# Coarse Graining of Electric Field Interactions with Materials

### Abstract

In this work, we present our continuum limit calculations of electrical interactions in ionic crystals and dielectrics. Continuum limit calculations serve two main purposes. First, they give an idea of how the macroscopic behavior of the material is related to the interactions at the atomistic scale. Second, they help in developing a multiscale numerical method, where the goal is to model the material both at the scale of atoms and at the macroscale. We consider two important settings: nanorod-like materials, where the thickness of a material in the lateral direction is of the order of the atomic spacing, and the materials, where atoms are randomly fluctuating due to the thermal energy. Our calculations, for the nanorod-like materials, show that the electrostatics energy is not long-range in continuum limit. We also consider the discrete system of dipole moments along the straight line and along the helix. We then compute the limit of the energy as the separation between the dipole moments tends to zero. The energy, in the continuum limit, is short-range in nature. This agrees with the calculations of Gioia and James for the magnetic thin films. We consider the system of atoms which are fluctuating due to thermal energy. We model the charge density field as a random field and compute the continuum limit of the electrostatics energy.

Date
Mar 21, 2017 12:00 AM
Event
AEM Mechanics Research Seminar, UMN
Location
Minneapolis, USA
##### Prashant K. Jha
###### Research Associate

My research is driven by the application of mathematics and computational science to present-day relevant and challeng- ing problems. Specific areas of interest include mechanics of solids and granular media, computational oncology, and multiscale modeling.