Understanding the fundamentals of composting science from a pragmatic perspective of necessity involves mixtures of different sizes and types of particles in constantly changing environmental conditions, in particular temperature. The complexity of composting is affected by this environmental variation. With so much "noise" in the system, a question arises as to the need to understand the detail of this complexity as understanding any part of composting with more precision than this level of noise is not likely to result in greater understanding of the system. Yet some compost piles generate offensive odours while others don‟t and science should be able to explain this difference. A driver for this research was greater understanding of potential odour, which is assumed to arise from the anaerobic core of a composting particle. It follows that the size of this anaerobic core could be used as an indicator of odour potential. A first step in this understanding is the need to determine which parts of a composting particle are aerobic, from which the anaerobic proportion can be determined by difference. To this end, this thesis uses a finite volume method of analysis to determine the distribution of oxygen at sub-particle scales. Diffusion laws were used to determine the thickness of each finite volume. The resulting model, called micro-environment analysis, was applied to a composting particle to enable determination of onion ring type volumes of compost (called micro-environments) containing substrates (further subdivided into substrate fractions) whose concentrations could be determined to high precision by the application of first-order degradation kinetics to each of these finite volumes. Determination of the oxygen concentration at a micro-environment's inner boundary was achieved by using the Stępniewski equation. The Stępniewski model was derived originally for application to soil aeration and enables each micro-environment to have its own oxygen uptake rate and diffusion coefficient. This first version of micro-environment analysis was derived from the simpler solution to diffusion laws, based on the assumption of non-diffusible substrate. It was tested against three sets of experimental data with two different substrates: Particle size trials using dog sausage as substrate – where the peak composting rate was successfully predicted, as a function of particle size. Temperature trials using pig faeces and a range of particle sizes – the results showed the potential of micro-environment analysis to identify intriguing temperature effects, in particular, a different temperature effect (Q10) and fraction proportion was indicated for each substrate fraction. Smaller particle sizes, and possibly outward diffusion of substrate confounded a clear experimental signal. Diffusion into a pile trials which showed that the time course of particles deeper in the pile could be predicted by the physics of oxygen distribution. A fully computed prediction would need an added level of computational complexity in micro-environment analysis, arising from there being two intertwined phases, gas phase and substrate (particle) phase. Each phase needs its own micro-environment calculations which can not be done in isolation from each other. Unexplainable parts of the composting time course are likely to be partly explained by the outward diffusion of substrate towards the inward-moving oxygen front. Although the possibility of alternative electron acceptors can not be discounted as a partial explanation. To test the theory, a new experimental reactor was developed using calorimetry. With an absolute sensitivity of 0.132 J hr-1 L-1 and a measurement frequency of 30 minutes, the reactor was able to detect the energy required to humidify the input air, and "see" when composting begins to decline as oxygen is consumed. Optimisation of the aeration pumping frequency using the evidence from the data was strikingly apparent immediately after setting the optimum frequency. Micro-environment analysis provides a framework by which several physical effects can be incorporated into compost science.

Reservoir testing and analysis are fundamental tools in understanding reservoir hydraulics and hence forecasting reservoir responses. The quality of the analysis is very dependent on the conceptual model used in investigating the responses under different flowing conditions. The use of reservoir testing in the characterization and derivation of reservoir parameters is widely established, especially in conventional oil and gas reservoirs. However, with depleting conventional reserves, the quest for unconventional reservoirs to secure the increasing demand for energy is increasing; which has triggered intensive research in the fields of reservoir characterization. Gas hydrate reservoirs, being one of the unconventional gas reservoirs with huge energy potential, is still in the juvenile stage with reservoir testing as compared to the other unconventional reservoirs. The endothermic dissociation hydrates to gas and water requires addressing multiphase flow and heat energy balance, which has made efforts to develop reservoir testing models in this field difficult. As of now, analytically quantifying the effect on hydrate dissociation on rate and pressure transient responses are till date a huge challenge. During depressurization, the heat energy stored in the reservoir is used up and due to the endothermic nature of the dissociation; heat flux begins from the confining layers. For Class 3 gas hydrates, just heat conduction would be responsible for the heat influx and further hydrate dissociation; however, the moving boundary problem could also be an issue to address in this reservoir, depending on the equilibrium pressure. To address heat flux problem, a proper definition of the inner boundary condition for temperature propagation using a Clausius-Clapeyron type hydrate equilibrium model is required. In Class 1 and 2, crossflow problems would occur and depending on the layer of production, convective heat influx from the free fluid layer and heat conduction from the cap rock of the hydrate layer would be further issues to address. All these phenomena make the derivation of a suitable reservoir testing model very complex. However, with a strong combination of heat energy and mass balance techniques, a representative diffusivity equation can be derived. Reservoir testing models have been developed and responses investigated for different boundary conditions in normally pressured Class 3 gas hydrates, over-pressured Class 3 gas hydrates (moving boundary problem) and Class 1 and 2 gas hydrates (crossflow problem). The effects of heat flux on the reservoir responses have been addressed in detail.

