Solving large-scale dynamic systems using band Lanczos method in Rockwell NASTRAN on CRAY X-MP

The improved cost effectiveness using better models, more accurate and faster algorithms and large scale computing offers more representative dynamic analyses. The band Lanczos eigen-solution method was implemented in Rockwell's version of 1984 COSMIC-released NASTRAN finite element structural analysis computer program to effectively solve for structural vibration modes including those of large complex systems exceeding 10,000 degrees of freedom. The Lanczos vectors were re-orthogonalized locally using the Lanczos Method and globally using the modified Gram-Schmidt method for sweeping rigid-body modes and previously generated modes and Lanczos vectors. The truncated band matrix was solved for vibration frequencies and mode shapes using Givens rotations. Numerical examples are included to demonstrate the cost effectiveness and accuracy of the method as implemented in ROCKWELL NASTRAN. The CRAY version is based on RPK's COSMIC/NASTRAN. The band Lanczos method was more reliable and accurate and converged faster than the single vector Lanczos Method. The band Lanczos method was comparable to the subspace iteration method which was a block version of the inverse power method. However, the subspace matrix tended to be fully populated in the case of subspace iteration and not as sparse as a band matrix

Control of synchronization regimes in networks of mobile interacting agents

We investigate synchronization in a population of mobile pulse-coupled agents with a view towards implementations in swarm robotics systems and mobile sensor networks. Previous theoretical approaches dealt with range and nearest neighbor interactions. In the latter case, a synchronization-hindering regime for intermediate agent mobility was found. In the present work, we investigate the robustness of this intermediate regime under practical scenarios. We show that synchronization in the intermediate regime can be predicted by means of a suitable metric of the phase response curve. Furthermore, we study more realistic K-nearest neighbors and cone of vision interactions, showing that it is possible to control the extent of the synchronization-hindering region by appropriately tuning the size of the neighborhood. To assess the effect of noise, we analyze the propagation of perturbations over the network and draw an analogy between the response in the hindering regime and stable chaos. Our findings reveal the conditions for the control of clock or activity synchronization of agents with intermediate mobility. In addition, the emergence of the intermediate regime is validated experimentally using a swarm of physical robots interacting with cone of vision interactions

Desynchronization in diluted neural networks

The dynamical behaviour of a weakly diluted fully-inhibitory network of pulse-coupled spiking neurons is investigated. Upon increasing the coupling strength, a transition from regular to stochastic-like regime is observed. In the weak-coupling phase, a periodic dynamics is rapidly approached, with all neurons firing with the same rate and mutually phase-locked. The strong-coupling phase is characterized by an irregular pattern, even though the maximum Lyapunov exponent is negative. The paradox is solved by drawing an analogy with the phenomenon of ``stable chaos'', i.e. by observing that the stochastic-like behaviour is "limited" to a an exponentially long (with the system size) transient. Remarkably, the transient dynamics turns out to be stationary.Comment: 11 pages, 13 figures, submitted to Phys. Rev.

Firefly-Inspired Synchronization in Swarms of Mobile Agents

Recently, there has been growing interest in the synchronization of mobile pulse-coupled oscillators. We build on the work by Prignano et al. (Phys. Rev. Lett. 110, 114101) and show that agents that interact exclusively with others in their cone of vision can exhibit different synchronization regimes. Depending on their speed, synchronization emerges as a slow process through spreading of the local coherence, as a fast process where global synchronization dominates, or it is inhibited for a range of intermediate speeds. In addition, we show that, not only the speed of the agents, but also their angle and range of interaction can tune the appearance of this intermediate regime

Integrate and Fire Neural Networks, Piecewise Contractive Maps and Limit Cycles

We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the stable asymptotic dynamics consists of limit cycles. We also find sufficient conditions for the synchronization of networks containing excitatory neurons. The proofs are based on the analysis of the equivalent dynamics of a piecewise continuous Poincar\'e map associated to the system. We show that for strong interactions the Poincar\'e map is piecewise contractive. Using this contraction property, we prove that there exist a countable number of limit cycles attracting all the orbits dropping into the stable subset of the phase space. This result applies not only to the Poincar\'e map under study, but also to a wide class of general n-dimensional piecewise contractive maps.Comment: 46 pages. In this version we added many comments suggested by the referees all along the paper, we changed the introduction and the section containing the conclusions. The final version will appear in Journal of Mathematical Biology of SPRINGER and will be available at http://www.springerlink.com/content/0303-681

A method for determining gas-hydrate or free-gas saturation of porous media from seismic measurements

