This work is focused on the workload management of data warehouses based on Teradata technologies using Active System Management architecture. Objectives of this work are to characterize and analyze Active System Management architecture and types of rules, used in the workload management of Teradata data warehouses. These objectives have been achieved by a search of available resources and their subsequent analysis. Informations obtained from the analysis were empirically verified on a particular instance of a data warehouse and their synthesis is presented in this work The contributions of this work are in the documentation of technology that is currently not well known and widespread in the Czech Republic. Another contribution is identification of risks, drawbacks and presentation of recommendations in the workload management using Active System Management based on empirical tests. The repeatable implementation procedure based on induction has been proposed in the work. Maturity of the architecture for a production environment is evaluated. The work is hierarchically divided into several chapters that are dedicated to Teradata database technologies, workload management, Active System Management and implementation procedure. The first three chapters are focused on theory, however, they also contain practical informations related to the processed theory. The latter chapter is focused practically, therein is designed a repeatable Active System Management architecture implementation procedure.

Les alliages à mémoire de forme (AMF) sont des matériaux métalliques qui présentent des propriétés thermomécaniques particulières, et notamment l’effet mémoire de forme. L’étude réalisée durant la thèse concerne la création de systèmes actifs double-sens à l'aide de fils AMF à effet mémoire simple-sens. Trois modèles analogiques simples, représentant trois catégories de solutions constructives, ont été développés. Ces modèles correspondent à des types de couplages mécaniques différents entre un (ou des) fil(s) AMF et une structure mécanique. Par exemple, le modèle le plus simple consiste à utiliser un unique fil AMF couplé à un système mécanique constitué d’une structure monolithique déformable. Lorsque l’on chauffe l’AMF, on active l’effet mémoire de forme, ce qui entraîne une déformation de la structure. Lorsque l’on refroidit l’AMF, la rigidité propre de la structure entraîne une déformation dans le sens inverse à celui de la phase de chauffage. Plusieurs démonstrateurs ont été également construits et analysés durant la thèse. Cette étude montre la possibilité de concevoir des structures actives pilotées par des AMF, ce qui ouvre des perspectives pour le contrôle des déformations ou des contraintes dans des structures. / Shape memory alloys (SMA) are metallic materials that have particular thermomechanical properties, including the shape memory effect. The study carried out during the thesis concerns the creation of two-way active systems using SMA wires exhibiting one-way memory effect. Three simple analog models, representing three classes of constructive solutions, have been developed. These models correspond to different types of mechanical coupling between one (or more) SMA wire(s) and a mechanical structure. For example, the simplest configuration is a single SMA wire coupled to a mechanical system consisting of a deformable monolithic structure. When the SMA is heated, the shape memory effect is activated, which causes the deformation of the structure. When cooling the SMA, the inherent rigidity of the structure causes a deformation in the opposite direction to that of the heating phase. Several demonstrators were also constructed and analyzed during the thesis. This study demonstrates the possibility of designing active structures driven by SMAs, which opens prospects for the control of deformations or stresses in structures.

A human thermoregulation model has been adapted for predicting the thermal response of Typical Older Persons. The model known as the Older Persons Model predicts the core body temperature and regulatory responses of the older people in environmental exposures of cold, warm and hot. The model was developed by modifying an existing dynamic human thermoregulation model using anthropometric and thermo-physical properties of older people. The Model defines the body as two interrelating systems of the body structure (passive system) and the control system of the central nervous system (active system). The Older person's passive system of the model was developed by meticulously extracting relevant experimental data from selected published research works relating to anthropometric and thermo-physical properties of older people. The resultant body structure (passive system) is a multi-segmented representation of a Typical Older Person. The active system (central nervous system) was developed by the application of a novel optimization method based on the working principles of Genetic Algorithms. The use of Genetic Algorithm enables the complex characteristics of the central nervous system of the older persons to be well represented and evaluated based on available data. Active system control signal coefficients for sweating, shivering, vasodilation and vasoconstriction were explicitly derived based on experimental data sourced from literature. The Older Persons Model has been validated using independent experimental data and its results show good agreement with measured data. Furthermore, the Older Persons Model has been applied to several test cases extracted from published literature and its results show good agreement with published findings on the thermal behaviour of older persons. An interview study conducted as part of this research revealed that, professionals (built environment specialists) found the Older Persons Model useful in assisting to further understand the thermal response of the older persons. In conclusion, the adaptation of an existing human thermoregulation model has resulted in a new model, which allows improved prediction of heat and cold strain of the older person although there exist limitations.

