Spatial maps of polymer density.

<p>Each column of images corresponds to simulations run with a different value for monomer diffusivity (in sites/cycle), and each row has a different value for polymer diffusivity (in sites/cycle). All data shown are for kinetic rate constants , , and . All maps correspond to cycles. The color scale is in units of polymers/site. Simulations were only run for cases in which monomer diffusivity is greater than or equal to the polymer diffusivity.</p

Exploring kinetic parameter space.

<p>Plots of quasi steady-state values of Average Species Lifetime (in units of number of cycles), Average Species Population, Extant Species, Total Population Size, Sequence Exploration Rate (in units of number of novel sequences generated per cycle), and Average Local Diversity. Time averages were taken from cycles, and each point is the ensemble average over five realizations. Error bars denote the sample standard deviation (most are smaller than symbols). The rate constant for spontaneous sequence nucleation is , and the diffusion rate constants are sites/cycle and sites/cycle. The blue data set shows the reference case with , where no polymers replicate.</p

Spatial distribution maps for no functional species, one functional species, and two functional species.

<p>The three scenarios shown are all identical up to cycles, at which time the system has achieved a quasi-steady state distribution. In the first scenario, no functional sequences appear. In the second scenario, a functional zyme appears at  = 2500. In the third scenario, the same functional zyme appears at  = 2500, and a functional zyme also appears at  = 4000. A: Time evolution of the Species Populations of the zyme and zyme. The units of time are in number of cycles. The red curve corresponds to the second scenario, having only the zyme, while the black and blue curves correspond to the third scenario with both enzymes emerging. B: The time evolution of the Total Polymer Population for the three scenarios. C: The spatial distribution of the polymer (total) and monomer concentrations, at  = 5000 cycles. White arrow indicates contour containing % of zyme polymers, cyan arrow indicates contour containing 95% of zyme polymers. Kinetic rate constants are , , and , and diffusive rate constants are and sites/cycle.</p

Sequence evolution of the polymer pool.

<p>A: Time evolution of the populations of seven specific sequences; B: Time evolution of the total polymer population; C: Spatial snapshots of the total polymer and monomer concentrations at four representative times. Species ID indicates the order of appearance of the first individual of a particular sequence in the polymer pool. The kinetic rate constants are , , and , and polymer and monomer diffusivities are set as and sites/cycle, respectively. Units of time are in number of cycles.</p

Selection for functional sequences.

<p>Plots illustrating the propagation of a functional zyme, compared to nonfunctional sequences. A: Average Species Lifetime (in units of number of cycles), and B: Average Population Size. Each data point is the ensemble average over twenty-five runs, with error bars denoting the sample standard deviation. Kinetic rate constants are , , and , with a polymer diffusion rate constant of sites/cycle. The green points represent overall population statistics for realizations with no zyme (plotted in green in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0034166#pone-0034166-g004" target="_blank">Figure 4</a>). The black points represent statistics for a single functional zyme. The blue points represent statistics for a nonfunctional sequence introduced at the same location and cycle as in the zyme simulations, except with no functionality.</p

Exploring diffusive parameter space.

<p>Plots of quasi steady-state values of Average Species Lifetime (in units of number of cycles), Average Species Population, Extant Species, Total Population Size, Sequence Exploration Rate (in units of number of novel sequences generated per cycle), and Average Local Diversity. Time averages were taken from cycles, and each point is the ensemble average over ten realizations. Error bars denote the sample standard deviation (most are smaller than symbols). The kinetic rate constants are , , and . The blue data set shows the case where the , where polymers are completely immobile.</p

