Design of engineering systems in Polish mines in the third quarter of the 20th century

Participation of mathematicians in the implementation of economic projects in Poland, in which mathematics-based methods played an important role, happened sporadically in the past. Usually methods known from publications and verified were adapted to solving related problems. The subject of this paper is the cooperation between mathematicians and engineers in Wroc{\l}aw in the second half of the twentieth century established in the form of an analysis of the effectiveness of engineering systems used in mining. The results of this cooperation showed that at the design stage of technical systems it is necessary to take into account factors that could not have been rationally controlled before. The need to explain various aspects of future exploitation was a strong motivation for the development of mathematical modeling methods. These methods also opened research topics in the theory of stochastic processes and graph theory. The social aspects of this cooperation are also interesting.Comment: 45 pages, 11 figures, 116 reference

Liquid jet eruption from hollow relaxation

A cavity hollowed out on a free liquid surface is relaxing, forming an intense liquid jet. Using a model experiment where a short air pulse sculpts an initial large crater, we depict the different stages in the gravitational cavity collapse and in the jet formation. Prior eversion, all cavity profiles are found to exhibit a shape similarity. Following hollow relaxation, a universal scaling law establishing an unexpected relation between the jet eruption velocity, the initial cavity geometry and the liquid viscosity is evidenced experimentally. On further analysing the jet forms we demonstrate that the stretched liquid jet also presents shape similarity. Considering that the jet shape is a signature of the initial flow focusing, we elaborate a simple model capturing the key features of the erupting jet velocity scaling

A pressure impulse theory for hemispherical liquid impact problems

Liquid impact problems for hemispherical fluid domain are considered. By using the concept of pressure impulse we show that the solution of the flow induced by the impact is reduced to the derivation of Laplace's equation in spherical coordinates with Dirichlet and Neumann boundary conditions. The structure of the flow at the impact moment is deduced from the spherical harmonics representation of the solution. In particular we show that the slip velocity has a logarithmic singularity at the contact line. The theoretical predictions are in very good agreement both qualitatively and quantitatively with the first time step of a numerical simulation with a Navier-Stokes solver named Gerris.Comment: 11 pages, 14 figures, Accepted for publication in European Journal of Mechanics - B/Fluid

Soft beams: when capillarity induces axial compression

We study the interaction of an elastic beam with a liquid drop in the case where bending and extensional effects are both present. We use a variational approach to derive equilibrium equations and constitutive relation for the beam. This relation is shown to include a term due to surface energy in addition of the classical Young's modulus term, leading to a modification of Hooke's law. At the triple point where solid, liquid, and vapor phases meet we find that the external force applied on the beam is parallel to the liquid-vapor interface. Moreover, in the case where solid-vapor and solid-liquid interface energies do not depend on the extension state of the beam, we show that the extension in the beam is continuous at the triple point and that the wetting angle satisfy the classical Young-Dupr\'e relation

On the physics of fizzing: How bubble bursting controls droplets ejection

Bubbles at a free surface surface usually burst in ejecting myriads of droplets. Focusing on the bubble bursting jet, prelude for these aerosols, we propose a simple scaling for the jet velocity and we unravel experimentally the intricate roles of bubble shape, capillary waves, gravity and liquid properties. We demonstrate that droplets ejection unexpectedly changes with liquid properties. In particular, using damping action of viscosity, self-similar collapse can be sheltered from capillary ripples and continue closer to the singular limit, therefore producing faster and smaller droplets.These results pave the road to the control of the bursting bubble aerosols

Decentralizacja władzy publicznej jako efekt przemian ustrojowych w Polsce

The main aim of this paper is to answer the following questions: does the present model of local government, professional associations and self-regulatory business associations fulfil the idea of decentralisation? Does it meet the expectations of the authors of the 1989 system reform? The currently functioning model of administration assumes the execution of administrative tasks by both the centralised governmental administration and a multifarious system of independent bodies and institutions which carry out public tasks vested in them by legislation. Apart from some obligatory units, like the units of local government, there are some other entities which have a significant role in the public sphere: professional associations and self-regulatory business associations.Przedmiotem tego opracowania jest próba udzielenia odpowiedzi na pytanie: Czy obecnie funkcjonujący model samorządu terytorialnego, zawodowego i gospodarczego jest urzeczywistnieniem idei decentralizacji i spełnieniem oczekiwań twórców reformy systemowej z roku 1989?Obecnie funkcjonujący model administracji zakłada jej wykonywanie zarówno przez aparat scentralizowanej administracji rządowej, jak również wieloraki układ organów czy instytucji działających samodzielnie i wykonujących powierzone im w drodze ustaw zadania publiczne w imieniu własnym i na własną odpowiedzialność. Oprócz jednostek obligatoryjnych o podstawowym znaczeniu, jak na przykład jednostki samorządu terytorialnego, równie istotną role w sferze publicznej odgrywa samorząd zawodowy i gospodarczy