Calculation of the vibrational linewidth and line shape of Raman spectra using the relaxation function : II. application to the mixture neon-nitrogen with inhomogeneous broadening due to concentration fluctuations

The Raman spectra of nitrogen in the mixture neon-nitrogen have been measured for neon mole fractions, ¿M, of 0.10, 0.65, and 0.95 at 296 K and 408 K up to the solidification pressure. It was found that the frequency increases as a function of ¿M. The linewidth is strongly composition dependent, with a very large value for ¿M=0.65. Further, it is shown that the width decreases as a function of temperature. Molecular dynamics simulations have been performed in order to calculate the linewidth and shape, using the relaxation function. The simulations are in good agreement with experiment. It is shown that the increase in linewidth in the intermediate concentration range is due to an increase of the correlation time, rather than an increase of the amplitude of modulation. In this range inhomogeneous broadening due to concentration fluctuations occur: the vibrational line shape starts to deviate from a Lorentzian curve, and gets a Gaussian component. The simulations also provide insight into the relatively large decrease of the width as a function of temperature in the intermediate concentration range. When the temperature is increased from 296 to 408 K, the amplitude of modulation increases, but the correlation time decreases more. © 2000 American Institute of Physics

Exact and Efficient Sampling of Conditioned Walks

A computationally challenging and open problem is how to efficiently generate equilibrated samples of conditioned walks. We present here a general stochastic approach that allows one to produce these samples with their correct statistical weight and without rejections. The method is illustrated for a jump process conditioned to evolve within a cylindrical channel and forced to reach one of its ends. We obtain analytically the exact probability density function of the jumps and offer a direct method for gathering equilibrated samples of a random walk conditioned to stay in a channel with suitable boundary conditions. Unbiased walks of arbitrary length can thus be generated with linear computational complexity\ue2\u80\u94even when the channel width is much smaller than the typical bond length of the unconditioned walk. By profiling the metric properties of the generated walks for various bond lengths we characterize the crossover between weak and strong confinement regimes with great detail