Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Narrow band quantitative and multivariate electroencephalogram analysis of peri-adolescent period

ABSTRACT: BACKGROUND: The peri-adolescent period is a crucial developmental moment of transition from childhood to emergent adulthood. The present report analyses the differences in Power Spectrum (PS) of the Electroencephalogram (EEG) between late childhood (24 children between 8 and 13 years old) and young adulthood (24 young adults between 18 and 23 years old). RESULTS: The narrow band analysis of the Electroencephalogram was computed in the frequency range of 0--20 Hz. The analysis of mean and variance suggested that six frequency ranges presented a different rate of maturation at these ages, namely: low delta, delta-theta, low alpha, high alpha, low beta and high beta. For most of these bands the maturation seems to occur later in anterior sites than posterior sites. Correlational analysis showed a lower pattern of correlation between different frequencies in children than in young adults, suggesting a certain asynchrony in the maturation of different rhythms. The topographical analysis revealed similar topographies of the different rhythms in children and young adults. Principal Component Analysis (PCA) demonstrated the same internal structure for the Electroencephalogram of both age groups. Principal Component Analysis allowed to separate four subcomponents in the alpha range. All these subcomponents peaked at a lower frequency in children than in young adults. CONCLUSIONS: The present approaches complement and solve some of the incertitudes when the classical brain broad rhythm analysis is applied. Children have a higher absolute power than young adults for frequency ranges between 0-20 Hz, the correlation of Power Spectrum (PS) with age and the variance age comparison showed that there are six ranges of frequencies that can distinguish the level of EEG maturation in children and adults. The establishment of maturational order of different frequencies and its possible maturational interdependence would require a complete series including all the different ages.     

On the bidirectional vortex and other similarity solutions in spherical coordinates

The bidirectional vortex refers to the bipolar, coaxial swirling motion that can be triggered, for example, in cyclone separators and some liquid rocket engines with tangential aft-end injectors. In this study, we present an exact solution to describe the corresponding bulk motion in spherical coordinates. To do so, we examine both linear and nonlinear solutions of the momentum and vorticity transport equations in spherical coordinates. The assumption will be that of steady, incompressible, inviscid, rotational, and axisymmetric flow. We further relate the vorticity to some power of the stream function. At the outset, three possible types of similarity solutions are shown to fulfill the momentum equation. While the first type is incapable of satisfying the conditions for the bidirectional vortex, it can be used to accommodate other physical settings such as Hill’s vortex. This case is illustrated in the context of inviscid flow over a sphere. The second leads to a closed-form analytical expression that satisfies the boundary conditions for the bidirectional vortex in a straight cylinder. The third type is more general and provides multiple solutions. The spherical bidirectional vortex is derived using separation of variables and the method of variation of parameters. The three-pronged analysis presented here increases our repertoire of general mean flow solutions that rarely appear in spherical geometry. It is hoped that these special forms will permit extending the current approach to other complex fluid motions that are easier to capture using spherical coordinates.     

Crystal polymorphism of protein GB1 examined by solid-state NMR spectroscopy and X-ray diffraction

The study of micro- or nanocrystalline proteins by magic-angle spinning (MAS) solid-state NMR (SSNMR) gives atomic-resolution insight into structure in cases when single crystals cannot be obtained for diffraction studies. Subtle differences in the local chemical environment around the protein, including the characteristics of the cosolvent and the buffer, determine whether a protein will form single crystals. The impact of these small changes in formulation is also evident in the SSNMR spectra; however, the changes lead only to correspondingly subtle changes in the spectra. Here, we demonstrate that several formulations of GB1 microcrystals yield very high quality SSNMR spectra, although only a subset of conditions enable growth of single crystals. We have characterized these polymorphs by X-ray powder diffraction and assigned the SSNMR spectra. Assignments of the 13C and 15N SSNMR chemical shifts confirm that the backbone structure is conserved, indicative of a common protein fold, but side chain chemical shifts are changed on the surface of the protein, in a manner dependent upon crystal packing and electrostatic interactions with salt in the mother liquor. Our results demonstrate the ability of SSNMR to reveal minor structural differences among crystal polymorphs. This ability has potential practical utility for studying the formulation chemistry of industrial and therapeutic proteins, as well as for deriving fundamental insights into the phenomenon of single-crystal growth.     

