Transition to synchrony in a three-dimensional swarming model with helical trajectories.

We investigate the transition from incoherence to global collective motion in a three-dimensional swarming model of agents with helical trajectories, subject to noise and global coupling. Without noise this model was recently proposed as a generalization of the Kuramoto model and it was found that alignment of the velocities occurs discontinuously for arbitrarily small attractive coupling. Adding noise to the system resolves this singular limit and leads to a continuous transition, either to a directed collective motion or to center-of-mass rotations.

Coupled Möbius maps as a tool to model Kuramoto phase synchronization.

We propose Möbius maps as a tool to model synchronization phenomena in coupled phase oscillators. Not only does the map provide fast computation of phase synchronization, it also reflects the underlying group structure of the sinusoidally coupled continuous phase dynamics. We study map versions of various known continuous-time collective dynamics, such as the synchronization transition in the Kuramoto-Sakaguchi model of nonidentical oscillators, chimeras in two coupled populations of identical phase oscillators, and Kuramoto-Battogtokh chimeras on a ring, and demonstrate similarities and differences between the iterated map models and their known continuous-time counterparts.

Repulsively coupled Kuramoto-Sakaguchi phase oscillators ensemble subject to common noise.

We consider the Kuramoto-Sakaguchi model of identical coupled phase oscillators with a common noisy forcing. While common noise always tends to synchronize the oscillators, a strong repulsive coupling prevents the fully synchronous state and leads to a nontrivial distribution of oscillator phases. In previous numerical simulations, the formation of stable multicluster states has been observed in this regime.

Nonspectral relaxation in one dimensional Ornstein-Uhlenbeck processes.

The relaxation of a dissipative system to its equilibrium state often shows a multiexponential pattern with relaxation rates, which are typically considered to be independent of the initial condition. The rates follow from the spectrum of a Hermitian operator obtained by a similarity transformation of the initial Fokker-Planck operator. However, some initial conditions are mapped by this similarity transformation to functions which grow at infinity.

Cloning, sequencing and recombinant expression of the open reading frame encoding a novel member of the Sarcocystis muris (Apicomplexa) microneme lectin family.

Micronemes are characteristic secretory organelles located within the apical cell region of apicomplexan parasites. The protein contents are exocytosed during an early phase of host cell invasion and contribute to parasite motility and the invasion of target cells. We report here on the cloning and heterologous expression of a novel member of the Sarcocystis muris microneme lectin family.