Phase reduction approach to synchronisation of nonlinear oscillators

Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are often modelled as nonlinear limit-cycle oscillators. In this article, we briefly review phase reduction theory, which is a simple and powerful method for analysing the synchronisation properties of limit-cycle oscillators exhibiting rhythmic dynamics. Through phase reduction theory, we can systematically simplify the nonlinear multi-dimensional differential equations describing a limit-cycle oscillator to a one-dimensional phase equation, which is much easier to analyse. Classical applications of this theory, i.e. the phase locking of an oscillator to a periodic external forcing and the mutual synchronisation of interacting oscillators, are explained. Further, more recent applications of this theory to the synchronisation of non-interacting oscillators induced by common noise and the dynamics of coupled oscillators on complex networks are discussed. We also comment on some recent advances in phase reduction theory for noise-driven oscillators and rhythmic spatiotemporal patterns.     

On the importance of low-energy beta beams for supernova neutrino physics

We argue that isotropization and, consequently, thermalization of the system of gluons and quarks produced in an ultrarelativistic heavy-ion collision does not follow from Feynman diagram analysis to any order in the coupling constant. We conclude that the apparent thermalization of quarks and gluons, leading to success of perfect fluid hydrodynamics in describing heavy-ion collisions at RHIC, can only be attributed to the non-perturbative QCD effects not captured by Feynman diagrams. We proceed by modeling these non-pertrubative thermalization effects using viscous hydrodynamics. We point out that matching Color Glass Condensate inital conditions with viscous hydrodynamics leads to a continuous evolution of all the components of the energy-momentum tensor and, unlike the case of ideal hydrodynamics, does not give rise to a discontinuity in the longitudinal pressure. An important consequence of such a matching is a relationship between the thermalization time and shear viscosity: we observe that small viscosity leads to short thermalization time.     

非临界相位匹配RTP晶体1.6 μm光参量振荡器

采用非临界相位匹配切割,尺寸4 mm4 mm20 mm的磷酸钛氧铷（RTP）晶体作为非线性光学晶体,进行了半导体激光端面抽运Nd:YAG/RTP的内腔式光参量振荡获得人眼安全激光的实验研究。对比了不同声光调Q重复频率下的信号光输出特性。在10.5 W的抽运功率和15 kHz的重复频率下,获得了最高900 mW的1.62 m人眼安全激光输出,光光转换效率达8.6%。1.62 m信号光和对应的1.06 m基频光的脉冲宽度分别为4.6和8.2 ns。信号光中心波长在1618 nm,谱线宽度小于0.5 nm。     

Rotation selectivity of random phase encoding in volume holograms

We present the study of angular selectivity for holographic multiplexing based on random phase encoding by a ground glass. The rotational selectivity of the volume hologram is calculated theoretically and coincides with the experimental measurement. By controlling the parameters including rotational center, effective numerical aperture of both volume hologram and the ground glass, we can obtain different rotational selectivity applied to random phase encoding in volume holographic storage.     

Improved surface morphology of flow-modulated MOVPE grown AIN on sapphire using thin medium-temperature AIN buffer layer

High-temperature (HT) AIN films were grown on (0 0 0 1) sapphire by low-pressure flow-modulated (FM) metal organic vapor phase epitaxy (MOVPE) with and without inserting a thin medium-temperature (MT) AIN layer. To suppress parasitic reactions between the sources of trimethylaluminum (TMA) and ammonia (NH₃), TMA and NH₃ was introduced to the reactor of MOVPE by alternating supply way. Surface morphology and crystalline quality were characterized by a scanning electronic microscopy (SEM), atomic force microscopy (AFM) and X-ray rocking curve (XRC) measurements of (0 0 0 2) and (10-12) diffractions. The AFM and SEM measurements indicated that the thin MT-AIN layer had a strong influence on the surface morphology of the HT-AIN films. The surface morphology became quite smooth by inserting the thin MT-AIN layer and surface RMS roughness values were 0.84 nm and 13.4 nm for the HT-AIN films with and without inserting the thin MT-AIN buffer layer, respectively. By etching the samples in aqueous KOH solution, it was found that the polarity of AIN films was different, the HT-AIN film with the thin MT-AIN layer could not be etched, indicating that the film had an Al-polar surface; however, the film without the MT-AIN layer was etched, which was explained that that film had a N- or mixed-polar surface. The mechanism for the origin of the different polarity of HT-AIN with and without the thin MT-AIN layer was proposed and discussed in detail.     

