长环等离子体平衡位形的稳定性研究

1981年V.M.Glagolev等人首次提出一种含有直线段的长环等离子体平衡位形(Drakon)的新概念,这种长环等离子体平衡位形包括两个长的较小磁场的直线段和两端由较强磁场的曲线平衡段连接。在每一个曲线平衡段,Pfirsch-Schlüter电流由于曲线平衡段轴曲率矢量的方向改变而补偿,因此Pfirsch-Schlüter电流是闭合的,不流进直线段,     

单模光纤中偏振模色散的仿真模型

利用琼斯矩阵法研究了长单模光纤中偏振模色散的仿真模型.考虑到偏振模色散的随机性,该模型中单模光纤被看作是一系列短双折射光纤段的级联,相邻两段之间耦合角是随机的.研究结果表明,当短双折射光纤段等长时,偏振模色散呈现随波长周期性变化的特点;不符合实际情况.当短双折射光纤段不等长且服从高斯分布时,周期性逐渐消失;当其长度均方差为均值的20%,周期性完全消失.最后比较了偏振模色散的时域统计特性.取短双折射光纤段的长度服从高斯分布且均方差为均值的20%,偏振模色散的统计特性接近于实际分布.因此得出结论:为了正确估计偏振模色散的影响,在单模光纤的级联模型中,短双折射光纤段的长度应服从高斯分布,均方差为其均值的20%.     

Helix-coil transformation and titration curve of poly-L-glutamic acid

The titration curve of poly-L-glutamic acid was studied in connection with the helix-coil transformation.

In aqueous solution the transformation has its origin in the ionization of the polar group COOH in the side chain. Conversely the ionization and the titration curve of this molecule are affected by the change of the electrostatic interaction produced by its transformation.

It is shown in this report that the experimental result, the titration curve and its modified plot, can be divided into three sections, that is, the ionization of the perfect helix, the region of the helix-coil transformation, and the ionization of the perfect coil.     

The formation of a dislocation spiral on the (101) face of a monoclinic lysozyme crystal: High-resolution experiments

The elementary processes of crystal growth in the case of a low kink density on step edges have been studied by in situ atomic force microscopy. High-resolution images of the first turn of the polygonal dislocation spiral on the (101) face of monoclinic lysozyme crystals, which allow one to discern separate crystal cells, have been obtained. It has been shown that the dependence of the spiral segment velocity on its length is inconsistent with the Gibbs-Thomson law and is represented by several rectilinear sections. The results were explained by taking into account the features of the growth of crystals with a low kink density at low supersaturation.     

Non-Gaussian statistical models for scattering calculations

In calculating the properties of waves scattered by random media it is almost always assumed that variations of the media constitute a joint Gaussian process. In this paper two alternative models are investigated. It is shown that whilst some features of the statistics of the scattered waves are more sensitive to the spectrum of the fluctuations in the medium than to the basic statistical model, in general significantly different properties are predicted using the alternative models.     

Transformation of the probability density function in an optical parametric amplifier: Application to rogue-wave-like statistics

We study how the probability density function of a weak seed intensity is transformed in a nonlinear process such as optical parametric amplification. The character of the transformation strongly depends on the amplification regime accessed: in the small-gain (undepleted-pump) regime the statistics of the seed are transferred to the statistics of the amplified signal almost unaltered. In contrast, in the gain saturation regime the modification of the statistics is considerable. In particular, we demonstrate that rogue-wave-like (long-tailed) statistics of the seed are completely suppressed, and resulting probability distribution function of the amplified signal becomes Gaussian. The theoretical findings are supported by the experiments carried out in supercontinuum-seeded noncollinear optical parametric amplifier.     

Non-Gaussian statistical models for scattering calculations

Abstract

In calculating the properties of waves scattered by random media it is almost always assumed that variations of the media constitute a joint Gaussian process. In this paper two alternative models are investigated. It is shown that whilst some features of the statistics of the scattered waves are more sensitive to the spectrum of the fluctuations in the medium than to the basic statistical model, in general significantly different properties are predicted using the alternative models.     

