On classification ofN=2 supersymmetric theories

We find a relation between the spectrum of solitons of massiveN=2 quantum field theories ind=2 and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetricN=2 conformal theories and their massive deformations in terms of a suitable generalization of Dynkin diagrams (which coincides with the A-D-E Dynkin diagrams for minimal models). The Landau-Ginzburg theories are a proper subset of this classification. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity; the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of Picard-Lefschetz theory.     

Shear banding in biphasic liquid-liquid systems

In this Letter, we present the first systematic report of shear-induced banding in microconfined biphasic liquid-liquid systems, i.e., formation of alternating regions of high and low volume fraction of dispersed-phase droplets in a parallel plate flow cell. Such a flow-driven, gap-dependent phenomenon is only observed at low values of the viscosity ratio between the dispersed and the continuous phase, and in a given range of the applied shear rate. Based on rheological measurements, band formation is found to be associated with a viscosity decrease as compared to the homogeneous, structureless case, thus showing that system microstructure is somehow evolving towards reduced viscous dissipation under shear flow.     

A Hierarchical Model of Quantum Anharmonic Oscillators: Critical Point Convergence

We study the two-dimensional gauge theory of the symmetric group S_n describing the statistics of branched n-coverings of Riemann surfaces. We consider the theory defined on the disc and on the sphere in the large-n limit. A non trivial phase structure emerges, with various phases corresponding to different connectivity properties of the covering surface. We show that any gauge theory on a two-dimensional surface of genus zero is equivalent to a random walk on the gauge group manifold: in the case of S_n, one of the phase transitions we find can be interpreted as a cutoff phenomenon in the corresponding random walk. A connection with the theory of phase transitions in random graphs is also pointed out. Finally we discuss how our results may be related to the known phase transitions in Yang-Mills theory. We discover that a cutoff transition occurs also in two dimensional Yang-Mills theory on a sphere, in a large N limit where the coupling constant is scaled with N with an extra logN compared to the standard t Hooft scaling.     

Synthesis of carbon nanotubes by CVD: Effect of acetylene pressure on nanotubes characteristics

The effect of acetylene partial pressure on the structural and morphological properties of multi-walled carbon nanotubes (MWCNTs) synthesized by CVD on iron nanoparticles dispersed in a SiO₂ matrix as catalyst was investigated. The general growing conditions were: 110 cm³/min flow rate, 690 °C synthesis temperature, 180 Torr over pressure and two gas compositions: 2.5% and 10% C₂H₂/N₂. The catalyst and nanotubes were characterized by HR-TEM, SEM and DRX. TGA and DTA were also carried out to study degradation stages of synthesized CNTs. MWCNTs synthesized with low acetylene concentration are more regular and with a lower amount of amorphous carbon than those synthesized with a high concentration. During the synthesis of CNTs, amorphous carbon nanoparticles nucleate on the external wall of the nanotubes. At high acetylene concentration carbon nanoparticles grow, covering all CNTs’ surface, forming a compact coating. The combination of CNTs with this coating of amorphous carbon nanoparticles lead to a material with high decomposition temperature.     

Control of crystalline phases in magnetic Fe nanoparticles inserted inside a matrix of porous carbon

Two magnetic composites made up of Fe nanoparticles (Fe-NPs) embedded in a porous amorphous carbon matrix are presented. One of the samples, Fe-S-AC, was obtained with the aid of sucrose and the other, Fe-AC, in the absence of this substance. The XRD patterns show Bragg diffraction peaks associated with α-Fe and γ-Fe crystalline phases in the Fe-AC sample, while only peaks corresponding to the α-Fe phase are observed for Fe-S-AC powders. The Fe-NPs exhibit broad particle-size distributions for both samples, 5–50 nm for Fe-AC, whereas two populations (2–8 and 10–70 nm) for the Fe-S-AC composite are found. This fact gives rise to poorly defined blocking temperatures, as it can be deduced from the broad maxima observed in M_ZFC(T) variations. In addition, M(H) curves for both Fe-AC and Fe-S-AC samples reveal the existence of exchange-bias effect for T<60 K, probably due to a magnetic coupling within a core/shell structure of the Fe-NPs, although this effect was observed to be less significant for Fe-S-AC.     

Temperature dependence of the Mössbauer spectra of amorphous and nanocrystallized Fe86Zr7Cu1B6

Mössbauer measurements have been performed on amorphous and nanocrystalline alloy ribbons of nominal composition Fe₈₆Zr₇Cu₁B₆. The nanocrystalline samples were obtained by annealing the as-quenched alloy at different temperatures in the range between 650 and 870 K. Mössbauer spectra of the as-quenched amorphous sample have been recorded at 77 K, room temperature and above the Curie temperature (330 K) at 360 K. We have also performed Mössbauer measurements at room temperature in the nanocrystalline alloys to characterize the phases that appear after the annealing and their relative concentration. The as-quenched sample spectra reveal the existence of two inequivalent sites for Fe. Such a feature is also observed in the remaining amorphous phase of the annealed samples. In the first steps of crystallization, -Fe precipitates and its concentration increases with the annealing temperature. The experimental results suggest that the composition of the whole amorphous phase does not suffer large changes during crystallization.     

Accurate control of a liquid-crystal display to produce a homogenized Fourier transform for holographic memories

We show an accurate procedure to obtain a Fourier transform (FT) with no dc term using a commercial twisted-nematic liquid-crystal display. We focus on the application to holographic storage of binary data pages, where a drastic decrease of the dc term in the FT is highly desirable. Two different codification schemes are considered: binary pi radians phase modulation and hybrid ternary modulation. Any deviation in the values of the amplitude and phase shift generates the appearance of a strong dc term. Experimental results confirm that the calculated configurations provide a FT with no dc term, thus showing the effectiveness of the proposal.     

Mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with non-smooth coefficients

We prove surface and volume mean value formulas for classical solutions to uniformly parabolic equations in the divergence form with low regularity of the coefficients. We then use them to prove the parabolic strong maximum principle and the parabolic Harnack inequality. We emphasize that our results only rely on the classical theory, and our arguments follow the lines used in the original theory of harmonic functions. We provide two proofs relying on two different formulations of the divergence theorem, one stated for sets with almost C¹-boundary, the other stated for sets with finite perimeter.