Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities

A model dynamical system with a great many degrees of freedom is proposed for which the critical condition for the onset of collective oscillations, the evolution of a suitably defined order parameter, and its fluctuations around steady states can be studied analytically. This is a rotator model appropriate for a large population of limit cycle oscillators. It is assumed that the natural frequencies of the oscillators are distributed and that each oscillator interacts with all the others uniformly. An exact self-consistent equation for the stationary amplitude of the collective oscillation is derived and is extended to a dynamical form. This dynamical extension is carried out near the transition point where the characteristic time scales of the order parameter and of the individual oscillators become well separated from each other. The macroscopic evolution equation thus obtained generally involves a fluctuating term whose irregular temporal variation comes from a deterministic torus motion of a subpopulation. The analysis of this equation reveals order parameter behavior qualitatively different from that in thermodynamic phase transitions, especially in that the critical fluctuations in the present system are extremely small.Dedicated to Ilya Prigogine on the occasion of his 70th birthday.     

Eden-Staudacher and Beisert-Eden-Staudacher equations in the $$\mathcal{N} = 4$$ supersymmetric gauge theory

We investigate the Eden-Staudacher and Beisert-Eden-Staudacher equations for the anomalous dimension of twist-2 operators at a large spin s in the supersymmetric gauge theory. We reduce these equations to a set of linear algebraic equations and calculate their kernels analytically. We demonstrate that in the perturbation theory, the anomalous dimension is a sum of products of the Euler functions ζ(k) having the maximum transcendentality property. We also show that at a large coupling, the “singular” solution of the Beisert-Eden-Staudacher equation reproduces the anomalous dimension constants predicted from the string side of the AdS/CFT correspondence. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 117–129, April, 2008.     

Refinement of the cation distribution in Nb-Mo double oxide

The structure of Nb₂Mo₃O₁₄ double oxide is refined from powder data using synchrotron radiation and the anomalous scattering effect; space group P $ \bar 4 The structure of Nb₂Mo₃O₁₄ double oxide is refined from powder data using synchrotron radiation and the anomalous scattering effect; space group P 2₁ m is found for the material. It is demonstrated that in the tetragonal unit cell with parameters a = 23.173 ?, c = 4.0027 ? Nb⁵⁺ and Mo⁶⁺ ions are stochastically distributed in MO₆ octahedra and MO₇ pentagonal bipyramids of the polygonal network structure of the Mo₅O₁₄ type. Original Russian Text Copyright ? 2008 by T. Yu. Kardash, L. M. Plyasova, V. M. Bondareva, and A. N. Shmakov __________ Translated from Zhurnal Strukturnoi Khimii, Vol. 49, No. 4, pp. 729–735, May–June, 2008.     

Magnetic correction to the anomalous magnetic moment of electrons

We investigate the leading order correction of anomalous magnetic moment (AMM) to electrons in a weak magnetic field and find that the magnetic correction is negative and magnetic field dependent, indicating a magnetic catalysis effect for the electron gas. In the laboratory, to measure the g − 2, the magnitude of the magnetic field B is several T, and correspondingly the magnetic correction to the AMM of electron/muon is around 10⁻³⁴/10⁻⁴², therefore the magnetic correction can be safely neglected in the current measurement. However, when the magnitude of the magnetic field strength is comparable with the electron mass, the magnetic correction of the electron's AMM will become considerable. This general magnetic correction to the charged fermion's AMM can be extended to study quantum chromodynamic matter under a strong magnetic field.     

Control of Wave Propagation and Effect of Kerr Nonlinearity on Group Index

We use four-level atomic system and control the wave propagation via forbidden decay rate. The Raman gain process becomes dominant on electromagnetically induced transparency (EIT) medium by increasing the forbidden decay rate via increasing the number of atoms [G.S. Agarwal and T.N. Dey, Phys. Rev. A 74 (2005) 043805 and K. Harada, T. Kanbashi, and M. Mitsunaga, Phys. Rev. A 73 (2006) 013803]. The behavior of wave propagation is dramatically changed from normal (subluminal) to anomalous (superluminal) dispersion by increasing the forbidden decay rate. The system can also give a control over the group velocity of the light propagating through the medium via Kerr field.     

