Structure, conformation, stereodynamics, dimer formation, and absolute configuration of axially chiral atropisomers of hindered biphenyl carbinols

NMR spectra of biphenyl derivatives bearing a single CR2OH substituent in the ortho position indicate that they exist as sp (more stable) and ap (less stable) conformers, due to the restricted rotation about the Ar-CR2OH bond. When R = Et (compound 2) the corresponding rotation barrier was determined (7.5 kcal mol-1) by line shape simulation of the low-temperature NMR spectra. Introduction of the prochiral i-Pr group in the position 3' of a biphenyl with the CMe2OH substituent in the position 2 (4) allowed the determination of the enantiomerization barrier (due to the Ar-Ar bond rotation) for the stereolabile axially chiral atropisomers (13.95 kcal mol(-1)). DFT computations of these barriers were all in agreement with the experiments. Biphenyls bearing two CR2OH groups in the 2,2' positions were found to exist as configurationally stable atropisomers: when R = Me (7) they were separated by enantioselective HPLC and the absolute configuration assigned on the basis of the corresponding CD spectra. In solution, compounds 6 (R = H) and 7 (R = Me) were found to originate a dimer, due to H-bond interactions between two enantiomers. In the case of 7, the free energy of activation (9.5 kcal mol-1) for the exchange of the monomer with the dimer could be measured, for the first time, by dynamic NMR. The conformational preferences, predicted by computations for the biphenyls with two CR2OH substituents in the 2,2' positions, were confirmed by X-ray diffraction in the case of R = H (6), R = Me (7), and R = i-Pr (9).     

Conformation and stereodynamics of symmetrically ortho-disubstituted aryl carbinols and aryl ethers

By making use of low-temperature dynamic NMR spectroscopy, the rotation barriers about the sp3-sp2 bond have been determined in a number of hindered benzyl alcohols symmetrically substituted in the ortho positions, the substituents being F, Cl, Br, and Me. The free energies of activation covered the range 4.6-10.1 kcal mol-1. Ab initio computations matched satisfactorily the trend of these values and predicted the conformation adopted by these compounds. In one case, this result could be also confirmed by the X-ray diffraction structure. In the case of the corresponding methyl ethers two barriers could be measured, corresponding to the passage across two distinguishable transition states: the higher barriers covered the range 5.0-8.1 kcal mol-1 and the lower ones the range 4.7-6.2 kcal mol-1.     

Crotylation versus propargylation: two routes for the synthesis of the C13-C18 fragment of the antibiotic branimycin

The C13-C18 fragment 3 of the novel antibiotic branimycin was prepared along two highly stereocontrolled routes. The first one uses a standard Roush crotylation protocol, whereas the second one proceeds via an allenyl silane propargylation with unexpected stereochemical consequences, which are discussed in detail.     

Nonlinear response of SDOF systems under combined deterministic and random excitations

Dynamical systems subjected to random excitations exhibit non-linear behavior for sufficiently large motion. The multiple time scale method has been extensively utilized in the framework of non-linear deterministic analysis to obtain two averaged first-order differential equations describing the slow time scale modulation of amplitude and phase response. In this paper the multiple time scale method, opportunely modified to take properly into account the correlation structure of the stochastic input process, is adopted to derive a stochastic frequency-response relationship involving the response amplitude statistics and the input power spectral density. A low-intensity noise is assumed to separate the strong mean motion from its weak fluctuations. The moment differential equations of phase and amplitude are derived and a linearization technique applied to evaluate the second order statistics. The theory is validated through digital simulations on a nonlinear single degree of freedom model for the transversal oscillation of a cantilever beam with tip force and to a Duffing-Rayleigh oscillator, to analyze non-linear damping effects.     

Minimum weight limit design under uncertainty

Summary The problem of probabilistic minimum weight limit design is formulated as a stochastic programming problem. The theoretical treatment considers monodimensional structures, geometrical parameters and integer design variables. An algorithm is proposed and illustrated for the case of pin-jointed structures with two random continuous variables. The paper follows previous researches of the Authors in the field of probabilistic approach to structural safety [29 ÷ 33].

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Sommario Il problema della progettazione a rottura per minimo peso su basi probabilistiche viene formulato quale problema di programmazione stocastica. La trattazione teorica si estende alle strutture monodimensionali, comprende variabili di tipo geometrico nonchè variabili intere: l'algoritmo proposto ed illustrato per la risoluzione numerica riguarda le strutture reticolari interessate da due variabili casuali continue. Il lavoro fa seguito a precedenti ricerche degli scriventi in tema di concezione probabilistica della sicurezza [29 ÷ 33].

