Exact solutions for cluster-growth kinetics with evolving size and shape profiles

In this paper we construct a model for the simultaneous compaction by which clusters are restructured, and growth of clusters by pairwise coagulation. The model has the form of a multicomponent aggregation problem in which the components are cluster mass and cluster diameter. Following suitable approximations, exact explicit solutions are derived which may be useful for the verification of simulations of such systems. Numerical simulations are presented to illustrate typical behaviour and to show the accuracy of approximations made in deriving the model. The solutions are then simplified using asymptotic techniques to show the relevant timescales of the kinetic processes and elucidate the shape of the cluster distribution functions at large times.

Otolith shape variation provides a marker of stock origin for north Atlantic bluefin tuna (Thunnus thynnus)

Two stocks of bluefin tuna (Thunnus thynnus) inhabit the north Atlantic; the western and eastern stocks spawn in the Gulf of Mexico and the Mediterranean Sea respectively. Trans-Atlantic movements occur outside spawning time whereas natal homing maintains stock structure. Commercial fisheries may exploit a mixed assemblage of both stocks. The incorporation of mixing rates into stock assessment is precluded by uncertainties surrounding stock discrimination. Otolith shape descriptors were used to characterise western and eastern stocks of Atlantic bluefin tuna in the present study and to estimate stock composition in catches of unknown origin. Otolith shape varied with length and between locations and years. Within a restricted size range (200-297-cm fork length (FL)) the two stocks were distinguished with an accuracy of 83%. Bayesian stock mixture analysis indicated that samples from the east Atlantic and Mediterranean were predominantly of eastern origin. The proportion assigned to the eastern stock showed slight spatial variation; however, overlapping 95% credible intervals indicated no significant difference (200-297 cm FL: central Atlantic, 73-100%; Straits of Gibraltar, 73-100%; Morocco, 50-99%; Portugal 64-100%). Otolith shape could be used in combination with other population markers to improve the accuracy of mixing rate estimates for Atlantic bluefin tuna.

Designing Hydrogels that Transform their Shape in Response to Molecular Cues

There has been considerable interest in developing shape-changing soft materials for potential applications in drug delivery, microfluidics and biosensing. These shape- changing materials are inspired by the morphological changes exhibited by plants in nature, such as the Venus flytrap. One specific class of shape-change is that from a flat sheet to a folded structure (e.g., a tube). Such “self-folding” materials are usually composed of polymer hydrogels, and these typically fold in response to external stimuli such as pH and temperature. In order to develop these hydrogels for the previously described applications, it is necessary to expand the range of triggers. The focus of this dissertation is the advancement of shape-changing polymer hydrogels that are sensitive to uncommon cues such as specific biomolecules (enzymes), the substrates for such enzymes, or specific multivalent cations. First, we describe a hybrid gel that responds to the presence of low concentrations of a class of enzymes known as matrix metalloproteinases (MMPs). The hybrid gel was created by utilizing photolithographic techniques to combine two or more gels with distinct chemical composition into the same material. Certain portions of the hybrid gel are composed of a biopolymer derivative with crosslinkable groups. The hybrid gel is flat in water; however, in the presence of MMPs, the regions containing the biopolymer are degraded and the flat sheet folds to form a 3D structure. We demonstrate that hydrogels with different patterns can transform into different 3D structures such as tubes, helices and pancakes. Furthermore, this shape change can be made to occur at physiological concentrations of enzymes. Next, we report a gel with two layers that undergoes a shape change in the presence of glucose. The enzyme glucose oxidase (GOx) is immobilized in one of the layers. GOx catalyzes the conversion of glucose to gluconic acid. The production of gluconic acid decreases the local pH. The decrease in local pH causes one of the layers to swell. As a result, the flat sheet folds to form a tube. The tube unfolds to form a flat sheet when it is transferred to a solution with no glucose present. Therefore, this biomolecule- triggered shape transformation is reversible, meaning the glucose sensing gel is reusable. Furthermore, this shape change only occurs in the presence of glucose and it does not occur in the presence of other small sugars such as fructose. In our final study, we report the shape change of a gel with two layers in the presence of multivalent ions such as Ca2+ and Sr2+. The gel consists of a passive layer and an active layer. The passive layer is composed of dimethylyacrylamide (DMAA), which does not interact with multivalent ions. The active layer consists of DMAA and the biopolymer alginate. In the presence of Ca2+ ions, the alginate chains crosslink and the active layer shrinks. As a result, the gel converts from a flat sheet to a folded tube. What is particularly unusual is the direction of folding. In most cases, when flat rectangular gels fold, they do so about their short-side. However, our gels typically fold about their long-side. We hypothesize that non-homogeneous swelling determines the folding axis.

