Fractals and Scaling in Fracture Induced by Microcrack Coalescence

A numerical model is proposed to simulate fracture induced by the coalescence of numerous microcracks, in which the condition for coalescence between two randomly nucleated microcracks is determined in terms of a load-sharing principle. The results of the simulation show that, as the number density of nucleated microcracks increases, stochastic coalescence first occurs followed by a small fluctuation, and finally a newly nucleated microcrack triggers a cascade coalescence of microcracks resulting in catastrophic failure. The fracture profiles exhibit self-affine fractal characteristics with a universal roughness exponent, but the critical damage threshold is sensitive to details of the model. The spatiotemporal distribution of nucleated microcracks in the vicinity of critical failure follows a power-law behaviour, which implies that the microcrack system may evolve to a critical state.

Scaling relationships in indentation of power-law creep solids using self-similar indenters

We use dimensional analysis to derive scaling relationships for self-similar indenters indenting solids that exhibit power-law creep. We identify the parameter that represents the indentation strain rate. The scaling relationships are applied to several types of indentation creep experiment with constant displacement rate, constant loading rate or constant ratio of loading rate over load. The predictions compare favourably with experimental observations reported in the literature. Finally, a connection is found between creep and 'indentation-size effect' (i.e. changing hardness with indentation depth or load).

Extended self-similar scaling law of multi-scale eddy structure in wall turbulence

The longitudinal fluctuating velocity of a turbulent boundary layer was measured in a water channel at a moderate Reynolds number. The extended self-similar scaling law of structure function proposed by Benzi was verified. The longitudinal fluctuating velocity, in the turbulent boundary layer was decomposed into many multi-scale eddy structures by wavelet transform. The extended self-similar scaling law of structure function for each scale eddy velocity was investigated. The conclusions are I) The statistical properties of turbulence could be self-similar not only at high Reynolds number, but also at moderate and low Reynolds number, and they could be characterized by the same set of scaling exponents xi (1)(n) = n/3 and xi (2)(n) = n/3 of the fully developed regime. 2) The range of scales where the extended self-similarity valid is much larger than the inertial range and extends far deep into the dissipation range,vith the same set of scaling exponents. 3) The extended selfsimilarity is applicable not only for homogeneous turbulence, but also for shear turbulence such as turbulent boundary layers.

Scaling, Dimensional Analysis, and Indentation Measurements

We provide an overview of the basic concepts of scaling and dimensional analysis, followed by a review of some of the recent work on applying these concepts to modeling instrumented indentation measurements. Specifically, we examine conical and pyramidal indentation in elastic-plastic solids with power-law work-hardening, in power-law creep solids, and in linear viscoelastic materials. We show that the scaling approach to indentation modeling provides new insights into several basic questions in instrumented indentation, including, what information is contained in the indentation load-displacement curves? How does hardness depend on the mechanical properties and indenter geometry? What are the factors determining piling-up and sinking-in of surface profiles around indents? Can stress-strain relationships be obtained from indentation load-displacement curves? How to measure time dependent mechanical properties from indentation? How to detect or confirm indentation size effects? The scaling approach also helps organize knowledge and provides a framework for bridging micro- and macroscales. We hope that this review will accomplish two purposes: (1) introducing the basic concepts of scaling and dimensional analysis to materials scientists and engineers, and (2) providing a better understanding of instrumented indentation measurements.

Scaling the iHMM: Parallelization versus Hadoop

This paper compares parallel and distributed implementations of an iterative, Gibbs sampling, machine learning algorithm. Distributed implementations run under Hadoop on facility computing clouds. The probabilistic model under study is the infinite HMM [1], in which parameters are learnt using an instance blocked Gibbs sampling, with a step consisting of a dynamic program. We apply this model to learn part-of-speech tags from newswire text in an unsupervised fashion. However our focus here is on runtime performance, as opposed to NLP-relevant scores, embodied by iteration duration, ease of development, deployment and debugging. © 2010 IEEE.

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.

Scaling Functions In Conical Indentation Of Elastic-Plastic Solids

The finite element method was used to simulate the conical indentation of elastic-plastic solids with work hardening. The ratio of the initial yield strength to the Young's modulus Y/E ranged from 0 to 0.02. Based on the calculation results, two sets of scaling functions for non-dimensional hardness H/K and indenter penetration h are presented in the paper, which have closed simple mathematical form and can be used easily for engineering application. Using the present scaling functions, indentation hardness and indentation loading curves can be easily obtained for a given set of material properties. Meanwhile one can use these scaling functions to obtain material parameters by an instrumented indentation load-displacement curve for loading and unloading if Young's modulus E and Poisson's ratio nu are known.

About generalized scaling for passive scalars in fully developed turbulence

In this paper we use a simple normal form approach of scale invariant fields to investigate scaling laws of passive scalars in turbulence. The coupling equations for velocity and passive scalar moments are scale covariant. Their solution shows that passive scalars in turbulence do not generically follow a general scaling observed for velocity field because of coupling effects.