We present an efficient method to compute the electrostatic fields, torques and forces in dipolar systems, which is based on the fast Fourier transform for nonequispaced data (NFFT). We consider 3d-periodic, 2d-periodic, 1d-periodic as well as 0d-periodic (open) boundary conditions. The method is based on the corresponding Ewald formulas, which immediately lead to an efficient algorithm only in the 3d-periodic case. In the other cases we apply the NFFT based fast summation in order to approximate the contributions of the nonperiodic dimensions in Fourier space. This is done by regularizing or periodizing the involved functions, which depend on the distances of the particles regarding the nonperiodic dimensions. The final algorithm enables a unified treatment of all types of periodic boundary conditions, for which only the precomputation step has to be adjusted.

We present an efficient method to compute the electrostatic fields, torques and forces in dipolar systems, which is based on the fast Fourier transform for nonequispaced data (NFFT). We consider 3d-periodic, 2d-periodic, 1d-periodic as well as 0d-periodic (open) boundary conditions. The method is based on the corresponding Ewald formulas, which immediately lead to an efficient algorithm only in the 3d-periodic case. In the other cases we apply the NFFT based fast summation in order to approximate the contributions of the nonperiodic dimensions in Fourier space. This is done by regularizing or periodizing the involved functions, which depend on the distances of the particles regarding the nonperiodic dimensions. The final algorithm enables a unified treatment of all types of periodic boundary conditions, for which only the precomputation step has to be adjusted.

<p>Dipole-dipole interactions are ubiquitous fundamental physical phenomena that govern physical effects such as Casimir Forces, van der Waals forces, collective Lamb shifts, cooperative decay, and resonance energy transfer. These interactions are associated with real and virtual photon exchange between the interacting emitters. Such interactions are crucial in realizing quantum memories, novel super-radiant light sources, and light-harvesting devices. Owing to this, the control and modification of dipole-dipole interactions have been a longstanding theme. The electromagnetic environment plays a crucial role in enhancing the range and strength of the interactions. This work focuses on modifying the nanophotonic environment near interacting emitters to enhance dipole-dipole interactions instead of spontaneous emission. To this end, we focus on engineering the nanophotonic environment to enhance the strength and range of dipole-dipole interactions between an ensemble of emitters. We explore ordered and disordered nanophotonic structures. We experimentally demonstrate long-range dipole-dipole interactions mediated by surface lattice resonances in a periodic plasmonic nanoparticle lattice. Further, the modified electromagnetic environment reduces the apparent dimensionality of the interacting system compared to non-resonant in-homogeneous and homogeneous environments. We also develop a spectral domain inverse design technique for the accelerated discovery of disordered metamaterials with unique spectral features. </p> <p>Further, we explore the novel regimes of light localization at near-zero-index in such disordered media. The disordered near-zero-index medium reveals enhanced localization and near-field chirality. This work paves the way to engineer the electromagnetic nanophotonic environment to realize enhanced long-range dipole-dipole interactions.</p>

Объектом исследования является ансамбль взаимодействующих магнитных наночастиц, который моделирует феррокомпозит. Цель исследования — в рамках бидисперсного приближения изучить влияние полидисперсности на структурные и магнитные свойства ансамбля неподвижных взаимодействующих магнитоактивных наночастиц: будет рассмотрена бидисперсная модель. Для достижения цели были поставлены следующие задачи: построить математическую модель, учитывающую бидисперсность наполнителя и межчастичные взаимодействия; вывести аналитические формулы для магнитных и структурных свойств; проанализировать влияние системных параметров на структурные и магнитные свойства материала. В ходе работы были применены различные методы: статистической физики, вириального разложения и комбинаторики. В магистерской диссертации разработана теория, которая позволяет прогнозировать свойства композитных материалов с магнитным наполнителем, обладающим ориентационным текстурированием. Теория включает в себя диполь-дипольные взаимодействия между частицами и учитывает бидисперсность наполнителя. Это дает возможность связать условия полимеризации с ориентационно-пространственным распределением магнитного наполнителя и, как следствие, с физическими свойствами получаемого композита. / The object of study is an ensemble of interacting magnetic nanoparticles that models a ferrocomposite. The aim of the research is to study, within the framework of a bidisperse approximation, the effect of polydispersity on the structural and magnetic properties of an ensemble of stationary interacting magnetoactive nanoparticles: a bidisperse model will be considered. To achieve the goal, the following tasks were set: to create a mathematical model that takes into account the bidispersity of the filler and the interparticle interactions; to derive analytical formulas for the magnetic and structural properties; to analyze the effect of system parameters on the structural and magnetic properties of the material. During the work, various methods were applied: statistical physics, virial expansion, and combinatorics. In the master's thesis, a theory was developed that allows predicting the properties of composite materials with a magnetic filler that possesses orientational texturing. The theory includes dipole-dipole interactions between particles and takes into account the bidispersity of the filler. This makes it possible to link the conditions of polymerization with the orientational-spatial distribution of the magnetic filler and, consequently, with the physical properties of the resulting composite.

В данной работе, основываясь на решении уравнения Фоккера-Планка-Брауна аналитически определена динамическая магнитная восприимчивость обездвиженных магнитных частиц к слабым переменным магнитным полям с учетом межчастичных диполь-дипольных взаимодействий. Полученное решение, а также известные из литературы аналитические и численные данные динамической восприимчивости систем подвижных и обездвиженных взаимодействующих магнитных частиц использовались для моделирования и анализа удельной поглощаемой мощности в зависимости от режимных параметров рассматриваемой системы. / In that work, based on the solution of the Fokker-Planck-Brown equation, the dynamic magnetic susceptibility of immobilized magnetic particles to weak alternating magnetic fields is analytically determined taking into account interparticle dipole-dipole interactions. The solution obtained, as well as the analytical and numerical data of the dynamic susceptibility of systems of moving and immobilized interacting magnetic particles known from the literature, were used to model and analyze the specific loss power depending on the regime parameters of the system under consideration.