Three-dimensional kinetic simulations of active suspensions: effect of chemotaxis and steric interaction

In this work, the effects of chemotaxis and steric interactions in active suspensions are analyzed by extending the kinetic model proposed by Saintillan and Shelley [1, 2]. In this model, a conservation equation for the active particle configuration is coupled to the Stokes equation for the flow arising from the force dipole exerted by the particles on the fluid. The fluid flow equations are solved spectrally and the conservation equation is solved by second-order finite differencing in space and second-order Adams-Bashforth time marching. First, the dynamics in suspensions of oxytactic run-and-tumble bacteria confined in thin liquid films surrounded by air is investigated. These bacteria modify their tumbling behavior by making temporal comparisons of the oxygen concentration, and, on average, swim towards high concentrations of oxygen. The kinetic model proposed by Saintillan and Shelley [1, 2] is modified to include run-and-tumble effects and oxygentaxis. The spatio-temporal dynamics of the oxygen and bacterial concentration are analyzed. For small film thicknesses, there is a weak migration of bacteria to the boundaries, and the oxygen concentration is high inside the film as a result of diffusion; both bacterial and oxygen concentrations quickly reach steady states. Above a critical film thickness (approximately 200 micron), a transition to chaotic dynamics is observed and is characterized by turbulent-like 3D motion, the formation of bacterial plumes, enhanced oxygen mixing and transport into the film, and hydrodynamic velocities of magnitudes up to 7 times the single bacterial swimming speed. The simulations demonstrate that the combined effects of hydrodynamic interactions and oxygentaxis create collective three-dimensional instabilities which enhances oxygen availability for the bacteria. Our simulation results are consistent with the experimental findings of Sokolov et al. [3], who also observed a similar transition with increasing film thickness. Next, the dynamics in concentrated suspensions of active self-propelled particles in a 3D periodic domain are analyzed. We modify the kinetic model of Saintillan and Shelley [1, 2] by including an additional nematic alignment torque proportional to the local concentration in the equation for the rotational velocity of the particles, causing them to align locally with their neighbors (Doi and Edwards [4]). Large-scale three- dimensional simulations show that, in the presence of such a torque both pusher and puller suspensions are unstable to random fluctuations and are characterized by highly nematic structures. Detailed measures are defined to quantify the degree and direction of alignment, and the effects of steric interactions on pattern formation will be presented. Our analysis shows that steric interactions have a destabilizing effect in active suspensions.

On L2 grammar and processing: the case of oblique relative clauses and the Null-Prep phenomenon

This dissertation investigates the acquisition of oblique relative clauses in L2 Spanish by English and Moroccan Arabic speakers in order to understand the role of previous linguistic knowledge and its interaction with Universal Grammar on the one hand, and the relationship between grammatical knowledge and its use in real-time, on the other hand. Three types of tasks were employed: an oral production task, an on-line self-paced grammaticality judgment task, and an on-line self-paced reading comprehension task. Results indicated that the acquisition of oblique relative clauses in Spanish is a problematic area for second language learners of intermediate proficiency in the language, regardless of their native language. In particular, this study has showed that, even when the learners’ native language shares the main properties of the L2, i.e., fronting of the obligatory preposition (Pied-Piping), there is still room for divergence, especially in production and timed grammatical intuitions. On the other hand, reaction time data have shown that L2 learners can and do converge at the level of sentence processing, showing exactly the same real-time effects for oblique relative clauses that native speakers had. Processing results demonstrated that native and non-native speakers alike are able to apply universal processing principles such as the Minimal Chain Principle (De Vincenzi, 1991) even when the L2 learners still have incomplete grammatical representations, a result that contradicts some of the predictions of the Shallow Structure Hypothesis (Clahsen & Felser, 2006). Results further suggest that the L2 processing and comprehension domains may be able to access some type of information that it is not yet available to other grammatical modules, probably because transfer of certain L1 properties occurs asymmetrically across linguistic domains. In addition, this study also explored the Null-Prep phenomenon in L2 Spanish, and proposed that Null-Prep is an interlanguage stage, fully available and accounted within UG, which intermediate L2 as well as first language learners go through in the development of pied-piping oblique relative clauses. It is hypothesized that this intermediate stage is the result of optionality of the obligatory preposition in the derivation, when it is not crucial for the meaning of the sentence, and when the DP is going to be in an A-bar position, so it can get default case. This optionality can be predicted by the Bottleneck Hypothesis (Slabakova, 2009c) if we consider that these prepositions are some sort of functional morphology. This study contributes to the field of SLA and L2 processing in various ways. First, it demonstrates that the grammatical representations may be dissociated from grammatical processing in the sense that L2 learners, unlike native speakers, can present unexpected asymmetries such as a convergent processing but divergent grammatical intuitions or production. This conclusion is only possible under the assumption of a modular language system. Finally, it contributes to the general debate of generative SLA since in argues for a fully UG-constrained interlanguage grammar.