In this work, the multiscale problem of modeling fluctuations in boundary layers in stochastic elliptic partial differential equations is solved by homogenization. A homogenized equation for the covariance of the solution of stochastic elliptic PDEs is derived. In addition to the homogenized equation, a rate for the covariance and variance as the cell size tends to zero is given. For the homoge...

In this study, nanoscale zero-valent iron nanoparticles (NZVIs) were coated with silica and polydopamine using a two-step process. The coated nanoparticles were applied as adsorbents for removal of two common polycyclic aromatic hydrocarbons pollutants, phenanthrene (PHE) and anthracene (ANT) from aqueous system. Adsorption kinetics followed a pseudo-second-order model. Isotherms and thermodyna...

Using time-dependent current-density functional theory, we derive analytically the dynamical exchange-correlation correction to the dc conductance of nanoscale junctions. The correction pertains to the conductance calculated in the zero-frequency limit of time-dependent density functional theory within the adiabatic local-density approximation. In particular, we show that in linear response, th...

To learn about the basic aspects of nanoscale spherical molecular shells during their formation, spherically curved two-dimensional N-particle Lennard-Jones systems are simulated, studying curvature evolution paths at zero temperature. For many N values (N<800) equilibrium configurations are traced as a function of the curvature radius R. Sharp jumps for tiny changes in R between trajectories w...

This paper derives both open-loop and closed-loop control policies that steer a finite set of differential-drive robots to desired positions in a two-dimensional workspace, when all robots receive the same control inputs but each robot turns at a slightly different rate. In the absence of perturbation, the open-loop policy achieves zero error in finite time. In the presence of perturbation, the...

We study quantum optical properties of a dipole emitter coupled to a rectangular nanoscale waveguide with dielectric core and silver cladding. We investigate enhanced spontaneous emission and the photonic Lamb shift for emitters whose resonant frequencies are near the waveguide frequency cutoff where the waveguide behaves as an ɛ-near-zero metamaterial. Via a dyadic Green's function-based field...