Calibration Procedures for a Computational Model of Ductile Fracture

A recent extension of the Gurson constitutive model of damage and failure of ductile structural alloys accounts for localization and crack formation under shearing as well as tension. When properly calibrated against a basic set of experiments, this model has the potential to predict the emergence and propagation of cracks over a wide range of stress states. This paper addresses procedures for calibrating the damage parameters of the extended constitutive model. The procedures are demonstrated for DH36 steel using data from three tests: (i) tension of a round bar, (ii) mode I cracking in a compact tension specimen, and (iii) shear localization and mode II cracking in a shear-off specimen. The computational model is then used to study the emergence of the cup-cone fracture mode in the neck of a round tensile bar. Ductility of a notched round bar provides additional validation.Engineering and Applied Science

Rolling at small scales

The rolling process is widely used in the metal forming industry and has been so for many years. However, the process has attracted renewed interest as it recently has been adapted to very small scales where conventional plasticity theory cannot accurately predict the material response. It is well-established that gradient effects play a role at the micron scale, and the objective of this study is to demonstrate how strain gradient hardening affects the rolling process. Specifically, the paper addresses how the applied roll torque, roll forces, and the contact conditions are modified by strain gradient plasticity. Metals are known to be stronger when large strain gradients appear over a few microns; hence, the forces involved in the rolling process are expected to increase relatively at these smaller scales. In the present numerical analysis, a steady-state modeling technique that enables convergence without dealing with the transient response period is employed. This allows for a comprehensive parameter study. Coulomb friction, including a stick–slip condition, is used as a first approximation. It is found that length scale effects increase both the forces applied to the roll, the roll torque, and thus the power input to the process. The contact traction is also affected, particularly for sheet thicknesses on the order of 10 μm and below. The influences of the length parameter and the friction coefficient are emphasized, and the results are presented for multiple sheet reductions and roll sizes.</jats:p

Unsupervised Category Learning with Integral-Dimension Stimuli

Despite the recent surge in research on unsupervised category learning, the majority of studies have focused on unconstrained tasks in which no instructions are provided about the underlying category structure. Relatively little research has focused on constrained tasks in which the goal is to learn pre-defined stimulus clusters in the absence of feedback. The few studies that have addressed this issue have focused almost exclusively on stimuli for which it is relatively easy to attend selectively to the component dimensions (i.e., separable dimensions). In the present study, we investigated the ability of participants to learn categories constructed from stimuli for which it is difficult, if not impossible, to attend selectively to the component dimensions (i.e., integral dimensions). The experiments demonstrate that individuals are capable of learning categories constructed from the integral dimensions of brightness and saturation, but this ability is generally limited to category structures requiring selective attention to brightness. As might be expected with integral dimensions, participants were often able to integrate brightness and saturation information in the absence of feedback – an ability not observed in previous studies with separable dimensions. Even so, there was a bias to weight brightness more heavily than saturation in the categorization process, suggesting a weak form of selective attention to brightness. These data present an important challenge for the development of models of unsupervised category learning

Non-equilibrium dynamics: Studies of reflection of Bose-Einstein condensates

The study of the non-equilibrium dynamics in Bose-Einstein condensed gases has been dominated by the zero-temperature, mean field Gross-Pitaevskii formalism. Motivated by recent experiments on the reflection of condensates from silicon surfaces, we revisit the so-called {\em classical field} description of condensate dynamics, which incorporates the effects of quantum noise and can also be generalized to include thermal effects. The noise is included in a stochastic manner through the initial conditions. We show that the inclusion of such noise is important in the quantitative description of the recent reflection experiments

A tool for simulating and communicating uncertainty when modelling species distributions under future climates

Tools for exploring and communicating the impact of uncertainty on spatial prediction are urgently needed, particularly when projecting species distributions to future conditions. We provide a tool for simulating uncertainty, focusing on uncertainty due to data quality. We illustrate the use of the tool using a Tasmanian endemic species as a case study. Our simulations provide probabilistic, spatially explicit illustrations of the impact of uncertainty on model projections. We also illustrate differences in model projections using six different global climate models and two contrasting emissions scenarios. Our case study results illustrate how different sources of uncertainty have different impacts on model output and how the geographic distribution of uncertainty can vary. Synthesis and applications: We provide a conceptual framework for understanding sources of uncertainty based on a review of potential sources of uncertainty in species distribution modelling; a tool for simulating uncertainty in species distribution models; and protocols for dealing with uncertainty due to climate models and emissions scenarios. Our tool provides a step forward in understanding and communicating the impacts of uncertainty on species distribution models under future climates which will be particularly helpful for informing discussions between researchers, policy makers, and conservation practitioners

Strongly Non-Equilibrium Bose-Einstein Condensation in a Trapped Gas

We present a qualitative (and quantitative, at the level of estimates) analysis of the ordering kinetics in a strongly non-equilibrium state of a weakly interacting Bose gas, trapped with an external potential. At certain conditions, the ordering process is predicted to be even more rich than in the homogeneous case. Like in the homogeneous case, the most characteristic feature of the full-scale non-equilibrium process is the formation of superfluid turbulence.Comment: 4 pages, revtex, no figures. Submitted to PR

Theory of coherent Bragg spectroscopy of a trapped Bose-Einstein condensate

We present a detailed theoretical analysis of Bragg spectroscopy from a Bose-Einstein condensate at T=0K. We demonstrate that within the linear response regime, both a quantum field theory treatment and a meanfield Gross-Pitaevskii treatment lead to the same value for the mean evolution of the quasiparticle operators. The observable for Bragg spectroscopy experiments, which is the spectral response function of the momentum transferred to the condensate, can therefore be calculated in a meanfield formalism. We analyse the behaviour of this observable by carrying out numerical simulations in axially symmetric three-dimensional cases and in two dimensions. An approximate analytic expression for the observable is obtained and provides a means for identifying the relative importance of three broadening and shift mechanisms (meanfield, Doppler, and finite pulse duration) in different regimes. We show that the suppression of scattering at small values of q observed by Stamper-Kurn et al. [Phys. Rev. Lett. 83, 2876 (1999)] is accounted for by the meanfield treatment, and can be interpreted in terms of the interference of the u and v quasiparticle amplitudes. We also show that, contrary to the assumptions of previous analyses, there is no regime for trapped condensates for which the spectral response function and the dynamic structure factor are equivalent. Our numerical calculations can also be performed outside the linear response regime, and show that at large laser intensities a significant decrease in the shift of the spectral response function can occur due to depletion of the initial condensate.Comment: RevTeX4 format, 16 pages plus 7 eps figures; Update to published version: minors changes and an additional figure. (To appear in Phys. Rev. A

Exponential Divergence and Long Time Relaxation in Chaotic Quantum Dynamics

Phase space representations of the dynamics of the quantal and classical cat map are used to explore quantum--classical correspondence in a K-system: as $\hbar \to 0$, the classical chaotic behavior is shown to emerge smoothly and exactly. The quantum dynamics near the classical limit displays both exponential separation of adjacent distributions and long time relaxation, two characteristic features of classical chaotic motion.Comment: 10 pages, ReVTeX, to appear in Phys. Rev. Lett. 13 figures NOT included. Available either as LARGE (uuencoded gzipped) postscript files or hard-copies from [email protected]