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).

Slow isocharged sequence ions with helium collisions: Projectile core dependence

The collisions of the isocharged sequence ions of q=6 (C6+, N6+, O6+, F6+, Ne6+, Ar6+, and Ca6+), q=7 (F7+, Ne7+, S7+, Ar7+, and Ca7+), q=8 (F8+, Ne8+, Ar8+, and Ca8+), q=9 (F9+, Ne9+, Si9+, S9+, Ar9+, and Ca9+) and q=11 (Si11+, Ar11+, and Ca11+) with helium at the same velocities were investigated. The cross-section ratios of the double-electron transfer (DET) to the single-electron capture (SEC) sigma(DET)/sigma(SEC) and the true double-electron capture (TDC) to the double-electron transfer sigma(TDC)/sigma(DET) were measured. It shows that for different ions in an isocharged sequence, the experimental cross-section ratio sigma(DET)/sigma(SEC) varies by a factor of 3. The results confirm that the projectile core is another dominant factor besides the charge state and the collision velocity in slow (0.35-0.49v(0); v(0) denotes the Bohr velocity) highly charged ions (HCIs) with helium collisions. The experimental cross-section ratio sigma(DET)/sigma(SEC) is compared with the extended classical over-barrier model (ECBM) [A. Barany , Nucl. Instrum. Methods Phys. Res. B 9, 397 (1985)], the molecular Coulombic barrier model (MCBM) [A. Niehaus, J. Phys. B 19, 2925 (1986)], and the semiempirical scaling laws (SSL) [N. Selberg , Phys. Rev. A 54, 4127 (1996)]. It also shows that the projectile core properties affect the initial capture probabilities as well as the subsequent relaxation of the projectiles. The experimental cross-section ratio sigma(TDC)/sigma(DET) for those lower isocharged sequences is dramatically affected by the projectile core structure, while for those sufficiently highly isocharged sequences, the autoionization always dominates, hence the cross-section ratio sigma(TDC)/sigma(DET) is always small.

Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.

Kaolinite particle sizes in the <2 µM range using laser scattering

The Clay Minerals Society Source Clay kaolinites, Georgia KGa-1 and KGa-2, have been subjected to particle size determinations by 1) conventional sedimentation methods, 2) electron microscopy and image analysis, and 3) laser scattering using improved algorithms for the interaction of light with small particles. Particle shape, size distribution, and crystallinity vary considerably for each kaolinite. Replicate analyses of separated size fractions showed that in the <2 µm range, the sedimentation/centrifugation method of Tanner and Jackson (1947) is reproducible for different kaolinite types and that the calculated size ranges are in reasonable agreement with the size bins estimated from laser scattering. Particle sizes determined by laser scattering must be calculated using Mie theory when the dominant particle size is less than ∼5 µm. Based on this study of two well-known and structurally different kaolinites, laser scattering, with improved data reduction algorithms that include Mie theory, should be considered an internally consistent and rapid technique for clay particle sizing.

Characterisation of microstructure and evaluation of optical and EPR properties of superhydrophobic copper dodecanoate films

Copper dodecanoate films prepared by emulsion method exhibit superhydrophobic property with water contact angle of 155 degrees and sliding angle of <2 degrees. The films have been characterised by using X-ray diffraction, field emission scanning electron microscopy and Fourier transform infrared spectroscopy techniques. Surface microstructure of copper dodecanoate consists of numerous microscale papillas of about 6-12 mu m in length with a diameter in the range of 360-700 nm. The superhydrophobicity of the films is due to their dual micronano surface morphology. The wetting behaviour of the film surface was studied by a simple water immersion test. The results show that copper dodecanoate film retained superhydrophobic property even after immersing in water for about 140 h. The optical absorption spectrum exhibits two broadbands centred at 388 and 630 nm that have been assigned to B-2(1g) -> E-2(g) and B-2(1g) -> B-2(2g) transitions of Cu2+ ions, respectively. The electron paramagnetic resonance spectrum exhibits two resonance signals with effective g values at g(parallel to)approximate to 2.308 and g(perpendicular to) approximate to 2.071, which suggests that the unpaired electron occupies d(x2-y2) orbital in the ground state. Copyright (C) 2011 John Wiley & Sons, Ltd.

