This thesis describes the work of three research projects, the background research that motivated the work, and the resultant project findings. The three projects concerned: (i) Geometric stochastic resonance in a double cavity, (ii) Synchronisation of geometric stochastic resonance by a bi-harmonic drive, and (iii) Rectification of Brownian particles with oscillating radii in asymmetric corrugated channels. In the project 'Geometric stochastic resonance in a double cavity', we investigated synchronisation processes for the geometric stochastic resonance of particles diffusing across a porous membrane and subject to a periodic driving force. Non-interacting particle currents were driven through a symmetric membrane pore either parallel or perpendicular to the membrane. Then, harmonic mixing spectral current components were generated by the combined action of parallel and perpendicular drives. The role of the repulsive interaction of particles as a controlling factor with potential applications to the transport of colloids and biological molecules through narrow pores was also investigated. In 'Synchronisation of geometric stochastic resonance by a bi-harmonic drive', we simulated the stochastic dynamics of an elliptical particle using the Langevin equation. The particle was simultaneously driven by low and high frequency harmonic drives across a porous inter-cavity membrane. It was observed that the particle oscillated out of phase with the low frequency drive. This effect was due to the absolute negative mobility the particle would have exhibited if the low frequency drive had been replaced by a dc static force. It was also observed that the magnitude of this out-of-phase stochastic resonance depends on how the combined action of the driving forces and noise fluctuations affect the particle orientation, and as such was shown to be sensitive to the particle shape. This emphasises the importance of particle geometry, in addition to chamber geometry, to the realisation and optimisation of geometric stochastic resonance. In the project 'Rectification of Brownian particles with oscillating radii in asymmetric corrugated channels', we simulated the transport of a Brownian particle with an oscillating radius freely diffusing in an asymmetric corrugated channel over a range of driving forces for a series of temperatures and angular frequencies of radial oscillation. It was observed that there was a strong influence of self-oscillation frequency upon the average particle velocity. This effect can be used to control rectification of biologically active particles as well as for their separation according to their activity, for instance in the separation of living and dead cells. The background research is described in Chapter One and the research findings are described along with their related projects in Chapters Two and Three.

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Lorsque des particules actives, des particules pouvant se mouvoir par elles-mêmes, sont mises en suspension dans un fluide, celles-ci peuvent avoir un comportement collectif. Dans ce document, nous présentons des travaux expérimentaux utilisant des Escherichia Coli, une particule biologique, des techniques microfluidiques, ainsi que des simulations numériques. Ceux-ci nous ont permis de caractériser les comportements collectifs de ces nageurs, leur modification en présence d'un cisaillement extérieur ainsi que l'impact de ces comportements microscopiques sur sa viscosité. Nous avons ainsi mis au jour le caractère progressif de l'apparition des mouvements collectifs avec la concentration, l'existence d'un taux de cisaillement critique commun pour les comportements individuels et collectifs des nageurs, ainsi qu'une rhéologie non-newtonienne de ces suspensions. / If we put active particles, ie. motile particles, in suspension into a _uid, collective behaviors can occur. In this document, we present experimental works using Escherichia Coli, a biological particle, micro_uidic devices, and numerical simulations. By these ways, we caracterized these swimmers, their collective motions, the impact of an external shear on their behavior, and rheological behavior of this kind of suspensions. We show that the typical size of these collective motions increases smoothly with the volume fraction, and that a critical shear rate exist and is the same for individual and collective motion under shear. We also show for that bacterial suspensions have a non-newtonian viscosity and describe their rheological behavior.

