Description: This article discusses anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation. Abstract: We consider the d=1 nonlinear Fokker-Planck-like equation with fractional derivatives (∂/∂t)P(x,t) = D(∂ƴ/∂xƴ)[P(x,t]v. Exact time-dependent solutions are found for v = (2 - y)/(1 + y)(-∞ < y ⩽ 2). By considering the long-distance asymptotic behavior of these solutions, a connection is established, namely, q = (y + 3)/(Y + 1)(0 < y ⩽ 2), with the solutions optimizing the nonextensive entropy characterized by index q. Interestingly enough, this relation coincides with the only already known for Lévy-like superdiffusion (i.e., v = 1 and 0 < y ⩽ 2). Finally, for (y,v) = (2,0) the authors obtain q=5/3, which differs from the value q = 2 corresponding to the y = 2 solutions available in the literature (v < 1 porous medium equation), thus exhibiting nonuniform convergence.

Description: Article containing an interview of James Marshall by Brian Coppola regarding Marshall's "Rediscovery of the Elements" articles. Marshall discusses his motivations for traveling to European locations where elements were discovered, his plans for the future, and other projects.

Description: This article discusses high sensitivity measurement of implanted As in the presence of Ge in Ge(x)Si(1-x)/Si layered alloys using trace element accelerator mass spectrometry. Abstract: Various devices can be realized on strained GeSi/Si substrates by doping the substrate with different impurities such as As. As is an n-type dopant in both Ge and Si. As cross contamination can also arise during germanium preamorphization implantation due to inadequate mass resolution in the implanter. Thus, it is important to be able to accurately measure low-level As concentrations in the presence of Ge. Secondary ion mass spectrometry (SIMS) is the standard technique for these types of measurements but is constrained by mass interferences from molecular ions (⁷⁴GeH, ²⁹Si³⁰Si¹⁶O). The trace element accelerator mass accelerator technique allows the breakup of interfering molecules. As is measured in a GeSi matrix with sensitivity significantly better than SIMS.

Description: This article discusses inter- and intramolecular experimental and calculated equilibrium isotope effects. Abstract: Intermolecular equilibrium isotope effects (EIEs) were measured (26.5 ˚C) and calculated for (silox)₂₋ (ᵗBu₃SiND)TiRᴅ (1-ND-Rᴅ) + RʜH ⇆ (silox)₂(ᵗBu₃SiNH)TiRʜH/RᴅD = CH₄/CD₄, 2.00(6), calcd 1.88; C₂H₆/C₂D₆, 2.22(8), 1.93; ᶜC₃H₆/C₃D₆, 1.71(4), 1.48; C₂H₄/C₂D₄, 1.41(11), 1.34; C₆H₆/C₆D₆, 1.22(7), 1.26; C₇H₈/C₇D₈ (50.0 ˚C), 1.59(6), 1.55. Related intramolecular EIEs for (silox)₂(ᵗBu₃SiND)- TiR' (1-ND-R') ⇆ (silox)₂(ᵗBu₃SiNH)TiR (1-R) are provided: RH = R'D = CH₃D, 3.16(25), calcd 2.60; CH₂D₂, 1.13(8), 0.911; CHD₃, 0.389(20), 0.303; CH₃CD₃, 1.53(3), 1.44; 1, 1-ᶜC₃H₄D₂, 2.58(6), 2.53; trans-HDC=CHD, 1.00(2), 1.00; 1,3,5-C₆H₃D₃, 1.273(4), 1.25; PhCH₂D (50.0 ˚C), 2.06(2), 1.98. Calculations of pertinent model complexes (e.g., (HO)₂(H₂N)TiR (1'R)) generated the vibrational frequencies necessary to interpret the EIEs in terms of a statistical mechanics description utilizing gas-phase partition functions; EIE = SYM x MMI x EXC x EXP[-(∆∆ZPE/kʙT)]. The large MMI term in the intermolecular cases-a consequence of using perprotio vs perdeuterio small molecule substrates-is attenuated by EXC and EXP[-(∆∆ZPE/kʙT)] contributions derived from low-energy core vibrations. The EIEs are differentiated on the basis of the EXP [-(∆∆ZPE/kʙT)] term, with CH-based bending vibrations playing the major role. Substrate bending vibrations that are absent in intramolecular cases are primarily responsible for the greater intermolecular values. ...

Description: This article discusses Bär's conformal lower bound for the spectrum of generalized Dirac operators. Abstract: We use the orthogonal splitting of a certain Clifford module as a direct sum of generalized spinors and twistors to give a short and natural proof to Bär's conformal lower bound for the spectrum of a generalized Dirac operator on a compact Riemannian manifold.