Brownian Particles far from Equilibrium

We study a model of Brownian particles which are pumped with energy by means of a non-linear friction function, for which different types are discussed. A suitable expression for a non-linear, velocity-dependent friction function is derived by considering an internal energy depot of the Brownian particles. In this case, the friction function describes the pumping of energy in the range of small velocities, while in the range of large velocities the known limit of dissipative friction is reached. In order to investigate the influence of additional energy supply, we discuss the velocity distribution function for different cases. Analytical solutions of the corresponding Fokker-Planck equation in 2d are presented and compared with computer simulations. Different to the case of passive Brownian motion, we find several new features of the dynamics, such as the formation of limit cycles in the four-dimensional phase-space, a large mean squared displacement which increases quadratically with the energy supply, or non-equilibrium velocity distributions with crater-like form. Further, we point to some generalizations and possible applications of the model.Comment: 10 pages, 12 figure

The SUMER Data in the SOHO Archive

We have released an archive of all observational data of the VUV spectrometer Solar Ultraviolet Measurements of Emitted Radiation (SUMER) on SOHO that has been acquired until now. The operational phase started with 'first light' observations on 27 January 1996 and will end in 2014. Future data will be added to the archive when they become available. The archive consists of a set of raw data (Level 0) and a set of data that are processed and calibrated to the best knowledge we have today (Level 1). This communication describes step by step the data acquisition and processing that has been applied in an automated manner to build the archive. It summarizes the expertise and insights into the scientific use of SUMER spectra that has accumulated over the years. It also indicates possibilities for further enhancement of the data quality. With this article we intend to convey our own understanding of the instrument performance to the scientific community and to introduce the new, standard-FITS-format database.Comment: 38 pages, 9 figures, accepted for publication by Solar Physic

Zur Spannungsverteilung in thermisch beanspruchten elastisch-plastischen Kreisscheiben bei einem speziellen nichtlinearen Verfestigungsgesetz

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On the attractors of two-dimensional Rayleigh oscillators including noise

We study sustained oscillations in two-dimensional oscillator systems driven by Rayleigh-type negative friction. In particular we investigate the influence of mismatch of the two frequencies. Further we study the influence of external noise and nonlinearity of the conservative forces. Our consideration is restricted to the case that the driving is rather weak and that the forces show only weak deviations from radial symmetry. For this case we provide results for the attractors and the bifurcations of the system. We show that for rational relations of the frequencies the system develops several rotational excitations with right/left symmetry, corresponding to limit cycles in the four-dimensional phase space. The corresponding noisy distributions have the form of hoops or tires in the four-dimensional space. For irrational frequency relations, as well as for increasing strength of driving or noise the periodic excitations are replaced by chaotic oscillations.Comment: 9 pages, 5 figure

LT3 Drive: substitution of differentials in the drivetrain

The basic principle of the LT3 drive system is a planetary gearing with a rotatable ring gear. Rolling piston cylinders enable this rotation by acting on the cam disk shaped outside of the ring gear which fix or loosen the ring gear accordingly. By fixing the ring gear via the cylinders the gear ratio corresponds to the normal mechanical ratio of the gearing which is given by the combination of the planet gears and the ring gear. By loosening the ring gear completely there is no more power transmission to the carrier; hence, the carrier doesn’t rotate anymore. In between, the rotational speed can be adjusted continuously between 0 and the maximum speed within only a few milliseconds, “online”, as it were, depending on the compensatory need. The technology was verified by the chair of Mobile Machines (Mobima) at Karlsruhe Institute of Technology. During the current second development process, the controlling of the system via high pressure components was elaborated. Furthermore, LT3 was designed for high torques up to 8,000 Nm. A feasibility study for heavy-duty vehicles was completed successfully in 2016. The LT3 technology thereupon was ‘downsized’ for smaller systems. Possible applications for LT3 are all systems where synchronisation functions or to allow a superposition of the rotation speeds are necessary, especially with the objective to substitute the differential gear in electric vehicles with central motor. In today’s differential gears advanced driver-assistance systems normally intervene by brake action on the critical wheel. However, LT3 enables a planned control of each driven wheel. With that, active Torque Vectoring is possible which can operate foresightedly in every driving situation. Saving potential mainly in production is the result of using the LT3 system. Viscous coupling unit or Haldex unit as well as Torsen differential are dropped. Also, the ASR assistant is no longer needed. In E-mobility application, mainly in small vehicles, space could be used in a better way or rather the packaging could be designed more favourable because the LT3 drive takes two functions at once: speed reduction of the motor and differential compensation of the driven wheels

Noise-Induced Transition from Translational to Rotational Motion of Swarms

We consider a model of active Brownian agents interacting via a harmonic attractive potential in a two-dimensional system in the presence of noise. By numerical simulations, we show that this model possesses a noise-induced transition characterized by the breakdown of translational motion and the onset of swarm rotation as the noise intensity is increased. Statistical properties of swarm dynamics in the weak noise limit are further analytically investigated.Comment: 7 pages, 7 figure