Lateral connection problem and Stokes phenomenon for certain functional spaces

1991 ◽  
Vol 4 (3) ◽  
pp. 215-233
Author(s):  
A.I. Tovbis
Keyword(s):  
Stokes Phenomenon ◽  
Connection Problem ◽  
Lateral Connection

scholarly journals High resolution stratigraphy of initial stages of rifting, Sergipe-Alagoas Basin, Brazil

2017 ◽  
Vol 47 (4) ◽  
pp. 657-671 ◽  
Author(s):  
Carrel Kifumbi ◽  
Claiton Marlon dos Santos Scherer ◽  
Fábio Herbert Jones ◽  
Juliano Kuchle
Keyword(s):  
Radical Change ◽  
High Rate ◽  
Tectonic Activity ◽  
Accommodation Space ◽  
Facies Associations ◽  
Half Graben ◽  
Lateral Connection ◽  
Depositional Units ◽  
Two Parameters ◽  
Channel Deposits

ABSTRACT: The present work aims to characterize the Neo-Jurassic to Neocomian succession of the Sergipe-Alagoas Basin, located in northeast region of Brazil, in order to discover the influence of tectonics on sedimentation in detailed scale and thus separating this sedimentary succession in tectono-stratigraphic units. Fieldwork observations and stratigraphic sections analysis allowed subdividing this rift succession into three depositional units that indicate different paleogeographic contexts. Unit I, equivalent to the top of Serraria Formation, is characterized by braided fluvial channel deposits, with paleocurrent direction to SE; unit II, corresponding to the base of Feliz Deserto Formation, is composed of anastomosed fluvial channel and floodplain facies associations; and unit III, equivalent to the major part of Feliz Deserto Formation, is characterized by delta deposits with polymodal paleocurrent pattern. The changes of depositional system, as well as paleocurrent direction, suggest that the previously described units were deposited in different evolutionary stages of rifting. Units I and II represent the record of a wide and shallow basin associated with the first stage of rifting. Unit I is characterized by incipient extensional stress generating a wide synclinal depression, associated to the low rate of accommodation and low tectonic activity. These two parameters progressively increase in unit II. The paleocurrent direction of unit I indicates that the depocenter of this wide basin was located at SE of the studied area. No conclusion could be done on paleocurrent from unit II because of the low amount of measurements. Unit III suggests a second stage marked by a deeper basin context, with a high rate of accommodation space associated with the lateral connection of faults and individualization of the half-graben. The scattering in the paleocurrent direction in this unit indicates sedimentary influx coming from several sectors of the half-graben. The boundary between these two stages is marked by a flooding surface that indicates an extremely fast transition and suggests a radical change in geometric characteristics of the basin due to the increase of tectonic activity.

Application and Validation of Practical Tools for Nonlinear Soil-Foundation Interaction Analysis

2010 ◽  
Vol 26 (1) ◽  
pp. 111-129 ◽  
Author(s):  
Sivapalan Gajan ◽  
Prishati Raychowdhury ◽  
Tara C. Hutchinson ◽  
Bruce L. Kutter ◽  
Jonathan P. Stewart
Keyword(s):  
Interaction Analysis ◽  
Model Performance ◽  
Shallow Foundations ◽  
Winkler Foundation ◽  
Gap Formation ◽  
Foundation Soil ◽  
Lateral Connection ◽  
Practical Guidelines ◽  
Soil Foundation ◽  
The Moment

Practical guidelines for characterization of soil-structure interaction (SSI) effects for shallow foundations are typically based on representing foundation-soil interaction in terms of viscoelastic impedance functions that describe stiffness and damping characteristics. Relatively advanced tools can describe nonlinear soil-foundation behavior, including temporary gap formation, foundation settlement and sliding, and hysteretic energy dissipation. We review two tools that describe such effects for shallow foundations and that are implemented in the computational platform OpenSees: a beam-on-nonlinear-Winkler foundation (BNWF) model and a contact interface model (CIM). We review input parameters and recommend parameter selection protocols. Model performance with the recommended protocols is evaluated through model-to-model comparisons for a hypothetical shear wall building resting on clay and model-data comparisons for several centrifuge test specimens on sand. The models describe generally consistent moment-rotation behavior, although shear-sliding and settlement behaviors deviate depending on the degree of foundation uplift. Pronounced uplift couples the moment and shear responses, often resulting in significant shear sliding and settlements. Such effects can be mitigated through the lateral connection of foundation elements with tie beams.

Asymptotic expansions and converging factors I. General theory and basic converging factors

1958 ◽  
Vol 244 (1239) ◽  
pp. 456-475 ◽  
Keyword(s):  
Asymptotic Expansion ◽  
General Theory ◽  
Asymptotic Expansions ◽  
General Term ◽  
Stokes Phenomenon

It is shown that by the application of Borel’s method of summation to the later terms of an asymptotic expansion, the ‘sum’ of such terms can normally be replaced by an easily calculable series involving ‘basic converging factors’. As particular consequences, [i] the remainder in a truncated asymptotic expansion can be written down once the general term in the expansion is known; [ii] the converging factor for a given asymptotic expansion can conveniently be calculated from the basic converging factors; and [iii] the Stokes phenomenon is simply expressed in terms of discontinuities in these basic quantities. Formulae and tables are given for the basic converging factors.

Hyperasymptotics

1990 ◽  
Vol 430 (1880) ◽  
pp. 653-668 ◽  
Keyword(s):  
Asymptotic Expansion ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Transition Point ◽  
Asymptotic Series ◽  
Stokes Phenomenon ◽  
Numerical Computations ◽  
Borel Summation ◽  
Nested Sequence ◽  
Exponentially Small

We develop a technique for systematically reducing the exponentially small (‘superasymptotic’) remainder of an asymptotic expansion truncated near its least term, for solutions of ordinary differential equations of Schrödinger type where one transition point dominates. This is achieved by repeatedly applying Borel summation to a resurgence formula discovered by Dingle, relating the late to the early terms of the original expansion. The improvements form a nested sequence of asymptotic series truncated at their least terms. Each such ‘hyperseries’ involves the terms of the original asymptotic series for the particular function being approximated, together with terminating integrals that are universal in form, and is half the length of its predecessor. The hyperasymptotic sequence is therefore finite, and leads to an ultimate approximation whose error is less than the square of the original superasymptotic remainder. The Stokes phenomenon is automatically and exactly incorporated into the scheme. Numerical computations confirm the efficacy of the technique.

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