Nonlinear earthquake location: Theory and examples

1985 ◽  
Vol 75 (3) ◽  
pp. 779-790
Author(s):  
Clifford H. Thurber
Keyword(s):  
Travel Time ◽  
Location Theory ◽  
Nonlinear Behavior ◽  
Second Order ◽  
Earthquake Location ◽  
Source Position ◽  
Realistic Assessment ◽  
Location Algorithm ◽  
Expected Benefits ◽  
Derivatives Of

Abstract A fundamental modification to Geiger's method of earthquake location for local earthquakes is described which incorporates nonlinear behavior of travel time as a function of source position. The use of Newton's method rather than the usual Gauss-Newton method allows the inclusion of second-order partial derivatives of travel time with respect to source coordinates in the location algorithm. These second-order derivatives can be calculated quite easily for half-space and layered crustal models. Expected benefits are improved convergence and stability, as demonstrated in a series of examples, and more realistic assessment of solution uncertainty.

scholarly journals Sensitivity of the Second Order Homogenized Elasticity Tensor to Topological Microstructural Changes

2021 ◽  
Author(s):  
V. Calisti ◽  
A. Lebée ◽  
A. A. Novotny ◽  
J. Sokolowski
Keyword(s):  
Circular Inclusion ◽  
Elasticity Tensor ◽  
Second Order ◽  
Topological Derivative ◽  
Microstructural Changes ◽  
Topological Derivatives ◽  
Spatial Dimensions ◽  
Elasticity Tensors ◽  
Derivatives Of ◽  
Optimization Of Microstructures

AbstractThe multiscale elasticity model of solids with singular geometrical perturbations of microstructure is considered for the purposes, e.g., of optimum design. The homogenized linear elasticity tensors of first and second orders are considered in the framework of periodic Sobolev spaces. In particular, the sensitivity analysis of second order homogenized elasticity tensor to topological microstructural changes is performed. The derivation of the proposed sensitivities relies on the concept of topological derivative applied within a multiscale constitutive model. The microstructure is topologically perturbed by the nucleation of a small circular inclusion that allows for deriving the sensitivity in its closed form with the help of appropriate adjoint states. The resulting topological derivative is given by a sixth order tensor field over the microstructural domain, which measures how the second order homogenized elasticity tensor changes when a small circular inclusion is introduced at the microscopic level. As a result, the topological derivatives of functionals for multiscale models can be obtained and used in numerical methods of shape and topology optimization of microstructures, including synthesis and optimal design of metamaterials by taking into account the second order mechanical effects. The analysis is performed in two spatial dimensions however the results are valid in three spatial dimensions as well.

scholarly journals On the derivatives of the principal invariants of a second-order tensor

1986 ◽  
Vol 16 (2) ◽  
pp. 221-224 ◽  
Author(s):  
Donald E. Carlson ◽  
Anne Hoger
Keyword(s):  
Second Order ◽  
Order Tensor ◽  
Derivatives Of

Operational Effects of the Consolidated Intersection Design on Urban and Suburban Arterials

2018 ◽  
Vol 2672 (17) ◽  
pp. 96-107
Author(s):  
Daniel J. Cook
Keyword(s):  
Travel Time ◽  
Signalized Intersections ◽  
Signal Timing ◽  
Left Turn ◽  
Vehicle Delay ◽  
Cycle Lengths ◽  
Expected Benefits ◽  
Traffic Signal Timing ◽  
Critical Phases ◽  
Pedestrian Crossing

Along urban and suburban arterials, closely-spaced signalized intersections are commonly used to provide access to adjacent commercial developments. Often, these signalized intersections are designed to provide full access to developments on both sides of the arterial and permit through, left-turn, and right-turn movements from every intersection approach. Traffic signal timing is optimized to reduce vehicle delay or provide progression to vehicles on the arterial, or both. However, meeting both of these criteria can be cumbersome, if not impossible, under high-demand situations. This research proposes a new design that consolidates common movements at three consecutive signalized intersections into strategic fixed locations along the arterial. The consolidation of common movements allows the intersections to cycle between only two critical phases, which, in turn, promotes shorter cycle lengths, lower delay, and better progression. This research tested the consolidated intersection concept by modeling a real-world site in microsimulation software and obtaining values for delay and travel time for multiple vehicle paths along the corridor and adjacent commercial developments in both existing and proposed conditions. With the exception of unsignalized right turns at the periphery of the study area, all non-displaced routes showed a reduction in travel time and delay. Additional research is needed to understand how additional travel through the commercial developments adjacent to the arterial may effect travel time and delay. Other expected benefits of the proposed design include a major reduction in conflict points, shorter pedestrian crossing and wait times, and the opportunity to provide pedestrian refuge areas in the median.

On second-order directional derivatives of value functions

Optimization ◽  
2013 ◽  
Vol 64 (2) ◽  
pp. 389-407 ◽  
Author(s):  
L. Minchenko ◽  
A. Tarakanov
Keyword(s):  
Second Order ◽  
Directional Derivatives ◽  
Value Functions ◽  
Derivatives Of
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