Automated Analysis of Orientational Order in Images of Fibrillar Materials

Nanofibers are a ubiquitous structural motif in a variety of functional materials. In the field of organic electronics, π–π-stacking of conjugated polymers leads to fibrillar morphologies with a wide array of fiber packing behavior. Fiber orientation and alignment are known to influence the charge transport properties of devices such as organic field effect transistors. The solution processing methods used to create these devices give rise to large variations in these structural parametershowever, they are only observable with imaging techniques such as atomic force microscopy (AFM). To bring more rigorous quantification of orientation and alignment to these materials, a comprehensive image analysis tool is introduced to quantify the two-dimensional orientation and alignment of nanofibers from AFM images. It has been developed in MATLAB and packaged as a stand-alone application, so that researchers with no computational expertise can produce publication-ready figures directly from their images. AFM frequently yields images with low contrast and moderate noise, making quantitative feature extraction a significant challenge. In this protocol, each image is analyzed in the context of an Orientation Map, in which nanofibers are thinned to single-pixel width and an orientation is extracted for each of these pixels. The Orientation Map is obtained through a five-step process: fiber smoothing by anisotropic diffusion filtering, contrast enhancement by top hat filtering, binarization by adaptive thresholding, skeletonization, and recovery of orientations from the result of diffusion filtering. Each step involves parameters that can be set using physical heuristics, which are examined in detail. This Orientation Map yields an orientation distribution and a plot of <i>S</i>_2D, an orientational order parameter, as a function of frame size. The image analysis procedure is used to quantify differences in P3HT nanofiber morphology induced by various solution processing recipes, as well as the effect of spin-coating when used to deposit solutions of nanofibers. All examples presented in this protocol can be reproduced from beginning to end using the included software, with visualizations produced at each stage of processing

Quantifying Dense Multicomponent Slurries with In-Line ATR-FTIR and Raman Spectroscopies: A Hanford Case Study

The multiphase nature of slurries can make them difficult to process and monitor in real time. For example, the nuclear waste slurries present at the Hanford site in Washington State are multicomponent, multiphase, and inhomogeneous. Current analytical techniques for analyzing radioactive waste at Hanford rely on laboratory results from an on-site analytical laboratory, which can delay processing speed and create exposure risks for workers. However, in-line probes can provide an alternative route to collect the necessary composition information. In the present work, Raman spectroscopy and attenuated total reflectance–Fourier transform infrared (ATR-FTIR) spectroscopy are tested on simulants of nuclear waste slurries containing up to 23.2 wt % solids. We observe ATR-FTIR spectroscopy to be effective in measuring the solution phase of the studied slurry systems (3.52% mean percent error), while Raman spectroscopy provides information about the suspended solids in the slurry system (18.21% mean percent error). In-line measurement of multicomponent solids typical of nuclear waste processing has been previously unreported. The composition of both the solution and solid phases is vital in ensuring stable glass formulation and effective disposal of nuclear waste at Hanford. Raman and ATR-FTIR spectroscopies can provide a safer and faster alternative for acquiring compositional information on nuclear waste slurries

Data-Driven Modeling and Dynamic Programming Applied to Batch Cooling Crystallization

In this article, we demonstrate a model-based approach for controlling the average size of crystals produced by batch cooling crystallization. The method is distinguished most notably in the modeling strategy. Rather than developing a crystallization model within the population-balance framework, as is usually done, we apply a machine-learning technique to identify an empirical model from measurement data. The model is low-dimensional and can therefore be discretized and used with dynamic programming to obtain optimal control policies for producing crystals of targeted average sizes in prespecified batch run times. Experimental results are reported that demonstrate the use of the identified policies to produce crystals of the desired average sizes in the specified run times

Feedback Control of Multicomponent Salt Crystallization

A closed-loop strategy is developed for controlling batch cooling multicomponent crystallization. The strategy represents the sequential application of two established feedback control techniques: direct nucleation control followed by supersaturation control. Experimental results show that such a control scheme produces larger crystals (compared to linear cooling crystallization with the same batch time). In using this scheme to control the crystallization of a double salt from a solution containing sodium nitrate and sodium sulfate, we demonstrate the application of supersaturation control to a multicomponent salt crystallizationwhich requires knowledge of the solubility as a function of temperature, the ability to monitor concentrations in a multicomponent solution, and an appropriate expression for the driving force for crystallization of a salt. In this paper, a methodology for rapidly identifying the solubility of a solute in a multicomponent solution is presented and a new expression for supersaturationtermed the molar supersaturationis advanced as a measure of the driving force for crystallization of salts