Hyperelliptic continued fractions and generalized jacobians: Minicourse given by Umberto Zannier

These are notes from the minicourse given by Umberto Zannier (Scuola Normale Superiore di Pisa). The notes were worked out by Laura Capuano, Peter Jossen,1 Christina Karolus, and Francesco Veneziano. Most of the material of these lectures, except for the numerical examples which were added by us, is already available in [45], The authors wish to thank Umberto Zannier for the lively discussions in Alpbach, and Olaf Merkert for providing computations of the examples 3.17, 3.28, 3.29, 3.33, and 3.25

Current density distribution in cylindrical Li-Ion cells during impedance measurements

In this work, modified commercial cylindrical lithium-ion cells with multiple separate current tabs are used to analyze the influence of tab pattern, frequency and temperature on electrochemical impedance spectroscopy. In a first step, the effect of different current tab arrangements on the impedance spectra is analyzed and possible electrochemical causes are discussed. In a second step, one terminal is used to apply a sinusoidal current while the other terminals are used to monitor the local potential distribution at different positions along the electrodes of the cell. It is observed that the characteristic decay of the voltage amplitude along the electrode changes non-linearly with frequency, where high-frequent currents experience a stronger attenuation along the current collector than low-frequent currents. In further experiments, the decay characteristic is controlled by the cell temperature, driven by the increasing resistance of the current collector and the enhanced kinetic and transport properties of the active material and electrolyte. Measurements indicate that the ac current distribution depends strongly on the frequency and the temperature. In this context, the challenges for electrochemical impedance spectroscopy as cell diagnostic technique for commercial cells are discussed

Module design and fault diagnosis in electric vehicle batteries

Systems integration issues, such as electrical and thermal design and management of full battery packs - often containing hundreds of cells - have been rarely explored in the academic literature. In this paper we discuss the design and construction of a 9 kWh battery pack for a motorsports application. The pack contained 504 lithium cells arranged into 2 sidepods, each containing 3 modules, with each module in a 12P7S configuration. This paper focuses particularly on testing the full battery pack and diagnosing subsequent problems related to cells being connected in parallel. We demonstrate how a full vehicle test can be used to identify malfunctioning strings of cells for further investigation. After individual cell testing it was concluded that a single high inter-cell contact resistance was causing currents to flow unevenly within the pack, leading to cells being unequally worked. This is supported by a Matlab/Simulink model of one battery module, including contact resistances. Over time the unequal current flowing through cells can lead to significant differences in cells' state of charge and open circuit voltages, large currents flowing between cells even when the load is disconnected, cells discharging and aging more quickly than others, and jeopardise capacity and lifetime of the pack

Temperature dependency of state of charge inhomogeneities and their equalization in cylindrical lithium-ion cells

The influence of cell temperature on the current density distribution and accompanying inhomogeneities in state of charge (SOC) during cycling is analyzed in this work. To allow for a detailed insight in the electrochemical behavior of the cell, commercially available 26650 cells were modified to allow for measuring local potentials at four different, nearly equidistant positions along the electrodes. As a follow-up to our previous work investigating local potentials within a cell, we apply this method for studying SOC deviations and their sensitivity to cell temperature. The local potential distribution was studied during constant current discharge operations for various current rates and discharge pulses in order to evoke local inhomogeneities for temperatures ranging from 10 °C to 40 °C. Differences in local potentials were considered for estimating local SOC variations within the electrodes. It could be observed that even low currents such as 0.1C can lead to significant inhomogeneities, whereas a higher cell temperature generally results in more pronounced inhomogeneities. A rapid SOC equilibration can be observed if the variation in the SOC distribution corresponds to a considerable potential difference defined by the open circuit voltage of either the positive or negative electrode. With increasing temperature, accelerated equalization effects can be observed

Diagenetic evolution of lower Jurassic platform carbonates flanking the Tazoult salt wall (Central High Atlas, Morocco)

Platform carbonates diagenesis in salt basins could be complex due to potential alterations of fluids related and non‐related to diapirism. This paper presents the diagenetic history of the Hettangian to Pliensbachian platform carbonates from the Tazoult salt wall area (central High Atlas, Morocco). Low structural relief and outcrop conditions allowed to define the entire diagenetic evolution occurred in the High Atlas diapiric basins since early stages of the diapiric activity up to their tectonic inversion. Precipitation of dolomite and calcite from both warmed marine‐derived and meteoric fluids characterised diagenetic stages during Pliensbachian, when the carbonate platforms were exposed and karstified. Burial diagenesis occurred from Toarcian to Middle Jurassic, due to changes of salt‐induced dynamic related to increase in siliciclastic input, fast diapir rise and rapid burial of Pliensbachian platforms. During this stage, the diapir acted as a physical barrier for fluid circulation between the core and the flanking sediments. In the carbonates and breccias flanking the structures, dolomite and calcite precipitated from basinal brines, whereas carbonate slivers located in the core of the structure, were affected by the circulation of Mn‐rich fluids. The final diagenetic event is characterised by the income of meteoric fluids into the system during uplift caused by Alpine orogeny. These results highlight the relevant influence of diapirism on the diagenetic modifications in salt‐related basins in terms of diagenetic events and involved fluids