Biological cells consist of many subunits that form distinct compartments and work together to allow for life. These compartments are clearly separated from each other and their sizes are often strongly correlated with cell size. Examples for those structures are centrosomes, which we consider in this thesis. Centrosomes are essential for many processes inside cells, most importantly for organizing cell division, and they provide an interesting example of cellular compartments without a membrane. Experiments suggest that such compartments can be described as liquid-like droplets. In this thesis, we suggest a theoretical description of the growth phase of centrosomes. We identify a possible mechanism based on phase separation by which the centrosome may be organized. Specifically, we propose that the centrosome material exists in a soluble and in a phase separating form. Chemical reactions controlling the transitions between these forms then determine the temporal evolution of the system. We investigate various possible reaction schemes and generally find that droplet sizes and nucleation properties deviate from the known equilibrium results. Additionally, the non-equilibrium effects of the chemical reactions can stabilize multiple droplets and thus counteract the destabilizing effect of surface tension. Interestingly, only a reaction scheme with autocatalytic growth can account for the experimental data of centrosomes. Here, it is important that the centrioles found at the center of all centrosomes also catalyze the production of droplet material. This catalytic activity allows the centrioles to control the onset of centrosome growth, to stabilize multiple centrosomes, and to center themselves inside the centrosome. We also investigate a stochastic version of the model, where we find that the autocatalytic growth amplifies noise. Our theory explains the growth dynamics of the centrosomes of the round worm Caenorhabditis elegans for all embryonic cells down to the eight-cell stage. It also accounts for data acquired in experiments with aberrant numbers of centrosomes and altered cell volumes. Furthermore, the model can describe unequal centrosome sizes observed in cells with disturbed centrioles. Our example thus suggests a general picture of the organization of membrane-less organelles. / Biologische Zellen bestehen aus vielen Unterstrukturen, die zusammen arbeiten um Leben zu ermöglichen. Die Größe dieser meist klar voneinander abgegrenzten Strukturen korreliert oft mit der Zellgröße. In der vorliegenden Arbeit werden als Beispiel für solche Strukturen Zentrosomen untersucht. Zentrosomen sind für viele Prozesse innerhalb der Zelle, insbesondere für die Zellteilung, unverzichtbar und sie besitzen keine Membran, welche ihnen eine feste Struktur verleihen könnte. Experimentelle Untersuchungen legen nahe, dass solche membranlose Strukturen als Flüssigkeitstropfen beschrieben werden können. In dieser Arbeit wird eine theoretische Beschreibung der Wachstumsphase von Zentrosomen hergeleitet, welche auf Phasenseparation beruht. Im Modell wird angenommen, dass das Zentrosomenmaterial in einer löslichen und einer phasenseparierenden Form existiert, wobei der Übergang zwischen diesen Formen durch chemische Reaktionen gesteuert wird. Die drei verschiedenen in dieser Arbeit untersuchten Reaktionen führen unter anderem zu Tropfengrößen und Nukleationseigenschaften, welche von den bekannten Ergebnissen im thermodynamischen Gleichgewicht abweichen. Insbesondere verursachen die chemischen Reaktionen ein thermisches Nichtgleichgewicht, in dem mehrere Tropfen stabil sein können und der destabilisierende Effekt der Oberflächenspannung unterdrückt wird. Konkret kann die Wachstumsdynamik der Zentrosomen nur durch eine selbstverstärkende Produktion der phasenseparierenden Form des Zentrosomenmaterials erklärt werden. Hierbei ist zusätzlich wichtig, dass die Zentriolen, die im Inneren jedes Zentrosoms vorhanden sind, ebenfalls diese Produktion katalysieren. Dadurch können die Zentriolen den Beginn des Zentrosomwachstums kontrollieren, mehrere Zentrosomen stabilisieren und sich selbst im Zentrosom zentrieren. Des Weiteren führt das selbstverstärkende Wachstum zu einer Verstärkung von Fluktuationen der Zentrosomgröße. Unsere Theorie erklärt die Wachstumsdynamik der Zentrosomen des Fadenwurms Caenorhabditis elegans für alle Embryonalzellen bis zum Achtzellstadium und deckt dabei auch Fälle mit anormaler Zentrosomenanzahl und veränderter Zellgröße ab. Das Modell kann auch Situationen mit unterschiedlich großen Zentrosomen erklären, welche auftreten, wenn die Struktur der Zentriolen verändert wird. Unser Beispiel beschreibt damit eine generelle Möglichkeit, wie membranlose Zellstrukturen organisiert sein können.

