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Design of a control structure in distillation columns involves selecting proper sets of manipulated and controlled variables (often including tray temperatures for inferential control of product compositions) and one-to-one pairing between the two sets. In this paper, various mathematical tools for achieving this goal are reviewed. First, traditional methods such as Singular Value Decomposition (SVD) and Relative Gain Array (RGA) that build upon a simplified steady-state or dynamic model of the column are explored. The role of optimization in systematizing the control design procedures is also investigated. Then, more recent inferential control techniques that rely on statistical methods such as Principal Component Regression (PCR), Partial Least Squares Regression (PLSR), and other machine learning techniques such as Artificial Neural Networks (ANN) and Support Vector Machine Regression (SVMR) are discussed extensively. The discussions include newer distillation technologies with complex configurations such as dividing-wall columns. Finally, the use of process simulators in aiding the control structure design of distillation columns is surveyed.

Recent experiments have reported intriguing trends for the molecular weight (MW) dependence of the conductivity of block copolymer lamellae that contrast with the behavior of homopolymer matrices. By using coarse-grained simulations of the sorption and transport of penetrant cations, we probe the possible mechanisms underlying such behavior. Our results indicate that the MW dependence of conductivity of homopolymeric and block copolymeric matrices arise from different mechanisms. On the one hand, the solvation energies of cations, and, in turn, the charge carrier concentrations, themselves, exhibit a MW dependence in block copolymer matrices. Such trends are shown to arise from variations in the thickness of the conducting phase relative to that of the interfacial zones. Moreover, distinct mechanisms are shown to be responsible for the diffusivities of ions in homopolymer and block copolymer matrices. In the former, diffusivity effects associated with the free ends of the polymers play an important role. In contrast, in block copolymer lamellae, the interfacial zone between the blocks presents a zone of hindered diffusivity for ions and manifests as a molecular weight dependence of the ionic diffusivity. Together, the preceding mechanisms are shown to provide a plausible explanation for the experimentally observed trends for the conductivity of block copolymer matrices.

Stock prices are co-integrated with fundamental valuation factors (earnings, revenue, cash flow, etc.). This has allowed legendary value investors such as Warren Buffett to enjoy tremendous investment success over the long-term. However, the market is efficient at discounting past information and consensus future expectations. Having the ability to read non-obvious information and to have a better prediction at future valuation factors (surprises from consensus estimates) would likely lead to investment outperformance (generating alpha returns) over the long run. In a recently published work, Alberg and Lipton used various artificial neural networks (ANN) to predict companies’ valuation ratios from their historical fundamental factors and suggested promising results. Aligned with this thought, this research project aims at using Long Short-Term Memory (LSTM) neural network, a type of recurrent neural network (RNN), to predict future fundamental valuation factors of companies and then test investment results by applying active risk-return optimized portfolio strategies. The reasons for choosing LSTM network for this study are the following: (1) like a deep neural network, LSTM is a flexible universal function approximator suited for time-series forecast; (2) LSTM, unlike vanilla version of RNN, does not suffer from “vanishing gradient problem” and is well suited in discovering long-range characteristics, hence its name. Given that LSTM network (or deep neural network in general) enjoys a reputation of being prone to over-fitting to in-sample data, we spend a significant amount of efforts in studying the over-fitting behavior and try to lay out systematic procedures in detecting and mitigating such issues. The current work gives us confidence and excitement that much more can be explored to potentially further improve the prediction performance and investment returns.

Diffusion of small molecules in amorphous polymers is known to follow a form of so-called hopping motion: penetrant molecules are trapped in microscopic cavities for extended time periods; diffusion is made possible by rare but fast jumps between neighboring cavities. Existing understanding of the hopping mechanism is based on the inspection of molecular images during individual molecular-dynamics trajectories. We focus on the diffusion of water molecules in a hydrophilic polymer below its glass transition temperature. The transition path ensemble of one hopping event is sampled with aimless shooting, a type of transition path sampling technique. In these trajectories, configurations of both the penetrant and the polymer change during the transition. Statistical analysis of the ensemble using likelihood maximization leads to a reaction coordinate of the transition, whose key components include the penetrant configuration and distances between penetrant-host atom pairs that have strong electrostatic interactions. Polymer motions do not contribute directly to the reaction coordinate. This result points toward a transition mechanism dominated by the penetrant movement. Molecular insights from this study can benefit the development of computational tools that better predict material transport properties, facilitating the design of new materials, including polymers with engineered drying properties.

