Experimental studies of the variation of the mean square displacement (MSD) of a particle in a confined colloid suspension that exhibits density variations on the scale length of the particle diameter are not in agreement with the prediction that the spatial variation in MSD should mimic the spatial variation in density. The predicted behavior is derived from the expectation that the MSD of a particle depends on the system density and the assumption that the force acting on a particle is a point function of position. The experimental data come from studies of the MSDs of particles in narrow ribbon channels and between narrowly spaced parallel plates, and from new data, reported herein, of the radial and azimuthal MSDs of a colloid particle in a dense colloid suspension confined to a small circular cavity. In each of these geometries a dense colloid suspension exhibits pronounced density oscillations with spacing of a particle diameter. We remove the discrepancy between prediction and experiment using the Fisher-Methfessel interpretation of how local equilibrium in an inhomogeneous system is maintained to argue that the force acting on a particle is delocalized over a volume with radius equal to a particle diameter. Our interpretation has relevance to the relationship between the scale of inhomogeneity and the utility of translation of the particle MSD into a position dependent diffusion coefficient, and to the use of a spatially dependent diffusion coefficient to describe mass transport in a heterogeneous system.
The thermal state of the intergalactic medium (IGM) contains vital information about the epoch of reionization, one of the most transformative yet poorly understood periods in the young universe. This thermal state is encoded in the small-scale structure of Lyman-α (Lyα) absorption in quasar spectra. The 1D flux power spectrum measures the average small-scale structure along quasar sightlines. At high redshifts, where the opacity is large, averaging mixes high signal-to-noise ratio transmission spikes with noisy absorption troughs. Wavelet amplitudes are an alternate statistic that maintains spatial information while quantifying fluctuations at the same spatial frequencies as the power spectrum, giving them the potential to more sensitively measure the small-scale structure. Previous Lyα forest studies using wavelet amplitude probability density functions (PDFs) used limited spatial frequencies and neglected strong correlations between PDF bins and across wavelets scales, resulting in sub-optimal and unreliable parameter inference. Here we present a novel method for performing statistical inference using wavelet amplitude PDFs that spans the full range of spatial frequencies probed by the power spectrum and that fully accounts for these correlations. We applied this procedure to realistic mock data drawn from a simple thermal model parameterized by the temperature at mean density, T0, and find that wavelets deliver 1σ constraints on T0 that are on average 7 per cent more sensitive at z = 5 (12 per cent at z = 6) than those from the power spectrum. We consider the possibility of combing wavelet PDFs with the power, but find that this does not lead to improved sensitivity.
Fluctuations in Lyman-α (Lyα) forest transmission towards high-z quasars are partially sourced from spatial fluctuations in the ultraviolet background (UVB), the level of which are set by the mean free path of ionizing photons (λmfp). The auto-correlation function of Lyα forest flux characterizes the strength and scale of transmission fluctuations and, as we show, is thus sensitive to λmfp. Recent measurements at z ∼ 6 suggest a rapid evolution of λmfp at z > 5.0 which would leave a signature in the evolution of the auto-correlation function. For this forecast, we model mock Lyα forest data with properties similar to the XQR-30 extended data set at 5.4 ≤ z ≤ 6.0. At each z we investigate 100 mock data sets and an ideal case where mock data matches model values of the auto-correlation function. For ideal data with λmfp = 9.0 cMpc at z = 6.0, we recover $\lambda _{\text{mfp}}=12^{+6}_{-3}$ cMpc. This precision is comparable to direct measurements of λmfp from the stacking of quasar spectra beyond the Lyman limit. Hypothetical high-resolution data leads to a $\sim 40{{\%}}$ reduction in the error bars over all z. The distribution of mock values of the auto-correlation function in this work is highly non-Gaussian for high-z, which should caution work with other statistics of the high-z Lyα forest against making this assumption. We use a rigorous statistical method to pass an inference test, however future work on non-Gaussian methods will enable higher precision measurements.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.