775 research outputs found
Amplitude equations for systems with long-range interactions
We derive amplitude equations for interface dynamics in pattern forming
systems with long-range interactions. The basic condition for the applicability
of the method developed here is that the bulk equations are linear and solvable
by integral transforms. We arrive at the interface equation via long-wave
asymptotics. As an example, we treat the Grinfeld instability, and we also give
a result for the Saffman-Taylor instability. It turns out that the long-range
interaction survives the long-wave limit and shows up in the final equation as
a nonlocal and nonlinear term, a feature that to our knowledge is not shared by
any other known long-wave equation. The form of this particular equation will
then allow us to draw conclusions regarding the universal dynamics of systems
in which nonlocal effects persist at the level of the amplitude description.Comment: LaTeX source, 12 pages, 4 figures, accepted for Physical Review
Phase Field Modeling of Fast Crack Propagation
We present a continuum theory which predicts the steady state propagation of
cracks. The theory overcomes the usual problem of a finite time cusp
singularity of the Grinfeld instability by the inclusion of elastodynamic
effects which restore selection of the steady state tip radius and velocity. We
developed a phase field model for elastically induced phase transitions; in the
limit of small or vanishing elastic coefficients in the new phase, fracture can
be studied. The simulations confirm analytical predictions for fast crack
propagation.Comment: 5 pages, 11 figure
Seeing Is Believing: Peer Video Coaching as Professional Development Done With Me and for Me
As part of their graduate education, in-service teachers identified an area of instructional focus, video recorded their classroom instruction at two intervals in a semester-long course, formed peer groups, and shared their videos for the purpose of obtaining feedback for professional growth. After the conclusion of the course, participants were contacted and presented with a summary of four benefits of the peer video review process, as identified in a recent professional article. Through online survey, participants were asked to share their perceptions of the peer video review experiences in the course and address any evidence related to the benefits raised in the professional article. Qualitative analysis revealed evidence of individual and collective benefits at personal and professional levels and consensus around the value of the experience, despite common apprehension about the vulnerability involved in sharing. Additionally, participants identified strengths of the video medium and provided suggestions for practical applications of peer video review in the field
Chat It Up: Backchanneling to Promote Reflective Practice Among In-Service Teachers
In a graduate education course geared toward developing reflective teaching practice in in-service teachers, backchannels, in the form of chat rooms, were employed in small groups to facilitate peer feedback during viewings of video recorded instruction. This study examined the nature and quality of peer feedback exchanged in the digital medium and gauged graduate students’ impressions of the technology, with potential for carryover into their professional practices in P-12 instruction. Results revealed that the backchannel was perceived as an easy-to-use tool that promoted rich, real-time, high-quality feedback and a space to collaborate and exchange ideas, while improving engagement. Backchannel comments had mostly positive or neutral tone, and took the form of observations, compliments, and helpful coaching prompts. Comments were overwhelmingly focused on instructional strategies, teacher behavior, and the learning environment. Participants saw value in utilizing backchannels in P-12 settings, but some expressed hesitation in using such tools with young students
Influence of uniaxial stress on the lamellar spacing of eutectics
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.
M\"uller-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.Comment: 8 pages RevTex, 6 included ps-figures, accepted for Phys. Rev.
Pattern formation in directional solidification under shear flow. I: Linear stability analysis and basic patterns
An asymptotic interface equation for directional solidification near the
absolute stabiliy limit is extended by a nonlocal term describing a shear flow
parallel to the interface. In the long-wave limit considered, the flow acts
destabilizing on a planar interface. Moreover, linear stability analysis
suggests that the morphology diagram is modified by the flow near the onset of
the Mullins-Sekerka instability. Via numerical analysis, the bifurcation
structure of the system is shown to change. Besides the known hexagonal cells,
structures consisting of stripes arise. Due to its symmetry-breaking
properties, the flow term induces a lateral drift of the whole pattern, once
the instability has become active. The drift velocity is measured numerically
and described analytically in the framework of a linear analysis. At large flow
strength, the linear description breaks down, which is accompanied by a
transition to flow-dominated morphologies, described in a companion paper.
Small and intermediate flows lead to increased order in the lattice structure
of the pattern, facilitating the elimination of defects. Locally oscillating
structures appear closer to the instability threshold with flow than without.Comment: 20 pages, Latex, accepted for Physical Review
Fracture in Mode I using a Conserved Phase-Field Model
We present a continuum phase-field model of crack propagation. It includes a
phase-field that is proportional to the mass density and a displacement field
that is governed by linear elastic theory. Generic macroscopic crack growth
laws emerge naturally from this model. In contrast to classical continuum
fracture mechanics simulations, our model avoids numerical front tracking. The
added phase-field smoothes the sharp interface, enabling us to use equations of
motion for the material (grounded in basic physical principles) rather than for
the interface (which often are deduced from complicated theories or empirical
observations). The interface dynamics thus emerges naturally. In this paper, we
look at stationary solutions of the model, mode I fracture, and also discuss
numerical issues. We find that the Griffith's threshold underestimates the
critical value at which our system fractures due to long wavelength modes
excited by the fracture process.Comment: 10 pages, 5 figures (eps). Added 2 figures and some text. Removed one
section (and a figure). To be published in PR
Water And Ice Nucleation Sites From Ion Implantation Of Silicon
Ion implantation has a substantial effect on the heterogeneous nucleation of water and ice. An enhancement of water nucleation and a suppression of ice nucleation occurred for samples of silicon implanted with ions of various species and dosage. These effects were noticeable only for samples implanted with ion doses approaching or exceeding the critical dose necessary to produce amorphous silicon. The behavior of the water droplet and ice crystal growth can be related to the amount of ion produced damage to the substrate surface. The nature of the damage can be controlled by variation of the incident ion species, dose, and energy and thus offers a means of quantifying the surface damage while studying its relationship to heterogeneous nucleation. © 1980 American Chemical Society
Extending the scope of microscopic solvability: Combination of the Kruskal-Segur method with Zauderer decomposition
Successful applications of the Kruskal-Segur approach to interfacial pattern
formation have remained limited due to the necessity of an integral formulation
of the problem. This excludes nonlinear bulk equations, rendering convection
intractable. Combining the method with Zauderer's asymptotic decomposition
scheme, we are able to strongly extend its scope of applicability and solve
selection problems based on free boundary formulations in terms of partial
differential equations alone. To demonstrate the technique, we give the first
analytic solution of the problem of velocity selection for dendritic growth in
a forced potential flow.Comment: Submitted to Europhys. Letters, No figures, 5 page
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