This thesis has been concerned with a few problems in systems driven at the scale of particles. The problems dealt with here can be extended and elaborated upon in a variety of ways. In 2 we examine the dynamics of a fluid membrane in contact with a fluid containing active particles. In particular, we show that such a membrane generically enters a statistical steady state with wave-like dispersion. While the numerical results are satisfying, a one-step coarse-graining calculation, in line with [66,93], will, we expect, yield a pair of coupled stochastic differential equations (probably KPZ like at least in one dimension) with wave-like dispersion. This calculation in of interest from a theoretical point-of-view. Further, the numerical exploration of the full set of equations is also left for future work, but can be relevant to many biological systems. In 3 we show that an active fluid confined in an annular channel starts to rotate spontaneously. Further, we predict the existence of banded concentration profile. Such profiles have not yet been observed in experiments. Further, it will be interesting to study what happens to our conclusions if we include the effect of treadmilling in our calculation. In 4 we describe a solid driven by active particles. Specifically, we only concern ourselves with the polar elastomeric phase of the material. However, the questions regarding the transition into that phase are interesting and have not been explored. How exactly does a polarisation transition happen in an active polar elastomer? Is it the same as in an active nematic elastomer? What is the nature of the gelation transition in an active polar fluid? What is the dynamics of nematic defects in an elastomer? Can the presence of the elastomer prevent defect separation? We are at present trying to answer these questions. In 5 we examine the dynamics of an active fluid confined in a channel. It will be interesting to test the prediction about fluctuations in a confined active system, which we show will be normal, in experiments on highly confined actomyosin systems. In 6 we write down the coupled equations of a conformation tensor and the apolar order parameter. This is a generic framework for studying viscoelastic active fluids. A fuller study of the effect of increasing the cross-linker density in such system remains to be done, both theoretically and experimentally. In general, we have shown in the thesis that the understanding of active systems can provide a mechanistic explanation of various biological observations. However, at times the comparison between theory and biological experiments become complicated due to the inherently complicated nature of the experimental systems. Thus, for a more rigorous experimental test of the theory, it is necessary to construct cleaner reconstituted systems with possibly as few as three components. Efforts in this direction have recently borne fruit [129]. However, a complete theoretical understanding of the rich behaviour evinced in these systems is as yet lacking. We expect that the conformation tensor theory we developed in chapter 6 will provide an explanation for the anomalous rheological behaviour observed in these systems. Even in the theoretical front, lot of questions remain to be answered. The dry polar active system, described by the Toner-Tu equations have been shown to undergo a transition to a state with LRO. However, though mean-field theory predicts a second order transition [151, 152, 156], detailed numerical analysis suggests that it is actually first-order with pre-transitional solitonic bands. This has been recently examined by Chate et al. [26] who mapped it to a dynamical system, but a complete theory is still lacking. Apolar systems present another set of challenges. First, the concentration coupling with the order parameter should create similar pre-transitional effects at the order-disorder transition for this system also. This has been studied to a certain extent [133]. However, the more interesting question concerns the role of defects in apolar systems and whether they allow for the possibility of even QLRO in two dimensions. The +1/2 nematic defect has a polarity, and can thus move balistically [51, 108, 115, 149] in a dry system. However, the −1/2 defect has a three-fold symmetry [27] and its motion is thus purely diffusive. Now consider a pair of +1/2 and −1/2 defect pair that can form due to noise in the system (since it does not violate charge conservation). Depending on the configuration and the kind of activity, this defect pair can unbind at zero temperature. Unbound defects would imply that the order is short-ranged. However, it appears from detailed simulations of an agent based Vicsek-like model of active nematics, that there exists a QLRO nematic in two dimensions [111]! How does an active nematic escape being destroyed by defect unbinding? Does concentration have a major role to play? If so, does making the concentration a non-conserved, and thus fast, variable by, for example, including evaporation-deposition rules in the model studied by Chate et al. [28] destroy the QLRO? Also, does the hydrodynamic theory for Malthusian (i.e. one in which the concentration relaxes fast to a steady value) nematics show only short-ranged order, while the one in which mass is conserved show QLRO? These questions are being studied at present by simulating both the agent-based model due to Chate with evaporation-deposition and the dynamical equation for the active nematic order-parameter. These studies should clarify the role of concentration in assisting apolar order. It must be borne in mind, however, that numerical simulations of active models are more difficult than their passive counterparts due to the larger number of parameters present in the problem. In passive systems Onsager symmetry relations constrain some parameters. However, the absence of an equivalent rule for systems far away from equilibrium implies that the spatial symmetry allowed couplings will all have independent kinetic coefficients. This increases the size of the parameter space in many problems. Also, many techniques like Monte Carlo have to be carefully modified to suit such systems. A new and exciting area of research from the point of view of statistical mechanics of active systems is an examination of collective behaviour of run-and-tumble particles pioneered by Tailleur and Cates [25]. This has led to fruitful active generalisations of models of dynamic critical phenomena like model B and model H. Also, it has led to an exploration of rules for selecting a state in a region of phase coexistence – an out of equilibrium generalisation of the Maxwell construction. Another interesting avenue is building up active matter equations from microscopics. This has been done for Vicsek model by Thomas Ihle [64,65], for a simple generalisation of Vicsek-type model for both polar and apolar alignment interactions by Bertin et al. and Chate et al. [15, 16, 107], and for a model of hard rods by Marchetti et al. [10, 11]. The issues of closure still remain to be fully resolved however in deriving the macroscopic equations. A particularly exciting new system that has been recently studied extensively is a collection of chemotactic Janus particles [127]. The far-field interaction in this case does not promote polar order but state with proliferation of asters. The coarse-grained hydrodynamic equations have been derived in this case starting from a microscopic picture of colloids coated axisymetrically with a catalyst in an inhomogeneous concentration of reactants by Saha et al. [127]. Another theoretical issue that plagues the derivation of hydrodynamic equations is that of noise. So far most theories have modelled the noise as Gaussian and white, akin to equilibrium systems, but with unknown strength. However, it is likely that the noise also depends on activity, thus requiring a microscopic picture treating the active forces as stochastic quantities. It is known that multiplicative character of the noise induces interesting features at least in the case of active nematics [104]. Thus, a lot of questions need to be answered if theories of active matter have to graduate from merely offering qualitative explanations of biological experiments to becoming the prototypical theory of systems in which energy input and dissipation both occur at a scale smaller than the coarse-graining volume.

