252 research outputs found
Dislocation mutual interactions mediated by mobile impurities and the conditions for plastic instabilities
Matallic alloys, such as Al or Cu, or mild steel, display plastic
instabilities in a well defined range of temperatures and deformation rates, a
phenomenon known as the Portevin-Le Chatelelier (PLC) effect. The stick-slip
behavior, or serration, typical of this effect is due to the discontinuous
motion of dislocations as they interact with solute atoms. Here we study a
simple model of interacting dislocations and show how the classical Einstein
fluctuation-dissipation relation can be used to define the temperature in a
range of model parameters and to construct a phase diagram of serration that
can be compared to experimental results. Furthermore, performing analytical
calculations and numerically integrating the equations of motion, we clarify
the crucial role played by dislocation mutual interactions in serration
Size effects in dislocation depinning models for plastic yield
Typically, the plastic yield stress of a sample is determined from a
stress-strain curve by defining a yield strain and reading off the stress
required to attain it. However, it is not a priori clear that yield strengths
of microscale samples measured this way should display the correct finite size
scaling. Here we study plastic yield as a depinning transition of a 1+1
dimensional interface, and consider how finite size effects depend on the
choice of yield strain, as well as the presence of hardening and the strength
of elastic coupling. Our results indicate that in sufficiently large systems,
the choice of yield strain is unimportant, but in smaller systems one must take
care to avoid spurious effects.Comment: 7 pages, 8 figure
Depinning of a dislocation: the influence of long-range interactions
The theory of the depinning transition of elastic manifolds in random media
provides a framework for the statistical dynamics of dislocation systems at
yield. We consider the case of a single flexible dislocation gliding through a
random stress field generated by a distribution of immobile dislocations
threading through its glide plane. The immobile dislocations are arranged in a
"restrictedly random" manner and provide an effective stress field whose
statistical properties can be calculated explicitly. We write an equation of
motion for the dislocation and compute the associated depinning force, which
may be identified with the yield stress. Numerical simulations of a discretized
version of the equation confirm these results and allow us to investigate the
critical dynamics of the pinning-depinning transition.Comment: 8 pages, 4 figures. To appear in the proceedings of the
Dislocations2000 meeting (published by Materials Science and Engeneering A
Critical exponents in stochastic sandpile models
We present large scale simulations of a stochastic sandpile model in two
dimensions. We use moments analysis to evaluate critical exponents and finite
size scaling method to consistently test the obtained results. The general
picture resulting from our analysis allows us to characterize the large scale
behavior of the present model with great accuracy.Comment: 6 pages, 4 figures. Invited talk presented at CCP9
Self-organized criticality as an absorbing-state phase transition
We explore the connection between self-organized criticality and phase
transitions in models with absorbing states. Sandpile models are found to
exhibit criticality only when a pair of relevant parameters - dissipation
epsilon and driving field h - are set to their critical values. The critical
values of epsilon and h are both equal to zero. The first is due to the absence
of saturation (no bound on energy) in the sandpile model, while the second
result is common to other absorbing-state transitions. The original definition
of the sandpile model places it at the point (epsilon=0, h=0+): it is critical
by definition. We argue power-law avalanche distributions are a general feature
of models with infinitely many absorbing configurations, when they are subject
to slow driving at the critical point. Our assertions are supported by
simulations of the sandpile at epsilon=h=0 and fixed energy density (no drive,
periodic boundaries), and of the slowly-driven pair contact process. We
formulate a field theory for the sandpile model, in which the order parameter
is coupled to a conserved energy density, which plays the role of an effective
creation rate.Comment: 19 pages, 9 figure
Dynamically Driven Renormalization Group
We present a detailed discussion of a novel dynamical renormalization group
scheme: the Dynamically Driven Renormalization Group (DDRG). This is a general
renormalization method developed for dynamical systems with non-equilibrium
critical steady-state. The method is based on a real space renormalization
scheme driven by a dynamical steady-state condition which acts as a feedback on
the transformation equations. This approach has been applied to open non-linear
systems such as self-organized critical phenomena, and it allows the analytical
evaluation of scaling dimensions and critical exponents. Equilibrium models at
the critical point can also be considered. The explicit application to some
models and the corresponding results are discussed.Comment: Revised version, 50 LaTex pages, 6 postscript figure
Universality classes and crossover scaling of Barkhausen noise in thin films
We study the dynamics of head-to-head domain walls separating in-plane
domains in a disordered ferromagnetic thin film. The competition between the
domain wall surface tension and dipolar interactions induces a crossover
between a rough domain wall phase at short length-scales and a large-scale
phase where the walls display a zigzag morphology. The two phases are
characterized by different critical exponents for Barkhausen avalanche dynamics
that are in quantitative agreement with experimental measurements on MnAs thin
films.Comment: 5 pages, 5 figure
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