skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Dimensional Reduction for the Ferroelectric Smectic A-Type Phase of Bent-Core Liquid Crystals
We analytically derive and numerically simulate a two-dimensional energy functional modelling the effects of a constant electric field on a thin sample of a bent-core liquid crystal in the ferromagnetic SmA-like phase. We start from a three-dimensional domain and show that under proper rescaling and in the limit of small thickness the electric self-interactions term gives rise to boundary terms. We compare our results to previously proposed models.  more » « less
Award ID(s):
1909268
PAR ID:
10528822
Author(s) / Creator(s):
; ;
Publisher / Repository:
springer
Date Published:
Journal Name:
Journal of Nonlinear Science
ISSN:
0938-8974,1432-1467
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    Electric-magnetic duality or S-duality, extending the symmetry of Maxwell’s equations by including the symmetry between Noether electric charges and topological magnetic monopoles, is one of the most fundamental concepts of modern physics. In two-dimensional systems harboring Cooper pairs, S-duality manifests in the emergence of superinsulation, a state dual to superconductivity, which exhibits an infinite resistance at finite temperatures. The mechanism behind this infinite resistance is the linear charge confinement by a magnetic monopole plasma. This plasma constricts electric field lines connecting the charge–anti-charge pairs into electric strings, in analogy to quarks within hadrons. However, the origin of the monopole plasma remains an open question. Here, we consider a two-dimensional Josephson junction array (JJA) and reveal that the magnetic monopole plasma arises as quantum instantons, thus establishing the underlying mechanism of superinsulation as two-dimensional quantum tunneling events. We calculate the string tension and the dimension of an electric pion determining the minimal size of a system capable of hosting superinsulation. Our findings pave the way for study of fundamental S-duality in desktop experiments on JJA and superconducting films. 
    more » « less
  2. Concepts covered in introductory electricity and magnetism such as electric and magnetic field vectors, solenoids, and electromagnetic waves are difficult concepts for students to visualize. Part of this difficulty may be due to the representation of three-dimensional objects on the two-dimensional planes of course textbooks and classroom whiteboards. The use of two-dimensional platforms limits the visualization of phenomena such as the vector field of a point charge or test charges traveling in the three-dimensional space of an electric field. In addition, working in two dimensions may add to students’ difficulties orienting their body correctly to use the right-hand rule when determining the direction of a magnetic field. These difficulties in visualization may limit the conceptual understanding of these fundamental topics. To promote conceptual understanding of electromagnetism we are cyclically developing and researching three spatial computing 3D environments covering electric fields, magnetic fields and electromagnetic waves. Each environment will be developed and tested in both augmented and virtual reality. The first of our environments, the electric field, has been built and tested in augmented reality (AR) with introductory physics students in the Fall 2023 semester. Our study is currently in phase IV of the National Science Foundation’s Design and Development Cycle. Data collected during phase II is being analyzed to support revision to the environment as well as data collection protocols. This article will outline findings from qualitative data gathered during the AR experience as well as during student post interviews following participation in the electric field space. These findings are characterized and then responded to with recommendations for the design team regarding content and testing procedures. In what follows, we first present a framework listing current knowledge regarding students' difficulties learning electric fields and how these guided our design of this electric field augmented reality environment. We next present themes that emerged from discussions during the experience as well as the post interviews. We conclude with suggestions to inform our second round of environmental design. 
    more » « less
  3. Dust grains have been used as minimally invasive probes to determine plasma parameters including the plasma density, temperature, and electric field in a plasma discharge. However, the dust grains in a plasma generate local potential disturbances due to the collection of charge and the subsequent electrostatic interactions between the dust and charged plasma particles. Dust grains in close proximity to one another exhibit interesting non-reciprocal interactions and self-organize into structures such as one-dimensional filamentary chains, two-dimensional “zigzags,” and three-dimensional helices, among others. The formation of these structures suggests that although the dust grains may be less invasive than traditional plasma probes, the disturbance to the local plasma environment introduced by dust grains is non-trivial. Commonly used analytic forms of the electric potential describing complex plasmas have failed to resolve the near-dust region, and as a result are insufficient to provide insight about the formation of complex dust structures. Here, we use an N-body simulation to compute the electric potential from ion densities near various dust grain configurations. We provide an alternative description to the standard analytic model for the electric potential of dust and ion wakes based on a Gaussian shaped cloud of ions. The electric potential obtained from simulations is used to identify minimum energy configurations for two and three dust grains. It is further demonstrated that the minimum potential region identified for N dust grains and their associated ion wakes does not predict the minimum-energy configuration of N + 1 dust grains. 
    more » « less
  4. We study an inverse problem for the time-dependent Maxwell system in an inhomogeneous and anisotropic medium. The objective is to recover the initial electric field $$\mathbf{E}_0$$ in a bounded domain $$\Omega \subset \mathbb{R}^3$$, using boundary measurements of the electric field and its normal derivative over a finite time interval. Informed by practical constraints, we adopt an under-determined formulation of Maxwell's equations that avoids the need for initial magnetic field data and charge density information. To address this inverse problem, we develop a time-dimension reduction approach by projecting the electric field onto a finite-dimensional Legendre polynomial-exponential basis in time. This reformulates the original space-time problem into a sequence of spatial systems for the projection coefficients. The reconstruction is carried out using the quasi-reversibility method within a minimum-norm framework, which accommodates the inherent non-uniqueness of the under-determined setting. We prove a convergence theorem that ensures the quasi-reversibility solution approximates the true solution as the noise and regularization parameters vanish. Numerical experiments in a fully three-dimensional setting validate the method's performance. The reconstructed initial electric field remains accurate even with $$10\%$$ noise in the data, demonstrating the robustness and applicability of the proposed approach to realistic inverse electromagnetic problems. 
    more » « less
  5. The two-dimensional (2D) materials, represented by graphene, stand out in the electrical industry applications of the future and have been widely studied. As commonly existing in electronic devices, the electric field has been extensively utilized to modulate the performance. However, how the electric field regulates thermal transport is rarely studied. Herein, we investigate the modulation of thermal transport properties by applying an external electric field ranging from 0 to 0.4 V Å −1 , with bilayer graphene, monolayer silicene, and germanene as study cases. The monotonically decreasing trend of thermal conductivity in all three materials is revealed. A significant effect on the scattering rate is found to be responsible for the decreased thermal conductivity driven by the electric field. Further evidence shows that the reconstruction of internal electric field and generation of induced charges lead to increased scattering rate from strong phonon anharmonicity. Thus, the ultralow thermal conductivity emerges with the application of external electric fields. Applying an external electric field to regulate thermal conductivity illustrates a constructive idea for highly efficient thermal management. 
    more » « less