2,255 research outputs found
Nonlinear Two-Dimensional Green's Function in Smectics
The problem of the strain of smectics subjected to a force distributed over a
line in the basal plane has been solved
Melting of alloys along the inter-phase boundaries in eutectic and peritectic systems
We discuss a simple model of the melting kinetics along the solid-solid
interface in eutectic and peritectic systems. The process is controlled by the
diffusion inside the liquid phase and the existence of a triple junction is
crucial for the velocity selection problem. Using the lubrication approximation
for the diffusion field in the liquid phase we obtain scaling results for the
steady-state velocity of the moving pattern depending on the overheating above
the equilibrium temperature and on the material parameters of the system,
including the dependences on the angles at the triple junction
Comment on ``Solidification of a Supercooled Liquid in a Narrow Channel''
Comment on PRL v. 86, p. 5084 (2001) [cond-mat/0101016]. We point out that
the authors' simulations are consistent with the known theory of steady-state
solutions in this system
The influence of short range forces on melting along grain boundaries
We investigate a model which couples diffusional melting and nanoscale
structural forces via a combined nano-mesoscale description. Specifically, we
obtain analytic and numerical solutions for melting processes at grain
boundaries influenced by structural disjoining forces in the experimentally
relevant regime of small deviations from the melting temperature. Though
spatially limited to the close vicinity of the tip of the propagating melt
finger, the influence of the disjoining forces is remarkable and leads to a
strong modification of the penetration velocity. The problem is represented in
terms of a sharp interface model to capture the wide range of relevant length
scales, predicting the growth velocity and the length scale describing the
pattern, depending on temperature, grain boundary energy, strength and length
scale of the exponential decay of the disjoining potential. Close to
equilibrium the short-range effects near the triple junctions can be expressed
through a contact angle renormalisation in a mesoscale formulation. For higher
driving forces strong deviations are found, leading to a significantly higher
melting velocity than predicted from a purely mesoscopic description.Comment: 10 page
Elastic and plastic effects on heterogeneous nucleation and nanowire formation
We investigate theoretically the effects of elastic and plastic deformations
on heterogeneous nucleation and nanowire formation. In the first case, the
influence of the confinement of the critical nucleus between two parallel
misfitting substrates is investigated using scaling arguments. We present phase
diagrams giving the nature of the nucleation regime as a function of the
driving force and the degree of confinement. We complement this analytical
study by amplitude equations simulations. In the second case, the influence of
a screw dislocation inside a nanowire on the development of the morphological
surface stability of the wire, related to the Rayleigh-Plateau instability, is
examined. Here the screw dislocation provokes a torsion of the wire known as
Eshelby twist. Numerical calculations using the finite element method and the
amplitude equations are performed to support analytical investigations. It is
shown that the screw dislocation promotes the Rayleigh-Plateau instability.Comment: 16 page
Pattern formation during diffusion limited transformations in solids
We develop a description of diffusion limited growth in solid-solid
transformations, which are strongly influenced by elastic effects. Density
differences and structural transformations provoke stresses at interfaces,
which affect the phase equilibrium conditions. We formulate equations for the
interface kinetics similar to dendritic growth and study the growth of a stable
phase from a metastable solid in both a channel geometry and in free space. We
perform sharp interface calculations based on Green's function methods and
phase field simulations, supplemented by analytical investigations. For pure
dilatational transformations we find a single growing finger with symmetry
breaking at higher driving forces, whereas for shear transformations the
emergence of twin structures can be favorable. We predict the steady state
shapes and propagation velocities, which can be higher than in conventional
dendritic growth.Comment: submitted to Philosophical Magazin
Velocity selection problem for combined motion of melting and solidification fronts
We discuss a free boundary problem for two moving solid-liquid interfaces
that strongly interact via the diffusion field in the liquid layer between
them. This problem arises in the context of liquid film migration (LFM) during
the partial melting of solid alloys. In the LFM mechanism the system chooses a
more efficient kinetic path which is controlled by diffusion in the liquid
film, whereas the process with only one melting front would be controlled by
the very slow diffusion in the mother solid phase. The relatively weak
coherency strain energy is the effective driving force for LFM. As in the
classical dendritic growth problems, also in this case an exact family of
steady-state solutions with two parabolic fronts and an arbitrary velocity
exists if capillary effects are neglected. We develop a velocity selection
theory for this problem, including anisotropic surface tension effects. The
strong diffusion interaction and coherency strain effects in the solid near the
melting front lead to substantial changes compared to classical dendritic
growth.Comment: submitted to PR
Influence of Strain on the Kinetics of Phase Transitions in Solids
We consider a sharp interface kinetic model of phase transitions accompanied
by elastic strain, together with its phase-field realization. Quantitative
results for the steady-state growth of a new phase in a strip geometry are
obtained and different pattern formation processes in this system are
investigated
Writing for the Humanities and Arts
This Writing for the Humanities website includes the syllabus, schedule, assignments, and OER reading materials for the course. The syllabus covers a number of genres, and examines what it means to write for the humanities. This stretches beyond Art and Literature to cover History, Philosophy, Theater, Music, and Media Communications. The assignments are designed to help students in their future careers, especially if they aim to work in the Humanities, which include teaching, curating, counseling, technical writing and journalism. The assignments will teach students how to compose an effective resume and cover letter, how to create a focused report based on an interview, how to write an op-ed, how to write an informative review of an event, and how to write a compelling grant proposal. Students will also learn how to create an online portfolio, and how to share their ideas in multimedia presentations
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