Generalised quaternion methods in conformal geometry

A new approach to Penrose's twistor algebra is given. It is based on the use of a generalised quaternion algebra for the translation of statements in projective five-space into equivalent statements in twistor (conformal spinor) space. The formalism leads toSO(4, 2)-covariant formulations of the Pauli-Kofink and Fierz relations among Dirac bilinears, and generalisations of these relations.

Flow of metal in a wedge-shaped cavity

The wedge shape is a fairly common cross-section found in many non-axisymmetric components used in machines, aircraft, ships and automobiles. If such components are forged between two mutually inclined dies the metal displaced by the dies flows into the converging as well as into the diverging channels created by the inclined dies. The extent of each type of flow (convergent/divergent) depends on the die—material interface friction and the included die angle. Given the initial cross-section, the length as well as the exact geometry of the forged cross-section are therefore uniquely determined by these parameters. In this paper a simple stress analysis is used to predict changes in the geometry of a wedge undergoing compression between inclined platens. The flow in directions normal to the cross-section is assumed to be negligible. Experiments carried out using wedge-shaped lead billets show that, knowing the interface friction and as long as the deformation is not too large, the dimensional changes in the wedge can be predicted with reasonable accuracy. The predicted flow behaviour of metal for a wide range of die angles and interface friction is presented: these characteristics can be used by the die designer to choose the die lubricant (only) if the die angle is specified and to choose both of these parameters if there is no restriction on the exact die angle. The present work shows that the length of a wedge undergoing compression is highly sensitive to die—material interface friction. Thus in a situation where the top and bottom dies are inclined to each other, a wedge made of the material to be forged could be put between the dies and then compressed, whereupon the length of the compressed wedge — given the degree of compression — affords an estimate of the die—material interface friction.

X-Ray Structure Of A Ternary Metal-Complex - Copper(Ii) Inosine 5'-Monophosphate Imidazole - Metal-Binding To The N(7) Atom Of The Nucleotide In A Mixed-Ligand System Containing An Aromatic Amine

A ternary metal-nucleotide complex, Na2[Cu(5’-IMP)2(im)o,8(H20)l,2(H20)2h]as~ 1be2e.n4 pHr2ep0a,r ed and its structure analyzed by X-ray diffraction (5’-IMP = inosine 5’-monophos hate; im = imidazole). The complex crystallizes in space group C222, with a = 8.733 (4) A, b = 23.213 (5) A, c = 21.489 (6) 1, and Z = 4. The structure was solved by the heavy-atom method and refined by full-matrix least-squares technique on the basis of 2008 observed reflections to a final R value of 0.087. Symmetry-related 5’-IMP anions coordinate in cis geometry through the N(7) atoms of the bases. The other cis positions of the coordination plane are statistically occupied by nitrogen atoms of disordered im groups and water oxygens with occupancies 0.4 and 0.6, respectively. Water oxygens in axial positions complete the octahedral coordination of Cu(I1). The complex is isostructural with C~S-[P~(S’-IMP),(NH~)~a] m”,o del proposed for Pt(I1) binding to DNA. The base binding observed in the present case is different from the typical ”phosphate only” binding shown from earlier studies on metal-nucleotide complexes containing various other ?r-aromatic amines.

Thermodynamic and structural consequences of changing a sulfur atom to a methylene group in the M13Nle mutation in ribonuclease-S

Two fragments of pancreatic ribonuclease A, a truncated version of S-peptide (residues 1-15) and S-protein (residues 21-124), combine to give a catalytically active complex. We have substituted the wild-type residue at position 13, methionine (Met), with norleucine (Nle), where the only covalent change is the replacement of the sulfur atom with a methylene group. The thermodynamic parameters associated with the binding of this variant to S-protein, determined by titration calorimetry in the temperature range 10-40 degrees C, are reported and compared to values previously reported [Varadarajan, R., Connelly, P. R., Sturtevant, J. M., & Richards, F. M. (1992) Biochemistry 31, 1421-1426] for other position 13 analogs. The differences in the free energy and enthalpy of binding between the Met and Nle peptides are 0.6 and 7.9 kcal/mol at 25 degrees C, respectively. These differences are slightly larger than, but comparable to, the differences in the values for the Met/Ile and Met/Leu pairs. The structure of the mutant complex was determined to 1.85 Angstrom resolution and refined to an R-factor of 17.4% The structures of mutant and wild-type complexes are practically identical although the Nle side chain has a significantly higher average B-factor than the corresponding Met side chain. In contrast, the B-factors of the atoms of the cage of residues surrounding position 13 are all somewhat lower in the Nle variant than in the Met wild-type. Thus, the large differences in the binding enthalpy appear to reside entirely in the difference in chemical properties or dynamic behavior of the -S- and -CH2- groups and not in differences in the geometry of the side chains or the internal cavity surface. In addition, a novel method of obtaining protein stability data by means of isothermal titration calorimetry is introduced.