Magic-angle spinning solid-state NMR spectroscopy of the beta1 immunoglobulin binding domain of protein G (GB1): 15N and 13C chemical shift assignments and conformational analysis

Magic-angle spinning solid-state NMR (SSNMR) studies of the beta1 immunoglobulin binding domain of protein G (GB1) are presented. Chemical shift correlation spectra at 11.7 T (500 MHz 1H frequency) were employed to identify signals specific to each amino acid residue type and to establish backbone connectivities. High sensitivity and resolution facilitated the detection and assignment of every 15N and 13C site, including the N-terminal (M1) 15NH3, the C-terminal (E56) 13C', and side-chain resonances from residues exhibiting fast-limit conformational exchange near room temperature. The assigned spectra lend novel insight into the structure and dynamics of microcrystalline GB1. Secondary isotropic chemical shifts report on conformation, enabling a detailed comparison of the microcrystalline state with the conformation of single crystals and the protein in solution; the consistency of backbone conformation in these three preparations is the best among proteins studied so far. Signal intensities and line widths vary as a function of amino acid position and temperature. High-resolution spectra are observed near room temperature (280 K) and at <180 K, whereas resolution and sensitivity greatly degrade substantially near 210 K; the magnitude of this effect is greatest among the side chains of residues at the intermolecular interface of the microcrystal lattice, which we attribute to intermediate-rate translational diffusion of solvent molecules near the glass transition. These features of GB1 will enable its use as an excellent model protein not only for SSNMR methods development but also for fundamental studies of protein thermodynamics in the solid state.     

Long-range 19F-15N distance measurements in highly-13C, 15N-enriched solid proteins with 19F-dephased REDOR shift (FRESH) spectroscopy

We present a novel rotational-echo double resonance (REDOR) method for detection of multiple (19)F-(15)N distances in solid proteins. The method is applicable to protein samples containing a single (19)F label, in addition to high levels of (13)C and (15)N enrichment. REDOR dephasing pulses are applied on the (19)F channel during an indirect constant time chemical shift evolution period on (15)N, and polarization is then transferred to (13)C for detection, with high-power (1)H decoupling throughout the sequence. This four-channel experiment reports site-specifically on (19)F-(15)N distances, with highly accurate determinations of approximately 5 A distances and detection of correlations arising from internuclear distances of at least 8 A. We demonstrate the method on the well-characterized 56-residue model protein GB1, where the sole tryptophan residue (Trp-43) has been labeled with 5-(19)F-Trp, in a bacterial growth medium also including (13)C-glucose and (15)N ammonium chloride. In GB1, 11 distances are determined, all agreeing within 20% of the X-ray structure distances. We envision the experiment will be utilized to measure quantitative long-range distances for protein structure determination.     

Effect of Pr-Ca substitution on the transport and magnetic behavior of LaMnO3 perovskite

The effect of simultaneous substitution of a fluctuating cation and a divalent cation in LaMnO₃ perovskite modifies the properties of the material to exhibit large valence colossal magnetoresistance (CMR) effect. A good example of these properties is (La_1−2x Pr _x Ca _x )MnO₃ (LPCMO) type CMR material. In this communication it is reported that, with the increase in x (for x=0.1, 0.15, 0.2), the T _c varies between 100 and 120 K with improvisation in metal-insulator transition. Interestingly, resistance increases with x from few hundred ohms to few kilo ohms with corresponding decrease in the unit cell volume. The results of the studies using X-ray diffraction (XRD), electrical resistivity, magnetoresistance and ac susceptibility measurements on LPCMO samples for understanding the structural, transport and magnetic properties are discussed in detail.     

Reduction of RF-induced sample heating with a scroll coil resonator structure for solid-state NMR probes

Heating due to high power 1H decoupling limits the experimental lifetime of protein samples for solid-state NMR (SSNMR). Sample deterioration can be minimized by lowering the experimental salt concentration, temperature or decoupling fields; however, these approaches may compromise biological relevance and/or spectroscopic resolution and sensitivity. The desire to apply sophisticated multiple pulse experiments to proteins therefore motivates the development of probes that utilize the RF power more efficiently to generate a high ratio of magnetic to electric field in the sample. Here a novel scroll coil resonator structure is presented and compared to a traditional solenoid. The scroll coil is demonstrated to be more tolerant of high sample salt concentrations and cause less RF-induced sample heating. With it, the viable experimental lifetime of a microcrystalline ubiquitin sample has been extended by more than an order of magnitude. The higher B1 homogeneity and permissible decoupling fields enhance polarization transfer efficiency in 15N-13C correlation experiments employed for protein chemical shift assignments and structure determination.