scholarly journals Higher-dimensional models in gravitational theories of quartic Lagrangians

1997 ◽  
Vol 38 (6) ◽  
pp. 3166-3188 ◽  
Author(s):  
K. Kleidis ◽  
A. Kuiroukidis ◽  
D. B. Papadopoulos ◽  
H. Varvoglis
Keyword(s):  
Gravitational Theories ◽  
Higher Dimensional ◽  
Dimensional Models

Characteristics of earthquake sequences: comparison from 0D to 3D

2021 ◽  
Author(s):  
Meng Li ◽  
Casper Pranger ◽  
Ylona van Dinther
Keyword(s):  
Stress Drop ◽  
Dynamic Models ◽  
Numerical Models ◽  
Recurrence Interval ◽  
Staggered Grid ◽  
Earthquake Parameters ◽  
Higher Dimensional ◽  
Dimensional Models ◽  
As Stress ◽  
Earthquake Sequences

<p>Numerical models are well-suited to overcome limited spatial-temporal observations to understand earthquake sequences, which is fundamental to ultimately better assess seismic hazard. However, high-resolution numerical models in 3D are computationally time and memory consuming. This is not optimal if the aspects of lateral or depth variations within the results are not needed to answer a particular objective. In this study we quantify and summarize the limitations and advantages for simulating earthquake sequences in all spatial dimensions.</p><p> </p><p>We simulate earthquake sequences on a strike-slip fault with rate-and-state friction from 0D to 3D using both quasi-dynamic and fully dynamic approaches. This cross-dimensional comparison is facilitated by our newly developed, flexible code library <em>Garnet</em>, which adopts a finite difference method with a fully staggered grid. We have validated our models using problems BP1-QD & FD and BP4-QD & FD of the SEAS (Sequences of Earthquakes and Aseismic Slip) benchmarks from the Southern California Earthquake Center.</p><p> </p><p>Our results demonstrate that lower-dimensional/quasi-dynamic models are qualitatively similar in terms of earthquake cycle characteristics to their higher-dimensional/fully-dynamic counterparts, while they could be hundreds to millions times faster at the same time. Quantitatively, we observe that certain earthquake parameters, such as stress drop and fracture energy release, can be accurately reproduced in each of these simpler models as well. However, higher dimensional models generally produce lower maximum slip velocities and hence longer coseismic durations. This is mainly due to lower rupture speeds, which result from increased energy consumption along added rupture front directions. In the long term, higher dimensional models produce shorter recurrence interval and hence smaller total slip, which is mainly caused by the higher interseismic stress loading rate inside the nucleation zone. The same trend is also observed when comparing quasi-dynamic models to fully dynamic ones. We extend a theoretical calculation that to first order approximates the aforementioned physical observables in 3D to all other dimensions. These theoretical considerations confirm the same trend as what is observed for stress drop, recurrence interval and total slip across dimensions. These findings on similarities and differences of different dimensional models and a corresponding quantification of computational efficiency can guide model design and facilitate result interpretation in future studies.</p>

HIGHER DIMENSIONAL MODELS OF CROSS-COUPLED OSCILLATORS AND APPLICATION TO DESIGN

2010 ◽  
Vol 19 (04) ◽  
pp. 787-799 ◽  
Author(s):  
A. S. ELWAKIL ◽  
K. N. SALAMA
Keyword(s):  
Coupled Oscillators ◽  
Design Procedure ◽  
Sinusoidal Oscillation ◽  
Relaxation Mode ◽  
Oscillation Condition ◽  
Higher Dimensional ◽  
Lc Oscillators ◽  
Dimensional Models ◽  
Graphical Design ◽  
Classical Cross

We present four-dimensional and five-dimensional models for classical cross-coupled LC oscillators. Using these models, sinusoidal oscillation condition, frequency and amplitude can be found. Further, undesired behaviors such as relaxation-mode oscillations and latchup can be explained and detected. A simple graphical design procedure is also described.

scholarly journals Extra-dimensional models on the lattice

2016 ◽  
Vol 31 (22) ◽  
pp. 1643002 ◽  
Author(s):  
Francesco Knechtli ◽  
Enrico Rinaldi
Keyword(s):  
Perturbation Theory ◽  
Gauge Theories ◽  
Higgs Field ◽  
Quantum Corrections ◽  
Higgs Potential ◽  
Strongly Coupled ◽  
Four Dimensions ◽  
Ongoing Effort ◽  
Higher Dimensional ◽  
Dimensional Models

In this review we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is generated by quantum corrections and is protected from divergences by the higher dimensional gauge symmetry. Dimensional reduction to four dimensions can occur through compactification or localization. Gauge-Higgs unification models are often studied using perturbation theory. Numerical lattice simulations are used to go beyond these perturbative expectations and to include nonperturbative effects. We describe the known perturbative predictions and their fate in the strongly-coupled regime for various extra-dimensional models.

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