Dynamics of collapse of an impact central uplift: Evidence from folds and faults in the collar of the Vredefort Dome, South Africa

2021 ◽  
Author(s):  
Shalene Manzi ◽  
Roger L. Gibson ◽  
Asinne Tshibubudze
Keyword(s):  
South Africa ◽  
Structural Analysis ◽  
Large Scale ◽  
Second Order ◽  
Upward Flow ◽  
Downward Flow ◽  
Kinematic Pattern ◽  
Central Uplift ◽  
Convergent Flow ◽  
Order Structures

ABSTRACT Structural analysis of overturned metasedimentary strata of the lower Witwatersrand Supergroup in the inner collar of the Vredefort Dome reveals the presence of tangential folds and faults associated with the 2.02 Ga impact. The folds are distinct from previously identified subradially oriented, vertical to plunging-inclined, gentle folds that are interpreted as the products of convergent flow (constriction) during the initial stages of central uplift formation. The tangential folds comprise disharmonic, open, asymmetric, horizontal to plunging-inclined anticline-syncline pairs with centripetally dipping axial planes and right-way-up intermediate limbs. They display centripetal-down vergence (anticline radially outward of the syncline) that is consistent with steep inward-directed shear of the overturned strata. We attribute this kinematic pattern to subvertical collapse of the Vredefort central uplift during the latter stages of crater modification. The folds are cut by pseudotachylite-bearing steep to vertical tangential faults that display center-down slip of <10 m up to ~150 m. Both the tangential folds and the faults suggest that the large-scale overturning of strata related to outward collapse of the Vredefort central uplift was accompanied by a component of inward-directed collapse via layer-parallel shearing and folding, followed by faulting. Subradially oriented faults with conjugate strike separations of 1–2 km in the NNE collar of the dome suggest penecontemporaneous tangential extension of the inner collar rocks. This evidence indicates that second-order structures in the metasedimentary collar of the Vredefort Dome preserve a complex, multistage record of evolving strain associated with both initial convergent and upward flow (constriction) related to central uplift rise and later divergent and downward flow (flattening) linked to its collapse, and that centripetally directed collapse features may be important components of the structural inventory of very large central uplifts.

The role of Constitutional Courts in Transitional Justice: Colombia and South Africa

2016 ◽  
Vol 9 (15) ◽  
Author(s):  
Nadiehezka Paola Palencia Tejedor
Keyword(s):  
South Africa ◽  
Structural Analysis ◽  
Transitional Justice ◽  
Critical Analysis ◽  
Historical Context ◽  
Constitutional Courts ◽  
Political Background ◽  
Similarities And Differences ◽  
Peace And Reconciliation

This work focuses on a compared analysis of the South Afri- can decision related to the “peace and reconciliation act” of this country’s Parliament, and the Colombian decision regarding the amendment of the constitution called “The juridical framework for the peace.” Turning to the structure, it is developed in three major topics: 1. It provides a brief of the historical context, political background and an overview of the two decisions.2. It gives a structural analysis of the powers that each Court has and the nature of the constitutional mechanism through which both Courts decided the constitutionality of the said norms 3. It presents a critical analysis on the similarities and differences between the two systems and judgments. It presents some con- clusions. 

Behavior Models of Voltage Differencing Inverting Buffered Amplifier and Applications in Circuit Analysis

2019 ◽  
Vol 12 (4) ◽  
pp. 298-303
Author(s):  
YongAn LI
Keyword(s):  
Large Scale ◽  
Vlsi Design ◽  
Circuit Analysis ◽  
Second Order ◽  
Very Large Scale Integration ◽  
Behavioral Models ◽  
Order Filter ◽  
Large Scale Integration ◽  
Scale Integration ◽  
Behavior Models

Background: The symbolic nodal analysis acts as a pivotal part of the very large scale integration (VLSI) design. Methods: In this work, based on the terminal relations for the pathological elements and the voltage differencing inverting buffered amplifier (VDIBA), twelve alternative pathological models for the VDIBA are presented. Moreover, the proposed models are applied to the VDIBA-based second-order filter and oscillator so as to simplify the circuit analysis. Results: The result shows that the behavioral models for the VDIBA are systematic, effective and powerful in the symbolic nodal circuit analysis.</P>

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

scholarly journals Meta-Descent for Online, Continual Prediction

2019 ◽  
Vol 33 ◽  
pp. 3943-3950
Author(s):  
Andrew Jacobsen ◽  
Matthew Schlegel ◽  
Cameron Linke ◽  
Thomas Degris ◽  
Adam White ◽  
...  
Keyword(s):  
Gradient Descent ◽  
Large Scale ◽  
Time Series Prediction ◽  
Real Data ◽  
Second Order ◽  
Stochastic Gradient Descent ◽  
Step Size ◽  
Vector Approximation ◽  
Prediction Problems ◽  
Stationary Problems

This paper investigates different vector step-size adaptation approaches for non-stationary online, continual prediction problems. Vanilla stochastic gradient descent can be considerably improved by scaling the update with a vector of appropriately chosen step-sizes. Many methods, including AdaGrad, RMSProp, and AMSGrad, keep statistics about the learning process to approximate a second order update—a vector approximation of the inverse Hessian. Another family of approaches use meta-gradient descent to adapt the stepsize parameters to minimize prediction error. These metadescent strategies are promising for non-stationary problems, but have not been as extensively explored as quasi-second order methods. We first derive a general, incremental metadescent algorithm, called AdaGain, designed to be applicable to a much broader range of algorithms, including those with semi-gradient updates or even those with accelerations, such as RMSProp. We provide an empirical comparison of methods from both families. We conclude that methods from both families can perform well, but in non-stationary prediction problems the meta-descent methods exhibit advantages. Our method is particularly robust across several prediction problems, and is competitive with the state-of-the-art method on a large-scale, time-series prediction problem on real data from a mobile robot.

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