The nature of triad interactions in active turbulence

Generalized Navier-Stokes (GNS) equations describing three-dimensional (3D) active fluids with flow-dependent spectral forcing have been shown to possess numerical solutions that can sustain significant energy transfer to larger scales by realising chiral Beltrami-type chaotic flows. To rationalise these findings, we study here the triad truncations of polynomial and Gaussian GNS models focusing on modes lying in the energy injection range. Identifying a previously unknown cubic invariant, we show that the asymptotic triad dynamics reduces to that of a forced rigid body coupled to a particle moving in a magnetic field. This analogy allows us to classify triadic interactions by their asymptotic stability: unstable triads correspond to rigid-body forcing along the largest and smallest principal axes, whereas stable triads arise from forcing along the middle axis. Analysis of the polynomial GNS model reveals that unstable triads induce exponential growth of energy and helicity, whereas stable triads develop a limit cycle of bounded energy and helicity. This suggests that the unstable triads dominate the initial relaxation stage of the full hydrodynamic equations, whereas the stable triads determine the statistically stationary state. To test this hypothesis, we introduce and investigate the Gaussian active turbulence model, which develops a Kolmogorov-type $-5/3$ energy spectrum at large wavelengths. Similar to the polynomial case, the steady-state chaotic flows spontaneously accumulate non-zero mean helicity while exhibiting Beltrami statistics and upward energy transport. Our results suggest that self-sustained Beltrami-type flows and an inverse energy cascade may be generic features of 3D active turbulence models with flow-dependent spectral forcing.Comment: 28 pages, 10 figure

Distribution of endangered and protected species of synanthropic plants in Łask

The article presents description and distribution of protected and endangered species of synanthropic plants found in the Łask area in 2001-2002. The research was carried out with the use of a cartogram method. As a result, ten species of protected plants were found in the researched area, four of which under strict protection, and six under partial protection. Eight out of the ten protected species are in the danger of extinction.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 dofinansowane zostało ze środków MNiSW w ramach działalności upowszechniającej naukę

Vascular plants flora of the railway grounds of Łask

In the paper a list and general characterization of vascular plants flora recorded on railway grounds of Łask is presented. The great diversity of habitats within the railway grounds as well as their readiness to accept numerous introduced species result in high variety of vascular plants there. This flora consists of 369 taxa.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 dofinansowane zostało ze środków MNiSW w ramach działalności upowszechniającej naukę

Geometry and topology of CC and CQ states

We show that multipartite mixed bipartite CC and CQ states are geometrically and topologically distinguished in the space of states. They are characterized by non-vanishing Euler-Poincar\'{e} characteristics on the topological side and by the existence of symplectic structure on the geometric side.Comment: Corrected version, Accepted for publication in JM

Lost in the quest for novelty : remarks on the role of openness of the culture to repetitions

Repetitions can be analysed from various perspectives: historical, moral, legal, commercial etc. Their evaluation varies depending on the point of view one chooses to adopt. For instance, plain repetition (copying) can be considered a theft from the moral perspective, while in the same time it can be considered beneficial from the perspective of culture propagation. From the perspective of memetics, such repetitions are necessary for the memes to survive and the tendency to repeat those “memes” constitutes their fitness to cultural environment. To be closer to biological analogy one should recognize those repetitions as replications. From such perspective the program of reducing replications through the means of “prohibition” becomes not only absurd and unreachable but also it would significantly slow or even push the process of evolution backwards. One should notice that any restrictions on copying were absent in various historical periods. For instance, one of the most important ideals of culture in middle ages was exact copying and preserving the works of the Antique, obviously without any permission of the authors or their successors. It is not until the time when the artistic value becomes reduced to its commercial value that the problem of an intellectual theft arises. No artist works in an intellectual vacuum, thus no one has the full rights to the composition. There are two main reasons for such introducing the concept of an intellectual value. The first is the liberalization of the society leading to its decay into individuals aiming at their own interests. The other is the rapid growth of the “new media” technology, which allows for mindless copying – disregarding any justification or understanding. The latter is not a big problem due to the error elimination in the process of evolution. The former, however, as leading to the disintegration of society is really dangerous. In the nature it would result in the species extinction. In the culture some similarities can also be seen and will be analysed in the present paper