Tunable Photoluminescence and Cathodoluminescence Properties of Eu3+-Doped LaInO3 Nanocrystalline Phosphors

LaInO3:Eu3+ phosphors were prepared by a Pechini sol-gel process. X-ray diffraction (XRD), field-emission scanning electron microscopy (FE-SEM), diffuse reflectance, photoluminescence, cathodoluminescence spectra, as well as lifetimes were utilized to characterize the synthesized phosphors. XRD results reveal that the sample begins to crystallize at 600 degrees C and pure LaInO3 phase can be obtained at 800 degrees C. The crystallinity increases upon raising the annealing temperature. The FE-SEM images indicate that LaInO3:Eu3+ phosphors are composed of fine and spherical grains around 40-80 nm in size. Under the excitation of UV light and low-voltage electron-beams, LaInO3:Eu3+ phosphors show the characteristic emissions of the Eu3+ (D-5(J)-F-7(J) J,J(')=0,1,2,3 transitions). The luminescence colors can be tuned from yellowish warm white to red by changing the doping concentration of Eu3+ to some extent. The corresponding luminescence mechanisms have been proposed.

Tunable luminescence properties of CaIn2O4 : Eu3+ phosphors

CaIn2O4:Eu3+ phosphors were prepared by a Pechini so-gel process. X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), photoluminescence (PL), cathodoluminescence (CL) spectra as well as lifetimes were utilized to characterize the samples. The XRD results reveal that the samples begin to crystallize at 800 degrees C, and the crystallinity increases upon raising the annealing temperature. The FE-SEM images indicate that the CaIn2O4:Eu3+ samples consist of fine and spherical grains with size around 200-400 nm. Under the excitation of ultraviolet light and low-voltage electron beams, the CaIn2O4:Eu3+ phosphors show the characteristic emissions of Eu3+ ((DJ-7FJ ')-D-5 J, J ' = 0, 1, 2, 3 transitions). The luminescence color can be tuned from white to orange to red by adjusting the doping concentration of EU3+. The corresponding luminescence mechanisms have been proposed.

Enhanced photoluminescence of Ba2GdNbO6: Eu3+/Dy3+ phosphors by Li+ doping

The Ba2GdNbO6: Eu3+/Dy3+ and Li+-doped Ba2GdNbO6: Eu3+/Dy3+ phosphors were prepared by solid-state reaction process. X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM) and photoluminescence (PL) as well as lifetimes, was utilized to characterize the resulting phosphors. Under the excitation of ultraviolet light, the Ba2GdNbO6: Eu3+/Dy3+ and Li+-doped Ba2GdNbO6: Eu3+/Dy3+ show the characteristic emissions of Eu3+ (D-5(0)-F-7(1,2,3) transitions dominated by D-5(0)-F-7(1) at 593 nm) and Dy3+ (F-4(9/2)-H-6(15/2),(13/2) transitions dominated by F-4(9/2)-H-6(15/2) at 494 nm), respectively. The incorporation of Li+ ions into the Ba2GdNbO6: Eu3+/Dy3+ phosphors has enhanced the PL intensities depending on the doping concentration of Li+, and the highest emission was obtained in Ba2Gd0.9NbO6: 0.10Eu(3+), 0.01Li(+) and Ba2Gd0.95NbO6: 0.05Dy(3+), 0.07Li(+), respectively. An energy level diagram was proposed to explain the luminescence process in the phosphors.

Up-conversion spectrum properties of the oxy-fluoride glass co-doped with Er3+ and Yb3+

Up-conversion of 45PbF(2)-45GeO(2)-10WO(3) oxy-fluoride glasses co-doped with Yb3+ and Er3+ ions were prepared by fusion method through melting at 1223 K and then annealing at 653 K for 4 h. Transmittance of the undoped host glass was beyond 73% in a range of 0.6-2.5 mu m and the co-doped glasses still provided good transmittance beyond 50%. Refractive indices of the host and co-doped glasses were 1.517 and 1.650, respectively. Blue, green and red fluorescence spectra were observed in a range of 400-700 nm under 980 nm diode laser excitation. Up-conversion spectra at about 410, 518, 530and 650 nm were assigned to the 4f electron transitions of H-2(9/2) -> I-4(15)/(2), H-2(15/2) -> I-4(15/2) S-4(3/2) -> I-4(15/2) and F-4(9/2) -> I-4(15/2) of Er3+ ion, respectively. The mechanism of energy transfer between Yb3+ and Er3+ ions in the glass was analyzed. Raman shift shows the non-radiative relaxation of the glass sample is low.