Synthesis and structure of La14V6CuO36.5: a transparent Cu(I) vanadate containing [OCuO](3-) sticks

The title compound, La14V6CuO36.5, was prepared from a stoichiometric mixture of La2O3,V2O5, and CuO at 1050-1080 degreesC. The compound forms transparent, pale green crystals and was characterized by wavelength dispersive spectroscopy and single crystal X-ray diffraction. The structure contains isolated VO43- tetrahedra and [OCuO](3-) sticks dispersed in a lanthanum oxide network. Films of La14V6CuO36.5 were grown on R-plane sapphire by using pulsed laser deposition. Rutherford backscattering spectroscopic and X-ray diffraction analyses of the films showed oriented growth of the title phase, a similar to5 eV optical band gap and n-type conductivity. The compound is an example of a transparent copper(I) oxide.

Role of carrier density and disorder on anisotropic charge transport in polypyrrole

Polypyrrole (PPy) has been synthesized electrochemically on platinum substrate by varying synthesis temperature and dopant concentration. The charge transport in PPy has been investigated as a function of temperature for both in-plane and out-of-plane geometry in a wide temperature range of 5K-300 K. The charge transport showed strong anisotropy and various mechanisms were used to explain the transport. The conductivity ratio, sigma(r) = sigma(300 K)/sigma(5 K) is calculated for each sample to quantify the relative disorder. At all the temperatures, the conductivity values for in-plane transport are found to be more for PPy synthesized at lower temperature, while the behavior is found to be different for out-of-plane transport. The carrier density is found to play a crucial role in case of in-plane transport. An effort has been made to correlate charge transport to morphology by analyzing temperature and frequency dependence of conductivity. Charge transport in lateral direction is found to be dominated by hopping whereas tunneling mechanisms are dominated in vertical direction. Parameters such as density of states at the Fermi level N(E-F)], average hopping distance (R), and average hopping energy (W) have been estimated for each samples in both geometry. (C) 2013 American Institute of Physics. http://dx.doi.org/10.1063/1.4775405]

Optically transparent polymer devices for in situ assessment of cell electroporation

In order to study cell electroporation in situ, polymer devices have been fabricated from poly-dimethyl siloxane with transparent indium tin oxide parallel plate electrodes in horizontal geometry. This geometry with cells located on a single focal plane at the interface of the bottom electrode allows a longer observation time in both transmitted bright-field and reflected fluorescence microscopy modes. Using propidium iodide (PI) as a marker dye, the number of electroporated cells in a typical culture volume of 10-100 mu l was quantified in situ as a function of applied voltage from 10 to 90 V in a series of 2-ms pulses across 0.5-mm electrode spacing. The electric field at the interface and device current was calculated using a model that takes into account bulk screening of the transient pulse. The voltage dependence of the number of electroporated cells could be explained using a stochastic model for the electroporation kinetics, and the free energy for pore formation was found to be kT at room temperature. With this device, the optimum electroporation conditions can be quickly determined by monitoring the uptake of PI marker dye in situ under the application of millisecond voltage pulses. The electroporation efficiency was also quantified using an ex situ fluorescence-assisted cell sorter, and the morphology of cultured cells was evaluated after the pulsing experiment. Importantly, the efficacy of the developed device was tested independently using two cell lines (C2C12 mouse myoblast cells and yeast cells) as well as in three different electroporation buffers (phosphate buffer saline, electroporation buffer and 10 % glycerol).

Experimentally validated Raman Monte Carlo simulation for a cuboid object to obtain Raman spectroscopic signatures for hidden material

In conventional Raman spectroscopic measurements of liquids or surfaces the preferred geometry for detection of the Raman signal is the backscattering (or reflection) mode. For non-transparent layered materials, sub-surface Raman signals have been retrieved using spatially offset Raman spectroscopy (SORS), usually with light collection in the same plane as the point of excitation. However, as a result of multiple scattering in a turbid medium, Raman photons will be emitted in all directions. In this study, Monte Carlo simulations for a three-dimensional layered sample with finite geometry have been performed to confirm the detectability of Raman signals at all angles and at all sides of the object. We considered a non-transparent cuboid container (high density polyethylene) with explosive material (ammonium nitrate) inside. The simulation results were validated with experimental Raman intensities. Monte Carlo simulation results reveal that the ratio of sub-surface to surface signals improves at geometries other than backscattering. In addition, we demonstrate through simulations the effects of the absorption and scattering coefficients of the layers, and that of the diameter of the excitation beam. The advantage of collecting light from all possible 4 angles, over other collection modes, is that this technique is not geometry specific and molecular identification of layers underneath non-transparent surfaces can be obtained with minimal interference from the surface layer. To what extent all sides of the object will contribute to the total signal will depend on the absorption and scattering coefficients and the physical dimensions. Copyright (c) 2015 John Wiley & Sons, Ltd.

