4,956 research outputs found
Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude equation analysis of the phase field crystal model
Morphological properties of strained epitaxial films are examined through a
mesoscopic approach developed to incorporate both the film crystalline
structure and standard continuum theory. Film surface profiles and properties,
such as surface energy, liquid-solid miscibility gap and interface thickness,
are determined as a function of misfit strains and film elastic modulus. We
analyze the stress-driven instability of film surface morphology that leads to
the formation of strained islands. We find a universal scaling relationship
between the island size and misfit strain which shows a crossover from the
well-known continuum elasticity result at the weak strain to a behavior
governed by a "perfect" lattice relaxation condition. The strain at which the
crossover occurs is shown to be a function of liquid-solid interfacial
thickness, and an asymmetry between tensile and compressive strains is
observed. The film instability is found to be accompanied by mode coupling of
the complex amplitudes of the surface morphological profile, a factor
associated with the crystalline nature of the strained film but absent in
conventional continuum theory.Comment: 16 pages, 10 figures; to be published in Phys. Rev.
Phase field crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures
The dynamics of phase field crystal (PFC) modeling is derived from dynamical
density functional theory (DDFT), for both single-component and binary systems.
The derivation is based on a truncation up to the three-point direct
correlation functions in DDFT, and the lowest order approximation using scale
analysis. The complete amplitude equation formalism for binary PFC is developed
to describe the coupled dynamics of slowly varying complex amplitudes of
structural profile, zeroth-mode average atomic density, and system
concentration field. Effects of noise (corresponding to stochastic amplitude
equations) and species-dependent atomic mobilities are also incorporated in
this formalism. Results of a sample application to the study of surface
segregation and interface intermixing in alloy heterostructures and strained
layer growth are presented, showing the effects of different atomic sizes and
mobilities of alloy components. A phenomenon of composition overshooting at the
interface is found, which can be connected to the surface segregation and
enrichment of one of the atomic components observed in recent experiments of
alloying heterostructures.Comment: 26 pages, 5 figures; submitted to Phys. Rev.
Diffusive Atomistic Dynamics of Edge Dislocations in Two Dimensions
The fundamental dislocation processes of glide, climb, and annihilation are
studied on diffusive time scales within the framework of a continuum field
theory, the Phase Field Crystals (PFC) model. Glide and climb are examined for
single edge dislocations subjected to shear and compressive strain,
respectively, in a two dimensional hexagonal lattice. It is shown that the
natural features of these processes are reproduced without any explicit
consideration of elasticity theory or ad hoc construction of microscopic
Peierls potentials. Particular attention is paid to the Peierls barrier for
dislocation glide/climb and the ensuing dynamic behavior as functions of strain
rate, temperature, and dislocation density. It is shown that the dynamics are
accurately described by simple viscous motion equations for an overdamped point
mass, where the dislocation mobility is the only adjustable parameter. The
critical distance for the annihilation of two edge dislocations as a function
of separation angle is also presented.Comment: 13 pages with 17 figures, submitted to Physical Review
Dynamic scaling and quasi-ordered states in the two dimensional Swift-Hohenberg equation
The process of pattern formation in the two dimensional Swift-Hohenberg
equation is examined through numerical and analytic methods. Dynamic scaling
relationships are developed for the collective ordering of convective rolls in
the limit of infinite aspect ratio. The stationary solutions are shown to be
strongly influenced by the strength of noise. Stationary states for small and
large noise strengths appear to be quasi-ordered and disordered respectively.
