Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations

We study small perturbations of three linear Delay Differential Equations (DDEs) close to Hopf bifurcation points. In analytical treatments of such equations, many authors recommend a center manifold reduction as a first step. We demonstrate that the method of multiple scales, on simply discarding the infinitely many exponentially decaying components of the complementary solutions obtained at each stage of the approximation, can bypass the explicit center manifold calculation. Analytical approximations obtained for the DDEs studied closely match numerical solutions.

Synthesis of acicular hydrogoethite (alpha-FeOOH center dot xH(2)O; 0.1 < x < 0.22) particles using morphology controlling cationic additives and magnetic properties of maghemite derived from hydrogoethite

A method for the preparation of acicular hydrogoethite (alpha -FeOOH.xH(2)O, 0.1 < x < 0.22) particles of 0.3-1 mm length has been optimized by air oxidation of Fe( II) hydroxide gel precipitated from aqueous (NH4)(2)Fe(SO4)(2) solutions containing 0.005-0.02 atom% of cationic Pt, Pd or Rh additives as morphology controlling agents. Hydrogoethite particles are evolved from the amorphous ferrous hydroxide gel by heterogeneous nucleation and growth. Preferential adsorption of additives on certain crystallographic planes thereby retarding the growth in the perpendicular direction, allows the particles to acquire acicular shapes with high aspect ratios of 8-15. Synthetic hydrogoethite showed a mass loss of about 14% at similar to 280 degreesC, revealing the presence of strongly coordinated water of hydration in the interior of the goethite crystallites. As evident from IR spectra, excess H2O molecules (0.1- 0.22 per formula unit) are located in the strands of channels formed in between the double ribbons of FeO6 octahedra running parallel to the c- axis. Hydrogoethite particles constituted of multicrystallites are formed with Pt as additive, whereas single crystallite particles are obtained with Pd (or Rh). For both dehydroxylation as well as H-2 reduction, a lower reaction temperature (similar to 220 degreesC) was observed for the former (Pt treated) compared to the latter (Pd or Rh) (similar to 260 degreesC). Acicular magnetite (Fe3O4) was prepared either by reducing hydrogoethite (magnetite route) or dehydroxylating hydrogoethite to hematite and then reducing it to magnetite (hematite- magnetite route). According to TEM studies, preferential dehydroxylation of hydrogoethite along < 010 > leads to microporous hematite. Maghemite (gamma -Fe2O3 (-) (delta), 0 < < 0.25) was obtained by reoxidation of magnetite. The micropores are retained during the topotactic transformation to magnetite and finally to maghemite, whereas cylindrical mesopores are formed due to rearrangement of the oxygen sublattice from hexagonal to cubic close packing during the conversion of hydrogoethite to magnetite and then to maghemite. Accordingly, three different types of maghemite particles are realized: strongly oriented multicrystalline particles, single crystalline acicular particles with micropores or crystallites having mesopores. Higher values of saturation magnetization ((s) = 74 emu g(-1)) and coercivity (H-c = 320 Oe) are obtained for single crystalline mesoporous particles. In the other cases, the smaller size of particles and larger distribution of micropores decreases sigma (s) considerably ( < 60 emu g(-1)) due to relaxation effects of spins on the surface atoms as revealed by Mossbauer spectroscopy.

Progressively More Prolate Dark Matter Halo In the Outer Galaxy As Traced by Flaring Hi gas

A galactic disk in a spiral galaxy is generally believed to be embedded in an extended dark matter halo, which dominates its dynamics in the outer parts. However, the shape of the halo is not clearly understood. Here we show that the dark matter halo in the Milky Way is prolate in shape. Further, it is increasingly more prolate at larger radii, with the vertical-to-planar axis ratio monotonically increasing to 2.0 at 24 kpc. This is obtained by modeling the observed steeply flaring atomic hydrogen gas layer in the outer Galactic disk, where the gas is supported by pressure against the net gravitational field of the disk and the halo. The resulting prolate-shaped halo can explain several long-standing puzzles in galactic dynamics, for example, it permits long-lived warps thus explaining their ubiquitous nature.

Nature and strength of C-H center dot center dot center dot O interactions involving formyl hydrogen atoms: computational and experimental studies of small aldehydes

Structural and electronic properties of C-H center dot center dot center dot O contacts in compounds containing a formyl group are investigated from the perspective of both hydrogen bonding and dipole-dipole interactions, in a systematic and graded approach. The effects of a-substitution and self-association on the nature of the formyl H-atom are studied with the NBO and AIM methodologies. The relative dipole-dipole contributions in formyl C-H center dot center dot center dot O interactions are obtained for aldehyde dimers. The stabilities and energies of aldehyde clusters (dimer through octamer) have been examined computationally. Such studies have an implication in crystallization mechanisms. Experimental X-ray crystal structures of formaldehyde, acrolein and N-methylformamide have been determined in order to ascertain the role of C-H center dot center dot center dot O interactions in the crystal packing of formyl compounds.

