The predictability of advection-dominated flux-transport solar dynamo models

Space weather is a matter of practical importance in our modern society. Predictions of forecoming solar cycles mean amplitude and duration are currently being made based on flux-transport numerical models of the solar dynamo. Interested in the forecast horizon of such studies, we quantify the predictability window of a representative, advection-dominated, flux-transport dynamo model by investigating its sensitivity to initial conditions and control parameters through a perturbation analysis. We measure the rate associated with the exponential growth of an initial perturbation of the model trajectory, which yields a characteristic time scale known as the e-folding time $\tau_e$. The e-folding time is shown to decrease with the strength of the $\alpha$-effect, and to increase with the magnitude of the imposed meridional circulation. Comparing the e-folding time with the solar cycle periodicity, we obtain an average estimate for $\tau_e$ equal to 2.76 solar cycle durations. From a practical point of view, the perturbations analysed in this work can be interpreted as uncertainties affecting either the observations or the physical model itself. After reviewing these, we discuss their implications for solar cycle prediction.Comment: 33 pages, 12 figure

GEN-IV LFR development: Status & perspectives

Since Lead-cooled Fast Reactors (LFR) have been conceptualized in the frame of Generation IV International Forum (GIF), great interest has focused on the development and testing of new technologies related to Heavy Liquid Metal (HLM) nuclear reactors. In this frame, ENEA developed one of the larger European experimental fleet of experimental facilities aiming at investigating HLM thermal-hydraulics, coolant chemistry control, corrosion behavior for structural materials, and at developing components, instrumentations and innovative systems, supported by experiments and numerical tools. The present work aims at highlighting the capabilities and competencies developed by ENEA so far in the frame of the liquid metal technologies for GEN-IV LFR. In particular, an overview on the ongoing R&D experimental program will be depicted considering the actual fleet of facilities: CIRCE, NACIE-UP, LIFUS5, LECOR and HELENA. CIRCE (CIRColazione Eutettico) is the largest HLM pool facility presently in operation worldwide. Full scale component tests, thermal stratification studies, operational and accidental transients and integral tests for the nuclear safety and SGTR (Steam Generator Tube Rupture) events in a large pool system can be studied. NACIE-UP (NAtural CIrculation Experiment-UPgraded) is a loop with a HLM primary and pressurized water secondary side and a 250 kW power Fuel Pin Simulator working in natural and mixed convection. LIFUS5 (lithium for fusion) is a separated effect facility devoted to the HLM/Water interaction. HELENA (HEavy Liquid metal Experimental loop for advanced Nuclear applications) is a pure lead loop with a mechanical pump for high flow rates experiments. LECOR (LEad CORrosion) is a corrosion loop facility with oxygen control system installed. All the experiment actually ongoing on these facilities are described in the paper, depicting their role in the context of GEN-IV LFR development

Gene expression time delays & Turing pattern formation systems

The incorporation of time delays can greatly affect the behaviour of partial differential equations and dynamical systems. In addition, there is evidence that time delays in gene expression due to transcription and translation play an important role in the dynamics of cellular systems. In this paper, we investigate the effects of incorporating gene expression time delays into a one-dimensional putative reaction diffusion pattern formation mechanism on both stationary domains and domains with spatially uniform exponential growth. While oscillatory behaviour is rare, we find that the time taken to initiate and stabilise patterns increases dramatically as the time delay is increased. In addition, we observe that on rapidly growing domains the time delay can induce a failure of the Turing instability which cannot be predicted by a naive linear analysis of the underlying equations about the homogeneous steady state. The dramatic lag in the induction of patterning, or even its complete absence on occasions, highlights the importance of considering explicit gene expression time delays in models for cellular reaction diffusion patterning

Nontrivial rheological exponents in sheared yield stress fluids

In this work we discuss possible physical origins for non-trivial exponents in the athermal rheology of soft materials at low but finite driving rates. A key ingredient in our scenario is the presence of a self-consistent mechanical noise that stems from the spatial superposition of long-range elastic responses to localized plastically deforming regions. We study analytically a mean-field model, in which this mechanical noise is accounted for by a stress diffusion term coupled to the plastic activity. Within this description we show how a dependence of the shear modulus and/or the local relaxation time on the shear rate introduces corrections to the usual mean-field prediction, concerning the Herschel-Bulkley-type rheological response of exponent 1/2. This feature of the mean-field picture is then shown to be robust with respect to structural disorder and partial relaxation of the local stress. We test this prediction numerically on a mesoscopic lattice model that implements explicitly the long-range elastic response to localized shear transformations, and we conclude on how our scenario might be tested in rheological experiments

Insights into biopharmaceutical freezing processes - Characterization and impact of freeze concentration

