Bootstrap percolation on homogeneous trees has 2 phase transitions

We study the threshold theta bootstrap percolation model on the homogeneous tree with degree b + 1, 2 <= theta <= b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call p(f), such that a) for p > p(f), the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p < p(f) , then for almost every initial configuration, the final bootstrapped configuration has density of occupied vertices less than 1. In this paper, we establish the existence of a distinct critical value for p, p(c), such that 0 < p(c) < p(f), with the following properties: 1) if p <= p(c), then for almost every initial configuration there is no infinite cluster of occupied vertices in the final bootstrapped configuration; 2) if p > p(c), then for almost every initial configuration there are infinite clusters of occupied vertices in the final bootstrapped configuration. Moreover, we show that 3) for p < p(c), the distribution of the occupied cluster size in the final bootstrapped configuration has an exponential tail; 4) at p = p(c), the expected occupied cluster size in the final bootstrapped configuration is infinite; 5) the probability of percolation of occupied vertices in the final bootstrapped configuration is continuous on [0, p(f)] and analytic on (p(c), p(f) ), admitting an analytic continuation from the right at p (c) and, only in the case theta = b, also from the left at p(f).

DFT study of the electronic, vibrational, and optical properties of SnO(2)

We report results on the electronic, vibrational, and optical properties of SnO(2) obtained using first-principles calculations performed within the density functional theory. All the calculated phonon frequencies, real and imaginary parts of complex dielectric function, the energy-loss spectrum, the refractive index, the extinction, and the absorption coefficients show good agreement with experimental results. Based on our calculations, the SnO(2) electron and hole effective masses were found to be strongly anisotropic. The lattice contribution to the low-frequency region of the SnO(2) dielectric function arising from optical phonons was also determined resulting the values of E > (1aSyen) (latt) (0) = 14.6 and E > (1ayen) (latt) (0) = 10.7 for directions perpendicular and parallel to the tetragonal c-axis, respectively. This is in excellent agreement with the available experimental data. After adding the electronic contribution to the lattice contribution, a total average value of E >(1)(0) = 18.2 is predicted for the static permittivity constant of SnO(2).

Study on the observation of Eu(2+) and Eu(3+) valence states in low silica calcium aluminosilicate glasses

The optical, magnetic and structural properties of Eu doped low silica calcium aluminosilicate glasses were investigated. The optical absorption coefficient presented two bands at 39 246 and 29 416 cm(-1), which were assigned respectively to the 4f(7) ((8)S(7/2)) -> 4f(6) (4F(J)) 5d (T(2g)), and 4f(7) ((8)S(7/2)) -> 4f(6) (4F(J)) 5d (E(g)) transitions of Eu(2+). The fluorescence measured at 300 K on a sample doped with 0.5 wt% of Eu(2)O(3) exhibited a broad band centered at 17 350 cm(-1), which is attributed to the 4f(6)5d -> 4f(7) transition of Eu(2+), whereas the additional peaks are due to the (5)D(0) -> (7)F(J) (J = 1, 2, 4) transitions of Eu(3+). From magnetization and XANES data it was possible to evaluate the fractions of Eu(2+) and Eu(3+) for the sample doped with 0.5 and 5.0 wt% of Eu(2)O(3), the values of which were approximately 30 and 70%, respectively.

Magneto-intersubband oscillations in triple quantum wells

We present magnetotransport studies of high-density triple quantum well samples with different barrier widths. Because of electron transitions between three occupied 2D subbands, the magneto-resistance shows magneto-intersubband oscillations whose periodicity is determined by the subband separation energies. Temperature-dependent measurements allow us to extract quantum lifetime of electrons. A theoretical consideration of the observed phenomenon is also presented. (C) 2009 Elsevier B.V. All rights reserved.

Empirical analysis of the Lieb-Oxford bound in ions and molecules

Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, in particular, are important for the construction of improved density functionals. Here we investigate one such universal property-the Lieb-Oxford lower bound-for ionic and molecular systems. In recent work [J Chem Phys 127, 054106 (2007)], we observed that for atoms and electron liquids this bound may be substantially tightened. Calculations for a few ions and molecules suggested the same tendency, but were not conclusive due to the small number of systems considered. Here we extend that analysis to many different families of ions and molecules, and find that for these, too, the bound can be empirically tightened by a similar margin as for atoms and electron liquids. Tightening the Lieb-Oxford bound will have consequences for the performance of various approximate exchange-correlation functionals. (C) 2008 Wiley Periodicals Inc.