Reservoir testing and analysis are fundamental tools in understanding reservoir hydraulics and hence forecasting reservoir responses. The quality of the analysis is very dependent on the conceptual model used in investigating the responses under different flowing conditions. The use of reservoir testing in the characterization and derivation of reservoir parameters is widely established, especially in conventional oil and gas reservoirs. However, with depleting conventional reserves, the quest for unconventional reservoirs to secure the increasing demand for energy is increasing; which has triggered intensive research in the fields of reservoir characterization. Gas hydrate reservoirs, being one of the unconventional gas reservoirs with huge energy potential, is still in the juvenile stage with reservoir testing as compared to the other unconventional reservoirs. The endothermic dissociation hydrates to gas and water requires addressing multiphase flow and heat energy balance, which has made efforts to develop reservoir testing models in this field difficult. As of now, analytically quantifying the effect on hydrate dissociation on rate and pressure transient responses are till date a huge challenge. During depressurization, the heat energy stored in the reservoir is used up and due to the endothermic nature of the dissociation; heat flux begins from the confining layers. For Class 3 gas hydrates, just heat conduction would be responsible for the heat influx and further hydrate dissociation; however, the moving boundary problem could also be an issue to address in this reservoir, depending on the equilibrium pressure. To address heat flux problem, a proper definition of the inner boundary condition for temperature propagation using a Clausius-Clapeyron type hydrate equilibrium model is required. In Class 1 and 2, crossflow problems would occur and depending on the layer of production, convective heat influx from the free fluid layer and heat conduction from the cap rock of the hydrate layer would be further issues to address. All these phenomena make the derivation of a suitable reservoir testing model very complex. However, with a strong combination of heat energy and mass balance techniques, a representative diffusivity equation can be derived. Reservoir testing models have been developed and responses investigated for different boundary conditions in normally pressured Class 3 gas hydrates, over-pressured Class 3 gas hydrates (moving boundary problem) and Class 1 and 2 gas hydrates (crossflow problem). The effects of heat flux on the reservoir responses have been addressed in detail.

No description available.

In this thesis, we study mathematical models that describe the morphology of a generalized biological cell in equilibrium or under the influence of external forces. Within these models, the cell is considered as a thermodynamic system, where streaming effects in the cell bulk and the surrounding are coupled with a Helfrich-type model for the cell membrane. The governing evolution equations for the cell given in a continuum formulation are derived using an energy variation approach. Such two-phase flow problems that combine streaming effects with a free boundary problem that accounts for bending and surface tension can be described effectively by a diffuse interface approach. An advantage of the diffuse interface approach is that models for e.g. different biophysical processes can easily be combined. That makes this method suitable to describe complex phenomena such as cell motility and multi-cell dynamics. Within the first model for cell motility, we combine a biological network for GTPases with the hydrodynamic Helfrich-type model. This model allows to account for cell motility driven by membrane protrusion as a result of actin polymerization. Within the second model, we moreover extend the Helfrich-type model by an active gel theory to account for the actin filaments in the cell bulk. Caused by contractile stress within the actin-myosin solution, a spontaneous symmetry breaking event occurs that lead to cell motility. In this thesis, we further study the dynamics of multiple cells which is of wide interest since it reveals rich non-linear behavior. To apply the diffuse interface framework, we introduce several phase field variables to account for several cells that are coupled by a local interaction potential. In a first application, we study white blood cell margination, a biological