Haldane's instanton in 2D Heisenberg model revisited: Along the avenue of topology

Deconfined quantum phase transition from Néel phase to valence bond crystal state in 2D Heisenberg model is under debate nowadays. One crucial issue is the suppression of Haldane's instanton on quantum critical point which drives the spinon deconfined. In this Letter, by making use of the ?-mapping topological current theory, we reexamine the Haldane's instanton in an alternative way along the direction of topology. We find that the monopole events are space-time singularities of Néel field , the corresponding topological charges are the wrapping number of around the singularities which can be expressed in terms of the Hopf indices and Brouwer degrees of ?-mapping. The suppression of the monopole events can only be guaranteed when the ?-field possesses no zero points. Moreover, the quadrapolarity of monopole events in the Heisenberg model due to the Berry phase is also reproduced in this topological argument.     

Fibrillation of solar magnetic fields

Solar magnetic structures are often observed in the form of flux tubes composed of a number of smaller elements called fibres or threads, although theoretically such concentrations should not appear but should be flattened by magnetic diffusivity into a uniform, low intensity field. In this paper we describe a mechanism which may be responsible for the fibrillation and also for the very large diffusivity which dissipates magnetic flux tubes in hours instead of years. Firstly, the electric current associated with magnetic field gradients usually increases the local electron temperature and reduces the resistivity, so that the current becomes concentrated into sheets or streamers. Secondly, the magnetic field gradients continue to increase until the current magnitude reaches its limit, which is determined by the electron-ion streaming instability. Then with appropriate temperature and number densities, the Larmor radius of the ions overlaps the near discontinuity in B_z and generates a sharply peaked fluid motion at the edge that is close to the thermal speed. Finally, the resulting vorticity generates an axial magnetic field opposing B_z in the term , and if this is sufficient to change the sign of this term, the very unstable backward heat equation results. This instability repeatedly switches on and off and maintains the magnetic structure in the fibrillated form. Such structures are eventually eliminated by magnetic diffusivity in the usual way, but because of the fluctuations in B_z, this occurs at a vastly increased rate. We show that this phenomenon increases the magnetic diffusivity, D, by a factor ~ 10⁸ in agreement with some observations of plasma loops and supergranules.     

The double M-effect induced by noble gases activated with negative ions

The M-effect (monochromatization-effect) is a powerful tool which can give high intensity monochromatic spectra with a certain wavelength depending on the type of used gas mixtures to generate plasma state. The effect consists in the emission of a single spectral line of plasmas ignited in certain gas mixtures. The main condition to obtain the M effect is the presence of an electropositive and an electronegative gas mixture. For example, in the case of Ne+H₂ monochrome radiation was obtained, the wavelength of Ne being 585.3 nm (1s²–2p⁵). In this paper we prove the general character of this effect, i.e. if the optical emission spectra reduced to nearly one line can be observed also in other gas mixture discharges, for example in the case of one electronegative gas and two electropositive gases. Different other mixtures, as Xe+Ne+H₂ and Xe+Ar+H₂ have been studied. In all these cases, the M-effect appeared without doubt.     

A lower bound for the symbolic multifractal spectrum of a self-similar multifractal with arbitrary overlaps

By now the multifractal structure of self-similar measures satisfying the so-called Open Set Condition is well understood. However, if the Open Set Condition is not satisfied, then almost nothing is known. In this paper we prove a nontrivial lower bound for the symbolic multifractal spectrum of an arbitrary self-similar measure. We emphasize that we are considering arbitrary self-similar measures (and sets) which are not assumed to satisfy the Open Set Condition or similar separation conditions. Our results also have applications to self-similar sets which do not satisfy the Open Set Condition (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Percolation in two-scale porous media

Two-scale porous media are generated by filtering a Gaussian random correlated field with a random correlated threshold field. The percolation threshold and the critical exponent ν are derived with the help of a finite-size scaling method. The percolation threshold for the three-dimensional media is a decreasing function of the variance and correlation length of the threshold field. A simplified model predicts these trends in 3d; moreover, it suggested some effects in 2d which were all numerically verified. Received 17 August 2000     

Temperature-dependent susceptibility in ALON

Herein, we propose a stochastic model of the complex susceptibility in aluminum nitride (ALON), a polycrystalline transparent ceramic. The proposed model yields an inverse power-law dependence of the dielectric loss tangent on frequency, in remarkably close agreement with data. In addition, the phenomenological parameters are found to be strongly temperature-dependent. This temperature dependence is determined, in the theoretical model, to be a consequence of the thermodynamic properties of the molecular dipoles in the material.     

Structure of gels and aggregates of disk-like colloids

The static structure factor (S(q)) of dispersions and gels of disk-like mineral colloids (Laponite) was investigated using time- and ensemble-averaged light scattering. The evolution of S(q) in time after increasing the ionic strength of well-dispersed Laponite suspensions shows that Laponite aggregates and forms fractal clusters. The structure of the aggregates does not depend on the ionic strength, but the rate of growth increases very strongly with the ionic strength. At concentrations below about 3 g/l (0.12% v/v) the aggregates sediment while at higher concentrations space-filling gels are formed. The gels are homogeneous on length scales larger than the correlation length which decreases strongly with decreasing ionic strength and increasing concentration. However, the local structure is the same, independent of the concentration and the ionic strength. Received 6 August 2000 and Received in final form 16 March 2001     

Preparation of activated carbons previously treated with hydrogen peroxide: Study of their porous texture

Cedar wood was used as raw material for the preparation of activated carbons by treatment with hydrogen peroxide of different concentrations. The samples were next carbonised and activated under CO₂ atmosphere. The activated carbons were characterised by means of the adsorption isotherms of N₂ at 77 K, as well as by applying the Density Functional Theory (DFT) method and mercury porosimetry. The experimental results corresponding to the activated samples indicate a more remarkable porous development as a consequence of the treatment with hydrogen peroxide, probably due to the elimination of surface complexes produced during the activation step. The DFT diagrams point out that the activating treatment favours the development of medium and narrow-size micropores whereas the carbonisation process leads to the development of wide micropores of size close to that corresponding to mesopores.     

Construction of recurrent bivariate fractal interpolation surfaces and computation of their box-counting dimension

Recurrent bivariate fractal interpolation surfaces (RBFISs) generalise the notion of affine fractal interpolation surfaces (FISs) in that the iterated system of transformations used to construct such a surface is non-affine. The resulting limit surface is therefore no longer self-affine nor self-similar. Exact values for the box-counting dimension of the RBFISs are obtained. Finally, a methodology to approximate any natural surface using RBFISs is outlined.