Statistical properties of partially coherent cw fiber lasers

We perform a detailed quantitative numerical analysis of a partially coherent quasi-cw fiber laser on the example of a high-Q normal dispersion cavity Raman fiber laser. The key role of precise spectral performances of fiber Bragg gratings forming the laser cavity is clarified. It is shown that cross-phase modulation between the pump and Stokes waves does not affect the generation. Amplitudes of different longitudinal modes strongly fluctuate, obeying the Gaussian distribution. As the intensity statistics is noticeably nonexponential, longitudinal modes should be correlated.     

Factorial moments analyses show a characteristic length scale in DNA sequences

A unique feature of most of the DNA sequences, found through the factorial moments analysis, is the existence of a characteristic length scale around which the density distribution is nearly Poissonian. Above this point, the DNA sequences, irrespective of their intron contents, show long range correlations with a significant deviation from the Gaussian statistics, while, below this point, the DNA statistics are essentially Gaussian. The famous DNA walk representation is also shown to be a special case of the present analysis.     

Lens axicon illuminated by polychromatic Gaussian beams for generating uniform focal segments

In this paper, we investigate a lens axicon, which actually is a lens with spherical aberration, illuminated by a polychromatic Gaussian beam for producing an extended axial line image of a desired length and nearly uniform intensity. A numerical calculation is performed to investigate the dependence of the axial intensity distribution of the focal segment on the parameters of the incident polychromatic Gaussian beam. It is shown that, compared with monochromatic Gaussian beam illumination, the illumination of the polychromatic Gaussian beam may improve the uniformity of the distribution of the axial intensity, and this improvement in the uniformity of the axis intensity is strongly dependent on the spectral width of the incident Gaussian beam. Moreover, apodization with annular super-Gaussian amplitude distribution is employed to reduce the undesired oscillation of the axial intensity.     

Mesoscopic phase statistics of diffuse ultrasound in dynamic matter

Temporal fluctuations in the phase of waves transmitted through a dynamic, strongly scattering, mesoscopic sample are investigated using ultrasonic waves, and compared with theoretical predictions based on circular Gaussian statistics. The fundamental role of phase in diffusing acoustic wave spectroscopy is revealed, and phase statistics are also shown to provide a sensitive and accurate way to probe scatterer motions at both short and long time scales.     

On the motion of the centers of inertia of light beams and pulses

It is shown that the velocity of the centers of inertia of localized structures of an electromagnetic field in vacuum does not exceed the speed of light in vacuum. The relation of this constraint with the properties of so-called X waves is discussed. For linear homogeneous anisotropic (dichroic) media, the transverse motion of the centers of Gaussian beams of monochromatic radiation is analyzed. It is found that, in the general case, the beam center moves along a hyperbola (curvilinearly), and, if the field envelope distribution is axisymmetric, this motion is rectilinear.     

Elasticity-driven spontaneous curvature of a 2D comb-like polymer with repulsive interactions in the side chains

We have shown that the rectilinear conformation of a 2D comb-like polymer with symmetrical left-right distribution of the side chains relative to the backbone is thermodynamically unstable. The minimum of the free energy of the comb molecule per unit of its length is attained at asymmetrical distribution of the side chains accompanied by the bending of the backbone. The curved conformation is characterized by a lower elastic energy of the side chains.Received: 11 August 2003, Published online: 4 November 2003PACS: 82.35.Jk Copolymers, phase transitions, structure - 89.75.Fb Structures and organization in complex systems     

Scarring and the Statistics of Tunnelling

We show that the statistics of tunnelling can be dramatically affected by scarring and derive distributions quantifying this effect. Strong deviations from the prediction of random matrix theory can be explained quantitatively by modifying the Gaussian distribution which describes wavefunction statistics. The modified distribution depends on classical parameters which are determined completely by linearised dynamics around a periodic orbit. This distribution generalises the scarring theory of L. Kaplan (1998, Phys. Rev. Lett.80, 2582) to describe the statistics of the components of the wavefunction in a complete basis, rather than the overlaps with single Gaussian wavepackets. In particular it is shown that correlations in the components of the wavefunction are present, which can strongly influence tunnelling-rate statistics. The resulting distribution for tunnelling rates is tested successfully on a two-dimensional double-well potential.     

