scholarly journals A Complexity View into the Physics of the Accelerating Seismic Release Hypothesis: Theoretical Principles

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 754 ◽  
Author(s):  
Filippos Vallianatos ◽  
Georgios Chatzopoulos
Keyword(s):  
Energy Conservation ◽  
Power Law ◽  
B Value ◽  
Tsallis Entropy ◽  
Fault System ◽  
Model Parameters ◽  
Time To Failure ◽  
Distribution Law ◽  
Background Rate ◽  
Benioff Strain

Observational indications support the hypothesis that many large earthquakes are preceded by accelerating-decelerating seismic release rates which are described by a power law time to failure relation. In the present work, a unified theoretical framework is discussed based on the ideas of non-extensive statistical physics along with fundamental principles of physics such as the energy conservation in a faulted crustal volume undergoing stress loading. We define a generalized Benioff strain function Ω ξ ( t ) = ∑ i = 1 n ( t ) E i ξ ( t ) , where Ei is the earthquake energy, 0 ≤ ξ ≤ 1 . and a time-to-failure power-law of Ω ξ ( t ) derived for a fault system that obeys a hierarchical distribution law extracted from Tsallis entropy. In the time-to-failure power-law followed by Ω ξ ( t ) the existence of a common exponent mξ which is a function of the non-extensive entropic parameter q is demonstrated. An analytic expression that connects mξ with the Tsallis entropic parameter q and the b value of Gutenberg—Richter law is derived. In addition the range of q and b values that could drive the system into an accelerating stage and to failure is discussed, along with precursory variations of mξ resulting from the precursory b-value anomaly. Finally our calculations based on Tsallis entropy and the energy conservation give a new view on the empirical laws derived in the literature, the associated average generalized Benioff strain rate during accelerating period with the background rate and connecting model parameters with the expected magnitude of the main shock.

scholarly journals De Sitter and power-law solutions in non-local Gauss–Bonnet gravity

2018 ◽  
Vol 15 (11) ◽  
pp. 1850188 ◽  
Author(s):  
E. Elizalde ◽  
S. D. Odintsov ◽  
E. O. Pozdeeva ◽  
S. Yu. Vernov
Keyword(s):  
Power Law ◽  
Sufficient Conditions ◽  
Model Parameters ◽  
Local Form ◽  
De Sitter ◽  
Dynamical Equations ◽  
Non Local ◽  
Necessary And Sufficient ◽  
The Universe ◽  
Universe Evolution

The cosmological dynamics of a non-locally corrected gravity theory, involving a power of the inverse d’Alembertian, is investigated. Casting the dynamical equations into local form, the fixed points of the models are derived, as well as corresponding de Sitter and power-law solutions. Necessary and sufficient conditions on the model parameters for the existence of de Sitter solutions are obtained. The possible existence of power-law solutions is investigated, and it is proven that models with de Sitter solutions have no power-law solutions. A model is found, which allows to describe the matter-dominated phase of the Universe evolution.

Application of a Composite Model in the Analysis of Creep Deformation at Low and Intermediate Temperatures

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Xinjun Yang ◽  
Xiang Ling
Keyword(s):  
Projection Method ◽  
Power Law ◽  
Creep Deformation ◽  
Primary Creep ◽  
Composite Model ◽  
Intermediate Temperature ◽  
Model Parameters ◽  
Creep Life ◽  
Temperature Creep ◽  
Multiaxial Creep

The creep behaviors of TA2 and R60702 at low and intermediate temperature were presented and discussed in this paper. Experimental results indicated that an apparent threshold stress was exhibited in the creep deformation of R60702. Meanwhile, the primary creep phase was found as the main pattern in the room temperature creep behavior of TA2. Compared with the exponential law, the power law has been proved to be a proper constitutive model in the description of primary creep phase. It also showed that θ projection method had its significant advantage in the evaluation of accelerated creep stage. Thus, a composite model which combined power law with θ projection method was applied in the creep curves evaluation at low and intermediate temperature. Based on the multiaxial creep deformation results, the model was modified and discussed. A linear relationship existed between composite model parameters and applied load. Finally, the creep life of TA2 and R60702 could be accurately predicted by the composite model, and it is suitable for the application in low and intermediate temperature creep life analysis.

