Poro-viscoelasticity modelling based on upscaling quasistatic fluid-saturated solids

In this paper, quasistatic models are developed for the slow flow of compressible fluids through porous solids, where the solid exhibits fading memory viscoelasticity. Problems of this type are important in practical geomechanics contexts, for example, in the context of fluid flow through unconsolidated reservoir sands and of wellbore deformation behaviour in gas and oil shale reservoirs, all of which have been studied extensively. For slow viscous fluid flow in the poro-viscoelastic media we are able to neglect the dynamic effects related to inertia forces, as well as the dissipation associated with the viscous flows. This is in contrast to the vast body of work in the poro-elastic context, where much faster flow of the viscous fluids may give rise to memory effects associated with microflows in pores of the solid media. Such problems have been treated extensively in both the dynamic and quasistatic cases. We are taking a specific type of the porous medium subject to slow deformation processes possibly inducing moderate pressure gradients and flow rates characterised by negligible inertia effects. As the result of homogenisation of such a two-phase medium, we observe the fading memory behaviour in the Biot modulus which controls the pressure increase due to skeleton macroscopic deformation and pore fluid content. Although our derivation leads to a result which is consistent with the formal phenomenological approach proposed by Biot (J Appl Phys 23:1482–1498, 1962), we offer the reader more insight into the structure of the poro-viscoelastic constitutive relations obtained; in particular, we can show that the Biot compressibility evolves in time according to the creep function while the skeleton stiffness is driven by the relaxation function.     

Evolution of the Solar Flare Energetic Electrons in the Inhomogeneous Inner Heliosphere

Solar flare accelerated electrons escaping into the interplanetary space and seen as type III solar radio bursts are often detected near the Earth. Using numerical simulations we consider the evolution of energetic electron spectrum in the inner heliosphere and near the Earth. The role of Langmuir wave generation, heliospheric plasma density fluctuations, and expansion of magnetic field lines on the electron peak flux and fluence spectra is studied to predict the electron properties as could be observed by Solar Orbiter and Solar Probe Plus. Considering various energy loss mechanisms we show that the substantial part of the initial energetic electron energy is lost via wave–plasma processes due to plasma inhomogeneity. For the parameters adopted, the results show that the electron spectrum changes mostly at the distances before ～?20 R _⊙. Further into the heliosphere, the electron flux spectrum of electrons forms a broken power law relatively similar to what is observed at 1 AU.     

Palaeoenvironmental evolution of Cenote Aktun Ha (Carwash) on the Yucatan Peninsula,Mexico and its response to Holocene sea-level rise

A 61-cm core was obtained from 4 m below the water table in Cenote Aktun Ha, on the Yucatan Peninsula, Mexico. The cenote is 8.6 km from the Caribbean coast and its formation and evolution have been largely affected by sea-level change. The base of the core dates to 6,940–6,740 cal year BP and overlying sediments were deposited rapidly over the subsequent ~200 years. The pollen record shows that the cenote evolved from a marsh dominated by red mangrove (Rhizophora mangle) and fern (Polypodiaceae) to an open-water system. These vegetation changes were controlled by water level and salinity and are thus useful indicators of past sea level. At the base, the δ¹³C_org isotopic ratios reveal the influence of terrestrial vegetation (−29‰ VPDB), but shift to more negative values up-core (−33‰), indicating an influence from particulate matter in the flooded cenote pool. Although microfossil populations were nearly absent through most of the core, the microfossil assemblage in the upper 6 cm of the core is dominated by the juvenile foraminifer Ammonia tepida and the thecamoebian genus Centropyxis. These populations indicate open-water conditions in the cenote and a major environmental shift around 6,600 cal year BP, which is related to sea-level rise in the Caribbean basin. These data fit well with previously established sea-level curves for the Caribbean Sea. Our reconstruction of the environmental history of Cenote Aktun Ha helps elucidate the floral and hydrological history of the region, and highlights the utility of cenote sediments for studying the Holocene sea-level history of the Caribbean Sea.     

Insights in the exhumation history of the NW Zagros from bedrock and detrital apatite fission‐track analysis: evidence for a long‐lived orogeny

We present the first fission‐track (FT) thermochronology results for the NW Zagros Belt (SW Iran) in order to identify denudation episodes that occurred during the protracted Zagros orogeny. Samples were collected from the two main detrital successions of the NW Zagros foreland basin: the Palaeocene–early Eocene Amiran–Kashkan succession and the Miocene Agha Jari and Bakhtyari Formations. In situ bedrock samples were furthermore collected in the Sanandaj‐Sirjan Zone. Only apatite fission‐track (AFT) data have been successfully obtained, including 26 ages and 11 track‐length distributions. Five families of AFT ages have been documented from analyses of in situ bedrock and detrital samples: pre‐middle Jurassic at ～171 and ～225 Ma, early–late Cretaceous at ～91 Ma, Maastrichtian at ～66 Ma, middle–late Eocene at ～38 Ma and Oligocene–early Miocene at ～22 Ma. The most widespread middle–late Eocene cooling phase, around ～38 Ma, is documented by a predominant grain‐age population in Agha Jari sediments and by cooling ages of a granitic boulder sample. AFT ages document at least three cooling/denudation periods linked to major geodynamic events related to the Zagros orogeny, during the late Cretaceous oceanic obduction event, during the middle and late Eocene and during the early Miocene. Both late Cretaceous and early Miocene orogenic processes produced bending of the Arabian plate and concomitant foreland deposition. Between the two major flexural foreland episodes, the middle–late Eocene phase mostly produced a long‐lasting slow‐ or nondepositional episode in the inner part of the foreland basin, whereas deposition and tectonics migrated to the NE along the Sanandaj‐Sirjan domain and its Gaveh Rud fore‐arc basin. As evidenced in this study, the Zagros orogeny was long‐lived and multi‐episodic, implying that the timing of accretion of the different tectonic domains that form the Zagros Mountains requires cautious interpretation.     

Approximate Analytical Theory of Satellite Orbit Prediction Presented in Spherical Coordinates Frame

A comparative review of analytic theories for the motion of Earth satellites in quasi-circular orbits written in the spherical coordinate frame is presented. The theory of motion is developed for satellites in quasi-circular and quasi-equatorial orbits subjected to geopotential, luni-solar and solar radiation pressure force perturbations. The intermediate orbit is Keplerian and the equations of motion are solved by the Lyapunov–Poincaré small parameter method. Both resonant and non-resonant cases are considered. The results can be useful for the development of a complete theory of weakly eccentric orbits.     

Determination of Electron Flux Spectra in a Solar Flare with an Augmented Regularization Method: Application to Rhessi Data

Kontar et al. (2004) have shown how to recover mean source electron spectra in solar flares through a physical constraint regularization analysis of the bremsstrahlung photon spectra I() that they produce. They emphasize the use of non-square inversion techniques, and preconditioning combined with physical properties of the spectra to achieve the most meaningful solution to the problem. Higher-order regularization techniques may be used to generate forms with certain desirable properties (e.g., higher-order derivatives). They further note that such analysis may be used to infer properties of the electron energy spectra at energies well above the maximum photon energy observed. In this paper we apply these techniques to data from a solar flare observed by RHESSI on 26 February, 2002. Results using different orders of regularization are presented and compared for various time intervals. Clear evidence is presented for a change in the value of the high-energy cutoff in the mean source electron spectrum with time. We also show how the construction of the injected electron spectrum F₀(E₀) (assuming that Coulomb collisions in a cold target dominate the electron transport) is facilitated by the use of higher-order regularization methods.     

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