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Movement is an essential feature of life. It allows organisms to move towards a more favorable environment and to search for food. There are many biological systems that fall under the category active matter, from molecular motors walking on microtubules inside cells to flocks of birds. What these systems have in common is that each of its constituents converts energy into directed motion, that is, they propel themselves forward. Besides the many biological examples, there is also synthetic active matter, these are self-propelled particles made in a laboratory. These are typically colloidal sized particles that can propel themselves forward by self-phoresis. In this work the focus is on the low Reynolds number regime, meaning that the typical size of the constituents is less than a few micrometers. The models that are used to describe such active matter are can be viewed as nonequilibrium extensions to Brownian motion (the thermal motion of small particles dissolved in a fluid). In many systems the self-propulsion speed (activity) is not homogeneous in space: the particles swim faster in some areas than in others. The main topic of this dissertation is how a single active particle, or a few active particles tied together by a potential, behave in such systems. It is known that a single active particle without any steering mechanism spends most time in the regions where it moves slowly, or in other words, they spend most time in regions where they are less active. However, here it is shown that, even though they spend most time in the less active regions, dynamical properties, such as the probability to move towards the more active regions is higher than moving towards the less active regions. Furthermore, when the active particles are connected to a passive Brownian 'cargo' particle, chained together to form a colloidal sized polymer, or fixed to another active particle, the resulting active dimers or polymers either accumulate in the high activity regions or the low activity regions, depending on the friction of the cargo particle, the number of monomers in the polymer, or the relative orientation of active particles. Lastly, when the activity is both time- and space-dependent, a steady drift of active particles can be induced, without any coupling between the self-propulsion direction and the gradient in the activity. This phenomenon can be used to position the particles depending on their size.:1. Brownian Motion 2. Active Matter 3. Modeling Active Matter 4. Introduction: Inhomogeneous activity 5. Pseudochemotaxis 6. Cargo-Carrying Particles 7. Active Colloidal Molecules 8. Time-Varying Activity Fields Appendix: Hydrodynamics

Active particle is a general term used to label a large set of different systems, spanning from a flock of birds flying in a coordinated pattern to a school of fish abruptly changing its direction or to a bacterium self-propelling itself while foraging nourishment. The common property shared by these systems is that their constituent agents, e.g. birds, fishes, or bacteria, are capable of harvesting energy from the surrounding environment and converting it into self-propulsion and directed motion. This peculiar feature characterizes them as out-of-equilibrium systems, in fact, the process of energy consumption and dissipation generates microscopically irreversible dynamics and drives them far from thermal equilibrium. Thanks to their intrinsic out-of-equilibrium nature, active particle systems often display characteristic patterns and behaviors that are not observed in equilibrium physics systems, such as collective motion or motility-induced phase separation. These features prompted the development of theories and algorithms to simulate and study active particles, giving rise to paradigmatic models capable of describing these phenomena, such as the Vicsek model for collective motion, the run-and-tumble model, or the active Brownian particle model. At the same time, synthetic agents have been designed to reproduce the behaviors of these natural active particle systems, and their evolution could play a fundamental role in the nanotechnology of the 21st century and the development of novel medical treatments, in particular controlled drug delivery. A specific type of active particle that uses its directed motion to move at the microscale is called a microswimmer. Examples of these agents are bacteria exploring their surroundings while searching for food or escaping external threats, spermatozoa looking for the egg, or artificial Janus particles designed for specific tasks. Active agents at these scales use different swimming mechanisms, such as rotating flagella or phoretic motion along chemical gradients that they can create. The outcome of their efforts is determined by the interplay of the translational diffusion intrinsic to the dynamics at these scales and the persistent motion that characterizes their self-propulsion. The problem of finding a specific target in a complex environment is essential for microswimmers and active agents in general. Target search is employed by animals and microorganisms for a variety of purposes, from foraging nourishment to escaping potential threats, such as in the case of bacterial chemotaxis. The study of this process is therefore fundamental to characterize the behavior of these systems in nature. Its complete description could then be employed in designing synthetic microswimmers for addressing specific problems, such as the aforementioned targeted drug delivery and the environmental cleansing of soil and polluted water. Here, we provide a detailed study of the target search process for microswimmers exploring complex environments. To this end, we generalize Transition Path Theory, the rigorous statistical mechanics description of transition processes, to the target-search problem. The most general way of modeling a complex environment that the microswimmer has to navigate is through an external potential. This potential can be characterized by high barriers separating metastable states in the system or by the presence of confining