Biological cells consist of many subunits that form distinct compartments and work together to allow for life. These compartments are clearly separated from each other and their sizes are often strongly correlated with cell size. Examples for those structures are centrosomes, which we consider in this thesis. Centrosomes are essential for many processes inside cells, most importantly for organizing cell division, and they provide an interesting example of cellular compartments without a membrane. Experiments suggest that such compartments can be described as liquid-like droplets. In this thesis, we suggest a theoretical description of the growth phase of centrosomes. We identify a possible mechanism based on phase separation by which the centrosome may be organized. Specifically, we propose that the centrosome material exists in a soluble and in a phase separating form. Chemical reactions controlling the transitions between these forms then determine the temporal evolution of the system. We investigate various possible reaction schemes and generally find that droplet sizes and nucleation properties deviate from the known equilibrium results. Additionally, the non-equilibrium effects of the chemical reactions can stabilize multiple droplets and thus counteract the destabilizing effect of surface tension. Interestingly, only a reaction scheme with autocatalytic growth can account for the experimental data of centrosomes. Here, it is important that the centrioles found at the center of all centrosomes also catalyze the production of droplet material. This catalytic activity allows the centrioles to control the onset of centrosome growth, to stabilize multiple centrosomes, and to center themselves inside the centrosome. We also investigate a stochastic version of the model, where we find that the autocatalytic growth amplifies noise. Our theory explains the growth dynamics of the centrosomes of the round worm Caenorhabditis elegans for all embryonic cells down to the eight-cell stage. It also accounts for data acquired in experiments with aberrant numbers of centrosomes and altered cell volumes. Furthermore, the model can describe unequal centrosome sizes observed in cells with disturbed centrioles. Our example thus suggests a general picture of the organization of membrane-less organelles.:1 Introduction 1.1 Organization of the cell interior 1.2 Biology of centrosomes 1.2.1 The model organism Caenorhabditis elegans 1.2.2 Cellular functions of centrosomes 1.2.3 The centriole pair is the core structure of a centrosome 1.2.4 Pericentriolar material accumulates around the centrioles 1.3 Other membrane-less organelles and their organization 1.4 Phase separation as an organization principle 1.5 Equilibrium physics of liquid-liquid phase separation 1.5.1 Spinodal decomposition and droplet formation 1.5.2 Formation of a single droplet 1.5.3 Ostwald ripening destabilizes multiple droplets 1.6 Non-equilibrium phase separation caused by chemical reactions 1.7 Overview of this thesis 2 Physical Description of Centrosomes as Active Droplets 2.1 Physical description of centrosomes as liquid-like droplets 2.1.1 Pericentriolar material as a complex fluid 2.1.2 Reaction-diffusion kinetics of the components 2.1.3 Centrioles described as catalytic active cores 2.1.4 Droplet formation and growth kinetics 2.1.5 Complete set of the dynamical equations 2.2 Three simple growth scenarios 2.2.1 Scenario A: First-order kinetics 2.2.2 Scenario B: Autocatalytic growth 2.2.3 Scenario C: Incorporation at the centrioles 2.3 Diffusion-limited droplet growth 2.4 Discussion 3 Isolated Active Droplets 3.1 Compositional fluxes in the stationary state 3.2 Critical droplet size: Instability of small droplets 3.3 Droplet nucleation facilitated by the active core 3.4 Interplay of critical droplet size and nucleation 3.5 Perturbations of the spherical droplet shape 3.5.1 Linear stability analysis of the spherical droplet shape 3.5.2 Active cores can center themselves in droplets 3.5.3 Surface tension stabilizes the spherical shape 3.5.4 First-order kinetics destabilize large droplets 3.6 Discussion 4 Multiple Interacting Active Droplets 4.1 Approximate description of multiple