Spin mixing in colliding spinor condensates: formation of an effective barrier

The dynamics of F=1 spinor condensates initially prepared in a double-well potential is studied in the mean field approach. It is shown that a small seed of $m=0$ atoms on a system with initially well separated m=1 and m=-1 condensates has a dramatic effect on their mixing dynamics, acting as an effective barrier for a remarkably long time. We show that this effect is due to the spinor character of the system, and provides an observable example of the interplay between the internal spin dynamics and the macroscopic evolution of the magnetization in a spinor Bose-Einstein condensate.Comment: Accepted for publication at the Europhysics Letter

Predicting spinor condensate dynamics from simple principles

We study the spin dynamics of quasi-one-dimensional F=1 condensates both at zero and finite temperatures for arbitrary initial spin configurations. The rich dynamical evolution exhibited by these non-linear systems is explained by surprisingly simple principles: minimization of energy at zero temperature, and maximization of entropy at high temperature. Our analytical results for the homogeneous case are corroborated by numerical simulations for confined condensates in a wide variety of initial conditions. These predictions compare qualitatively well with recent experimental observations and can, therefore, serve as a guidance for on-going experiments.Comment: 4 pages, 2 figures. v3: matches version appeared in PR

A comparison study on criteria to select the most adequate weighting matrix

The practice of spatial econometrics revolves around a weighting matrix, which is often supplied by the user on previous knowledge. This is the so-called W issue. Probably, the aprioristic approach is not the best solution although, presently, there are few alternatives for the user. Our contribution focuses on the problem of selecting aWmatrix from among a finite set of matrices, all of them considered appropriate for the case. We develop a new and simple method based on the entropy corresponding to the distribution of probability estimated for the data. Other alternatives, which are common in current applied work, are also reviewed. The paper includes a large study of Monte Carlo to calibrate the effectiveness of our approach compared to others. A well-known case study is also included

Estimation of inorganic constituents in the seeds of blue and white flowering capitulum of Silybum marianum

Silybum Marianum commonly known as milk thistle contains flavonolignans, collectively known as silymarin. The main components of silymarin are silybine, isosilybine, silychristin and silydinine. This study was aimed to estimate inorganic constituents in blue and white capitulum’s seeds from different areas of KPK. Concentration of Na was found to be high (6 mg/kg) in white capitulum seeds from Karak area, while K concentration was high (6 mg/kg) in the blue capitulum seeds from Khyber agency. High concentration of Ca (20 mg/kg) was seen in both white and blue capitulum’s seeds of Khyber agency. Less concentration of NO3 (0.09 mg/kg) was detected in white capitulum seeds from Kohat district and high concentration of SO4 (22.14 mg/kg) was recorded in blue capitulum seeds collected from Peshawar.Key words: Silybum marianum, capitulum’s seeds, inorganic profile

Spherical model of the Stark effect in external scalar and vector fields

The Bohr-Sommerfeld quantization rule and the Gamow formula for the width of quasistationary level are generalized by taking into account the relativistic effects, spin and Lorentz structure of interaction potentials. The relativistic quasi-classical theory of ionization of the Coulomb system (V_{Coul}=-\xi/r) by radial-constant long-range scalar (S_{l.r.}=(1-\lambda)(\sigma r+V_0)) and vector (V_{l.r.}=\lambda(\sigma r+V_0)) fields is constructed. In the limiting cases the approximated analytical expressions for the position E_r and width \Gamma of below-barrier resonances are obtained. The strong dependence of the width \Gamma of below-barrier resonances on both the bound level energy and the mixing constant \lambda is detected. The simple analytical formulae for asymptotic coefficients of the Dirac radial wave functions at zero and infinity are also obtained.Comment: 25 pages, 4 figures. Submitted to Int. J. Mod. Phys.

Visual features as stepping stones toward semantics: Explaining object similarity in IT and perception with non-negative least squares.

Object similarity, in brain representations and conscious perception, must reflect a combination of the visual appearance of the objects on the one hand and the categories the objects belong to on the other. Indeed, visual object features and category membership have each been shown to contribute to the object representation in human inferior temporal (IT) cortex, as well as to object-similarity judgments. However, the explanatory power of features and categories has not been directly compared. Here, we investigate whether the IT object representation and similarity judgments are best explained by a categorical or a feature-based model. We use rich models (>100 dimensions) generated by human observers for a set of 96 real-world object images. The categorical model consists of a hierarchically nested set of category labels (such as "human", "mammal", and "animal"). The feature-based model includes both object parts (such as "eye", "tail", and "handle") and other descriptive features (such as "circular", "green", and "stubbly"). We used non-negative least squares to fit the models to the brain representations (estimated from functional magnetic resonance imaging data) and to similarity judgments. Model performance was estimated on held-out images not used in fitting. Both models explained significant variance in IT and the amounts explained were not significantly different. The combined model did not explain significant additional IT variance, suggesting that it is the shared model variance (features correlated with categories, categories correlated with features) that best explains IT. The similarity judgments were almost fully explained by the categorical model, which explained significantly more variance than the feature-based model. The combined model did not explain significant additional variance in the similarity judgments. Our findings suggest that IT uses features that help to distinguish categories as stepping stones toward a semantic representation. Similarity judgments contain additional categorical variance that is not explained by visual features, reflecting a higher-level more purely semantic representation