boundaries. If a high energy barrier is located between the initial position of the microswimmer and its target, the target search becomes a rare event. Rare events have been thoroughly investigated in equilibrium physics, and several algorithms have been designed to cope with the separation of timescales intrinsic to these problems and enable their investigation via efficient computer simulations. Despite the large set of tools developed for studying passive particles performing rare transitions, the characterization of this process for non-equilibrium systems, such as active particles, is still lacking. One of the main results of this thesis is the generalization to non-equilibrium systems of the Transition Path Sampling (TPS) algorithm, which was originally designed to simulate rare transitions in passive systems. This algorithm relies on the generation of productive trajectories, i.e. trajectories linking the initial state of the particle to the target state, via a Monte Carlo procedure, without the need of simulating long thermal oscillations in metastable states. These trajectories are then accepted according to a Metropolis criterion and are subsequently used to obtain the transition path ensemble, i.e. the ensemble of all reactive paths that completely characterizes the process. The TPS algorithm relies on microscopic reversibility to generate the productive trajectories, therefore its generalization to out-of-equilibrium systems lacking detailed balance and microscopic reversibility has remained a major challenge. Within this work, after deriving a path integral representation for active Brownian particles, we provide a new rule for the generation and acceptance of productive non-equilibrium trajectories, which reduces to the usual expression for passive particles when the activity of the microswimmer is set to zero. This new rule allows us to generalize the TPS algorithm to the case of active Brownian particles and to obtain a first insight into the counterintuitive target-search pathways explored by these particles. In fact, while passive particles perform barrier crossing following the minimum energy path linking the initial state to the target state, we found that active particles, thanks to their activity and persistence of motion, can reach the target more often by surfing higher energy regions of the landscape that lie far from the minimum energy path. The second result of this thesis is a systematic characterization of the target-search path ensemble for an active particle exploring an energy landscape. We do so by analyzing the system’s response to changes in the two adimensional parameters that define the parameter space of the model: the Péclet number and the persistence of the active particle. Our findings show that active Brownian particles can increase their target-finding rates by tuning their Péclet number and their persistence according to the shape and characteristics of the external landscape. We perform this analysis in two different landscapes, namely a double-well potential and the Brown-Müller potential, finding robust features in the target-search patterns. In contrast, other observables of the system, e.g. the target-finding rates, are more responsive to the features of the external environment. Interestingly, our results suggest that, differently from what happens for passive particles, the presence of additional metastable states in the system does not hinder the target-search dynamics of active particles. The third original contribution of this Ph.D. thesis is the generalization of the concept of the committor function to target-search problems. The committor function was first introduced in the framework of Transition Path Theory to study reaction processes. If a definition for a reactant and a product state embedded in the configuration space of the system is provided, the committor function quantifies the probability that a trajectory starting in a given configuration reaches the product state before it can enter the reactant. For this reason, it has been proven to be pivotal for a complete characterization of these events and it is often regarded as the optimal reaction coordinate for thermally activated transitions. The target search problem shares many similarities with transition processes since it is characterized by an initial state from which the agent begins its journey and a target state that the particle is aiming to reach, and often some barriers or obstacles separate the two. Exploiting these similarities, we take advantage of the concept of the committor function to fully characterize a target-search process performed by an active agent. First, we derive the Fokker-Planck equation for an active Brownian particle subject to an external potential, and we use its associated probability current to define the committor function for an active agent. Then, we prove that the active committor satisfies the Backward-Kolmogorov equation analogously to the committor for passive particles. We take advantage of this property to efficiently compute the committor function using a finite-difference algorithm, validating it with brute-force simulations. Finally, we further validate our theory with experiments of a camphor self-propelled disk. This self-propelled disk is capable of moving on a water surface and is studied during its exploration of a circular confining environment. We start by analyzing long recorded trajectories of such a disk moving in a Petri dish, and, after defining a reactant and a product region in the system, we proceed to compute the committor function in three different regions contained in the dish. We analyze all the trajectory slices passing through those regions and we measure how many of them hit the product region and how many hit instead the reactant first, and we obtain the committor in the three regions as a function of the angle. Finally, we simulate a long trajectory of an active Brownian particle exploring a circular confining environment, and we compare the committor as an angular function obtained from brute-force simulations with the committor estimated from experimental data.

