Liquids display an astonishing array of phenomena that, at first glance, seem to have little in common. In this thesis, we study two of these phenomena. The first is the hydrophobic effect, the well-known tendency of oil and water to demix and the driving force for biological assembly. The second is the glass transition, the process by which liquids cooled to very low temperatures become increasingly viscous until succumbing to structural arrest and displaying the rigidity of a solid with none of its microscopic ordering.

In the first part of this thesis, we expand upon our prior understanding of the hydrophobic effect. We study the behavior of water in the confined volume created by a pair of RNA helices at the inter-subunit interface of the bacterial ribosome, which provides an opportunity to apply our contemporary understanding of the hydrophobic effect, first detailed by Lum, Chandler, and Weeks almost twenty years ago, to a context that is less idealized than previously studied. We also discuss and improve upon computational models of hydrophobic solvation, expanding their applicability to more complicated solute geometries.

In the second part of this thesis, we study the glass transition from the perspective of the East model, a kinetically constrained lattice model of glass formers. We review and derive a number of results for East model glasses that we expect to emerge in more realistic, atomistic models of glass formers. We choose one such model and drive it out of equilibrium by cooling, forming a glass. We then check whether our East model predictions are correct. Of particular interest to us is whether inter-excitation correlations emerge out of equilibrium, a key prediction of the East model. Our atomistic results suggest that they do not, forcing us to reconsider our conceptual mapping between the highly abstract East model and more realistic models of glass formers.

The common thread in these seemingly disparate parts of the thesis is the importance of collective fluctuations in liquid-state phenomena. The hydrophobic effect is a physical consequence of liquid-vapor interfacial fluctuations near extended hydrophobic surfaces, while dynamics in supercooled liquids, the precursors to glasses, are dominated by small, collective motions of particles in an otherwise jammed material. The importance of fluctuations in these and other liquid-state phenomena make the tools of statistical mechanics particularly suitable to their study. In this thesis, we employ these tools in the service of furthering our understanding of the liquid state.

At ambient conditions, water sits close to phase coexistence with its crystal. More so than in many other materials, this fact is manifested in the fluctuations that maintain a large degree of local order in the liquid. These fluctuations and how they result in long-ranged order, or its absence, are emergent features of many interacting molecules. Their study therefore requires using the tools of statistical mechanics for their their systematic understanding. In this dissertation we develop such an understanding. In particular, we focus on collective behavior that emerges in liquid and solid water. At room temperatures, the thermophysical properties of water are quantified and rationalized with simple molecular models. A key feature of these models is the correct characterization of the competition between entropic forces of packing and the energetic preference for tetrahedral order. At cold temperatures, the properties of ice surfaces are studied with statistical field theory. The theory we develop for the long wavelength features of ice interfaces allows us to explain the existence of a premelting layer on the surface of ice and the stability of ice in confinement. In between these extremes, the dynamics of supercooled water are considered. A detailed theory for the early stages of coarsening is developed and used to explain the peculiar observation of a transient second liquid state of water. When coarsening dynamics are arrested, the result is the formation of a glassy states of water. We show that out-of-equilibrium the phase diagram for supercooled water exhibits a rich amount of structure, including a triple point between two glass phases of water and the liquid. At the end, we explore possible technological implications for the interplay between ordering and frustration in studies of water at metal interfaces.

In October 1979 the first university-based mediation service in the United States was born in the political science department of the University of Hawaii. Student and faculty volunteers developed an administrative system in facilities donated by the university. Mediation trainers were brought in to train the first 18 mediators who represented a cross section of the community. Student and faculty volunteers conducted outreach to citizen groups and agencies, the arranging and staffing of mediations, the collection of case materials and records, and the training of new mediators. This paper reports on the outcomes of the first nine months of the project’s operation.

Note: This working paper was originally published in 1982 by the Institute for the Study of Social Change, now the Institute for the Study of Societal Issues.

The nature of supercooled liquids and the glass transition has been debated by many scientists. Several theories have been put forth to describe the remarkable properties of this out-of-equilibrium material. Each of these theories makes specific predictions as to how the scaling of various transport properties in supercooled materials should behave. Given access to a large pool of high-quality supercooled liquid data we seek to compare these theories to one another. Moreover, we explore properties of a pair of models which are the basis for one particularly attractive theory - Chandler-Garrahan theory - and discuss the models' behavior in space-time and possible implications to the behavior of experimental supercooled liquids.

Here we investigate the nature of dynamics in supercooled liquids using a two pronged approach. First we analyze the transport properties found in experiments and simulations of supercooled liquids. Then, we analyze simulation trajectories for lattice models which reproduce many of the interesting properties of supercooled liquids. In doing so, we illuminate several glass universalities, common properties of a wide variety of glass formers.

