Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9901120

Influence of uniaxial stress on the lamellar spacing of eutectics

Jens Kappey·Klaus Kassner·Chaouqi Misbah
View original source ↗Read source document ↗Export metadata ↓

Abstract

Directional solidification of lamellar eutectic structures submitted to uniaxial stress is investigated. In the spirit of an approximation first used by Jackson and Hunt, we calculate the stress tensor for a two-dimensional crystal with triangular surface, using a Fourier expansion of the Airy function. crystal with triangular surface in contact with its melt, given that a uniaxial external stress is applied. The effect of the resulting change in chemical potential is introduced into the standard model for directional solidification of a lamellar eutectic. This calculation is motivated by an observation, made recently [I. Cantat, K. Kassner, C. Misbah, and H. Müller-Krumbhaar, Phys. Rev. E, in press] that the thermal gradient produces similar effects as a strong gravitational field in the case of dilute-alloy solidification. Therefore, the coupling between the Grinfeld and the Mullins-Sekerka instabilities becomes strong, as the critical wavelength of the former instability gets reduced to a value close to that of the latter. Analogously, in the case of eutectics, the characteristic length scale of the Grinfeld instability should be reduced to a size not extremely far from typical lamellar spacings. In a Jackson-Hunt like approach we average the undercooling, including the stress term, over a pair of lamellae. Following Jackson and Hunt, we assume the selected wavelength to be determined by the minimum undercooling criterion and compute its shift due to the external stress. we realize the shifting of the wavelength by the application of external stress. In addition, we find that in general the volume fraction of the two solid phases is changed by uniaxial stress. Implications for experiments on eutectics are discussed.

Explore related subjects

cond-mat.stat-mechcond-mat.mtrl-sci

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jens Kappey, Klaus Kassner, Chaouqi Misbah. 1999-01-13. Influence of uniaxial stress on the lamellar spacing of eutectics. https://doi.org/10.1103/physreve.59.4298

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Nonuniform asymmetric exclusion process: Stationary densities and domain walls

We compute the stationary densities in totally asymmetric exclusion processes (TASEP) with open boundary conditions and spatially nonuniform hopping rates. The stationary densities in the low and and high density phases can be discontinuous, only when the space-dependent hopping rate is spatially discontinuous. In contrast, the stationary density profile in the maximal current phase can be discontinuous, even when the space-dependent hopping rate is continuous. We further investigate the domain walls, which are delocalised with complex shapes. In striking contrast to a delocalised domain wall (DDW) in an open, uniform TASEP, these DDWs can also form at the transitions between the low or high density phases and maximal current phase, and can cover the entire TASEP channel or a part of it, depending upon the specific forms of the site-dependence of the hopping rates and the associated phase transitions. We calculate their envelopes, which are curved lines, revealing their dependence on the spatial nonuniformity of the hopping rates. The phase diagrams in the plane of the control parameters show universal topology. The associated phase transitions are explored, which can be different from their counterparts in an open uniform TASEP.

cond-mat.stat-mech↗
arXiv2026

Intermittency in Wind-Driven Fires

We construct a wind-driven forest-fire model in one dimension in which a fire can jump gaps between trees to ignite disjoint downwind forests. The size of a gap that a fire can jump depends on the fire intensity, which increases as the fire propagates through trees and diminishes as the fire jumps gaps. Trees grow on empty sites at rate $r$ and lightning strikes each site with rate $f$. When $f\ll r/L$, where $L$ is the system length, lightning is sufficiently rare that quasi-deterministic dynamics arises where all trees are consumed when a lightning-induced fire occurs. For $f\gg L^{-μ}$ with $μ\approx 0.8$, lightning is sufficiently frequent that a steady state is reached, but with unexpected behaviors for the forest- and gap-size distributions. Intermittency arises in between these regimes, with coexisting temporal domains of deterministic and chaotic dynamics.

cond-mat.stat-mech↗
arXiv2026

Uphill and downhill first passage of an active Brownian particle: Asymmetry and exact path reweighting

First passage processes in active systems combine stochastic transport with self-propulsion and orientational persistence, making motion along and against an external bias sensitive to the internal active dynamics. For passive biased diffusion, opposite exits can have different splitting probabilities while their conditional first passage time distributions remain identical. We study how this relation changes for an active Brownian particle driven by a constant external force between two absorbing boundaries. Self-propulsion breaks the equality of the uphill and downhill first passage time distributions and modifies the splitting probabilities. Nevertheless, the two directional path ensembles remain exactly related by spatial reflection, which pairs downhill and uphill first passage paths of the same duration while preserving their orientational history. The log-ratio of the probabilities of a path and its reflected partner defines a path-dependent asymmetry functional and provides an exact reweighting between the two ensembles. In the symmetric half-weighted representation, the uphill and downhill first passage time distributions coincide for arbitrary orientational persistence. The same path relation also allows rare uphill statistics to be reconstructed from the more frequently sampled downhill trajectories. Numerical simulations confirm the weighted equality across the explored bias and persistence regimes, while perturbative and asymptotic analyses clarify how orientational persistence produces the directional asymmetry of the unweighted statistics. The exact relation between the two directional path ensembles suggests that similar symmetry-based reconstruction protocols may be found in other nonequilibrium first-passage problems.

cond-mat.stat-mech↗