droplets 4.2 Linear stability analysis of the symmetric state 4.3 Late stage droplet dynamics and Ostwald ripening 4.4 Active droplets can suppress Ostwald ripening 4.4.1 Perturbation growth rate in the simple growth scenarios 4.4.2 Parameter dependence of the stability of multiple droplets 4.4.3 Stability of more than two droplets 4.5 Discussion 5 Active Droplets with Fluctuations 5.1 Stochastic version of the active droplet model 5.1.1 Comparison with the deterministic model 5.1.2 Ensemble statistics and ergodicity 5.1.3 Quantification of fluctuations by the standard deviation 5.2 Noise amplification by the autocatalytic reaction 5.3 Transient growth regime of multiple droplets 5.4 Influence of the system geometry on the droplet growth 5.5 Discussion 6 Comparison Between Theory and Experiment 6.1 Summary of the experimental observations 6.2 Estimation of key model parameters 6.3 Fits to experimental data 6.4 Dependence of centrosome size on cell volume and centrosome count 6.5 Nucleation and stability of centrosomes 6.6 Multiple centrosomes with unequal sizes 6.7 Disintegration phase of centrosomes 7 Summary and Outlook Appendix A Coexistence conditions in a ternary fluid B Instability of multiple equilibrium droplets C Numerical solution of the droplet growth D Diffusion-limited growth of a single droplet E Approximate efflux of droplet material F Determining stationary states of single droplets G Droplet size including surface tension effects H Distortions of the spherical droplet shape H.1 Harmonic distortions of a sphere H.2 Physical description of the perturbed droplet H.3 Volume fraction profiles in the perturbed droplet H.4 Perturbation growth rates I Multiple droplets with gradients inside droplets J Numerical stability analysis of multiple droplets K Numerical implementation of the stochastic model / Biologische Zellen bestehen aus vielen Unterstrukturen, die zusammen arbeiten um Leben zu ermöglichen. Die Größe dieser meist klar voneinander abgegrenzten Strukturen korreliert oft mit der Zellgröße. In der vorliegenden Arbeit werden als Beispiel für solche Strukturen Zentrosomen untersucht. Zentrosomen sind für viele Prozesse innerhalb der Zelle, insbesondere für die Zellteilung, unverzichtbar und sie besitzen keine Membran, welche ihnen eine feste Struktur verleihen könnte. Experimentelle Untersuchungen legen nahe, dass solche membranlose Strukturen als Flüssigkeitstropfen beschrieben werden können. In dieser Arbeit wird eine theoretische Beschreibung der Wachstumsphase von Zentrosomen hergeleitet, welche auf Phasenseparation beruht. Im Modell wird angenommen, dass das Zentrosomenmaterial in einer löslichen und einer phasenseparierenden Form existiert, wobei der Übergang zwischen diesen Formen durch chemische Reaktionen gesteuert wird. Die drei verschiedenen in dieser Arbeit untersuchten Reaktionen führen unter anderem zu Tropfengrößen und Nukleationseigenschaften, welche von den bekannten Ergebnissen im thermodynamischen Gleichgewicht abweichen. Insbesondere verursachen die chemischen Reaktionen ein thermisches Nichtgleichgewicht, in dem mehrere Tropfen stabil sein können und der destabilisierende Effekt der Oberflächenspannung unterdrückt wird. Konkret kann die Wachstumsdynamik der Zentrosomen nur durch eine selbstverstärkende Produktion der phasenseparierenden Form des Zentrosomenmaterials erklärt werden. Hierbei ist zusätzlich wichtig, dass die Zentriolen, die im Inneren jedes Zentrosoms vorhanden sind, ebenfalls diese Produktion katalysieren. Dadurch können die Zentriolen den Beginn des Zentrosomwachstums kontrollieren, mehrere Zentrosomen stabilisieren und sich selbst im Zentrosom zentrieren. Des Weiteren führt das selbstverstärkende Wachstum zu einer Verstärkung von Fluktuationen der Zentrosomgröße. Unsere Theorie erklärt die Wachstumsdynamik der Zentrosomen des Fadenwurms Caenorhabditis elegans für alle Embryonalzellen bis zum Achtzellstadium und deckt dabei auch Fälle mit anormaler Zentrosomenanzahl und veränderter Zellgröße ab. Das Modell kann auch Situationen mit unterschiedlich großen Zentrosomen erklären, welche auftreten, wenn die Struktur der Zentriolen verändert wird. Unser Beispiel beschreibt damit