Optically probing the fine structure of a single Mn atom in an InAs quantum dot

We report on the optical spectroscopy of a single InAs/GaAs quantum dot doped with a single Mn atom in a longitudinal magnetic field of a few Tesla. Our findings show that the Mn impurity is a neutral acceptor state A0 whose effective spin J=1 is significantly perturbed by the quantum dot potential and its associated strain field. The spin interaction with photocarriers injected in the quantum dot is shown to be ferromagnetic for holes, with an effective coupling constant of a few hundreds of mueV, but vanishingly small for electrons.     

Stability and exponential convergence for the Boltzmann equation

We prove existence, uniqueness and stability for solutions of the nonlinear Boltzmann equation in a periodic box in the case when the initial data are sufficiently close to a spatially homogeneous function. The results are given for a range of spaces, including L ¹, and extend previous results in L for the non-homogeneous equation, as well as the more developed L ^p -theory for the spatially homogeneous Boltzmann equation.We also give new L -estimates for the spatially homogeneous equation in the case of Maxwellian interactions.     

Ansa‐Bridged Bis(benzene) Titanium Complexes

Taking advantage of an improved synthesis of [Ti(η⁶‐C₆H₆)₂], we report here the first examples of ansa‐bridged bis(benzene) titanium complexes. Deprotonation of [Ti(η⁶‐C₆H₆)₂] with nBuLi in the presence of N,N,N′,N′′,N′′‐pentamethyldiethylenetriamine (pmdta) leads to the corresponding 1,1′‐dilithio salt [Ti(η⁶‐C₆H₅Li)₂] ? pmdta that enables the preparation of the first one‐ and two‐atom‐bridged complexes by simple salt metathesis. The ansa complexes were fully characterized (NMR spectroscopy, UV/Vis spectroscopy, elemental analysis, and X‐ray crystallography) and further studied electrochemically and computationally. Moreover, [Ti(η⁶‐C₆H₆)₂] is found to react with the Lewis base 1,3‐dimethylimidazole‐2‐ylidene (IMe) to give the bent sandwich complex [Ti(η⁶‐C₆H₆)₂(IMe)].     

On Stability and Strong Convergence for the Spatially Homogeneous Boltzmann Equation for Fermi-Dirac Particles

 The paper considers the stability and strong convergence to equilibrium of solutions to the spatially homogeneous Boltzmann equation for Fermi-Dirac particles. Under a cutoff condition on the collision kernel, we prove a strong stability in L ¹ topology at any finite time interval, and, for hard and Maxwellian potentials, we prove that the solutions converge strongly in L ¹ to equilibrium under a high temperature condition. The basic tools used are moment-production estimates and the strong compactness of the collision gain term. (Accepted 25, October 2002) Published online March 14, 2003 Communicated by P.-L. Lions     

Detection of formate, rather than carbon monoxide, as the stoichiometric coproduct in conversion of fatty aldehydes to alkanes by a cyanobacterial aldehyde decarbonylase

The second of two reactions in a recently discovered pathway through which saturated fatty acids are converted to alkanes (and unsaturated fatty acids to alkenes) in cyanobacteria entails scission of the C1-C2 bond of a fatty aldehyde intermediate by the enzyme aldehyde decarbonylase (AD), a ferritin-like protein with a dinuclear metal cofactor of unknown composition. We tested for and failed to detect carbon monoxide (CO), the proposed C1-derived coproduct of alkane synthesis, following the in vitro conversion of octadecanal (R-CHO, where R = n-C(17)H(35)) to heptadecane (R-H) by the Nostoc punctiforme AD isolated following its overproduction in Escherichia coli. Instead, we identified formate (HCO(2)(-)) as the stoichiometric coproduct of the reaction. Results of isotope-tracer experiments indicate that the aldehyde hydrogen is retained in the HCO(2)(-) and the hydrogen in the nascent methyl group of the alkane originates, at least in part, from solvent. With these characteristics, the reaction appears to be formally hydrolytic, but the improbability of a hydrolytic mechanism having the primary carbanion as the leaving group, the structural similarity of the ADs to other O(2)-activating nonheme di-iron proteins, and the dependence of in vitro AD activity on the presence of a reducing system implicate some type of redox mechanism. Two possible resolutions to this conundrum are suggested.     

Optimization of preparative chromatographic separation of multiple rare earth elements

This work presents a method to optimize multi-product chromatographic systems with multiple objective functions. The system studied is a neodymium, samarium, europium, gadolinium mixture separated in an ion exchange chromatography step. A homogeneous Langmuir Mobile Phase Modified model is calibrated to fit the experiments, and then used to perform the optimization task. For the optimization a multi-objective Differential Evolution algorithm was used, with weighting based on relative value of the components to find optimal operation points along the Pareto front. The objectives of the Pareto front are weighted productivity and weighted yield with purity as an equality constraint. A prioritizing scheme based on relative values is applied for determining the pooling order. A simple rule of thumb for pooling strategy selection is presented. The multi-objective optimization gives a Pareto front which shows the rule of thumb, as a gap in one of the objective functions.