Modeling the phase diagram of carbon

We determined the phase diagram involving diamond, graphite, and liquid carbon using a recently developed semiempirical potential. Using accurate free-energy calculations, we computed the solid-solid and solid-liquid phase boundaries for pressures and temperatures up to 400 GPa and 12 000 K, respectively. The graphite-diamond transition line that we computed is in good agreement with experimental data, confirming the accuracy of the employed empirical potential. On the basis of the computed slope of the graphite melting line, we rule out the hotly debated liquid-liquid phase transition of carbon. Our simulations allow us to give accurate estimates of the location of the diamond melting curve and of the graphite-diamond-liquid triple point.     

Exact and approximate solutions of Schrödinger’s equation for a class of trigonometric potentials

The asymptotic iteration method is used to find exact and approximate solutions of Schrödinger’s equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent). Analytic and approximate solutions are obtained by first using a coordinate transformation to reduce the Schrödinger equation to a second-order differential equation with an appropriate form. The asymptotic iteration method is also employed indirectly to obtain the terms in perturbation expansions, both for the energies and for the corresponding eigenfunctions.     

The Critical Fugacity for Surface Adsorption of Self-Avoiding Walks on the Honeycomb Lattice is {1+\sqrt{2}}

In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a. honeycomb) lattice is ${\mu=\sqrt{2+\sqrt{2}}}$ . A key identity used in that proof was later generalised by Smirnov so as to apply to a general O(n) loop model with ${n\in [-2,2]}$ (the case n = 0 corresponding to self-avoiding walks). We modify this model by restricting to a half-plane and introducing a surface fugacity y associated with boundary sites (also called surface sites), and obtain a generalisation of Smirnov’s identity. The critical value of the surface fugacity was conjectured by Batchelor and Yung in 1995 to be ${y_{\rm c}=1+2/\sqrt{2-n}}$ . This value plays a crucial role in our generalized identity, just as the value of the growth constant did in Smirnov’s identity. For the case n = 0, corresponding to self-avoiding walks interacting with a surface, we prove the conjectured value of the critical surface fugacity. A crucial part of the proof involves demonstrating that the generating function of self-avoiding bridges of height T, taken at its critical point 1/μ, tends to 0 as T increases, as predicted from SLE theory.     

Momentum space distribution of electrons in an atom using hydrogenic wave functions

A formulation is developed to derive exact analytic expressions for electron-electron correlation and density of electrons in momentum space using hydrogenic wave functions. It is shown that for large atoms the expression for density of electrons has a simple form.     

Surfactant‐assisted specific‐acid catalysis of Diels–Alder reactions in aqueous media

Surfactant‐assisted specific‐acid catalysis (SASAC) for Diels–Alder reactions of dienophiles 1 and 4 with cyclopentadiene 2 in aqueous media at 32 °C was studied. This study showed that acidified anionic surfactants (pH 2) such as sodium dodecyl sulfate (SDS) and linear alkylbenzene sulfonic acid (LAS) accelerate Diels—Alder reactions. Conversely, under similar reaction conditions (pH 2) these reactions are inhibited by (acidified) cationic surfactants such as dodecyltrimethylammonium bromide (DTAB), dodecyldimethylammonium bromide (DDAB), and dodecylmethylammonium bromide (DMAB). A modest rate acceleration resulting from the surfactant hydrogen‐bonding capacity is also recorded for the Diels–Alder reaction of naphthoquinones ( 6 ) with cyclopentadiene ( 2 ) in aqueous media at 32 °C. Copyright © 2007 John Wiley & Sons, Ltd.     

Sum-rule conserving spectral functions from the numerical renormalization group

We show how spectral functions for quantum impurity models can be calculated very accurately using a complete set of discarded numerical renormalization group eigenstates, recently introduced by Anders and Schiller. The only approximation is to judiciously exploit energy scale separation. Our derivation avoids both the overcounting ambiguities and the single-shell approximation for the equilibrium density matrix prevalent in current methods, ensuring that relevant sum rules hold rigorously and spectral features at energies below the temperature can be described accurately.     

Effects of Refractive Index and Viscosity on Fluorescence and Anisotropy Decays of Enhanced Cyan and Yellow Fluorescent Proteins

The fluorescence lifetime strongly depends on the immediate environment of the fluorophore. Time-resolved fluorescence measurements of the enhanced forms of ECFP and EYFP in water–glycerol mixtures were performed to quantify the effects of the refractive index and viscosity on the fluorescence lifetimes of these proteins. The experimental data show for ECFP and EYFP two fluorescence lifetime components: one short lifetime of about 1 ns and a longer lifetime of about 3.7 ns of ECFP and for EYFP 3.4. The fluorescence of ECFP is very heterogeneous, which can be explained by the presence of two populations: a conformation (67% present) where the fluorophore is less quenched than in the other conformation (33% present). The fluorescence decay of EYFP is much more homogeneous and the amplitude of the short fluorescence lifetime is about 5%. The fluorescence anisotropy decays show that the rotational correlation time of both proteins scales with increasing viscosity of the solvent similarly as shown earlier for GFP. The rotational correlation times are identical for ECFP and EYFP, which can be expected since both proteins have the same shape and size. The only difference observed is the slightly lower initial anisotropy for ECFP as compared to the one of EYFP.     

Charge transport in anodic TiO2 nanotubes studied by terahertz spectroscopy

We report on the photoelectrochemical and terahertz measurements, of the charge transport properties of 1 μm thick self‐organized TiO₂ nanotube layers, prepared by the anodization of titanium. We provide evidence regarding the complexity of electron transport, and dynamics in the nanotubes. Shortly after photoexcitation, charge mobilites in amorphous and crystalline nanotubes are similar, but still lower compared to the bulk anatase. The mobility subsequently decreases due to trapping‐detrapping processes. The recombination rate in anatase nanotubes is much slower than in the amorphous ones, enabling the material to reach an internal photon to electron conversion efficiency exceeding 60%.