Large Decrease of Fluctuations for Supercooled Water in Hydrophobic Nanoconfinement

Using Monte Carlo simulations we study a coarse­grained model of a water layer confined in a fixed disordered matrix of hydrophobic nanoparticles at different particle concentrations c. For c = 0 we find a 1st order liquid­liquid phase transition (LLPT) ending in one critical point at low pressure P. For c > 0 our simulations are consistent with a LLPT line ending in two critical points at low and high pressure. For c = 25% at high P and low temperature T we find a dramatic decrease of compressibility, thermal expansion coefficient, and specific heat. Surprisingly, the effect is present also for c as low as 2.4%. We conclude that even a small presence of nanoscopic hydrophobes can drastically suppress thermodynamic fluctuations, making the detection of the LLPT more difficult.

Improving the Performance of Overlay Routing and P2P File Sharing using Selfish Neighbor Selection

A foundational issue underlying many overlay network applications ranging from routing to P2P file sharing is that of connectivity management, i.e., folding new arrivals into the existing mesh and re-wiring to cope with changing network conditions. Previous work has considered the problem from two perspectives: devising practical heuristics for specific applications designed to work well in real deployments, and providing abstractions for the underlying problem that are tractable to address via theoretical analyses, especially game-theoretic analysis. Our work unifies these two thrusts first by distilling insights gleaned from clean theoretical models, notably that under natural resource constraints, selfish players can select neighbors so as to efficiently reach near-equilibria that also provide high global performance. Using Egoist, a prototype overlay routing system we implemented on PlanetLab, we demonstrate that our neighbor selection primitives significantly outperform existing heuristics on a variety of performance metrics; that Egoist is competitive with an optimal, but unscalable full-mesh approach; and that it remains highly effective under significant churn. We also describe variants of Egoist's current design that would enable it to scale to overlays of much larger scale and allow it to cater effectively to applications, such as P2P file sharing in unstructured overlays, based on the use of primitives such as scoped-flooding rather than routing.

Implications of Selfish Neighbor Selection in Overlay Networks

In a typical overlay network for routing or content sharing, each node must select a fixed number of immediate overlay neighbors for routing traffic or content queries. A selfish node entering such a network would select neighbors so as to minimize the weighted sum of expected access costs to all its destinations. Previous work on selfish neighbor selection has built intuition with simple models where edges are undirected, access costs are modeled by hop-counts, and nodes have potentially unbounded degrees. However, in practice, important constraints not captured by these models lead to richer games with substantively and fundamentally different outcomes. Our work models neighbor selection as a game involving directed links, constraints on the number of allowed neighbors, and costs reflecting both network latency and node preference. We express a node's "best response" wiring strategy as a k-median problem on asymmetric distance, and use this formulation to obtain pure Nash equilibria. We experimentally examine the properties of such stable wirings on synthetic topologies, as well as on real topologies and maps constructed from PlanetLab and AS-level Internet measurements. Our results indicate that selfish nodes can reap substantial performance benefits when connecting to overlay networks composed of non-selfish nodes. On the other hand, in overlays that are dominated by selfish nodes, the resulting stable wirings are optimized to such great extent that even non-selfish newcomers can extract near-optimal performance through naive wiring strategies.

The Construction of Arbitrary Stable Dynamics in Non-Linear Neural Networks

In this paper, two methods for constructing systems of ordinary differential equations realizing any fixed finite set of equilibria in any fixed finite dimension are introduced; no spurious equilibria are possible for either method. By using the first method, one can construct a system with the fewest number of equilibria, given a fixed set of attractors. Using a strict Lyapunov function for each of these differential equations, a large class of systems with the same set of equilibria is constructed. A method of fitting these nonlinear systems to trajectories is proposed. In addition, a general method which will produce an arbitrary number of periodic orbits of shapes of arbitrary complexity is also discussed. A more general second method is given to construct a differential equation which converges to a fixed given finite set of equilibria. This technique is much more general in that it allows this set of equilibria to have any of a large class of indices which are consistent with the Morse Inequalities. It is clear that this class is not universal, because there is a large class of additional vector fields with convergent dynamics which cannot be constructed by the above method. The easiest way to see this is to enumerate the set of Morse indices which can be obtained by the above method and compare this class with the class of Morse indices of arbitrary differential equations with convergent dynamics. The former set of indices are a proper subclass of the latter, therefore, the above construction cannot be universal. In general, it is a difficult open problem to construct a specific example of a differential equation with a given fixed set of equilibria, permissible Morse indices, and permissible connections between stable and unstable manifolds. A strict Lyapunov function is given for this second case as well. This strict Lyapunov function as above enables construction of a large class of examples consistent with these more complicated dynamics and indices. The determination of all the basins of attraction in the general case for these systems is also difficult and open.

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.

