Billiard with a handle

Effectiveness of glass beads for plating cell cultures

Cell plating, the spreading out of a liquid suspension of cells on a surface followed by colony growth, is a common laboratory procedure in microbiology. Despite this, the exact impact of its parameters on colony growth has not been extensively studied. A common protocol involves the shaking of glass beads within a Petri dish containing solid growth media. We investigated the effects of multiple parameters in this protocol: the number of beads, the shape of movement, and the number of movements. Standard suspensions of Escherichia coli were spread while varying these parameters to assess their impact on colony growth. Results were assessed by a variety of metrics: the number of colonies, the mean distance between closest colonies, and the variability and uniformity of their spatial distribution. Finally, we devised a mathematical model of shifting billiard to explain the heterogeneities in the observed spatial patterns. Exploring the parameters that affect the most fundamental techniques in microbiology allows us to better understand their function, giving us the ability to precisely control their outputs for our exact needs.

Internal chaotic sea structure and chaos-chaos intermittency in Hamiltonian systems

In this paper, we study the inhomogeneity of chaotic sea properties far from islands in billiardlike systems and its influence on distributions of particle's return times. A visibly homogeneous chaotic sea at certain parameters has a nontrivial internal structure, in particular, being divided into two chaotic phases with different properties. These phases are not separated by any obstacles, neither in phase nor in configuration spaces, and are partially overlaying. The emergence of a chaotic sea structure may be explained by the existence of remnants of integrable behavior, like sites of regular trajectories of broken islands of stability built into the chaotic sea. In the case of such chaotic seas, we find distributions of return times with two main sites of exponential decay.

Thin structure of the transit time distributions of open billiards

It is known that typical open billiards distribution of transit times is an exponentially decaying function, possibly with a power-law tail. In the paper we show that on small scales some of such distributions change their appearance. These distributions contain a quasiperiodic thin structure, which carries a significant amount of information about the system. Origin and properties of this structure are discussed.