COOL CORE CYCLES: COLD GAS AND AGN JET FEEDBACK IN CLUSTER CORES

Using high-resolution 3D and 2D (axisymmetric) hydrodynamic simulations in spherical geometry, we study the evolution of cool cluster cores heated by feedback-driven bipolar active galactic nuclei (AGNs) jets. Condensation of cold gas, and the consequent enhanced accretion, is required for AGN feedback to balance radiative cooling with reasonable efficiencies, and to match the observed cool core properties. A feedback efficiency (mechanical luminosity approximate to epsilon(M) over dot(acc)c(2); where (M) over dot(acc). is the mass accretion rate at 1 kpc) as small as 6 x 10(-5) is sufficient to reduce the cooling/accretion rate by similar to 10 compared to a pure cooling flow in clusters (with M-200 less than or similar to 7 x 10(14) M-circle dot). This value is much smaller compared to the ones considered earlier, and is consistent with the jet efficiency and the fact that only a small fraction of gas at 1 kpc is accreted onto the supermassive black hole (SMBH). The feedback efficiency in earlier works was so high that the cluster core reached equilibrium in a hot state without much precipitation, unlike what is observed in cool-core clusters. We find hysteresis cycles in all our simulations with cold mode feedback: condensation of cold gas when the ratio of the cooling-time to the free-fall time (t(cool)/t(ff)) is less than or similar to 10 leads to a sudden enhancement in the accretion rate; a large accretion rate causes strong jets and overheating of the hot intracluster medium such that t(cool)/t(ff) > 10; further condensation of cold gas is suppressed and the accretion rate falls, leading to slow cooling of the core and condensation of cold gas, restarting the cycle. Therefore, there is a spread in core properties, such as the jet power, accretion rate, for the same value of core entropy t(cool)/t(ff). A smaller number of cycles is observed for higher efficiencies and for lower mass halos because the core is overheated to a longer cooling time. The 3D simulations show the formation of a few-kpc scale, rotationally supported, massive (similar to 10(11) M-circle dot) cold gas torus. Since the torus gas is not accreted onto the SMBH, it is largely decoupled from the feedback cycle. The radially dominant cold gas (T < 5 x 10(4) K; vertical bar v(r)vertical bar >vertical bar v(phi vertical bar)) consists of fast cold gas uplifted by AGN jets and freely infalling cold gas condensing out of the core. The radially dominant cold gas extends out to 25 kpc for the fiducial run (halo mass 7 x 10(14) M-circle dot and feedback efficiency 6 x 10(-5)), with the average mass inflow rate dominating the outflow rate by a factor of approximate to 2. We compare our simulation results with recent observations.

Macropores generated during shrinkage in two paddy soils using X-ray micro-computed tomography

Soil shrinkage curve represents a decrease of total porosity or an increase of bulk density with water loss. However, our knowledge of the dynamics of pores and their geometry during soil shrinkage is scarce, partially due to lack of reliable methods for determining soil pores in relation to change in soil water. This study aimed to investigate the dynamics of macropores (>30 mu m) of paddy soils during shrinkage. Two, paddy soils, which were sampled from one paddy field cultivated for 20 years (YPF) and the other one for over 100 years (OPF), represented difference in crack geometry in the field. Macropore parameters (volume, connectivity, and orientation of pores) and soil shrinkage parameters were determined on the same undisturbed soil cores by X-ray microtomography and shrinkage curve, respectively. Macroporosity was on average four times larger in the YPF than in the OPF whereas the shrinkage capacity was lower in the YPF as compared to the OPF (0.09 vs. 0.15 COLE). Soil shrinkage increased the volume of pores by 3.7% in the YPF and by 1.6% in the OPF as well as their connectivity. The formation of macropores occurred mostly in the proportional shrinkage phase. As a result, the slope of the proportional shrinkage phase was smaller in the YPF (0.65) than in the OPF (0.89). New macropores were cracks and extended pre-existing pores in the range of 225-1215 pm size without any preferential orientation. This work provides image evidences that in paddy soils with high shrinkage capacity more macropores are generated in the soil presenting a smaller proportional shrinkage slope. (C) 2015 Elsevier B.V. All rights reserved.

