Oscillatory processes in the theory of particulate formation in supersaturated chemical solutions

We study a nonlinear problem which occurs in the theory of particulate formation in supersaturated chemical solutions. Mathematically, the problem involves the bifurcation of time-periodic solutions in an initial-boundary value problem involving a nonlinear integro-differential equation. The mechanism controlling the oscillatory states is revealed by combining the theory of characteristics for first order partial differential equations with the multi-time scale perturbation analysis of a certain third order system of nonlinear ordinary differential equations

Elimination of spiral waves in cardiac tissue by multiple electrical shocks

We study numerically the elimination of a spiral wave in cardiac tissue by application of multiple shocks of external current. To account for the effect of shocks we apply a recently developed theory for the interaction of the external current with cardiac tissue. We compare two possible feedback algorithms for timing of the shocks: a "local" feedback algorithm (using an external electrode placed directly on the tissue) and a "global" feedback algorithm (using the electrocardiogram). Our main results are: application of the external current causes a parametric resonant drift similar to that reported in previous model computations; the ratio of the threshold of elimination of the spiral wave by multiple shocks to the threshold of conventional single shock defibrillation in our model for cardiac tissue is about 0.5, while earlier, less realistic models predicted the value about 0.2; we show that an important factor for successful defibrillation is the location of the feedback electrode and the best results are achieved if the feedback electrode or the ECG lead is located at the boundary (or edge) of the cardiac tissue; the "local" and the "global" feedback algorithms show similar efficiency

An Interface-Capturing Regularization Method for Solving the Equations for Two-Fluid Mixtures

Many problems in biology involve gels which are mixtures composed of a polymer network permeated by a fluid solvent (water). The two-fluid model is a widely used approach to described gel mechanics, in which both network and solvent coexist at each point of space and their relative abundance is described by their volume fractions. Each phase is modeled as a continuum with its own velocity and constitutive law. In some biological applications, free boundaries separate regions of gel and regions of pure solvent, resulting in a degenerate network momentum equation where the network volume fraction vanishes. To overcome this difficulty, we develop a regularization method to solve the two-phase gel equations when the volume fraction of one phase goes to zero in part of the computational domain. A small and constant network volume fraction is temporarily added throughout the domain in setting up the discrete linear equations and the same set of equation is solved everywhere. These equations are very poorly conditioned for small values of the regularization parameter, but the multigrid-preconditioned GMRES method we use to solve them is efficient and produces an accurate solution of these equations for the full range of relevant regularization parameter values

Measurement of the production of a W boson in association with a charm quark in pp collisions at √s = 7 TeV with the ATLAS detector

The production of a W boson in association with a single charm quark is studied using 4.6 fb−1 of pp collision data at s√ = 7 TeV collected with the ATLAS detector at the Large Hadron Collider. In events in which a W boson decays to an electron or muon, the charm quark is tagged either by its semileptonic decay to a muon or by the presence of a charmed meson. The integrated and differential cross sections as a function of the pseudorapidity of the lepton from the W-boson decay are measured. Results are compared to the predictions of next-to-leading-order QCD calculations obtained from various parton distribution function parameterisations. The ratio of the strange-to-down sea-quark distributions is determined to be 0.96+0.26−0.30 at Q 2 = 1.9 GeV2, which supports the hypothesis of an SU(3)-symmetric composition of the light-quark sea. Additionally, the cross-section ratio σ(W + +c¯¯)/σ(W − + c) is compared to the predictions obtained using parton distribution function parameterisations with different assumptions about the s−s¯¯¯ quark asymmetry