Dynamics of active particles in the presence of obstacles

Tese de mestrado, Física (Física Estatística e Não Linear), Universidade de Lisboa, Faculdade de Ciências, 2019As bactérias são um dos muitos tipos de organismos que têm a capacidade de metabolizar compostos do ambiente externo para executar movimento direcionado. Este mecanismo de autopropulsão permite-lhes explorar o ambiente de uma forma muito eficiente e evitar compostos tóxicos. Ao entender a sua dinâmica colectiva e quais podem ser as restrições para uma mobilidade eficiente, estamos mais preparados para lidar com problemas como a disseminaço de doenças bacterianas no corpo humano ou proliferação celular, mas também para desenhar novos micro-materiais com potenciais aplicações em diferentes contextos, como limpeza de oceanos. Matéria capaz de extrair energia do exterior e converte-la em energia cinética como de bactérias e células é designada como matéria activa. Quando em solução, dadas as suas dimensões, o seu movimento é afetado por flutuações térmicas, tal como acontece com as partículas passivas. No entanto, o fluxo de energia que resulta em movimento direcionado faz com que estes sistemas estejam fora do equilíbrio termodinâmico, colocando vários desafios ao seu estudo teórico. Este tipo de organismos (ou objectos artificiais) vivem (ou pretende-se que actuem) em ambientes complexos sendo de esperar que a sua dinâmica seja altamente influenciada por constrangimentos físicos, composição química e heterogeneidade do meio. Observa-se por exemplo que algumas partículas efectuam um movimento quiral quando confinadas a duas dimensões. Neste trabalho pretendemos estudar o movimento de bactérias em ambientes complexos, em particular compreender do ponto de vista teórico os resultados preliminares obtidos experimentalmente pelo grupo do Dr. Giorgio Volpe na University College de Londres. Estes resultados sugerem que a dinâmica individual e coletiva de bactérias (E:coli) é fortemente influenciada pela presença de obstáculos físicos. Um dos resultados principais mostra que a mobilidade geral das bactérias é de facto aumentada para uma concentração intermédia de obstáculos. Apresentamos um modelo numérico que reproduz o comportamento observado e que é capaz de identificar qual o mecanismo responsável pelo aumento de mobilidade para uma densidade óptima de obstáculos. Fazemos um estudo sistemático dos parâmetros que o compõe, com objectivo de perceber de que forma os diferentes constrangimentos físicos, estejam eles associados ao meio envolvente ou aos próprios elementos activos, influenciam o comportamento e em particular a mobilidade de matéria activa em ambientes complexos.Bacteria are among the simplest organisms that have the capability to metabolize nutrients from their environment and converting them into directed motion. This self-propulsion is what allows them to explore the environment in a very efficient way and to avoid toxic compounds. A deeper understanding of their collective dynamics and of the constraints to an efficient mobility is pivotal to solve open problems, such as, the spread of bacterial diseases in the human body or cell proliferation. The possibility of designing new micro-materials, inspired by these biological agents, might also be of a relevant technological impact in different contexts, such as cleaning of oceans or in the development of non-invasive medical treatments. When moving near a substrate some bacteria exhibit chiral trajectories moving in circular like paths. In this work, we aim at studying the motion of such chiral active particles in complex environments, in particular, to help to elucidate the results obtained experimentally by the group of Dr. Giorgio Volpe at the University College of London, showing how the individual and collective dynamics of bacteria (E:coli) are strongly influenced by the presence of physical obstacles. The main results show that the overall mobility of bacteria is in fact enhanced for an optimal concentration of obstacles. The main results of this thesis have been published in Nature Communications [10, 4110 (2019)]

Diffusion, subdiffusion, and trapping of active particles in heterogeneous media

We study the transport properties of a system of active particles moving at constant speed in an heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles avoid. Obstacle avoidance is characterized by the particle turning speed $\gamma$. We show, through simulations and analytical calculations, that the mean square displacement of particles exhibits two regimes as function of the density of obstacles $\rho_o$ and $\gamma$. We find that at low values of $\gamma$, particle motion is diffusive and characterized by a diffusion coefficient that displays a minimum at an intermediate obstacle density $\rho_o$. We observe that in high obstacle density regions and for large $\gamma$ values, spontaneous trapping of active particles occurs. We show that such trapping leads to genuine subdiffusive motion of the active particles. We indicate how these findings can be used to fabricate a filter of active particles.Comment: to appear in Phys. Rev. Let

Quantum Hall effect in exfoliated graphene affected by charged impurities: metrological measurements

