The Hyperfine Spin Splittings In Heavy Quarkonia

The hyperfine spin splittings in heavy quarkonia are studied using the recently developed renormalization group improved spin-spin potential which is independent of the scale parameter $\mu$. The calculated energy difference between the $J/\psi$ and the $\eta_c$ fits the experimental data well, while the predicted energy difference $\Delta M_p$ between the center of the gravity of $1^3P_{0,1,2}$ states and the $1^1P_1$ state of charmonium has the correct sign but is somewhat larger than the experimental data. This is not surprising since there are several other contributions to $\Delta M_p$, which we discuss, that are of comparable size ($\sim 1$ MeV) that should be included, before precise agreement with the data can be expected. The mass differences of the $\psi'-\eta_c'$, $\Upsilon(1S)-\eta_b$, $\Upsilon(2S)-\eta_b'$, and $B_c^*-B_c$ are also predicted.Comment: 17 page

Charmonium states in QCD-inspired quark potential model using Gaussian expansion method

We investigate the mass spectrum and electromagnetic processes of charmonium system with the nonperturbative treatment for the spin-dependent potentials, comparing the pure scalar and scalar-vector mixing linear confining potentials. It is revealed that the scalar-vector mixing confinement would be important for reproducing the mass spectrum and decay widths, and therein the vector component is predicted to be around 22%. With the state wave functions obtained via the full-potential Hamiltonian, the long-standing discrepancy in M1 radiative transitions of $J/\psi$ and $\psi^{\prime}$ are alleviated spontaneously. This work also intends to provide an inspection and suggestion for the possible $c\bar{c}$ among the copious higher charmonium-like states. Particularly, the newly observed X(4160) and X(4350) are found in the charmonium family mass spectrum as $M(2^1D_2)= 4164.9$ MeV and $M(3^3P_2)= 4352.4$ MeV, which strongly favor the $J^{PC}=2^{-+}, 2^{++}$ assignments respectively. The corresponding radiative transitions, leptonic and two-photon decay widths have been also predicted theoretically for the further experimental search.Comment: 16 pages,3 figure

A Spectral Bernstein Theorem

We study the spectrum of the Laplace operator of a complete minimal properly immersed hypersurface $M$ in $\R^{n+1}$. (1) Under a volume growth condition on extrinsic balls and a condition on the unit normal at infinity, we prove that $M$ has only essential spectrum consisting of the half line $[0, +\infty)$. This is the case when $\lim_{\tilde{r}\to +\infty}\tilde{r}\kappa_i=0$, where $\tilde{r}$ is the extrinsic distance to a point of $M$ and $\kappa_i$ are the principal curvatures. (2) If the $\kappa_i$ satisfy the decay conditions $|\kappa_i|\leq 1/\tilde{r}$, and strict inequality is achieved at some point $y\in M$, then there are no eigenvalues. We apply these results to minimal graphic and multigraphic hypersurfaces.Comment: 16 pages. v2. Final version: minor revisions, we add Proposition 3.2. Accepted for publication in the Annali di Matematica Pura ed Applicata, on the 05/03/201

Macrosegregation Caused by Thermosolutal Convection During Directional Solidification of Pb-Sb Alloys

Pb-2.2 and 5.8 wt pet Sb alloys were directionally solidified with a positive thermal gradient of 140 K cm(-1) at growth speeds ranging from 0.8 to 30 mu m s(-1), and then quenched to retain the mushy-zone morphology. Chemical analysis along the length of the directionally solidified portion and in the quenched melt ahead of the dendritic array showed extensive longitudinal macrosegregation, Cellular morphologies growing at smaller growth speeds are associated with larger amounts of macrosegregation as compared with the dendrites growing at higher growth speeds. Convection is caused, mainly, by the density inversion in the overlying melt ahead of the cellular/dendritic array because of the antimony enrichment at the array tip. Mixing of the interdendritic and bulk melt during directional solidification is responsible for the observed longitudinal macrosegregation

Second harmonic generation and birefringence of some ternary pnictide semiconductors

