Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Numerical Initial Value Problems in Ordinary Differential Equations

One of the research direction of Horst Lippmann during his whole scientific career was devoted to the possibilities to explain complex material behavior by generalized continua models. A representative of such models is the Cosserat continuum. The basic idea of this model is the independence of translations and rotations (and by analogy, the independence of forces and moments). With the help of this model some additional effects in solid and fluid mechanics can be explained in a more satisfying manner. They are established in experiments, but not presented by the classical equations. In this paper the Cosserat-type theories of plates and shells are debated as a special application of the Cosserat theory.

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On generalized Cosserat-type theories of plates and shells: a short review and bibliography

Hydrodynamic and hydromagnetic stability

We document a 1 week long slow slip event (SSE) with an equivalent moment magnitude of 6.0-6.3 which occurred in August 2010 below La Plata Island (Ecuador), south of the rupture area of the 1906 Mw= 8.8 megathrust earthquake. GPS data reveal that the SSE occurred at a depth of about 10 km, within the downdip part of a shallow (<15 km), isolated, locked patch along the subduction interface. The availability of both broadband seismometer and continuous geodetic station located at the La Plata Island, 10 km above the SSE, enables a careful analysis of the relationships between slow and rapid processes of stress release along the subduction interface. During the slow slip sequence, the seismic data show a sharp increase of the local seismicity, with more than 650 earthquakes detected, among which 50 have a moment magnitude between 1.8 and 4.1. However, the cumulative moment released through earthquakes accounts, at most, for 0.2% of the total moment release estimated from GPS displacements. Most of the largest earthquakes are located along or very close to the subduction interface with focal mechanism consistent with the relative plate motion. While the earthquake sizes show a classical distribution (Gutenberg-Richter law with a b-value close to 1), the space-time occurrence presents a specific pattern. First, the largest earthquakes appear to occur randomly during the slow slip sequence, which further evidence that the seismicity is driven by the stress fluctuations related to aseismic slip. Moreover, the seismicity observed during the SSE consists in individual events and families of repeating earthquakes. These observations indicate that the stress increment induced by the episodic aseismic slip may lead both to sudden seismic moment release and to progressive rupture within small locked patches. This study offers an a posteriori interpretation of the seismogenesis in the Central Ecuador subduction zone, where intense seismic swarms have been regularly observed (1977, 1998, 2002, and 2005). These swarms have likely been triggered by large-magnitude slow slip events.

https://hal.archives-ouvertes.fr/hal-01067233/document

Intense interface seismicity triggered by a shallow slow slip event in the Central Ecuador subduction zone

In this paper, the governing relations and equations are derived for nonlocal elastic solid with voids. The propagation of time harmonic plane waves is investigated in an infinite nonlocal elastic solid material with voids. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent transverse wave may travel with distinct speeds. The sets of coupled waves are found to be dispersive, attenuating and influenced by the presence of voids and nonlocality parameters in the medium. The transverse wave is dispersive but non-attenuating, influenced by the nonlocality and independent of void parameters. Furthermore, the transverse wave is found to face critical frequency, while the coupled waves may face critical frequencies conditionally. Beyond each critical frequency, the respective wave is no more a propagating wave. Reflection phenomenon of an incident coupled longitudinal waves from stress-free boundary surface of a nonlocal elastic solid half-space with voids has also been studied. Using appropriate boundary conditions, the formulae for various reflection coefficients and their respective energy ratios are presented. For a particular model, the effects of non-locality and dissipation parameter (
 $\tau $
 ) have been depicted on phase speeds and attenuation coefficients of propagating waves. The effect of nonlocality on reflection coefficients has also been observed and shown graphically.

Waves in Nonlocal Elastic Solid with Voids

This work is concerned with the propagation of time harmonic plane waves in an infinite nonlocal thermoelastic solid having void pores. Three sets of coupled dilatational waves and an independent transverse wave may travel with distinct speeds in the medium. All these waves are found to be dispersive in nature, but the coupled dilatational waves are attenuating, while transverse wave is nonattenuating. Coupled dilatational waves are found to be influenced by the presence of voids, thermal field and elastic nonlocal parameter. While the transverse wave is found to be influenced by the nonlocal parameter, but independent of void and thermal parameters. For a particular model, the effects of frequency, void parameters, thermal parameter and nonlocality have been studied numerically on the phase speeds, attenuation coefficients and specific losses of all the propagating waves. All the computed results obtained have been depicted graphically and explained.

Sushil K. Tomar

Papers

Waves in Nonlocal Elastic Solid with Voids

Plane waves in nonlocal thermoelastic solid with voids

Plane waves in thermo-elastic material with voids

Reflection and transmission of elastic waves at an elastic/porous solid saturated by two immiscible fluids

Rayleigh-type waves in nonlocal micropolar solid half-space.