Stochastic impact in Fitzhugh–Nagumo neural system with time delays driven by colored noises

In this paper, stochastic behavior of FitzHugh–Nagumo neural system with two different kinds of time delays driven by colored noises is investigated. Based on the extended unified colored noise theory and the method of the probability density approximation, the Fokker–Planck equation and the steady-state probability density function are derived. Then through the two-state theory, the analytical expression of the signal-to-noise ratio (SNR) is also obtained. Finally, the effects of time delays and noise auto-correlation times in nonlinear dynamical system on the stationary probability density and the SNR are discussed respectively.     

DKP equation under a vector Yukawa-type potential

Approximate analytical solutions of the Duffin-Kemmer-Petiau equation are obtained for a vector Yukawa potential. The solutions are reported for any J state. The results are obtained based on an exponential approximation as well as the NU analytical technique. Energy solutions are numerically discussed for various quantum numbers and different η, α.     

In Support of n-Correlation

In this paper we examine n-correlation for either the eigenvalues of a unitary group of random matrices or for the zeros of a unitary family of L-functions in the important situation when the correlations are detected via test functions whose Fourier transforms have limited support. This problem first came to light in the work of Rudnick and Sarnak in their study of the n-correlation of zeros of a fairly general automorphic L-function. They solved the simplest instance of this problem when the total support was most severely limited, but had to work extremely hard to show their result matched random matrix theory in the appropriate limit. This is because they were comparing their result to the familiar determinantal expressions for n-correlation that arise naturally in random matrix theory. In this paper we deal with arbitrary support and show that there is another expression for the n-correlation of eigenvalues that translates easily into the number theory case and allows for immediate identification of which terms survive the restrictions placed on the support of the test function.     

Surface morphology characterization of pentacene thin film and its substrate with under-layers by power spectral density using fast Fourier transform algorithms

Surface morphology of pentacene thin films and their substrates with under-layers is characterized by using atomic force microscopy (AFM). The power values of power spectral density (PSD) for the AFM digital data were determined by the fast Fourier transform (FFT) algorithms instead of the root-mean-square (rms) and peak-to-valley value. The PSD plots of pentacene films on glass substrate are successfully approximated by the k-correlation model. The pentacene film growth is interpreted the intermediation of the bulk and surface diffusion by parameter C of k-correlation model. The PSD plots of pentacene film on Au under-layer is approximated by using the linear continuum model (LCM) instead of the combination model of the k-correlation model and Gaussian function. The PSD plots of SiO₂ layer on Au under-layer as a gate insulator on a gate electrode of organic thin film transistors (OTFTs) have three power values of PSD. It is interpreted that the specific three PSD power values are caused by the planarization of the smooth SiO₂ layer to rough Au under-layer.     

Entanglement Capacity of Two-Qubit Unitary Operator with the Help of Auxiliary System

The＇entanglement capacity of general two-qubit unitary operators is studied when auxiliary systems are allowed, and the analytical results based on linear entropy when input states are disentangled are given. From the results the condition for perfect entangler, α1 = α2 = π/4, is obtained. Contrary to the case without auxiliary system, the parameter α3 may play active role to the entanglement capacity when auxiliary systems are allowed.     

Time-dependent xx-correlation functions in the one-dimensional XY-model

The structure of the time-dependent xx-correlation functions of the one-dimensional XY-model is investigated in some detail on the basis of an extension of the thermodynamic Wick theorem. The results amount to a generalization of a rigorous result for the autocorrelation function of the x-component of the magnetization obtained in a previous paper.     

Proton pick-up from Mo

The reaction ⁹²Mo(t, α)⁹¹Nb has been carried out at a triton bombarding energy of 12 MeV. Angular distributions of the emitted α-particles were obtained and compared with DWBA predictions. Relative spectroscopic factors were obtained for six low-lying states and are discussed with reference to shell-model calculations.     

