Dynamics of visual receptive fields in the macaque frontal eye field.

Neuronal receptive fields (RFs) provide the foundation for understanding systems-level sensory processing. In early visual areas, investigators have mapped RFs in detail using stochastic stimuli and sophisticated analytical approaches. Much less is known about RFs in prefrontal cortex. Visual stimuli used for mapping RFs in prefrontal cortex tend to cover a small range of spatial and temporal parameters, making it difficult to understand their role in visual processing. To address these shortcomings, we implemented a generalized linear model to measure the RFs of neurons in the macaque frontal eye field (FEF) in response to sparse, full-field stimuli. Our high-resolution, probabilistic approach tracked the evolution of RFs during passive fixation, and we validated our results against conventional measures. We found that FEF neurons exhibited a surprising level of sensitivity to stimuli presented as briefly as 10 ms or to multiple dots presented simultaneously, suggesting that FEF visual responses are more precise than previously appreciated. FEF RF spatial structures were largely maintained over time and between stimulus conditions. Our results demonstrate that the application of probabilistic RF mapping to FEF and similar association areas is an important tool for clarifying the neuronal mechanisms of cognition.

Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure

The focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.

We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.

We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.

The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.

Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.

The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.