Efficient algorithms for computing Reeb graphs

The Reeb graph tracks topology changes in level sets of a scalar function and finds applications in scientific visualization and geometric modeling. We describe an algorithm that constructs the Reeb graph of a Morse function defined on a 3-manifold. Our algorithm maintains connected components of the two dimensional levels sets as a dynamic graph and constructs the Reeb graph in O(nlogn+nlogg(loglogg)3) time, where n is the number of triangles in the tetrahedral mesh representing the 3-manifold and g is the maximum genus over all level sets of the function. We extend this algorithm to construct Reeb graphs of d-manifolds in O(nlogn(loglogn)3) time, where n is the number of triangles in the simplicial complex that represents the d-manifold. Our result is a significant improvement over the previously known O(n2) algorithm. Finally, we present experimental results of our implementation and demonstrate that our algorithm for 3-manifolds performs efficiently in practice.

On exact solutions of the unsteady navierstokes equationsâ the vortex with instantaneous curvilinear axis

The unsteady pseudo plane motions have been investigated in which each point of the parallel planes is subjected to non-torsional oscillations in their own plane and at any given instant the streamlines are concentric circles. Exact solutions are obtained and the form of the curve , the locus of the centers of these concentric circles, is discussed. The existence of three infinite sets of exact solutions, for the flow in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks, is established. Three cases arise according to whether is greater than, equal to or less than , where is angular velocity of the basic rotation and is the frequency of the superposed oscillations. For a symmetric solution of the flow these solutions reduce to a single unique solution. The nature of the curve is illustrated graphically by considering an example of the flow between coaxial rotating disks.

Application of ab initio molecular orbital calculations to the structural moieties of carbohydrates. 3

Ab initio RHF/4-31G level molecular orbital calculations have been carried out on dimethoxymethane as a model compound for the acetal moiety in methyl pyranosides. The calculations are consistent with the predictions of the anomeric effect and the exo-anomeric effect. They reproduce very successfully the differences in molecular geometry observed by x-ray and neutron diffraction of single crystals of the methyl cy-D- and methyl 0-D-pyranosides. Calculations carried out at the 6-3 1G* level for methanediol confirm the earlier calculations at the 4-31G level, with smaller energy differences between the four staggered conformations.

Interaction of substrate uridyl 3',5'-adenosine with ribonuclease A:a molecular dynamics study

A wealth of information available from x-ray crystallographic structures of enzyme-ligand complexes makes it possible to study interactions at the molecular level. However, further investigation is needed when i) the binding of the natural substrate must be characterized, because ligands in the stable enzyme-ligand complexes are generally inhibitors or the analogs of substrate and transition state, and when ii) ligand binding is in part poorly characterized. We have investigated these aspects i? the binding of substrate uridyl 3',5'-adenosine (UpA) to ribonuclease A (RNase A). Based on the systematically docked RNase A-UpA complex resulting from our previous study, we have undertaken a molecular dynamics simulation of the complex with solvent molecules. The molecular dynamics trajectories of this complex are analyzed to provide structural explanations for varied experimental observations on the ligand binding at the B2 subsite of ribonuclease A. The present study suggests that B2 subsite stabilization can be effected by different active site groups, depending on the substrate conformation. Thus when adenosine ribose pucker is O4'-endo, Gln69 and Glu111 form hydrogen-bonding contacts with adenine base, and when it is C2'-endo, Asn71 is the only amino acid residue in direct contact with this base. The latter observation is in support of previous mutagenesis and kinetics studies. Possible roles for the solvent molecules in the binding subsites are described. Furthermore, the substrate conformation is also examined along the simulation pathway to see if any conformer has the properties of a transition state. This study has also helped us to recognize that small but concerted changes in the conformation of the substrate can result in substrate geometry favorable for 2',3' cyclization. The identified geometry is suitable for intraligand proton transfer between 2'-hydroxyl and phosphate oxygen atom. The possibility of intraligand proton transfer as suggested previously and the mode of transfer before the formation of cyclic intermediate during transphosphorylation are discussed.

Characterizing and recognizing weak visibility polygons

A polygon is said to be a weak visibility polygon if every point of the polygon is visible from some point of an internal segment. In this paper we derive properties of shortest paths in weak visibility polygons and present a characterization of weak visibility polygons in terms of shortest paths between vertices. These properties lead to the following efficient algorithms: (i) an O(E) time algorithm for determining whether a simple polygon P is a weak visibility polygon and for computing a visibility chord if it exist, where E is the size of the visibility graph of P and (ii) an O(n2) time algorithm for computing the maximum hidden vertex set in an n-sided polygon weakly visible from a convex edge.