Embeddability of some strongly pseudoconvex CR manifolds

We obtain an embedding theorem for compact strongly pseudoconvex CR manifolds which are bounadries of some complete Hermitian manifolds. We use this to compactify some negatively curved Kaehler manifolds with compact strongly pseudoconvex boundary. An embedding theorem for Sasakian manifolds is also derived.Comment: 12 pages, AMSLate

A zero dimensional model of lithium-sulfur batteries during charge and discharge

Lithium-sulfur cells present an attractive alternative to Li-ion batteries due to their large energy density, safety, and possible low cost. Their successful commercialisation is dependent on improving their performance, but also on acquiring sufficient understanding of the underlying mechanisms to allow for the development of predictive models for operational cells. To address the latter, we present a zero dimensional model that predicts many observed features in the behaviour of a lithium-sulfur cell during charge and discharge. The model accounts for two electrochemical reactions via the Nernst formulation, power limitations through Butler-Volmer kinetics, and precipitation/dissolution of one species, including nucleation. It is shown that the precipitation/dissolution causes the flat shape of the low voltage plateau, typical of the lithium-sulfur cell discharge. During charge, it is predicted that the dissolution can act as a bottleneck, as for large enough currents smaller amounts dissolve. This results in reduced charge capacity and an earlier onset of the high plateau reaction, such that the two plateaus merge. By including these effects, the model improves on the existing zero dimensional models, while requiring considerably fewer input parameters and computational resources. The model also predicts that, due to precipitation, the customary way of experimentally measuring the open circuit voltage from a low rate discharge might not be suitable for lithium-sulfur. This model can provide the basis for mechanistic studies, identification of dominant effects in a real cell, predictions of operational behaviour under realistic loads, and control algorithms for applications

Nonadiabatic generation of spin currents in a quantum ring with Rashba and Dresselhaus spin-orbit interactions

When subjected to a linearly polarized terahertz pulse, a mesoscopic ring endowed with spin-orbit interaction (SOI) of the Rashba-Dresselhaus type exhibits nonuniform azimuthal charge and spin distributions. Both types of SOI couplings are considered linear in the electron momentum. Our results are obtained within a formalism based on the equation of motion satisfied by the density operator which is solved numerically for different values of the angle $\phi$, the angle determining the polarization direction of the laser pulse. Solutions thus obtained are later employed in determining the time-dependent charge and spin currents, whose values are calculated in the stationary limit. Both these currents exhibit an oscillatory behavior complicated in the case of the spin current by a beating pattern. We explain this occurrence on account of the two spin-orbit interactions which force the electron spin to oscillate between the two spin quantization axes corresponding to Rashba and Dresselhaus interactions. The oscillation frequencies are explained using the single particle spectrum.Comment: 9 pages, 5 figures, Conference "Advanced many-body and statistical methods in mesoscopic systems", June 27 -July 2, 2011, Constanta, Romani

Spin Density Waves in a Semiconductor Superlattice in a Tilted Magnetic Field

The ground state of a semiconductor superlattice (SL) placed in a tilted magnetic field is shown to exhibit a spin-density wave structure when the energy spectrum favors crossings between opposite-spin Landau minibands. The SL is modeled as an array of infinitely attractive quantum wells, whose single energy level is broadened into a miniband of width when weak interwell tunneling is considered. In the presence of the Coulomb interaction, by tailoring the relationship between and the cyclotron and Zeeman energies, the system transitions between paramagnetic, ferromagnetic, spin-density wave (SDW), and ferromagnetic-paramagnetic stripe ordering. These results are obtained by solving numerically a spin-density-wave gap equation derived at T = 0Kin aself-consistent formalism. We find that for a given value of the difference between the Landau energy and the Zeeman splitting, the initial paramagnetic or ferromagnetic order becomes unstable with respect to the formation of a SDW for within a certain range. At larger , the system exhibits alternate ferromagnetic-paramagnetic stripes. In the SDW regime, the fractional polarization is up to the order of several tens of percent

Szeg\"o kernel asymptotics and Morse inequalities on CR manifolds

We consider an abstract compact orientable Cauchy-Riemann manifold endowed with a Cauchy-Riemann complex line bundle. We assume that the manifold satisfies condition Y(q) everywhere. In this paper we obtain a scaling upper-bound for the Szeg\"o kernel on (0, q)-forms with values in the high tensor powers of the line bundle. This gives after integration weak Morse inequalities, analogues of the holomorphic Morse inequalities of Demailly. By a refined spectral analysis we obtain also strong Morse inequalities which we apply to the embedding of some convex-concave manifolds.Comment: 40 pages, the constants in Theorems 1.1-1.8 have been modified by a multiplicative constant 1/2 ; v.2 is a final updat

Zeros of Rydberg-Rydberg Foster Interactions

Rydberg states of atoms are of great current interest for quantum manipulation of mesoscopic samples of atoms. Long-range Rydberg-Rydberg interactions can inhibit multiple excitations of atoms under the appropriate conditions. These interactions are strongest when resonant collisional processes give rise to long-range C_3/R^3 interactions. We show in this paper that even under resonant conditions C_3 often vanishes so that care is required to realize full dipole blockade in micron-sized atom samples.Comment: 10 pages, 4 figures, submitted to J. Phys.

