Combinatorial and Topological Analysis of the Ising Chain in a Field

We present an alternative solution of the Ising chain in a field under free and periodic boundary conditions, in the microcanonical, canonical, and grand canonical ensembles, from a unified combinatorial and topological perspective. In particular, the computation of the per-site entropy as a function of the energy unveils a residual value for critical values of the magnetic field, a phenomenon for which we provide a topological interpretation and a connection with the Fibonacci sequence. We also show that, in the thermodynamic limit, the per-site microcanonical entropy is equal to the logarithm of the per-site Euler characteristic. The canonical and grand canonical partition functions are identified as combinatorial generating functions of the microcanonical problem, which allows us to evaluate them. A detailed analysis of the magnetic field-dependent thermodynamics, including positive and negative temperatures, reveals interesting features. Finally, we emphasize that our combinatorial approach to the canonical ensemble allows exact computation of the thermally averaged value <????> of the Euler characteristic associated with the spin configurations of the chain, which is discontinuous at the critical fields, and whose thermal behavior is expected to determine the phase transition of the model. Indeed, our results show that the conjecture <????>?(T _C)?=?0, where T _C is the critical temperature, is valid for the Ising chain.     

Stability of benzoporphyrin photosensitizers in water/ethanol mixtures: pKa determination and self‐aggregation processes

Benzoporphyrin monoacid derivatives, here named B3A and B3B, are promising new drugs for photodynamic therapy. Although both isomers show interesting characteristics as photosensitizing compounds, they have some distinct physicochemical properties such as the tendency to self‐aggregate in water‐rich media. Because pH drives the presence of each species, the pK_a of these compounds assumes strategic importance. However, traditional micro‐titration methods and UV–Vis absorption techniques fail to give reliable pK_a values due to the characteristics of this highly complex system, such as the precipitation of hydrophobic species, close pK_a values, and high absorption band superposition. In the present work, chemometric tools are employed to evaluate pK_a, and the kinetic tendency of monomers to undergo self‐aggregation is investigated. In solvent mixtures at low water percentage in ethanol, both B3A and B3B are stabilized in a monomeric state. However, in mixtures with a high water content, self‐aggregation takes place, mainly under a mild pH acid condition (3 < pH < 6), in which the prevalent protolytic species of both isomers is the neutral charged form, compounds with carboxylic and porphyrin free‐base groups. It is demonstrated that both isomers can undergo aggregation following a self‐catalytic mechanism, which is 2000 times slower to B3A than B3B. For B3A, the aggregation is manifested by a decrease in the monomer band with the aggregation band probably superposed to that of the monomer. For B3B, together with the decrease in the monomer band, a new band related to self‐aggregates is observed. Copyright © 2010 John Wiley & Sons, Ltd.     

Ricci dark energy in Chern–Simons modified gravity

In this work, we have considered the Ricci dark energy model, where the energy density of the universe is proportional to the Ricci scalar curvature, in the dynamic Chern–Simons modified gravity. We show that in this context the evolution of the scale factor is similar to that displayed by the modified Chaplygin gas.     

Strain-induced interference effects on the resonance Raman cross section of carbon nanotubes

In this Letter, we report the effects of strain on the electronic properties of single-wall carbon nanotubes. When we normalize the electronic transition energies to the corresponding values obtained for unstrained tubes, we obtain that, regardless of the tube diameter, all the data collapse onto universal curves following an n - m = constant family pattern. In the case of metallic tubes, quantum interference effects on the Raman cross section are predicted for strained tubes when the energies of the lower and the upper components have nearly the same values. Experimental evidence for the strain-induced Raman cross section changes is observed in single nanotube spectroscopy.     

Macroscale and microscale evolutions of mechanically alloyed FeZn systems

The present work aims to correlate, in time, macroscale and microscale phenomenological evolutions of the microstructure of Fe and FeZn alloys processed by mechanical milling (MM) and alloying (MA), respectively. Powders were characterized for particle size distribution (PSD), particle morphology (optical microscopy, OM, scanning electron microscopy, SEM), microhardness, crystallite size, differential scanning calometry (DSC) and transmission electron microscopy (TEM). Two macroscopic regimes of PSD behavior were distinguished: the first one dominated by the cold welding process; and, the other where both fracture and agglomeration play a significant role. Solid solubilization of Zn on bcc Fe was found to reduce the final microhardness as well as increase the lattice parameter and is very well predicted by Miedema's thermodynamical approach. Microhardness and solid solution formation kinetics were correlated in time and both could be precisely described by a logistic function. After 5 h of planetary milling, microhardness and the lattice parameter become stable as well as the PSD and particle morphology, indicating that the system has already reached steady state. Indeed, this condition can be monitored by both macroscopic and microscopic parameters. Prior to an homogeneous powder, DSC results suggest an endothermic solid-state amorphization reaction for samples processed for up to 1 h as a result of the formation of clean Fe/Zn interfaces during MA.