Comparison of the classical and the global solutions of the Ideal Resonance Problem

The Ideal Resonance Problem is defined by the Hamiltonian $$F = B(y) + 2\varepsilon A(y) \sin ^2 x,\varepsilon \ll 1.$$ The classical solution of the Problem, expanded in powers of ε, carries the derivativeB′ as a divisor and is, therefore, singular at the zero ofB′, associated with resonance. With α denoting theresonance parameter, defined by $$\alpha \equiv - B'/|4AB''|^{1/2} \mu ,\mu = \varepsilon ^{1/2} ,$$ it is shown here that the classical solution is valid only for $$\alpha ^2 \geqslant 0(1/\mu ).$$ In contrast, the global solution (Garfinkelet al., 1971), expanded in powers ofμ=ε^1/2, removes the classical singularity atB′=0, and is valid for all α. It is also shown here that the classical solution is an asymptotic approximation, for largeα ², of the global solution expanded in powers ofα ^?2. This result leads to simplified expressions for resonancewidth and resonantamplification. The two solutions are compared with regard to their general behavior and their accuracy. It is noted that the global solution represents a perturbed simple pendulum, while the classical solution is the limiting case of a pendulum in a state offast circulation.     

Rapid biotic molecular transformation of fulvic acids in a karst aquifer

The study of molecular transformation processes of dissolved organic carbon (DOC) in the environment significantly contributes to a better understanding of the global biogeochemical organic matter cycle. In an oxic karst groundwater system, in which the most powerful abiotic DOC degradative reactions, photodegradation and metal-mediated redox chemistry, are at best marginal contributors, a near complete turnover of fulvic acids (FAs) has been observed within decades (∼60 years). Depletion of oxygen for a very extensive range of aliphatic and aromatic carbon chemical environments has been confirmed as well as the formation of novel classes of compounds, suggesting a major contribution from biotic processes. From these results we infer that FAs must be perceived as a rather active participant in the global carbon cycle. Molecular-level alterations of such magnitude and rapidity on such short-time scales ought to be considered as widespread in the processing of “refractory” DOC in the environment.     

Probabilistic elasto-plasticity: solution and verification in 1D

In this paper, a solution is presented for evolution of probability density function (PDF) of elastic–plastic stress–strain relationship for material models with uncertain parameters. Developments in this paper are based on already derived general formulation presented in the companion paper. The solution presented is then specialized to a specific Drucker–Prager elastic–plastic material model. Three numerical problems are used to illustrate the developed solution. The stress–strain response (1D) is given as a PDF of stress as a function of strain. The presentation of the stress–strain response through the PDF differs significantly from the traditional presentation of such results, which are represented by a single, unique curve in stress–strain space. In addition to that the numerical solutions are verified against closed form solutions where available (elastic). In cases where the closed form solution does not exist (elastic–plastic), Monte Carlo simulations are used for verification.     

Three-dimensional sedimentary architecture of Quaternary sand and gravel resources: a case study of economic sedimentology (SW Germany)

Quaternary sands and gravels form important, yet often highly heterogeneous economic deposits. Detailed 3-D analysis of the sedimentary structure and stratigraphy of these deposits allows for an accurate estimation of exploitable material. This paper presents a case study in SW Germany reconstructing the 3-D distribution of glacial sediments based on a high-resolution, process-orientated sedimentary facies classification and lithostratigraphy integrated within the geo-modelling package gOcad. Situated along the maximal ice-extent of the Rhine glacier during the last glaciation, the study area is characterised by a morphologically prominent terminal moraine and its associated sandur, which form the stratigraphically youngest sediments of a glacial basin, partially exposed in two gravel pits. These outcrops helped to reconstruct the complex sedimentary architecture of the northern part of the glacial basin. The regional analysis is based on core data, as well as geoelectric and geomagnetic surveys. All data were integrated into km-scale, high-resolution geological 3-D models, depicting the large-scale dynamics of multiple glacier advances and retreats during the Early to Late Pleistocene. These models allow quantifying the thickness and volume distribution of exploitable sandy gravel and help to evaluate the occurrence of non-exploitable interbedded diamicton horizons. The high quality and quantity of gravels particularly north of the terminal moraine classifies the investigated area as very prospective for raw materials exploitation in the future.     