Complete suppression of metastable phase and significant enhancement of magnetic properties of B-rich PrFeB nanocomposites prepared by devitrifying amorphous ribbons

The effect of refractory element addition on phase transformation, crystallization behavior and magnetic properties of Pr_8.5Fe_81.5B₁₀ (addition-free) and Pr_8.5Fe_81.5M₂B₁₀ (M=V, Cr, Nb, Zr, Ti) ribbons has been investigated. The annealed addition-free ribbon as well as the samples with V or Cr additions are mainly composed of the metastable Pr₂Fe₂₃B₃ phase, whereas annealed ribbons with Nb, Zr or Ti additions primarily consist of Pr₂Fe₁₄B and a minor amount of Fe₃B/boride. The complete suppression of the metastable Pr₂Fe₂₃B₃ phase due to Nb, Zr or Ti additions leads to a significant enhancement of the magnetic properties. For example, the remanence, the coercivity and the energy product are remarkably increased from 2.5 kG, 0.4 kOe and 0.2 MG Oe for the addition-free material to 9.2 kG, 4.7 kOe and 7.6 MG Oe for the specimens with Nb addition. The successful elimination of the metastable Pr₂Fe₂₃B₃ phase is believed to profit from two factors: (a) Nb, Zr or Ti atoms substitute the Pr site, comparatively increase the Pr content, and thus inhibit the nucleation of Pr-lean Pr₂Fe₂₃B₃ phases, and (b) the formation of Nb, Zr, or Ti borides consumes some part of B, which hinders the generation of the B-rich Pr₂Fe₂₃B₃ phase.     

Carrier-envelope phase measurement using plasmonic-field-enhanced high-order harmonic generation of H atom in few-cycle laser pulses

We investigate the plasmonic-field-enhanced high-order harmonic generation (HHG) of H atom driven by few-cycle laser pulses, by solving the time-dependent Schrödinger equation (TDSE). Compared with the homogeneous field, HHG spectra generated by inhomogeneous field exhibit two-plateau structure. We analyze the origin of the two plateaus by using the semiclassical trajectory method. Our results from both classical and TDSE simulations show that the cutoffs of the two plateaus are dramatically affected by the carrier-envelope phase (CEP) of laser pulse in the inhomogeneous field, even for a little longer pulse. Thus, we can determine the CEP of driving laser based on the cutoff position of HHG generated in the inhomogeneous field.     

双螺旋叠栅条纹检测光束准直性的两种方法

介绍双螺旋叠栅条纹检测光束准直性的基本原理,进一步就双螺旋叠栅条纹的特征参量与被测光束发散角(即光束准直精度)的关系进行分析和推导。在分析双螺旋叠栅条纹进行时,首先采用频域低通滤波提取纯叠栅条纹,然后提取纯叠栅条纹的特征参量。提出两种特征参量的提取方法,一种依次进行傅里叶变换计算相位信息的傅里叶变换方法,另一种是受传统时间相移算法启发而提出的空间相移算法,讨论了在两种方法中极坐标的重采样问题和相应的计算公式,并进行了计算机模拟。结果表明,傅里叶变换方法和空间相移算法实质都是获取叠栅条纹全场趋势的平均值,使最终光束发散角的检测具有很高的精度,对自成像条纹周期的检测误差在±2.8‰以内。     

Critical Behavior of the Blume-Emery-Griffiths Model for a Simple Cubic Lattice on the Cellular Automaton

The spin-1 Ising model with the nearest-neighbour bilinear and biquadratic interactions and single-ion anisotropy is simulated on a cellular automaton which improved from the Creutz cellular automaton (CCA) for a simple cubic lattice. The simulations have been made for several k=K/J and d=D/J in the 0≤d<3 and −2≤k≤0 parameter regions. We confirm the existence of the re-entrant and the successive re-entrant phase transitions near the phase boundary. The phase diagrams characterizing phase transitions are presented for comparison with those obtained from other calculations. The static critical exponents are estimated within the framework of the finite-size scaling theory at d=0, 1 and 2 in the interval −2≤k≤0. The results are compatible with the universal Ising critical behavior.