455 research outputs found
Scaling properties of critical bubble of homogeneous nucleation in stretched fluid of square-gradient density-functional model with triple-parabolic free energy
The square-gradient density-functional model with triple-parabolic free
energy is used to study homogeneous bubble nucleation in a stretched liquid to
check the scaling rule for the work of formation of the critical bubble as a
function of scaled undersaturation , the
difference in chemical potential between the bulk undersaturated
and saturated liquid divided by between the liquid
spinodal and saturated liquid. In contrast to our study, a similar
density-functional study for a Lennard-Jones liquid by Shen and Debenedetti [J.
Chem. Phys. {\bf 114}, 4149 (2001)] found that not only the work of formation
but other various quantities related to the critical bubble show the scaling
rule, however, we found virtually no scaling relationships in our model near
the coexistence. Although some quantities show almost perfect scaling relations
near the spinodal, the work of formation divided by the value deduced from the
classical nucleation theory shows no scaling in this model even though it
correctly vanishes at the spinodal. Furthermore, the critical bubble does not
show any anomaly near the spinodal as predicted many years ago. In particular,
our model does not show diverging interfacial width at the spinodal, which is
due to the fact that compressibility remains finite until the spinodal is
reached in our parabolic models.Comment: 10 pages, 10 figures, Journal of Chemical Physics accepted for
publicatio
Direct numerical simulation of homogeneous nucleation and growth in a phase-field model using cell dynamics method
Homogeneous nucleation and growth in a simplest two-dimensional phase field
model is numerically studied using the cell dynamics method. Whole process from
nucleation to growth is simulated and is shown to follow closely the
Kolmogorov-Johnson-Mehl-Avrami (KJMA) scenario of phase transformation.
Specifically the time evolution of the volume fraction of new stable phase is
found to follow closely the KJMA formula. By fitting the KJMA formula directly
to the simulation data, not only the Avrami exponent but the magnitude of
nucleation rate and, in particular, of incubation time are quantitatively
studied. The modified Avrami plot is also used to verify the derived KJMA
parameters. It is found that the Avrami exponent is close to the ideal
theoretical value m=3. The temperature dependence of nucleation rate follows
the activation-type behavior expected from the classical nucleation theory. On
the other hand, the temperature dependence of incubation time does not follow
the exponential activation-type behavior. Rather the incubation time is
inversely proportional to the temperature predicted from the theory of
Shneidman and Weinberg [J. Non-Cryst. Solids {\bf 160}, 89 (1993)]. A need to
restrict thermal noise in simulation to deduce correct Avrami exponent is also
discussed.Comment: 9 pages, 8 figures, Journal of Chemical Physics to be publishe
A diffusion-induced transition in the phase separation of binary fluid mixtures subjected to a temperature ramp
Demixing of binary fluids subjected to slow temperature ramps shows repeated
waves of nucleation which arise as a consequence of the competition between
generation of supersaturation by the temperature ramp and relaxation of
supersaturation by diffusive transport and flow. Here, we use an
advection-reaction-diffusion model to study the oscillations in the weak- and
strong-diffusion regime. There is a sharp transition between the two regimes,
which can only be understood based on the probability distribution function of
the composition rather than in terms of the average composition. We argue that
this transition might be responsible for some yet unclear features of
experiments, like the appearance of secondary oscillations and bimodal droplet
size distributions.Comment: 6 pages, 3 color figure
Event-Based Modeling with High-Dimensional Imaging Biomarkers for Estimating Spatial Progression of Dementia
Event-based models (EBM) are a class of disease progression models that can
be used to estimate temporal ordering of neuropathological changes from
cross-sectional data. Current EBMs only handle scalar biomarkers, such as
regional volumes, as inputs. However, regional aggregates are a crude summary
of the underlying high-resolution images, potentially limiting the accuracy of
EBM. Therefore, we propose a novel method that exploits high-dimensional
voxel-wise imaging biomarkers: n-dimensional discriminative EBM (nDEBM). nDEBM
is based on an insight that mixture modeling, which is a key element of
conventional EBMs, can be replaced by a more scalable semi-supervised support
vector machine (SVM) approach. This SVM is used to estimate the degree of
abnormality of each region which is then used to obtain subject-specific
disease progression patterns. These patterns are in turn used for estimating
the mean ordering by fitting a generalized Mallows model. In order to validate
the biomarker ordering obtained using nDEBM, we also present a framework for
Simulation of Imaging Biomarkers' Temporal Evolution (SImBioTE) that mimics
neurodegeneration in brain regions. SImBioTE trains variational auto-encoders
(VAE) in different brain regions independently to simulate images at varying
stages of disease progression. We also validate nDEBM clinically using data
from the Alzheimer's Disease Neuroimaging Initiative (ADNI). In both
experiments, nDEBM using high-dimensional features gave better performance than
state-of-the-art EBM methods using regional volume biomarkers. This suggests
that nDEBM is a promising approach for disease progression modeling.Comment: IPMI 201
Conductance Fluctuations of Generic Billiards: Fractal or Isolated?