Simulation of α-Zr structural stability under pressure using the molecular dynamics method

The structural stability of α-Zr was studied using the molecular dynamics method in wide temperature and pressure ranges. The interatomic interaction was described by a pair potential calculated within the Animalu pseudopotential model. The potential parameters were selected using α-Zr phonon spectra. The features in the dynamics of the α-β and α-ω phase transitions at various temperatures and pressures were considered. The calculated hysteresis of forward and backward phase transitions and its pressure and temperature dependences are discussed. The data obtained were used to plot phase equilibrium lines in the P-T phase diagram.     

α-石英晶体中旋光性对Raman散射的影响

讨论了旋光性对Raman散射的影响。在α-石英晶体中获得了消除旋光影响的纯Raman谱,在此基础上,讨论了α-石英晶体(单轴晶体)的Raman谱中,x轴和y轴的非等价性问题,以及与这种非等价性相应的振动模的对称性。 关键词：     

Magnetically induced phase separation in the Co–Cr binary system

Direct evidence of phase separation in the Co-rich corner of the Co–Cr binary system, the transformation of high-temperature FCC α-Co into a ferromagnetic α_f phase and a paramagnetic α_p phase, has been experimentally obtained by using diffusion couple technique, scanning electron microscopy with energy dispersion analysis of X-ray (SEM-EDX), analytical transmission electron microscopy, optical microscopy and X-ray diffraction. Thermodynamic calculation, on the basis of the presently obtained phase equilibrium data, has verified that this phase separation arises from magnetic ordering, and that a similar phase separation appears in the HCP phase below 469°C which is transformed into a ferromagnetic ε_f phase and a paramagnetic ε_p phase. It is therefore concluded that magnetically induced phase separation must be responsible for the microscopic composition modulation of Cr in the CoCr thin film magnetic recording media.     

Waveform Measurement of Ultra-Short Optical Pulses Based on Two-Photon Absorption in Si-Image Sensor

We demonstrate a novel waveform mesurement system of ultra-short optical pulses based on the two-photon absorption process in a Si-image sensor. Using an interferometer with a tilt mirror in the reference path, the relative time difference between the signal and reference pulses is spatially distributed on the Si-image sensor, so the intensity auto-correlation is monitored as an image at a time without using moving parts. This system can create or remove an interference fringe pattern overlapped on the auto-correlation image by controlling the polarization states of the laser pulse, which is useful for measuring the crossing angle between the signal and reference beams as well as avoiding contamination of the interference fringe into the auto-correlation image. We successfully measured optical pulses less than 100 fs from a fiber ring laser with a temporal resolution of 0.4 fs. The obtained waveform agreed well with that observed with a conventional second harmonic generation (SHG) based auto-correlator.     

Fundamental weak interaction studies using polarised nuclei and ion traps

Two experiments to search for new physics beyond the standard model for electroweak interactions by measuring correlations between different spin and momentum vectors in nuclear β-decay are discussed. In the first experiment the correlation between the emission asymmetry and the longitudinal polarisation of positrons emitted by polarised nuclei is determined. This type of measurement is sensitive to the presence of right-handed currents but also to possible scalar and tensor-type currents in the weak interaction. The aim of the second experiment is to determine the βν-correlation in β-decay by measuring the energy spectrum of the recoil ions, using a Penning trap and a retardation spectrometer. In this case the focus is on the search for scalar currents in the weak interaction. The results of the experiments presented here are complementary to results from experiments in muon decay and at high-energy colliders. This revised version was published online in July 2006 with corrections to the Cover Date.     

Spin splitting of the density of electronic states of thin superconductors in magnetic field

The spin splitting of the density of states of a thin superconducting film in a parallel magnetic field was investigated. The analytical expression for the density of states in the limit case of impurity parameters of theory β ～ α² ? 1 is obtained for different energetical intervals. The expression for the energy gap ω_g is also given.     

Characterisation of soil-oxide analogs by applied-field 57Fe Mössbauer spectroscopy

In this contribution, the effect of high external magnetic fields upon the Mössbauer spectra of aluminous α- and γ-Fe₂O₃, of aluminous α- and γ-FeOOH and of aluminous Fe₃O₄ is reviewed. It is shown that the shapes of these spectra are characteristic of these materials and also to some extent of their crystallinities and Al-for-Fe substitutions. Based upon this evaluation, the potential for application of external-field Mössbauer spectroscopy to soil-related analytical purposes is demonstrated for two soil samples. Limitations of the technique are discussed. Finally, some suggestions for further research in this field are indicated.     

