Self-similar solutions to the isothermal compressible Navier-Stokes equations

^** Email: guo_zhenhua{at}iapcm.ac.cn^*** Email: jiang{at}iapcm.ac.cn We investigate the self-similar solutions to the isothermalcompressible Navier–Stokes equations. The aim of thispaper is to show that there exist neither forward nor backwardself-similar solutions with finite total energy. This generalizesthe results for the incompressible case in Neas, J., Rika, M.& verák, V. (1996, On Leray's self-similar solutionsof the Navier-Stokes equations. Acta. Math., 176, 283–294),and is consistent with the (unproved) existence of regular solutionsglobally in time for the compressible Navier–Stokes equations.     

Involutive operator algebras

Positivity - Examples of operator algebras with involution include the operator $$*$$-algebras occurring in noncommutative differential geometry studied recently by Mesland, Kaad, Lesch, and...     

联图$K_5+P_n$的交叉数

A join graph denoted by G + H,is illustrated by connecting each vertex of graph G to each vertex of graph H.In this paper,we prove the crossing number of join product of K_5 + P_n is Z(5,n) + 2 n + [n/2] + 4 for n ≥ 2.     

A predictor-corrector smoothing method for second-order cone programming

In this paper, the second order cone programming problem is studied. By introducing a parameter into the Fischer-Burmeister function, a predictor-corrector smoothing Newton method for solving the problem is presented. The proposed algorithm does neither have restrictions on its starting point nor need additional computation which keep the iteration sequence staying in the given neighborhood. Furthermore, the global and the local quadratic convergence of the algorithm are obtained, among others, the local quadratic convergence of the algorithm is established without strict complementarity. Preliminary numerical results indicate that the algorithm is effective.     

On the Construction of Finite Oscillator Dictionary

A finite oscillator dictionary which has important applications in sequences designs and the compressive sensing was introduced by Gurevich, Hadani, and Sochen in [3 Gurevich , S. , Hadani , R. , Sochen , N. (2008). The finite harmonic oscillator and its applications to sequences, communication and radar. IEEE Trans. Inform. Theory 54(9):4239–4253.[Crossref], [Web of Science ®] , [Google Scholar]]. In this paper, closed formulae of the finite split oscillator dictionary 𝔖 ^s are revisited by a simple proof, the structure of nonsplit tori of the group SL(2, 𝔽 _p ) is studied, and an explicit algorithm for computing the finite nonsplit oscillator dictionary 𝔖 ^ns is described.     

An experimental and modeling study of the autoignition of 3-methylheptane

An experimental and kinetic modeling study of the autoignition of 3-methylheptane, a compound representative of the high molecular weight lightly branched alkanes found in large quantities in conventional and synthetic aviation kerosene and diesel fuels, is reported. Shock tube and rapid compression machine ignition delay time measurements are reported over a wide range of conditions of relevance to combustion engine applications: temperatures from 678 to 1356 K; pressures of 6.5, 10, 20, and 50 atm; and equivalence ratios of 0.5, 1.0, and 2.0. The wide range of temperatures examined provides observation of autoignition in three reactivity regimes, including the negative temperature coefficient (NTC) regime characteristic of paraffinic fuels. Comparisons made between the current ignition delay measurements for 3-methylheptane and previous results for n-octane and 2-methylheptane quantifies the influence of a single methyl substitution and its location on the reactivity of alkanes. It is found that the three C₈ alkane isomers have indistinguishable high-temperature ignition delay but their ignition delay times deviate in the NTC and low-temperature regimes in correlation with their research octane numbers. The experimental results are compared with the predictions of a proposed kinetic model that includes both high- and low-temperature oxidation chemistry. The model mechanistically explains the differences in reactivity for n-octane, 2-methylheptane, and 3-methylheptane in the NTC through the influence of the methyl substitution on the rates of isomerization reactions in the low-temperature chain branching pathway, that ultimately leads to ketohydroperoxide species, and the competition between low-temperature chain branching and the formation of cyclic ethers, in a chain propagating pathway.     

Mode locked Er-doped fiber laser with single-wall carbon nanotube saturable absorber

A mode locked Er-doped fiber laser based on a single-wall carbon nanotube saturable absorber is demonstrated. A high quality single-wall carbon nanotubes （SWCNTs） absorber film is fabricated by a polymer composite. The pulse duration is 488 fs with 9.6-nm spectral width at the center of 1564 nm. The repetition rate is 30.4 MHz. The maximum output power is 3 mW. And the single pulse energy is 0.1 nJ.     

Thickness and stacking geometry effects on high frequency overtone and combination Raman modes of graphene

We investigate two high frequency Raman overtone and combination modes of graphene named 2D' and 2D + G bands, and located at ~3240 and ~ 4260 cm^–1, respectively. The graphene thickness and stacking geometry effects for these two modes are systematically studied. The features of the 2D' band, which arises from intravalley double resonance, are not sensitive to the variation of thickness with single Lorentzian peak and fixed linewidth. We explain it theoretically by calculating the phonon dispersion mode in k‐space and find that the flat band region of longitudinal optical phonon near Γ point is the mechanism leading to the 2D' band nonsplit. With the thickness increasing, the band position exhibits blueshift and the linewidth increases for the 2D + G band. With changing thickness and stacking geometry of graphene, the intensities of these two high‐frequency bands show obvious different evolution compared with that of G band. Copyright © 2012 John Wiley & Sons, Ltd.     

Effect of Stretching on β-Phase Content of Isotactic Polypropylene Melt Containing β-Nucleating Agent

Pure isotactic polypropylene (iPP) and that containing 0.2 wt% of a β-nucleating agent (β-NA) were extruded through a slit die. Simultaneously, the extruded melt was stretched at the die exit with different stretching rates (SR). The change of β-phase content with different SR was investigated by differential scanning calorimetry (DSC) and wide-angle X-ray diffraction (WAXD). The results indicate that, for pure iPP, the content of β-phase first increases with increasing SR till it reaches a maximum and then it gradually decreases. However, for the case of β-nucleated iPP, it decreases monotonously with increasing SR. The spatial confinement is considered as the best explanation for the suppression of β-phase in the nucleated iPP melt upon stretching.