Simulation of viscoelastic fluids in a 2D abrupt contraction by spectral element method

This study presents the vortex structure and numerical instability increase occurring when the level of elasticity is enhanced in inertial flows in planar contraction configuration for finitely extensible nonlinear elastic model by Peterlin (FENE‐P) fluid 1 . The re‐entrant corner effect on corner vortices is also considered. The calculations are performed using extended matrix logarithm formulation described in a previous paper: A. Jafari et al. A new extended matrix logarithm formulation for the simulation of viscoelastic fluids by spectral elements. Computer & Fluids 2010; 39 (9):1425–1438. In that reference, the proposed algorithm has been tested for simple geometry such as Poiseuille flow. In this study, we are interested in the capability of this algorithm for more complex geometry. This formulation helps to reach higher values of the Weissenberg number when compared with the classical one. Copyright © 2015 John Wiley & Sons, Ltd.     

A simple line shape technique for electron number density diagnostics of helium and helium-seeded plasmas

The results of an experimental study of the He I 447.1 nm line and its forbidden component at high electron number density are presented and compared with profiles calculated using computer simulation method. Michelson interferometer at 632.8 nm was used to measure plasma electron number density in the range (1–7) × 10²³ m^− 3 while electron temperatures for the same experimental conditions in the range of 25 000 K to 35 000 K were determined using several spectroscopic techniques. The agreement of experimental overall line shape with computer simulation results is within 10% of what is well within theoretical and experimental uncertainty. This favorable comparison enabled the development of a simple approximate formula for the evaluation of electron number density from the measurement of wavelength separation between peaks of allowed and forbidden lines. This technique of plasma diagnostics is not sensitive to the presence of self-absorption of strong He I allowed line. The derivation of approximate formula with estimated accuracy of 15% was followed by detailed comparison with other experimental and theoretical data.     

A generalization of the Erdös-Ko-Rado theorem

In this note, we investigate some properties of local Kneser graphs defined in [János Körner, Concetta Pilotto, Gábor Simonyi, Local chromatic number and sperner capacity, J. Combin. Theory Ser. B 95 (1) (2005) 101-117]. In this regard, as a generalization of the Erdös-Ko-Rado theorem, we characterize the maximum independent sets of local Kneser graphs. Next, we provide an upper bound for their chromatic number.     

Two-vibron bound states in the β--Fermi--Pasta--Ulam model

This paper studies the two-vibron bound states in the β- Fermi Pasta-Ulam model by means of the number conserving approximation combined with the number state method. The results indicate that on-site, adjacent-site and mixed two-vibron bound states may exist in the model. Specially, wave number has a significant effect on such bound states, which may be considered as the quantum effects of the localized states in quantum systems.     

An explanation for deviations from the quark number scaling of elliptic flows in low pT region

We carry out a systematic study of the different contributions to the deviations of the elliptic flows from the quark number scaling in high energy heavy ion collision in a quark combination model.The effects that we considered are:the resonance decay,the flavor dependence of the quark elliptic flow and the combination of quarks/antiquarks with slightly different transverse momenta.Our results show that the deviations observed in experiments can be well reproduced within the combination framework if all the three effects are considered. We make a detailed analysis of the different contributions using a Monte-Carlo program and suggest measuring the quark number scaling in intermediate pT range more precisely.     

ON THE GENERALIZED GLAISHER－HONG‘S CONGRUENCES

51. Notations and IntroductionListed below are some general notations which wi1l be used thIoughout this note:pea prime number greater than 3,cl l, mt r, s E N,(:) = n!/(kl(n -- k)!)--the binomial coefficient,Bk--the kth Bernoulli number in the "even suthe" notation, e.g., Bo = 1, B1 =--1/2, B2 = 1/6, B3 = 0,',B.(x) = Z (:)Bkx"--*--the Bernoulli polynomial.k=0As is known, the Bernoulli numbers are defined by the symbolic recurrence relationB.+l = (B + 1)"+', n = 1, 2,', Bo = l, whic…     

The ABC Conjecture Implies Vojta's Height Inequality for Curves

Following Elkies (Internat. Math. Res. Notices7 (1991) 99-109) and Bombieri (Roth's theorem and the abc-conjecture, preprint, ETH Zürich, 1994), we show that the ABC conjecture implies the one-dimensional case of Vojta's height inequality. The main geometric tool is the construction of a Belyǐ function. We take care to make explicit the effectivity of the result: we show that an effective version of the ABC conjecture would imply an effective version of Roth's theorem, as well as giving an (in principle) explicit bound on the height of rational points on an algebraic curve of genus at least two.     

Topological Aspects of Liquid Crystals

Using -mapping method and topological current theory, the properties and behaviors of disclination points in three-dimensional liquid crystals are studied. By introducing the strength density and the topological current of many disclination points, the total disclination strength is topologically quantized by the Hopf indices and Brouwer degrees at the singularities of the general director field when the Jacobian determinant of the general director field does not vanish. When the Jacobian determinant vanishes, the origin, annihilation, and bifurcation of disclination points are detailed in the neighborhoods of the limit point and bifurcation point, respectively. The branch solutions at the limit point and the different directions of all branch curves at the first- and second-order degenerated points are calculated. It is pointed out that a disclination point with a higher strength is unstable and will evolve to the lower strength state through the bifurcation process. An original disclination point can split into at most four disclination points at one time.