No abstract

[1] The evolution of the first five nonnegative integer-order spatial moments (corresponding to the mass, mean, variance, skewness, and kurtosis) are investigated systematically for spatiotemporal nonlocal, fractional dispersion. Three commonly used fractional-order transport equations, including the time fractional advection-dispersion equation (Time-FADE), the fractal mobile-immobile (MIM) equation, and the fully fractional advection-dispersion equation (FFADE), are considered. Analytical solutions verify our numerical results and reveal the anomalous evolution of the moments. Following Adams and Gelhar's (1992) work on the classical ADE, we find that a simultaneous analysis of all moments is critical in discriminating between different nonlocal models. The evolution of dispersion among the subdiffusive to superdiffusive rates is then further explored numerically by a non-Markovian random walk particletracking method that can be used for any heterogeneous boundary or initial value problem in three dimensions. Both the analytical and the numerical results also show the similarity (at the early time) and the difference (at the late time) of moment growth for solutes in different phases (mobile versus total) described by the MIM models. Further simulations of the 1-D bromide snapshots measured at the MADE experiments, using all three models with parameters fitted by the observed zeroth to fourth moments, indicate that (1) both the time and space nonlocality strongly affect the solute transport at the MADE site, (2) all five spatial moments should be considered in transport model selection and calibration because those up to the variance cannot effectively discriminate between nonlocal models, and (3) the log concentration should be used when evaluating the plume leading edge and the effects of space nonlocality.

The past two decades witnessed the development of a new type of solvent system, named deep eutectic solvents, which have become increasingly investigated because they offer new and potentially favorable properties, such as wide tunability in electrochemical, mechanical, and transport properties. Deep eutectic solvent (DES) systems are composed of at least one main solvent and an additional component that is meant to interrupt the original solvent/solvent interactions, thereby introducing lower melting points relative to each individual component. Ethaline (a 1:2 mol % mixture of choline chloride and ethylene glycol) is one of the most promising DES systems. However, it is also known to be very hygroscopic, which is a constant concern because water absorption during the use of ethaline alters its properties. Within this work, we demonstrate that modest amounts of water addition (1−10%) to ethaline are of little concern for practical use and can even lead to performance improvements, such as accelerated relaxation and solvation. In contrast, very small amounts of <1% of water lead to additional slowing of the solvent response. Thus, we suggest that the attempt to dry ethaline below 1% moisture is rather counterproductive if one attempts to achieve effective solvation and charge transport properties from DESs. This study investigates the effect of water content on the diffusional relaxation dynamics of ethaline. A set of independent spectroscopic experiments and computational simulations are aimed to provide insight into the solvent response of the DES system using femtosecond timeresolved absorption spectroscopy (fs-TA), broadband dielectric spectroscopy (BDS), nuclear magnetic resonance (NMR) diffusometry and broadband relaxometry, and molecular dynamics simulations (MDS) on ethaline with 0, 0.1, 1, 10, and 28.5 wt % added water. For dry ethaline, we identify choline chloride as the rate-limiting solvation component in ethaline. However, the role of the solvent components changes gradually as water is added. We provide quantitative solvent relaxation rates using the different presented time-resolved spectroscopic techniques and find remarkable agreement between them. Based on the solvent relaxation rates and combined with MDS, we develop a molecular understanding of the individual solvent components and their interactions in dry and wet ethaline with varying amounts of water content.

We present efficient and accurate numerical methods for computing the ground state and dynamics of the nonlinear Schrödinger equation (NLSE) with nonlocal interactions based on a fast and accurate evaluation of the long-range interactions via the nonuniform fast Fourier transform (NUFFT). We begin with a review of the fast and accurate NUFFT based method in [28] for nonlocal interactions where the singularity of the Fourier symbol of the interaction kernel at the origin can be canceled by switching to spherical or polar coordinates. We then extend the method to compute other nonlocal interactions whose Fourier symbols have stronger singularity at the origin that cannot be canceled by the coordinate transform. Many of these interactions do not decay at infinity in the physical space, which adds another layer of complexity since it is more difficult to impose the correct artificial boundary conditions for the truncated bounded computational domain. The performance of our method against other existing methods is illustrated numerically, with particular attention on the effect of the size of the computational domain in the physical space. Finally, to study the ground state and dynamics of the NLSE, we propose efficient and accurate numerical methods by combining the NUFFT method for potential evaluation with the normalized gradient flow using backward Euler Fourier pseudospectral discretization and time-splitting Fourier pseudospectral method, respectively. Extensive numerical comparisons are carried out between these methods and other existing methods for computing the ground state and dynamics of the NLSE with various nonlocal interactions. Numerical results show that our scheme performs much better than those existing methods in terms of both accuracy and efficiency.