In this paper, a cascaded fractional Kalman filter for state of charge and branch current estimation of largescale battery systems is proposed. As a centralized approach for the estimation of a large-scale system is costly in terms of effort and time, a partition into smaller and, therefore, simpler subsystems is applied. Since the overall system is divided into smaller units, a local computation is allowed and complexity reduced. In these distributed systems, usually, the subsystems communicate with each other to exchange relevant data. Using a model based on mesh currents, we receive a cascaded system structure which results in a hierarchical arrangement of all subsystems. This concludes in a one-directional information flow and, therefore, reduces the overall communication effort. Using this proposed approach, it is not only possible to estimate the states of each branch locally but also to calculate the branch currents when the total current is known. Finally, a practical test with real measurement data is presented.

Aqueous two-phase systems of poly(ethylene) glycol and a salt are considered as extraction media for large-scale downstream processing of industrially important enzymes. The present paper deals with one of such two-phase systems. New experimental results are presented for the composition of the coexisting liquid phases of the system (water + poly(ethylene glycol) + sodium citrate) at 298.15 K for three poly(ethylene) glycols of different molar masses of about (600, 1500, and 3000) g·mol−1, respectively. The experimental results are described within experimental uncertainty by a semiempirical expression for the excess Gibbs energy.

Background: The human heart is a masterpiece of the highest complexity coordinating multi-physics aspects on a multi-scale range. Thus, modeling the cardiac function in silico to reproduce physiological characteristics and diseases remains challenging. Especially the complex simulation of the blood's hemodynamics and its interaction with the myocardial tissue requires a high accuracy of the underlying computational models and solvers. These demanding aspects make whole-heart fully-coupled simulations computationally highly expensive and call for simpler but still accurate models. While the mechanical deformation during the heart cycle drives the blood flow, less is known about the feedback of the blood flow onto the myocardial tissue.Methods and Results: To solve the fluid-structure interaction problem, we suggest a cycle-to-cycle coupling of the structural deformation and the fluid dynamics. In a first step, the displacement of the endocardial wall in the mechanical simulation serves as a unidirectional boundary condition for the fluid simulation. After a complete heart cycle of fluid simulation, a spatially resolved pressure factor (PF) is extracted and returned to the next iteration of the solid mechanical simulation, closing the loop of the iterative coupling procedure. All simulations were performed on an individualized whole heart geometry. The effect of the sequential coupling was assessed by global measures such as the change in deformation and—as an example of diagnostically relevant information—the particle residence time. The mechanical displacement was up to 2 mm after the first iteration. In the second iteration, the deviation was in the sub-millimeter range, implying that already one iteration of the proposed cycle-to-cycle coupling is sufficient to converge to a coupled limit cycle.Conclusion: Cycle-to-cycle coupling between cardiac mechanics and fluid dynamics can be a promising approach to account for fluid-structure interaction with low computational effort. In an individualized healthy whole-heart model, one iteration sufficed to obtain converged and physiologically plausible results.

Mitral regurgitation alters the flow conditions in the left ventricle. To account for quantitative changes and to investigate the behavior of different flow components, a realistic computational model of the whole human heart was employed in this study. While performing fluid dynamics simulations, a scalar transport equation was solved to analyze vortex formation and ventricular wash-out for different regurgitation severities. Additionally, a particle tracking algorithm was implemented to visualize single components of the blood flow. We confirmed a significantly lowered volume of the direct flow component as well as a higher vorticity in the diseased case.

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