Kinetics and Mechanism of Metal Nanoparticle Growth via Optical Extinction Spectroscopy and Computational Modeling: The Curious Case of Colloidal Gold

An overarching computational framework unifying several optical theories to describe the temporal evolution of gold nanoparticles (GNPs) during a seeded growth process is presented. To achieve this, we used the inexpensive and widely available optical extinction spectroscopy, to obtain quantitative kinetic data. In situ spectra collected over a wide set of experimental conditions were regressed using the physical model, calculating light extinction by ensembles of GNPs during the growth process. This model provides temporal information on the size, shape, and concentration of the particles and any electromagnetic interactions between them. Consequently, we were able to describe the mechanism of GNP growth and divide the process into distinct genesis periods. We provide explanations for several longstanding mysteries, for example, the phenomena responsible for the purple-greyish hue during the early stages of GNP growth, the complex interactions between nucleation, growth, and aggregation events, and a clear distinction between agglomeration and electromagnetic interactions. The presented theoretical formalism has been developed in a generic fashion so that it can readily be adapted to other nanoparticulate formation scenarios such as the genesis of various metal nanoparticles.Comment: Main text and supplementary information (accompanying MATLAB codes available on the journal webpage

The noisy edge of traveling waves

Traveling waves are ubiquitous in nature and control the speed of many important dynamical processes, including chemical reactions, epidemic outbreaks, and biological evolution. Despite their fundamental role in complex systems, traveling waves remain elusive because they are often dominated by rare fluctuations in the wave tip, which have defied any rigorous analysis so far. Here, we show that by adjusting nonlinear model details, noisy traveling waves can be solved exactly. The moment equations of these tuned models are closed and have a simple analytical structure resembling the deterministic approximation supplemented by a nonlocal cutoff term. The peculiar form of the cutoff shapes the noisy edge of traveling waves and is critical for the correct prediction of the wave speed and its fluctuations. Our approach is illustrated and benchmarked using the example of fitness waves arising in simple models of microbial evolution, which are highly sensitive to number fluctuations. We demonstrate explicitly how these models can be tuned to account for finite population sizes and determine how quickly populations adapt as a function of population size and mutation rates. More generally, our method is shown to apply to a broad class of models, in which number fluctuations are generated by branching processes. Because of this versatility, the method of model tuning may serve as a promising route toward unraveling universal properties of complex discrete particle systems.Comment: For supplementary material and published open access article, see http://www.pnas.org/content/108/5/1783.abstract?sid=693e63f3-fd1a-407a-983e-c521efc6c8c5 See also Commentary Article by D. S. Fisher, http://www.pnas.org/content/108/7/2633.extrac

The Blind Watchmaker Network: Scale-freeness and Evolution

It is suggested that the degree distribution for networks of the cell-metabolism for simple organisms reflects an ubiquitous randomness. This implies that natural selection has exerted no or very little pressure on the network degree distribution during evolution. The corresponding random network, here termed the blind watchmaker network has a power-law degree distribution with an exponent gamma >= 2. It is random with respect to a complete set of network states characterized by a description of which links are attached to a node as well as a time-ordering of these links. No a priory assumption of any growth mechanism or evolution process is made. It is found that the degree distribution of the blind watchmaker network agrees very precisely with that of the metabolic networks. This implies that the evolutionary pathway of the cell-metabolism, when projected onto a metabolic network representation, has remained statistically random with respect to a complete set of network states. This suggests that even a biological system, which due to natural selection has developed an enormous specificity like the cellular metabolism, nevertheless can, at the same time, display well defined characteristics emanating from the ubiquitous inherent random element of Darwinian evolution. The fact that also completely random networks may have scale-free node distributions gives a new perspective on the origin of scale-free networks in general.Comment: 5 pages, 3 figure

Distributed Evaluation and Convergence of Self-Appraisals in Social Networks

We consider in this paper a networked system of opinion dynamics in continuous time, where the agents are able to evaluate their self-appraisals in a distributed way. In the model we formulate, the underlying network topology is described by a rooted digraph. For each ordered pair of agents $(i,j)$, we assign a function of self-appraisal to agent $i$, which measures the level of importance of agent $i$ to agent $j$. Thus, by communicating only with her neighbors, each agent is able to calculate the difference between her level of importance to others and others' level of importance to her. The dynamical system of self-appraisals is then designed to drive these differences to zero. We show that for almost all initial conditions, the trajectory generated by this dynamical system asymptotically converges to an equilibrium point which is exponentially stable

Collapse and Fragmentation of Magnetized Cylindrical Clouds

Gravitational collapse of the cylindrical elongated cloud is studied by numerical magnetohydrodynamical simulations. In the infinitely long cloud in hydrostatic configuration, small perturbations grow by the gravitational instability. The most unstable mode indicated by a linear perturbation theory grows selectively even from a white noise. The growth rate agrees with that calculated by the linear theory. First, the density-enhanced region has an elongated shape, i.e., prolate spheroidal shape. As the collapse proceeds, the high-density fragment begins to contract mainly along the symmetry axis. Finally, a spherical core is formed in the non-magnetized cloud. In contrast, an oblate spheroidal dense disk is formed in a cloud in which the magnetic pressure is nearly equal to the thermal one. The radial size of the disk becomes proportional to the initial characteristic density scale-height in the r-direction. As the collapse proceeds, a slowly contracting dense part is formed (approximately < 10% in mass) inside of the fast contracting disk. And this is separated from other part of the disk whose inflow velocity is accelerated as reaching the center of the core. From arguments on the Jeans mass and the magnetic critical mass, it is concluded that the fragments formed in a cylindrical elongated cloud can not be supported against the self- gravity and it will eventually collapse.Comment: 20 pages, figures available upon request, LaTeX, NIGAST040

Analyzing large-scale conservation interventions with Bayesian hierarchical models: a case study of supplementing threatened Pacific salmon.

Myriad human activities increasingly threaten the existence of many species. A variety of conservation interventions such as habitat restoration, protected areas, and captive breeding have been used to prevent extinctions. Evaluating the effectiveness of these interventions requires appropriate statistical methods, given the quantity and quality of available data. Historically, analysis of variance has been used with some form of predetermined before-after control-impact design to estimate the effects of large-scale experiments or conservation interventions. However, ad hoc retrospective study designs or the presence of random effects at multiple scales may preclude the use of these tools. We evaluated the effects of a large-scale supplementation program on the density of adult Chinook salmon Oncorhynchus tshawytscha from the Snake River basin in the northwestern United States currently listed under the U.S. Endangered Species Act. We analyzed 43 years of data from 22 populations, accounting for random effects across time and space using a form of Bayesian hierarchical time-series model common in analyses of financial markets. We found that varying degrees of supplementation over a period of 25 years increased the density of natural-origin adults, on average, by 0-8% relative to nonsupplementation years. Thirty-nine of the 43 year effects were at least two times larger in magnitude than the mean supplementation effect, suggesting common environmental variables play a more important role in driving interannual variability in adult density. Additional residual variation in density varied considerably across the region, but there was no systematic difference between supplemented and reference populations. Our results demonstrate the power of hierarchical Bayesian models to detect the diffuse effects of management interventions and to quantitatively describe the variability of intervention success. Nevertheless, our study could not address whether ecological factors (e.g., competition) were more important than genetic considerations (e.g., inbreeding depression) in determining the response to supplementation