Isotropic Raman spectra of liquid (isotope) mixtures: Intermolecular coupling of vibrational modes

The theory presented in this paper investigates the isotropic Raman spectra of liquid binary mixtures. It is found that the collective vibrational modes of different molecular species can be significantly coupled. This is a consequence of the (nearly) resonant vibrational transfer processes, which give rise to distinct vibrational correlations (i.e. correlations between adjacent molecules). The coupling, however, occurs only with weakly-separated or overlapping bands. The more general results of the theory are applied to isotope mixtures. The spectral information available from relevant dilution experiments is interpreted. In particular it is shown that the spectral properties of the vibrational self-correlation part can be concluded from the observed collective correlation function. The significance of the distinct vibrational correlations with respect to the infrared and depolarized Raman spectra is discussed.     

纳米晶FeCuNbMSiB（M＝Nb，V，Mo）合金的微结构及其电阻率与压力的关系

 X射线衍射和透射电镜的结果表明：非晶FeCuNbMSiB（M＝Nb，V，Mo）合金在540 ℃退火20 min，表面析出的纳米晶是α-FeSi固溶体，粒度为10~20 nm。此外，在0.000 1~2.4 GPa范围内测量了它们的常压室温电阻率以及电阻率随静水压的变化，得到了电阻率与压力的线性关系式。最后探讨了热处理方式和温度对非晶Fe_73.1Cu_1.2Nb_3.2Si_12.5B₁₀合金退火形成纳米晶的影响。     

球形α-Fe2O3超微粒的红外光学特性和表面模吸收

用改进的水解法制备了大小均匀、形状规则的球状α-Fe₂O₃超微粒;分别测量了两种不同粒度超微粒的红外透射谱;观测到了球状α-Fe₂O₃超微粒的全部表面模;讨论了微粒的聚集对吸收的影响;并用柱状微晶来近似链状聚集解释了光谱中的两个展宽吸收带;介绍了将多原子立方结构超微粒的表面模理论推广应用到单轴晶体结构的α-Fe₂O₃超微粒的情况。对表面模吸收频率进行了计算,理论数据同实验结果 关键词：     

Comparison of nuclear Bragg scattering with Mössbauer spectroscopy for the measurement of hyperfine interactions

Fourier analysis of the time evolution of the nuclear Bragg scattering from the (7, 7, 7) reflection in α-hematite (⁵⁷Fe) excited by synchrotron radiation was used to extract values of Zeeman splitting of the ground and 14.413-keV states of⁵⁷Fe in the crystal magnetic field. The results so obtained apparently do not agree with the corresponding values obtained from Mössbauer spectroscopy on α-hematite. Possible reasons for the discrepancy are discussed.     

Generalized analytical solutions for certain coupled simple chaotic systems

We present a generalized analytical solution to the normalized state equations of a class of coupled simple secondorder non-autonomous circuit systems. The analytical solutions thus obtained are used to study the synchronization dynamics of two different types of circuit systems, differing only by their constituting nonlinear element. The synchronization dynamics of the coupled systems is studied through two-parameter bifurcation diagrams, phase portraits, and time-series plots obtained from the explicit analytical solutions. Experimental figures are presented to substantiate the analytical results. The generalization of the analytical solution for other types of coupled simple chaotic systems is discussed. The synchronization dynamics of the coupled chaotic systems studied through two-parameter bifurcation diagrams obtained from the explicit analytical solutions is reported for the first time.     

一类广义N维非线性Schr?dinger方程的孤子解及其性质研究

研究一类N维广义非线性Schr?dinger方程的孤子解及其性质，研究非线性参数α变化（α→0及α→∞）时孤子性态的变化规律，同时研究该问题的数值解法，得到了该方程的P-R差分格式的收敛性和稳定性条件． 关键词：