Bendadaite, a new iron arsenate mineral of the arthurite group

Bendadaite, ideally Fe(2+)Fe(2)(3+)(AsO(4))(2)(OH)(2 center dot).4H(2)O, is a new member of the arthurite group It was found as a weathering product of arsenopyrite on a single hand specimen from the phosphate pegmatite Bendada. central Portugal (type locality) Co-type locality is the granite pegmatite of La via do Almerindo (Almerindo mine), Linopolis, Divmo das Laranjeiras county, Minas Gerais, Brazil Further localities are the Vein Negra mine, Copiapo province, Chile, mid-East, Bou Azzer district, Morocco, and Para Inferida yard, Fenugu Sibirt mine, Gonnosfanadiga, Medio Campidano Province, Sardinia. Italy Type bendadaite occurs as blackish green to dark brownish tufts (<0 1 mm long) and flattened radiating aggregates. in intimate association with an intermediate member of the scorodite-mansfieldite series It is monoclinic. space group P2(l/c). with a = 10 239(3) angstrom. b = 9 713(2) angstrom, c = 5 552(2) angstrom. beta = 94 11(2)degrees. = 550 7(2) angstrom(3). Z = 2 Electron-microprobe analysis yielded (wt %). CaO 0 04, MnO 0 03. CuO 006, ZnO 004. Fe(2)O(3) (total) 43 92, Al(2)O(3) 115. SnO(2) 0 10, As(2)O(5) 43 27. P(2)O(5) 1 86, SO(3) 0.03 The empirical formula is (Fe(0 52)(2+)Fe(0 32)(3+)rectangle(0 16))(Sigma 1 00)(Fe(1 89)(3+)Al(0 11))(Sigma 2 00)(As(1 87)P(0 13))(Sigma 2 00)O(8)(OH)(2 00) 4H(2)O based. CM 2(As,P) and assuming ideal 80, 2(OH), 4H2O and complete occupancy of the ferric on site by Fe(3+) and Al Optically, bendadaite is biaxial, positive, 2V(est) = 85+/-4 degrees, 2V(eale) = 88 degrees, with alpha 1 734(3). 13 1 759(3), 7 1 787(4) Pleochrosim is medium strong X pale reddish brown. Y yellowish brown, Z dark yellowish brown. absorption Z > V > X, optical dispersion weak, r > v. Optical axis plane Is parallel to (010), with X approximately parallel to a and Z nearly parallel to c Bendadaite has vitreous to sub-adamantine luster, is translucent and non-fluorescent It is brittle, shows irregular fracture and a good cleavage parallel to 1010} 3 15 0 10 g/cm(3), 3 193 g/cm3 (for the empirical formula) The five strongest powder diffraction lines [d in angstrom (I)(hkl] are 10 22 (10)(100), 7 036 (8)(110), 4 250 (5)(11 I), 2 865 (4)(311), 4 833 (3)(020,011) The d spacings are very similar to those of its Zn analogue, ojelaite The crystal structure of bendadaite was solved and refined using a crystal from the co-type locality with the composition (Fe(0 95)(2+)rectangle(0 05))(Sigma 1 00)(Fe(1 80)(3+)Al(0 20))Sigma(2 00)(As(1 48)P(0 52))(Sigma 2 00)O(8)) (OH)(2) 4H(2)O (R = 16%) and confirms an arthurite-type atomic arrangement

Observation of two-magnon bound states in the spin-1 anisotropic Heisenberg antiferromagnetic chain system NiCl2-4SC(NH2)(2)

Results of systematic tunable-frequency ESR studies of the spin dynamics in NiCl2-4SC(NH2)(2) (known as DTN), a gapped S = 1 chain system with easy-plane anisotropy dominating over the exchange coupling (large-D chain), are presented. We have obtained direct evidence for two-magnon bound states, predicted for S = 1 large-D spin chains in the fully spin-polarized (FSP) phase. The frequency-field dependence of the corresponding excitations was calculated using the set of parameters obtained earlier [S.A. Zvyagin, et al., Phys. Rev. Lett. 98 (2007) 047205]. Very good agreement between the calculations and the experiment was obtained. It is argued that the observation of transitions from the ground to two-magnon bound states might indicate a more complex picture of magnetic interactions in DTN, involving a finite in-plane anisotropy. (C) 2007 Elsevier B.V. All rights reserved.

Preparation and characterization of Cd(2)Nb(2)O(7) thin films on Si substrates

Thin Cd(2)Nb(2)O(7) films were grown on single-crystal p-type SiO(2)/Si substrates by the metallo-organic decomposition (MOD) technique. The films were investigated by X-ray diffraction, X-ray energy-dispersive spectroscopy, and field emission scanning electron microscopy, and showed a single phase (cubic pyrochlore), a crack-free spherical grain structure, and nanoparticles with a mean size of about 68 nm. A Cauchy model was also used in order to obtain the thickness and index of refraction of the stack layers (transparent layer/SiO(2)/Si) by spectroscopic ellipsometry (SE). The dielectric constant (K) of the films was calculated to be about 25 from the capacitance-voltage (C-V) measurements. (c) 2008 Elsevier Ltd. All rights reserved.

