Rheological characterization of well-defined tetrafluoroethylene/hexafluoropropylene copolymers

The rheology of tetrafluoroethylene/hexafluoropropylene (TFE/HFP) copolymers, also known as Teflon FEP polymers, having different molecular weight and composition (HFP content) was studied by means of a parallel-plate rheometer. Two groups of polymers having different molecular weights with nearly constant polydispersity (around 2.5) were considered; namely, one group having a relatively low melting temperature (amorphous with a high content of HFP) and a second group having a higher melting point (semi-crystalline with a lower content of HFP). The relaxation time spectrum, H(λ), calculated by use of the BSW model (developed for monodisperse linear polymers) followed a scaling relationship in the terminal zone with scaling exponent of 0.13. However, at higher frequencies the model fails to predict adequately the experimental data. The longest relaxation time calculated from both the BSW model and discrete relaxation spectra (λ _i ,g _i ), which was determined by use of a parsimonious fitting software, depends on the molecular weight in a similar way as the zero-shear viscosity does with the well-established scaling factor of 3.4. The critical molecular weight for the onset of entanglements, M _c , was found to be about 100000, a value much higher than those previously reported in literature for other polymers. The rheology of resins in the second group (higher melting point) was found to exhibit a strong dependence on thermal history during oscillatory-shear measurements. The data obtained in experiments at different temperatures without a preheating to a certain value (330°C) exhibited a violation of the time-temperature superposition principle and no well-defined values of the zero-shear viscosity. This is attributed to residual crystallinity even at temperatures well above their melting point (260°C). However, the same experiments with preheating and subsequent cooling to desired temperature resulted into a very good time-temperature scaling. Received: 13 January 1998 Accepted: 6 April 1998     

Dichotomy Spectrum for Nonautonomous Differential Equations

For nonautonomous linear differential equations x=A(t) x with locally integrable A: RR ^N×N the so-called dichotomy spectrum is investigated in this paper. As the closely related dichotomy spectrum for skew product flows with compact base (Sacker–Sell spectrum) our dichotomy spectrum for nonautonomous differential equations consists of at most N closed intervals, which in contrast to the Sacker–Sell spectrum may be unbounded. In the constant coefficients case these intervals reduce to the real parts of the eigenvalues of A. In any case the spectral intervals are associated with spectral manifolds comprising solutions with a common exponential growth rate. The main result of this paper is a spectral theorem which describes all possible forms of the dichotomy spectrum.     

激光通过散射介质的聚焦

基于角谱衍射公式和散射介质的圆形高斯分布模型,数值模拟光通过散射介质的聚焦.通过反馈优化算法实现散射光束的波前整形,在目标位置处形成一个很亮的聚焦光斑.改变聚焦目标位置后,可实现任意位置处的单点或多点聚焦.讨论了空间光调制器上的总调制单元个数、每个调制单元相位准确度与光强增长因子的关系.结果表明:目标位置处的光强随着总像素单元数的增加而线性地增强,并且随着调制单元的相位准确度的增加而增强.     

Energy structure and absorption spectra of colloidal CdS nanocrystals in gelatin matrix

We investigate the energy structure of colloidal CdS nanocrystals by measuring the UV–vis absorption spectra. Nanocrystals were synthesized by sol–gel method in a gelatin matrix in the size range from 2.5 to 3.9 (±0.2) nm. In order to interpret the UV–vis absorption spectra we calculate the energy spectrum of electron quasi-stationary states using the model of open nanocrystal as well as the hole stationary spectrum in a two-band approach. It is shown that the main contribution to the absorption spectrum is made by interband transitions 1S_3/2→1S_e and 1P_3/2→1P_e, and its shape is determined by the size distribution of nanoparticles. For this system the estimated values of the effective masses of the heavy hole and light hole are 1.44m₀ and 0.28m₀, respectively.     

Analysis of marine atmospheric turbulence effects on infrared imaging system by angle of arrival fluctuations

For the long-range infrared imaging system, the marine atmospheric turbulence degrades seriously the probability of object recognition and tracking. In this study, the angle of arrival fluctuations of an optical wave, which describes the distortion effects of marine atmospheric turbulence on an infrared optical imaging system, is investigated in detail both analytically and numerically. Analytic expressions of the angle of arrival fluctuations are derived for optical plane and spherical waves propagating through weak marine atmospheric turbulence with horizontal path, and they consider simultaneously finite turbulence inner scale, turbulence outer scale, wavelength, and aperture diameters. Numerical calculations are conducted to analyze the influence of marine weak turbulence on the infrared imaging. The results are useful for understanding the potential impact of deviations from the terrestrial turbulence.     

Global bifurcation of solutions for a predator–prey model with prey‐taxis

We study pattern formations in a predator–prey model with prey‐taxis. It is proved that a branch of nonconstant solutions can bifurcate from the positive equilibrium only when the chemotactic is repulsive. Furthermore, we find the stable bifurcating solutions near the bifurcation point under suitable conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

Multi-way dual Cheeger constants and spectral bounds of graphs

We introduce a set of multi-way dual Cheeger constants and prove universal higher-order dual Cheeger inequalities for eigenvalues of normalized Laplace operators on weighted finite graphs. Our proof proposes a new spectral clustering phenomenon deduced from metrics on real projective spaces. We further extend those results to a general reversible Markov operator and find applications in characterizing its essential spectrum.     

The depth spectrums of constacyclic codes over finite chain rings

In light of the generator polynomials of constacyclic codes over finite chain rings, the depth spectrum of constacyclic codes can be determined if (n,p)=1$(n,p)=1$.     

Criteria for the absence of quantum fluctuations after spontaneous symmetry breaking

The lowest-energy state of a macroscopic system in which symmetry is spontaneously broken, is a very stable wavepacket centered around a spontaneously chosen, classical direction in symmetry space. However, for a Heisenberg ferromagnet the quantum groundstate is exactly the classical groundstate, there are no quantum fluctuations. This coincides with seven exceptional properties of the ferromagnet, including spontaneous time-reversal symmetry breaking, a reduced number of Nambu–Goldstone modes and the absence of a thin spectrum (Anderson tower of states). Recent discoveries of other non-relativistic systems with fewer Nambu–Goldstone modes suggest these specialties apply there as well. I establish precise criteria for the absence of quantum fluctuations and all the other features. In particular, it is not sufficient that the order parameter operator commutes with the Hamiltonian. It leads to a measurably larger coherence time of superpositions in small but macroscopic systems.     

认知无线电网络中利用FEC和DE的多节点频谱感知算法

针对认知无线电网络(CRN)中空闲频谱感知困难的问题,本文提出了基于前向纠错和差分进化算法的多节点频谱感知算法。首先,利用基于差分进化算法的协同检测完成信号感知;然后,研究了信道噪声对频谱感知性能的影响;最后,分析了前向纠错技术在信道存在噪声时对频谱感知性能的影响。仿真实验将纠错和无纠错控制信道的不同信噪比作为依据,采用三种不同的检测方法评估了本文算法。仿真实验结果表明,在存在噪声的认知无线电网络中,本文算法提高了系统的性能和检测概率,且协同感知算法的性能随着节点数目的增加而提高,该算法适合应用于实时性要求较高的应用程序。