Retarded long-range potentials for the alkali-metal atoms and a perfectly conducting wall

The retarded long-range potentials for hydrogen and alkali-metal atoms in their ground states and a perfectly conducting wall are calculated. The potentials are given over a wide range of atom-wall distances and the validity of the approximations used is established.Comment: RevTeX, epsf, 11 pages, 2 fig

A REVIEW OF PHYTOREMEDIATION STRATEGIES FOR SOILS POLLUTED WITH HEAVY METALS

Mining operations, industrial production and domestic and agricultural use of metal and metal containing compound have resulted in the release of toxic metals into the environment. Heavy metal pollution has serious implications for the human health and the environment. Since heavy metals are nonbiodegradable, they accumulate in the environment and subsequently contaminate the food chain. Few heavy metals are toxic and lethal in trace concentrations and can be teratogenic, mutagenic, endocrine disruptors while others can cause behavioral and neurological disorders among infants and children. Therefore, remediation of heavy metals contaminated soil could be the only effective option to reduce the negative effects on ecosystem health. Different physical and chemical methods used for this purpose suffer from serious limitations like high cost, intensive labor, alterationof soil properties and disturbance of soil native microorganisms. Phytoremediationis the use of plants and associated soil microbes to reduce the concentrations or toxic effects of contaminants in the environments. In this article are reviewed the stratagies in the phytoremediation for remediating heavy metals from polluted soils. Phytoextraction and phytostabilization are the most promising and alternative methods for soil reclamation

Nonlinear dynamics of a solid-state laser with injection

We analyze the dynamics of a solid-state laser driven by an injected sinusoidal field. For this type of laser, the cavity round-trip time is much shorter than its fluorescence time, yielding a dimensionless ratio of time scales $\sigma \ll 1$. Analytical criteria are derived for the existence, stability, and bifurcations of phase-locked states. We find three distinct unlocking mechanisms. First, if the dimensionless detuning $\Delta$ and injection strength $k$ are small in the sense that $k = O(\Delta) \ll \sigma^{1/2}$, unlocking occurs by a saddle-node infinite-period bifurcation. This is the classic unlocking mechanism governed by the Adler equation: after unlocking occurs, the phases of the drive and the laser drift apart monotonically. The second mechanism occurs if the detuning and the drive strength are large: $k =O(\Delta) \gg \sigma^{1/2}$. In this regime, unlocking is caused instead by a supercritical Hopf bifurcation, leading first to phase trapping and only then to phase drift as the drive is decreased. The third and most interesting mechanism occurs in the distinguished intermediate regime $k, \Delta = O(\sigma^{1/2})$. Here the system exhibits complicated, but nonchaotic, behavior. Furthermore, as the drive decreases below the unlocking threshold, numerical simulations predict a novel self-similar sequence of bifurcations whose details are not yet understood.Comment: 29 pages in revtex + 8 figs in eps. To appear in Phys. Rev. E (scheduled tentatively for the issue of 1 Oct 98

A REVIEW OF CYCLODEXTRINS POTENTIAL IN INCREASING PETROLEUM HYDROCARBONS BIODEGRADATION

Petroleum hydrocarbons are organic pollutants that are released into the environment mainly due to anthropogenic activities and are considered as priority pollutants. The petroleum hydrocarbons degrading microorganisms occur in most environments, where hydrocarbons may serve as organic carbon sources. Bioremediation is based on the use of microorganisms or microbial processes to degrade environmental contaminants, and offers several advantages over the conventional chemical and physical technologies. It can be a cost effective, environmental friendly technology. The intensity of biodegradation is influenced by several environmental factors, such as quality, quantity and activity of the indigenous microbial populations, levels of nutrients, aerobic conditions, pH, temperature, water content and other soil properties. Moreover, low biodegradability and bioavailability of the contaminants / pollutants may limit the biodegradation in a contaminated / polluted site. Cyclodextrins have successfully been used in soil cleaning technologies as solubilisercarrier molecules. These molecules can transfer the insoluble contaminants / pollutants from the soil surface to the aqueous phase by complex formation. In the aqueous phase the microorganisms can degrade the contaminants / pollutants much easier partly because these molecules become available for the microbial cells, partly because the entrapment of contaminants by cyclodextrins reduces their toxicity. The effects of cyclodextrins on the hydrocarbon contaminants in soils (solubilisation, enhancement of desorption from soil, toxicity and bioavailability modulation, catalytic and stabilising effects) have been recently reviewed. Addition of cyclodextrins in aqueous washing solutions has been shown to increase the removal efficiency several times, while being non-toxic agents