A first-principles study of the birefringence and the frequency dependent second harmonic generation (SHG) coefficients of the ternary pnictide semiconductors with formula ABC$_2$ (A = Zn, Cd; B = Si, Ge; C = As, P) with the chalcopyrite structures was carried out. We show that a simple empirical observation that a smaller value of the gap is correlated with larger value of SHG is qualitatively true. However, simple inverse power scaling laws between gaps and SHG were not found. Instead, the real value of the nonlinear response is a result of a very delicate balance between different intraband and interband terms.Comment: 13 pages, 12 figure

Threshold pi^0 photo- and electro-production in a meson-exchange model

We show that, within a meson-exchange dynamical model describing well most of the existing pion electromagnetic production data up to the second resonance region, one is also able to obtain a good agreement with the pi^0 photo- and electroproduction data near threshold. In the case of pi^0 production, the effects of final state interaction in the threshold region are nearly saturated by single charge exchange rescattering. This indicates that in ChPT, it might be sufficient to carry out the calculation just up to one-loop diagrams for threshold neutral pion production.Comment: 6 pages LATEX including 1 tables and 4 figures, uses espcrc1.st

QuizMap: Open social student modeling and adaptive navigation support with TreeMaps

In this paper, we present a novel approach to integrate social adaptive navigation support for self-assessment questions with an open student model using QuizMap, a TreeMap-based interface. By exposing student model in contrast to student peers and the whole class, QuizMap attempts to provide social guidance and increase student performance. The paper explains the nature of the QuizMap approach and its implementation in the context of self-assessment questions for Java programming. It also presents the design of a semester-long classroom study that we ran to evaluate QuizMap and reports the evaluation results. © 2011 Springer-Verlag Berlin Heidelberg

Magnetic Quantum Wire as a Spin Filter: An Exact Study

We propose that a magnetic quantum wire composed of magnetic and non-magnetic atomic sites can be used as a spin filter for a wide range of applied bias voltage. We adopt a simple tight-binding Hamiltonian to describe the model where the quantum wire is attached to two semi-infinite one-dimensional non-magnetic electrodes. Based on single particle Green's function formalism all the calculations are performed numerically which describe two-terminal conductance and current through the wire. Our exact results may be helpful in fabricating mesoscopic or nano-scale spin filter.Comment: 6 pages, 5 figure

Scalar conservation laws with nonconstant coefficients with application to particle size segregation in granular flow

Granular materials will segregate by particle size when subjected to shear, as occurs, for example, in avalanches. The evolution of a bidisperse mixture of particles can be modeled by a nonlinear first order partial differential equation, provided the shear (or velocity) is a known function of position. While avalanche-driven shear is approximately uniform in depth, boundary-driven shear typically creates a shear band with a nonlinear velocity profile. In this paper, we measure a velocity profile from experimental data and solve initial value problems that mimic the segregation observed in the experiment, thereby verifying the value of the continuum model. To simplify the analysis, we consider only one-dimensional configurations, in which a layer of small particles is placed above a layer of large particles within an annular shear cell and is sheared for arbitrarily long times. We fit the measured velocity profile to both an exponential function of depth and a piecewise linear function which separates the shear band from the rest of the material. Each solution of the initial value problem is non-standard, involving curved characteristics in the exponential case, and a material interface with a jump in characteristic speed in the piecewise linear case

Localization of 102 exons to a 2.5 Mb region involved in Down syndrome

Exon amplification has been applied to a 2.5 Mb region of chromosome 21 that has been associated with some features of Down syndrome (DS). Identification of the majority of genes from this region will facilitate the correlation of the over-expression of particular genes with specific phenotypes of DS. Over 100 gene fragments have been isolated from this 2.5 Mb segment. The exons have been characterized by sequence analysis, comparison with public databases and expansion to cDNA clones. Localization of the exons to chromosome 21 has been determined by hybridization to genomic Southern blots and to YAC and cosmid clones representing the region. This has resulted in a higher resolution physical map with a marker approximately every 25 kb. This integrated physical and transcript map will be valuable for fine mapping of DNA from individuals with partial aneuploidy of chromosome 21 as well as for assessing and ultimately generating a complete gene map of this segment of the genom