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.

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

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

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.

The Value of Information for Populations in Varying Environments

The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness, which is itself an elusive notion. Here, we present a model of population dynamics where this problem is amenable to a mathematical analysis. In the limit where any information about future environmental variations is common to the members of the population, our model is equivalent to known models of financial investment. In this case, the population can be interpreted as a portfolio of financial assets and previous analyses have shown that a key quantity of Shannon's communication theory, the mutual information, sets a fundamental limit on the value of information. We show that this bound can be violated when accounting for features that are irrelevant in finance but inherent to biological systems, such as the stochasticity present at the individual level. This leads us to generalize the measures of uncertainty and information usually encountered in information theory

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

Metabolic and nutritional support of critically ill patients: consensus and controversies.

The results of recent large-scale clinical trials have led us to review our understanding of the metabolic response to stress and the most appropriate means of managing nutrition in critically ill patients. This review presents an update in this field, identifying and discussing a number of areas for which consensus has been reached and others where controversy remains and presenting areas for future research. We discuss optimal calorie and protein intake, the incidence and management of re-feeding syndrome, the role of gastric residual volume monitoring, the place of supplemental parenteral nutrition when enteral feeding is deemed insufficient, the role of indirect calorimetry, and potential indications for several pharmaconutrients

Top A_FB at the Tevatron vs. charge asymmetry at the LHC in chiral U(1) flavor models with flavored Higgs doublets

We consider the top forward-backward (FB) asymmetry at the Tevatron and top charge asymmetry at the LHC within chiral U(1)^\prime models with flavor-dependent U(1)^\prime charges and flavored Higgs fields, which were introduced in the ref. [65]. The models could enhance not only the top forward-backward asymmetry at Tevatron, but also the top charge asymmetry at LHC, without too large same-sign top pair production rates. We identify parameter spaces for the U(1)^\prime gauge boson and (pseudo)scalar Higgs bosons where all the experimental data could be accommodated, including the case with about 125 GeV Higgs boson, as suggested recently by ATLAS and CMS.Comment: 11 pages, 6 figures, figures and discussion adde