The continuously expanding biopharmaceutical product pipeline ranges from monoclonal antibodies (mAb) to insulin and messenger ribonucleic acid (mRNA). Over the last decade, the pressure on rapid process development has been intensified and peaked during the outbreak of the COVID-19 pandemic due to the urgent need for novel therapeutics and vaccines. Especially the optimization of storage conditions and temperatures was relevant for novel vaccines. While storage of liquid formulations in a frozen state at 80 °C is considered a safe option with regards to integrity of the active pharmaceutical ingredient (API), the need for cryo-technology restricts the handleability and availability of the drug. At elevated freezing temperatures, however, freezing-induced stresses such as freeze concentration are more pronounced. The necessary optimization of storage temperatures and freezing processes poses a challenge, leading to a potential overestimation of the required storage temperature during rapid process development. Conducted formulation studies to investigate the stability of biopharmaceuticals are time and material consuming with durations of up to 24 months and freezing volumes of up to hundred liters during transportation. High-throughput screenings of formulations at microliter-scale are used to study protein stability and freeze-thaw behavior, for example cold denaturation of proteins. However, mass transport phenomena due to freeze concentration are neglected, which are more pronounced at larger scales. Milliliter-scale models are therefore proposed to study freeze concentration behavior, bridging the gap between high-throughput screening and production scale. For comparison and validation of differently scaled models, process analytical technology (PAT) is essential. Monitoring quality attributes and process parameters such as temperature can improve process understanding as requested by regulatory authorities for process approval. PAT may generate experimental data on transient phenomena and enable process control, for example by determination of the freezing endpoint. Furthermore, the real-time data may be used to validate models, such as in silico simulations, which are becoming a valuable tool for process prediction and optimization in the biopharmaceutical industry. To facilitate freezing process design and optimization, it is the aim of this thesis to improve process understanding of biopharmaceutical freezing processes. Therefore, a scale-down model was designed and characterized by two novel PAT approaches. Process parameters affecting the freeze concentration were identified and monitored. The generated transient data on the freezing process were used to investigate the applicability of existing computational fluid dynamic (CFD) models to describe and predict freezing processes by an in-silico model. Lastly, a case study with a monoclonal antibody (mAb) process intermediate was conducted to evaluate the impact of freeze concentration on mAb process development and manufacturing. In the first study (Chapter 3), the novel freeze-thaw device was described and characterized by an improved temperature setup. The small-scale freeze-thaw device was designed as a slice from a larger hollow cylinder, which is actively cooled from the in- and outside. To minimize freezing at the bottom of the container, an insulating layer as well as an additional counteracting cooling loop at the container bottom were installed. Furthermore, the insulating layer divided the container into six individual chambers with working volume of up to 100 mL. Biopharmaceutical freezing processes are usually monitored by a small number or even a single temperature probe. Heat conduction, convection, and freezing point depression with ongoing freeze concentration pose measurement challenges, which are difficult to overcome by temperature probes at low spatial resolution. In this study, the spatial resolution was improved by a temperature probe array using Fiber-Bragg-Grating sensors. Monitoring of the freeze front progression was further improved by evaluation of the second time derivative of temperature to overcome the influence of freeze point depression on the detection of freezing. For freezing of concentrated buffer solutions, elevated freezing temperatures above 30 °C led to a settlement of the last point to freeze (LPTF) in the container from top to bottom. Furthermore, a longer freezing time increased the degree of freeze concentration measured in the frozen bulk. As a result, the freezing time was identified as a critical process parameter (CPP). Using purified water as a cheap and widely available model liquid, a correlation between freezing time and freezing temperature was put into theoretical context with the Plank equation, which is commonly applied in the food industry. Furthermore, the freezing time was not only dependent on the set freezing temperature but also on the heat dissipation capacity of the attached refrigeration unit. Therefore, in rapid freezing processes, such as those found in common freezing bags, reducing the set freezing temperature may not improve the homogeneity of the freeze concentration. While the temperature in biopharmaceutical freezing processes is often monitored continuously, it does not directly reflect a quality attribute of the drug. The protein and additive concentrations, however, have been classified as critical quality attributes (CQA). Until now, they have only been measured by sampling from the frozen bulk after completion of the freezing process. A non-destructive analytical method to monitor freeze concentration is missing yet, leading to a knowledge gap in the origin of freeze concentration and mass transport phenomena. Without this process understanding, predicting freeze concentration after changes in formulation or freezing temperature remains challenging. Therefore, the process characterization was advanced by the application of Raman spectroscopy as a novel PAT for real-time monitoring of freeze concentration in a second study (Chapter 4). The concentrations of each solute in multi-component model formulations were monitored simultaneously using partial least squares (PLS) regression modelling. The concentrations predicted simultaneously for each component were