Metrological investigations of the quantum Hall effect (QHE) completed by transport measurements at low magnetic field are carried out in a-few-$\mu\mathrm{m}$-wide Hall bars made of monolayer (ML) or bilayer (BL) exfoliated graphene transferred on $\textrm{Si/SiO}_{2}$ substrate. From the charge carrier density dependence of the conductivity and from the measurement of the quantum corrections at low magnetic field, we deduce that transport properties in these devices are mainly governed by the Coulomb interaction of carriers with a large concentration of charged impurities. In the QHE regime, at high magnetic field and low temperature ($T<1.3 \textrm{K}$), the Hall resistance is measured by comparison with a GaAs based quantum resistance standard using a cryogenic current comparator. In the low dissipation limit, it is found quantized within 5 parts in $10^{7}$ (one standard deviation, $1 \sigma$) at the expected rational fractions of the von Klitzing constant, respectively $R_{\mathrm{K}}/2$ and $R_{\mathrm{K}}/4$ in the ML and BL devices. These results constitute the most accurate QHE quantization tests to date in monolayer and bilayer exfoliated graphene. It turns out that a main limitation to the quantization accuracy, which is found well above the $10^{-9}$ accuracy usually achieved in GaAs, is the low value of the QHE breakdown current being no more than $1 \mu\mathrm{A}$. The current dependence of the longitudinal conductivity investigated in the BL Hall bar shows that dissipation occurs through quasi-elastic inter-Landau level scattering, assisted by large local electric fields. We propose that charged impurities are responsible for an enhancement of such inter-Landau level transition rate and cause small breakdown currents.Comment: 14 pages, 9 figure

Fundamental limits to optical response in absorptive systems

At visible and infrared frequencies, metals show tantalizing promise for strong subwavelength resonances, but material loss typically dampens the response. We derive fundamental limits to the optical response of absorptive systems, bounding the largest enhancements possible given intrinsic material losses. Through basic conservation-of-energy principles, we derive geometry-independent limits to per-volume absorption and scattering rates, and to local-density-of-states enhancements that represent the power radiated or expended by a dipole near a material body. We provide examples of structures that approach our absorption and scattering limits at any frequency, by contrast, we find that common "antenna" structures fall far short of our radiative LDOS bounds, suggesting the possibility for significant further improvement. Underlying the limits is a simple metric, $|\chi|^2 / \operatorname{Im} \chi$ for a material with susceptibility $\chi$, that enables broad technological evaluation of lossy materials across optical frequencies.Comment: 21 pages and 6 figures (excluding appendices, references

Semi-analytic modeling of stacked metasurfaces

Ziel dieser Arbeit war die Entwicklung eines semi-analytischen Models mehrschichtiger nano- strukturierter Oberflächen. Einzelne Schichten werden hierbei in Forschungsgemeinschaft als “Metasurface” bezeichnet. In Folge nennt man Schichtsysteme aus Metasurfaces “Metasurface Stacks” oder “Stacked Metasurfaces”. Das besondere an Metasurfaces liegt an einer speziellen Art der Licht-Materie-Wechselwirkung. Im Gegensatz zu herkömmlichen, natürlich vorkommenden optischen Materialien, welche im Wesentlichen durch ihre atom- und molekularphysikalischen Eigenschaften wechselwirken, besitzen Metasurfaces mesoskopische Strukturen. Diese haben Größen, die der von Lichtwellen entsprechen. Dadurch entstehen zum einen Streuphänomene die komplexe Feldwechselwirkungen erzeugen. Darüberhinaus sorgen evaneszente Felder, die auf der Oberfläche der Nano-Strukturen angeregt werden können, für ein geändertes Resonanzverhalten, welches sich durch verschiedene Reflektions- und Absorptionseigenschaften auszeichnet. Sind die Strukturen einer Metasurface periodisch angeordnet lassen sich die dort angeregten Felder durch sogenannte Bloch-Moden beschreiben. Diese sind periodische Feldlösungen der Maxwell-Gleichungen. Betrachtet man nun die Gesamtheit aller Bloch-Moden der Metasurface, kann man eine dominante Mode mit, im Vergleich zu allen anderen, maximalem Energietransport in das Fernfeld identifizieren. Diese nennt man in der Literatur Fundamentalmode. Ist die Metasurface so beschaffen, dass bei Wechselwirkung mit Licht einer bestimmten Wellenlänge diese Fundamentalmode signifikant alle anderen Moden dominiert und letztere stark dämpfen, das heißt evaneszent abfallen, so kann das betreffende Medium als homogen gedeutet werden. Darauf basierend wurde in der vorliegenden Arbeit ein semi-analytisches Model von Stacked Metasurfaces entwickelt, welches verschiedenen experimentellen Tests stand hielt. Ein besonderer Erfolg liegt in der Erweiterung des Modells zur Untersuchung von Feynman-Pfaden

