Computational Electromagnetic at Fractional Dimensions

Abstract

According to Mandelbrot’s work on fractals, many objects are in fractional dimensions thatthe traditional calculus or differential equations are not sufficient. Thus fractional models solvingthe relevant differential equations are critical to understand the physical dynamics of such objects.In this project, we will develop computational electromagnetics or Maxwell equations in fractionaldimensions. For a given degree of imperfection, impurity, roughness, anisotropy orinhomogeneity, we consider the complicated object can be formulated into a fractionaldimensional continuous object characterized by an effective fractional dimension D, which can becalculated from a self-developed algorithm. With this non-integer value of D, we will develop thecomputational methods to design and analysis of EM scattering problems involving rough surfacesor irregularities in an efficient framework. The fractional electromagnetic based model can beextended to other key differential equations such as Schrodinger or Dirac equations, which will beuseful for design of novel 2D materials stacked up in complicated device configuration forapplications in electronics and photonics. The fundamental findings from this proposal will berelevant to various programs in AFOSR, such as computational mathematics, electromagnetics,laser and optics physics. For example, the propagation and scattering of electromagnetic waves inand from a fractal medium in communication. It can be used to study the nonlinear optical effectswhich are critical for new devices using novel materials for photonics applications. Anotherexample is the light absorption in organic or porous like materials, and this model will be usefulto improve the performance like power efficiency of such organic solar cell to be used as wearableelectronics as part of solider system. Thus, we conclude this proposal should be of interests ofAFOSR in the broad aspect of defence and security applications.

Document Details

Document Type
DoD Grant Award
Publication Date
May 02, 2017
Source ID
FA23861714020

Entities

People

  • Lay Kee Ang

Organizations

  • Air Force Office of Scientific Research
  • Singapore University of Technology and Design
  • United States Air Force

Tags

Fields of Study

  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Data Mining and Knowledge Discovery.
  • Wave Propagation and Nonlinear Chaotic Dynamics.

Technology Areas

  • Directed Energy
  • Microelectronics