A study on the effects of electrical and thermal stresses on void formation and migration lifetime of Sn3.0Ag0.5Cu solder joints

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yanruoyue Li ◽  
Guicui Fu ◽  
Bo Wan ◽  
Zhaoxi Wu ◽  
Xiaojun Yan ◽  
...  
Keyword(s):  
Solder Joint ◽  
Thermal Stresses ◽  
Solder Joints ◽  
Void Formation ◽  
Model Parameters ◽  
Time To Failure ◽  
Current Crowding ◽  
Theoretical Derivation ◽  
Content Type ◽  
And Migration

Purpose The purpose of this study is to investigate the effect of electrical and thermal stresses on the void formation of the Sn3.0Ag0.5Cu (SAC305) lead-free ball grid array (BGA) solder joints and to propose a modified mean-time-to-failure (MTTF) equation when joints are subjected to coupling stress. Design/methodology/approach The samples of the BGA package were subjected to a migration test at different currents and temperatures. Voltage variation was recorded for analysis. Scanning electron microscope and electron back-scattered diffraction were applied to achieve the micromorphological observations. Additionally, the experimental and simulation results were combined to fit the modified model parameters. Findings Voids appeared at the corner of the cathode. The resistance of the daisy chain increased. Two stages of resistance variation were confirmed. The crystal lattice orientation rotated and became consistent and ordered. Electrical and thermal stresses had an impact on the void formation. As the current density and temperature increased, the void increased. The lifetime of the solder joint decreased as the electrical and thermal stresses increased. A modified MTTF model was proposed and its parameters were confirmed by theoretical derivation and test data fitting. Originality/value This study focuses on the effects of coupling stress on the void formation of the SAC305 BGA solder joint. The microstructure and macroscopic performance were studied to identify the effects of different stresses with the use of a variety of analytical methods. The modified MTTF model was constructed for application to SAC305 BGA solder joints. It was found suitable for larger current densities and larger influences of Joule heating and for the welding ball structure with current crowding.

The time to failure of fiber bundles subjected to random loads

1979 ◽  
Vol 11 (03) ◽  
pp. 527-541 ◽  
Author(s):  
Howard M. Taylor
Keyword(s):  
Simple Model ◽  
Power Law ◽  
Failure Time ◽  
Constant Load ◽  
Asymptotic Distributions ◽  
Asymptotic Independence ◽  
Time To Failure ◽  
Random Load ◽  
The Mean ◽  
Wave Induced

The effect on cable reliability of random cyclic loading such as that generated by the wave-induced rocking of ocean vessels deploying these cables is examined. A simple model yielding exact formulas is first explored. In this model, the failure time of a single fiber under a constant load is assumed to be exponentially distributed, and the random loadings are a two-state stationary Markov process. The effect of load on failure time is assumed to follow a power law breakdown rule. In this setting, exact results concerning the distribution of bundle or cable failure time, and especially the mean failure time, are obtained. Where the fluctuations in load are frequent relative to bundle life, such as may occur in long-lived cables, it is shown that randomness in load tends to decrease mean bundle life, but it is suggested that the reduction in mean life often can be restored by modestly reducing the base load on the structure or by modestly increasing the number of elements in the bundle. In later pages this simple model is extended to cover a broader range of materials and random loadings. Asymptotic distributions and mean failure times are given where fibers follow a Weibull distribution of failure time under constant load, and loads that are general non-negative stationary processes subject only to some mild condition of asymptotic independence. When the power law breakdown exponent is large, the mean time to bundle failure depends heavily on the exact form of the marginal probability distribution for the random load process and cannot be summarized by the first two moments of this distribution alone.

SELF-ORGANIZED CRITICALITY MODEL FOR EARTHQUAKES: QUIESCENCE, FORESHOCKS AND AFTERSHOCKS

1999 ◽  
Vol 09 (12) ◽  
pp. 2249-2255 ◽  
Author(s):  
S. HAINZL ◽  
G. ZÖLLER ◽  
J. KURTHS
Keyword(s):  
Power Law ◽  
B Value ◽  
Power Law Distribution ◽  
Aftershock Activity ◽  
Omori Law ◽  
Self Organized ◽  
Spatiotemporal Clustering ◽  
Self Organized Criticality ◽  
Clustering Of Events ◽  
Foreshock Activity

We introduce a crust relaxation process in a continuous cellular automaton version of the Burridge–Knopoff model. Analogously to the original model, our model displays a robust power law distribution of event sizes (Gutenberg–Richter law). The principal new result obtained with our model is the spatiotemporal clustering of events exhibiting several characteristics of earthquakes in nature. Large events are accompanied by a precursory quiescence and by localized fore- and aftershocks. The increase of foreshock activity as well as the decrease of aftershock activity follows a power law (Omori law) with similar exponents p and q. All empirically observed power law exponents, the Richter B-value, p and q and their variability can be reproduced simultaneously by our model, which depends mainly on the level of conservation and the relaxation time.

scholarly journals Stability and phase space analysis in f(R) theory with generalized exponential f(R) model

