We examine how the choice of the movement algorithm can affect the success of a swarm of simple mobile robots attempting to disperse themselves in an unknown environment. We assume there is no central control, and the robots have limited processing power, simple sensors, and no active communication. We evaluate different movement algorithms based on the percentage of the environment that the gr...

Dispersing billiards with cusps are deterministic dynamical systems with a mild degree of chaos, exhibiting “intermittent” behavior that alternates between regular and chaotic patterns. Their statistical properties are therefore weak and delicate. They are characterized by a slow (power-law) decay of correlations, and as a result the classical central limit theorem fails. We prove that a non-cl...

Let T be a measure-preserving and mixing action of a countable abelian group G on a probability space (X, S, μ) and A a locally compact second countable abelian group. A cocycle c : G × X 7−→ A for T disperses if limg→∞ c(g, ·) − α(g) = ∞ in measure for every map α : G −→ A. We prove that such a cocycle c does not disperse if and only if there exists a compact subgroup A0 ⊂ A such that the comp...

Synthetic biology involves the engineering of biological organisms by using modular and generalizable designs with the ultimate goal of developing useful solutions to real-world problems. One such problem involves bacterial biofilms, which are crucial in the pathogenesis of many clinically important infections and are difficult to eradicate because they exhibit resistance to antimicrobial treat...

Let f : [0,+∞) −→ (0,+∞) be a sufficiently smooth convex function, vanishing at infinity. Consider the planar domain Q delimited by the positive x-semiaxis, the positive y-semiaxis, and the graph of f . Under certain conditions on f , we prove that the billiard flow in Q has a hyperbolic structure and, for some examples, that it is also ergodic. This is done using the cross section correspondin...

The aim of this study was to formulate and evaluate microencapsulated controlled release preparations of a highly water/soluble drug, salbutamol sulphate by (water in oil) in oil emulsion technique using ethyl cellulose as the retardant material. Various processing and formulation parameters such as drug/polymer ratio, stirring speed, volume of processing medium were optimized to maximize the e...

In the paper, in order to pre-concentrate and measure the low values of Cu ions, the new, simple,quick and very sensitive method of Dispersed Liquid-Liquid Micro Extraction (DLLME) coupledwith flame Atomic Absorption spectrometry (AA) has been utilized. The DLLME techniquecoupled with AA )AA-DLLME) was run inside one narrow tube which constitute aqueous samples.In this m...