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.     

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.     

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.     

A new approach to treating pressure oscillations in combustion instability phenomena

Developing exact models of combustion instabilities is not an easy task to carry out and requires a great deal of time prior to obtaining success. The present study proposes a low-order model for pressure oscillations that does not require any knowledge of the systems, any new physical findings nor intricate details regarding its operating condition. This new approach is obtained using a Modified Van der Pol’s equation (MVDP) which is tuned by use of a Dual Extended Kalman Filter (DKEF) as a recursive estimator with perspectives in control by computer. This phenomenological model is used to predict the pressure signal from a variety of different combustors. Input data were taken from experimental cases such as a Rijke tube, a gas turbine and a liquid-fuel aero-engine combustor. Furthermore, a simulation considering high frequency oscillations to show the capability of the new approach is presented. In all cases, the results demonstrated the feasibility of applying the tractable model MVDP and DKEF running together to investigate pressure oscillations in practical cases.     

EPR study of Cu(II) dopant ions in single crystals of bis(l-asparaginato)Zn(II)

We report an electron paramagnetic resonance (EPR) study at 33.9 GHz and room temperature of oriented single crystal samples of bis(l-asparaginato)Zn(II) doped with Cu(II). The variation of the spectra with magnetic field orientation was measured in three crystal planes (a*b, bc and a*c, with a*=b×c). These spectra display two groups of four peaks arising from the hyperfine interaction with the I_Cu=3/2 nuclear spins of copper. They were assigned to Cu(II) ions in two lattice sites related by a 180° rotation around the b-crystal axis. The g and hyperfine coupling (A) tensors of the Cu(II) ions were evaluated from the single crystal data. Some indeterminacy in the assignment of the signals was avoided measuring the EPR spectrum of a powder sample. Their principal values are g₁=2.060(1), g₂=2.068(2), g₃=2.283(2), and A₁≈0.1×10⁻⁴, A₂=13×10⁻⁴ and A₃=165×10⁻⁴ cm⁻¹. The eigenvectors corresponding to g₃ and A₃ are coincident within the experimental error; the other eigenvectors are rotated 5.6° in the perpendicular plane. Considering the crystal structure of bis(l-asparaginato)Zn(II), our EPR results indicate that the Cu(II) impurities replace Zn(II) ions in the host crystal. We propose a molecular model based on the EPR data and the structural information, and analyse the results comparing the measured values with those obtained in similar systems.     

Compact laser system for atom interferometry

We describe an optical bench in which we lock the relative frequencies or phases of a set of three lasers in order to use them in a cold atom interferometry experiment. As a new feature, the same two lasers serve alternately to cool atoms and to realize the atomic interferometer. This requires a fast change of the optical frequencies over a few GHz. The number of required independent laser sources is then only three, which enables the construction of the whole laser system on a single transportable optical bench. Recent results obtained with this optical setup are also presented. PACS 32.80.Pj; 42.50.Vk; 39.20.+q