Microwave spectroscopic and theoretical studies on the phenylacetylene center dot center dot center dot H(2)O complex: C-H center dot center dot center dot O and O-H center dot center dot center dot pi hydrogen bonds as equal partners

Rotational spectra of five isotopologues of the title complex, C(6)H(5)CCH center dot center dot center dot H(2)O, C(6)H(5)CCH center dot center dot center dot HOD, C(6)H(5)CCH center dot center dot center dot D(2)O, C(6)H(5)CCH center dot center dot center dot H(2)(18)O and C(6)H(5)CCD center dot center dot center dot H(2)O, were measured and analyzed. The parent isotopologue is an asymmetric top with kappa = -0.73. The complex is effectively planar (ab inertial plane) and both `a' and `b' dipole transitions have been observed but no c dipole transition could be seen. All the transitions of the parent complex are split into two resulting from an internal motion interchanging the two H atoms in H(2)O. This is confirmed by the absence of such doubling for the C(6)H(5)CCH center dot center dot center dot HOD complex and a significant reduction in the splitting for the D(2)O analog. The rotational spectra, unambiguously, reveal a structure in which H(2)O has both O-H center dot center dot center dot pi (pi cloud of acetylene moiety) and C-H center dot center dot center dot O (ortho C-H group of phenylacetylene) interactions. This is in agreement with the structure deduced by IR-UV double resonance studies (Singh et al., J. Phys. Chem. A, 2008, 112, 3360) and also with the global minimum predicted by advanced electronic structure theory calculations (Sedlack et al., J. Phys. Chem. A, 2009, 113, 6620). Atoms in Molecule (AIM) theoretical analysis of the complex reveals the presence of both O-H center dot center dot center dot pi and C-H center dot center dot center dot O hydrogen bonds. More interestingly, based on the electron densities at the bond critical points, this analysis suggests that both these interactions are equally strong. Moreover, the presence of both these interactions leads to significant deviation from linearity of both hydrogen bonds.

Microwave spectrum and structure of C(6)H(5)CCH center dot center dot center dot H(2)S complex

Rotational spectra of C(6)H(5)CCH center dot center dot center dot H(2)S, C(6)H(5)CCH center dot center dot center dot H(2)(34)S, C(6)H(5)CCH center dot center dot center dot HDS, C(6)H(5)CCH center dot center dot center dot D(2)S and C(6) H(5)CCD center dot center dot center dot H(2)S complexes have been observed using a pulsed nozzle Fourier transform microwave spectrometer. The observed spectrum is consistent with a structure in which hydrogen sulfide is located over the phenyl ring pi cloud and the distance between the centers of masses of the two monomers is 3.74 +/- 0.01 angstrom. In the complex, the H(2)S unit is shifted from the phenyl ring center towards the acetylene group. The vibrationally averaged structure has an effective Cs symmetry. Ab initio calculations were performed at MP2/aug-cc-pVDZ level of theory to locate the possible geometries of the complex. The calculations reveal the experimentally observed structure to be more stable than a coplanar arrangement of the monomers, which was observed for the C(6)H(5)CCH center dot center dot center dot H(2)O complex. Atoms in molecule theoretical analysis shows the presence of S-H center dot center dot center dot pi hydrogen bond. For the parent isotopologue, each transition frequency was found to split into two resulting from an interchange of the equivalent hydrogens of H(2)S unit in the complex. (C) 2011 Elsevier Inc. All rights reserved.

Weak C-H center dot center dot center dot O hydrogen bonds in anisaldehyde, salicylaldehyde and cinnamaldehyde

In situ cryocrystallization has been employed to grow single crystals of 4-methoxybenzaldehyde (anisaldehyde), C(8)H(8)O(2), 2-hydroxybenzaldehyde (salicylaldehyde), C(7)H(6)O(2), and (2E)-3-phenylprop-2-enal (cinnamaldehyde), C(9)H(8)O, all of which are liquids at room temperature. Several weak C-H center dot center dot center dot O interactions of the types C(aryl)-H center dot center dot center dot O, C(formyl)-H center dot center dot center dot O and Csp(3)-H center dot center dot center dot O are present in these related crystal structures.