phenomenon that results from the complex relation between collisions, different mechanical properties and lift forces of red blood cells and white blood cells within the vascular system. Here, it is shown that inertial effects, which can become of relevance in various parts of the cardiovascular system, lead to a decreasing tendency for margination with increasing Reynolds number. Finally, we combine the active polar gel theory and the multi-cell approach that is capable of studying collective migration of cells. This hydrodynamic approach predicts that collective migration emerges spontaneously forming coherently-moving clusters as a result of the mutual alignment of the velocity vectors during inelastic collisions. We further observe that hydrodynamics heavily influence those systems. However, a complete suppression of the onset of collective migration cannot be confirmed. Moreover, we give a brief insight how such highly coupled systems can be treated numerically using finite elements and how the numerical costs can be limited using operator splitting approaches and problem parallelization with OPENMP. / Diese Dissertation beschäftigt sich mit mathematischen Modellen zur Beschreibung von Gleichgewichts- und dynamischen Zuständen von verallgemeinerten biologischen Zellen. Die Zellen werden dabei als thermodynamisches System aufgefasst, bei dem Strömungseffekte innerhalb und außerhalb der Zelle zusammen mit einem Helfrich-Modell für Zellmembranen kombiniert werden. Schließlich werden durch einen Energie-Variations-Ansatz die Evolutionsgleichungen für die Zelle hergeleitet. Es ergeben sie dabei Mehrphasen-Systeme, die Strömungseffekte mit einem freien Randwertproblem, das zusätzlich physikalischen Einflüssen wie Biegung und Oberflächenspannung unterliegt, vereinen. Um solche Probleme effizient zu lösen, wird in dieser Arbeit die Diffuse-Interface-Methode verwendet. Ein Vorteil dieser Methode ist, dass es sehr einfach möglich ist, Modelle, die verschiedenste Prozesse beschreiben, miteinander zu vereinen. Dies erlaubt es, komplexe biologische Phänomene, wie zum Beispiel Zellmotilität oder auch die kollektive Bewegung von Zellen, zu beschreiben. In den Modellen für Zellmotilität wird ein biologisches Netzwerk-Modell für GTPasen oder auch ein Active-Polar-Gel-Modell, das die Aktinfilamente im Inneren der Zellen als Flüssigkristall auffasst, mit dem Multi-Phasen-Modell kombiniert. Beide Modelle erlauben es, komplexe Vorgänge bei der selbst hervorgerufenen Bewegung von Zellen, wie das Vorantreiben der Zellmembran durch Aktinpolymerisierung oder auch die Kontraktionsbewegung des Zellkörpers durch kontraktile Spannungen innerhalb des Zytoskelets der Zelle, zu verstehen. Weiterhin ist die kollektive Bewegung von vielen Zellen von großem Interesse, da sich hier viele nichtlineare Phänomene zeigen. Um das Diffuse-Interface-Modell für eine Zelle auf die Beschreibung mehrerer Zellen zu übertragen, werden mehrere Phasenfelder eingeführt, die die Zellen jeweils kennzeichnen. Schließlich werden die Zellen durch ein lokales Abstoßungspotential gekoppelt. Das Modell wird angewendet, um White blood cell margination, das die Annäherung von Leukozyten an die Blutgefäßwand bezeichnet, zu verstehen. Dieser Prozess wird dabei bestimmt durch den komplexen Zusammenhang zwischen Kollisionen, den jeweiligen mechanischen Eigenschaften der Zellen, sowie deren Auftriebskraft innerhalb der Adern. Die Simulationen zeigen, dass diese Annäherung sich in bestimmten Gebieten des kardiovaskulären Systems stark vermindert, in denen die Blutströmung das Stokes-Regime verlässt. Schließlich wird das Active-Polar-Gel-Modell mit dem Modell für die kollektive Bewegung vom Zellen kombiniert. Dies macht es möglich, die kollektive Bewegung der Zellen und den Einfluss von Hydrodynamik auf diese Bewegung zu untersuchen. Es zeigt sich dabei, dass der Zustand der kollektiven gerichteten Bewegung sich spontan aus der Neuausrichtung der jeweiligen Zellen durch inelastische Kollisionen ergibt. Obwohl die Hydrodynamik einen großen Einfluss auf solche Systeme hat, deuten die Simulationen nicht daraufhin, dass Hydrodynamik die kollektive Bewegung vollständig unterdrückt. Weiterhin wird in dieser Arbeit gezeigt, wie die stark gekoppelten Systeme numerisch gelöst werden können mit Hilfe der Finiten-Elemente-Methode und wie die Effizienz der Methode gesteigert werden kann durch die Anwendung von Operator-Splitting-Techniken und Problemparallelisierung mittels OPENMP.

