The Planck length and the constancy of the speed of light in five dimensional space parametrized with two time coordinates

In relativity and quantum field theory, the vacuum speed of light is assumed to be constant; the range of validity of general relativity is determined by the Planck length. However, there has been no convincing theory explaining the constancy of the light speed. In this paper, we assume a five dimensional spacetime with three spatial dimensions and two local time coordinates giving us a hint about the constancy of the speed of light. By decomposing the five dimensional spacetime vector into four-dimensional vectors for each time dimension and by minimizing the resulting action, for a certain class of additional time dimensions, we observe the existence of a minimal length scale, which we identify as the Planck scale. We derive an expression for the speed of light as a function of space and time and observe the constancy of the vacuum speed of light in the observable universe

Thinking in Terms of System Hierarchies and Velocites. What makes Development Sustainable?

In order to understand the context for sustainable development policies it is necessary to understand how different rates of evolution and velocities of change within social and ecological systems affect interactions between and the co-evolution of those systems. Sustainable development policies will bear fruit only when we can discuss sustainable development not only of separate interdependent or nested systems in a global hierarchy, but also in relation to their widely varying, but interrelated rates and courses of development and evolution.

Statistical analysis of bacteria locomotion

Many bacteria swim by employing their helical appendages, the flagella. We studied the statistics of this locomotion. To obtain more natural and especially long trajectories compared to two-dimensional tracking strategies, we developed a measurement-setup suitable to track bacteria in three-dimensions.The main component of this setup is an electrically focus tunable lens (ETL), able to adapt it’s shape via an applied electrical current, resulting in a change of the current focal plane. This setup has no mechanical interaction with the sample to avoid adulteration of the measured trajectories. We found that for times smaller than the average running-time, the slope of the mean-squared displacement MSD of the tracked bacteria obeys a ballistic behavior, whereas for longer times we saw a clear diffusive behavior. To allow for a more efficient evaluation of the measured trajectories we introduce the Kalman-Filter. By using simulated trajectories we could show that the Kalman-Filter allows a more accurate determination of the rotational-diffusion coefficient than conventional methods. Furthermore we could show that evaluation of three-dimensional trajectories obeys slightly different statistics than the evaluation of projected two-dimensional trajectories due to missing information.Through the qualitative simulation of bacteria locomotion we could show that the flagella-positioning has a crucial impact on the tumbling dynamics.Viele Bakterien schwimmen durch Nutzung ihrer spiralförmigen Anhänge,den Flagellen. Wir untersuchten die Statistik dieser Bewegung. Um natürlichere und vor allem längere Trajektorien - verglichen mit konventionellen zweidimensionalen Trackingmethoden - zu erhalten, haben wir einen Messaufbau zum dreidimensionalen tracken von Bakterien entwickelt. Die Hauptkomponente dieses Setups ist eine elektrische, fokusanpassbare Linse (ETL),welche ihre Form durch Anlegen eines elektrischen Stroms ändern kann,was zu einer Änderung der Fokusebene führt. Dieser Messaufbau hat keine mechanischen Wechselwirkungen mit der Probe, wodurch Verfälschungender gemessenen Trajektorien verhindert werden. Wir konnten zeigen dassfür Zeiten kleiner als die durchschnittlicherunning-Zeit (dt.Renn-Zeit), die mittlere quadratische Verschiebung (MSD) der getrackten Bakterien ein ballistisches Verhalten zeigt, wohingegen für längere Zeiten ein diffusives Verhalten vorliegt. Um eine effizientere Auswertung der gemessenen Trajektorien zu erlauben, führten wir den Kalman-Filter ein. Durch Nutzung simulierterTrajektorien konnten wir zeigen dass der Kalman-Filter eine genauere Bestimmung des Rotations-Diffusionskoeffizienten - verglichen mit konventionellen Methoden - erlaubt.Weiterhin konnten wir zeigen, dass die Auswertung dreidimensionaler Trajektorien leicht andere Statistiken als die Auswertung zweidimensionaler Trajektorien liefert, was durch den Verlust an Information zu erklären ist. Durch die qualitative Simulation der Bewegung von Bakterien konnten wir zeigen, dass die Position der Flagellen einen wesentlichen Einfluss auf die Tumbling-Dynamik (dt.Taumel-Dynamik) hat

Characterisation of liver progenitor cells and their microenvironment during chronic liver disease and hepatocarcinogenesis

The studies in this thesis aimed to characterise liver progenitor cells and their microenvironment during chronic liver injury conditions. A comprehensive comparison of the two common murine chronic liver disease models, CDE versus TAA, was performed. Parameters such as hepatocyte health, inflammation, fibrosis and the LPC response were investigated during stages of injury induction, establishment, maintenance, progression and carcinogenesis. Furthermore, the relationship between LPCs and HCC development in humans was investigated in a retrospective study

The emission of energetic electrons from the complex streamer corona adjacent to leader stepping

We here propose a model to capture the complexity of the streamer corona adjacent to leader stepping and relate it to the production of energetic electrons serving as a source of X-rays and $\gamma$-rays, manifesting in terrestrial gamma-ray flashes (TGFs). During its stepping, the leader tip is accompanied by a corona consisting of multitudinous streamers perturbing the air in its vicinity and leaving residual charge behind. We explore the relative importance of air perturbations and preionization on the production of energetic run-away electrons by 2.5D cylindrical Monte Carlo particle simulations of streamers in ambient fields of 16 kV cm$^{-1}$ and 50 kV cm$^{-1}$ at ground pressure. We explore preionization levels between $10^{10}$ m$^{-3}$ and $10^{13}$ m$^{-3}$, channel widths between 0.5 and 1.5 times the original streamer widths and air perturbation levels between 0\% and 50\% of ambient air. We observe that streamers in preionized and perturbed air accelerate more efficiently than in non-ionized and uniform air with air perturbation dominating the streamer acceleration. We find that in unperturbed air preionization levels of $10^{11}$ m$^{-3}$ are sufficient to explain run-away electron rates measured in conjunction with terrestrial gamma-ray flashes. In perturbed air, the production rate of runaway electrons varies from $10^{10}$ s$^{-1}$ to $10^{17}$ s$^{-1}$ with maximum electron energies from some hundreds of eV up to some hundreds of keV in fields above and below the breakdown strength. In the presented simulations the number of runaway electrons matches with the number of energetic electrons measured in alignment with the observations of terrestrial gamma-ray flashes. Conclusively, the complexity of the streamer zone ahead of leader tips allows explaining the emission of energetic electrons and photons from streamer discharges.Comment: 29 pages, 11 figures, 2 table