Dynamics of a Charge Carrier Driven by Oscillating Fields in Materials with Impurities

In conductive materials and semiconductors, a charge carrier under the effects of an electric field will suffer collisions due to thermal fluctuations and impurities in the lattice, altering their trajectory. The electronic properties of these materials depend on the nature and frequency of these collisions; thus, they must be accounted for in any model dealing with electrical conduction. Tracking all collisions individually, while it may be possible within certain limits, forces the model to a large degree of approximation. This work introduces a Monte Carlo-based methodology to electrical transport in Ohmic materials that consists of two parts, the utilization of probability distribution functions (PDFs) for a set of collisions (coarse grain), as opposed to solving the transport equations for individual collisions and the use of homotopies to parameterize PDFs what produces a continuous set of PDFs once a relatively small number of them are explicitly parameterized. With the current approach, simulation times are from a few hundred to a few thousand times smaller than explicitly solving the transport equations. Average collision times are generated from distributions for a set of n collisions (the grain size), and from there, transport properties are calculated. Simulations were used to solve equations of motion based on the Drude’s Model of electrical conductivity. The results of the simulations are then used to generate probability distributions for various combinations of input parameters in order to coarse-grain the transport model. Grain sizes of n=5 and n=50 were considered. A homotopy on start time was first created by evaluating select distribution parameters across a half cycle. An excellent agreement non-coarse grained model was obtained.The electric field was then incorporated into the model parameterization leading to a PDF that, via a homotopy, can generate average collision time for any initial position of the carrier under any electric field within a continuous range). Results were validated using the non-coarse grained simulation under conditions not used for the parametrization for up to 500,000 collisions, with current density values being above 98.9% accurate. The goal of this work was to build a homotopy or mapping that, given some input parameters, could output some transport properties to aid experimental studies. The material of choice for this work was an ideal ohmic conductor with a mean free path of 4.3× 10−9m

An investigation of molecular dynamics for simple liquids

This thesis contains work expanding the theoretical understanding of molecular dynamics used to aid the study of simple liquids. It does so by focusing on investigating forces, which govern the dynamics of manybody systems. We loosely address three questions: How can we categorise force distributions? What can we gauge from force data? When do forces obey Newton’s third law? The first of these questions is addressed using statistical mechanics to derive standardised moments of the force distribution for a simple LennardJones liquid in both 1d and 3d with the aid of molecular dynamics. To answer the second question, we introduce the notions of force spaces and configurations spaces, and look at equivalence of these. We begin the investigation using the harmonic potential, and develop homotopy continuation methods for non-linear forces like Lennard-Jones. Convergent behaviour and limitations are explored for many-body systems, and a general two-body direct inversion is developed and implemented. The final question is entrenched in classical potential theory, and approached through work focusing on understanding the functional dependence of the interatomic potential. We develop theorems and provide corresponding constructive proofs concluding that potentials which obey certain symmetries can be described by distances, as opposed to positions. This enables us to understand when forces display reciprocity

Refining self-propelled particle models for collective behaviour

Swarming, schooling, flocking and herding are all names given to the wide variety of collective behaviours exhibited by groups of animals, bacteria and even individual cells. More generally, the term swarming describes the behaviour of an aggregate of agents (not necessarily biological) of similar size and shape which exhibit some emergent property such as directed migration or group cohesion. In this paper we review various individual-based models of collective behaviour and discuss their merits and drawbacks. We further analyse some one-dimensional models in the context of locust swarming. In specific models, in both one and two dimensions, we demonstrate how varying the parameters relating to how much attention individuals pay to their neighbours can dramatically change the behaviour of the group. We also introduce leader individuals to these models with the ability to guide the swarm to a greater or lesser degree as we vary the parameters of the model. We consider evolutionary scenarios for models with leaders in which individuals are allowed to evolve the degree of influence neighbouring individuals have on their subsequent motion

Defects in liquid crystals: surface and interfacial anchoring effects

Abstract This review discusses static properties of topological defects, such as line defectsdisclinations and dislocations, point defects -hedgehogs (monopoles) and boojums; focal conic domains and tilt grain boundaries in basic types of liquid crystals: uniaxial and biaxial nematics, cholesterics and smectics. We present the most popular experimental techniques to study defects in soft matter, namely, polarizing microscopy and fluorescence confocal polarizing microscopy. The role of bounding surfaces and the so-called surface anchoring that lifts the degeneracy of the order parameter in stability of defects is discussed. Because of the surface anchoring, the equilibridm state of a bounded liquid crystal might contain topological defects. For example, nematic bubbles nucleating during the first-order phase transition from the isotropic melt, might contain point defects (hedgehogs and boojums) and disclination loops when their size is larger than the anchoring extrapolation length defined by the ratio of the Frank elastic constant of the director curvature and the (polar) anchoring coefficient. Depending on the strength of surface anchoring, an edge dislocation might be expelled from the system with ID positional order or be stabilized in the bulk. Furthermore, focal conic domains play the role of "surface anchoring facets" by providing the necessary orientation of the liquid crystal director at the smectic boundary. Introduction Liquid crystals are endowed with continuous symmetries and physical prevalence of correlations of orientation over correlations of position and thus show rich and complex variety of topological defects. Defects in liquid crystals are of various dimensionalities, not only line defects, but also points, walls, and "configurations" (walls, topological solitons). In this review, we consider basic properties (mainly static) of defects in the simplest types of liquid crystals, nematics and smectics, mostly in relationship to the experimental studies and effects that the bounding surfaces have on defects. The experimental techniques of regular polarizing microscopy and more recent fluorescent confoca

Sign Gradient Descent Algorithms for Kinetostatic Protein Folding

This paper proposes a sign gradient descent (SGD) algorithm for predicting the three-dimensional folded protein molecule structures under the kinetostatic compliance method (KCM). In the KCM framework, which can be used to simulate the range of motion of peptide-based nanorobots/nanomachines, protein molecules are modeled as a large number of rigid nano-linkages that form a kinematic mechanism under motion constraints imposed by chemical bonds while folding under the kinetostatic effect of nonlinear interatomic force fields. In a departure from the conventional successive kinetostatic fold compliance framework, the proposed SGD-based iterative algorithm in this paper results in convergence to the local minima of the free energy of protein molecules corresponding to their final folded conformations in a faster and more robust manner. KCMbased folding dynamics simulations of the backbone chains of protein molecules demonstrate the effectiveness of the proposed algorithm.Comment: 6 pages, Accepted in 2023 International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS 2023

Geometric theory of topological defects: methodological developments and new trends

Liquid crystals generally support orientational singularities of the director field known as topological defects. These latter modifiy transport properties in their vicinity as if the geometry was non-Euclidean. We present a state of the art of the differential geometry of nematic liquid crystals, with a special emphasis on linear defects. We then discuss unexpected but deep connections with cosmology and high-energy-physics, and conclude with a review on defect engineering for transport phenomena