In this thesis, we study mathematical models that describe the morphology of a generalized biological cell in equilibrium or under the influence of external forces. Within these models, the cell is considered as a thermodynamic system, where streaming effects in the cell bulk and the surrounding are coupled with a Helfrich-type model for the cell membrane. The governing evolution equations for the cell given in a continuum formulation are derived using an energy variation approach. Such two-phase flow problems that combine streaming effects with a free boundary problem that accounts for bending and surface tension can be described effectively by a diffuse interface approach. An advantage of the diffuse interface approach is that models for e.g. different biophysical processes can easily be combined. That makes this method suitable to describe complex phenomena such as cell motility and multi-cell dynamics. Within the first model for cell motility, we combine a biological network for GTPases with the hydrodynamic Helfrich-type model. This model allows to account for cell motility driven by membrane protrusion as a result of actin polymerization. Within the second model, we moreover extend the Helfrich-type model by an active gel theory to account for the actin filaments in the cell bulk. Caused by contractile stress within the actin-myosin solution, a spontaneous symmetry breaking event occurs that lead to cell motility. In this thesis, we further study the dynamics of multiple cells which is of wide interest since it reveals rich non-linear behavior. To apply the diffuse interface framework, we introduce several phase field variables to account for several cells that are coupled by a local interaction potential. In a first application, we study white blood cell margination, a biological phenomenon that results from the complex relation between collisions, different mechanical properties and lift forces of red blood cells and white blood cells within the vascular system. Here, it is shown that inertial effects, which can become of relevance in various parts of the cardiovascular system, lead to a decreasing tendency for margination with increasing Reynolds number. Finally, we combine the active polar gel theory and the multi-cell approach that is capable of studying collective migration of cells. This hydrodynamic approach predicts that collective migration emerges spontaneously forming coherently-moving clusters as a result of the mutual alignment of the velocity vectors during inelastic collisions. We further observe that hydrodynamics heavily influence those systems. However, a complete suppression of the onset of collective migration cannot be confirmed. Moreover, we give a brief insight how such highly coupled systems can be treated numerically using finite elements and how the numerical costs can be limited using operator splitting approaches and problem parallelization with OPENMP. / Diese Dissertation beschäftigt sich mit mathematischen Modellen zur Beschreibung von Gleichgewichts- und dynamischen Zuständen von verallgemeinerten biologischen Zellen. Die Zellen werden dabei als thermodynamisches System aufgefasst, bei dem Strömungseffekte innerhalb und außerhalb der Zelle zusammen mit einem Helfrich-Modell für Zellmembranen kombiniert werden. Schließlich werden durch einen Energie-Variations-Ansatz die Evolutionsgleichungen für die Zelle hergeleitet. Es ergeben sie dabei Mehrphasen-Systeme, die Strömungseffekte mit einem freien Randwertproblem, das zusätzlich physikalischen Einflüssen wie Biegung und Oberflächenspannung unterliegt, vereinen. Um solche Probleme effizient zu lösen, wird in dieser Arbeit die Diffuse-Interface-Methode verwendet. Ein Vorteil dieser Methode ist, dass es sehr einfach möglich ist, Modelle, die verschiedenste Prozesse beschreiben, miteinander zu vereinen. Dies erlaubt es, komplexe biologische Phänomene, wie zum Beispiel Zellmotilität oder auch die kollektive Bewegung von Zellen, zu beschreiben. In den Modellen für Zellmotilität wird ein biologisches Netzwerk-Modell für GTPasen oder auch ein Active-Polar-Gel-Modell, das die Aktinfilamente im Inneren der Zellen als Flüssigkristall auffasst, mit dem Multi-Phasen-Modell kombiniert. Beide Modelle erlauben es, komplexe Vorgänge bei der selbst hervorgerufenen Bewegung von Zellen, wie das Vorantreiben der Zellmembran durch Aktinpolymerisierung oder auch die Kontraktionsbewegung des Zellkörpers durch kontraktile Spannungen innerhalb des Zytoskelets der Zelle, zu verstehen. Weiterhin ist die kollektive Bewegung von vielen Zellen von großem Interesse, da sich hier viele nichtlineare Phänomene zeigen. Um das Diffuse-Interface-Modell für eine Zelle auf die Beschreibung mehrerer Zellen zu übertragen, werden mehrere Phasenfelder eingeführt, die die Zellen jeweils kennzeichnen. Schließlich werden die Zellen durch ein lokales Abstoßungspotential gekoppelt. Das Modell wird angewendet, um White blood cell margination, das die Annäherung von Leukozyten an die Blutgefäßwand bezeichnet, zu verstehen. Dieser Prozess wird dabei bestimmt durch den komplexen Zusammenhang zwischen Kollisionen, den jeweiligen mechanischen Eigenschaften der Zellen, sowie deren Auftriebskraft innerhalb der Adern. Die Simulationen zeigen, dass diese Annäherung sich in bestimmten Gebieten des kardiovaskulären Systems stark vermindert, in denen die Blutströmung das Stokes-Regime verlässt. Schließlich wird das Active-Polar-Gel-Modell mit dem Modell für die kollektive Bewegung vom Zellen kombiniert. Dies macht es möglich, die kollektive Bewegung der Zellen und den Einfluss von Hydrodynamik auf diese Bewegung zu untersuchen. Es zeigt sich dabei, dass der Zustand der kollektiven gerichteten Bewegung sich spontan aus der Neuausrichtung der jeweiligen Zellen durch inelastische Kollisionen ergibt. Obwohl die Hydrodynamik einen großen Einfluss auf solche Systeme hat, deuten die Simulationen nicht daraufhin, dass Hydrodynamik die kollektive Bewegung vollständig unterdrückt. Weiterhin wird in dieser Arbeit gezeigt, wie die stark gekoppelten Systeme numerisch gelöst werden können mit Hilfe der Finiten-Elemente-Methode und wie die Effizienz der Methode gesteigert werden kann durch die Anwendung von Operator-Splitting-Techniken und Problemparallelisierung mittels OPENMP.