Self-collimation in photonic crystals with anisotropic constituents

In a photonic crystal composed of anisotropic constituents we quantify the range of input angles and the degree of collimation of the beam inside the crystal. The optical properties of a photobleached 4-dimethylamino-N-methyl-4-stilbazolium-tosylate (DAST) crystal are used in our model to demonstrate the efficacy of the self-collimation features.     

Graph problems arising from parameter identification of discrete dynamical systems

This paper focuses on combinatorial feasibility and optimization problems that arise in the context of parameter identification of discrete dynamical systems. Given a candidate parametric model for a physical system and a set of experimental observations, the objective of parameter identification is to provide estimates of the parameter values for which the model can reproduce the experiments. To this end, we define a finite graph corresponding to the model, to each arc of which a set of parameters is associated. Paths in this graph are regarded as feasible only if the sets of parameters corresponding to the arcs of the path have nonempty intersection. We study feasibility and optimization problems on such feasible paths, focusing on computational complexity. We show that, under certain restrictions on the sets of parameters, some of the problems become tractable, whereas others are NP-hard. In a similar vein, we define and study some graph problems for experimental design, whose goal is to support the scientist in optimally designing new experiments.     

防护板尺寸对Whipple防护结构撞击损伤影响的实验研究

通过高速撞击实验,探讨了采用小尺寸防护板的可行性。实验中采用的Whipple结构由尺寸变化的1 mm厚防护板（前板）和尺寸固定的3 mm厚舱壁板（后板）组成,防护板与舱壁板间隔10 cm。防护板为边长分别为8、12、16和20 cm的方形2A12铝合金板,舱壁板为边长为20 cm的方形5A06铝合金板。实验过程中均采用直径为4 mm的铝合金球形弹丸,撞击速度为1.45~1.71 km/s。实验结果表明:Whipple防护结构在舱壁板被击穿的概率大于0.8的条件下和击穿概率为0的条件下的极限速度以及舱壁板临界击穿条件下的速度都与防护板尺寸无关;并且,防护板前后表面击穿孔的直径及击穿孔侧壁的倾斜角也与防护板尺寸无关;但是,在速度相同的条件下随着板尺寸的增大,防护板板面的最大挠度增大,而且,防护板挠曲面的凸凹方向也由单一的凹向变成凸凹方向交替出现;随着速度的增加和板尺寸的增大,防护板最大挠度的增量减小。     

Ultrashort-pulse fiber ring lasers

Received: 18 February 1997/Revised version: 22 April 1997     

Statistical dynamics of conserved densities for the hard-sphere Lorentz gas

The statistical dynamics of a particle scattered by randomly positioned stationary hard spheres are investigated. We examine the somewhat unusual long-wavelength, low-frequency fluctuation spectra resulting from the existence of an infinite set of mutually coupled conserved densities of which the number density and energy density are two members. The analytically soluble infinite-mode correlation functions are compared with the corresponding functions obtained by truncating the set of slow modes at successively increasing orders. Furthermore, we evaluate the long-wavelenght number density autocorrelation function for a fixed speed, υ₀, in terms of a frequency-dependent diffusivity D(ω;υ₀) and obtain the fluctuation spectra of all conserved densities by an additional velocity average with the appropriate canonical weights. The effect of the frequency-dependent diffusivity D(ω;υ₀) on the density fluctuation spectra at frequencies small compared to the mean collision frequency is elucidated.     

Controllability of quasi-linear Hamiltonian NLS equations

We prove internal controllability in arbitrary time, for small data, for quasi-linear Hamiltonian NLS equations on the circle. We use a procedure of reduction to constant coefficients up to order zero and HUM method to prove the controllability of the linearized problem. Then we apply a Nash–Moser–Hörmander implicit function theorem as a black box.     

A polynomial time approximation algorithm for the two-commodity splittable flow problem

We consider a generalization of the unsplittable maximum two-commodity flow problem on undirected graphs where each commodity ${i \in \{1, 2\}}$ can be split into a bounded number k _i of equally-sized chunks that can be routed on different paths. We show that in contrast to the single-commodity case this problem is NP-hard, and hard to approximate to within a factor of α > 1/2. We present a polynomial time 1/2-approximation algorithm for the case of uniform chunk size over both commodities and show that for even k _i and a mild cut condition it can be modified to yield an exact method. The uniform case can be used to derive a 1/4-approximation for the maximum concurrent (k ₁, k ₂)-splittable flow without chunk size restrictions for fixed demand ratios.     

The lowest electronic states of Ne2 +, Ar2 + and Kr2 +: comparison of theory and experiment

Non-relativistic configuration interaction (CI) ab initio calculations using large basis sets have been carried out to determine the potential curves of the first electronic states of Ne₂ ⁺, Ar₂ ⁺ and Kr₂ ⁺. The spin—orbit interaction was treated assuming that the spin—orbit coupling constant is independent of the internuclear separation (R). For Ar₂ ⁺, calculated dissociation energies and equilibrium separations are in good agreement with experimental results. The calculations for Ne₂ ⁺ suggest that the lowest vibrational level of the I(1/2u) ground state observed by threshold photoelectron spectroscopy by Hall et al. [1995, J. Phys. B: At. molec. opt. Phys., 28, 2435] and assigned to either ν = 0 or ν = 2 actually corresponds to ν = 4. The calculations also predict the I(1/2g) state of Ne₂ ⁺ and Ar₂ ⁺ to possess a double-well potential and that of Kr₂ ⁺ to be repulsive at short range and to only possess a single shallow well at large internuclear separation. The ab initio calculations provide an explanation for the observation made by Yoshii et al. [2002, J. chem. Phys., 117, 1517] that Kr₂ ⁺ and Xe₂ ⁺ dissociate after photoemission from the II(1/2u) state to the I(1/2g) state whereas Ar₂ ⁺ does not.     

Asynchronous phase-modulated optical fiber-ring buffer

We investigate the dynamics of a 5-Gbit/s packet of ones and zeros loaded into a 0.5-kbit, phase-modulated optical fiber-ring buffer. A new mode of operation is explored in which the cavity length of the buffer is slightly detuned from the frequency driving the phase modulator. We examine the conditions for successful packet loading and the packet storage behavior. In addition, relaxation oscillations, which affected the storage time of previous high-speed optical ring buffers, are nearly eliminated with a cw holding beam, and significantly enhanced storage times are obtained.     

Quantification of the pore size distribution (porosity profiles) in microfiltration membranes by SEM,TEM and computer image analysis

Transport properties of membranes are closely related to morphological properties like surface porosity and variation of their inner pore structure. Scanning electron microscopy (SEM) as well as transmission electron microscopy (TEM) are powerful tools to characterise the microscopical pore structure of membranes in a qualitative manner. In order to provide more quantitative data of surface and cross-sectional pores computer image analysis can be used. Parameters like ‘porous area fraction’ and ‘mean free path length’ have been selected to describe the pore distribution within porosity profiles in order to consider the effect that the pores within the cross-section are connected to each other.