Semiclassics around a phase space caustic: An illustration using the Nelson Hamiltonian

The semiclassical formula for the coherent-state propagator is written in terms of complex classical trajectories of an equivalent classical system. Depending on the parameters involved, more than one trajectory may contribute to the calculation. Eventually, however, two contributing trajectories coalesce, characterizing what is called phase space caustic. In this case, the usual semiclassical formula for the propagator diverges, so that a uniform approximation is required to avoid this singularity. In this Letter, we present a non-trivial numerical application illustrating this scenario, showing the accuracy of the uniform formula that we have previously derived.     

Complex networks: Effect of subtle changes in nature of randomness

In two different classes of network models, namely, the Watts Strogatz type and the Euclidean type, subtle changes have been introduced in the randomness. In the Watts Strogatz type network, rewiring has been done in different ways and although the qualitative results remain the same, finite differences in the exponents are observed. In the Euclidean type networks, where at least one finite phase transition occurs, two models differing in a similar way have been considered. The results show a possible shift in one of the phase transition points but no change in the values of the exponents. The WS and Euclidean type models are equivalent for extreme values of the parameters; we compare their behaviour for intermediate values.     

Microphase separation in polydisperse miktoarm star copolymers

A two or more chemically different homopolymers attached to a single junction point form a macromolecule of miktoarm star copolymer. The model of such copolymer composed of an arbitrary number of types of homopolymer arms is considered. The lengths distributions of arms are assumed to be arbitrary, provided that average length of an each arm is long enough. The algorithm is suggested to find the contributions into the Landau free energy of this copolymer melt which are necessary to obtain a phase diagram in weak segregation regime. Using this algorithm the contributions are found up to the fourth order. The phase diagrams have been constructed for the simple model of AB₂ copolymer melt whose macromolecules consist of polydisperse A-block and two monodisperse B-blocks.     

Effects of the bond dilution on the phase diagrams of a spin-1 transverse Ising model with crystal field interaction on a honeycomb lattice

A bond diluted spin-1 Ising model with crystal and transverse field interactions is examined for honeycomb lattice by introducing an effective field approximation that takes into account the correlations between different spins that emerge when expanding the identities. The effects of the crystal field as well as the transverse field and dilution on the phase diagrams and order parameter m_z are discussed in detail. A number of interesting and unusual phenomena such as reentrant phenomena and three successive phase transitions originating from the crystal field as well as the transverse field and bond dilution have been found.     

Correlation and entanglement of a three-level atom inside a dissipative cavity

We discuss the correlation and entanglement of a three-level atom with a single-mode quantized field in a coherent state inside a phase-damped cavity. We analyze the influence of dissipation on the quantum and classical entropy. It has been shown that the quantum, classical and nonextensive entropy are sensitive to any change in the initial state setting of the atom and the quantized field. The relation between the long lived entanglement and dissipation is observed. On the other hand, a short disentanglement can be generated through special values of the atomic motion parameter.     

Quantitative T(1)(ρ) imaging using phase cycling for B0 and B1 field inhomogeneity compensation

T_1ρ imaging is useful in a number of clinical applications. T_1ρ preparation methods, however, are sensitive to non-uniformities of the B₀ magnetic field and the B₁ RF field. These common system imperfections can result in image artifacts and quantification errors in T_1ρ imaging. We report on a phase-cycling method which can eliminate B₁ RF inhomogeneity effects in T_1ρ imaging. This method does not only correct for image artifacts but also for T_2ρ contamination caused by B₁ RF inhomogeneity. The presence of B₀ magnetic field inhomogeneity can compromise the effectiveness of this method for B₁ RF inhomogeneity correction. We demonstrate that, by combining the spin-locking scheme reported by Dixon et al. (Myocardial suppression in vivo by spin locking with composite pulses. Magn Reson Med 1996; 36:90-94) with phase cycling, we can simultaneously correct B₀ magnetic field inhomogeneity effects and B₁ RF inhomogeneity effects in T_1ρ imaging. Phantom and in vivo data sets are used to demonstrate the proposed methods and to compare them with other existing T_1ρ preparation methods.     

基于多级微反射镜的傅里叶变换红外光谱仪中准直误差的分析

通过对基于多级微反射镜的空间调制傅里叶变换红外光谱仪准直误差的分析,模拟了准直误差的存在而导致的干涉图大光程差处对比度反转和光谱图边频噪声的产生。讨论了在不同的误差系数下复原光谱图的信噪比和分辨率,并且分析了干涉图大光程差处对比反转以及光谱图边频分量的产生原因。仿真结果表明,在误差系数α=0.15°.mm-1时,光谱的信噪比会下降到6 dB,同时光谱分辨率会退化到13.4cm-1。本文的结论将应用于微型光谱仪系统的光学设计与装调。     

Low cost a posteriori error estimators for an augmented mixed FEM in linear elasticity

We consider an augmented mixed finite element method applied to the linear elasticity problem and derive a posteriori error estimators that are simpler and easier to implement than the ones available in the literature. In the case of homogeneous Dirichlet boundary conditions, the new a posteriori error estimator is reliable and locally efficient, whereas for non-homogeneous Dirichlet boundary conditions, we derive an a posteriori error estimator that is reliable and satisfies a quasi-efficiency bound. Numerical experiments illustrate the performance of the corresponding adaptive algorithms and support the theoretical results.