Dislocation core field. I. Modeling in anisotropic linear elasticity theory

Aside from the Volterra field, dislocations create a core field, which can be modeled in linear anisotropic elasticity theory with force and dislocation dipoles. We derive an expression of the elastic energy of a dislocation taking full account of its core field and show that no cross term exists between the Volterra and the core fields. We also obtain the contribution of the core field to the dislocation interaction energy with an external stress, thus showing that dislocation can interact with a pressure. The additional force that derives from this core field contribution is proportional to the gradient of the applied stress. Such a supplementary force on dislocations may be important in high stress gradient regions, such as close to a crack tip or in a dislocation pile-up

1/f1/f noise and avalanche scaling in plastic deformation

We study the intermittency and noise of dislocation systems undergoing shear deformation. Simulations of a simple two-dimensional discrete dislocation dynamics model indicate that the deformation rate exhibits a power spectrum scaling of the type $1/f^{\alpha}$. The noise exponent is far away from a Lorentzian, with $\alpha \approx 1.5$. This result is directly related to the way the durations of avalanches of plastic deformation activity scale with their size.Comment: 6 pages, 5 figures, submitted to Phys. Rev.

Mesoscopic Analysis of Structure and Strength of Dislocation Junctions in FCC Metals

We develop a finite element based dislocation dynamics model to simulate the structure and strength of dislocation junctions in FCC crystals. The model is based on anisotropic elasticity theory supplemented by the explicit inclusion of the separation of perfect dislocations into partial dislocations bounding a stacking fault. We demonstrate that the model reproduces in precise detail the structure of the Lomer-Cottrell lock already obtained from atomistic simulations. In light of this success, we also examine the strength of junctions culminating in a stress-strength diagram which is the locus of points in stress space corresponding to dissolution of the junction.Comment: 9 Pages + 4 Figure

Voltage from mechanical stress in type-II superconductors: Depinning of the magnetic flux by moving dislocations

Mechanical stress causes motion of defects in solids. We show that in a type-II superconductor a moving dislocation generates a pattern of current that exerts the depinning force on the surrounding vortex lattice. Concentration of dislocations and the mechanical stress needed to produce critical depinning currents are shown to be within practical range. When external magnetic field and transport current are present this effect generates voltage across the superconductor. Thus a superconductor can serve as an electrical sensor of the mechanical stress.Comment: 3 pages, 1 figure

Ground state of a large number of particles on a frozen topography

Problems consisting in finding the ground state of particles interacting with a given potential constrained to move on a particular geometry are surprisingly difficult. Explicit solutions have been found for small numbers of particles by the use of numerical methods in some particular cases such as particles on a sphere and to a much lesser extent on a torus. In this paper we propose a general solution to the problem in the opposite limit of a very large number of particles M by expressing the energy as an expansion in M whose coefficients can be minimized by a geometrical ansatz. The solution is remarkably universal with respect to the geometry and the interaction potential. Explicit solutions for the sphere and the torus are provided. The paper concludes with several predictions that could be verified by further theoretical or numerical work.Comment: 9 pages, 9 figures, LaTeX fil

Using short-term postseismic displacements to infer the ambient deformation conditions of the upper mantle

Author Posting. © American Geophysical Union, 2012. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophyscial Research 117 (2012): B01409, doi:10.1029/2011JB008562.To interpret short-term postseismic surface displacements in the context of key ambient conditions (e.g., temperature, pressure, background strain rate, water content, creep mechanism), we combined steady state and transient flow into a single constitutive relation that can explain the response of a viscoelastic material to a change in stress. The flow law is then used to investigate mantle deformation beneath the Eastern California Shear Zone following the 1999 M7.1 Hector Mine earthquake. The flow law parameters are determined using finite element models of relaxation processes, constrained by surface displacement time series recorded by 55 continuous GPS stations for 7 years following the earthquake. Results suggest that postseismic flow following the Hector Mine earthquake occurs below a depth of ~50 km and is controlled by dislocation creep of wet olivine. Diffusion creep models can also explain the data, but require a grain size (3.5 mm) that is smaller than the inferred grain size (10–20 mm) based on the mantle conditions at these depths. In addition, laboratory flow laws predict dislocation creep would dominate at the stress/grain size conditions that provide the best fit to diffusion creep models. Model results suggest a transient creep phase that lasts ~1 year and has a viscosity ~10 times lower than subsequent steady state flow, in general agreement with laboratory observations. The postseismic response is best explained as occurring within a relatively hot upper mantle (e.g., 1200–1300°C at 50 km depth) with a long-term background mantle strain rate of 0.1–0.2 μstrain/yr, consistent with the observed surface strain rate. Long-term background shear stresses at the top of the mantle are ~4 MPa, then decrease with depth to a minimum of 0.1–0.2 MPa at 70 km depth before increasing slowly with depth due to the pressure dependence of viscosity. These conditions correspond to a background viscosity of 1021 Pa s within a thin mantle lid that decreases to ~5 × 1019 Pa s within the underlying asthenosphere. This study shows the utility of using short-term postseismic observations to infer long-term mantle conditions that are not readily observable by other means.This work was supported by the National Science Foundation grants EAR-0952234 (A.M.F.), EAR-0810188 (G.H.), and EAR-0854673 (M.D.B.).2012-07-3

