Bifurcations in valveless pumping techniques from a coupled fluid-structure-electrophysiology model in heart development

We explore an embryonic heart model that couples electrophysiology and muscle-force generation to flow induced using a $2D$ fluid-structure interaction framework based on the immersed boundary method. The propagation of action potentials are coupled to muscular contraction and hence the overall pumping dynamics. In comparison to previous models, the electro-dynamical model does not use prescribed motion to initiate the pumping motion, but rather the pumping dynamics are fully coupled to an underlying electrophysiology model, governed by the FitzHugh-Nagumo equations. Perturbing the diffusion parameter in the FitzHugh-Nagumo model leads to a bifurcation in dynamics of action potential propagation. This bifurcation is able to capture a spectrum of different pumping regimes, with dynamic suction pumping and peristaltic-like pumping at the extremes. We find that more bulk flow is produced within the realm of peristaltic-like pumping.Comment: 11 pages, 13 figures. arXiv admin note: text overlap with arXiv:1610.0342

Locally Equivalent Correspondences

Given a pair of number fields with isomorphic rings of adeles, we construct bijections between objects associated to the pair. For instance we construct an isomorphism of Brauer groups that commutes with restriction. We additionally construct bijections between central simple algebras, maximal orders, various Galois cohomology sets, and commensurability classes of arithmetic lattices in simple, inner algebraic groups. We show that under certain conditions, lattices corresponding to one another under our bijections have the same covolume and pro-congruence completion. We also make effective a finiteness result of Prasad and Rapinchuk.Comment: Final Version. To appear in Ann. Inst. Fourie

Convergence in Income Inequality: Further Evidence from the Club Clustering Methodology across States in the U.S.

This paper contributes to the sparse literature on inequality convergence by empirically testing convergence across states in the U.S. This sample period encompasses a series of different periods that the existing literature discusses -- the Great Depression (1929–1944), the Great Compression (1945–1979), the Great Divergence (1980-present), the Great Moderation (1982–2007), and the Great Recession (2007–2009). This paper implements the relatively new method of panel convergence testing, recommended by Phillips and Sul (2007). This method examines the club convergence hypothesis, which argues that certain countries, states, sectors, or regions belong to a club that moves from disequilibrium positions to their club-specific steady-state positions. We find strong support for convergence through the late 1970s and early 1980s, and then evidence of divergence. The divergence, however, moves the dispersion of inequality measures across states only a fraction of the way back to their levels in the early part of the twentieth century