284 research outputs found
Non-equilibrium Phase-Ordering with a Global Conservation Law
In all dimensions, infinite-range Kawasaki spin exchange in a quenched Ising
model leads to an asymptotic length-scale
at because the kinetic coefficient is renormalized by the broken-bond
density, . For , activated kinetics recovers the
standard asymptotic growth-law, . However, at all temperatures,
infinite-range energy-transport is allowed by the spin-exchange dynamics. A
better implementation of global conservation, the microcanonical Creutz
algorithm, is well behaved and exhibits the standard non-conserved growth law,
, at all temperatures.Comment: 2 pages and 2 figures, uses epsf.st
Persistence in systems with algebraic interaction
Persistence in coarsening 1D spin systems with a power law interaction
is considered. Numerical studies indicate that for sufficiently
large values of the interaction exponent ( in our
simulations), persistence decays as an algebraic function of the length scale
, . The Persistence exponent is found to be
independent on the force exponent and close to its value for the
extremal () model, . For smaller
values of the force exponent (), finite size effects prevent the
system from reaching the asymptotic regime. Scaling arguments suggest that in
order to avoid significant boundary effects for small , the system size
should grow as .Comment: 4 pages 4 figure
Interaction of Ihh and BMP/Noggin Signaling during Cartilage Differentiation
AbstractBone morphogenetic proteins (BMPs) have been implicated in regulating multiple stages of bone development. Recently it has been shown that constitutive activation of theBMP receptor-IAblocks chondrocyte differentiation in a similar manner as misexpression ofIndian hedgehog.In this paper we analyze the role of BMPs as possible mediators of Indian hedgehog signaling and useNogginmisexpression to gain insight into additional roles of BMPs during cartilage differentiation. We show by comparative analysis ofBMPandIhhexpression domains that the borders ofIndian hedgehogexpression in the chondrocytes are reflected in changes of the expression level of severalBMPgenes in the adjacent perichondrium. We further demonstrate that misexpression ofIndian hedgehogappears to directly upregulateBMP2andBMP4expression, independent of the differentiation state of the flanking chondrocytes. In contrast, changes inBMP5andBMP7expression in the perichondrium correspond to altered differentiation states of the flanking chondrocytes. In addition,NogginandChordin,which are both expressed in the developing cartilage elements, also change their expression pattern afterIhhmisexpression. Finally, we use retroviral misexpression ofNoggin,a potent antagonist of BMP signaling, to gain insight into additional roles of BMP signaling during cartilage differentiation. We find that BMP signaling is necessary for the growth and differentiation of the cartilage elements. In addition, this analysis revealed that the members of the BMP/Noggin signaling pathway are linked in a complex autoregulatory network
Fast and Accurate Coarsening Simulation with an Unconditionally Stable Time Step
We present Cahn-Hilliard and Allen-Cahn numerical integration algorithms that
are unconditionally stable and so provide significantly faster
accuracy-controlled simulation. Our stability analysis is based on Eyre's
theorem and unconditional von Neumann stability analysis, both of which we
present. Numerical tests confirm the accuracy of the von Neumann approach,
which is straightforward and should be widely applicable in phase-field
modeling. We show that accuracy can be controlled with an unbounded time step
Delta-t that grows with time t as Delta-t ~ t^alpha. We develop a
classification scheme for the step exponent alpha and demonstrate that a class
of simple linear algorithms gives alpha=1/3. For this class the speed up
relative to a fixed time step grows with the linear size of the system as N/log
N, and we estimate conservatively that an 8192^2 lattice can be integrated 300
times faster than with the Euler method.Comment: 14 pages, 6 figure
Dynamical Scaling: the Two-Dimensional XY Model Following a Quench
To sensitively test scaling in the 2D XY model quenched from
high-temperatures into the ordered phase, we study the difference between
measured correlations and the (scaling) results of a Gaussian-closure
approximation. We also directly compare various length-scales. All of our
results are consistent with dynamical scaling and an asymptotic growth law , though with a time-scale that depends on the
length-scale in question. We then reconstruct correlations from the
minimal-energy configuration consistent with the vortex positions, and find
them significantly different from the ``natural'' correlations --- though both
scale with . This indicates that both topological (vortex) and
non-topological (``spin-wave'') contributions to correlations are relevant
arbitrarily late after the quench. We also present a consistent definition of
dynamical scaling applicable more generally, and emphasize how to generalize
our approach to other quenched systems where dynamical scaling is in question.
Our approach directly applies to planar liquid-crystal systems.Comment: 10 pages, 10 figure
Determination of the Critical Point and Exponents from short-time Dynamics
The dynamic process for the two dimensional three state Potts model in the
critical domain is simulated by the Monte Carlo method. It is shown that the
critical point can rigorously be located from the universal short-time
behaviour. This makes it possible to investigate critical dynamics
independently of the equilibrium state. From the power law behaviour of the
magnetization the exponents and are determined.Comment: 6 pages, 4 figure
Local scale invariance as dynamical space-time symmetry in phase-ordering kinetics
The scaling of the spatio-temporal response of coarsening systems is studied
through simulations of the 2D and 3D Ising model with Glauber dynamics. The
scaling functions agree with the prediction of local scale invariance,
extending dynamical scaling to a space-time dynamical symmetry.Comment: Latex, 4 pages, 4 figure
Comment on ``Phase ordering in chaotic map lattices with conserved dynamics''
Angelini, Pellicoro, and Stramaglia [Phys. Rev. E {\bf 60}, R5021 (1999),
cond-mat/9907149] (APS) claim that the phase ordering of two-dimensional
systems of sequentially-updated chaotic maps with conserved ``order parameter''
does not belong, for large regions of parameter space, to the expected
universality class. We show here that these results are due to a slow crossover
and that a careful treatment of the data yields normal dynamical scaling.
Moreover, we construct better models, i.e. synchronously-updated coupled map
lattices, which are exempt from these crossover effects, and allow for the
first precise estimates of persistence exponents in this case.Comment: 3 pages, to be published in Phys. Rev.
Monte Carlo Simulation of the Short-time Behaviour of the Dynamic XY Model
Dynamic relaxation of the XY model quenched from a high temperature state to
the critical temperature or below is investigated with Monte Carlo methods.
When a non-zero initial magnetization is given, in the short-time regime of the
dynamic evolution the critical initial increase of the magnetization is
observed. The dynamic exponent is directly determined. The results
show that the exponent varies with respect to the temperature.
Furthermore, it is demonstrated that this initial increase of the magnetization
is universal, i.e. independent of the microscopic details of the initial
configurations and the algorithms.Comment: 14 pages with 5 figures in postscrip
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