We investigate coarse-grained models of suspended self-thermophoretic microswimmers. Upon heating, the Janus spheres, with hemispheres made of different materials, induce a heterogeneous local solvent temperature that causes the self-phoretic particle propulsion. Starting from molecular dynamics simulations that schematically resolve the molecular composition of the solvent and the microswimmer, we verify the coarse-grained description of the fluid in terms of a local molecular temperature field, and its role for the particle’s thermophoretic self-propulsion and hot Brownian motion. The latter is governed by effective nonequilibrium temperatures, which are measured from simulations by confining the particle position and orientation. They are theoretically shown to remain relevant for any further spatial coarse-graining towards a hydrodynamic description of the entire suspension as a homogeneous complex fluid.

Active Particles at the Temelin NPP, Radiobiological Risks and Protective Precautions The term active particle (AC) was applied on Temelín NPP (ETE) in order to denominate small fragments of high radioactive matters, sized up to 1 millimeter, forming into primary circuit. In accordance with latest available know-how, the ACs major contains corrosion products, that were activated during passing through reactor core. After primary circuit opening, due to carry out outage works, the ACs will spread into ETE radiation controlled area. In proportion to their size, the ACs activity is relative high, so that the ACs can jeopard workers, who will contact them. This jeopardy is namely associated with AC penetration into organism - ingestion or inhalation. The main goal of this dissertation is to determine grounds of ACs occurence in Temelín NPP, to review ACs radiobiological risks and to evaluate procedures and protective aids, used for assurance of workers radiation protection. This dissertation is resuming actual know-how about ACs occured and occuring in Temelín NPP, including suggestions for radiation protection procedures and for protective aids utilization, that are to be used for reduction of above mentioned jeopardy. Next areas are concerned: - analysis of ACs forming and matters composition - description of ACs physical-radiation parameters - identification of main ACs sources in primary circuit - assesment and evaluation of radiobiological jeopardies, associated with ACs occurence in Temelín NPP radiation controlled area - assesment of procedures and protective aids used for protection of workers, who can be endangered by ACs

The aim of the Master thesis is the investigation of the influence of microwave discharge for skin wound healing. Microwave discharge used for this work was argon microwave plasma generated by the surface wave and direct vortex torch. The theoretical part is focused on basic information about plasma and processes that occur in plasma discharge under specific conditions. Plasma generates various active particles such as hydroxyl radicals, nitric oxide radicals, excited nitrogen molecules, atomic nitrogen, argon and oxygen. All of these particles together with plasma generated photons are usable in biomedical applications and summary of them is shown in the theoretical part. The experimental part is focused on the comparison of torch discharge and microwave plasma generated surface wave in skin wound healing. The model wounds on laboratory mousses were treated by plasma and wound healing was examined during 3 weeks after the plasma treatment. Both plasma systems showed healing acceleration. Application of torch discharge was proved to be the most effective method in the healing of skin defects. Additionally, determination of active particles was taken by optical emission spectroscopy. Based on these measurements, plasma parameters were determined: electron temparutare, rotational and vibrational temperatures. To determine role of different plasma active species, the treatment of indigo coloured artificial skin model was treated under various conditions by both plasma systems. Results show that the direct interaction between plasma particles is the main effect, role of radiation, only, is more or less negligible. Finally, the plasma vortex system was visualized using fast camera at selected powers and gas flows.

