Nonequilibrium thermodynamics and fluctuation relations for small systems

In this review, we give a retrospect of the recent progress in nonequilibrium statistical mechanics and thermodynamics in small dynamical systems. For systems with only a few number of particles, fluctuations and nonlinearity become significant and contribute to the nonequilibrium behaviors of the systems, hence the statistical properties and thermodynamics should be carefully studied. We review recent developments of this topic by starting from the Gallavotti–Cohen fluctuation theorem, and then to the Evans–Searles transient fluctuation theorem, Jarzynski free-energy equality, and the Crooks fluctuation relation. We also investigate the nonequilibrium free energy theorem for trajectories involving changes of the heat bath temperature and propose a generalized free-energy relation. It should be noticed that the non-Markovian property of the heat bath may lead to the violation of the free-energy relation.     

长白山地区几种红景天品种的傅里叶变换红外光谱法鉴别研究

分别用石油醚,氯仿,甲醇对长白山地区的野生和栽培高山红景天和长白红景天进行了提取,并首次对提取物进行了傅里叶变换红外光谱法测定,还用红景天块做了相应的验证研究。结果表明,长白山地区的野生和栽培高山红景天和长白红景天的红外光谱图谱有明显不同,故可用作鉴别其品种或评价其质量的一种手段。     

Codimension reduction in symmetric spaces

In this paper we give a short geometric proof of a generalization of a well-known result about reduction of codimension for submanifolds of Riemannian symmetric spaces.     

The mm-wave dielectric measurements with an electric-field cross-correlation Fourier transform spectrometer

A method for measuring complex permittivity based on an electric-field cross-correlation Fourier transform spectrometer was proposed. Its principle can be extended over the whole microwave region. Two typical solid media, teflon and plexigrass, and a kind of sand were measured in 8mm-wave region by the method. The results show that this method has potentialities to perform accurate permittivity measurements.Supported by Foundation of Specialities Opened to Doctorate Study     

Photo-detachment cross section of H- near two parallel interfaces

The photo-detachment cross section of H^- near two parallel elastic interfaces is derived and calculated by using the closed orbit theory. The photo-detachment cross section of H^- near two interfaces is shown to exhibit multi-periodic oscillations when the distance between the H^- and the interface is varied. Each peak in the Fourier transformed photo-detachment cross section corresponds to the length of a closed orbit, which is quite similar to the case of atomic spontaneous emissions in a dielectric slab. This study provides a new understanding of the photo=detachment process of H^- in the presence of interfaces.     

Pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control

A new kind of generalized synchronization of two chaotic systems with uncertain parameters is proposed. Based on a pragmatical asymptotical stability theorem and an assumption of equal probability for ergodic initial conditions, an adaptive control law is derived so that it can be proved strictly that the common null solution of error dynamics and of parameter dynamics is actually asymptotically stable, i.e. these two identical systems are in generalized synchronization and the estimated parameters approach the uncertain values. It is called pragmatical generalized synchronization. Finally, two numerical examples are studied for two Quantum-CNN oscillator chaotic systems to show the effectiveness of the proposed generalized synchronization strategy with a double Duffing chaotic system as a goal system.     

Accurate, high-order representation of complex three-dimensional surfaces via Fourier continuation analysis

We present a new method for construction of high-order parametrizations of surfaces: starting from point clouds, the method we propose can be used to produce full surface parametrizations (by sets of local charts, each one representing a large surface patch – which, typically, contains thousands of the points in the original point-cloud) for complex surfaces of scientific and engineering relevance. The proposed approach accurately renders both smooth and non-smooth portions of a surface: it yields super-algebraically convergent Fourier series approximations to a given surface up to and including all points of geometric singularity, such as corners, edges, conical points, etc. In view of their C^∞ smoothness (except at true geometric singularities) and their properties of high-order approximation, the surfaces produced by this method are suitable for use in conjunction with high-order numerical methods for boundary value problems in domains with complex boundaries, including PDE solvers, integral equation solvers, etc. Our approach is based on a very simple concept: use of Fourier analysis to continue smooth portions of a piecewise smooth function into new functions which, defined on larger domains, are both smooth and periodic. The “continuation functions” arising from a function f converge super-algebraically to f in its domain of definition as discretizations are refined. We demonstrate the capabilities of the proposed approach for a number of surfaces of engineering relevance.     

不对称离散分数傅里叶变换实现数字图像的加密变换

利用不对称分数傅里叶变换的特性,提出了一种图像加密变换的新方法。对图像的x,y方向分别实施不同级次的一维分数傅里叶变换,得到加密图像。解密方法就是对变换后的图像实施对应级次的分数傅里叶逆变换,只有当x,y方向的逆变换级次分别与原变换级次都相同或者满足周期条件时,才能恢复原图像。加密变换有效地提高了图像加密和防伪力度。数值计算验证了方法的正确性和可行性。     

块菌的傅里叶变换红外光谱研究

块菌是珍稀野生食用菌,其蛋白质和糖类含量较高,块菌多糖具有潜在的药用价值。文章利用傅里叶变换红外光谱技术(FTIR)对五种云南野生块菌作了研究。结果表明,块菌属真菌有其独特的光谱特征,全谱最强峰为出现在1 042和1 077 cm-1附近的强双峰。在脂分子的羰基峰1 742 cm-1及糖类异构体的指纹区1 200～750 cm-1,不同种类、不同产地块菌的光谱有明显差异,另外,正常块菌和霉变块菌的光谱亦有明显差异,主要体现在谱峰吸收强度的变化上,部分谱峰吸收强度比的变化表明,块菌样品变质前后,其蛋白质和糖类物质的含量发生了变化。FTIR光谱提供了块菌成分的有关化学信息,为鉴别块菌和区分块菌的种类、质量提供了简便快捷的手段。     

Band Theory in the Context of the Hamilton-Jacobi Formulation

In the one-dimensional periodic potential case, we formulate the condition of Bloch periodicity for the reduced action by using the relation between the wave function and the reduced action established in the context of the equivalence postulate of quantum mechanics. Then, without appealing to the wave function properties, we reproduce the well-known dispersion relations which predict the band structure for the energy spectrum in the Krönig-Penney model.