Localization for a Random Walk in Slowly Decreasing Random Potential

We consider a continuous time random walk X in a random environment on ?⁺ such that its potential can be approximated by the function V:?⁺→? given by $V(x)=\sigma W(x) -\frac {b}{1-\alpha}x^{1-\alpha}$ where σW a Brownian motion with diffusion coefficient σ>0 and parameters b, α are such that b>0 and 0<α<1/2. We show that P-a.s. (where P is the averaged law) $\lim_{t\to\infty} \frac{X_{t}}{(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}}=1$ with $C^{*}=\frac{2\alpha b}{\sigma^{2}(1-2\alpha)}$ . In fact, we prove that by showing that there is a trap located around $(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}$ (with corrections of smaller order) where the particle typically stays up to time t. This is in sharp contrast to what happens in the “pure” Sinai’s regime, where the location of this trap is random on the scale ln² t.     

H2-broadening coefficients in the ν3 band of CH3D at low temperatures

Using a diode-laser spectrometer, we have measured H₂-broadening coefficients of CH₃D at low temperatures (153.5, 183.5, and 223.5 K) for four lines in the ν₃ band. The collisional widths are obtained by fitting each absorption line with three lineshape models: the Voigt, Rautian, and Galatry profiles. The broadening coefficients are also calculated on the basis of a semiclassical model of interacting linear molecules by considering an atom-atom Lennard-Jones potential in addition to electrostatic contributions. By comparing the broadening coefficients at room and low temperatures the temperature dependence of these broadenings has been determined both experimentally and theoretically.     

A note on the regularity of the holes for permeability property through a perforated domain for the 2D Euler equations Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday

For equations of order two with the Dirichlet boundary condition, as the Laplace problem, the Stokes and the Navier-Stokes systems, perforated domains were only studied when the distance between the holes d_ε is equal to or much larger than the size of the holes ε. Such a diluted porous medium is interesting because it contains some cases where we have a non-negligible effect on the solution when(ε, d_ε) →(0, 0).Smaller distances were avoided for mathematical reasons and for these large distances, the geometry of the holes does not affect or rarely affect the asymptotic result. Very recently, it was shown for the 2D-Euler equations that a porous medium is non-negligible only for inter-holes distances much smaller than the sizes of the holes.For this result, the boundary regularity of holes plays a crucial role, and the permeability criterion depends on the geometry of the lateral boundary. In this paper, we relax slightly the regularity condition, allowing a corner, and we note that a line of irregular obstacles cannot slow down a perfect fluid in any regime such thatε ln d_ε→ 0.     

Gadolinium chelate coated gold nanoparticles as contrast agents for both X-ray computed tomography and magnetic resonance imaging

Functionalized gold nanoparticles were applied as contrast agents for both in vivo X-ray and magnetic resonance imaging. These particles were obtained by encapsulating gold cores within a multilayered organic shell which is composed of gadolinium chelates bound to each other through disulfide bonds. The contrast enhancement in MRI stems from the presence of gadolinium ions which are entrapped in the organic shell, whereas the gold core provides a strong X-ray absorption. This study revealed that these particles suited for dual modality imaging freely circulate in the blood vessels without undesirable accumulation in the lungs, spleen, and liver.     

Photoinduced magnetization in copper octacyanomolybdate

This article describes the studies of a photomagnetic cyanide-bridged Cu-Mo bimetallic assembly, Cu(II)(2)[Mo(IV)(CN)(8)].8H(2)O (Cu(II), S = (1)/(2); Mo(IV), S = 0) (1), which has an intervalence transfer (IT) band from Mo(IV)-CN-Cu(II) to Mo(V)-CN-Cu(I) around 480 nm. Wide-angle X-ray scattering and X-ray spectroscopic studies provide precise information about the 3D connectivity and the local environment of the transition metal ions. Irradiating with blue light causes solid 1 to exhibit a spontaneous magnetization (Curie temperature = 25 K). The thermal reversibility is carefully studied and shows the long-time stability of the photoinduced state up to 100 K. Photoreversibility is also observed; i.e., the magnetization is induced by irradiation with light below 520 nm, while the magnetization is reduced by irradiation with light above 520 nm. The UV-vis absorption spectrum after irradiation shows a decrease of the IT band and the appearance of the reverse-IT band in the region of 600-900 nm (lambda(max) = 710 nm). This UV-vis absorption spectrum is recovered to the original spectrum by irradiation with 658-, 785-, and 840-nm light. In this photomagnetic effect, the excitation of the IT band causes an electron transfer from Mo(IV) to Cu(II), producing a ferromagnetic mixed-valence isomer of Cu(I)Cu(II)[Mo(V)(CN)(8)].8H(2)O (Cu(I), S = 0; Cu(II), S = (1)/(2); Mo(V), S = (1)/(2)) (1'). 1' returns to 1 by irradiation of the reverse-IT band, which obeys the scheme for the potential energy surface in mixed-valence class II compounds.     

A selective synthesis of hydroxyborate anions as novel anchors for zirconocene catalysts

A new family of hydroxytris(pentafluorophenyl)borate anions [B(C6F5)3OH](-) associated with organic and aprotic cations c+ (imidazolium, pyrrolidinium and phosphonium) has been prepared by a general one-pot synthesis that implies the chloride borate analogues [B(C6F5)3Cl](-)[c]+. The [c]+[B(C6F5)3OH](-) salts have been isolated and fully characterized. The borate anion [B(C6F5)3OH](-) has been shown to protonate the Zr-Me bond in the Cp2ZrMe2 complex forming CH4 and the first published example of anionic [Cp2Zr(Me)OB(C6F5)3](-) species. Standard spectroscopic methods demonstrate the covalent character of the Zr metal center and the anionic character of the boron atom. This protonolysis methodology using [B(C6F5)3OH](-) anion affords a new route for the incorporation of a covalently bonded anionic functionality on organometallic complexes. This provides a new way to immobilize transition metal complexes in ionic liquids.     

