Statistical properties of the Hamiltonian generating phase state derived by using the generalized Hellmann-Feynman theorem

We study statistical properties of the Hamiltonian generating phase state. Using the generalized Hellmann-Feynman theorem for ensemble average, we derive its mean energy and find the ratio of the mean energies contributed from the term a^†a to that from . The relation on the entropy-variation with respect to the dynamic parameters ω and κ is also examined.     

Effects of asymmetry and external field on phase transitions in the presence of an intermediate metastable state

Discovery of the anomalous generation and extinction of crystal nuclei in nonequilibrium supercooled liquids reflects essentially the effects of the real heterogeneous structure and its irreversible relaxation on the stability of the nucleus. The kinetic model involving one order parameter was developed to study the impact of both asymmetry and external field on crystallization, thus allowing looking, in particular, into the heterogeneous structure relaxation in such materials. The role of asymmetry and external field on phase transitions in the presence of an intermediate metastable state is described in comparison with such generic model. We found that the influence of the external field on the system with an intermediate metastable state is to reduce the stability of phases, and, therefore, the crystal nuclei generation could be slowed or even stopped. Meanwhile the role of cubic term in order parameter of the Landau-type potential associated to the asymmetry of the system is to increase the stability of new phase for the suitably varied control parameter. Finally, the cases which allow analytical solution of the problem and the realization of different transition scenarios are discussed.     

A first-order phase transition defines the random close packing of hard spheres

Randomly packing spheres of equal size into a container consistently results in a static configuration with a density of ∼64%. The ubiquity of random close packing (RCP) rather than the optimal crystalline array at 74% begs the question of the physical law behind this empirically deduced state. Indeed, there is no signature of any macroscopic quantity with a discontinuity associated with the observed packing limit. Here we show that RCP can be interpreted as a manifestation of a thermodynamic singularity, which defines it as the “freezing point” in a first-order phase transition between ordered and disordered packing phases. Despite the athermal nature of granular matter, we show the thermodynamic character of the transition in that it is accompanied by sharp discontinuities in volume and entropy. This occurs at a critical compactivity, which is the intensive variable that plays the role of temperature in granular matter. Our results predict the experimental conditions necessary for the formation of a jammed crystal by calculating an analogue of the “entropy of fusion”. This approach is useful since it maps out-of-equilibrium problems in complex systems onto simpler established frameworks in statistical mechanics.     

On the motif distribution in random block-hierarchical networks

The distribution of motifs in random hierarchical topological networks defined by nonsymmetric random block-hierarchical adjacency matrices, is constructed for the first time. According to the classification of U. Alon et al. of network superfamilies (Milo et al., 2004 [11]) by their motifs distributions, our artificial directed random hierarchical networks fall into the superfamily of natural networks to which the neuron networks belong. This is the first example of a class of “handmade” topological networks with the motifs distribution as in a special class of natural networks of essential biological importance.     

Synthesis methods of multiple phase-cycled SSFP images to reduce the band artifact and noise more reliably

The band artifact in steady-state free precession can be reduced by synthesizing the multiple images obtained through different phase increments of successive radiofrequency pulses. Even though the complex summation method was reported to be effective in reducing the band artifact, it has the pitfalls of intensity abnormality and sensitivity to the phase abnormality. Two new methods have been developed for more reliable reduction of the band artifact than the complex summation method. One method is to sum the complex images partially and to take the maximum intensity of the partially summed images. The other method is to sum the free induction decay (FID) and primary echo components of the Fourier series that are obtained through Fourier analysis of the complex base images. Both proposed methods were compared with other magnitude (maximum intensity projection, spectrally decomposed synthesis, sum-of-squares, nonlinear averaging) and complex-based (complex summation, magnitude-weighted complex summation) methods experimentally at 3 T for the phantom and volunteer's head imaging. Both proposed methods were confirmed to maintain the advantage of the complex summation in reducing both the dark and bright band artifacts while reducing the intensity abnormality and sensitivity to the phase abnormality from that of the complex summation method over a wide range of flip angles and relaxation times.     

