Typical properties of dynamic systems and the instability of hydrodynamic flows

Summary Based on Peixot's theorem of topological dynamics, the unstable behaviour of hydrodynamic flows on a two-dimensional annuloid T ² is analysed. The generating property is the curvature of the group of S ₀ Diff T ² diffeomorphisms of the (Riemannian) flow region T ² . This group is the configuration space of the ideal fluid flowing on T ² .

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a m ma u mn u ¶rt;uauu ¶rt;am mu n¶rt;uu¶rt;¶rt;uauu nm a ¶rt; m T ² u¶rt; mu. ¶rt;au m m a m uuann S ₀ Diff T ² ¶rt;uu amu mu ( uaa) T ² . manna m uau nmam ¶rt; u¶rt;a u¶rt;mu a T ² .

     

Role of crustal fluids in triggering the West Bohemia/Vogtland earthquake swarms: Just what we know (a review)

We summarise the results of seismological studies related to triggering mechanisms, driving forces and source processes of the West Bohemia/Vogtland earthquake swarms with the aim to disclose the role of crustal fluids in the preparation, triggering and governing of the swarms. We present basic characteristics distinguishing earthquake swarms from tectonic mainshock-aftershock sequences and introduce existing earthquakes swarm models. From the statistical characteristics and time-space distribution of the foci we infer that self-organization is a peculiarity of West Bohemia/Vogtland swarms. We discuss possible causes of the foci migration in these swarms from the viewpoint of co-seismic and/or post-seismic stress changes and diffusion of the pressurized fluids, and we summarize hitherto published models of triggering the 2000-swarm. Attention is paid to the source mechanisms, particularly to their non-shear components. We consider possible causes of different source mechanisms of the 1997-and 2000-swarms and infer that pure shear processes controlled solely by the regional tectonic stress prevail in them, and that additional tensile forces may appear only at unfavourably oriented faults. On data from the fluid injection experiment at the HDR site Soultz (Alsace), we also show that earthquakes triggered by fluids can represent purely shear processes. Thus we conclude that increased pore pressure of crustal fluids in the region plays a key role in bringing the faults from the subcritical to critical state. The swarm activities are mainly driven by stress changes due to co-seismic and post-seismic slips, which considerably depend on the frictional conditions at the fault; crustal fluids keep the fault in a critical state. An open question still remains the cause of the repeatedly observed almost simultaneous occurrence of seismic activity in different focal zones in a wider area of West Bohemia/Vogtland. The analysis of the space-time relations of seismicity in the area between 1991 and 2007 revealed that during a significant part of this time span the seismicity was switching among distant focal zones. This indicates a common triggering force which might be the effect of an increase of crustal-fluid pore-pressure affecting a wider epicentral region.     

The effect of surface topography on the lunar photoelectron sheath and electrostatic dust transport

The dayside near-surface lunar plasma environment is electrostatically complex, due to the interaction between solar UV-induced photoemission, the collection of ambient ions and electrons, and the presence of micron and sub-micron sized dust grains. Further complicating this environment, although less well understood in effect, is the presence of surface relief, typically in the form of craters and/or boulders. It has been suggested that such non-trivial surface topography can lead to complex electrostatic potentials and fields, including “mini-wakes” behind small obstacles to the solar wind flow and “supercharging” near sunlit-shadowed boundaries (Criswell, D.R., De, B.R. [1977]. J. Geophys. Res. 82 (7); De, B.R., Criswell, D.R. [1977]. J. Geophys. Res. 82 (7); Farrell, W.M., Stubbs, T.J., Vondrak, R.R., Delory, G.T., Halekas, J.S. [2007]. Geophys. Res. Lett. 34; Wang, X., Horányi, M., Sternovsky, Z., Robertson, S., Morfill, G.E. [2007]. Geophys. Res. Lett. 34, L16104). In this paper, we present results from a three-dimensional, self-consistent, electrostatic particle-in-cell code used to model the dayside near-surface lunar plasma environment over a variety of local times with the presence of a crater. Additionally, we use the particle-in-cell model output to study the effect of surface topography on the dynamics of electrostatic dust transport, with the goal of understanding previous observations of dust dynamics on the Moon and dust ponding on various asteroids.     

Layered Velocity Models of the Western Bohemia Region

A new robust and effective optimization algorithm – isometric algorithm – was used for the inversion of layered velocity models, with constant gradient in each layer, to find suitable 1-D models for the location of microearthquakes in the individual four subregions of the West Bohemian earthquake swarm region. Models which are considered as optimal yield the minimum sum of the absolute values of the travel-time residua in locating the whole group of earthquakes in the given subregion. The results obtained from the inversion of P and S waves and from P waves only are shown. For comparison, optimum homogeneous models derived by the grid search method, again using both P and S waves and P waves only, are given. The computations indicate that the models for the individual subregions differ from each other. For layered models the differences are more pronounced, as expected, in the upper parts, down to depths of about 5 km. In comparison with the subregions Nový Kostel and Plesná, the P and S wave velocities for subregion Lazy are relatively higher and the P and S velocities for subregion Klingenthal relatively lower. In the lower parts the differences are smaller and the velocities have practically identical gradients. The highest velocities were obtained for subregion Lazy and the lowest velocities for subregion Klingenthal, as well for the homogeneous models. The model that represents the whole swarm region was determined in a similar way. This model is compared with the previously published velocity-depth distribution, obtained from DSS profile VI/70 in the vicinity of the area under study.     

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