The nature of triad interactions in active turbulence

Generalised Navier-Stokes (GNS) equations describing three-dimensional active fluids with flow-dependent narrow spectral forcing have been shown to possess numerical solutions that can sustain significant energy transfer to larger scales by realising chiral Beltrami-type chaotic flows. To rationalise these findings, we study here the triad truncations of polynomial and Gaussian GNS models focusing on modes lying in the energy injection range. Identifying a previously unknown cubic invariant for the triads, we show that their asymptotic dynamics reduces to that of a forced rigid body coupled to a particle moving in a magnetic field. This analogy allows us to classify triadic interactions by their asymptotic stability: unstable triads correspond to rigid-body forcing along the largest and smallest principal axes, whereas stable triads arise from forcing along the middle axis. Analysis of the polynomial GNS model reveals that unstable triads induce exponential growth of energy and helicity, whereas stable triads develop a limit cycle of bounded energy and helicity. This suggests that the unstable triads dominate the initial relaxation stage of the full hydrodynamic equations, whereas the stable triads determine the statistically stationary state. To test whether this hypothesis extends beyond polynomial dispersion relations, we introduce and investigate an alternative Gaussian active turbulence model. Similar to the polynomial case, the steady-state chaotic flows in the Gaussian model spontaneously accumulate non-zero mean helicity while exhibiting Beltrami statistics and upward energy transport. Our results suggest that self-sustained Beltrami-type flows and an inverse energy cascade may arise generically in the presence of flow-dependent narrow spectral forcing

Koncepcja budowy systemu motywowania pracowników urzędów gmin miejskich

The presented article is taking issue of local government employees motivation and building the creative teams in local government units, paying the close attention to specificity of their work. As a result of the considerations, it has been shown, that the solutions of motivation systems used in the offices do not provide the level of employees motivation fit for the 21st century organization. In the article there were presented the idea, the rules and the conditions of local government functioning including the legal provisions of municipal district activity. The main purpose of undertaken research was to create the original, personalized motivation system of local government employees which would be coherent with municipal districts assignments because only effectively motivated employees are the most efficient, loyal to the organization, engaged in work, but above all they do their work at high level. The empirical research has been done among the employees of 21 chosen offices in Pomerania Province municipal districts. On the basis of performed studies there have been identified the employees expectations prioritised in the context of motivation. The research has also shown that different offices use similar motivation means. Due to conducted research, defining the effect of individual motivation factors on employees, the employer will be able to create the level of motivation which guarantees the high effectiveness and fits the specificity and difficulty of the assignments performed by local government employees. The article was written on the basis on elaborations and own research and also on specialist and periodic literature. The current legal regulations concerning on local government functioning have been very important, including internal regulations of examined local government units.Artykuł podejmuje problematykę motywowania pracowników i budowę zespołów w jednostkach samorządu terytorialnego, zwracając szczególną uwagę na specyfikę ich pracy. W wyniku rozważań wykazano, że stosowane w urzędach rozwiązania systemów motywowania nie zapewniają poziomu motywacji pracowników na miarę organizacji XXI wieku. W artykule zaprezentowano ideę, zasady oraz warunki funkcjonowania samorządu terytorialnego, w tym unormowania prawne działalności gminy. Główny cel podjętych badań stanowiło stworzenie autorskiego spersonalizowanego systemu motywowania pracowników jednostek samorządu terytorialnego spójnego z zadaniami gminy, ponieważ tylko skutecznie zmotywowani pracownicy są najbardziej efektywni, lojalni wobec organizacji, zaangażowani w pracę, ale przede wszystkim wykonują ją na wysokim poziomie. Badania empiryczne prowadzono wśród pracowników 21 losowo wybranych urzędów gmin miejskich województwa pomorskiego. W oparciu o przeprowadzone badania zidentyfikowano oczekiwania pracowników samorządowych, dokonując ich hierarchizacji w kontekście potencjału motywowania. Wykazały one również, że różne urzędy stosują podobne sposoby i narzędzia motywowania. Dzięki przeprowadzonym badaniom, określającym, jaki wpływ na pracowników mają poszczególne czynniki motywowania, pracodawca będzie mógł kształtować poziom motywacji, który gwarantuje dużą skuteczność działania oraz dopasowany jest do specyfiki i trudności zadań wykonywanych przez pracowników jednostek samorządu terytorialnego. Artykuł napisany został w oparciu o opracowania i badania własne oraz literaturę zwartą i periodyczną. Bardzo istotne były aktualne regulacje prawne działalności urzędów administracji samorządowej, w tym regulacje wewnętrzne badanych jednostek samorządu terytorialnego