Growth and decay of localized disturbances on a surfactant-coated spreading film

If the surface of a quiescent thin liquid film is suddenly coated by a patch of surface active material like a surfactant monolayer, the film is set in motion and begins spreading. An insoluble surfactant will rapidly attempt to coat the entire surface of the film thereby minimizing the liquid's surface tension. The shear stress that develops during the spreading process produces a maximum in surface velocity in the region where the moving film meets the quiescent layer. This region is characterized by a shock front with large interfacial curvature and a corresponding local buildup of surfactant which creates a spike in the concentration gradient. In this paper, we investigate the sensitivity of this region to infinitesimal disturbances. Accordingly, we introduce a measure of disturbance amplification and transient growth analogous to a kinetic energy that couples variations in film thickness to the surfactant concentration. These variables undergo significant amplification during the brief period in which they are convected past the downstream tip of the monolayer, where the variation in concentration gradient and surface curvature are largest. Once they migrate past this sensitive area, the perturbations weaken considerably and the system approaches a stable configuration. It appears that the localized disturbances of the type we consider here, cannot sustain asymptotic instability. Nonetheless, our study of the dynamics leading to the large transient growth clearly illustrates how the coupling of Marangoni and capillary forces work in unison to stabilize the spreading process against localized perturbations

Cycle-Level Products in Equivariant Cohomology of Toric Varieties

In this paper, we define an action of the group of equivariant Cartier divisors on a toric variety X on the equivariant cycle groups of X, arising naturally from a choice of complement map on the underlying lattice. If X is nonsingular, this gives a lifting of the multiplication in equivariant cohomology to the level of equivariant cycles. As a consequence, one naturally obtains an equivariant cycle representative of the equivariant Todd class of any toric variety. These results extend to equivariant cohomology the results of Thomas and Pommersheim. In the case of a complement map arising from an inner product, we show that the equivariant cycle Todd class obtained from our construction is identical to the result of the inductive, combinatorial construction of Berline-Vergne. In the case of arbitrary complement maps, we show that our Todd class formula yields the local Euler-Maclarurin formula introduced in Garoufalidis-Pommersheim.Comment: 15 pages, to be published in Michigan Mathematical Journal; LaTe

Work Incentives and the Cost of Redistribution via Tax-transfer Reforms under Constrained Labor Supply

Using information on desired and actual hours of work, we formulate a discrete choice model of constrained labor supply. Using the German Socio-Economic Panel and the microsimulation model STSM, we find that hours and participation elasticities are substantially smaller than those in the conventional model. We evaluate two reforms for Germany. Both redistribute to the working poor. The first reform is financed through an increase in the effective marginal tax rate for welfare recipients, the second through an increase in taxes. The first reform is desirable with equal weights, the second if the social planner has substantial redistributive taste

Thinning and disturbance growth in liquid films mobilized by continuous surfactant delivery

A generalized linear stability analysis is applied to the case of a thin liquid film propelled to spread by a continuous supply of surfactant. The time-dependent base states for the film thickness and surfactant concentration give rise to a nonautonomous system describing disturbance propagation. As a first approximation, the nonautonomous operator is treated as time independent, thereby reducing the system of equations to a standard eigenvalue problem. For the range of parameters investigated, this modal approximation reveals a band of unstable modes corresponding to the growth of transverse, sinusoidal corrugations. A transient growth analysis of the fully time-dependent system, which requires the solution of an initial value problem, also signals the possibility of large disturbance growth. In both cases, significant amplification of infinitesimal disturbances can be traced to the region of the film most rapidly thinned by Marangoni stresses, which is characterized by large interfacial curvature and a sharp variation in shear stress. In contrast to previous models implementing a finite surfactant source that predict asymptotic stability, large transient growth and asymptotic instability are possible for the case of sustained surfactant release

Comparative analysis of biopolymer-based scaffolds for therapeutically relevant cells

Im Rahmen dieser Arbeit wurde die Generierung somatischer, kardialer Zellen aus humanen pluripotenten Stammzellen in einen dynamischen Suspensionsbioreaktor übertragen und vergleichend mit der statischen „hängenden Tropfen“ Kultur hinsichtlich der Differenzierungseffizienz und der Reife der abgeleiteten Kardiomyozyten untersucht. Darüber hinaus wurden für die Dissoziierung der Zellen drei Enzyme vergleichend analysiert. Die Wirkung von adhäsiven, kontraktilen Biopolymeren auf die Kardiomyozytenphysiologie wurde am Beispiel von ultra-hoch viskosem Alginat untersucht. So konnte festgestellt werden, dass Kardiomyozyten auf solchen Biopolymeren eine reifere Organisation des Zytoskeletts und Geneexpression aufweisen. Des Weiteren wurde ein neuartiges Verfahren entwickelt welches die simultane Quantifizierung der Kontraktionskraft und der intrazellulären Kalziumströme erlaubt. Hierzu wurden die Kardiomyozyten unterschiedlichen Konzentrationen von Isoprenalin, ein Beta-Adrenozeptoragonist, ausgesetzt. Darüber hinaus wurde eine neuartige Methode für den 3D Druck von niedrig-konzentrierten Biopolymerlösungen entwickelt und hinsichtlich ihrer Druckauflösung charakterisiert. Kardiomyozyten wurden auf diesen Gerüststrukturen kultiviert und es konnte gezeigt werden, dass die Zytoskelette eine noch höhere Organisation aufweisen und spezifische, mit der physiologischen Reifung assoziierte Proteine, in erhöhtem Maße vorkommen.In this work, a process for the production of somatic, cardiac cells from human induced pluripotent stem cells in three-dimensional micro tissues was adapted to a dynamic, suspension-based bioreactor. The differentiation efficiency and the maturation of the generated cardiomyocytes in the bioreactor and the static hanging drop culture were analyzed. To dissociate the cardiac tissues into single cells, the performances of three enzymes were comparatively evaluated. To analyze the effect of contractile biopolymers on cardiomyocyte physiology ultra-high viscosity alginates were utilized. Cardiomyocytes cultured on these matrices for a prolonged period exhibit a matured cytoskeletal organization and gene expression. In addition, a novel approach was developed, which enables the simultaneous quantification of the generated contraction force and intracellular calcium transients. To this extent, different concentrations of the beta-adrenergic agonist isoprenaline were applied. A novel 3D printing method for the three-dimensional deposition of low concentrated biopolymer formulations was devised and evaluated concerning the printing resolution and pore formation. The culture of human cardiomyocytes on such 3D printed, biopolymer-based scaffolds led to a further maturation of the cytoskeletal organization and a higher abundance of proteins, which are associated with the maturation in vivo.Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung e.V

Bayle\u27s Theory of Toleration

This paper gives an overview of Pierre Bayle’s theory of toleration and derives a normative principle of toleration from it that is meant to compete with other normative principles of toleration such as the Harm principle