Contingent sensitivity to configuration in a nonlinear evolution system

A trans-scopic sensitivity of macroscopic failure to slight differentiation in the meso-scopic structure of a system with nonlinear evolution is reported. A periodical chain following a non-local load-sharing evolution was applied as a propotype in failure study. The results demonstrate that there is a transition region composed of globally stable (GS) and evolution induced catastrophic (EIC) modes. That is different from a critical threshold as predicted by percolation and renormalization group theories. Moreover, the EIC mode shows a distinctive sample specific behaviour. For instance, some neighbouring initial states may evolve into completely different final states, though different initial states can evolve into the same final states. As an example, a marginal configuration of EIC mode, a quasi-Fibonacci skeleton, is constructed.

Simulation of the Load-Unload Response Ratio and Critical Sensitivity in the Lattice Solid Model

The Load-Unload Response Ratio (LURR) method is an intermediate-term earthquake prediction approach that has shown considerable promise. It involves calculating the ratio of a specified energy release measure during loading and unloading where loading and unloading periods are determined from the earth tide induced perturbations in the Coulomb Failure Stress on optimally oriented faults. In the lead-up to large earthquakes, high LURR values are frequently observed a few months or years prior to the event. These signals may have a similar origin to the observed accelerating seismic moment release (AMR) prior to many large earthquakes or may be due to critical sensitivity of the crust when a large earthquake is imminent. As a first step towards studying the underlying physical mechanism for the LURR observations, numerical studies are conducted using the particle based lattice solid model (LSM) to determine whether LURR observations can be reproduced. The model is initialized as a heterogeneous 2-D block made up of random-sized particles bonded by elastic-brittle links. The system is subjected to uniaxial compression from rigid driving plates on the upper and lower edges of the model. Experiments are conducted using both strain and stress control to load the plates. A sinusoidal stress perturbation is added to the gradual compressional loading to simulate loading and unloading cycles and LURR is calculated. The results reproduce signals similar to those observed in earthquake prediction practice with a high LURR value followed by a sudden drop prior to macroscopic failure of the sample. The results suggest that LURR provides a good predictor for catastrophic failure in elastic-brittle systems and motivate further research to study the underlying physical mechanisms and statistical properties of high LURR values. The results provide encouragement for earthquake prediction research and the use of advanced simulation models to probe the physics of earthquakes.

Effects of mechanical and electrical coupling on the parametric sensitivity of mode localized sensors

We compare and contrast the effects of two distinctly different mechanisms of coupling (mechanical and electrical) on the parametric sensitivity of micromechanical sensors utilizing mode localization for sensor applications. For the first time, the strong correlation between mode localization and the phenomenon of 'eigenvalue loci-veering' is exploited for accurate quantification of the strength of internal coupling in mode localized sensors. The effects of capacitive coupling-spring tuning on the parametric sensitivity of electrically coupled resonators utilizing this sensing paradigm is also investigated and a mass sensor with sensitivity tunable by over 400% is realized. ©2009 IEEE.

Damage Localization, Sensitivity of Energy Release and the Catastrophe Transition

Large earthquakes can be viewed as catastrophic ruptures in the earth’s crust. There are two common features prior to the catastrophe transition in heterogeneous media. One is damage localization and the other is critical sensitivity; both of which are related to a cascade of damage coalescence. In this paper, in an attempt to reveal the physics underlying the catastrophe transition, analytic analysis based on mean-field approximation of a heterogeneous medium as well as numerical simulations using a network model are presented. Both the emergence of damage localization and the sensitivity of energy release are examined to explore the inherent statistical precursors prior to the eventual catastrophic rupture. Emergence of damage localization, as predicted by the mean-field analysis, is consistent with observations of the evolution of damage patterns. It is confirmed that precursors can be extracted from the time-series of energy release according to its sensitivity to increasing crustal stress. As a major result, present research indicates that the catastrophe transition and the critical point hypothesis (CPH) of earthquakes are interrelated. The results suggest there may be two cross-checking precursors of large earthquakes: damage localization and critical sensitivity.