The occurrence of gas hydrate or free gas in a porous medium changes the medium’s elastic properties. Explicit formulas for gas-hydrate or free-gas saturation of pore space on the basis of the Frenkel-Gassmann equations describe the elastic moduli and seismic velocities of a porous medium for low frequencies. A key assumption of the model is that either gas hydrate or free gas is present in the pore space in addition to water. Under this assumption, the method uses measured P- and S-wave velocities and bulk density along with estimates of the moduli and densities of the solid and fluid phases present to determine whether gas or hydrate is present. The method then determines the saturation level of either the gas or the hydrate. I apply the method to published velocity and density data from seismic studies at the antarctic Shetland margin and at the Storegga slide, offshore Norway, and to borehole log and core data from Ocean Drilling Program (ODP) Leg 164 at Blake Ridge, offshore South Carolina. A sensitivity analysis reveals that the standard deviations of the gas-hydrate and free-gas saturations reach 30%–70% of the saturations if the standard deviations of the P- and S-wave velocities and of the bulk density are 50m∕s ..

Seismic investigation of a bottom simulating reflector and quantification of gas hydrate in the Black Sea

A bottom simulating reflector (BSR), which marks the base of the gas hydrate stability zone, has been detected for the first time in seismic data of the Black Sea. The survey area is in the northwestern Black Sea at 44°–45°N and 31.5°–32.5°E. In this paper, seismic wide-angle ocean bottom hydrophone (OBH) and ocean bottom seismometer (OBS) data are investigated with the goal to quantify the gas hydrate and free gas saturation in the sediment. An image of the subsurface is computed from wide-angle data by using Kirchhoff depth migration. The image shows the BSR at 205–270 m depth below the seafloor and six to eight discrete layer boundaries between the seafloor and the BSR. The top of the hydrate layer and the bottom of the gas layer cannot be identified by seismic reflection signals. An analysis of traveltimes and reflection amplitudes leads to 1-D P-wave velocity–depth and density–depth models. An average S-wave velocity of 160 m s−1 between the seafloor and the BSR is determined from the traveltime of the P to S converted wave. The normal incidence PP reflection coefficient at the BSR is −0.11, where the P-wave velocity decreases from 1840 to 1475 m s−1. Velocities and density are used to compute the porosity and the system bulk modulus as a function of depth. The Gassmann equation for porous media is used to derive explicit formulae for the gas hydrate and free gas saturation, which depend on porosity and on the bulk moduli of the dry and saturated sediment. A gas hydrate saturation–depth profile is obtained, which shows that there is 38 ± 10 per cent hydrate in the pore space at the BSR depth, where the porosity is 57 per cent (OBS 24). This value is derived for the case that the gas hydrate does not cement the sediment grains, a model that is supported by the low S-wave velocities. There is 0.9 or 0.1 per cent free gas in the sediment below the BSR, depending on the model for the gas distribution in the sediment. The free gas layer may be more than 100 m thick as a result of a zone of enhanced reflectivity, which can be identified in the subsurface image

Acoustic imaging of the Dvurechenskii mud volcano in the Black Sea

In the CRIMEA project submarine gas emitting sites in the Black Sea are investigated in order to quantify methane transfer through the water column into the atmosphere. One target area is the Dvurechenskii mud volcano (DMV) in the Sorokin Trough south-east of the Crimea peninsula. The occurrence of gas hydrates and high methane concentrations in the sediment of this mud volcano are known. A seismic wide-angle experiment was performed at the DMV with twelve Ocean Bottom Hydrophones and Seismometers and a GI gun source with frequencies around 100 Hz. By using Kirchhoff depth migration the seismogram sections are transformed to images, which extent to 4 km laterally and 600 metres in depth. The images show the conduit of the DMVand the nearby sediment layers. The DMV has a diameter of 800-1000 m at the sea floor and its conduit has the same form and diameter up to 600 m depth. Several plane sediment layers are disrupted by the conduit, and strong reflectors are identified in 100 m and 400 m depth in the conduit. The lower bowl shaped reflectors are interpreted as collapsed parts of the disrupted sediment layers, which sunk in the lighter material of the conduit. This is also a possible explanation for the upper reflections. Compressional wave velocities are obtained from Kirchhoff migration, and the model is refined by using seismic ray tracing. Bulk density and shear wave velocity can also be obtained by analyzing the data. With the help of these elastic parameters and by using the Frenkel-Gassmann theory, the free gas saturation of the sediment pore space and the gas hydrate saturation can be quantified