Hysteresis of dynamos in rotating spherical shell convection

Bifurcations of dynamos in rotating and buoyancy-driven spherical Rayleigh-Bénard convection in an electrically conducting fluid are investigated numerically. Both nonmagnetic and magnetic solution branches comprised of rotating waves are traced by path-following techniques, and their bifurcations and interconnections for different Ekman numbers are determined. In particular, the question of whether the dynamo branches bifurcate super- or subcritically and whether a direct link to the primary pure convective states exists is answered

Hysteresis of dynamos in rotating spherical shell convection

Bifurcations of dynamos in rotating and buoyancy-driven spherical Rayleigh-Bénard convection in an electrically conducting fluid are investigated numerically. Both nonmagnetic and magnetic solution branches comprised of rotating waves are traced by path-following techniques, and their bifurcations and interconnections for different Ekman numbers are determined. In particular, the question of whether the dynamo branches bifurcate super- or subcritically and whether a direct link to the primary pure convective states exists is answered

On acceleration of Krylov-subspace-based Newton and Arnoldi iterations for incompressible CFD: replacing time steppers and generation of initial guess

We propose two techniques aimed at improving the convergence rate of steady state and eigenvalue solvers preconditioned by the inverse Stokes operator and realized via time-stepping. First, we suggest a generalization of the Stokes operator so that the resulting preconditioner operator depends on several parameters and whose action preserves zero divergence and boundary conditions. The parameters can be tuned for each problem to speed up the convergence of a Krylov-subspace-based linear algebra solver. This operator can be inverted by the Uzawa-like algorithm, and does not need a time-stepping. Second, we propose to generate an initial guess of steady flow, leading eigenvalue and eigenvector using orthogonal projection on a divergence-free basis satisfying all boundary conditions. The approach, including the two proposed techniques, is illustrated on the solution of the linear stability problem for laterally heated square and cubic cavities

Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow

Steady states and traveling waves play a fundamental role in understanding hydrodynamic problems. Even when unstable, these states provide the bifurcation-theoretic explanation for the origin of the observed states. In turbulent wall-bounded shear flows, these states have been hypothesized to be saddle points organizing the trajectories within a chaotic attractor. These states must be computed with Newton's method or one of its generalizations, since time-integration cannot converge to unstable equilibria. The bottleneck is the solution of linear systems involving the Jacobian of the Navier-Stokes or Boussinesq equations. Originally such computations were carried out by constructing and directly inverting the Jacobian, but this is unfeasible for the matrices arising from three-dimensional hydrodynamic configurations in large domains. A popular method is to seek states that are invariant under numerical time integration. Surprisingly, equilibria may also be found by seeking flows that are invariant under a single very large Backwards-Euler Forwards-Euler timestep. We show that this method, called Stokes preconditioning, is 10 to 50 times faster at computing steady states in plane Couette flow and traveling waves in pipe flow. Moreover, it can be carried out using Channelflow (by Gibson) and Openpipeflow (by Willis) without any changes to these popular spectral codes. We explain the convergence rate as a function of the integration period and Reynolds number by computing the full spectra of the operators corresponding to the Jacobians of both methods.Comment: in Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics, ed. Alexander Gelfgat (Springer, 2018

Bafilomycin A1 activates respiration of neuronal cells via uncoupling associated with flickering depolarization of mitochondria

Bafilomycin A1 (Baf) induces an elevation of cytosolic Ca2+ and acidification in neuronal cells via inhibition of the V-ATPase. Also, Baf uncouples mitochondria in differentiated PC12 (dPC12), dSH-SY5Y cells and cerebellar granule neurons, and markedly elevates their respiration. This respiratory response in dPC12 is accompanied by morphological changes in the mitochondria and decreases the mitochondrial pH, Ca2+ and ΔΨm. The response to Baf is regulated by cytosolic Ca2+ fluxes from the endoplasmic reticulum. Inhibition of permeability transition pore opening increases the depolarizing effect of Baf on the ΔΨm. Baf induces stochastic flickering of the ΔΨm with a period of 20 ± 10 s. Under conditions of suppressed ATP production by glycolysis, oxidative phosphorylation impaired by Baf does not provide cells with sufficient ATP levels. Cells treated with Baf become more susceptible to excitation with KCl. Such mitochondrial uncoupling may play a role in a number of (patho)physiological conditions induced by Baf

The Contribution of Coevolving Residues to the Stability of KDO8P Synthase

The evolutionary tree of 3-deoxy-D-manno-octulosonate 8-phosphate (KDO8P) synthase (KDO8PS), a bacterial enzyme that catalyzes a key step in the biosynthesis of bacterial endotoxin, is evenly divided between metal and non-metal forms, both having similar structures, but diverging in various degrees in amino acid sequence. Mutagenesis, crystallographic and computational studies have established that only a few residues determine whether or not KDO8PS requires a metal for function. The remaining divergence in the amino acid sequence of KDO8PSs is apparently unrelated to the underlying catalytic mechanism.The multiple alignment of all known KDO8PS sequences reveals that several residue pairs coevolved, an indication of their possible linkage to a structural constraint. In this study we investigated by computational means the contribution of coevolving residues to the stability of KDO8PS. We found that about 1/4 of all strongly coevolving pairs probably originated from cycles of mutation (decreasing stability) and suppression (restoring it), while the remaining pairs are best explained by a succession of neutral or nearly neutral covarions.Both sequence conservation and coevolution are involved in the preservation of the core structure of KDO8PS, but the contribution of coevolving residues is, in proportion, smaller. This is because small stability gains or losses associated with selection of certain residues in some regions of the stability landscape of KDO8PS are easily offset by a large number of possible changes in other regions. While this effect increases the tolerance of KDO8PS to deleterious mutations, it also decreases the probability that specific pairs of residues could have a strong contribution to the thermodynamic stability of the protein

Bifurcation Analysis for Timesteppers

Abstract. A collection of methods is presented to adapt a pre-existing time-stepping code to perform various bifurcation-theoretic tasks. It is shown that the implicit linear step of a time-stepping code can serve as a highly effective preconditioner for solving linear systems involving the full Jaco-bian via conjugate gradient iteration. The methods presented for steady-state solving, continuation, direct calculation of bifurcation points (all via Newton’s method), and linear stability analysis (via the inverse power method) rely on this preconditioning. Another set of methods can have as their basis any time-stepping method. These perform various types of stability analyses: linear stability analysis via the exponential power method, Floquet stability analysis of a limit cycle, and nonlinear stability analysis for determining the character of a bifurcation. All of the methods presented require minimal changes to the time-stepping code