhibits the soot forming propensity of i-C₄H₅ radicals. The bimolecular rate coefficient estimates used for the i-C₄H₅ + O₂ reaction in recent combustion simulations show significant variation and are up to two orders of magnitude slower than the current, measured value. All estimates, in contrast to our measurements, predict a positive temperature dependency. The observed products for the i-C₄H₅ + O₂ reaction were formaldehyde and ketene. This is in agreement with the one theoretical study available for i-C₄H₅ + O₂ reaction, which predicts the main bimolecular product channels to be H₂CO + C₂H₃ + CO and H₂CCO + CH₂CHO.     

Determination of signs of hyperfine coupling constants for an S = ½ system through E.P.R., ENDOR and double ENDOR

A systematic method of obtaining relative signs of hyperfine coupling constants is described. It applies to systems consisting of (a) a set of one or more nuclei coupled fairly strongly to the electron spin, and possessing a two-fold (or higher) axis of symmetry, together with (b) a set of weakly coupled nuclei defining superhyperfine transitions. ENDOR measurements for several E.P.R. hyperfine transitions, with the field oriented along the symmetry axis, give relative signs of hyperfine components for this direction. Signs for the other directions can then be obtained through ENDOR measurements on a single hyperfine transition at various field orientations. Additional double ENDOR measurements may be necessary for very weakly coupled nuclei. This method can complement double ENDOR studies in favourable cases. It is illustrated by the determination of signs of coupling constants of protons and of ⁷⁵As in the AsO₄ ^4- radical in KH₂AsO₄.     

Persistence of manifolds in nonequilibrium critical dynamics

We study the persistence probability P(t) that, starting from a random initial condition, the magnetization of a d'-dimensional manifold of a d-dimensional spin system at its critical point does not change sign up to time t. For d'>0 we find three distinct late-time decay forms for P(t): exponential, stretched exponential, and power law, depending on a single parameter zeta=(D-2+eta)/z, where D=d-d' and eta,z are standard critical exponents. In particular, we predict that for a line magnetization in the critical d=2 Ising model, P(t) decays as a power law while, for d=3, P(t) decays as a power of t for a plane magnetization but as a stretched exponential for a line magnetization. Numerical results are consistent with these predictions.