validated by samples taken close to the Raman probe. Overall, the freezing time had the largest impact on the freeze concentration, with increasing freezing time leading to increased freeze concentration. This confirms the findings of the first study (Chapter 3). An increase in initial sucrose concentration led to increased freeze concentration, which is important to consider during formulation development. In addition, convection currents as small as 1 mm were detected at the bottom of the vessel, highlighting the need for high-resolution PAT. Furthermore, the separation of solutes during freezing was shown, indicating potential destabilization of the API. The presented approach provides a robust, non-destructive PAT that can be applied at various scales in both industry and academia. Concluding Chapter 3 and 4, freezing time and freeze concentration were identified as CPP and CQA, respectively. As mentioned earlier, intensification of process development is of great importance and can be accelerated by in-silico models. Using the data on the freezing process, the applicability of an existing CFD model to describe and predict freezing processes was investigated (Chapter 5). Freezing times were simulated using water as a single component solidification system. The solution was evaluated by a mesh and time step size study with converging results indicating simulation reliability. The predicted freezing times at freezing temperatures between 60 and 20 °C agreed with experimental results with minor deviations, that were attributed to cooldown of system components such as the steel housing. To simulate freeze concentration, the simulation was extended by a species model. Sucrose was selected as a model component and its temperature- and concentration-dependent physical properties were implemented in the model. Initial results were able to provide qualitative insights into the freezing process and mass transport phenomena present, which substantiated the discussion in the other studies. However, mass imbalances due to discretization inaccuracies were found, making quantitative comparisons challenging. The predicted concentrations were dependent on discretization parameters whereby large time steps and small viscosities led to increasing mass imbalances. Increasing the time and mesh resolution was not feasible due to hardware restrictions. In the future, alternatives to the enthalpy-porosity method used to describe solidification, or improvement in the discretization methods, should be evaluated for quantitative prediction of freeze concentration. At last, the relevance of freeze concentration for the biopharmaceutical industry was investigated in a case study using an industrial process intermediate from a mAb platform process (Chapter 6). In between the typical production stages (Upstream, Downstream and Formulation), the process intermediates are handed over from one department to another. In contrast to the manufacturing process, where process intermediates are processed directly, the intermediates are often frozen during process development due to time and project limitations. To answer the question of comparability, the case study investigated the impact of freezing on the CQAs of a mAb purification process. Therefore, cell culture supernatant (CCS) was subjected to an additional freeze-thaw cycle at temperatures from -60 to -20 °C, subsequently filtered and captured by a protein A chromatography. After the capture step, the CQAs showed a significant decrease in the remaining host cell proteins (HCP) and mAb aggregates after slow freezing processes in comparison to a reference sample. This was attributed to aggregation of mAb and specific HCPs. These aggregates formed particles larger than 0.2 µm, that were removed by a common filtration step and thus lead to an overestimated quality of the protein A eluate. Furthermore, smaller HCPs in the CCS were freeze concentrated to a higher degree. As a result, the study revealed the dependency of freeze concentration on the diffusion coefficient. In summary, the thesis improves the overall process understanding of biopharmaceutical freezing processes by highlighting the contribution of mass transport phenomena to freeze concentration during the freezing process. Two novel tools to validate the scalability of freezing processes and potential in-silico models are presented. While currently existing CFD models were found to sufficiently estimate the freezing time of a container, the simulation of freeze concentration has to be carefully evaluated with regards to discretization and solution independency from physical properties. Overall, the thesis facilitates the development and optimization of novel freezing containers, formulations and freezing processes with regards to freeze concentration and required freezing temperature

How large should whales be?

The evolution and distribution of species body sizes for terrestrial mammals is well-explained by a macroevolutionary tradeoff between short-term selective advantages and long-term extinction risks from increased species body size, unfolding above the 2g minimum size induced by thermoregulation in air. Here, we consider whether this same tradeoff, formalized as a constrained convection-reaction-diffusion system, can also explain the sizes of fully aquatic mammals, which have not previously been considered. By replacing the terrestrial minimum with a pelagic one, at roughly 7000g, the terrestrial mammal tradeoff model accurately predicts, with no tunable parameters, the observed body masses of all extant cetacean species, including the 175,000,000g Blue Whale. This strong agreement between theory and data suggests that a universal macroevolutionary tradeoff governs body size evolution for all mammals, regardless of their habitat. The dramatic sizes of cetaceans can thus be attributed mainly to the increased convective heat loss is water, which shifts the species size distribution upward and pushes its right tail into ranges inaccessible to terrestrial mammals. Under this macroevolutionary tradeoff, the largest expected species occurs where the rate at which smaller-bodied species move up into large-bodied niches approximately equals the rate at which extinction removes them.Comment: 7 pages, 3 figures, 2 data table