Respiratory noise correction using phase information

Respiratory noise is a confounding factor in functional magnetic resonance imaging (MRI) data analysis. A novel method called Respiratory noise Correction using Phase information is proposed to retrospectively correct for the respiratory noise in functional MRI (fMRI) time series. It is demonstrated that the respiratory movement and the phase of functional MRI images are highly correlated in time. The signal fluctuation due to respiratory movements can be effectively estimated from the phase variation and removed from the functional MRI time series using a Wiener filtering technique. In our experiments, this new method is compared with RETROICOR, which requires recording respiration signal simultaneously in an fMRI experiment. The two techniques show comparable performance with respect to the respiratory noise correction for fMRI time series. However, this technique is more advantageous because there is no need for monitoring the subjects’ respiration or changing functional MRI protocols. This technique is also potentially useful for correcting respiratory noise from abnormal breathing or when the respiration is not periodic.     

The a.c. susceptibility third harmonic component of NdO1−0.14F0.14FeAs: A flux dynamic magnetic analysis

In this contribution we present the analysis of the third harmonic susceptibility data of the new superconductor NdFeAs_1−0.14F_0.14. ‘Cole-Cole’ polar plots respect to the magnetic frequency of the exciting field are presented and discussed. Data show that NdFeAs_1−0.14F_0.14 exhibit a ‘bulk pinning’ with a 3D flux dynamic character. A comparison of the responses of high T_c materials and an evaluation of theoretical critical states is also presented.     

Solvothermal synthesis and characterization of CdSe nanocrystals with controllable phase and morphology

Zinc blende (ZB) CdSe hollow nanospheres were solvothermally synthesized from the reaction of Cd(NO₃)₂·4H₂O with a homogeneously secondary Se source, which was first prepared by dissolving Se powder in the mixture of ethanol and oleic acid at 205 °C. As Se power directly reacted with Cd(NO₃)₂·4H₂O in the above mixed solvents, wurtzite (W) CdSe solid nanoparticles were produced. Time-dependent experiments suggested that the formation of CdSe hollow nanospheres was attributed to an inside-out Ostwald ripening process. The influences of reaction time, temperature and ethanol/oleic acid volume ratio on the morphology, phase and size of the hollow nanospheres were also studied. Infrared (IR) spectroscopy investigations revealed that oleic acid with long alkene chains behaved as a reducing agent to reduce Se powder to Se²⁻ in the synthesis. Photoluminescence (PL) measurements showed that the ZB CdSe hollow nanospheres presented an obvious blue-shifted emission by 42 nm, and the W CdSe solid nanoparticles exhibited a band gap emission of bulk counterpart.     

Study of surface-bulk mass transport and phase transformation in nano-TiO2 using hyperfine interaction technique

Phase transition from anatase to rutile for the 70 nm TiO₂ crystallite has been investigated by the time differential perturbed angular correlation (TDPAC) technique. The study involved the annealing of the TiO₂ nanocrystals, adsorbed with the nuclear probe (¹⁸¹Hf/¹⁸¹Ta) at trace level, at different temperatures for different durations. The TDPAC measurement was also supported by XRD measurement where the width of the peaks increases with the increase in annealing temperature indicating a crystal growth. The samples annealed up to 823 K for 4 h showed no phase transition, except for the growth of the crystallites. However, it showed phase transition at the same temperature (823 K), when annealed for longer duration, indicating the slower kinetics of the phase transition process. Further the sample, when annealed at 1123 K for 4 h, showed phase transition. It has also been observed that the ¹⁸¹Hf tracer, adsorbed on 70 nm anatase TiO₂, diffuses from surface to bulk during the phase transition process and the extent of diffusion in anatase differs from that in rutile phase. However, surface to bulk mass-transfer is found to play a significant role in the phase transition process.     

Temperature-induced particle self-assembly

Agglomeration of monodisperse thiol-stabilized gold particles with diameters of 6 nm, suspended in organic solvents, was induced by the cooling of the suspension. A sharp transition between the stable suspension and agglomeration resulted. The temperature of the transition depends on the concentration and the compatibility of the solvent. The morphology of the formed particle structures upon agglomeration implies that the used metal colloid can be described as a van der Waals-gas. The particles undergo phase transitions from a stable fluid phase to a metastable phase, in which nucleation and growth occur, or to an instable phase, in which spinodal decomposition occurs. The results will direct research on routes to nanostructured materials using nanoparticles as building blocks.