THE BLOW-UP PROPERLIES OF SOLUTIONS TO SEMILINEAR HEAT EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

1IntroductionInthispaper,weconsidertheinitial-boundaryvalueproblem,where"o(x)isnon-negativesmoothfunctionsatisfying"o.(0)=0,"o.(1)=1'Whenconsideringtheblow-upofsolution,thefollowingproblemarisenaturally:Doesblow-upoccur?Howdoesthesolutionapproachtheblow-uptime'!Andwilersisthehotspotlocated(blow-upset)?WelookattheheatequationwithanonlillearboundaryconditiollHerefiisaboundeddomaininR",p>1isarealnumber.IthasbeenknownforalongtimethattheDroblelil(1.1).(1.2)withAL(~,0)--'no(x)doesnothaveaglobals…     

布拉格方程在高聚物结构研究中的应用

本文将布拉格方程推广应用到高聚物的结构研究中，得到了经不同剂量辐照的聚乙烯单晶的长周期，并辅以示差扫描量热法研究了γ－射线辐照对聚乙烯单晶结构的影响．     

Unconventional antiferromagnetic correlations of the doped Haldane gapsystem Y 2 BaNi 1 - x Zn x O 5

We make a new proposal to describe the very low temperature susceptibility of the doped Haldane gap compound Y₂BaNi_1-xZn_xO₅. We propose a new mean field model relevant for this compound. The ground state of this mean field model is unconventional because antiferromagnetism coexists with random dimers. We present new susceptibility experiments at very low temperature. We obtain a Curie-Weiss susceptibility χ( T ) ∼ C /(Θ + T ) as expected for antiferromagnetic correlations but we do not obtain a direct signature of antiferromagnetic long range order. We explain how to obtain the “impurity” susceptibility ( T ) by subtracting the Haldane gap contribution to the total susceptibility. In the temperature range [1 K, 300 K] the experimental data are well fitted by T ( T ) = C _imp 1 + T _imp / T . In the temperature range [100 mK, 1 K] the experimental data are well fitted by T ( T ) = A ln( T / T _c ), where T _c increases with x. This fit suggests the existence of a finite Néel temperature which is however too small to be probed directly in our experiments. We also obtain a maximum in the temperature dependence of the ac-susceptibility ( T ) which suggests the existence of antiferromagnetic correlations at very low temperature. Received 17 July 2001     

宇宙学常数疑难

当代天文学的一系列观测事实都支持应该存在一个非零的正的宇宙学常数，但是，人们发现当前宇宙学常数值太小，而且宇宙学常数即真空能量密度与现在的物质密度巧合地具有相同的量级，然而现有物理学理论还无法给出合理的解释，因此宇宙学常数问题成为物理学和天文学上最重大的疑难之一。文章综述了近年来宇宙在加速膨胀这一重大的天文发现和宇宙学常数的观测结果以及当前理论物理学在宇宙学常数问题上的一些尝试。     

Zeroth and second laws of thermodynamics simultaneously questioned in the quantum microworld

A new and rather trivial model is suggested with mechanism that implies simultaneous violation of the zeroth and the second laws of thermodynamics. Mathematically rigorous quantum theory reduces to a trivial application of the Golden rule formula. It yields exciton on-energy-shell diffusion caused by bath-nonassisted excitation hopping between tails of different exciton site levels ε₁ < ε₂ broadened by bath-assisted finite life-time effects. The elastic character of the hopping implies 1 ↔ 2-symmetric transfer rate W. Thus the net diffusion exciton flow W(P ₁ - P ₂) and also, as argued, the net energy flow are possible due to different near-to-equilibrium exciton populations P ₁ > P ₂. As the sites are provided with two different baths, the population imbalance and the flows survive even for slightly different local bath temperatures T ₁ < T ₂ < T ₁ε₂/ε₁. Thus spontaneous exciton and also energy flows against temperature step become possible, in contradiction with the Clausius form of the second law. Violations of both the laws disappear in the high-temperature, i.e. classical limit Received 16 May 2001 and Received in final form 20 September 2001     

Determination of the Constants of Binding of Acridine Dyes with Micelles of Sodium Dodecyl Sulfate Using the Quenching of Delayed Fluorescence by Heavy Atoms

The constants of binding dye molecules with the micelles of sodium dodecyl sulfate are determined using quenching of delayed fluorescence of acridine dyes by sodium iodide in aqueous–micellar solutions. Kinetic equations have been composed that describe the processes of deactivation of the excited states of dyes. By solving these equations at the concentration of the quencher sodium iodide corresponding to the minimum lifetime of triplet states and at the concentration of micelles corresponding to the least value of the delayed fluorescence quenching rate constants, we obtained the constants of binding dyes with micelles equal to 1.3·10⁷, 2.9·10⁷, and 3.1·10⁷ M^–1 for trypaflavine, acridine orange, and acridine yellow, respectively. We calculated the rate constants of quenching of the triplet states of the molecules of dyes by iodide ions (I ^–) that decreased in transition from trypaflavine to acridine orange and acridine yellow.     

