Fracture in Mode I using a Conserved Phase-Field Model

We present a continuum phase-field model of crack propagation. It includes a phase-field that is proportional to the mass density and a displacement field that is governed by linear elastic theory. Generic macroscopic crack growth laws emerge naturally from this model. In contrast to classical continuum fracture mechanics simulations, our model avoids numerical front tracking. The added phase-field smoothes the sharp interface, enabling us to use equations of motion for the material (grounded in basic physical principles) rather than for the interface (which often are deduced from complicated theories or empirical observations). The interface dynamics thus emerges naturally. In this paper, we look at stationary solutions of the model, mode I fracture, and also discuss numerical issues. We find that the Griffith's threshold underestimates the critical value at which our system fractures due to long wavelength modes excited by the fracture process.Comment: 10 pages, 5 figures (eps). Added 2 figures and some text. Removed one section (and a figure). To be published in PR

Quiet Supersonic Flights 2018 (QSF18) Test: Galveston, Texas Risk Reduction for Future Community Testing with a Low-Boom Flight Demonstration Vehicle

The Quiet Supersonic Flights 2018 (QSF18) Program was designed to develop tools and methods for demonstration of overland supersonic flight with an acceptable sonic boom, and collect a large dataset of responses from a representative sample of the population. Phase 1 provided the basis for a low amplitude sonic boom testing in six different climate regions that will enable international regulatory agencies to draft a noise-based standard for certifying civilian supersonic overland flight. Phase 2 successfully executed a large scale test in Galveston, Texas, developed well documented data sets, calculated dose response relationships, yielded lessons, and identified future risk reduction activities

Stable propagation of an ordered array of cracks during directional drying

We study the appearance and evolution of an array of parallel cracks in a thin slab of material that is directionally dried, and show that the cracks penetrate the material uniformly if the drying front is sufficiently sharp. We also show that cracks have a tendency to become evenly spaced during the penetration. The typical distance between cracks is mainly governed by the typical distance of the pattern at the surface, and it is not modified during the penetration. Our results agree with recent experimental work, and can be extended to three dimensions to describe the properties of columnar polygonal patterns observed in some geological formations.Comment: 8 pages, 4 figures, to appear in PR

Statistical Physics of Fracture Surfaces Morphology

Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich phenomenology of anomalous scaling. We argue that traditional models of fracture fail to reproduce this rich phenomenology and new ideas and concepts are called for. We present some recent models that introduce the effects of deviations from homogeneous linear elasticity theory on the morphology of fracture surfaces, succeeding to reproduce the multiscaling phenomenology at least in 1+1 dimensions. For surfaces in 2+1 dimensions we introduce novel methods of analysis based on projecting the data on the irreducible representations of the SO(2) symmetry group. It appears that this approach organizes effectively the rich scaling properties. We end up with the proposition of new experiments in which the rotational symmetry is not broken, such that the scaling properties should be particularly simple.Comment: A review paper submitted to J. Stat. Phy

Structural Relaxation, Self Diffusion and Kinetic Heterogeneity in the Two Dimensional Lattice Coulomb Gas

We present Monte Carlo simulation results on the equilibrium relaxation dynamics in the two dimensional lattice Coulomb gas, where finite fraction $f$ of the lattice sites are occupied by positive charges. In the case of high order rational values of $f$ close to the irrational number $1-g$ ($g\equiv(\sqrt{5} -1)/2$ is the golden mean), we find that the system exhibits, for wide range of temperatures above the first-order transition, a glassy behavior resembling the primary relaxation of supercooled liquids. Single particle diffusion and structural relaxation show that there exists a breakdown of proportionality between the time scale of diffusion and that of structural relaxation analogous to the violation of the Stokes-Einstein relation in supercooled liquids. Suitably defined dynamic cooperativity is calculated to exhibit the characteristic nature of dynamic heterogeneity present in the system.Comment: 12 pages, 20 figure

Diffusion and viscosity in a supercooled polydisperse system

We have carried out extensive molecular dynamics simulations of a supercooled polydisperse Lennard-Jones liquid with large variations in temperature at a fixed pressure. The particles in the system are considered to be polydisperse both in size and mass. The temperature dependence of the dynamical properties such as the viscosity ($\eta$) and the self-diffusion coefficients ($D_i$) of different size particles is studied. Both viscosity and diffusion coefficients show super-Arrhenius temperature dependence and fit well to the well-known Vogel-Fulcher-Tammann (VFT) equation. Within the temperature range investigated, the value of the Angell's fragility parameter (D $\approx 1.4$) classifies the present system into a strongly fragile liquid. The critical temperature for diffusion ($T_o^{D_i}$) increases with the size of the particles. The critical temperature for viscosity ($T_o^{\eta}$) is larger than that for the diffusion and a sizeable deviations appear for the smaller size particles implying a decoupling of translational diffusion from viscosity in deeply supercooled liquid. Indeed, the diffusion shows markedly non-Stokesian behavior at low temperatures where a highly nonlinear dependence on size is observed. An inspection of the trajectories of the particles shows that at low temperatures the motions of both the smallest and largest size particles are discontinuous (jump-type). However, the crossover from continuous Brownian to large length hopping motion takes place at shorter time scales for the smaller size particles.Comment: Revtex4, 7 pages, 8 figure

A Flight Research Overview of WSPR, a Pilot Project for Sonic Boom Community Response

In support of NASAs ongoing effort to bring supersonic commercial travel to the public, NASA Dryden Flight Research Center and NASA Langley Research Center, in cooperation with other industry organizations, conducted a flight research experiment to identify the methods, tools, and best practices for a large-scale quiet (or low) sonic boom community human response test. The name of the effort was Waveforms and Sonic boom Perception and Response. Such tests will go towards building a dataset that governing agencies like the Federal Aviation Administration and International Civil Aviation Organization will use to establish regulations for acceptable sound levels of overland sonic booms. Until WSPR, there had never been an effort that studied the response of people in their own homes and performing daily activities to non-traditional, low sonic booms.WSPR was a NASA collaborative effort with several industry partners, in response to a NASA Aeronautics Research Mission Directorate Research Opportunities in Aeronautics. The primary contractor was Wyle. Other partners included Gulfstream Aerospace Corporation, Pennsylvania State University, Tetra Tech, and Fidell Associates, Inc.A major objective of the effort included exposing a community with the sonic boom magnitudes and occurrences expected in high-air traffic regions with a network of supersonic commercial aircraft in place. Low-level sonic booms designed to simulate those produced by the next generation of commercial supersonic aircraft were generated over a small residential community. The sonic boom footprint was recorded with an autonomous wireless microphone array that spanned the entire community. Human response data was collected using multiple survey methods. The research focused on essential elements of community response testing including subject recruitment, survey methods, instrumentation systems, flight planning and operations, and data analysis methods.This paper focuses on NASAs role in the efforts logistics and operations including human response subject recruitment, the operational processes involved in implementing the surveys throughout the community, instrumentation systems, logistics, flight planning, and flight operations. Findings discussed in this paper include critical lessons learned in all of those areas. The paper also discusses flight operations results. Analysis of the accuracy and repeatability of planning and executing the unique aircraft maneuver used to generate low sonic booms concluded that the sonic booms had overpressures within 0.15 pounds-per-square-feet of the planned values for 76 of t he attempts. Similarly, 90 of the attempts to generate low sonic booms within the community were successful