Nonlinear dynamics of a spinor Bose-Einstein condensate in a double-well potential

We examine the nonlinear dynamical behavior of a spinor Bose-Einstein condensate in a double-well potential. Considering a condensate with large number of atoms, such that it can be described using the mean field theory, we separate the spinor dynamics from the spatial dynamics under the single-mode approximation. We limit ourselves to certain initial conditions under which the spatial mode is frozen so that we can focus on the spinor dynamics only. Identifying collective spin variables of our system, we derive the corresponding nonlinear equations of motion for them. Employing standard stability analysis, we find and characterize fixed points of the system. For a wide range of physical parameters such as tunneling strength and non-linear interactions, as well as for various initial preparations of the system, we identify qualitatively different dynamical regimes possible in the system. In particular, complete and incomplete oscillations of spin variables between quantum wells are found. We also show that by bringing some fixed points close to each other in the phase space of the system, it is possible to induce amplitude modulation to those otherwise regular tunneling oscillations.     

Metal complexes of a homopolymer system containing diethanolamine side group: synthesis and dielectrical behaviors

In this work, 4-diethanolaminomethyl styrene (DEAMSt) monomer was prepared by modification of 4-chloromethyl styrene with diethanolamine. The homopolymerization of styrene modificated was carried out by free radical polymerization method at 60?°C in presence of 1,4-dioxane and AIBN. The metal complexes were prepared by reaction of the homopolymer used as ligand P(DEAMSt)L^l and Ni(II), Co(II) metal ions in presence of ethanol and dilute NaOH at 65?°C for 48?h in pH 6.

The structure of modificated monomer, homopolymer used as ligand and polymer-metal complexes were characterized by (FT-IR), ¹H-NMR, ¹³C-NMR, Raman spectroscopy tecniques, elemental analysis, SEM, XRD and magnetic measurements. Their geometric structures according to magnetic measurements of Co(II) and Ni(II) complexes were estimated that have a tetrahedral structure. P(DEAMSt)L^l polymer has a transition state between amorphous and crystalline, whereas metal complexes (Co(II) and Ni(II) are with a large crystal structure. The molecular weight of P(DEAMSt)L¹ homopolymer was determined by gel permeation chromatography (GPC). The glass transition temperature (Tg) of homopolymer was measured by differantial scanning calorimeter (DSC). The thermal behaviors of both ligand and polymer-metal complexes were investigated by thermogravimetric analysis (TGA) and (DTA). The results obtained were compared with each other. Then, the dielectrical measurements (dielectric constant, dielectric loss and conductivity) of the ligand and polymer-metal complexes were investigated as a function of temperature and frequency. The activation energies (Ea) of the ligand and metal complexes were determined from the conductivity measurements.     

Vinyl nosylates as partner in copper and silver co-catalyzed Sonogashira cross-coupling reactions

Vinyl nosylates, readily obtained from β-dicarbonyl derivatives, could be efficiently engaged in Sonogashira cross-coupling reactions, either cocatalyzed by copper or silver salts. The para-nitrobenzenesulfonate (nosylate) group allows this coupling to be performed under very mild conditions (room temperature). These new leaving group and mild conditions could be applied to the synthesis of acetylenic coumarinyl derivatives and to the total synthesis of an acetylenic monoterpene natural product, named cleviolide.     

Thermoelectric properties of n-type Bi2Te3 alloys produced by a combined process of magnetic pulsed compaction (MPC) and spark plasma sintering (SPS)

In this study, n-type 95 %Bi₂Te₃-5 %Bi₂Se₃ thermoelectric materials have been produced by a combined process of gas atomization with subsequent magnetic pulsed compaction and spark plasma sintering, and then we investigated the behavior of transport properties with sintering temperature. The microstructural observation was performed by optical microscopy and scanning electron microscopy. The crystal structures were analyzed by X-ray diffractometer. The mechanical properties were calculated by measuring the density and micro-Vickers hardness of the samples. It was found that with increasing sintering temperature the gaps between powder particles decreases and the grain sizes were coarsened. The mechanical properties shows higher values along the parallel direction compared to the perpendicular direction to the pressing. The transport properties of the thermoelectric material were investigated with variation of the sintering temperatures. The maximum power factor 1.7 × 10^?3 Wm^?1 K^?2 was measured at the sintering temperature of 450 °C.     

New analytical expressions,symmetry relations and numerical solutions for the rotational overlap integrals

In this article, extremely simple analytical formulas are obtained for rotational overlap integrals which occur in integrals over two reduced rotation matrix elements. The analytical derivations are based on the properties of the Jacobi polynomials and beta functions. Numerical results and special values for rotational overlap integrals are obtained by using symmetry properties and recurrence relationships for reduced rotation matrix elements. The final results are of surprisingly simple structures and very useful for practical applications. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz–Morrey spaces of the third kind

Positivity - In the present paper, we will characterize the boundedness of the generalized fractional integral operators $$I_{\rho }$$ and the generalized fractional maximal operators $$M_{\rho }$$...