变频压缩机空调系统的理论分析及实验研究

变频空调器是由变频压缩机驱动的空调系统,压缩机通过变频调节其转速使压缩机单位时间内的排气量变化,从而达到调节制冷量的目的。本文提出了变频空调器制冷系统的原理和设计方法,具体给出了制冷量和压缩机频率的关系方程,并从理论和实验两方面对变频空调器制冷系统进行了分析,得到了频率曲线图,为变频空调器制冷系统的设计提供了依据。     

Characteristics of Ti0.97Co0.03O2:Sb0.01 dilute magnetic semiconducting thin films deposited at 500 °C by pulsed laser deposition

Epitaxial Ti_0.97Co_0.03O₂:Sb_0.01(TCO:Sb) films were deposited on R-Al₂O₃ (1 1 0 2) substrates at 500 °C in various deposition pressures by pulsed laser deposition. The solubility of cobalt within the films increases with decreasing deposition pressure at a deposition temperature of 500 °C. The TCO:Sb films deposited at 5×10⁻⁶ Torr exhibit a p-type anomalous Hall effect having a hole concentration of 6.1×10²²/cm³ at 300 K. On the other hand, films deposited at 4×10⁻⁴ Torr exhibits an n-type anomalous Hall effect having an electron concentration of about 1.1×10²¹/cm³. p- or n-type DMS characteristics depends on the change of the structure of TCO:Sb films and the solubility of Co is possible by controlling the deposition pressure.     

Boiling heat transfer characteristics of nanofluids in a flat heat pipe evaporator with micro-grooved heating surface

An experimental study was performed to understand the nucleate boiling heat transfer of water–CuO nanoparticles suspension (nanofluids) at different operating pressures and different nanoparticle mass concentrations. The experimental apparatus is a miniature flat heat pipe (MFHP) with micro-grooved heat transfer surface of its evaporator. The experimental results indicate that the operating pressure has great influence on the nucleate boiling characteristics in the MFHP evaporator. The heat transfer coefficient and the critical heat flux (CHF) of nanofluids increase greatly with decreasing pressure as compared with those of water. The heat transfer coefficient and the CHF of nanofluids can increase about 25% and 50%, respectively, at atmospheric pressure whereas about 100% and 150%, respectively, at the pressure of 7.4 kPa. Nanoparticle mass concentration also has significant influence on the boiling heat transfer and the CHF of nanofluids. The heat transfer coefficient and the CHF increase slowly with the increase of the nanoparticle mass concentration at low concentration conditions. However, when the nanoparticle mass concentration is over 1.0 wt%, the CHF enhancement is close to a constant number and the heat transfer coefficient deteriorates. There exists an optimum mass concentration for nanofluids which corresponds to the maximum heat transfer enhancement and this optimum mass concentration is 1.0 wt% at all test pressures. The experiment confirmed that the boiling heat transfer characteristics of the MFHP evaporator can evidently be strengthened by using water/CuO nanofluids.     

Thermochemically induced binding of methyl orange to polycations containing primary amine groups

The thermochemical transformation of electrostatically formed complexes of methyl orange (MO) with polycations containing primary amine groups such as ammonium salts afforded new polymers with a high concentration of covalently bound 4‐N,N‐dimethylaminoazobenzene groups in the side chain. Poly(allylamine hydrochloride) and poly(β‐aminoethylene acrylamide hydrochloride) were employed as support polycations for MO. The transformation of sulfonate–ammonium ion pairs into sulfonamide bonds, via heating at an elevated temperature, was supported by the polymer properties before and after the thermal treatment. The polymer structure changes were monitored with elemental analysis, Fourier transform infrared, ¹H NMR, and ultraviolet–visible absorption spectroscopy, and thermogravimetric analysis. The spacer length between the backbone and azobenzene structures used as side chains strongly influenced the polymer properties before and after the heat‐induced reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5898–5908, 2006