Crystal packing and melting temperatures of small oxalate esters: the role of C-H center dot center dot center dot O hydrogen bonding

The simple dialkyl oxalates are generally liquids at room temperature except for dimethyl and di-tert-butyl oxalate which melt at 327 and 343 K. The crystal structures of diethyl, di-iso-propyl, di-n-butyl, di-tert-butyl and methyl ethyl oxalates were determined. The liquid esters were crystallized using the cryocrystallization technique. A comparison of the intermolecular interactions and packing features in these crystal structures was carried out. The crystal structure of dimethyl oxalate was redetermined at various temperatures. The other compounds were also studied at several temperatures in order to assess the attractive nature of the hydrogen bonds therein. A number of moderate to well defined C-H center dot center dot center dot O interactions account for the higher melting points of the two solid esters. Additionally, a diminished entropic contribution Delta S(m) in di-tert-butyl oxalate possibly increases the melting point of this compound further.

Extending the Supramolecular Synthon Based Fragment Approach (SBFA) for Transferability of Multipole Charge Density Parameters to Monofluorobenzoic Acids and their Cocrystals with Isonicotinamide: Importance of C-H center dot center dot center dot O, C-H center dot center dot center dot F, and F center dot center dot center dot F Intermolecular Regions

An extension of the supramolecular synthon-based fragment approach (SBFA) method for transferability of multipole charge density parameters to include weak supramolecular synthons is proposed. In particular, the SBFA method is applied to C-H center dot center dot center dot O, C-H center dot center dot center dot F, and F center dot center dot center dot F containing synthons. A high resolution charge density study has been performed on 4-fluorobenzoic acid to build a synthon library for C-H center dot center dot center dot F infinite chain interactions. Libraries for C-H center dot center dot center dot O and F center dot center dot center dot F synthons were taken from earlier work. The SBFA methodology was applied successfully to 2- and 3-fluorobenzoic acids, data sets for which were collected in a routine manner at 100 K, and the modularity of the synthons was demonstrated. Cocrystals of isonicotinamide with all three fluorobenzoic acids were also studied with the SBFA method. The topological analysis of inter- and intramolecular interaction regions was performed using Bader's AIM approach. This study shows that the SBFA method is generally applicable to generate charge density maps using information from multiple intermolecular regions.

Evidence for the ``Amphoteric'' Nature of Fluorine in Halogen Bonds: An Instance of Cl center dot center dot center dot F Contact

This study presents unambiguous experimental evidence in support of the highly debated ``halogen bond donor'' character of organic fluorine. Two examples of intermolecular Cl center dot center dot center dot F contacts, with F-atom as halogen bond acceptor and donor, have been analyzed by in situ cryocrystallography and theoretical charge density studies.

Cause and Effect of Feedback: Multiphase Gas in Cluster Cores Heated by AGN Jets

Multiwavelength data indicate that the X-ray-emitting plasma in the cores of galaxy clusters is not cooling catastrophically. To a large extent, cooling is offset by heating due to active galactic nuclei (AGNs) via jets. The cool-core clusters, with cooler/denser plasmas, show multiphase gas and signs of some cooling in their cores. These observations suggest that the cool core is locally thermally unstable while maintaining global thermal equilibrium. Using high-resolution, three-dimensional simulations we study the formation of multiphase gas in cluster cores heated by collimated bipolar AGN jets. Our key conclusion is that spatially extended multiphase filaments form only when the instantaneous ratio of the thermal instability and free-fall timescales (t(TI)/t(ff)) falls below a critical threshold of approximate to 10. When this happens, dense cold gas decouples from the hot intracluster medium (ICM) phase and generates inhomogeneous and spatially extended Ha filaments. These cold gas clumps and filaments ``rain'' down onto the central regions of the core, forming a cold rotating torus and in part feeding the supermassive black hole. Consequently, the self-regulated feedback enhances AGN heating and the core returns to a higher entropy level with t(TI)/t(ff) > 10. Eventually, the core reaches quasi-stable global thermal equilibrium, and cold filaments condense out of the hot ICM whenever t(TI)/t(ff) less than or similar to 10. This occurs despite the fact that the energy from AGN jets is supplied to the core in a highly anisotropic fashion. The effective spatial redistribution of heat is enabled in part by the turbulent motions in the wake of freely falling cold filaments. Increased AGN activity can locally reverse the cold gas flow, launching cold filamentary gas away from the cluster center. Our criterion for the condensation of spatially extended cold gas is in agreement with observations and previous idealized simulations.

