Studies in the application of recurrence relations to special perturbation methods

The numerical integration of the differential equations describing dynamical systems has been shown in previous papers of this series to be most effectively accomplished by an explicit Taylor series method.In this paper we show that one explicit Taylor series method, developed earlier in this series and which appears to possess a high degree of versatility, yields considerable gains in efficiency over classical single-step and multi-step methods. (In this context efficiency is a measure of the time taken to carry out a calculation of a specific accuracy).For a given accuracy criterion governing the local truncation error (LTE) it is found that the Taylor series method is generallytwice as fast as the classical multi-step method and up totwenty times faster than the classical single-step method.     

Optimizing urban stormwater control strategies and assessing aquifer recharge through drywells in an urban watershed

Hydrogeology Journal - A coupled simulation-optimization model (SOM) is developed in this work that links the US Environmental Protection Agency’s Storm Water Management Model (SWMM) with a...     

A first classification scheme of flow-bed interaction for clay-laden density currents and soft substrates

Many aquatic environments exhibit soft, muddy substrates, but this important property has largely been ignored in process-based models of Earth-surface flow. Novel laboratory experiments were carried out to shed light on the feedback processes that occur when particulate density currents (turbidity currents) move over a soft mud substrate. These experiments revealed multiple types of flow-bed interaction and large variations in bed deformation and bed erosion, which are interpreted to be related to the interplay between the shear forces of the current and the stabilising forces in the bed. Changes in this force balance were simulated by varying the clay concentrations in the flow and in the bed. Five different interaction types are described, and dimensional and non-dimensional phase diagrams for flow-bed interaction are presented.     

Comparative efficiency analysis of different nonlinear modelling strategies to simulate the biaxial response of RC columns

The performance of different nonlinear modelling strategies to simulate the response of RC columns subjected to axial load combined with cyclic biaxial horizontal loading is compared. The models studied are classified into two categories according to the nonlinearity distribution assumed in the elements: lumped-plasticity and distributed inelasticity. For this study, results of tests on 24 columns subjected to cyclic uniaxial and biaxial lateral displacements were numerically reproduced. The analyses show that the global envelope response is satisfactorily represented with the three modelling strategies, but significant differences were found in the strength degradation for higher drift demands and energy dissipation.     

The effect of Na vapor on the Na content of chondrules

Abstract— Chondrules contain higher concentrations of volatiles (Na) than expected for melt droplets in the solar nebula. Recent studies have proposed that chondrules may have formed under non-canonical nebular conditions such as in particle/gas-rich clumps. Such chondrule formation areas may have contained significant Na vapor. To test the hypothesis of whether a Na-rich vapor would minimize Na volatilization reaction rates in a chondrule analog and maintain the Na value of the melt, experiments were designed where a Na-rich vapor could be maintained around the sample. A starting material with a melting point lower that typical chondrules was required to keep the logistics of working with Na volatilization from NaCl within the realm of feasiblity. The Knippa basalt, a MgO-rich alkali olivine basalt with a melting temperature of 1325°± 5 °C and a Na₂O content of 3.05 wt%, was used as the chondrule analog. Experiments were conducted in a 1 atm, gas-mixing furnace with the fO₂ controlled by a CO/CO₂ gas mixture and fixed at the I-W buffer curve. To determine the extent of Na loss from the sample, initial experiments were conducted at high temperatures (1300 °C–1350 °C) for duration of up to 72 h without a Na-rich vapor present. Almost all (up to 98%) Na was volatilized in runs of 72 h. Subsequent trials were conducted at 1330 °C for 16 h in the presence of a Na-rich vapor, supplied by a NaCl-filled crucible placed in the bottom of the furnace. Succeeding Knudsen cell weight-loss mass-spectrometry analysis of NaCl determined the P_Na for these experimental conditions to be in the 10^?6 atm range. This value is considered high for nebula conditions but is still plausible for non-canonical environments. In these trials the Na₂O content of the glass was maintained or in some cases increased; Na₂O values ranged from 2.62% wt to 4.37% wt. The Na content of chondrules may be controlled by the Na vapor pressure in the chondrule formation region. Most heating events capable of producing chondrules are sufficient to volatilize Na. Sodium volatilization reaction rates will be reduced to varying degrees from melt droplets, depending on the magnitude of the P_Na generated. A combination of Na vapor during, and Na diffusion back into chondrules after, formation could maintain and/or enrich Na concentrations in chondrules.     

Geometry of growth strata in a transpressive fold belt in field and analogue model: Gosau Group at Muttekopf,Northern Calcareous Alps,Austria

The thrust sheets of the Northern Calcareous Alps were emplaced during Late Cretaceous thrust‐dominated transpression expressed by thrust sheets segmented by closely spaced tear faults. Thrust sheet‐top sediments were deposited during thrusting and associated fold growth and were controlled by active folding and tearing. We observe two types of angular unconformities: (1) Angular unconformities above folds between tear faults conform with the model of progressive unconformities. Across these unconformities dip decreases upsection. (2) Here, we define progressive unconformities that are related to tear faults and are controlled by both folding and tearing. Across these unconformities both strike and dip change. In growth strata overlying folds dissected by high‐angle faults, such unconformities are expected to be common. We used analogue modelling to define the geometry of the tear faults and related unconformities. Within the syn‐tectonic sediments, a steep, upward flattening thrust within a broader, roughly tulip‐shaped drag zone develops. The thrust roots in the tear fault in pre‐tectonic deposits and is curved upward toward the downthrown block. Vertical offset on the thrust is related to differential vertical uplift caused by, for example, growth of folds with different wavelength and amplitude on either side of the tear fault. Formation of progressive unconformities is governed by the relationship between the rates of deposition and vertical growth of a structure. Fault‐related progressive unconformities are additionally controlled by the growth of the vertical step across the tear fault. When the rates of vertical growth of two neighbouring folds separated by a tear fault are similar, the rate of growth across the tear fault is small; if the first differ, the latter is high. Episodic tear fault activity may create several angular unconformities attached to a tear fault or allow the generation of angular unconformities near tear faults in sedimentary systems that have a rate of deposition too high to generate classical progressive unconformities between the tear faults.