The effects of osmotic stress on the structure and function of the cell nucleus.

Osmotic stress is a potent regulator of the normal function of cells that are exposed to osmotically active environments under physiologic or pathologic conditions. The ability of cells to alter gene expression and metabolic activity in response to changes in the osmotic environment provides an additional regulatory mechanism for a diverse array of tissues and organs in the human body. In addition to the activation of various osmotically- or volume-activated ion channels, osmotic stress may also act on the genome via a direct biophysical pathway. Changes in extracellular osmolality alter cell volume, and therefore, the concentration of intracellular macromolecules. In turn, intracellular macromolecule concentration is a key physical parameter affecting the spatial organization and pressurization of the nucleus. Hyper-osmotic stress shrinks the nucleus and causes it to assume a convoluted shape, whereas hypo-osmotic stress swells the nucleus to a size that is limited by stretch of the nuclear lamina and induces a smooth, round shape of the nucleus. These behaviors are consistent with a model of the nucleus as a charged core/shell structure pressurized by uneven partition of macromolecules between the nucleoplasm and the cytoplasm. These osmotically-induced alterations in the internal structure and arrangement of chromatin, as well as potential changes in the nuclear membrane and pores are hypothesized to influence gene transcription and/or nucleocytoplasmic transport. A further understanding of the biophysical and biochemical mechanisms involved in these processes would have important ramifications for a range of fields including differentiation, migration, mechanotransduction, DNA repair, and tumorigenesis.

Finite size effects in the presence of a chemical potential: A study in the classical nonlinear O(2) sigma model

In the presence of a chemical potential, the physics of level crossings leads to singularities at zero temperature, even when the spatial volume is finite. These singularities are smoothed out at a finite temperature but leave behind nontrivial finite size effects which must be understood in order to extract thermodynamic quantities using Monte Carlo methods, particularly close to critical points. We illustrate some of these issues using the classical nonlinear O(2) sigma model with a coupling β and chemical potential μ on a 2+1-dimensional Euclidean lattice. In the conventional formulation this model suffers from a sign problem at nonzero chemical potential and hence cannot be studied with the Wolff cluster algorithm. However, when formulated in terms of the worldline of particles, the sign problem is absent, and the model can be studied efficiently with the "worm algorithm." Using this method we study the finite size effects that arise due to the chemical potential and develop an effective quantum mechanical approach to capture the effects. As a side result we obtain energy levels of up to four particles as a function of the box size and uncover a part of the phase diagram in the (β,μ) plane. © 2010 The American Physical Society.

Morphological characteristics of urban water bodies: mechanisms of change and implications for ecosystem function.

The size, shape, and connectivity of water bodies (lakes, ponds, and wetlands) can have important effects on ecological communities and ecosystem processes, but how these characteristics are influenced by land use and land cover change over broad spatial scales is not known. Intensive alteration of water bodies during urban development, including construction, burial, drainage, and reshaping, may select for certain morphometric characteristics and influence the types of water bodies present in cities. We used a database of over one million water bodies in 100 cities across the conterminous United States to compare the size distributions, connectivity (as intersection with surface flow lines), and shape (as measured by shoreline development factor) of water bodies in different land cover classes. Water bodies in all urban land covers were dominated by lakes and ponds, while reservoirs and wetlands comprised only a small fraction of the sample. In urban land covers, as compared to surrounding undeveloped land, water body size distributions converged on moderate sizes, shapes toward less tortuous shorelines, and the number and area of water bodies that intersected surface flow lines (i.e., streams and rivers) decreased. Potential mechanisms responsible for changing the characteristics of urban water bodies include: preferential removal, physical reshaping or addition of water bodies, and selection of locations for development. The relative contributions of each mechanism likely change as cities grow. The larger size and reduced surface connectivity of urban water bodies may affect the role of internal dynamics and sensitivity to catchment processes. More broadly, these results illustrate the complex nature of urban watersheds and highlight the need to develop a conceptual framework for urban water bodies.

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.