The dynamics of ordering from an initially inhomogeneous state is very slow in
the former case and fast in the latter. Both numerical and analytic
calculations indicate that the slow dynamics can be characterized by a simple
scaling relationship, with a characteristic dynamic exponent of in the
intermediate time regime
Ordering kinetics of stripe patterns
We study domain coarsening of two dimensional stripe patterns by numerically
solving the Swift-Hohenberg model of Rayleigh-Benard convection. Near the
bifurcation threshold, the evolution of disordered configurations is dominated
by grain boundary motion through a background of largely immobile curved
stripes. A numerical study of the distribution of local stripe curvatures, of
the structure factor of the order parameter, and a finite size scaling analysis
of the grain boundary perimeter, suggest that the linear scale of the structure
grows as a power law of time with a craracteristic exponent z=3. We interpret
theoretically the exponent z=3 from the law of grain boundary motion.Comment: 4 pages, 4 figure
Abundant and equipotent founder cells establish and maintain acute lymphoblastic leukaemia
High frequencies of blasts in primary acute lymphoblastic leukaemia (ALL) samples have the potential to induce leukaemia and to engraft mice. However, it is unclear how individual ALL cells each contribute to drive leukaemic development in a bulk transplant and the extent to which these blasts vary functionally. We used cellular barcoding as a fate mapping tool to track primograft ALL blasts in vivo. Our results show that high numbers of ALL founder cells contribute at similar frequencies to leukaemic propagation over serial transplants, without any clear evidence of clonal succession. These founder cells also exhibit equal capacity to home and engraft to different organs, although stochastic processes may alter the composition in restrictive niches. Our findings enhance the stochastic stem cell model of ALL by demonstrating equal functional abilities of singular ALL blasts and show that successful treatment strategies must eradicate the entire leukaemic cell population
Dynamical transitions and sliding friction of the phase-field-crystal model with pinning
We study the nonlinear driven response and sliding friction behavior of the
phase-field-crystal (PFC) model with pinning including both thermal
fluctuations and inertial effects. The model provides a continuous description
of adsorbed layers on a substrate under the action of an external driving force
at finite temperatures, allowing for both elastic and plastic deformations. We
derive general stochastic dynamical equations for the particle and momentum
densities including both thermal fluctuations and inertial effects. The
resulting coupled equations for the PFC model are studied numerically. At
sufficiently low temperatures we find that the velocity response of an
initially pinned commensurate layer shows hysteresis with dynamical melting and
freezing transitions for increasing and decreasing applied forces at different
critical values. The main features of the nonlinear response in the PFC model
are similar to the results obtained previously with molecular dynamics
simulations of particle models for adsorbed layers.Comment: 7 pages, 8 figures, to appear in Physcial Review
Glassy phases and driven response of the phase-field-crystal model with random pinning
We study the structural correlations and the nonlinear response to a driving
force of a two-dimensional phase-field-crystal model with random pinning. The
model provides an effective continuous description of lattice systems in the
presence of disordered external pinning centers, allowing for both elastic and
plastic deformations. We find that the phase-field crystal with disorder
assumes an amorphous glassy ground state, with only short-ranged positional and
orientational correlations even in the limit of weak disorder. Under increasing
driving force, the pinned amorphous-glass phase evolves into a moving
plastic-flow phase and then finally a moving smectic phase. The transverse
response of the moving smectic phase shows a vanishing transverse critical
force for increasing system sizes
Grain boundary motion in layered phases
We study the motion of a grain boundary that separates two sets of mutually
perpendicular rolls in Rayleigh-B\'enard convection above onset. The problem is
treated either analytically from the corresponding amplitude equations, or
numerically by solving the Swift-Hohenberg equation. We find that if the rolls
are curved by a slow transversal modulation, a net translation of the boundary
follows. We show analytically that although this motion is a nonlinear effect,
it occurs in a time scale much shorter than that of the linear relaxation of
the curved rolls. The total distance traveled by the boundary scales as
, where is the reduced Rayleigh number. We obtain
analytical expressions for the relaxation rate of the modulation and for the
time dependent traveling velocity of the boundary, and especially their
dependence on wavenumber. The results agree well with direct numerical
solutions of the Swift-Hohenberg equation. We finally discuss the implications
of our results on the coarsening rate of an ensemble of differently oriented
domains in which grain boundary motion through curved rolls is the dominant
coarsening mechanism.Comment: 16 pages, 5 figure
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