Adsorption of L-lysine on Cu(110): a RAIRS study from UHV to the liquid phase

The adsorption of L-lysine on a Cu(110) surface has been investigated under UHV conditions from the sublimation of a crystalline phase. The adsorption was characterized by Fourier transform reflection absorption infrared spectroscopy (FT-RAIRS) during exposure and Auger electron spectroscopy (AES). At room temperature, the lysine molecules' adsorption geometry varies as a function of the exposure. At low coverage, the molecules are adsorbed via the oxygen atoms of the deprotonated carboxylate group and the nitrogen atom of the amino group. At high coverage, close to the monolayer, the molecules reorient to be anchored to the surface via one oxygen of a sideways-tilted carboxylate moiety. This first step is followed by the growth of multilayers of nonoriented molecules. In contrast, adsorption on an oxygen-modified copper surface leads to a rather disordered layer. The results are compared with the adsorption carried out on a polycrystalline copper surface after immersion in solutions of lysine at various pH values. The adsorption was monitored by polarization modulation infrared spectroscopy (PM-IRRAS). The chemistry of the adsorbed molecules is function of the starting chemical form of the lysine molecules imposed by the pH of the solution. The combination of the two techniques and various sets of adsorption conditions will give important insight into the adsorption of biomolecules on metal surfaces and the influence of water and surface oxygen.     

Reactivity differences between molecular and surface silanols in the preparation of homogeneous and heterogeneous olefin metathesis catalysts

The reaction of Mo(N)(CH₂tBu)₃ (1) and SiO_2-(700) generates (SiO)Mo(NH)(CHtBu)(CH₂tBu) (2) when performed in C₆H₆ (material [1/SiO_2-(700)]_C6H6). The grafting occurs presumably by protonation of the nitrido ligand to form an intermediate (SiO)Mo(NH)(CH₂tBu)₃ (3), a pentacoordinated complex, which decomposes into 2 and 2,2-dimethylpropane. While [1/SiO_2-(700)]_C6H6 is highly active in olefin metathesis, [1/SiO_2-(700)]_CH2Cl2 and [1/SiO_2-(700)]_THF are poorly active or inactive catalysts respectively. In contrast, when Mo(N)(CH₂tBu)₃ reacts with a molecular silanol derivative, a soluble model of the surface of SiO_2-(700), it yields a very stable complex, (c-C₅H₉)₇Si₇O₁₂SiO-Mo(NH)(CH₂tBu)₃ (3m), which does not spontaneously generate 2,2-dimethylpropane and an alkylidene complex in contrast to the surface complex. Moreover, 3m does not catalyse olefin metathesis at room temperature as it does not already contain the initiating carbene ligand, and it is necessary to heat up the reaction mixture to 110 °C to obtain low catalytic activity. Nevertheless, the complex 3m generates well-defined metallocarbenes when heated in the presence of PMe₃: (c-C₅H₉)₇Si₇O₁₂SiO-Mo(N)(CHtBu)(P(CH₃)₃)₂ (4m) as a 10:1 mixture of its syn and anti rotamers with the loss of 2 equiv. of 2,2-dimethylpropane.     

An SFG/DFG investigation of CN− adsorption at an Au electrode in 1-butyl-1-methyl-pyrrolidinium bis(trifluoromethylsulfonyl) amide ionic liquid

In this paper we report an SFG/DFG investigation of the adsorption of CN^? – used as a probe molecule to study the electrochemical double-layer structure – at a polycrystalline Au electrode in 1-butyl-1-methyl-pyrrolidinium bis(trifluoromethylsulfonyl) amide ([BMP][TFSA]) room-temperature ionic liquid (RTIL). The adsorption of CN^? yielded single SFG and DFG bands in the range from ca. 2125 to 2135 cm^?1, exhibiting a Stark tuning of ca. 3 cm^?1 V^?1. Vibrational resonances – corresponding to modes of the RTIL coadsorbed with CN^?, were found in the range from ca. 1200 to 1500 cm^?1. The study of the double-layer structure was complemented by cyclic voltammetry (CV) and electrochemical impedance spectroscopy (EIS) measurements, from which the differential double-layer capacity (C_DL) was estimated.     

A rhodium-catalyzed C-H activation/cycloisomerization tandem

A reaction cascade comprising a rhodium-catalyzed C-H activation, a subsequent hydrometalation of an alkylidene cyclopropane in vicinity, regioselective C-C bond activation of the flanking cyclopropane ring, followed by reductive elimination of the resulting metallacycle, opens a new entry into functionalized cycloheptene derivatives. This crossover of C-H activation and higher order cycloaddition has been performed in two different formats, either using alkylidenecyclopropanes with a lateral vinylpyridine moiety or with a pending aldehyde group as the trigger. The reaction tolerates various functional groups, leaves chiral centers alpha to the reacting sites unaffected, and proceeds with excellent stereoselectivity. Labeling experiments support the proposed mechanism explaining the observed net cycloisomerization process.