Universal fluctuations in the support of the random walk

A random walk starts from the origin of ad-dimensional lattice. The occupation numbern(x,t) equals unity if aftert steps site x has been visited by the walk, and zero otherwise. We study translationally invariant sumsM(t) of observables defined locally on the field of occupation numbers. Examples are the numberS(t) of visited sites, the areaE(t) of the (appropriately defined) surface of the set of visited sites, and, in dimension d=3, the Euler index of this surface. Ind≤ 3, theaverages - M(t) all increase linearly witht ast ® ∞. We show that in d=3, to leading order in an asymptotic expansion int, thedeviations from average ΔM(t) = M(t) -M(t) are, up to a normalization, allidentical to a single “universal” random variable. This result resembles an earlier one in dimensiond=2; we show that this universality breaks down ford>3.     

A least square finite element formulation of the collimated irradiation in frequency domain for optical tomography applications

This paper presents an extension of the least square finite element formulation associated to the discrete ordinates method to solve collimated irradiation problems in frequency domain. The features of the method are shown with a separation of the intensity into its collimated and scattered parts for a better handling of discontinuities due to the boundary conditions of Dirichlet type used in optical tomography applications. Numerical tests are used to gauge the accuracy of the model in both isotropic and anisotropic scattering media, with and without frequency modulation. The results show that the method is accurate compared to some reference solutions.     

Measurement of subpicosecond optical waveforms using a resonator-based phase modulator

We propose a method for the measurement of periodic optical waveforms based on the use of an electrooptic phase modulator placed in an optical Fabry-Perot or ring resonator. Significant broadening of the modulation spectrum extends the recently developed method of periodic modulation for pulse characterization into femtosecond scales. We numerically demonstrate the characterization of a 300-fs optical pulse. We also present a technique based on the temporal fractional Talbot effect for restoration of the pulse phase profile. After fast linear processing, subpicosecond pulses will be observed on the screen of a real-time oscilloscope. This complete characterization of optical pulses is entirely linear and therefore highly sensitive and simple in implementation.     

Supernova neutrino detection by terrestrial nuclear detectors

We present and discuss differential cross sections for the ^128,130Te isotopes, contents of the COBRA double beta decay detector. The response of these isotopes to energy spectra of supernova neutrinos is explored by convoluting the original results, calculated in the context of the quasi-particle random phase approximation (QRPA) using realistic two-body forces, with a two-parameter Fermi-Dirac (FD) and a Power-Law (PL) neutrino energy distributions.     

Exchange bias with Fe substitution in LaMnO<Subscript>3</Subscript>

We observe the negative shift of the magnetic hysteresis loop at 5 K, while the sample is cooled in external magnetic field in case of 30% of Fe substitution in LaMnO₃. The negative shift and training effect of the hysteresis loops indicate the phenomenon of exchange bias. The cooling field dependence of the negative shift increases with the cooling field below 7.0 kOe and then, decreases with further increase of cooling field. The temperature dependence of the negative shift of the hysteresis loops exhibits that the negative shift decreases sharply with increasing temperature and vanishes above 20 K. Temperature dependence of dc magnetization and ac susceptibility measurements show a sharp peak (T_p) at 51 K and a shoulder (T_f) around 20 K. The relaxation of magnetization shows the ferromagnetic and glassy magnetic components in the relaxation process, which is in consistent with the cluster-glass compound.     

Pinning of cracks in two-dimensional disordered media

We study the statistics of crack pinning in two dimensions by experiments and simulations of directed polymers in random media. Mode I tensile tests on paper samples show a delocalization phenomenon as the notch length is varied if the fraction of cracks pinned to the notch is monitored. This is compared with the behavior of directed polymers in the presence of both an energetically favorable localized pinning center and bulk disorder. An analysis of the crack interface roughness indicates self-affine behavior with a roughness exponent ζ in the proximity of the minimum energy surface value 2/3. Received 4 April 2000 and Received in final form 10 October 2000     

Analysis theory of random energy of train derailment in wind

Based on the analysis theory of random energy of train derailment, an analysis theory of random energy of train derailment in wind is suggested. Two methods are proposed -the time domain method and the frequency domain method of analysis theory of random energy of train derailment in wind. The curves of σ pw -v under various wind speeds are obtained through the computation. The original curve of σ p -v is expanded, which turns the analysis theory of random energy of train derailment into the all-weather theory. Train derailment condition has been established under wind action. The first and second criterions of train derailment have been proposed in light of wind action. The analysis of train derailment cases at home or abroad is made, in- cluding the first analysis of Xinjiang train derailment case encountered 13-level of gale, which explained the inevitability of train derailment. The analysis theory of random energy of train derailment in wind shows its validity and accuracy. The input energy σ pw of the transverse vibration of train-track(bridge)-wind system is linked to train speed. With the establishment of the analysis theory of random energy of train derailment in wind, It is likely to initiate an all-weather speed limit map for a train or any high-speed train.     

Enhanced Kerr Nonlinearities Caused by Cross Talk Between Optical and Microwave Transitions

We investigate the enhanced Kerr nonlinearities in four-level atomic vapors driven by a coupling, probe and microwave fields. Under the optical one-photon and two-photon resonant conditions, the linear and nonlinear responses of the weak probe field can be modified by the cross talk among optical and microwave transitions. The enhanced Kerr nonlinearity can form bright optical solitons of the probe field.     

DISTRIBUTION OF RANDOM ELEMENTS SUBJECTED TO A FLEXIBLE BOUNDARY CONDITION

The probability distribution function of n random elements subjected to the flexible boundary condition is derived. The probability density is a descending curve and converges to a delta function as n tends to infinity. The distribution of the minimum value is discussed in context of ordered statistics.     

B值随机元阵列加权和的收敛性与大数定律

令｛Ｘｎｉ，１≤ｉ≤ｋｎ↑∞，ｎ≥１｝为Ｂ值随机元阵列，｛ａｎｉ，１≤ｉ≤ｋｎ，ｎ≥１｝为实数阵列．讨论加权和Ｓｎ＝ｋｎｉ＝１ａｎｉＸｎｉ，ｎ≥１的收敛性．在条件ｓｕｐｎ，ｉＰ（Ｘｎｉ＞ｘ）＝０（ｘ－ｒ）下给出了一些收敛性结果（１≤ｒ＜ｐ≤２），同时用这种收敛性刻划了Ｂａｎａｃｈ空间的ｐ型性质