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K R Elder

Publications and source records attributed to K R Elder.

6 recordsLinked to original sources
PubMed2002

Instabilities and resistance fluctuations in thin accelerated superconducting rings.

The nonequilibrium properties of a driven quasi-one-dimensional superconducting ring subjected to a constant electromotive force (emf) is studied. The emf accelerates the superconducting electrons until the critical current is reached and a dissipative phase slip occurs that lowers the current. The phase-slip phenomena is examined as a function of the strength of the emf, thermal noise, and normal state resistivity. Numerical and analytic methods are used to make detailed predictions for the magnitude of phase slips and subsequent dissipation.

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PubMed2002

Modeling elasticity in crystal growth.

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to time scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth.

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PubMed2001

Interface pinning in spontaneous imbibition.

Evaporation and gravity induced pinning in spontaneous imbibition are examined within a phase field formalism. Evaporation is introduced via a nonconserving term and gravity through a convective term that constrains the influx of liquid. Their effects are described by dimensionless coupling constants epsilon and g, respectively. From liquid conservation, the early time behavior of the average interface position follows H(t) approximately t1/2 until a crossover time t*(g,epsilon). After that the pinning height Hp(g,epsilon) is approached exponentially in time, in accordance with mean field theory. The statistical roughness of the interface is described by an exponent chi approximately 1.25 at all stages of the rise, but the dynamic length scale controlling roughness crosses over from xi(x) approximately H1/2 to a time independent pinning length scale xi(p)(epsilon,g).

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PubMed2001

Sharp interface limits of phase-field models.

The use of continuum phase-field models to describe the motion of well-defined interfaces is discussed for a class of phenomena that includes order-disorder transitions, spinodal decomposition and Ostwald ripening, dendritic growth, and the solidification of eutectic alloys. The projection operator method is used to extract the "sharp-interface limit" from phase-field models which have interfaces that are diffuse on a length scale xi. In particular, phase-field equations are mapped onto sharp-interface equations in the limits xi(kappa)<<1 and xi(v)/D<<1, where kappa and v are, respectively, the interface curvature and velocity and D is the diffusion constant in the bulk. The calculations provide one general set of sharp-interface equations that incorporate the Gibbs-Thomson condition, the Allen-Cahn equation, and the Kardar-Parisi-Zhang equation.

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PubMed2000

Phase-field modeling of eutectic growth.

A phase-field model of eutectic growth is proposed in terms of a free energy F, which is a functional of a liquid-solid order parameter psi, and a conserved concentration field c. The model is shown to recover the important features of a eutectic phase diagram and to reduce to the standard sharp-interface formulation of nonequilibrium growth. It is successfully applied to the study of directional solidification when the solid phase is a single or two phase state. The crystallization of a eutectic compound under isothermal conditions is also considered. For that process, the transformed volume fraction and psi-field structure factor, both measured during numerical simulations, closely match theoretical predictions. Three possible growth mechanisms are also identified: diffusion-limited growth, lamellar growth, and spinodal decomposition.

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