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).

Optimization Of Off-Null Ellipsometry For Air/Solid Interfaces

The optimization of off-null ellipsometry is described with emphasis on the improvement of sample thickness sensitivity. Optimal conditions are dependent on azimuth angle settings of the polarizer, compensator, and analyzer in a polarizer-compensator-sample-analyzer ellipsometer arrangement. Numerical simulation utilized offers an approach to present the dependence of the sensitivity on the azimuth angle settings, from which optimal settings corresponding to the best sensitivity are derived. For a series of samples of SiO2 layer (thickness in the range of 1.8-6.5 nm) on silicon substrate, the theory analysis proves that sensitivity at the optimal settings is increased 20 times compared to that at null settings used in most works, and the relationship between intensity and thickness is simplified as a linear type instead of the original nonlinear type, with the relative error reduced to similar to 1/100 at the optimal settings. Furthermore the discussion has been extended toward other factors affecting the sensitivity of the practical system, such as the linear dynamic range of the detector, the signal-to-noise ratio and the intensity from the light source, etc. Experimental results from the investigation Of SiO2 layer on silicon substrate are chosen to verify the optimization. (c) 2007 Optical Society of America.

Designing Of Partial Similarity Models And Evaluation Method In Polymer Flooding Experiment

Based on the scaling criteria of polymer flooding reservoir obtained in our previous work in which the gravity and capillary forces, compressibility, non-Newtonian behavior, absorption, dispersion, and diffusion are considered, eight partial similarity models are designed. A new numerical approach of sensitivity analysis is suggested to quantify the dominance degree of relaxed dimensionless parameters for partial similarity model. The sensitivity factor quantifying the dominance degree of relaxed dimensionless parameter is defined. By solving the dimensionless governing equations including all dimensionless parameters, the sensitivity factor of each relaxed dimensionless parameter is calculated for each partial similarity model; thus, the dominance degree of the relaxed one is quantitatively determined. Based on the sensitivity analysis, the effect coefficient of partial similarity model is defined as the summation of product of sensitivity factor of relaxed dimensionless parameter and its relative relaxation quantity. The effect coefficient is used as a criterion to evaluate each partial similarity model. Then the partial similarity model with the smallest effect coefficient can be singled out to approximate to the prototype. Results show that the precision of partial similarity model is not only determined by the number of satisfied dimensionless parameters but also the relative relaxation quantity of the relaxed ones.

Receptivity To Free-Stream Disturbance Waves For Hypersonic Flow Over A Blunt Cone

A high-order shock-fitting finite difference scheme is studied and used to do direction numerical simulation (DNS) of hypersonic unsteady flow over a blunt cone with fast acoustic waves in the free stream, and the receptivity problem in the blunt cone hypersonic boundary layers is studied. The results show that the acoustic waves are the strongest disturbance in the blunt cone hypersonic boundary layers. The wave modes of disturbance in the blunt cone boundary layers are first, second, and third modes which are generated and propagated downstream along the wall. The results also show that as the frequency decreases, the amplitudes of wave modes of disturbance increase, but there is a critical value. When frequency is over the critial value, the amplitudes decrease. Because of the discontinuity of curvature along the blunt cone body, the maximum amplitudes as a function of frequencies are not monotone.

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.

Notch sensitivity of circular rings subjected to impact loading

'Notch-sensitive regions' have been observed during a series of experimental investigations into the dynamic plastic behaviour and failure of thin-walled metallic radially notched circular rings with are-shaped supports subjected to concentrated impact loads. The experimental results show that the exterior notches at some regions have no effect on the deformation of the rings, but do have effect at the remaining regions. The notch-sensitive region is theoretically determined by using the equivalent structures technique; fairly good agreement has been reached between the simple theory and the experimental results. Both dimensional and theoretical analyses prove that whether a plastic hinge formed or not at the notched section does not depend on the mean radius of the ring and the input kinetic energy. It depends on the weak coefficient of the notched section and the angle of the support. Generally speaking, there are mainly three failure modes for a notched circular ring with are-shaped support under impact loading: Mode I, large inelastic deformation when the notch is outside the sensitive region, in this case the ring deforms as a normal one; Mode II, large inelastic deformation only at some part of the ring and tearing occurred at the notched sections; Mode III, large inelastic deformation and total rupture occurred at the notched sections. It is believed that the present study could assist the understanding of the dynamic behaviour and failure of other kinds of nonstraight components with macroscopic imperfections under impulsive loading.

Complete solution of the columbus problem for large-disturbance cases

The Columbus problem has been rigorously solved by Lyapunov's direct approach to the continuous system in gencral cases of large disturbance and the theory has proved to be in strict consistency with Kelvin's experiments.

Numerical Sensitivity Analysis and Partial Similarity of Porous Media Flows

A numerical optimisation approach to identify dominant dimensionless variables in porous media flows by sensitivity analysis is proposed. We have validated the approach at first by examining a simple oil reservoir theoretically and numerically as well. A more complex water-flooding reservoir is examined based on sensitivity analysis of oil recovery to the similarity parameters, thus demonstrating the feasibility of the proposed approach to identify dominant similarity parameters for water-oil two-phase flows.

Experimental Evidence of Critical Sensitivity in Catastrophe

The paper presents an experimental study on critical sensitivity in rocks. Critical sensitivity means that the response of a system to external controlling variable may become significantly sensitive as the system approaches its catastrophic rupture point. It is found that the sensitivities measured by responses on three scales (sample scale, locally macroscopic scales and mesoscopic scale) display increase prior to catastrophic transition point. These experimental results do support the concept that critical sensitivity might be a common precursory feature of catastrophe. Furthermore, our previous theoretical model is extended to explore the fluctuations in critical sensitivity in the rock tests.

Receptivity to free-stream disturbance waves for blunt cone axial symmetry hypersonic boundary layer

Based on high-order compact upwind scheme, a high-order shock-fitting finite difference scheme is studied to simulate the generation of boundary layer disturbance waves due to free-stream waves. Both steady and unsteady flow solutions of the receptivity problem are obtained by resolving the full Navier-Stokes equations. The interactions of bow-shock and free-stream disturbance are researched. Direct numerical simulation (DNS) of receptivity to free-stream disturbances for blunt cone hypersonic boundary layers is performed.

Intrinsic correlation between dilatation and pressure sensitivity of plastic flow in metallic glasses

Taking shear-induced dilatation into consideration in shear transformation zone (STZ) operations, we derive a new yield criterion that reflects the pressure sensitivity in plastic flow in metallic glasses (MGs), which agrees well with experiments. Furthermore, an intrinsic theoretical correlation between the pressure sensitivity coefficient and the dilatation factor is revealed. It is found that the pressure sensitivity of plastic flow of MGs originates in the dilatation of microscale STZs.