On some properties of Goursat–Darboux systems with distributed and boundary controls

In this paper, a Goursat–Darboux control system is considered. In the first part, the bang-bang principle and some approximation results concerning the piecewise constant controls, for a linear system with distributed and boundary controls, are proved. In the second part, an approximation result concerning the bang-bang controls, for a special case of nonlinear (in a state) system with distributed controls, is derived.     

Energy Absorption by a Single Abrikosov’s Vortex in NbTi and YBaCuO Superconductors

The calculations of the absorption energy and the Q-factor of vibration of a vortex line under the effect of an external uniform harmonic force have been presented. The line tension of the vortex line and its effective mass, Magnus force, pinning force, and viscosity force were included in the equation of the dynamics. Two peaks of absorption in accordance with two modes of the oscillation spectrum were observed. The first peak of absorption is a result of flux pinning, which coincides with the De Gennes–Matricon solution in some limits. The second (high-frequency) peak is a result of a novel mode related to the effective mass of a vortex line. Temperature dependencies of absorption peaks were calculated for the NbTi and YBaCuO superconductors for orientations H∥c and H⊥c. The resonant frequency of the resonance peaks of absorption decreases with an increase in temperature. Some other peculiarities of the oscillating dynamics of the vortex line were discussed.     

Local controllability of quantum systems

We give a criterion that is sufficient for controllability of multipartite quantum systems. We generalize the graph infection criterion to the quantum systems that cannot be described with the use of a graph theory. We introduce the notation of hypergraphs and reformulate the infection property in this setting. The introduced criterion has a topological nature and therefore it is not connected to any particular experimental realization of quantum information processing.     

Organic whey as a source of Lactobacillus strains with selected technological and antimicrobial properties

Twenty‐five strains, isolated from raw, non‐pasteurised, organic whey samples, were identified phenotypically and genotypically. Biochemical tests were performed, and enzyme profiles, antibiotic resistance and antimicrobial properties were investigated. Sixteen strains were identified as genus Lactobacillus. Based on 16S rDNA gene sequence, the strains were identified as Lb. plantarum and Lb. fermentum. All of the strains had β‐galactosidase activity, and some of them reduced nitrate content. All strains utilised carbohydrates. The tested strains were characterised by low or average lipolytic and esterolytic activity. Moreover, the strains showed low proteolytic activity which is advantageous for their use as starter cultures for foods with low protein content. Strains Lb. fermentum S20, SM1, SM3, S2R and Lb. plantarum SM5 produced harmful N‐acetyl‐β‐glucosaminidase; moreover, the strain S20 produced also β‐glucuronidase. None of the strains produced α‐chymotrypsin. In phenotypic studies, most of the test strains were susceptible to gentamicin, ampicillin, tetracycline, chloramphenicol, penicillin and erythromycin. Strains Lb. plantarum S1 and Lb. fermentum S4, S7, S8, S10, SM1 and SM3 did not possess any transfer resistance genes. Antagonistic activity of the culture LAB strains was assessed as high or moderate in relation to the indicator strains, with the greatest zones of inhibition for E.coli and the smallest for L. monocytogenes ATCC 15313. This study reveals that the LAB strains isolated from organic whey have high potential for food application. Some strains of species Lb. fermentum (S4, S7, S8, S10) have been identified as the best candidates.     

The role of mechanical forces in the planar-to-bulk transition in growing Escherichia coli microcolonies

Mechanical forces are obviously important in the assembly of three-dimensional multicellular structures, but their detailed role is often unclear. We have used growing microcolonies of the bacterium Escherichia coli to investigate the role of mechanical forces in the transition from two-dimensional growth (on the interface between a hard surface and a soft agarose pad) to three-dimensional growth (invasion of the agarose). We measure the position within the colony where the invasion transition happens, the cell density within the colony and the colony size at the transition as functions of the concentration of the agarose. We use a phenomenological theory, combined with individual-based computer simulations, to show how mechanical forces acting between the bacterial cells, and between the bacteria and the surrounding matrix, lead to the complex phenomena observed in our experiments—in particular the observation that agarose concentration non-trivially affects the colony size at transition. Matching these approaches leads to a prediction for how the friction between the bacteria and the agarose should vary with agarose concentration. Our experimental conditions mimic numerous clinical and environmental scenarios in which bacteria invade soft matrices, as well as shedding more general light on the transition between two- and three-dimensional growth in multicellular assemblies.