Variational theory for a single polyelectrolyte chain

Variational methods are applied to a single polyelectrolyte chain. The polymer is modeled as a Gaussian chain with screened electrostatic repulsion between all monomers. As a variational Hamiltonian, the most general Gaussian kernel, including the possibility of a classical or mean polymer path, is employed. The resulting self-consistent equations are systematically solved both for large and small monomer-monomer separations along the chain. In the absence of screening, the polymer is stretched on average. It is described by a straight classical path with Gaussian fluctuations around it. If the electrostatic repulsion is screened, the polymer is isotropically swollen for large separations, and for small separations the polymer correlation function is calculated as an analytic expansion in terms of the monomer-monomer separation along the chain. The electrostatic persistence length and the electrostatic blobsize are inferred from the crossover between distinct scaling ranges. We perform a global analysis of the scaling behavior as a function of the screening length and electrostatic interaction strength , where is the Bjerrum length and A is the distance of charges along the polymer chain. We find three different scaling regimes. i) A Gaussian-persistent regime with Gaussian behavior at small, persistent behavior at intermediate, and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and only for intermediate values of the screening length. The electrostatic persistence length is defined as the crossover length between the persistent and the asymptotically swollen behavior and is given by and thus disagrees with previous (restricted) variational treatments which predict a linear dependence on the screening length .ii) A Gaussian regime with Gaussian behavior at small and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and/or strong screening, and the electrostatic repulsion between monomers only leads to subfluent corrections to Gaussian scaling at small separations. The concept of a persistence length is without meaning in this regime. iii) A persistent regime , where the chain resembles a stretched rod on intermediate and small scales. Here the persistence length is given by the original Odijk prediction, , if the overstretching of the chain is avoided. We also investigate the effects of a finite polymer length and of an additional excluded-volume interaction, which modify the resultant scaling behavior. Applications to experiments and computer simulations are discussed. Received 24 December 1997     

Spontaneous bending of 2D molecular bottle-brush

Using a scaling approach we consider a 2D comb copolymer brush under bending deformations. We show that the rectilinear brush is locally stable and can be characterized by a persistence length λ increasing with the molecular weight of grafting side chains as λ ∼ M³. A bending instability due to redistribution of the side chains appears in the non-linear regime where bending is strong. Arguments are presented that the brush conformations consist of alternating rectilinear and bent sections corresponding to the different free-energy minima.     

Amplitude Statistics of Sea-Ice Clutter Using a Millimeter Wave Radar

Sea-ice clutter was measured using a millimeter wave radar with frequency of 34.86GHz and pulse length of 30ns. To determine the sea-ice clutter amplitude statistics, we investigated the log-normal, Weibull, log-Weibull and K-distributions using the Akaike Information Criterion (AIC), which is more rigorous fit of the distribution to the data than the least-squares method. It is shown that the amplitude of sea-ice clutter obeys almost a log-Weibull distribution.     

Propagation properties of ultrashort chirped pulsed Gaussian beams in the free space

Based on the Rayleigh diffraction integral and complex analytical signal representation, the free-space analytical propagation equation and its Fourier spectrum for ultrashort chirped pulsed Gaussian beams with constant diffraction length are derived. The effect of chirp parameter on the spatiotemporal and spectral properties is illustrated with analytical formulas and numerical calculation results. It is shown that the axial spectra of ultrashort chirped pulsed Gaussian beams become broadened with increasing chirp parameter. For single optical cycle, the transversal intensity distribution is affected by increasing chirp parameter, but almost not affected for several optical cycles. Moreover, the positive or negative sign of the chirp parameter has no effect on the spectral distribution and intensity distribution.     

A non-Gaussian model in polymeric network

We investigate a finite chain approximation, the non-Gaussian Tsallis distribution, to the polymeric network, which gives an improvement to the Gaussian model. This distribution presents some necessary characteristics, like a cutoff to the maximum chain length and a continuous limit to the Gaussian one for a large number of monomers. It also presents a simple quadratic structure that allows to generalize the Gaussian properties such as exact-moments calculation and Wick theorem. We obtain the free-energy density in its full tensorial structure.