REGULATION OF SHAPE DYNAMICS AND ACTIN POLYMERIZATION DURING COLLECTIVE CELL MIGRATION

This thesis aims to understand how cells coordinate their motion during collective migration. As previously shown, the motion of individually migrating cells is governed by wave-like cell shape dynamics. The mechanisms that regulate these dynamic behaviors in response to extracellular environment remain largely unclear. I applied shape dynamics analysis to Dictyostelium cells migrating in pairs and in multicellular streams and found that wave-like membrane protrusions are highly coupled between touching cells. I further characterized cell motion by using principle component analysis (PCA) to decompose complex cell shape changes into a serial shape change modes, from which I found that streaming cells exhibit localized anterior protrusion, termed front narrowing, to facilitate cell-cell coupling. I next explored cytoskeleton-based mechanisms of cell-cell coupling by measuring the dynamics of actin polymerization. Actin polymerization waves observed in individual cells were significantly suppressed in multicellular streams. Streaming cells exclusively produced F-actin at cell-cell contact regions, especially at cell fronts. I demonstrated that such restricted actin polymerization is associated with cell-cell coupling, as reducing actin polymerization with Latrunculin A leads to the assembly of F-actin at the side of streams, the decrease of front narrowing, and the decoupling of protrusion waves. My studies also suggest that collective migration is guided by cell-surface interactions. I examined the aggregation of Dictyostelim cells under distinct conditions and found that both chemical compositions of surfaces and surface-adhesion defects in cells result in altered collective migration patterns. I also investigated the shape dynamics of cells suspended on PEG-coated surfaces, which showed that coupling of protrusion waves disappears on touching suspended cells. These observations indicate that collective migration requires a balance between cell-cell and cell-surface adhesions. I hypothesized such a balance is reached via the regulation of cytoskeleton. Indeed, I found cells actively regulate cytoskeleton to retain optimal cell-surface adhesions on varying surfaces, and cells lacking the link between actin and surfaces (talin A) could not retain the optimal adhesions. On the other hand, suspended cells exhibited enhanced actin filament assembly on the periphery of cell groups instead of in cell-cell contact regions, which facilitates their aggregation in a clumping fashion.

Improving robustness of rolling stock circulations in rapid transit networks

The rolling stock circulation depends on two different problems: the rolling stock assignment and the train routing problems, which up to now have been solved sequentially. We propose a new approach to obtain better and more robust circulations of the rolling stock train units, solving the rolling stock assignment while accounting for the train routing problem. Here robustness means that difficult shunting operations are selectively penalized and propagated delays together with the need for human resources are minimized. This new integrated approach provides a huge model. Then, we solve the integrated model using Benders decomposition, where the main decision is the rolling stock assignment and the train routing is in the second level. For computational reasons we propose a heuristic based on Benders decomposition. Computational experiments show how the current solution operated by RENFE (the main Spanish train operator) can be improved: more robust and efficient solutions are obtained

Train scheduling and rolling stock assignment in high speed trains

The Train Timetabling Problem (TTP) has been widely studied for freight and passenger rail systems. A lesser effort has been devoted to the study of high-speed rail systems. A modeling issue that has to be addressed is to model departure time choice of passengers on railway services. Passengers who use these systems attempt to travel at predetermined hours due to their daily life necessities (e.g., commuter trips). We incorporate all these features into TTP focusing on high-speed railway systems. We propose a Rail Scheduling and Rolling Stock (RSch-RS) model for timetable planning of high-speed railway systems. This model is composed of two essential elements: i) an infrastructure model for representing the railway network: it includes capacity constraints of the rail network and the Rolling-Stock constraints; and ii) a demand model that defines how the passengers choose the departure time. The resulting model is a mixed-integer programming model which objective function attempts to maximize the profit for the rail operator

Elemental Anisotropic Growth and Atomic-Scale Structure of Shape-Controlled Octahedral Pt–Ni–Co Alloy Nanocatalysts

Multimetallic shape-controlled nanoparticles offer great opportunities to tune the activity, selectivity, and stability of electrocatalytic surface reactions. However, in many cases, our synthetic control over particle size, composition, and shape is limited requiring trial and error. Deeper atomic-scale insight in the particle formation process would enable more rational syntheses. Here we exemplify this using a family of trimetallic PtNiCo nanooctahedra obtained via a low-temperature, surfactant-free solvothermal synthesis. We analyze the competition between Ni and Co precursors under coreduction “one-step” conditions when the Ni reduction rates prevailed. To tune the Co reduction rate and final content, we develop a “two-step” route and track the evolution of the composition and morphology of the particles at the atomic scale. To achieve this, scanning transmission electron microscopy and energy dispersive X-ray elemental mapping techniques are used. We provide evidence of a heterogeneous element distribution caused by element-specific anisotropic growth and create octahedral nanoparticles with tailored atomic composition like Pt1.5M, PtM, and PtM1.5 (M = Ni + Co). These trimetallic electrocatalysts have been tested toward the oxygen reduction reaction (ORR), showing a greatly enhanced mass activity related to commercial Pt/C and less activity loss than binary PtNi and PtCo after 4000 potential cycles.