Regularization of point vortices for the Euler equation in dimension two

In this paper, we construct stationary classical solutions of the incompressible Euler equation approximating singular stationary solutions of this equation. This procedure is carried out by constructing solutions to the following elliptic problem [ -\ep^2 \Delta u=(u-q-\frac{\kappa}{2\pi}\ln\frac{1}{\ep})_+^p, \quad & x\in\Omega, u=0, \quad & x\in\partial\Omega, ] where $p>1$, $\Omega\subset\mathbb{R}^2$ is a bounded domain, $q$ is a harmonic function. We showed that if $\Omega$ is simply-connected smooth domain, then for any given non-degenerate critical point of Kirchhoff-Routh function $\mathcal{W}(x_1,...,x_m)$ with the same strength $\kappa>0$, there is a stationary classical solution approximating stationary $m$ points vortex solution of incompressible Euler equations with vorticity $m\kappa$. Existence and asymptotic behavior of single point non-vanishing vortex solutions were studied by D. Smets and J. Van Schaftingen (2010).Comment: 32page

On the Dynamical Ferromagnetic, Quantum Hall, and Relativistic Effects on the Carbon Nanotubes Nucleation and Growth Mechanism

The mechanism of carbon nanotube (CNT) nucleation and growth has been a mystery for over 15 years. Prior models have attempted the extension of older classical transport mechanisms. In July 2000, a more detailed and accurate nonclassical, relativistic mechanism was formulated considering the detailed dynamics of the electronics of spin and orbital rehybridization between the carbon and catalyst via novel mesoscopic phenomena and quantum dynamics. Ferromagnetic carbon was demonstrated. Here, quantum (Hall) effects and relativistic effects of intense many body spin-orbital interactions for novel orbital rehybridization dynamics (Little Effect) are proposed in this new dynamical magnetic mechanism. This dynamic ferromagnetic mechanism is proven by imposing dynamic and static magnetic fields during CNT syntheses and observing the different influence of these external magnetic environments on the catalyzing spin currents and spin waves and the resulting CNT formation

Chiral phase properties of finite size quark droplets in the Nambu--Jona-Lasinio model

Chiral phase properties of finite size hadronic systems are investigated within the Nambu--Jona-Lasinio model. Finite size effects are taken into account by making use of the multiple reflection expansion. We find that, for droplets with relatively small baryon numbers, chiral symmetry restoration is enhanced by the finite size effects. However the radius of the stable droplet does not change much, as compared to that without the multiple reflection expansion.Comment: RevTex4, 9 pages, 6 figures, to be published in Phys. Rev.

The nuclear shell effects near the r-process path in the relativistic Hartree-Bogoliubov theory

We have investigated the evolution of the shell structure of nuclei in going from the r-process path to the neutron drip line within the framework of the Relativistic Hartree-Bogoliubov (RHB) theory. By introducing the quartic self-coupling of $\omega$ meson in the RHB theory in addition to the non-linear scalar coupling of $\sigma$ meson, we reproduce the available data on the shell effects about the waiting-point nucleus $^{80}$Zn. With this approach, it is shown that the shell effects at N=82 in the inaccessible region of the r-process path become milder as compared to the Lagrangian with the scalar self-coupling only. However, the shell effects remain stronger as compared to the quenching exhibited by the HFB+SkP approach. It is also shown that in reaching out to the extreme point at the neutron drip line, a terminal situation arises where the shell structure at the magic number is washed out significantly.Comment: 18 pages (revtex), 8 ps figures, to appear in Phys. Rev.

Masses of Multiquark Droplets

The mass formulae for finite lumps of strange quark matter with $u$, $d$ and $s$ quarks, and non-strange quark matter consisting of $u$ and $d$ quarks are derived in a non-relativistic potential model. The finite-size effects comprising the surface, curvature and even, the Gauss curvature were consistently obtained, which shows a converging trend. It is found that there is a possibility for the formation of metastable strangelets of large mass. The model predicts low charge to mass ratio as the characteristic signature of strange matter in agreement with the relativistic studies. This study also yields an independent estimate for the bag energy density $B$, which is in agreement with the M.I.T bag model value.Comment: 24pages + 5 figures available upon request,Latex,IP/BBSR/93-3

LLL 44 - 2 - Micronutrients in clinical nutrition: Vitamins.

Vitamins are essential organic molecules, which are required in the diet in relatively small amounts in any form of nutrition (oral, enteral, parenteral). Despite the small amounts that are required, the vitamins are essential both for maintenance of health, growth, and treatment of disease. After reminding about the principal function of all the vitamins, their needs and the clinical consequences of their deficit, the text present some common clinical problems: the impact of inflammation on the assessment of status. The reasons and diseases which cause increased requirements are presented, with the indications to monitoring of blood levels which remain the classical way to assess status in clinical settings. The text summarises the most relevant clinical manifestations of vitamins depletion and deficiency, the difficulties in assessing status, and makes recommendations for provision for medical nutrition therapy

Quantum lattice dynamical effects on the single-particle excitations in 1D Mott and Peierls insulators

As a generic model describing quasi-one-dimensional Mott and Peierls insulators, we investigate the Holstein-Hubbard model for half-filled bands using numerical techniques. Combining Lanczos diagonalization with Chebyshev moment expansion we calculate exactly the photoemission and inverse photoemission spectra and use these to establish the phase diagram of the model. While polaronic features emerge only at strong electron-phonon couplings, pronounced phonon signatures, such as multi-quanta band states, can be found in the Mott insulating regime as well. In order to corroborate the Mott to Peierls transition scenario, we determine the spin and charge excitation gaps by a finite-size scaling analysis based on density-matrix renormalization group calculations.Comment: 5 pages, 5 figure

Charge and critical density of strange quark matter

The electric charge of strange quark matter is of vital importance to experiments. A recent investigation shows that strangelets are most likely highly negatively charged, rather than slightly positively charged as previously believed. Our present study indicates that negative charges can indeed lower the critical density, and thus be favorable to the experimental searches in heavy ion collisions. However, too much negative charges can make it impossible to maintain flavor equilibrium.Comment: 4 pages, LATeX with REVTeX style, one PS figure. To be published in Phys. Rev. C 59(6), 199

Nanoscale tunable reduction of graphene oxide for graphene electronics

International audienceGraphene is now recognized as the most likely carbon-based successor material for CMOS electronics. Recently, interest in graphene oxide (GO) has risen for producing large-scale flexible conductors and for its potential to open an electronic gap in graphene structures. We report on a means to tune the topographical and electrical properties of graphene-based materials with nanoscopic resolution by local thermal reduction of GO with a nano-size tip. The reduced GO nanostructures show an increase in conductivity up to four orders of magnitude as compared to pristine GO. No sign of tip wear or sample tearing was observed. Variably conductive nanoribbons with dimensions down to 12 nm have been produced in oxidized epitaxial graphene films in a single step that is clean, rapid and reliable

Strange quark matter in a chiral SU(3) quark mean field model

We apply the chiral SU(3) quark mean field model to investigate strange quark matter. The stability of strange quark matter with different strangeness fraction is studied. The interaction between quarks and vector mesons destabilizes the strange quark matter. If the strength of the vector coupling is the same as in hadronic matter, strangelets can not be formed. For the case of beta equilibrium, there is no strange quark matter which can be stable against hadron emission even without vector meson interactions.Comment: 19 pages, 8 figure