Anisotropic scattering and quantum magnetoresistivities of a periodically modulated 2D electron gas

We calculate the longitudinal conductivities of a two-dimensional noninteracting electron gas in a uniform magnetic field and a lateral electric or magnetic periodic modulation in one spatial direction, in the quantum regime. We consider the effects of the electron-impurity scattering anisotropy through the vertex corrections on the Kubo formula, which are calculated with the Bethe-Salpeter equation, in the self-consistent Born approximation. We find that due to the scattering anisotropy the band conductivity increases, and the scattering conductivities decrease and become anisotropic. Our results are in qualitative agreement with recent experiments.Comment: 19 pages, 8 figures, Revtex, to appear in Phys. Rev.

Guiding center picture of magnetoresistance oscillations in rectangular superlattices

We calculate the magneto-resistivities of a two-dimensional electron gas subjected to a lateral superlattice (LSL) of rectangular symmetry within the guiding-center picture, which approximates the classical electron motion as a rapid cyclotron motion around a slowly drifting guiding center. We explicitly evaluate the velocity auto-correlation function along the trajectories of the guiding centers, which are equipotentials of a magnetic-field dependent effective LSL potential. The existence of closed equipotentials may lead to a suppression of the commensurability oscillations, if the mean free path and the LSL modulation potential are large enough. We present numerical and analytical results for this suppression, which allow, in contrast to previous quantum arguments, a classical explanation of similar suppression effects observed experimentally on square-symmetric LSL. Furthermore, for rectangular LSLs of lower symmetry they lead us to predict a strongly anisotropic resistance tensor, with high- and low-resistance directions which can be interchanged by tuning the externally applied magnetic field.Comment: 12 pages, 9 figure

On the Convergence of Fuzzy Sets and the Completeness of the Space of Fuzzy Sets

AbstractIn this article, we first introduce several convergence concepts of fuzzy sets. Then we construct an embedding of the space of fuzzy sets in a normed linear space. We prove that the space of fuzzy sets is a complete metric space under the embedding. This framework enables us to study the calculus of fuzzy functions

Can black holes be torn up by phantom dark energy in cyclic cosmology?

Infinitely cyclic cosmology is often frustrated by the black hole problem. It has been speculated that this obstacle in cyclic cosmology can be removed by taking into account a peculiar cyclic model derived from loop quantum cosmology or the braneworld scenario, in which phantom dark energy plays a crucial role. In this peculiar cyclic model, the mechanism of solving the black hole problem is through tearing up black holes by phantom. However, using the theory of fluid accretion onto black holes, we show in this paper that there exists another possibility: that black holes cannot be torn up by phantom in this cyclic model. We discussed this possibility and showed that the masses of black holes might first decrease and then increase, through phantom accretion onto black holes in the expanding stage of the cyclic universe.Comment: 6 pages, 2 figures; discussions adde

A hollow fiber membrane-based liquid desiccant air dehumidification system for solar energy reclamation

Paper presented to the 3rd Southern African Solar Energy Conference, South Africa, 11-13 May, 2015.A mathematical model is proposed to study the heat and mass transfer performance of a hot water driven hollow fiber membrane-based liquid desiccant air dehumidification system. The system can be extended to solar energy cooling in summer, especially in hot and humid regions. The benefit with this technology is that the liquid desiccant is not in direct contact with the process air, therefore the problem of liquid droplets cross over is prevented. With the model, the effects of various operating parameters like fresh air temperature and humidity on system performance, in terms of SDP (specific dehumidification power) and COP (coefficient of performance), are discussed.cf201

Asymptotic behavior of w in general quintom model

For the quintom models with arbitrary potential $V=V(\phi,\sigma)$, the asymptotic value of equation of state parameter w is obtained by a new method. In this method, w of stable attractors are calculated by using the ratio (d ln V)/(d ln a) in asymptotic region. All the known results, have been obtained by other methods, are reproduced by this method as specific examples.Comment: 8 pages, one example is added, accepted for publication in Gen. Rel. Gra

Collapse of ρxx\rho_{xx} ringlike structures in 2DEGs under tilted magnetic fields

In the quantum Hall regime, the longitudinal resistivity $\rho_{xx}$ plotted as a density--magnetic-field ($n_{2D}-B$) diagram displays ringlike structures due to the crossings of two sets of spin split Landau levels from different subbands [e.g., Zhang \textit{et al.}, Phys. Rev. Lett. \textbf{95}, 216801 (2005)]. For tilted magnetic fields, some of these ringlike structures "shrink" as the tilt angle is increased and fully collapse at $\theta_c \approx 6^\circ$. Here we theoretically investigate the topology of these structures via a non-interacting model for the 2DEG. We account for the inter Landau-level coupling induced by the tilted magnetic field via perturbation theory. This coupling results in anti-crossings of Landau levels with parallel spins. With the new energy spectrum, we calculate the corresponding $n_{2D}-B$ diagram of the density of states (DOS) near the Fermi level. We argue that the DOS displays the same topology as $\rho_{xx}$ in the $n_{2D}-B$ diagram. For the ring with filling factor $\nu=4$, we find that the anti-crossings make it shrink for increasing tilt angles and collapse at a large enough angle. Using effective parameters to fit the $\theta = 0^\circ$ data, we find a collapsing angle $\theta_c \approx 3.6^\circ$. Despite this factor-of-two discrepancy with the experimental data, our model captures the essential mechanism underlying the ring collapse.Comment: 3 pages, 2 figures; Proceedings of the PASPS V Conference Held in August 2008 in Foz do Igua\c{c}u, Brazi

wd=−1w_d=-1 in interacting quintessence model

A model consisting of quintessence scalar field interacting with cold dark matter is considered. Conditions required to reach $w_d=-1$ are discussed. It is shown that depending on the potential considered for the quintessence, reaching the phantom divide line puts some constraints on the interaction between dark energy and dark matter. This also may determine the ratio of dark matter to dark energy density at $w_d=-1$.Comment: 10 pages, references updated, some notes added, minor changes applied, accepted for publication in Eur. Phys. J.

New mechanism to cross the phantom divide

Recently, type Ia supernovae data appear to support a dark energy whose equation of state $w$ crosses -1, which is a much more amazing problem than the acceleration of the universe. We show that it is possible for the equation of state to cross the phantom divide by a scalar field in the gravity with an additional inverse power-law term of Ricci scalar in the Lagrangian. The necessary and sufficient condition for a universe in which the dark energy can cross the phantom divide is obtained. Some analytical solutions with $w<-1$ or $w>-1$ are obtained. A minimal coupled scalar with different potentials, including quadratic, cubic, quantic, exponential and logarithmic potentials are investigated via numerical methods, respectively. All these potentials lead to the crossing behavior. We show that it is a robust result which is hardly dependent on the concrete form of the potential of the scalar.Comment: 11 pages, 5 figs, v3: several references added, to match the published versio