Large-scale production of polypropylenimine dendrimers

The synthesis and characterization of a new series of polypropylenimine dendrimers is reported. Using a repetition of the sequence of a Michael addition to a primary amine, followed by a heterogeneously catalyzed hydrogenation, ultra-pure polypropylenimine macromolecules with molecular weights up to 6912 are synthesized. The reaction sequence allows the preparation of these dendrimers at very large scales, whilst the availability of a simple purification in the sequence affords ultra-pure samples. The polypropylenimine dendrimers are fully characterized; apart from the first 0.5 generation they are all oils, possess a Tg in the range from −90 to −40 °C, are unexpectedly stable, and their intrinsic viscosity drops after generation 4.     

Modeling Geometric State for Fluids in Porous Media: Evolution of the Euler Characteristic

Multiphase flow in porous media is strongly influenced by the pore-scale arrangement of fluids. Reservoir-scale constitutive relationships capture these effects in a phenomenological way, relying only on fluid saturation to characterize the macroscopic behavior. Working toward a more rigorous framework, we make use of the fact that the momentary state of such a system is uniquely characterized by the geometry of the pore-scale fluid distribution. We consider how fluids evolve as they undergo topological changes induced by pore-scale displacement events. Changes to the topology of an object are fundamentally discrete events. We describe how discontinuities arise, characterize the possible topological transformations and analyze the associated source terms based on geometric evolution equations. Geometric evolution is shown to be hierarchical in nature, with a topological source term that constrains how a structure can evolve with time. The challenge associated with predicting topological changes is addressed by constructing a universal geometric state function that predicts the possible states based on a non-dimensional relationship with two degrees of freedom. The approach is validated using fluid configurations from both capillary and viscous regimes in ten different porous media with porosity between 0.10 and 0.38. We show that the non-dimensional relationship is independent of both the material type and flow regime. We demonstrate that the state function can be used to predict history-dependent behavior associated with the evolution of the Euler characteristic during two-fluid flow.

     

A feedback fluid queue with two congestion control thresholds

Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper we present and analyze a fluid queue with a feedback-based traffic rate adaptation scheme which uses two thresholds. The higher threshold B ₁ is used to signal the beginning of congestion while the lower threshold B ₂ signals the end of congestion. These two parameters together allow to make the trade-off between maximizing throughput performance and minimizing delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the traffic source. In our model the input source can behave like either of two Markov fluid processes. The first applies as long as the upper threshold B ₁ has not been hit from below. As soon as that happens, the traffic source adapts and switches to the second process, until B ₂ (smaller than B ₁) is hit from above. We analyze the model by setting up the Kolmogorov forward equations, then solving the corresponding balance equations using a spectral expansion, and finally identifying sufficient constraints to solve for the unknowns in the solution. In particular, our analysis yields expressions for the stationary distribution of the buffer occupancy, the buffer delay distribution, and the throughput.     

Sulfide determination in hydrothermal seawater samples using a vibrating gold micro-wire electrode in conjunction with stripping chronopotentiometry

A rapid electrochemical stripping chronopotentiometric procedure to determined sulfide in unaltered hydrothermal seawater samples is presented. Sulfide is deposited at −0.25 V (vs Ag/AgCl, KCl 3 M) at a vibrating gold microwire and then stripped through the application of a reductive constant current (typically −2 μA). The hydrodynamic conditions are modulated by vibration allowing a short deposition step, which is shown here to be necessary to minimize H₂S volatilization. The limit of detection (LOD) is 30 nM after a deposition step of 7 s. This LOD is in the same range as the most sensitive cathodic voltammetric technique using a mercury drop electrode and is well below those reported previously for other electrodes capable of being implemented in situ.     

The number of edges in a bipartite graph of given radius

Vizing established an upper bound on the size of a graph of given order and radius. We find a sharp upper bound on the size of a bipartite graph of given order and radius.     

Homoclinic Solutions for Swift-Hohenberg and Suspension Bridge Type Equations

We establish the existence of homoclinic solutions for a class of fourth-order equations which includes the Swift-Hohenberg model and the suspension bridge equation. In the first case, the nonlinearity has three zeros, corresponding to a double-well potential, while in the second case the nonlinearity is asymptotically constant on one side. The Swift-Hohenberg model is a higher-order extension of the classical Fisher-Kolmogorov model. Its more complicated dynamics give rise to further possibilities of pattern formation. The suspension bridge equation was studied by Chen and McKenna (J. Differential Equations136 (1997), 325-355); we give a positive answer to an open question raised by the authors.     

Correlated random networks

We develop a statistical theory of networks. A network is a set of vertices and links given by its adjacency matrix c, and the relevant statistical ensembles are defined in terms of a partition function Z= summation operator exp([-betaH(c)]. The simplest cases are uncorrelated random networks such as the well-known Erd?s-Rényi graphs. Here we study more general interactions H(c) which lead to correlations, for example, between the connectivities of adjacent vertices. In particular, such correlations occur in optimized networks described by partition functions in the limit beta--> infinity. They are argued to be a crucial signature of evolutionary design in biological networks.