A model for calculating EM field in layered medium with application to biological implants

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Modern wireless telecommunication devices (GSM Mobile system) (cellular telephones and wireless modems on laptop computers) have the potential to interfere with implantable medical devices/prostheses and cause possible malfunction. An implant of resonant dimensions within a homogeneous dielectric lossy sphere can enhance local values of SAR (the specific absorption rate). Also antenna radiation pattern and other characteristics are significantly altered by the presence of the composite dielectric entities such as the human body. Besides, the current safety limits do not take into account the possible effect of hot spots arising from metallic implants resonant at mobile phone frequencies. Although considerable attention has been given to study and measurement of scattering from a dielectric sphere, no rigorous treatment using electromagnetic theory has been given to the implanted dielectric spherical head/cylindrical body. This thesis aims to deal with the scattering of a plane electromagnetic wave from a perfectly conducting or dielectric spherical/cylindrical implant of electrically small radius (of resonant length), embedded eccentrically into a dielectric spherical head model. The method of dyadic Green's function (DGF) for spherical vector wave functions is used. Analytical expressions for the scattered fields of both cylindrical and spherical implants as well as layered spherical head and cylindrical torso models are obtained separately in different chapters. The whole structure is assumed to be uniform along the propagation direction. To further check the accuracy of the proposed solution, the numerical results from the analytical expressions computed for the problem of implanted head/body are compared with the numerical results from the Finite-Difference Time-Domain (FDTD) method using the EMU-FDTD Electromagnetic simulator. Good agreement is observed between the numerical results based on the proposed method and the FDTD numerical technique. This research presents a new approach, away from simulation work, to the study of exact computation of EM fields in biological systems. Its salient characteristics are its simplicity, the saving in memory and CPU computational time and speed.Cochlear UK Limited and EPSR

Electromagnetic Waves

This volume is based on the contributions of several authors in electromagnetic waves propagations. Several issues are considered. The contents of most of the chapters are highlighting non classic presentation of wave propagation and interaction with matters. This volume bridges the gap between physics and engineering in these issues. Each chapter keeps the author notation that the reader should be aware of as he reads from chapter to the other

Method of Moment Analysis of Partially Shielded Chiral Bodies of Revolution

A chiral body of revolution (BOR) which is partially covered by a thin conducting shield is analyzed using the method of moments (MOM). The axisymmetric system is excited by a plane wave. The total internal fields and the far scattered fields are computed. The problem is solved using the surface equivalence principle. The scattered fields outside the structure are assumed to be produced by an equivalent magnetic surface current that exists on the unshielded part of the BOR surface and an external equivalent electric surface current that exists over all of the BOR surface . These two currents are assumed to radiate in the unbounded external medium. Similarly, the total internal fields are assumed to be produced by the negative of the above magnetic current and an internal equivalent electric surface current that exists over all of the BOR surface, but is the negative of an independent unknown only on the shielded part of . These two currents radiate in the unbounded internal medium. Enforcing continuity of the tangential components of total electric field (E) and total magnetic field (H) on S gives a two coupled integral equations for the two unknown surface currents. The two unknown surface currents are the external equivalent electric surface current and the union of magnetic current ( ) on the unshielded part of and the negative of the internal equivalent electric surface current on the shielded part of . The method of moments as applied to bodies of revolution is used to solve these integral equations numerically. Piecewise linear variation of the currents is assumed along the generating curve of the BOR. The variation of the currents along the circumferential direction is represented by Fourier series. An approximate Galerkin\u27s method is used for testing. Conical and spherical BORs are studied. Computed results for the partially shielded spherical chiral body are in excellent agreement with other data. Theoretical framework developed in chapters two through six factually validated the underlying firm foundation of mathematical physics and sound computational electromagnetic methods of our theory by producing correct scattered fields and radar cross sections of the chiral and perfectly conducting sphere, chiral and perfectly conducting cylinder, chiral and perfectly conducting cone. Chapter seven demonstrates the soundness of the theoretical foundation of this thesis by producing computed results and graphs of not only the case of a perfectly conducting sphere, cylinder and cone but those of the chiral sphere, chiral cylinder, and chiral cone and those of the chiral sphere, chiral cylinder and chiral cone partially covered by rotationally symmetric perfectly conducting surface. The computed results and graphs obtained in chapter seven by the application of our theoretical framework were almost one hundred percent accurate with respect to the conformability of our graph mappings, form of our graphs and accuracy of our graph readings with respect to analytically calculated results and graphs. Our computed results and graphs with respect to the computed results and graphs of early research works that used numerical approach distinctly different than ours were in good agreement