Enhancing parametric sensitivity using mode localization in electrically coupled mems resonators

We use vibration localization as a sensitive means of detecting small perturbations in stiffness in a pair of weakly coupled micromechanical resonators. For the first time, the variation in the eigenstates is studied by electrostatically coupling nearly identical resonators to allow for stronger localization of vibrational energy due to perturbations in stiffness. Eigenstate variations that are orders of magnitude greater than corresponding shifts in resonant frequency for an induced stiffness perturbation are experimentally demonstrated. Such high, voltagetunable parametric sensitivities together with the added advantage of intrinsic common mode rejection pave the way to a new paradigm of mechanical sensing. ©2009 IEEE.

Critical Sensitivity and Trans-Scale Fluctuations in Catastrophic Rupture

Rupture in the heterogeneous crust appears to be a catastrophe transition. Catastrophic rupture sensitively depends on the details of heterogeneity and stress transfer on multiple scales. These are difficult to identify and deal with. As a result, the threshold of earthquake-like rupture presents uncertainty. This may be the root of the difficulty of earthquake prediction. Based on a coupled pattern mapping model, we represent critical sensitivity and trans-scale fluctuations associated with catastrophic rupture. Critical sensitivity means that a system may become significantly sensitive near catastrophe transition. Trans-scale fluctuations mean that the level of stress fluctuations increases strongly and the spatial scale of stress and damage fluctuations evolves from the mesoscopic heterogeneity scale to the macroscopic scale as the catastrophe regime is approached. The underlying mechanism behind critical sensitivity and trans-scale fluctuations is the coupling effect between heterogeneity and dynamical nonlinearity. Such features may provide clues for prediction of catastrophic rupture, like material failure and great earthquakes. Critical sensitivity may be the physical mechanism underlying a promising earthquake forecasting method, the load-unload response ratio (LURR).

Sensitivity Analysis Of The Dimensionless Parameters In Scaling A Polymer Flooding Reservoir

A set of scaling criteria of a polymer flooding reservoir is derived from the governing equations, which involve gravity and capillary force, compressibility of water, oil, and rock, non-Newtonian behavior of the polymer solution, absorption, dispersion, and diffusion, etc. A numerical approach to quantify the dominance degree of each dimensionless parameter is proposed. With this approach, the sensitivity factor of each dimensionless parameter is evaluated. The results show that in polymer flooding, the order of the sensitivity factor ranges from 10(-5) to 10(0) and the dominant dimensionless parameters are generally the ratio of the oil permeability under the condition of the irreducible water saturation to water permeability under the condition of residual oil saturation, density, and viscosity ratios between water and oil, the reduced initial oleic phase saturation and the shear rate exponent of the polymer solution. It is also revealed that the dominant dimensionless parameters may be different from case to case. The effect of some physical variables, such as oil viscosity, injection rate, and permeability, on the dominance degree of the dimensionless parameters is analyzed and the dominant ones are determined for different cases.

Threshold diversity and trans-scales sensitivity in a finite nonlinear evolution model of materials failure

We present a slice-sampling method and study the ensemble evolution of a large finite nonlinear system in order to model materials failure. There is a transitional region of failure probability. Its size effect is expressed by a slowly decaying scaling law. In a meso-macroscopic range (similar to 10(5)) in realistic failure, the diversity cannot be ignored. Sensitivity to mesoscopic details governs the phenomena. (C) 1997 Published by Elsevier Science B.V.

Effects of physical parameter range on dimensionless variable sensitivity in water flooding reservoirs

The similarity criterion for water flooding reservoir flows is concerned with in the present paper. When finding out all the dimensionless variables governing this kind of flow, their physical meanings are subsequently elucidated. Then, a numerical approach of sensitivity analysis is adopted to quantify their corresponding dominance degree among the similarity parameters. In this way, we may finally identify major scaling law in different parameter range and demonstrate the respective effects of viscosity, permeability and injection rate.

Effects of physical parameter range on dimensionless variable sensitivity in water flooding reservoirs

The similarity criterion for water flooding reservoir flows is concerned with in the present paper. When finding out all the dimensionless variables governing this kind of flow, their physical meanings are subsequently elucidated. Then, a numerical approach of sensitivity analysis is adopted to quantify their corresponding dominance degree among the similarity parameters. In this way, we may finally identify major scaling law in different parameter range and demonstrate the respective effects of viscosity, permeability and injection rate.