The Dopaminergic System in the Aging Brain of Drosophila

Drosophila models of Parkinson's disease are characterized by two principal phenotypes: the specific loss of dopaminergic (DA) neurons in the aging brain and defects in motor behavior. However, an age-related analysis of these baseline parameters in wildtype Drosophila is lacking. Here we analyzed the DA system and motor behavior in aging Drosophila. DA neurons in the adult brain can be grouped into bilateral symmetric clusters, each comprising a stereotypical number of cells. Analysis of TH > mCD8::GFP and cell type-specific MARCM clones revealed that DA neurons show cluster-specific, stereotypical projection patterns with terminal arborization in target regions that represent distinct functional areas of the adult brain. Target areas include the mushroom bodies, involved in memory formation and motivation, and the central complex, involved in the control of motor behavior, indicating that similar to the mammalian brain, DA neurons in the fly brain are involved in the regulation of specific behaviors. Behavioral analysis revealed that Drosophila show an age-related decline in startle-induced locomotion and negative geotaxis. Motion tracking however, revealed that walking activity, and exploration behavior, but not centrophobism increase at late stages of life. Analysis of TH > Dcr2, mCD8::GFP revealed a specific effect of Dcr2 expression on walking activity but not on exploratory or centrophobic behavior, indicating that the siRNA pathway may modulate distinct DA behaviors in Drosophila. Moreover, DA neurons were maintained between early- and late life, as quantified by TH > mCD8::GFP and anti-TH labeling, indicating that adult onset, age-related degeneration of DA neurons does not occur in the aging brain of Drosophila. Taken together, our data establish baseline parameters in Drosophila for the study of Parkinson's disease as well as other disorders affecting DA neurons and movement control

Cooperation, collective action, and the archeology of large-scale societies

Archeologists investigating the emergence of large-scale societies in the past have renewed interest in examining the dynamics of cooperation as a means of understanding societal change and organizational variability within human groups over time. Unlike earlier approaches to these issues, which used models designated voluntaristic or managerial, contemporary research articulates more explicitly with frameworks for cooperation and collective action used in other fields, thereby facilitating empirical testing through better definition of the costs, benefits, and social mechanisms associated with success or failure in coordinated group action. Current scholarship is nevertheless bifurcated along lines of epistemology and scale, which is understandable but problematic for forging a broader, more transdisciplinary field of cooperation studies. Here, we point to some areas of potential overlap by reviewing archeological research that places the dynamics of social cooperation and competition in the foreground of the emergence of large-scale societies, which we define as those having larger populations, greater concentrations of political power, and higher degrees of social inequality. We focus on key issues involving the communal-resource management of subsistence and other economic goods, as well as the revenue flows that undergird political institutions. Drawing on archeological cases from across the globe, with greater detail from our area of expertise in Mesoamerica, we offer suggestions for strengthening analytical methods and generating more transdisciplinary research programs that address human societies across scalar and temporal spectra

Lattice Resistance and Peierls Stress in Finite-size Atomistic Dislocation Simulations

Atomistic computations of the Peierls stress in fcc metals are relatively scarce. By way of contrast, there are many more atomistic computations for bcc metals, as well as mixed discrete-continuum computations of the Peierls-Nabarro type for fcc metals. One of the reasons for this is the low Peierls stresses in fcc metals. Because atomistic computations of the Peierls stress take place in finite simulation cells, image forces caused by boundaries must either be relaxed or corrected for if system size independent results are to be obtained. One of the approaches that has been developed for treating such boundary forces is by computing them directly and subsequently subtracting their effects, as developed by V. B. Shenoy and R. Phillips [Phil. Mag. A, 76 (1997) 367]. That work was primarily analytic, and limited to screw dislocations and special symmetric geometries. We extend that work to edge and mixed dislocations, and to arbitrary two-dimensional geometries, through a numerical finite element computation. We also describe a method for estimating the boundary forces directly on the basis of atomistic calculations. We apply these methods to the numerical measurement of the Peierls stress and lattice resistance curves for a model aluminum (fcc) system using an embedded-atom potential.Comment: LaTeX 47 pages including 20 figure

Buried dislocation networks designed to organize the growth of III-V semiconductor nanostructures

We first report a detailed transmission electron microscopy study of dislocation networks (DNs) formed at shallowly buried interfaces obtained by bonding two GaAs crystals between which we establish in a controlled manner a twist and a tilt around a k110l direction. For large enough twists, the DN consists of a twodimensional network of screw dislocations accommodating mainly the twist and of a one-dimensional network of mixed dislocations accommodating mainly the tilt. We show that in addition the mixed dislocations accommodate part of the twist and we observe and explain slight unexpected disorientations of the screw dislocations with respect to the k110l directions. By performing a quantitative analysis of the whole DN, we propose a coherent interpretation of these observations which also provides data inaccessible by direct experiments. When the twist is small enough, one screw subnetwork vanishes. The surface strain field induced by such DNs has been used to pilot the lateral ordering of GaAs and InGaAs nanostructures during metal-organic vapor phase epitaxy. We prove that the dimensions and orientations of the nanostructures are correlated with those of the cells of the underlying DN and explain how the interface dislocation structure governs the formation of the nanostructures