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

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

Clustering and Sharing Incentives in BitTorrent Systems

Peer-to-peer protocols play an increasingly instrumental role in Internet content distribution. Consequently, it is important to gain a full understanding of how these protocols behave in practice and how their parameters impact overall performance. We present the first experimental investigation of the peer selection strategy of the popular BitTorrent protocol in an instrumented private torrent. By observing the decisions of more than 40 nodes, we validate three BitTorrent properties that, though widely believed to hold, have not been demonstrated experimentally. These include the clustering of similar-bandwidth peers, the effectiveness of BitTorrent's sharing incentives, and the peers' high average upload utilization. In addition, our results show that BitTorrent's new choking algorithm in seed state provides uniform service to all peers, and that an underprovisioned initial seed leads to the absence of peer clustering and less effective sharing incentives. Based on our observations, we provide guidelines for seed provisioning by content providers, and discuss a tracker protocol extension that addresses an identified limitation of the protocol

Crystallization of a supercooled liquid and of a glass - Ising model approach

Using Monte Carlo simulations we study crystallization in the three-dimensional Ising model with four-spin interaction. We monitor the morphology of crystals which grow after placing crystallization seeds in a supercooled liquid. Defects in such crystals constitute an intricate and very stable network which separate various domains by tensionless domain walls. We also show that the crystallization which occurs during the continuous heating of the glassy phase takes place at a heating-rate dependent temperature.Comment: 7 page

Statistics of transition times, phase diffusion and synchronization in periodically driven bistable systems

The statistics of transitions between the metastable states of a periodically driven bistable Brownian oscillator are investigated on the basis of a two-state description by means of a master equation with time-dependent rates. The results are compared with extensive numerical simulations of the Langevin equation for a sinusoidal driving force. Very good agreement is achieved both for the counting statistics of the number of transitions and the residence time distribution of the process in either state. The counting statistics corroborate in a consistent way the interpretation of stochastic resonance as a synchronisation phenomenon for a properly defined generalized Rice phase.Comment: 15 pages, 9 figure

Evaporation-Induced Self-Assembly of Metal Oxide Inverse Opals: From Synthesis to Applications

ConspectusInverse opals (IOs) are highly interconnected three-dimensional macroporous structures with applications in a variety of disciplines from optics to catalysis. For instance, when the pore size is on the scale of the wavelength of visible light, IOs exhibit structural color due to diffraction and interference of light rather than due to absorption by pigments, making these structures valuable as nonfading paints and colorants. When IO pores are in an ordered arrangement, the IO is a 3D photonic crystal, a structure with a plethora of interesting optical properties that can be used in a multitude of applications, from sensors to lasers. IOs also have interesting fluidic properties that arise from the re-entrant geometry of the pores, making them excellent candidates for colorimetric sensors based on fluid surface tension. Metal oxide IOs, in particular, can also be photo- and thermally catalytically active due to the catalytic activity of the background matrix material or of functional nanoparticles embedded within the structure.Evaporation-induced self-assembly of sacrificial particles has been developed as a scalable method for forming IOs. The pore size and shape, surface chemistry, matrix material, and the macroscopic shape of the IO, as well as the inclusion of functional components, can be designed through the choice of deposition conditions such as temperature and humidity, types and concentrations of components in the self-assembly mixture, and the postassembly processing. These parameters allow researchers to tune the optical, mechanical, and thermal transport properties of IOs for optimum functionality.In this Account, we focus on experimental and theoretical studies to understand the self-assembly process and properties of metal oxide IOs without (bare) and with (hybrid) plasmonic or catalytic metal nanoparticles incorporated. Several synthetic approaches are first presented, together with a discussion of the various forces involved in the assembly process. The visualization of the deposition front with time-lapse microscopy is then discussed together with analytical theory and numerical simulations to determine the conditions needed for the deposition of a continuous IO film. Subsequently, we present high-resolution scanning electron microscopy (SEM) of assembled colloids over large areas, which provides a detailed view of the evolution of the assembly process, showing that the organization of the colloids is initially dictated by the meniscus of the evaporating suspension on the substrate, but that gradually all grains rotate to occupy the thermodynamically most favorable orientation. High-resolution 3D transmission electron microscopy (TEM) is then presented together with analysis of the wetting of the templating colloids by the matrix precursor to provide a detailed picture of the embedding of metallic nanoparticles at the pore-matrix interface. Finally, the resulting properties and applications in optics, wetting, and catalysis are discussed, concluding with an outlook on the future of self-assembled metal-oxide-based IOs

Stochastic Hysteresis and Resonance in a Kinetic Ising System

We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on small systems and weak field amplitudes at a temperature below $T_{c}$. For these restricted parameters, the magnetization switches through random nucleation of a single droplet of spins aligned with the applied field. We analyze the stochastic hysteresis observed in this parameter regime, using time-dependent nucleation theory and the theory of variable-rate Markov processes. The theory enables us to accurately predict the results of extensive Monte Carlo simulations, without the use of any adjustable parameters. The stochastic response is qualitatively different from what is observed, either in mean-field models or in simulations of larger spatially extended systems. We consider the frequency dependence of the probability density for the hysteresis-loop area and show that its average slowly crosses over to a logarithmic decay with frequency and amplitude for asymptotically low frequencies. Both the average loop area and the residence-time distributions for the magnetization show evidence of stochastic resonance. We also demonstrate a connection between the residence-time distributions and the power spectral densities of the magnetization time series. In addition to their significance for the interpretation of recent experiments in condensed-matter physics, including studies of switching in ferromagnetic and ferroelectric nanoparticles and ultrathin films, our results are relevant to the general theory of periodically driven arrays of coupled, bistable systems with stochastic noise.Comment: 35 pages. Submitted to Phys. Rev. E Minor revisions to the text and updated reference