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Abstract Recent theoretical work has predicted that dislocation patterning induces anisotropic flat bands in the electronic band diagram, which can lead to unusual effects such as unconventional superconductivity. This work develops a reduced-dimensional framework to provide insights into their origin. An effective one-dimensional dislocation potential is constructed by averaging over the spatial distributions of dislocations along a singular direction. The resulting model introduces a parameter that quantifies the strain modulation, thereby providing a transparent approach to analyze the role of dislocation strain in leading to flat band formation. 

Two-dimensional (2D) electronic materials are of significant technological interest due to their exceptional properties and broad applicability in engineering. The transition from nanoscale physics, which dictates their stable configurations, to macroscopic engineering applications requires the use of multiscale methods to systematically capture their electronic properties at larger scales. A key challenge in coarse-graining is the rapid and near-periodic variation of the charge density, which exhibits significant spatial oscillations at the atomic scale. Therefore, the polarization density field—the first moment of the charge density over the periodic unit cell—is used as a multiscale mediator that enables efficient coarse-graining by exploiting the almost-periodic nature of the variation. Unlike the highly oscillatory charge density, the polarization varies over lengthscales that are much larger than the atomic, making it suitable for continuum modeling. In this paper, we investigate the electrostatic potential arising from the charge distribution of arbitrarily-deformed 2D materials. Specifically, we consider a sequence of problems wherein the underlying lattice spacing vanishes and thus obtain the continuum limit. We consider three distinct limits: where the thickness is much smaller than, comparable to, and much larger than the in-plane lattice spacing. These limiting procedures provide the homogenized potential expressed in terms of the boundary charge and dipole distribution, subject to the appropriate boundary conditions that are also obtained through the limit process. Furthermore, we demonstrate that despite the intrinsic non-uniqueness in the definition of polarization, accounting for the boundary charges ensures that the total electrostatic potential, the associated electric field, and the corresponding energy of the homogenized system are uniquely determined. 

We report that a dielectric polymer chain, constrained at both ends, sharply collapses when exposed to a high electric field. The chain collapse is driven by nonlocal dipolar interactions and anisotropic polarization of monomers, a characteristic of real polymers that prior theories were unable to incorporate. Once collapsed, a large number of chain monomers accumulate at the center location between the chain ends, locally increasing the electric field and polarization by orders of magnitude. The chain collapse is sensitive to the orientation of the applied electric field and chain stretch. Our findings not only offer new ways for rapid actuation and sensing but also provide a pathway to discover the critical physics behind instabilities and electrical breakdown in dielectric polymers. 

Abstract This study investigates computationally the impact of particle size disparity and cohesion on force chain formation in granular media. The granular media considered in this study are bi-disperse systems under uniaxial compression, consisting of spherical, frictionless particles that interact through a modified Hookean model. Force chains in granular media are characterized as networks of particles that meet specific criteria for particle stress and inter-particle forces. The computational setup decouples the effects of particle packing on force chain formations, ensuring an independent assessment of particle size distribution and cohesion on force chain formation. The decoupling is achieved by characterizing particle packing through the radial density function, which enables the identification of systems with both regular and irregular packing. The fraction of particles in the force chains network is used to quantify the presence of the force chains. The findings show that particle size disparity promotes force chain formation in granular media with nearly-regular packing (i.e., an almost-ordered system). However, as particle size disparities grow, it promotes irregular packing (i.e., a disordered systems), leading to fewer force chains carrying larger loads than in ordered systems. Further, it is observed that the increased cohesion in granular systems leads to fewer force chains irrespective of particle size or packing.