Experimental Evidence of the Occurrence of Intramolecular Electron Transfer in Catalyzed 1,2-Dioxetane Decomposition

The activation parameters for the thermal decomposition of 13 acridinium-substituted 1,2-dioxetanes, bearing an aromatic moiety, were determined and their chemiluminescence emission quantum yields estimated, utilizing in situ photosensitized 1,2-dioxetane generation and observation of its thermal decomposition kinetics, without isolation of these highly unstable cyclic peroxides. Decomposition rate constants show linear free-energy correlation for electron-withdrawing substituents, with a Hammett reaction constant of rho = 1.3 +/- 0.1, indicating the occurrence of an intramolecular electron transfer from the acridinium moiety to the 1,2-dioxetane ring, as postulated by the intramolecular chemically initiated electron exchange luminescence (CIEEL) mechanism. Emission quantum yield behavior can also be rationalized on the basis of the intramolecular CIEEL mechanism, additionally evidencing its occurrence in this transformation. Both relations constitute the first experimental evidence for the occurrence of the postulated intramolecular electron transfer in the catalyzed and induced decomposition of properly substituted 1,2-dioxetanes.

Luminescent nanoparticles of MgAl(2)O(4):Eu, Dy prepared by citrate sol-gel method

MgAl(2)O(4):Eu, Dy nanoparticles were prepared by citrate sol-gel method and thermally treated at 600, 700, 800 and 900 degrees C. The trivalent europium ion is partially reduced to the divalent state at 700 and 800 degrees C. Infrared spectra of the phosphors showed bands around 700 and 520 cm(-1) corresponding to the AlO(6) groups. X-ray diffraction patterns present sharp reflections of samples heated from 700 to 900 degrees C indicating the MgAl(2)O(4) spinel phase. Grain size in the range 20-30 nm were observed by measurement of transmission electron microscopy (TEM). The emission spectra of the phosphors show a broadened band at 480 nm assigned to the 4f(G)5d -> 4f(7) ((8)S(7/2)) transition of Eu(2+) ion overlapped to the (4)F(9/2) -> (6)H(15/2) transition of the Dy(3+) ion. Besides, the (4)F(9/2) -> (6)H(13/2) transition (579 nm) of Dy(3+) ion is overlapped with the (5)D(0) -> (7)F(0) (578 nm) and (5)D(0) -> (7)F(1) (595 nm) transitions from the Eu(3+) ion. Excitation spectra of the sample heated at 900 degrees C monitoring the excitation at 615 nm of (5)D(0) -> (7)F(2) transition of Eu(3+) ion exhibit a broad band assigned to the O -> Eu(3+) ligand-to-metal charge-transfer states (LMCT) around 280 nm. The samples present green persistent luminescence after exposure to UV radiation. The chromaticity coordinates were obtained from the luminescence emission spectrum. (C) 2008 Elsevier B.V. All rights reserved.

Interfacial Electron Transfer Dynamics Following Laser Flash Photolysis of [Ru(bpy)(2)((4,4 `-PO(3)H(2))(2)bpy)](2+) in TiO(2) Nanoparticle Films in Aqueous Environments

Nanosecond laser flash photolysis has been used to investigate injection and back electron transfer from the complex [(Ru-(bpy)(2)(4,4`-(PO(3)H(2))(2)bpy)](2+) surface-bound to TiO(2) (TiO(2)-Ru(II)). The measurements were conducted under conditions appropriate for water oxidation catalysis by known single-site water oxidation catalysts. Systematic variations in average lifetimes for back electron transfer, - were observed with changes in pH, surface coverage, incident excitation intensity, and applied bias. The results were qualitatively consistent with a model involving rate-limiting thermal activation of injected electrons from trap sites to the conduction band or shallow trap sites followed by site-to-site hopping and interfacial electron transfer, TiO(2)(e(-))-Ru(3+) -> TiO(2)-Ru(2+). The appearance of pH-dependent decreases in the efficiency of formation of TiO(2)-Ru(3+) and in incident-photon-to-current efficiencies with the added reductive scavenger hydroquinone point to pH-dependent back electron transfer processes on both the sub-nanosecond and millisecond-microsecond time scales, which could be significant in limiting long-term storage of multiple redox equivalents.