2016 ◽  
Vol 25 (10) ◽  
pp. 1650098 ◽  
Author(s):  
R. D. Boko ◽  
M. J. S. Houndjo ◽  
J. Tossa
Keyword(s):  
Dynamical System ◽  
Power Law ◽  
Critical Points ◽  
Dynamical Analysis ◽  
Model Parameters ◽  
Stability Conditions ◽  
De Sitter ◽  
Text Model ◽  
The Stability ◽  
Specific Phase

We have studied in this paper, the stability of dynamical system in [Formula: see text] gravity. We have considered the [Formula: see text] [Formula: see text]-gravity and explored its dynamical analysis. We found six critical points among which only one describes a universe filled of both matter and dominated dark energy. It is shown that these critical points present specific phase spaces described by the corresponding fluids. Furthermore, we have investigated the stability conditions of these critical points and find that these conditions are dependent of the model parameters. We also study the stability of a new power-law [Formula: see text] model with de Sitter and power law solutions.

scholarly journals Brittle Creep Failure, Critical Behavior, and Time-to-Failure Prediction of Concrete under Uniaxial Compression

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yingchong Wang ◽  
Na Zhou ◽  
Fuqing Chang ◽  
Shengwang Hao
Keyword(s):  
Creep Rate ◽  
Uniaxial Compression ◽  
Power Law ◽  
Critical Behavior ◽  
Creep Process ◽  
Time To Failure ◽  
Secondary Creep ◽  
Creep Failure ◽  
Brittle Creep ◽  
Secondary Creep Rate

Understanding the time-dependent brittle deformation behavior of concrete as a main building material is fundamental for the lifetime prediction and engineering design. Herein, we present the experimental measures of brittle creep failure, critical behavior, and the dependence of time-to-failure, on the secondary creep rate of concrete under sustained uniaxial compression. A complete evolution process of creep failure is achieved. Three typical creep stages are observed, including the primary (decelerating), secondary (steady state creep regime), and tertiary creep (accelerating creep) stages. The time-to-failure shows sample-specificity although all samples exhibit a similar creep process. All specimens exhibit a critical power-law behavior with an exponent of −0.51 ± 0.06, approximately equal to the theoretical value of −1/2. All samples have a long-term secondary stage characterized by a constant strain rate that dominates the lifetime of a sample. The average creep rate expressed by the total creep strain over the lifetime (tf-t0) for each specimen shows a power-law dependence on the secondary creep rate with an exponent of −1. This could provide a clue to the prediction of the time-to-failure of concrete, based on the monitoring of the creep behavior at the steady stage.

New behavior of degree distribution in connected communication networks

2014 ◽  
Vol 25 (09) ◽  
pp. 1450040 ◽  
Author(s):  
Marwa Benyoussef ◽  
Hamid Ez-Zahraouy ◽  
Abdelilah Benyoussef
Keyword(s):  
Communication Networks ◽  
Power Law ◽  
Gaussian Distribution ◽  
Degree Distribution ◽  
Complex Structure ◽  
Average Degree ◽  
Distribution Law ◽  
Frequency Level

The behavior of the degree distribution of two interdependent Barabasi–Albert (BA) sub-networks has been investigated numerically. The final complex structure obtained after connection of the two BA subnets exhibits two different kind of degree distribution law, which depends strongly on the manner in which the connection between the two subnets has been made. When connecting two existing BA subnets, the degree distribution follows a Gaussian distribution, while ensuring that the highest frequency level is still around the average degree of the final network. Whereas, when the connection is established progressively at the same time of the formation of the two BA subnets, the degree distribution follows a power-law scaling observed in real networks. It is also found that the evolution of links formed over a time for a specific node follows the same behavior, as the BA networks.

scholarly journals Dynamics of an Anisotropic Universe inf(R,T)Theory

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
B. Mishra ◽  
Sankarsan Tarai ◽  
S. K. Tripathy
Keyword(s):  
Power Law ◽  
Modified Gravity ◽  
Bianchi Type ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Model Parameters ◽  
Anisotropic Universe ◽  
Expansion Of The Universe ◽  
Physical Features ◽  
The Universe

Dynamics of an anisotropic universe is studied inf(R,T)gravity using a rescaled functionalf(R,T), whereRis the Ricci Scalar andTis the trace of energy-momentum tensor. Three models have been constructed assuming a power law expansion of the universe. Physical features of the models are discussed. The model parameters are constrained from a dimensional analysis. It is found from the work that the anisotropic Bianchi typeVIh(BVIh) model in the modified gravity generally favours a quintessence phase when the parameterhis either-1or0. We may not get viable models in conformity with the present day observation forh=1.

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