Gravitational Radiation from Accreting Millisecond Pulsars

It is widely assumed that the observed reduction of the magnetic field of millisecond pulsars can be connected to the accretion phase during which the pulsar is spun up by mass accretion from a companion. A wide variety of reduction mechanisms have been proposed, including the burial of the field by a magnetic mountain, formed when the accreted matter is confined to the poles by the tension of the stellar magnetic field. A magnetic mountain effectively screens the magnetic dipole moment. On the other hand, observational data suggests that accreting neutron stars are sources of gravitational waves, and magnetic mountains are a natural source of a time-dependent quadrupole moment. We show that the emission is sufficiently strong to be detectable by current and next generation long-baseline interferometers. Preliminary results from fully three-dimensional magnetohydrodynamic (MHD) simulations are presented. We find that the initial axisymmetric state relaxes into a nearly axisymmetric configuration via toroidal magnetic modes. A substantial quadrupole moment is still present in the final state, which is stable (in ideal MHD) yet highly distorted.Comment: Proceedings of the 11th Marcel Grossmann Meeting on General Relativity, World Scientific 200

Zhexue-yu-wenhua : yuekan = Universitas : monthly review of philosophy and culture

We present a method for mesoscopic, dynamic Monte Carlo simulations of pattern formation in excitable reaction-diffusion systems. Using a two-level parallelization approach, our simulations cover the whole range of the parameter space, from the noise-dominated low-particle number regime to the quasi-deterministic high-particle number limit. Three qualitatively different case studies are performed that stand exemplary for the wide variety of excitable systems. We present mesoscopic stochastic simulations of the Gray-Scott model, of a simplified model for intracellular Ca2+ oscillations and, for the first time, of the Oregonator model. We achieve simulations with up to 10(10) particles. The software and the model files are freely available and researchers can use the models to reproduce our results or adapt and refine them for further exploration

Multi-dimensional, mesoscopic Monte Carlo simulations of inhomogeneous reaction-drift-diffusion systems on graphics-processing units

For many biological applications, a macroscopic (deterministic) treatment of reaction-drift-diffusion systems is insufficient. Instead, one has to properly handle the stochastic nature of the problem and generate true sample paths of the underlying probability distribution. Unfortunately, stochastic algorithms are computationally expensive and, in most cases, the large number of participating particles renders the relevant parameter regimes inaccessible. In an attempt to address this problem we present a genuine stochastic, multi-dimensional algorithm that solves the inhomogeneous, non-linear, drift-diffusion problem on a mesoscopic level. Our method improves on existing implementations in being multi-dimensional and handling inhomogeneous drift and diffusion. The algorithm is well suited for an implementation on data-parallel hardware architectures such as general-purpose graphics processing units (GPUs). We integrate the method into an operator-splitting approach that decouples chemical reactions from the spatial evolution. We demonstrate the validity and applicability of our algorithm with a comprehensive suite of standard test problems that also serve to quantify the numerical accuracy of the method. We provide a freely available, fully functional GPU implementation. Integration into Inchman, a user-friendly web service, that allows researchers to perform parallel simulations of reaction-drift-diffusion systems on GPU clusters is underway

Simulation parameters for the Oregonator model.

<p>Simulation parameters for the Oregonator model of the BZ reaction Eqs. (7)–(14).</p

Formation of a spike spiral wave in the model.

<p>Shown are snap-shots of a spiral wave in the model Eqs. (18)–(26), initialized as shown in the top left panel, at in the deterministic simulation (bottom left) and in stochastic simulations for different scale factors (rightmost columns).</p

Transition probabilities on a cell-centered grid.

<p>The particle jumps to the neighboring grid cells with probabilities , , and . The probability to stay put is given by .</p

Simulation runtimes for the Oregonator model.

<p>Simulation runtimes for the Oregonator model of the BZ reaction Eqs. (7)–(14).</p

Multiscale modelling and analysis of collective decision making in swarm robotics

We present a unified approach to describing certain types of collective decision making in swarm robotics that bridges from a microscopic individual-based description to aggregate properties. Our approach encompasses robot swarm experiments, microscopic and probabilistic macroscopic-discrete simulations as well as an analytic mathematical model. Following up on previous work, we identify the symmetry parameter, a measure of the progress of the swarm towards a decision, as a fundamental integrated swarm property and formulate its time evolution as a continuous-time Markov process. Contrary to previous work, which justified this approach only empirically and a posteriori, we justify it from first principles and derive hard limits on the parameter regime in which it is applicable

Nullclines in the Oregonator model.

<p>We display the nullclines (logarithmic scale) of the activator species (blue curve) and the inhibitor (brown curve) for the Oregonator model in the deterministic limit for the parameter set given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042508#pone-0042508-t006" target="_blank">Table 6</a> and . We assume that the intermediary species is in a steady-state equilibrium with and and ignore diffusion. The blue (brown) arrow illustrates the gradient in phase space of the activator (inhibitor) on either side of the nullcline and the unstable fix point is marked with . The system is in the unstable (oscillatory) regime. We plot an example trajectory (dashed curve) of a larger perturbation from the (linearly stable) trivial homogeneous state. Starting at point , the system enters a limit cycle in phase space.</p

Nullclines in the Gray-Scott model.

<p>We display the nullclines of the activator species (blue curve) and the inhibitor (brown curve) for the Gray-Scott model (without diffusion) in the deterministic limit for the parameter set given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042508#pone-0042508-t004" target="_blank">Table 4</a>. The blue (brown) arrow illustrates the direction of the gradient in phase space of the activator (inhibitor) on either side of the nullcline and the unstable fix point is marked with . We demonstrate that the system is in the excitable regime by plotting an example trajectory (dashed curve) for a larger perturbation, starting at point , from the stable homogeneous state (marked by in the figure). The system relaxes towards via a long excursion.</p