A Single Thermoresponsive Diblock Copolymer Can Form Spheres,Worms or Vesicles in Aqueous Solution

It is well‐known that the self‐assembly of AB diblock copolymers in solution can produce various morphologies depending on the relative volume fraction of each block. Recently, polymerization‐induced self‐assembly (PISA) has become widely recognized as a powerful platform technology for the rational design and efficient synthesis of a wide range of block copolymer nano‐objects. In this study, PISA is used to prepare a new thermoresponsive poly(N‐(2‐hydroxypropyl) methacrylamide)‐poly(2‐hydroxypropyl methacrylate) [PHPMAC‐PHPMA] diblock copolymer. Remarkably, TEM, rheology and SAXS studies indicate that a single copolymer composition can form well‐defined spheres (4 °C), worms (22 °C) or vesicles (50 °C) in aqueous solution. Given that the two monomer repeat units have almost identical chemical structures, this system is particularly well‐suited to theoretical analysis. Self‐consistent mean field theory suggests this rich self‐assembly behavior is the result of the greater degree of hydration of the PHPMA block at lower temperature, which is in agreement with variable temperature ¹H NMR studies.     

Uncertainty and stepwise investment

We analyze the optimal investment strategy of a firm that can complete a project either in one stage at a single freely chosen time point or in incremental steps at distinct time points. The presence of economies of scale gives rise to the following trade-off: lumpy investment has a lower total cost, but stepwise investment gives more flexibility by letting the firm choose the timing individually for each stage. Our main question is how uncertainty in market development affects this trade-off. The answer is unambiguous and in contrast with a conventional real-options intuition: higher uncertainty makes the single-stage investment more attractive relative to the more flexible stepwise investment strategy.     

Capital Accumulation and Embodied Technological Progress

This paper combines technology adoption with capital accumulation taking into account technological progress. We model this as a multi-stage optimal control problem and solve it using the corresponding maximum principle. The model with linear revenue can be solved analytically, while the model with market power is solved numerically. We obtain that investment jumps upwards right at the moment that a new technology is adopted. We find that, if the firm has market power, the firm cuts down on investment before a new technology is adopted. Furthermore, we find that larger firms adopt a new technology later.     

The Flooding Time in Random Graphs

Based on our analysis of the hopcount of the shortest path between two arbitrary nodes in the class G _p (N) of random graphs, the corresponding flooding time is investigated. The flooding time T _N (p) is the minimum time needed to reach all other nodes from one node. We show that, after scaling, the flooding time T _N (p) converges in distribution to the two-fold convolution ^(2*) of the Gumbel distribution function (z)=exp (–e ^–z ), when the link density p _N satisfies Np _N /(log N)³ if N .     

Construction of the Incipient Infinite Cluster for Spread-out Oriented Percolation Above 4 + 1 Dimensions

 We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ ^d × ℤ₊, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ ⁿ (E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n)  ℤ ^d × ℤ₊, summing this probability over x  ℤ ^d , and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ_∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n ⁻¹, we prove existence of a limiting measure ℚ_∞, with ℚ_∞ = ℙ_∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension of the cluster of the origin, under ℙ_∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented percolation to super-Brownian motion, for d+1 > 4+1. Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002 RID="*" ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl     

Integrated optical cross strip polarizer concept

Passing across an abrupt junction from a thick vertically bimodal waveguide to a thinner single mode segment, guided light can undergo complete destructive interference, provided that the geometry and the phases of the modes in the initial segment are properly adjusted. We propose to employ this effect to realize a simple polarizer configuration, using a strip that is etched from a planar waveguide. A beam of light is made to pass the strip perpendicularly. The light enters from the single mode waveguide outside the strip into the strip segment, which is configured to support two modes. At the end of the strip, apart from reflections, the amount of power that is guided in the following lower segment depends on the local phases of the two modes. These phases are different for TE and TM light, hence we may expect a polarization dependent power transfer, resulting in polarizer performance for a properly selected geometry. The paper describes in detail the modeling of the device in terms of rigorous mode expansion. Design guidelines and tolerance requirements for geometric and material parameters are discussed. For typical Si₃N₄/SiO₂ materials, our calculations predict a peak performance of 34 dB polarization discrimination and 0.3 dB insertion loss for a device with a total length of about 12 m that selects TE polarization at a wavelength of 1.3 m.     

Comment on “Theoretical studies on the ground states in [M(terpyridine)2] and [M(4-(4-(t-butyl)phenyl)terpyridine)2] (M = Fe, Ru, Os) and excited states in [Ru(terpyridine)2] using density functional theory”

The nature of the first excited state of [Fe(terpyridine)₂]²⁺ has been reinvestigated. In contrast to previous findings, it is metal-to-ligand charge transfer in nature, thus fitting in the series of the Ru and Os complexes.     

Geometry and Forces in Relativistic and Pre-Relativistic Theories

It has been shown elsewhere that in the case of relativistic theories, there exists a local differential-topological criterion which distinguishes sharply between geometry and forces. This criterion is also epistemologically effective. In this paper, we explain why this local criterion fails in the pre-relativistic context. The principal reason for the difference is that the causal structure is determined by a quadratic function of 3-velocity in the relativistic case and by a linear function of 3-velocity in the pre-relativistic case.