Numerical methods for the design and description of in vitro expansion processes of human mesenchymal stem cells

Human mesenchymal stem cells (hMSCs) are a valuable source of cells for clinical applications (e.g., treatment of acute myocardial infarction or inflammatory diseases), especially in the field of regenerative medicine. However, for autologous (patient-specific) and allogeneic (off-the-shelf) hMSC-based therapies, in vitro expansion is necessary prior to the clinical application in order to achieve the required cell numbers. Safe, reproducible, and economic in vitro expansion of hMSCs for autologous and allogeneic therapies can be problematic because the cell material is restricted and the cells are sensitive to environmental changes. It is beneficial to collect detailed information on the hydrodynamic conditions and cell growth behavior in a bioreactor system, in order to develop a so called “Digital Twin” of the cultivation system and expansion process. Numerical methods, such as Computational Fluid Dynamics (CFD) which has become widely used in the biotech industry for studying local characteristics within bioreactors or kinetic growth modelling, provide possible solutions for such tasks. In this review, we will present the current state-of-the-art for the in vitro expansion of hMSCs. Different numerical tools, including numerical fluid flow simulations and cell growth modelling approaches for hMSCs, will be presented. In addition, a case study demonstrating the applicability of CFD and kinetic growth modelling for the development of an microcarrier-based hMSC process will be shown

Novel probes for pH and dissolved oxygen measurements in cultivations from millilitre to benchtop scale

Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)pH value and the concentration of dissolved oxygen (DO) are key parameters to monitor and control cell growth in cultivation studies. Reliable, robust and accurate methods to measure these parameters in cultivation systems in real time guarantee high product yield and quality. This mini-review summarises the current state of the art of pH and DO sensors that are applied to bioprocesses from millilitre to benchtop scale by means of a short introduction on measuring principles and selected applications. Special emphasis is placed on single-use bioreactors, which have been increasingly employed in bioprocess development and production in recent years. Working principles, applications and the particular requirements of sensors in these cultivation systems are given. In such processes, optical sensors for pH and DO are often preferred to electrochemical probes, as they allow semi-invasive measurements and can be miniaturised to micrometre scale or lower. In addition, selected measuring principles of novel sensing technologies for pH and DO are discussed. These include solid-state sensors and miniaturised devices that are not yet commercially available, but show promising characteristics for possible use in bioprocesses in the near future

Simulation and measurement of local potentials of modified commercial cylindrical cells:I. Cell preparation and measurements

This work presents a modification approach and first measurements of commercial cylindrical Li-ion cells with multiple local potential probes and an internal temperature sensor. Local potential measurements at low currents show a non-uniform potential distribution along the electrode, dominated by the open circuit voltage (OCV) of the negative electrode. For higher currents, the overpotential along the current collector becomes dominant and instead of a corrugated potential distribution, a significant current dependent voltage gradient can be detected, indicating a highly non-uniform state of charge (SOC) distribution with increasing distance to the current collecting tab. After the discharge operation, a quick potential equalization can be witnessed which results in a non-detectable potential difference between the single electrode sections after 12 min, even though the overall cell voltage relaxation has not reached an equilibrium state yet. The presented modification approach combines the advantages of high quality industrial manufactured cells showing uniform coating thicknesses and packing density with the advantages of special tailor made cells for in situ measurements. Due to the low impact of the modification and its long-term stability, highly reproducible measurements can be conducted at different locations of the electrodes

Cerebellar Hypoperfusion in Migraine Attack: Incidence and Significance.

BACKGROUND AND PURPOSE Patients diagnosed with migraine with aura have an increased lifetime risk of ischemic stroke. It is not yet clear whether prolonged cortical hypoperfusion during an aura increases the immediate risk of cerebellar infarction because it may induce crossed cerebellar diaschisis and subsequent tissue damage. To address this question, we retrospectively analyzed potential relationships between cortical oligemia and cerebellar hypoperfusion in patients with migraine with aura and their potential relation to small infarct-like cerebellar lesions. MATERIALS AND METHODS One hundred six migraineurs who underwent MR imaging, including DSC perfusion, were included in the study. In patients with apparent perfusion asymmetry, we used ROI analysis encompassing 18 infra- and supratentorial ROIs to account for differences in regional cerebral blood flow and volume. The presence of cerebellar hypoperfusion was calculated using an asymmetry index, with values of >10% being considered significant. RESULTS We observed perfusion asymmetries in 23/106 patients, 22 in patients with migraine with aura (20.8%). Cerebellar hypoperfusion was observed in 12/23 patients (52.2%), and crossed cerebellar diaschisis, in 9/23 patients (39.1%) with abnormal perfusion. In none of the 106 patients were DWI restrictions observed during migraine with aura. CONCLUSIONS Cerebellar hypoperfusion and crossed cerebellar diaschisis are common in patients with migraine with aura and cortical perfusion abnormalities. Crossed cerebellar diaschisis in migraine with aura may be considered a benign phenomenon because we observed no association with DWI restriction or manifest cerebellar infarctions, even in patients with prolonged symptom-related perfusion abnormalities persisting for up to 24 hours