Das Konzept von aktiven Brownschen Teilchen kann benutzt werden, um das Verhalten einfacher biologischer Organismen oder künstlicher Objekte, welche die Möglichkeit besitzen sich von selbst fortzubewegen zu beschreiben. Als Bewegungsgleichungen für aktive Brownsche Teilchen kommen Langevin Gleichungen zum Einsatz. In dieser Arbeit werden aktive Teilchen mit konstanter Geschwindigkeit diskutiert. Im ersten Teil der Arbeit wirkt auf die Bewegungsrichtung des Teilchen weißes alpha-stabiles Rauschen. Es werden die mittlere quadratische Verschiebung und der effektive Diffusionskoeffizient bestimmt. Eine überdampfte Beschreibung, gültig für Zeiten groß gegenüber der Relaxationszeit wird hergleitet. Als experimentell zugängliche Meßgröße, welche als Unterscheidungsmerkmal für die unterschiedlichen Rauscharten herangezogen werden kann, wird die Kurtose berechnet. Neben weißem Rauschen wird noch der Fall eines Ornstein-Uhlenbeck Prozesses angetrieben von Cauchy verteiltem Rauschen diskutiert. Während eine normale Diffusion mit zu weißem Rauschen identischem Diffusionskoeffizienten bestimmt wird, kann die beobachtete Verteilung der Verschiebungen Nicht-Gaußförmig sein. Die Zeit für den Übergang zur Gaußverteilung kann deutlich größer als die Zeitskale Relaxationszeit und die Zeitskale des Ornstein-Uhlenbeck Prozesses sein. Eine Grenze der benötigten Zeit wird durch eine Näherung der Kurtosis ermittelt. Weiterhin werden die Grundlagen eines stochastischen Modells für lokale Suche gelegt. Lokale Suche ist die Suche in der näheren Umgebung eines bestimmten Punktes, welcher Haus genannt wird. Abermals diskutieren wir ein aktives Teilchen mit unveränderlichem Absolutbetrag der Geschwindigkeit und weißen alpha-stabilem Rauschen in der Bewegungsrichtungsdynamik. Die deterministische Bewegung des Teilchens wird analysiert bevor die Situation mit Rauschen betrachtet wird. Die stationäre Aufenthaltswahrscheinlichkeitsdichtefunktion wird bestimmt. Es wird eine optimale Rauschstärke für die lokale Suche, das heißt für das Auffinden eines neuen Ortes in kleinstmöglicher Zeit festgestellt. Die kleinstmögliche Zeit wird kaum von der Rauschart abhängen. Wir werden jedoch feststellen, dass die Rauschart deutlichen Einfluß auf die Rückkehrwahrscheinlichkeit zum Haus hat, wenn die Richtung des zu Hauses fehlerbehaftet ist. Weiterhin wird das Model durch eine an das Haus abstandsabhängige Kopplung erweitert werden. Zum Abschluß betrachten wir eine Gruppe von Suchern. / Active Brownian particles described by Langevin equations are used to model the behavior of simple biological organisms or artificial objects that are able to perform self propulsion. In this thesis we discuss active particles with constant speed. In the first part, we consider angular driving by white Levy-stable noise and we discuss the mean squared displacement and diffusion coefficients. We derive an overdamped description for those particles that is valid at time scales larger the relaxation time. In order to provide an experimentally accessible property that distinguishes between the considered noise types, we derive an analytical expression for the kurtosis. Afterwards, we consider an Ornstein-Uhlenbeck process driven by Cauchy noise in the angular dynamics of the particle. While, we find normal diffusion with the diffusion coefficient identical to the white noise case we observe a Non-Gaussian displacement at time scales that can be considerable larger than the relaxation time and the time scale provided by the Ornstein-Uhlenbeck process. In order to provide a limit for the time needed for the transition to a Gaussian displacement, we approximate the kurtosis. Afterwards, we lay the foundation for a stochastic model for local search. Local search is concerned with the neighborhood of a given spot called home. We consider an active particle with constant speed and alpha-stable noise in the dynamics of the direction of motion. The deterministic motion will be discussed before considering the noise to be present. An analytical result for the steady state spatial density will be given. We will find an optimal noise strength for the local search and only a weak dependence on the considered noise types. Several extensions to the introduced model will then be considered. One extension includes a distance dependent coupling towards the home and thus the model becomes more general. Another extension concerned with an erroneous understanding by the particle of the direction of the home leads to the result that the return probability to the home depends on the noise type. Finally we consider a group of searchers.