Exploring the physicochemical basis of cheese texture, rheology and functionality, with emphasis on cation-casein interactions

The physicochemical properties of cheese and milk gels are greatly influenced by molecular interactions between the casein proteins involving calcium. Novel experiments were designed to investigate the relationship between insoluble caseinbound cations and rheological properties of Cheddar cheese and rennet-induced milk gels. Cheddar cheese and rennet-induced milk gels were supplemented with Mg2+ or Sr2+ to compare their effects on their rheological properties to those previously reported in literature for Ca2+ supplementation. Sr2+ displayed behaviour similar to Ca2+ as observed by its ability to increase the rigidity of cheese and rennet milk gels and also decrease cheese meltability. Mg+2 had no influence on cheese rheological properties and was greatly inferior to Ca2+ and Sr2+ in its ability to increase rennet milk gel elasticity. Cheddar cheese was supplemented with the calcium-chelating salts trisodium citrate, disodium hydrogen phosphate or disodium EDTA, in an attempt to reduce the CCP content of cheese and thereby modify its rheological and functional properties. TSC and EDTA were successful in decreasing cheese CCP, whereas DSP caused an initial increase in CCP content. Cheddar cheese was supplemented with chlorides of iron, copper and zinc at salting to investigate the effects of concentrations of these elements in excess of those found innately or commonly in fortification studies, with emphasis on mineral equilibria changes and resultant alteration of rheological properties. Zinc addition was the only added metal that significantly influenced cheese rheological properties, leading to an increase in cheese rigidity and decreased cheese melt at elevated temperatures. Gum tragacanth was used as a fat-replacer in the manufacture of reduced-fat Cheddar cheese, in an attempt to improve the rheological, functional and sensory properties of reduced-fat Cheddar. Overall, the experimental work reported in this thesis generated new knowledge and theories about how casein-mineral interactions influence rheological properties of casein systems.

Thermodynamic analysis of ligand-induced changes in protein thermal unfolding applied to high-throughput determination of ligand affinities with extrinsic fluorescent dyes.

The quantification of protein-ligand interactions is essential for systems biology, drug discovery, and bioengineering. Ligand-induced changes in protein thermal stability provide a general, quantifiable signature of binding and may be monitored with dyes such as Sypro Orange (SO), which increase their fluorescence emission intensities upon interaction with the unfolded protein. This method is an experimentally straightforward, economical, and high-throughput approach for observing thermal melts using commonly available real-time polymerase chain reaction instrumentation. However, quantitative analysis requires careful consideration of the dye-mediated reporting mechanism and the underlying thermodynamic model. We determine affinity constants by analysis of ligand-mediated shifts in melting-temperature midpoint values. Ligand affinity is determined in a ligand titration series from shifts in free energies of stability at a common reference temperature. Thermodynamic parameters are obtained by fitting the inverse first derivative of the experimental signal reporting on thermal denaturation with equations that incorporate linear or nonlinear baseline models. We apply these methods to fit protein melts monitored with SO that exhibit prominent nonlinear post-transition baselines. SO can perturb the equilibria on which it is reporting. We analyze cases in which the ligand binds to both the native and denatured state or to the native state only and cases in which protein:ligand stoichiometry needs to treated explicitly.

Cyclic Pursuit: Symmetry, Reduction and Nonlinear Dynamics

In this dissertation, we explore the use of pursuit interactions as a building block for collective behavior, primarily in the context of constant bearing (CB) cyclic pursuit. Pursuit phenomena are observed throughout the natural environment and also play an important role in technological contexts, such as missile-aircraft encounters and interactions between unmanned vehicles. While pursuit is typically regarded as adversarial, we demonstrate that pursuit interactions within a cyclic pursuit framework give rise to seemingly coordinated group maneuvers. We model a system of agents (e.g. birds, vehicles) as particles tracing out curves in the plane, and illustrate reduction to the shape space of relative positions and velocities. Introducing the CB pursuit strategy and associated pursuit law, we consider the case for which agent i pursues agent i+1 (modulo n) with the CB pursuit law. After deriving closed-loop cyclic pursuit dynamics, we demonstrate asymptotic convergence to an invariant submanifold (corresponding to each agent attaining the CB pursuit strategy), and proceed by analysis of the reduced dynamics restricted to the submanifold. For the general setting, we derive existence conditions for relative equilibria (circling and rectilinear) as well as for system trajectories which preserve the shape of the collective (up to similarity), which we refer to as pure shape equilibria. For two illustrative low-dimensional cases, we provide a more comprehensive analysis, deriving explicit trajectory solutions for the two-particle "mutual pursuit" case, and detailing the stability properties of three-particle relative equilibria and pure shape equilibria. For the three-particle case, we show that a particular choice of CB pursuit parameters gives rise to remarkable almost-periodic trajectories in the physical space. We also extend our study to consider CB pursuit in three dimensions, deriving a feedback law for executing the CB pursuit strategy, and providing a detailed analysis of the two-particle mutual pursuit case. We complete the work by considering evasive strategies to counter the motion camouflage (MC) pursuit law. After demonstrating that a stochastically steering evader is unable to thwart the MC pursuit strategy, we propose a (deterministic) feedback law for the evader and demonstrate the existence of circling equilibria for the closed-loop pursuer-evader dynamics.

Models of open populations with space-limited recruitment: extension of theory and application to the barnacle Chthamalus montagui.

