Nuclear induction lineshape: Non-Markovian diffusion with boundaries

The dynamics of viscoelastic fluids are governed by a memory function, which is critical yet computationally intensive to determine, particularly when diffusion is restricted by boundaries. We introduce a computational method that effectively captures the memory effects by analyzing the time-correlation function of the pressure tensor, an indicator of viscosity, through the analytic continuation of the Stokes-Einstein equation to the Laplace domain. This equation is integrated with molecular dynamics (MD) simulations to obtain necessary parameters. Our method computes NMR lineshapes by employing a generalized diffusion coefficient that incorporates the influences of temperature and confinement geometry. This approach establishes a direct link between the memory function and thermal transport parameters, enabling precise computation of NMR signals for non-Markovian fluids in confined geometries.

, MD simulations were conducted to calculate the shear viscosity of gaseous xenon (Xe), as defined by Eq. (7). We utilized the Lennard-Jones (LJ) pair potential, expressed as U(r) = 4ϵ[(σ/r)12 − (σ/r)6], where interactions between xenon atoms were characterized by ϵ = 1.77 kJ/mol, the depth of the potential well, and σ = 4.1 Å, the distance at which the potential energy becomes zero. Our simulations of bulk fluid were conducted for isotropic diffusion by placing 2000 xenon atoms within a box defined by periodic boundary conditions. Throughout the simulations, we maintained a consistent particle count, volume, and temperature, adhering to the canonical ensemble (NVT ensemble). Each set of simulations was repeated for ten different random seeds for the initial positions and velocities of the particles to ensure robust statistical sampling and accuracy of the results. In the simulations of restricted diffusion (i.e., diffusion limited by the nanotube geometry), nanotubes of a fixed length an..., , # Nuclear Induction Lineshape: Non-Markovian Diffusion with Boundaries

The simulation was executed on the Hoffman2 cluster at UCLA. The \"submit_job.sh\" script was used for running a batch of simulations.
A sample of LAMMPS code for viscosity evaluation can be found in each folder, \"in.visc_Bulk\" and \"in.visc_SiO2\" for bulk and restricted simulations, respectively.
For data analysis in Jupyter Lab, we provide a Python code in the \"Viscosity Analysis.ipynb\" notebook.

### Description of the data and file structure

The various folders are marked to indicate different boundary conditions. The \"Xegas.zip\" folder contains the dataset for simulating Xe gas particles in bulk. Folders named A11-A75 hold datasets for cylindrical boundary conditions, with the tube radii in Angstroms represented by two digits in each folder's name. Each folder contains a file with the LAMMPS code named \"in.visc_SiO2\", a file titled \"submit_job.sh\" for batch submission of simulations to the HPC facility, several...