Heat Generation Using Lorentzian Nanoparticles. The Full Maxwell System

IF 1.9 4区 数学 Q1 MATHEMATICS, APPLIED
Arpan Mukherjee, Mourad Sini
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引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 285-315, February 2024.
Abstract. We analyze and quantify the amount of heat generated by a nanoparticle, injected in a background medium, while excited by incident electromagnetic waves. These nanoparticles are dispersive with electric permittivity following the Lorentz model. The purpose is to determine the quantity of heat generated extremely close to the nanoparticle (at a distance proportional to the radius of the nanoparticle). This study extends our previous results, derived in the 2D TM and TE regimes, to the full Maxwell system. We show that by exciting the medium with incident frequencies close to the plasmonic or Dielectric resonant frequencies, we can generate any desired amount of heat close to the injected nanoparticle while the amount of heat decreases away from it. These results offer a wide range of potential applications in the areas of photo-thermal therapy, drug delivery, and material science, to cite a few. To do so, we employ time-domain integral equations and asymptotic analysis techniques to study the corresponding mathematical model for heat generation. This model is given by the heat equation where the body source term comes from the modulus of the electric field generated by the used incident electromagnetic field. Therefore, we first analyze the dominant term of this electric field by studying the full Maxwell scattering problem in the presence of plasmonic or all-dielectric nanoparticles. As a second step, we analyze the propagation of this dominant electric field in the estimation of the heat potential. For both the electromagnetic and parabolic models, the presence of the nanoparticles is translated into the appearance of large scales in the contrasts for the heat-conductivity (for the parabolic model) and the permittivity (for the full Maxwell system) between the nanoparticle and its surroundings.
利用洛伦兹纳米粒子发热。完整的麦克斯韦系统
SIAM 应用数学杂志》第 84 卷第 1 期第 285-315 页,2024 年 2 月。 摘要我们分析并量化了注入背景介质的纳米粒子在入射电磁波激励下产生的热量。这些纳米粒子具有洛伦兹模型的电介电常数。研究的目的是确定极靠近纳米粒子(距离与纳米粒子半径成正比)时产生的热量。这项研究将我们之前在二维 TM 和 TE 状态下得出的结果扩展到了完整的麦克斯韦系统。我们的研究表明,通过用接近质子或介电谐振频率的入射频率来激励介质,我们可以在靠近注入纳米粒子的地方产生任何所需的热量,而远离纳米粒子的地方热量则会减少。这些结果为光热疗、药物输送和材料科学等领域提供了广泛的潜在应用。为此,我们采用时域积分方程和渐近分析技术来研究相应的发热数学模型。该模型由热方程给出,其中的体源项来自所用入射电磁场产生的电场模量。因此,我们首先通过研究等离子或全介质纳米粒子存在时的全麦克斯韦散射问题来分析该电场的主导项。第二步,我们在估算热势时分析该主导电场的传播。对于电磁模型和抛物线模型,纳米粒子的存在会导致纳米粒子与其周围环境之间的热导率(抛物线模型)和介电常数(全麦克斯韦系统)对比出现大尺度。
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来源期刊
CiteScore
3.60
自引率
0.00%
发文量
79
审稿时长
12 months
期刊介绍: SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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