Quasi-isotropic approximation of ray theory for anisotropic media

Wave propagation in weakly anisotropic inhomogeneous media is studied by the quasi-isotropic approximation of ray theory. The approach is based on the ray-tracing and dynamic ray-tracing differential equations for an isotropic background medium. In addition, it requires the integration of a system of two complex coupled differential equations along the isotropic ray.
The interference of the qS waves is described by traveltime and polarization corrections of interacting isotropic S waves. For qP waves the approach leads to a correction of the traveltime of the P wave in the isotropic background medium.
Seismograms and particle-motion diagrams obtained from numerical computations are presented for models with different strengths of anisotropy.
The equivalence of the quasi-isotropic approximation and the quasi-shear-wave coupling theory is demonstrated. The quasi-isotropic approximation allows for a consideration of the limit from weak anisotropy to isotropy, especially in the case of qS waves, where the usual ray theory for anisotropic media fails.     

Magnetostratigraphy of the lower Triassic volcanics from deep drill SG6 in western Siberia: evidence for long-lasting Permo–Triassic volcanic activity

The deep drill hole SG6 in western Siberia (66°N, 78.5°E) penetrated 1.1  km of lower Triassic basalts, which are possibly an extension of the central Siberian Permo– Triassic flood basalt province. About 300 samples of these basalts were progressively demagnetized and measured. Principal component analysis often shows multiple magnetizations carried by haematite and magnetite. The corrected mean inclinations are +77° and −77° for the haematite component. A magnetostratigraphic scale was derived and showed a N–R–N–R–N succession. This is quite different from the Noril'sk and Taimyr typical polarity scale, R–N.
  The basalts found in the SG6 deep drill hole are slightly younger than those of central Siberia and Taimyr. They correspond to middle–upper Induan age, whereas the Noril'sk and Taimyr sections correspond to an uppermost Permian and lower Induan age. Altogether they indicate that, after a high output rate of volcanic material near the Permo–Triassic boundary, this activity slowed down drastically on the Siberian platform and Taimyr, but persisted for several million years in western Siberia.     

Contrasting patterns of precipitation seasonality during the Holocene in the south‐ and north‐central Mediterranean

Pollen‐based quantitative estimates of seasonal precipitation from Lake Pergusa and lake‐level data from Lake Preola in Sicily (southern Italy) allow three successive periods to be distinguished within the Holocene: an early Holocene period before ca. 9800 cal a BP with rather dry climate conditions in winter and summer, a mid‐Holocene period between ca. 9800 and 4500 cal a BP with maximum winter and summer wetness, and a late Holocene period after 4500 cal a BP with declining winter and summer wetness. This evolution observed in the south‐central Mediterranean shows strong similarities to that recognized in the eastern Mediterranean. But, it contrasts with that reconstructed in north‐central Italy, where the mid‐Holocene appears to be characterized by a winter (summer) precipitation maximum (minimum), while the late Holocene coincided with a decrease (increase) in winter (summer) precipitation. Maximum precipitation at ca. 10 000–4500 cal a BP may have resulted from (i) increased local convection in response to a Holocene insolation maximum at 10 000 cal a BP and then (ii) the gradual weakening of the Hadley cell activity, which allowed the winter rainy westerlies to reach the Mediterranean area more frequently. After 4500 cal a BP, changes in precipitation seasonality may reflect non‐linear responses to orbitally driven insolation decrease in addition to seasonal and inter‐hemispheric changes of insolation. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical simulation of fully saturated porous materials

Fully coupled, porous solid–fluid formulation, implementation and related modeling and simulation issues are presented in this work. To this end, coupled dynamic field equations with u?p?U formulation are used to simulate pore fluid and soil skeleton (elastic–plastic porous solid) responses. Present formulation allows, among other features, for water accelerations to be taken into account. This proves to be useful in modeling dynamic interaction of media of different stiffnesses (as in soil–foundation–structure interaction). Fluid compressibility is also explicitly taken into account, thus allowing excursions into modeling of limited cases of non‐saturated porous media. In addition to these features, present formulation and implementation models in a realistic way the physical damping, which dissipates energy. In particular, the velocity proportional damping is appropriately modeled and simulated by taking into account the interaction of pore fluid and solid skeleton. Similarly, the displacement proportional damping is physically modeled through elastic–plastic processes in soil skeleton. An advanced material model for sand is used in present work and is discussed at some length. Also explored in this paper are the verification and validation issues related to fully coupled modeling and simulations of porous media. Illustrative examples describing the dynamical behavior of porous media (saturated soils) are presented. The verified and validated methods and material models are used to predict the behavior of level and sloping grounds subjected to seismic shaking. Copyright © 2008 John Wiley & Sons, Ltd.