1. Barnacles are a good model organism for the study of open populations with space-limited recruitment. These models are applicable to other species with open supply of new individuals and resource limitation. The inclusion of space in models leads to reductions in recruitment with increasing density, and thus predictions of population size and stability are possible. 2. Despite the potential generality of a demographic theory for open space-limited populations, the models currently have a narrow empirical base. In this study, a model for an open population with space-limited recruitment was extended to include size-specific survival and promotions to any size class. The assumptions of this model were tested using data from a pan-European study of the barnacle Chthamalus montagui Southward. Two models were constructed: a 6-month model and a periodic annual model. Predicted equilibria and their stabilities were compared between shores. 3. Tests of model assumptions supported the extension of the theory to include promotions to any size class. Mortality was found to be size-specific and density independent. Studied populations were open, with recruitment proportional to free space. 4. The 6-month model showed a significant interaction between time and location for equilibrium free space. This may have been due to contrasts in the timing of structuring processes (i.e. creating and filling space) between Mediterranean and Atlantic systems. Integration of the 6-month models into a periodic annual model removed the differences in equilibrium-free space between locations. 5. Model predictions show a remarkable similarity between shores at a European scale. Populations were persistent and all solutions were stable. This reflects the apparent absence of density-dependent mortality and a high adult survivorship in C. montagui. As populations are intrinsically stable, observations of fluctuations in density are directly attributable to variations in the environmental forcing of recruitment or mortality

A reactive force field simulation of liquid-liquid phase transitions in phosphorus

A force field model of phosphorus has been developed based on density functional (DF) computations and experimental results, covering low energy forms of local tetrahedral symmetry and more compact (simple cubic) structures that arise with increasing pressure. Rules tailored to DF data for the addition, deletion, and exchange of covalent bonds allow the system to adapt the bonding configuration to the thermodynamic state. Monte Carlo simulations in the N-P-T ensemble show that the molecular (P-4) liquid phase, stable at low pressure P and relatively low temperature T, transforms to a polymeric (gel) state on increasing either P or T. These phase changes are observed in recent experiments at similar thermodynamic conditions, as shown by the close agreement of computed and measured structure factors in the molecular and polymer phases. The polymeric phase obtained by increasing pressure has a dominant simple cubic character, while the polymer obtained by raising T at moderate pressure is tetrahedral. Comparison with DF results suggests that the latter is a semiconductor, while the cubic form is metallic. The simulations show that the T-induced polymerization is due to the entropy of the configuration of covalent bonds, as in the polymerization transition in sulfur. The transition observed with increasing P is the continuation at high T of the black P to arsenic (A17) structure observed in the solid state, and also corresponds to a semiconductor to metal transition. (C) 2004 American Institute of Physics.

Density functional and Monte Carlo studies of sulfur. I. Structure and bonding in S-n rings and chains (n=2-18) (vol 118, pg 9257, 2003)

Density functional calculations have been performed for ring isomers of sulfur with up to 18 atoms, and for chains with up to ten atoms. There are many isomers of both types, and the calculations predict the existence of new forms. Larger rings and chains are very flexible, with numerous local energy minima. Apart from a small, but consistent overestimate in the bond lengths, the results reproduce experimental structures where known. Calculations are also performed on the energy surfaces of S8 rings, on the interaction between a pair of such rings, and the reaction between one S8 ring and the triplet diradical S8 chain. The results for potential energies, vibrational frequencies, and reaction mechanisms in sulfur rings and chains provide essential ingredients for Monte Carlo simulations of the liquid–liquid phase transition. The results of these simulations will be presented in Part II.

Bounded Rationality and Repeated Network Formation

We define a finite-horizon repeated network formation game with consent and study the differences induced by two levels of individual rationality. Perfectly rational players will remain unconnected at the equilibrium, while nonempty equilibrium networks may form when players are assumed to behave as finite automata of limited complexity. We provide structural properties of the sequences of networks which are likely to form in Nash and subgame perfect Nash equilibria of the repeated game. For instance, players can form totally different connected networks at each period or the sequence of networks can exhibit a total order relationship.

Identical extraction behavior and coordination of trivalent or hexavalent f-element cations using ionic liquid and molecular solvents

The extraction of both UO22+ and trivalent lanthanide and actinide ions (Am3+, Nd3+, Eu3+) by dialkylphosphoric or dialkylphosphinic acids from aqueous solutions into the ionic liquid, 1-decyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide has been studied and compared to extractions into dodecane. Radiotracer partitioning measurements show comparable patterns of distribution ratios for both the ionic liquid/aqueous and dodecane/aqueous systems, and the limiting slopes at low acidity indicate the partitioning of neutral complexes in both solvent systems. The metal ion coordination environment, elucidated from EXAFS and UV-visible spectroscopy measurements, is equivalent in the ionic liquid and dodecane solutions with coordination of the uranyl cation by two hydrogen-bonded extractant dimers, and of the trivalent cations by three extractant dimers. This is the first definitive report of a system where both the biphasic extraction equilibria and metal coordination environment are the same in an ionic liquid and a molecular organic solvent.