158 research outputs found
Igniting homogeneous nucleation
Transient homogeneous nucleation is studied in the limit of large critical
sizes. Starting from pure monomers, three eras of transient nucleation are
characterized in the classic Becker-D\"oring kinetic equations with two
different models of discrete diffusivity: the classic Turnbull-Fisher formula
and an expression describing thermally driven growth of the nucleus. The latter
diffusivity yields time lags for nucleation which are much closer to values
measured in experiments with disilicate glasses. After an initial stage in
which the number of monomers decreases, many clusters of small size are
produced and a continuous size distribution is created. During the second era,
nucleii are increasing steadily in size in such a way that their distribution
appears as a wave front advancing towards the critical size for steady
nucleation. The nucleation rate at critical size is negligible during this era.
After the wave front reaches critical size, it ignites the creation of
supercritical clusters at a rate that increases monotonically until its steady
value is reached. Analytical formulas for the transient nucleation rate and the
time lag are obtained that improve classical ones and compare very well with
direct numerical solutions.Comment: 32 pages, 6 figures, to appear in Phys. Rev.
Modulation of the nucleation rate pre-exponential in a low-temperature Ising system
A metastable lattice gas with nearest-neighbor interactions and
continuous-time dynamics is studied using a generalized Becker-Doring approach
in the multidimensional space of cluster configurations. The pre-exponential of
the metastable state lifetime (inverse of nucleation rate) is found to exhibit
distinct peaks at integer values of the inverse supersaturation. Peaks are
unobservable (infinitely narrow) in the strict limit T->0, but become
detectable and eventually dominate at higher temperatures.Comment: 4 pages, 2 Postscript figures, LaTeX, submitted to Phys. Rev. Lett.
Changes: updated references, re-written section around eqs.(5),(6), typos,
minor wording changes in conclusion and other parts of text (mostly in
response to referees' comments). Paper resubmitted to PR
Exhaustion of Nucleation in a Closed System
We determine the distribution of cluster sizes that emerges from an initial
phase of homogeneous aggregation with conserved total particle density. The
physical ingredients behind the predictions are essentially classical:
Super-critical nuclei are created at the Zeldovich rate, and before the
depletion of monomers is significant, the characteristic cluster size is so
large that the clusters undergo diffusion limited growth. Mathematically, the
distribution of cluster sizes satisfies an advection PDE in "size-space".
During this creation phase, clusters are nucleated and then grow to a size much
larger than the critical size, so nucleation of super-critical clusters at the
Zeldovich rate is represented by an effective boundary condition at zero size.
The advection PDE subject to the effective boundary condition constitutes a
"creation signaling problem" for the evolving distribution of cluster sizes
during the creation era.
Dominant balance arguments applied to the advection signaling problem show
that the characteristic time and cluster size of the creation era are
exponentially large in the initial free-energy barrier against nucleation, G_*.
Specifically, the characteristic time is proportional to exp(2 G_*/ 5 k_B T)
and the characteristic number of monomers in a cluster is proportional to
exp(3G_*/5 k_B T). The exponentially large characteristic time and cluster size
give a-posteriori validation of the mathematical signaling problem. In a short
note, Marchenko obtained these exponentials and the numerical pre-factors, 2/5
and 3/5. Our work adds the actual solution of the kinetic model implied by
these scalings, and the basis for connection to subsequent stages of the
aggregation process after the creation era.Comment: Greatly shortened paper. Section on growth model removed. Added a
section analyzing the error in the solution of the integral equation. Added
reference
Two-state theory of nonlinear Stochastic Resonance
An amenable, analytical two-state description of the nonlinear population
dynamics of a noisy bistable system driven by a rectangular subthreshold signal
is put forward. Explicit expressions for the driven population dynamics, the
correlation function (its coherent and incoherent part), the signal-to-noise
ratio (SNR) and the Stochastic Resonance (SR) gain are obtained. Within a
suitably chosen range of parameter values this reduced description yields
anomalous SR-gains exceeding unity and, simultaneously, gives rise to a
non-monotonic behavior of the SNR vs. the noise strength. The analytical
results agree well with those obtained from numerical solutions of the Langevin
equation.Comment: 4 pages, 1 figur
Quantification of Cell Movement Reveals Distinct Edge Motility Types During Cell Spreading
Actin-based motility is central to cellular processes such as migration, bacterial engulfment, and cancer metastasis, and requires precise spatial and temporal regulation of the cytoskeleton. We studied one such process, fibroblast spreading, which involves three temporal phases: early, middle, and late spreading, distinguished by differences in cell area growth. In these studies, aided by improved algorithms for analyzing edge movement, we observed that each phase was dominated by a single, kinematically and biochemically distinct cytoskeletal organization, or motility type. Specifically, early spreading was dominated by periodic blebbing; continuous protrusion occurred predominantly during middle spreading; and periodic contractions were prevalent in late spreading. Further characterization revealed that each motility type exhibited a distinct distribution of the actin-related protein VASP, while inhibition of actin polymerization by cytochalasin D treatment revealed different dependences on barbed-end polymerization. Through this detailed characterization and graded perturbation of the system, we observed that although each temporal phase of spreading was dominated by a single motility type, in general cells exhibited a variety of motility types in neighboring spatial domains of the plasma membrane edge. These observations support a model in which global signals bias local cytoskeletal biochemistry in favor of a particular motility type
Multi-step particle emission probabilities in superheavy nuclei at moderate excitation energies
The probabilities of -, -, and -evaporation channels in
excited superheavy nuclei were evaluated using the Monte Carlo method. The
calculations utilized microscopically determined nuclear level densities and
were compared with results obtained from the phenomenological Jackson formula.
Effective temperatures derived from the microscopic approach were incorporated
into the Jackson formula for different evaporation channels at low and moderate
excitation energies. Additionally, an analytical formula was introduced to
estimate the average kinetic energy of emitted particles in multi-step
processes.Comment: 10 pages, 3 figure
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