33 research outputs found
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