The QED vacuum polarization function at four loops and the anomalous magnetic moment at five loops

The anomalous magnetic moment of the muon is one of the most fundamental observables. It has been measured experimentally with a very high precision and on theory side the contributions from perturbative QED have been calculated up to five-loop level by numerical methods. Contributions to the muon anomalous magnetic moment from certain diagram classes are also accessible by alternative methods. In this paper we present the evaluation of contributions to the QED corrections due to insertions of the vacuum polarization function at five-loop level.     

SERS activity and stability of the most frequently used silver colloids

Single‐molecule detection by surface‐enhanced resonance Raman scattering (SERRS) spectroscopy has been demonstrated for a variety of molecules. The detection of single molecules that do not have a resonance contribution, SERS, has been shown in the case of adenine. However, when colloidal particles isolated on planar substrates are used as the enhancing medium, the presence of anomalous signals significantly complicates the analysis of the spectra. Selection of a silver colloid that minimizes these spurious signals should improve the ultra‐sensitive detection of non‐resonant single molecules by SERS. A range of silver colloids, prepared by different methods, were investigated with respect to their activity and stability. Minimal anomalous signals were obtained from hydroxylamine‐reduced silver colloids, which suggests that this colloid will be better for ultra‐sensitive SE(R)RS experiments compared to the more common citrate‐ and borohydride‐reduced silver colloids. Copyright © 2011 John Wiley & Sons, Ltd.     

Challenges of sulfur SAD phasing as a routine method in macromolecular crystallography

The sulfur SAD phasing method allows the determination of protein structures de novo without reference to derivatives such as Se‐methionine. The feasibility for routine automated sulfur SAD phasing using a number of current protein crystallography beamlines at several synchrotrons was examined using crystals of trimeric Achromobacter cycloclastes nitrite reductase (AcNiR), which contains a near average proportion of sulfur‐containing residues and two Cu atoms per subunit. Experiments using X‐ray wavelengths in the range 1.9–2.4 Å show that we are not yet at the level where sulfur SAD is routinely successful for automated structure solution and model building using existing beamlines and current software tools. On the other hand, experiments using the shortest X‐ray wavelengths available on existing beamlines could be routinely exploited to solve and produce unbiased structural models using the similarly weak anomalous scattering signals from the intrinsic metal atoms in proteins. The comparison of long‐wavelength phasing (the Bijvoet ratio for nine S atoms and two Cu atoms is ～1.25% at ～2 Å) and copper phasing (the Bijvoet ratio for two Cu atoms is 0.81% at ～0.75 Å) for AcNiR suggests that lower data multiplicity than is currently required for success should in general be possible for sulfur phasing if appropriate improvements to beamlines and data collection strategies can be implemented.     

过冷Ni-P合金的凝固行为

以揭示共晶系合金在不同过冷度下凝固时初生相的选择规律和凝固组织形成机理为目的, 用熔融玻璃净化和循环过热相结合的方法, 将Ni_100-xP_x(x=18, 19, 19.6, 20, 21, 原子百分比)合金过冷至平衡液相线以下不同的温度, 用高速红外测温仪记录了试样的凝固冷却曲线, 详尽分析了试样的凝固组织.结果表明, 过冷Ni-P合金快速凝固过程中析出的初生相为α-Ni/Ni₃P耦合共晶时, 整个凝固过程中仅出现一次再辉, 在所形成的异常共晶组织中α-Ni颗粒大小分布均匀;而当某一共晶相优先析出时, 另外一相需要在残留液相中重新形核, 致使凝固过程中出现两次再辉, 相应形成颗粒相大小截然不同的两类异常共晶组织;据此绘制了Ni-P合金初生相为共生共晶的区域. Ni-P合金中α-Ni的生长动力学明显快于Ni₃P, 使得在大过冷度下过共晶合金也以α-Ni作为初生相进行凝固.     

双透射峰钠原子滤光器在太阳速度场观测中的应用

法拉第反常色散原子滤光器作为一种精密光谱仪器,具有光谱分辨力高、光谱稳定性好等优点。探讨了利用双透射峰钠原子滤光器进行高分辨力太阳多普勒观测的方法,在此基础之上开发了原子滤光器透射谱型理论模拟软件,研制出双透射峰钠原子滤光器样机并对其进行了透射谱型测试。测试结果表明,理论模拟的透射谱型与实验测试结果符合良好,在双峰间距、透射带宽等参数方面基本满足太阳多普勒观测的要求,为太阳观测提供另一种有效手段。