By analyzing relaxation time and viscosity data for over 50 data sets and 1200 points, we find that relaxation time can be collapsed onto a single, parabolic curve. This collapse supports a theory of universal glass behavior based on facilitated models proposed by David Chandler and Juan Garrahan in 2003. We then show that the parabolic fit parameters for any particular liquid are a material property: they converge fast and are capable of predicting behavior in regions beyond the included data sets. We compare this property to other popular fitting schemes such as the Vogel-Fulcher, double exponential, and fractional exponential forms and conclude that these three forms result in parameters which are non predictive and therefore not material properties. Additionally, we examine the role of attractive forces in liquids by comparing simulations of a Lennard-Jones mixture, which contains both attractions and repulsions, with that of a Weeks-Chandler-Andersen mixture, which only retains repulsive forces. We show that within the framework of the parabolic collapse, these two liquids behave identically. This suggests that attractive forces do not play a key role in glassy dynamics. Rather, repulsive forces - as has been shown in dense liquids - play the largest contributing role in jamming systems into glassy states. We further investigate the predicted fragile-to-strong crossover in glass formers and find no compelling evidence for the crossover in bulk materials at this time.

Additionally, we study ensembles of trajectories for a specific class of kinetically constrained models which reproduce the dynamic heterogeneity found in real glass formers. The one dimensional models we consider are the Fredrickson-Andersen (FA) model and the east model. These two models have been shown to behave as supercooled liquids reproducing properties such as the breakdown of the Stokes-Einstein equation relating diffusion constants and relaxation times. We use transition path sampling in the s-ensemble to bias the system into low activity regions. It has been previously shown that the FA model goes through a first-order dynamical phase transition in trajectory space. We extend this to include a slightly softened FA model, which we believe to be more representative of atomistic systems. We have determined that this first order coexistence line ends in a critical point where the surface tension between active and inactive trajectories in space-time disappears. Beyond this region as the softened FA model becomes unconstrained, the transition disappears and no phase transition is detected. Beyond simulations, these results were verified by analytical methods. This verification was achieved by mapping of soft FA model onto a model which undergoes a quantum phase transition. Beyond the FA model, we consider the softened east model. Unlike the FA model, however, the east model relaxes hierarchically and has a particular directionality. Many of the same conclusions - such as the appearance of a non-trivial critical point in space time - appear in the east model. Moreover, many of the same analytical tools can be used to determine the symmetry line that separates the active and inactive phases. However, the exact mapping of the critical point location is unknown and the location of the critical point is determined numerically. We also investigate how the inactive phase created by applying a dynamical field relaxes to the active state under no external field and find that the process appears barrierless.

Lastly, we propose current and ongoing work which seeks to understand how to numerically quantify the degree to which a system is dynamically facilitated by looking at multipoint correlation functions of endured kinks. We contrast this method with previously suggested methods based on locating avalanches by testing both methods on kinetically constrained models such as the east and FA models.

When a liquid is cooled below its melting temperature under conditions that prevent it from crystallizing, it forms an amorphous solid, or "glass." Glass-forming materials are ubiquitous, ranging from familiar silica glasses of which everyday windows are composed, to liquid water. While structurally indistinguishable from high-temperature liquids, supercooled liquids exhibit rich and complex dynamics. For instance, as the temperature is lowered, structural reorganization within supercooled liquids occurs over increasingly long time scales. Inspecting atomistic mobility over an interval of time reveals that dynamics is "heterogeneous," with distinct regions of mobility and immobility in space-time. In this dissertation, we characterize glassy dynamics in experimental systems and in coarse-grained lattice models. We show how the characteristic dynamics of atomistic glass-forming materials can be reproduced using a kinetically constrained lattice model referred to as the Arrow model, and thus present glassy dynamics "on a lattice." We then show that combining the Arrow model with a second lattice model that undergoes a thermodynamic phase transition captures the competition between crystallization and glass formation experienced by a material cooled below its melting temperature. With this combined model, we demonstrate how specific cooling protocols influence polycrystalline structure, and we qualitatively reproduce the non-monotonic temperature dependence of crystallization time scales. Finally, we explore glassy dynamics "in nature" by applying many of the same tools and ideas used to characterize glasses to study dynamical features of protein side-chains. We demonstrate the presence of supercooled liquid-like dynamics in a biomolecular system.

The hydrophobic effect, or the tendency for oil and water not to mix, is a fundamental force that strongly influences the shape, behavior and assembly of solutes in solution. Hydrophobicity emerges from the collective behavior of large numbers of solvent molecules, so its accurate treatment is challenging. A decade ago, Lum, Chandler and Weeks (LCW) addressed this challenge indirectly by modeling how solvent density fluctuations couple to external solutes and constraints, and then inferring hydrophobic behavior from the resulting mean solvent density. LCW theory is successful because it distinguishes between, and separately models, small-length-scale and large-length-scale density fluctuations. In this thesis, we develop methods for probing the statistics of large-length-scale density fluctuations in computer simulations of water. We use these tools to study solvation phenomena in model systems and in proteins, in bulk water and near surfaces, and we rationalize these phenomena in terms of LCW ideas. Building on these ideas and on past efforts by others, we construct a tractable, efficient and accurate theory of solvation on a coarse-grained lattice. The final theory allows us to model the solvation behavior of uncharged, static solutes of arbitrary shape, and we outline the steps necessary to model charged, dynamic solutes in the future. A unifying thread in our solvation studies is the importance of fluctuations of liquid-vapor interfaces. At the end of this thesis, we describe how these fluctuations may play a role in water evaporation.