Weak solvability and well-posedness of a coupled Schrödinger-Korteweg de Vries equation for capillary-gravity wave interactions

An interaction equation of the capillary-gravity wave is considered. We show that the Cauchy problem of the coupled Schrödinger-KdV equation,

is locally well-posed for weak initial data . We apply the analogous method for estimating the nonlinear coupling terms developed by Bourgain and refined by Kenig, Ponce, and Vega.

     

X-Band Pulsed ENDOR Study ofFe-Substituted Sodalite— The Effect of the Zero-Field Splitting

X-band (∼9.3 GHz) pulsed ENDOR measurements were carried out on⁵⁷Fe-substituted sodalite (FeSOD) which contains only one type of Fe(III) (S=) located at a framework site. The ENDOR spectrum recorded atg= 2 shows three doublets corresponding to the sixM_Smanifolds. The assignment of these signals was confirmed by hyperfine-selective and triple ENDOR experiments. The components of each of the doublets had different intensities, reflecting the different populations of the EPR energy levels at the measurement temperature, 1.8 K. ENDOR spectra were recorded at magnetic fields within the EPR powder pattern, and the field dependence observed showed an anisotropic behavior, unexpected from the isotropic character of the⁵⁷Fe(III) hyperfine coupling. This dependence was attributed to the high-order effects of the zero-field splitting (ZFS) interaction on the ENDOR frequencies. Three different theoretical approaches were used to account for the dependence of the ENDOR spectrum on the ZFS interaction. The first involves the exact diagonalization of the total spin Hamiltonian, the second uses third-order perturbation approximations, and the third employs an effective nuclear Hamiltonian for each of theM_Smanifolds. The simulations showed that the ENDOR signals of theM_S= ±5/2 (ν_±5/2) manifold are the least sensitive to the magnitude of the ZFS parameterDand are therefore the most appropriate for the determination ofa_iso. It is shown that at X band anda_isovalues of about 30 MHz, the perturbation approach is valid up toDvalues of 500 MHz if all three doublets are concerned. However, if only the ν_±5/2doublet is considered, then this approach is valid forD< 1000 MHz. The third approach was found inappropriate fora_isovalues of ∼30 MHz. Using the method of exact diagonalization together with orientation selectivity, the trends observed in the experimental spectra could be reproduced. The ENDOR spectra of the⁵⁷Fe-substituted zeolites ZSM5, L, and mazzite showed broad and ill-defined peaks since the ZFS of Fe(III) in these zeolites is significantly larger than that of FeSOD. Because this broadening is a high-order effect, it can be significantly reduced at higher spectrometer frequencies.     

A triple resonance hyperfine sublevel correlation experiment for assignment of electron-nuclear double resonance lines

A new, triple resonance, pulse electron paramagnetic resonance (EPR) sequence is described. It provides spin links between forbidden electron spin transitions (DeltaM(S)=+/-1, DeltaM(I) not equal 0) and allowed nuclear spin transitions (DeltaM(I) = +/-1), thus, facilitating the assignment of nuclear frequencies to their respective electron spin manifolds and paramagnetic centers. It also yields the relative signs of the hyperfine couplings of the different nuclei. The technique is based on the combination of electron-nuclear double resonance (ENDOR) and electron-electron double resonance (ELDOR)-detected NMR experiments in a way similar to the TRIPLE experiment. The feasibility and the information content of the method are demonstrated first on a single crystal of Cu-doped L-histidine and then on a frozen solution of a Cu-histidine complex.     

Resolving intermediate solution structures during the formation of mesoporous SBA-15

The evolution of the solution microstructures during the formation of the hexagonal mesoporous material SBA-15 was studied by direct imaging and freeze-fracture replication cryo-TEM. A reaction mixture was sampled at different times after the addition of tetramethoxyorthosilane (TMOS) to an acidic solution of Pluronic P123 held at 50 degrees C. Solution microstructures were detected by direct imaging cryo-TEM in the time window of 6.5-40 min after the addition of the TMOS (t = 0). The micrographs revealed that the initial spheroidal micelles evolve into threadlike micelles, which become longer and straighter with time. Then bundles with the dimensions similar to those found in the final material appeared, although there was no sign of a hexagonal arrangement up to 40 min. Due to the appearance of a precipitate at 40 min the sample became too viscous, preventing clear observation of its content. To observe the structures present after 40 min, freeze-fracture replication was carried out as well. Such samples were collected also at 22 min and showed the presence of threadlike micelles in agreement with the direct imaging cryo-TEM micrographs. The 2 h samples showed some areas of hexagonal ordered structures, which become very clear at 2 h 50 min. The cryo-TEM measurements were carried out under the same reaction conditions used in earlier in situ EPR experiments, thus allowing us to correlate molecular level events with the microstructure shape evolutions. This showed that the elongation of the micelles is a consequence of a reduction of the polarity and the water content within the micelles due to silicate adsorption and polymerization. Similar experiments were carried out also on SBA-15 prepared with HCl and TMOS at 35 degrees C. The appearance of threadlike micelles, followed by clustering of the TLMs, was observed under these conditions as well, but the reaction rate was faster. This suggests that the observed mechanism for the formation of SBA-15 is general.     