ELECTROCHEMICAL-BEHAVIOR OF BIS(2 /17-ARSENOTUNGSTATE) LANTHANATES AND THEIR ELECTROCATALYTIC REDUCTION FOR NITRITE

A series of new catalysts, K-14[Ln(As2W17O61)(2)]. xH(2)O (Ln = La, Pr, Sm, Eu, Gd, Tb, Dy, Tm and Yb) which can electrocatalyze reduction of nitrite are presented and their electrochemical behavior is described in this paper. Bis(2:17-arsenotungstate) lanthanates which are monovacant Dawson derivatives, exhibit two 2-electron and one 1-electron waves, attributed to electron addition and removal from the tungsten-oxide framework that comprises each anion structure. The formal potentials of redox couples are dependent on solution pH. Double-hump principle of formal potentials takes effect with increasing atomic number of lanthanide elements following their special electronic shell structure. The third waves of all the heteropolyanions have good electrocatalytic activities for nitrite reduction at pH 5.0.

Turning solid aluminium transparent by intense soft X-ray photoionization

Saturable absorption is a phenomenon readily seen in the optical and infrared wavelengths. It has never been observed in core-electron transitions owing to the short lifetime of the excited states involved and the high intensities of the soft X-rays needed. We report saturable absorption of an L-shell transition in aluminium using record intensities over 10(16)W cm(-2) at a photon energy of 92 eV. From a consideration of the relevant timescales, we infer that immediately after the X-rays have passed, the sample is in an exotic state where all of the aluminium atoms have an L-shell hole, and the valence band has approximately a 9 eV temperature, whereas the atoms are still on their crystallographic positions. Subsequently, Auger decay heats the material to the warm dense matter regime, at around 25 eV temperatures. The method is an ideal candidate to study homogeneous warm dense matter, highly relevant to planetary science, astrophysics and inertial confinement fusion.

MEASUREMENT OF THE PHOTO-PUMP STRENGTH OF THE 3D-5F TRANSITIONS IN THE AUTOMATICALLY LINE MATCHED NI-LIKE SM PHOTOPUMPED X-RAY LASER

The photo-pump strengths of both the ((3 (d) over bar(4))(0)(3d(6))(0))(0)-(((3 (d) over bar(3))(3/2)(3d(6))(0))(3/2)(5 (f) over bar)(5/2))(1) and the ((3 (d) over bar(4))(0)(3d(6))0)0-(((3 (d) over bar(4))(0)(3d(5))(5/2))(5/2)(5f)(7/2))(1) transitions in Ni-like Sm34+ have been measured to be 2.0 x 10(-4) and 2.4 x 10(-4) photons/mode respectively. The implications of the measurement are briefly discussed in a comparison of the merits of automatically line matched photo-pump scheme to those of the collisional excitation Ni-like Sm+34 scheme.

Addition stéréosélective de nucléophiles sur un centre acétal : synthèse de nucléosides 1’,2’-cis

Plusieurs analogues de nucléosides thérapeutiques (Ara-C, Clofarabine), utilisés pour le traitement de leucémies, présentent un arrangement 1’,2’-cis entre la nucléobase reliée au centre anomère et le substituant (électroattracteur) en C-2’. Récemment, notre laboratoire a développé une approche synthétique pour former sélectivement des analogues de nucléosides et de thionucléosides 1’,2’-trans et 1’,2’-cis à partir de précurseurs acycliques. Ce mémoire présente une nouvelle méthodologie pour accéder efficacement aux analogues de nucléosides 1’,2’-cis à partir de furanosides. Différents groupements en position anomérique ont été examinés, sous conditions cinétiques en utilisant le bromure de diméthylbore pour générer sélectivement des produits acycliques ou cycliques. Les intermédiaires cinétiques de différents furanosides de méthyle formés en présence de Me2BBr ont été piégés in situ par un thiol pour générer des thioacétals acycliques avec de bonnes voire d’excellentes diastéréosélectivités. Les produits générés sont en accord avec une rétention globale de l’information stéréochimique du centre acétal et deux déplacements SN2 consécutifs ont été suggérés pour rationaliser ces résultats. Toutefois, l’objectif de synthétiser des analogues de nucléosides à partir de furanosides de méthyle a échoué. Tel que démontré par le Dr Michel Prévost, l’activation par Me2BBr des lactols des quatres différents furanosides suivie d’une addition in situ d’une base silylée a permis de former diastéréosélectivement les analogues de nucléosides 1’,2’-cis correspondants avec d’excellents rendements. Nous avons démontré que d’autres substrats peuvent être employés et que l’induction stéréochimique est sous contrôle du substituant électroattracteur en C-2. D’autres acides de Lewis, tel que TMSBr, peuvent également être utilisés. Cette méthodologie a également été étendue à d’autres nucléophiles tels que des Grignards ou des éthers d’énols silylés, conduisant à de bonnes sélectivités.