eine generelle Möglichkeit, wie membranlose Zellstrukturen organisiert sein können.:1 Introduction 1.1 Organization of the cell interior 1.2 Biology of centrosomes 1.2.1 The model organism Caenorhabditis elegans 1.2.2 Cellular functions of centrosomes 1.2.3 The centriole pair is the core structure of a centrosome 1.2.4 Pericentriolar material accumulates around the centrioles 1.3 Other membrane-less organelles and their organization 1.4 Phase separation as an organization principle 1.5 Equilibrium physics of liquid-liquid phase separation 1.5.1 Spinodal decomposition and droplet formation 1.5.2 Formation of a single droplet 1.5.3 Ostwald ripening destabilizes multiple droplets 1.6 Non-equilibrium phase separation caused by chemical reactions 1.7 Overview of this thesis 2 Physical Description of Centrosomes as Active Droplets 2.1 Physical description of centrosomes as liquid-like droplets 2.1.1 Pericentriolar material as a complex fluid 2.1.2 Reaction-diffusion kinetics of the components 2.1.3 Centrioles described as catalytic active cores 2.1.4 Droplet formation and growth kinetics 2.1.5 Complete set of the dynamical equations 2.2 Three simple growth scenarios 2.2.1 Scenario A: First-order kinetics 2.2.2 Scenario B: Autocatalytic growth 2.2.3 Scenario C: Incorporation at the centrioles 2.3 Diffusion-limited droplet growth 2.4 Discussion 3 Isolated Active Droplets 3.1 Compositional fluxes in the stationary state 3.2 Critical droplet size: Instability of small droplets 3.3 Droplet nucleation facilitated by the active core 3.4 Interplay of critical droplet size and nucleation 3.5 Perturbations of the spherical droplet shape 3.5.1 Linear stability analysis of the spherical droplet shape 3.5.2 Active cores can center themselves in droplets 3.5.3 Surface tension stabilizes the spherical shape 3.5.4 First-order kinetics destabilize large droplets 3.6 Discussion 4 Multiple Interacting Active Droplets 4.1 Approximate description of multiple droplets 4.2 Linear stability analysis of the symmetric state 4.3 Late stage droplet dynamics and Ostwald ripening 4.4 Active droplets can suppress Ostwald ripening 4.4.1 Perturbation growth rate in the simple growth scenarios 4.4.2 Parameter dependence of the stability of multiple droplets 4.4.3 Stability of more than two droplets 4.5 Discussion 5 Active Droplets with Fluctuations 5.1 Stochastic version of the active droplet model 5.1.1 Comparison with the deterministic model 5.1.2 Ensemble statistics and ergodicity 5.1.3 Quantification of fluctuations by the standard deviation 5.2 Noise amplification by the autocatalytic reaction 5.3 Transient growth regime of multiple droplets 5.4 Influence of the system geometry on the droplet growth 5.5 Discussion 6 Comparison Between Theory and Experiment 6.1 Summary of the experimental observations 6.2 Estimation of key model parameters 6.3 Fits to experimental data 6.4 Dependence of centrosome size on cell volume and centrosome count 6.5 Nucleation and stability of centrosomes 6.6 Multiple centrosomes with unequal sizes 6.7 Disintegration phase of centrosomes 7 Summary and Outlook Appendix A Coexistence conditions in a ternary fluid B Instability of multiple equilibrium droplets C Numerical solution of the droplet growth D Diffusion-limited growth of a single droplet E Approximate efflux of droplet material F Determining stationary states of single droplets G Droplet size including surface tension effects H Distortions of the spherical droplet shape H.1 Harmonic distortions of a sphere H.2 Physical description of the perturbed droplet H.3 Volume fraction profiles in the perturbed droplet H.4 Perturbation growth rates I Multiple droplets with gradients inside droplets J Numerical stability analysis of multiple droplets K Numerical implementation of the stochastic model

This diploma thesis deals with adjusting the reverberation time of enclosed spaces. It is divided into two thematic areas. The first thematic area deals with active systems that adjust the reverberation time, with a stronger focus on usage of reverberators to simulate secondary spaces. The second thematic area is the implementation of reverberators and their fundamental building blocks in Matlab.