Compression of tetrahedrally bonded SiO2 liquid and silicate liquid‐crystal density inversion

We have investigated the response to pressure of liquid SiO2 by performing a quantitatively realistic Monte Carlo simulation. The model liquid was restricted to at most four‐fold Si‐O coordination by the effective imposition of an infinite potential barrier to a fifth bond. We thus obtained an unambiguous comparison of the compression mechanisms of solid and liquid tetrahedral networks. In spite of this restriction, the density of the simulated liquid exceeds that of the corresponding models of quartz, coesite and cristobalite at high pressure. The efficient compression of the liquid results from a continuous restructuring of the network that leaves the mean Si‐Si distance virtually unchanged and does not require an increase in the coordination number. The restructuring is effected by local breaking and reconnecting of bonds, a mechanism that is not available to a perfect crystal

Stability of (Mg,Fe)SiO3 perovskite and the structure of the lowermost mantle

Thermodynamic analysis shows that (Mg,Fe)SiO3 perovskite is stable throughout the likely pressure, temperature and compositional regime of the Earth's mantle. The breakdown of perovskite to its constituent oxides appears unlikely, even under the extreme conditions of the core-mantle boundary. This reaction had been proposed to reconcile estimates of silicate melting with seismic observation and proposed geotherms

Microsystems technology: objectives

This contribution focuses on the objectives of microsystems technology (MST). The reason for this is two fold. First of all, it should explain what MST actually is. This question is often posed and a simple answer is lacking, as a consequence of the diversity of subjects that are perceived as MST. The second reason is that a map of the somewhat chaotic field of MST is needed to identify sub-territories, for which standardization in terms of system modules an interconnections is feasible. To define the objectives a pragmatic approach has been followed. From the literature a selection of topics has been chosen and collected that are perceived as belonging to the field of MST by a large community of workers in the field (more than 250 references). In this way an overview has been created with `applications¿ and `generic issues¿ as the main characteristics

Statistical Mechanics of Steiner trees

The Minimum Weight Steiner Tree (MST) is an important combinatorial optimization problem over networks that has applications in a wide range of fields. Here we discuss a general technique to translate the imposed global connectivity constrain into many local ones that can be analyzed with cavity equation techniques. This approach leads to a new optimization algorithm for MST and allows to analyze the statistical mechanics properties of MST on random graphs of various types

Scale free effects in world currency exchange network

A large collection of daily time series for 60 world currencies' exchange rates is considered. The correlation matrices are calculated and the corresponding Minimal Spanning Tree (MST) graphs are constructed for each of those currencies used as reference for the remaining ones. It is shown that multiplicity of the MST graphs' nodes to a good approximation develops a power like, scale free distribution with the scaling exponent similar as for several other complex systems studied so far. Furthermore, quantitative arguments in favor of the hierarchical organization of the world currency exchange network are provided by relating the structure of the above MST graphs and their scaling exponents to those that are derived from an exactly solvable hierarchical network model. A special status of the USD during the period considered can be attributed to some departures of the MST features, when this currency (or some other tied to it) is used as reference, from characteristics typical to such a hierarchical clustering of nodes towards those that correspond to the random graphs. Even though in general the basic structure of the MST is robust with respect to changing the reference currency some trace of a systematic transition from somewhat dispersed -- like the USD case -- towards more compact MST topology can be observed when correlations increase.Comment: Eur. Phys. J. B (2008) in pres

Dynamic structural and topological phase transitions on the Warsaw Stock Exchange: A phenomenological approach

We study the crash dynamics of the Warsaw Stock Exchange (WSE) by using the Minimal Spanning Tree (MST) networks. We find the transition of the complex network during its evolution from a (hierarchical) power law MST network, representing the stable state of WSE before the recent worldwide financial crash, to a superstar-like (or superhub) MST network of the market decorated by a hierarchy of trees (being, perhaps, an unstable, intermediate market state). Subsequently, we observed a transition from this complex tree to the topology of the (hierarchical) power law MST network decorated by several star-like trees or hubs. This structure and topology represent, perhaps, the WSE after the worldwide financial crash, and could be considered to be an aftershock. Our results can serve as an empirical foundation for a future theory of dynamic structural and topological phase transitions on financial markets

MST radar detection of middle atmosphere tides

Meteorological and dynamical requirements pertaining to the specification of middle atmosphere tides by the MST radar technique are outlined. Major issues addressed include: (1) the extraction of tidal information from measurements covering a fraction of a day; (2) the ramifications of transient effects (tidal variability) on the determination and interpretation of tides; (3) required temporal and spatial resolutions and; (4) global distributions of MST radars, so as to complement existing MST, meteor wind, and partial reflection drift radar locations