     

Corrections for underresolved scalar measurements in turbulent flows using a DNS database

We estimate the effect of finite spatial resolution of a probe for scalar measurements, using a database from direct numerical simulations (DNS). These are for homogeneous isotropic turbulence in temporal decay, Schmidt number unity, and low Taylor-microscale Reynolds number (≃27–42). The probe could be a cold wire for measuring temperature in a turbulent flow. Correction factors for the scalar variance, scalar dissipation rate, and mixed velocity-scalar derivative skewness are estimated, for a sensor length up to 15 times the Batchelor length scale. It is shown that the lack of resolution yields the largest attenuation on the dissipation rate, followed by the scalar variance. On the contrary, the mixed skewness, which is affected the least, is overestimated. Further, it is shown that if one estimates the mixed skewness via the scalar variance dynamical equation and neglects the term involving the time derivative of the scalar energy spectrum, large errors in the correction factor of the mixed skewness are introduced. Finally, it is found that correction factors obtained assuming Kraichnan scalar model spectrum and following Wyngaard (in Phys Fluids 14:2052–2054, 1971) approach are close to those from the DNS.     

Time Fractional Diffusion: A Discrete Random Walk Approach

The time fractional diffusion equation is obtained from the standarddiffusion equation by replacing the first-order time derivative with afractional derivative of order (0, 1). From a physicalview-point this generalized diffusion equation is obtained from afractional Fick law which describes transport processes with longmemory. The fundamental solution for the Cauchy problem is interpretedas a probability density of a self-similar non-Markovian stochasticprocess related to a phenomenon of slow anomalous diffusion. By adoptinga suitable finite-difference scheme of solution, we generate discretemodels of random walk suitable for simulating random variables whosespatial probability density evolves in time according to this fractionaldiffusion equation.     

Homogenization limit for electrical conduction in biological tissues in the radio-frequency rangeLimite d'homogénéisation pour la conduction électrique dans les tissus biologiques dans le domaine des radiofréquences

We study an evolutive model for electrical conduction in biological tissues, where the conductive intra-cellular and extracellular spaces are separated by insulating cell membranes. The mathematical scheme is an elliptic problem, with dynamical boundary conditions on the cell membranes. The problem is set in a finely mixed periodic medium. We show that the homogenization limit u₀ of the electric potential, obtained as the period of the microscopic structure approaches zero, solves the equation $\text{?}\text{div}\text{(σ}{}_0\text{?}{}_{\mathrm{x}}\text{u}{}_0\text{+A}{}^0\text{?}{}_{\mathrm{x}}\text{u}{}_0\text{+∫}{}_0{}^{\mathrm{t}}\text{A}{}^1\text{(t?τ)?}{}_{\mathrm{x}}\text{u}{}_0\text{(x,τ)}\text{d}\text{τ?}\text{F}\text{(x,t))=0}$ where σ₀>0 and the matrices A⁰, A¹ depend on geometric and material properties, while the vector function $\text{F}$ keeps trace of the initial data of the original problem. Memory effects explicitly appear here, making this elliptic equation of non standard type. To cite this article: M. Amar et al., C. R. Mecanique 331 (2003).     

Direct Evidence for a Peroxide Intermediate and a Reactive Enzyme–Substrate–Dioxygen Configuration in a Cofactor‐free Oxidase

Cofactor‐free oxidases and oxygenases promote and control the reactivity of O₂ with limited chemical tools at their disposal. Their mechanism of action is not completely understood and structural information is not available for any of the reaction intermediates. Near‐atomic resolution crystallography supported by in crystallo Raman spectroscopy and QM/MM calculations showed unambiguously that the archetypical cofactor‐free uricase catalyzes uric acid degradation via a C5(S)‐(hydro)peroxide intermediate. Low X‐ray doses break specifically the intermediate C5? OO(H) bond at 100 K, thus releasing O₂ in situ, which is trapped above the substrate radical. The dose‐dependent rate of bond rupture followed by combined crystallographic and Raman analysis indicates that ionizing radiation kick‐starts both peroxide decomposition and its regeneration. Peroxidation can be explained by a mechanism in which the substrate radical recombines with superoxide transiently produced in the active site.