Spin delocalization over type zero copper

Hard-ligand, high-potential copper sites have been characterized in double mutants of Pseudomonas aeruginosa azurin (C112D/M121X (X = L, F, I)). These sites feature a small A(zz)(Cu) splitting in the EPR spectrum together with enhanced electron transfer activity. Due to these unique properties, these constructs have been called "type zero" copper sites. In contrast, the single mutant, C112D, features a large A(zz)(Cu) value characteristic of the typical type 2 Cu(II). In general, A(zz)(Cu) comprises contributions from Fermi contact, spin dipolar, and orbital dipolar terms. In order to understand the origin of the low A(zz)(Cu) value of type zero Cu(II), we explored in detail its degree of covalency, as manifested by spin delocalization over its ligands, which affects A(zz)(Cu) through the Fermi contact and spin dipolar contributions. This was achieved by the application of several complementary EPR hyperfine spectroscopic techniques at X- and W-band (～9.5 and 95 GHz, respectively) frequencies to map the ligand hyperfine couplings. Our results show that spin delocalization over the ligands in type zero Cu(II) is different from that of type 2 Cu(II) in the single C112D mutant. The (14)N hyperfine couplings of the coordinated histidine nitrogens are smaller by about 25-40%, whereas that of the (13)C carboxylate of D112 is about 50% larger. From this comparison, we concluded that the spin delocalization of type zero copper over its ligands is not dramatically larger than in type 2 C112D. Therefore, the reduced A(zz)(Cu) value of type zero Cu(II) is largely attributable to an increased orbital dipolar contribution that is related to its larger g(zz) value, as a consequence of the distorted tetrahedral geometry. The increased spin delocalization over the D112 carboxylate in type zero mutants compared to type 2 C112D suggests that electron transfer paths involving this residue are enhanced.     

Simulation of proliferation of neural stem cells on a surface with emphasis on spatial constraints on cell division

We present Monte Carlo lattice simulations of proliferation of cells on a surface in the situation when the cell-cell adhesion is relatively strong and the cells may form islands and/or flattened hemispheres. The model parameters were chosen to mimic proliferation of adult rat neural stem cells (or, more specifically, adult hippocampal progenitor cells) deposited on polyornithine and laminin coated polystyrene. The results obtained show that the spatial constraints on cell division may result in slowdown of the exponential growth. Depending on the rules used for cell division, this effect may be either nearly negligible or appreciable. In the latter case, the scale of the deviations from the exponential growth is comparable with that observed in our experiments. In the simulations, the slowdown of the growth starts however somewhat earlier and occurs in a less abrupt manner. This seems to indicate that the spatial constraints on division of cells are not the main factor behind the experimentally observed termination of the growth.     

High‐Field Pulsed EPR Spectroscopy for the Speciation of the Reduced [PV2Mo10O40]6− Polyoxometalate Catalyst Used in Electron‐Transfer Oxidations

An in‐depth spectroscopic EPR investigation of a key intermediate, formally notated as [PV^IVV^VMo₁₀O₄₀]^6? and formed in known electron‐transfer and electron‐transfer/oxygen‐transfer reactions catalyzed by H₅PV₂Mo₁₀O₄₀, has been carried out. Pulsed EPR spectroscopy have been utilized: specifically, W‐band electron–electron double resonance (ELDOR)‐detected NMR and two‐dimensional (2D) hyperfine sub‐level correlation (HYSCORE) measurements, which resolved ⁹⁵Mo and ¹⁷O hyperfine interactions, and electron–nuclear double resonance (ENDOR), which gave the weak ⁵¹V and ³¹P interactions. In this way, two paramagnetic species related to [PV^IVV^VMo₁₀O₄₀]^6? were identified. The first species (30–35 %) has a vanadyl (VO²⁺)‐like EPR spectrum and is not situated within the polyoxometalate cluster. Here the VO²⁺ was suggested to be supported on the Keggin cluster and can be represented as an ion pair, [PV^VMo₁₀O₃₉]^8?[V^IVO²⁺]. This species originates from the parent H₅PV₂Mo₁₀O₄₀ in which the vanadium atoms are nearest neighbors and it is suggested that this isomer is more likely to be reactive in electron‐transfer/oxygen‐transfer reaction oxidation reactions. In the second (70–65 %) species, the V^IV remains embedded within the polyoxometalate framework and originates from reduction of distal H₅PV₂Mo₁₀O₄₀ isomers to yield an intact cluster, [PV^IVV^VMo₁₀O₄₀]^6?.     

A Calibration Reaction for Rapid Freeze-Quench W-Band EPR

A simple setup for rapid freeze-quench electron paramagnetic resonance (EPR) at W-band is described. It is based on a BioLogic commercial apparatus and a modified sample collection appropriate for W-band capillaries. The standard reaction of myoglobin with azide, which converts high-spin Fe(III) to low-spin Fe(III), used for calibration of rapid freeze-quench X-band EPR is very inconvenient for high-field measurements. Here we propose a different simple calibration reaction for W-band: the reduction of a nitroxide free radical with sodium dithionite using Mn²⁺ as an internal standard. Using this calibration reaction we determined the dead time of our system to be less than 10 ms.     

High field 27Al ENDOR reveals the coordination mode of Cu2+ in low Si/Al zeolites

The siting of Cu2+ in zeolites with low exchange levels has been a subject for debate due to the lack of experimental evidence that provide directly the interaction between the Cu2+ ion and the zeolite framework. High field 27Al ENDOR provided highly resolved orientation selective ENDOR spectra from which both the 27Al hyperfine and quadrupole principal components and orientations relative to the g tensor principal axis system were determined for a dehydrated Cu2+ exchanged zeolite X with Si/Al = 1. The results show that all three Cu-Al distances in the six-member ring are equivalent, in contrast to DFT predictions using cluster models.