Na0.33V2O5 center dot 1.5H(2)O nanorings/nanorods and Na0.33V2O5 center dot 1.5H(2)O/RGO composite fabricated by a facile one pot synthesis and its lithium storage behavior

In this work, Na0.33V2O5 center dot 1.5H(2)O nanorings/nanorods and Na0.33V2O5 center dot 1.5H(2)O/reduced graphene oxide (RGO) composites have been prepared through a facile hydrothermal route in acidic medium at 200 degrees C for 2 days. The hydrothermally derived products have been characterized by powder X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR), Raman spectroscopy, UV-Visible spectroscopy, Thermogravimetric analysis (TGA), Field emission scanning electron microscopy (FESEM), Transmission electron microscopy (TEM) and electrochemical discharge-charge cycling in lithium ion battery. XRD pattern exhibits the layered structure of Na0.33V2O5 center dot 1.5H(2)O and the composite shows the presence of RGO at 2 theta = 25.8 degrees. FTIR spectrum shows that the band at 760 cm(-1) could be assigned to a V-OH2 stretching mode due to coordinated water. Raman spectrum shows that the band at 264 cm(-1) is due to the presence of water molecules between the layers. FESEM/TEM micrographs reveal that the products consist of nanorings of inner diameter 5 mu m and thickness of the ring is found to be 200-300 nm. Addition of exfoliated graphene oxide (EGO) destroys the formation of rings. The reduction of EGO sheets into RGO is also evidenced by the red shift of the absorbance peak from 228 nm to 264 nm. In this composite Na0.33V2O5 center dot 1.5H(2)O nanorods may adhere to the surface of RGO and/or embedded in the RGO nanosheets. As a result, an effective three-dimensional conducting network was formed by bridging RGO nanosheets, which can facilitate electron transport effectively and thus improve the kinetics and rate performance of Na0.33V2O5 center dot 1.5H(2)O nanorings/nanorods. The Na0.33V2O5 center dot 1.5H(2)O/RGO composites exhibited a discharge capacity of 340 mAh g(-1) at a current density of 0.1 mA g(-1) and also an improved cyclic stability. RGO plays a `flexible confinement' function to enwrap Na0.33V2O5 center dot 1.5H(2)O nanorods, which can compensate for the volume change and prevent the detachment and agglomeration of pulverized Na0.33V2O5 center dot 1.5H(2)O, thus extending the cycling life of the electrode. A probable reaction mechanism for the formation of Na0.33V2O5 center dot 1.5H(2)O nanorings is also discussed. (C) 2012 Elsevier B.V. All rights reserved.

Charge Density Analysis of Ferulic Acid: Robustness of a Trifurcated C-H center dot center dot center dot O Hydrogen Bond

The toplogical features of a sporadic trifurcated C-H center dot center dot center dot O interaction region, where an oxygen atom acts as an acceptor of three weak hydrogen bonds, has been investigated by experimental and theoretical charge density analysis of ferulic acid. The interaction energy of the asymmetric molecular dimer formed by the trifurcated C-H center dot center dot center dot O motif, based on the multipolar model, is shown to be greater than the corresponding asymmetric O-H center dot center dot center dot O dimer in this crystal structure. Further, the hydrogen bond energies associated with these interaction motifs have been estimated from the local kinetic and potential energy densities at the bond critical points. The trends suggest that the interaction energy of the trifurcated C-H center dot center dot center dot O region is comparable to that of a single O-H center dot center dot center dot O hydrogen bond.

Engagement of CF3 Group in N-H center dot center dot center dot F-C Hydrogen Bond in the Solution State: NMR Spectroscopy and MD Simulation Studies

Unambiguous evidence for the engagement of CF3 group in N-H center dot center dot center dot F-C hydrogen bond in a low polarity solvent, the first observation of its kind, is reported. The presence of such weak molecular interactions in the solution state is convincingly established by one and two-dimensional H-1, F-19, and natural abundant N-15 NMR spectroscopic studies. The strong and direct evidence is derived by the observation of through-space couplings, such as, (1h)J(FH), (1h)J(FN), and (2h)J(FF), where the spin polarization is transmitted through hydrogen bond. In an interesting example of a molecule containing two CF3 groups getting simultaneously involved in hydrogen bond, where hydrogen bond mediated couplings are not reflected in the NMR spectrum, F-19-F-19 NOESY experiment yielded confirmatory evidence. Significant deviations in the strengths of (1)J(NH), variable temperature, and the solvent induced perturbations yielded additional support. The NMR results are corroborated by both DFT calculations and MD simulations, where the quantitative information on different ways of involvement of fluorine in two and three centered hydrogen bonds, their percentage of occurrences, and geometries have been obtained. The hydrogen bond interaction energies have also been calculated.