We present results obtained using a drift-diffusion model for the structure−property correlations in photovoltaic devices based on self-assembly of rod−coil block copolymers. We use a self-consistent field theory model to generate the self-assembly morphologies of rod−coil block copolymers in confined situations. The density and orientational order parameter profiles so-obtained are then used as input to a recently proposed drift-diffusion model which predicts the photovoltaic device characteristics. The latter model allows for prescription of arbitrary morphologies of donor and acceptor phases while simultaneously incorporating the role of anisotropic charge transport of holes and excitons that arise in the ordered phases of rod−coil block copolymers. We present results elucidating the role of morphology of self-assembly, orientation of lamellar phases, domain widths, and the degree of phase separation and orientational ordering, upon the photovoltaic device characteristics.

The Flory−Huggins interaction is measured for a model rod−coil block copolymer system, poly(alkoxyphenylenevinylene-b-isoprene), by fitting the interfacial segregation of block copolymer to a homopolymer interface and by using the random phase approximation (RPA) for block copolymers. The measured interfacial segregation of a block copolymer to the interface between homopolymers, fit with a self-consistent field theory (SCFT) simulation using χ as a variable parameter, gives a functional form χ = 34.8/T − 0.091. When RPA is applied to neutron scattering curves for the rod−coil system above the order−disorder transition, the theoretical structure factors are inconsistent with observed scattering curves due to complex aggregated structures formed in the nematic and isotropic states. Using the Flory−Huggins parameter and a previously measured value of the Maier−Saupe parameter, the PPV-b-PI phase diagram may be converted from system-specific variables to dimensionless parameters. Under the assumptions that t...

We present a new model based on self-consistent field theory (SCFT) approach and complement it by strong segregation theory (SST) based calculations to characterize the self-assembly behavior in si...

Black Scholes option pricing model is one of the most important concepts in modern world of computational finance. However, its practical use can be challenging as one of the input parameters must be estimated; implied volatility of the underlying security. The more precisely these values are estimated, the more accurate their corresponding estimates of theoretical option prices would be. Here, we present a novel model based on Cuckoo Search Optimization (CS) which finds more precise estimates of implied volatility than Particle Swarm Optimization (PSO) and Genetic Algorithm (GA).

Nucleation is the key step in crystallization by which the molecules (or atoms or ions) aggregate together, find the right relative orientations, and start to grow to form the final crystal structure. Since nucleation is an activated step involving a large gap in time scales between molecular motions and the nucleation event itself, nucleation must be studied using rare events methods. We employ a technique developed previously in our group known as aimless shooting [Peters, B.; Trout, B. L. J. Chem. Phys., 2006, 125, 054108], which is based on transition path sampling, to generate reactive trajectories between the disordered and ordered phases of benzene. Using the likelihood maximization algorithm, we analyze the aimless shooting trajectories to identify the key order parameters or collective variables to describe the reaction coordinate for the nucleation of benzene from the melt. We find that the local bond orientation and local relative orientation order parameters are the most important collective variables in describing the reaction coordinate for homogeneous nucleation from the melt, as compared to cluster size and space-averaged order parameters. This study also demonstrates the utility of recently developed order parameters for molecular crystals [Santiso, E. E.; Trout, B. L. J. Chem. Phys., 2011, 134, 064109].

Recent experimental observations have suggested an intimate connection between the chain conformations and mechanical properties of semicrystalline multiblock copolymers. Motivated by these studies, we present a theoretical study evaluating the bridging/looping fractions in a model of semicrystalline multiblock copolymers. We model the noncrystalline block (A) as a flexible Gaussian chain and the crystalline block (B) as a semiflexible chain with a temperature dependent rigidity and interactions that favor the formation of parallel oriented bonds. Using self-consistent field theory, the bridging fractions of the various domains in different multiblock copolymers (ABA, BAB, ABABA, and BABAB) are evaluated and compared with their flexible counterparts. In general, we observe that for both triblock and pentablock copolymers, rendering one of the blocks crystallizable promotes bridging in that component while reducing the bridging in the other noncrystallizable component. Moreover, the bridging fractions in tri- and pentablock copolymers were seen to be quantitatively similar except insofar as being normalized by the volume fraction of bridgeable units.

We combine a simple lattice-gas model for fluid mixtures along with polymer mean-field theory for block copolymer melts to study the stability of thin films of diblock copolymers in the presence of compressible fluid solvents. Using a free energy analysis, the stable and unstable thicknesses of a copolymer thin film are obtained for given solvent conditions. Our results suggest that the interplay between confinement, the compressibility of the solvent, and its selectivity to polymer component can lead to significant changes on the ordering and stability of the diblock copolymer thin films. Our results are in qualitative agreement with recent experimental results.

We present a model for photovoltaic device characteristics based on drift-diffusion ideas which allows for prescription of arbitrary morphologies of donor and acceptor phases while simultaneously incorporating the role of anisotropic charge transport of holes and excitons. We use such a model to address the interplay between anisotropic charge transport and the orientational and/or crystalline ordering of donor molecules. We presents results illustrating the influence of the degree of orientational ordering, the impact of ordering parallel and perpendicular to the electrodes and the role of device thickness.