We study the signatures of a classical mixed phase space for open quantum
systems. We find the scaling of the break time up to which quantum mechanics
mimics the classical staying probability and derive the distribution of
resonance widths. Based on these results we explain why for mixed systems two
types of conductance fluctuat ions were found: quantum mechanics divides the
hierarchically structured chaotic component of phase space into two parts - one
yields fractal conductance fluctuations while the other causes isolated
resonances. In general, both types appear together, but on different energy
scales.Comment: restructured and new figure
Turbulence-induced melting of a nonequilibrium vortex crystal in a forced thin fluid film
To develop an understanding of recent experiments on the turbulence-induced
melting of a periodic array of vortices in a thin fluid film, we perform a
direct numerical simulation of the two-dimensional Navier-Stokes equations
forced such that, at low Reynolds numbers, the steady state of the film is a
square lattice of vortices. We find that, as we increase the Reynolds number,
this lattice undergoes a series of nonequilibrium phase transitions, first to a
crystal with a different reciprocal lattice and then to a sequence of crystals
that oscillate in time. Initially the temporal oscillations are periodic; this
periodic behaviour becomes more and more complicated, with increasing Reynolds
number, until the film enters a spatially disordered nonequilibrium statistical
steady that is turbulent. We study this sequence of transitions by using
fluid-dynamics measures, such as the Okubo-Weiss parameter that distinguishes
between vortical and extensional regions in the flow, ideas from nonlinear
dynamics, e.g., \Poincare maps, and theoretical methods that have been
developed to study the melting of an equilibrium crystal or the freezing of a
liquid and which lead to a natural set of order parameters for the crystalline
phases and spatial autocorrelation functions that characterise short- and
long-range order in the turbulent and crystalline phases, respectively.Comment: 31 pages, 56 figures, movie files not include
Scanning Quantum Decoherence Microscopy
The use of qubits as sensitive magnetometers has been studied theoretically
and recent demonstrated experimentally. In this paper we propose a
generalisation of this concept, where a scanning two-state quantum system is
used to probe the subtle effects of decoherence (as well as its surrounding
electromagnetic environment). Mapping both the Hamiltonian and decoherence
properties of a qubit simultaneously, provides a unique image of the magnetic
(or electric) field properties at the nanoscale. The resulting images are
sensitive to the temporal as well as spatial variation in the fields created by
the sample. As an example we theoretically study two applications of this
technology; one from condensed matter physics, the other biophysics. The
individual components required to realise the simplest version of this device
(characterisation and measurement of qubits, nanoscale positioning) have
already been demonstrated experimentally.Comment: 11 pages, 5 low quality (but arXiv friendly) image
The density functional theory of classical fluids revisited
We reconsider the density functional theory of nonuniform classical fluids
from the point of view of convex analysis. From the observation that the
logarithm of the grand-partition function is a convex
functional of the external potential it is shown that the Kohn-Sham free
energy is a convex functional of the density . and constitute a pair of Legendre transforms and each
of these functionals can therefore be obtained as the solution of a variational
principle. The convexity ensures the unicity of the solution in both cases. The
variational principle which gives as the maximum of a
functional of is precisely that considered in the density functional
theory while the dual principle, which gives as the maximum of
a functional of seems to be a new result.Comment: 10 page
Microcanonical Determination of the Interface Tension of Flat and Curved Interfaces from Monte Carlo Simulations
The investigation of phase coexistence in systems with multi-component order
parameters in finite systems is discussed, and as a generic example, Monte
Carlo simulations of the two-dimensional q-state Potts model (q=30) on LxL
square lattices (40<=L<=100) are presented. It is shown that the microcanonical
ensemble is well-suited both to find the precise location of the first order
phase transition and to obtain an accurate estimate for the interfacial free
energy between coexisting ordered and disordered phases. For this purpose, a
microcanonical version of the heatbath algorithm is implemented. The finite
size behaviour of the loop in the curve describing the inverse temperature
versus energy density is discussed, emphasizing that the extrema do not have
the meaning of van der Waals-like "spinodal points" separating metastable from
unstable states, but rather describe the onset of heterophase states:
droplet/bubble evaporation/condensation transitions. Thus all parts of these
loops, including the parts that correspond to a negative specific heat,
describe phase coexistence in full thermal equilibrium. However, the estimates
for the curvature-dependent interface tension of the droplets and bubbles
suffer from unexpected and unexplained large finite size effects which need
further study.Comment: submitted to special issue "Liquid Matter" of Journal of Physics C:
Condensed Matter on occasion of the 8th Liquid Matter Conference held Sept.
6-10, 2011 in Vienna, Austri
Scaling analysis of a divergent prefactor in the metastable lifetime of a square-lattice Ising ferromagnet at low temperatures
We examine a square-lattice nearest-neighbor Ising quantum ferromagnet
coupled to -dimensional phonon baths. Using the density-matrix equation, we
calculate the transition rates between configurations, which determines the
specific dynamic. Applying the calculated stochastic dynamic in Monte Carlo
simulations, we measure the lifetimes of the metastable state. As the magnetic
field approaches at low temperatures, the lifetime prefactor diverges
because the transition rates between certain configurations approaches zero
under these conditions. Near and zero temperature, the divergent
prefactor shows scaling behavior as a function of the field, temperature, and
the dimension of the phonon baths. With proper scaling, the simulation data at
different temperatures and for different dimensions of the baths collapse well
onto two master curves, one for and one for .Comment: published versio
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