The self-organization of a thermally relativistic magnetized plasmacomprising of electrons, positrons and static ions is investigated. Theself-organized state is found to be the superposition of three distinctBeltrami fields known as triple Beltrami (TB) state. In general, theeigenvalues associated with the multiscale self-organized vortices may be apair of complex conjugate and real one. It is shown that all the eigenvaluesbecome real when thermal energy increases or the positron density decreases.The impact of relativistic temperature and positron density on the formation ofself-organized structures is investigated. The self-organized field and flowvortices may vary simultaneously on vastly different length scales. Thedisparate variation of self-organized vortices is important in the context ofdynamo theory. The present work is useful to study the formation of multiscalevortices and dynamo mechanisms in multi-species thermally relativistic plasmas.
The self-organization in a multi-ion plasma composed of electrons and twospecies of positively charged ions is investigated. It is shown that whencanonical vorticities and velocities of all the plasma fluids are aligned, themagnetic field self-organizes to Quadruple Beltrami state (superposition offour Beltrami fields). The self-organized magnetic and velocity fields stronglydepend on the relative strengths of the generalized vorticities, flows, inertiaand densities of the plasma species. Thus, it is possible to generate a widevariety of multiscale magnetic field and flow structures. It is also shown thatrelaxed magnetic fields and velocities can vary on vastly different lengthscales simultaneously and are coupled together through singular perturbationgenerated by Hall effect. In this multi Beltrami self-organized states, then,the dynamo mechanism emerges naturally. The scale separation also suggests theheating of the plasma through a dissipative process. The work could be usefulto study the dynamics and morphology of the multiscale magnetic fieldconfigurations in laboratory and astrophysical plasmas.
This paper is concerned with identifying linear system dynamics without the knowledge of individual system trajectories, but from the knowledge of the system's reachable sets observed at different times. Motivated by a scenario where the reachable sets are known from partially transparent manufacturer specifications or observations of the collective behavior of adversarial agents, we aim to utilize such sets to determine the unknown system's dynamics. The paper has two contributions. Firstly, we show that the sequence of the system's reachable sets can be used to uniquely determine the system's dynamics for asymmetric input sets under some generic assumptions, regardless of the system's dimensions. We also prove the same property holds up to a sign change for two-dimensional systems where the input set is symmetric around zero. Secondly, we present an algorithm to determine the system's dynamics. We apply and verify the developed theory and algorithms on an unknown band-pass filter circuit solely provided the unknown system's reachable sets over a finite observation period.
Abstract In the Bushveld Complex, South Africa, open pit mines are faced with a challenge of rock slope stability due to geological structures (fractures, faults and dykes) that compartmentalize the rock mass. Geophysical surveys (seismics, magnetics and electrical methods) were conducted in a 0.2 km 2 area at Tharisa mine, with the goal to delineate fractures that may be potential conduits for water migration into the pit. Special processing techniques were applied to the dataset to obtain good quality seismic, magnetic and resistivity models. The P‐wave velocity models show distinct low velocities in the centre of the seismic profile, indicating the presence of weak zones associated with faulting or fracturing. Seismic reflection method was used to image the deeper discontinuities and mineralization contacts. Near surface reflections are observed throughout the profiles and are correlated with the contact between the chromitite and host rock. Ground magnetic surveys were conducted to delineate dykes and fractures. De‐trending and de‐culturing techniques were applied on the magnetic data for correcting regional and temporal variations. The low magnetic regions indicate the presence of fracture systems in the subsurface, whereas the high magnetic region is correlated with the dolerite dyke that crosscuts the pit. The electrical resistivity tomography exhibits linear low resistivity contrast zones that differentiate between the fractured and undisturbed hard rock at an estimated depth of 4–10 m. Resistivity shows discontinuities that suggests the presence of fracturing and dyke‐host rock contacts. Correlation among magnetics, P‐wave velocity models, resistivity section and seismic data is evident when overlaying the different datasets, implying that the low magnetic regions are highly weathered and prone to fracturing. The integration of geophysical data is encouraging, because it was able to image the depth to the bedrock, fractures within the host rock and dyke in a complex mining environment.