Levy area for the free Brownian motion: existence and non-existence

This note extends the work of Capitaine (J. Funct. Anal. 179 (1) (2001) 153) on the Levy area process for the free Brownian motion in two directions. First, we reprove that a Levy area for the Free Brownian motion exists in the Von Neumann tensor product, by exhibiting a non-commutative Burkholder-Davis-Gundy type inequality. Then, we show that there does not exist a Levy area in the projective tensor product.     

Metallo‐supramolecular micelles: Studies by analytical ultracentrifugation and electron microscopy

In aqueous solutions, amphiphilic block copolymers in which a polystyrene (PS) segment is connected to a poly(ethylene oxide) (PEO) block via a bis(2,2′:6′,2″‐ terpyridine ruthenium) complex can form micelles. Such micelles of the protomer type PS₂₀‐[Ru]‐PEO₇₀, according to the preparation procedure representing frozen micelles, were studied by sedimentation velocity and sedimentation equilibrium analysis in an analytical ultracentrifuge and by transmission electron microscopy, with different techniques applied for the sample preparation. The particles obtained were surprisingly multifarious in size. In ultracentrifugation experiments performed at relatively low salt concentrations, the distributions of the sedimentation coefficient s_20,w showed a pronounced peak at 9.6 S and a broad, only partly separated second peak around 14 S. The molar mass of the particles at the peak was around 430,000 g/mol, corresponding to an aggregation number of approximately 85. The average hydrodynamic diameter of the particles in the peak fraction was approximately 13 nm. In electron micrographs of negatively stained samples, spheres of diameters between 10 and 25 nm were the most abundant particles, but larger ones with a wide size range were also visible. The latter particles apparently were composed of smaller ones. The data from both sedimentation analysis and electron microscopy showed that (1) the studied compound formed primary micelles of diameters around 20 nm and (2) the primary micelles had a tendency toward aggregation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3159–3168, 2003     

Block copolymers of acrylic acid and butyl acrylate prepared by reversible addition–fragmentation chain transfer polymerization: Synthesis,characterization, and use in emulsion polymerization

Amphiphilic block copolymers of poly(acrylic acid‐b‐butyl acrylate) were prepared by reversible addition–fragmentation chain transfer polymerization in a one‐pot reaction. These copolymers were characterized by NMR, static and dynamic light scattering, tensiometry, and size exclusion chromatography. The aggregation characteristics of the copolymers corresponded to those theoretically predicted for a star micelle. In a butyl acrylate and methyl methacrylate emulsion polymerization, low amounts of these copolymers could stabilize latices with solid contents up to 50%. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 684–698, 2003     

Multiscale variety in complex systems

The Law of Requisite Variety is a mathematical theorem relating the number of control states of a system to the number of variations in control that is necessary for effective response. The Law of Requisite Variety does not consider the components of a system and how they must act together to respond effectively. Here we consider the additional requirement of scale of response and the effect of coordinated versus uncoordinated response as a key attribute of complex systems. The components of a system perform a task, with a number of such components needed to act in concert to perform subtasks. We apply the resulting generalization—a Multiscale Law of Requisite Variety—to understanding effective function of complex biological and social systems. This allows us to formalize an understanding of the limitations of hierarchical control structures and the inadequacy of central control and planning in the solution of many complex social problems and the functioning of complex social organizations, e.g., the military, healthcare, and education systems. © 2004 Wiley Periodicals, Inc. Complexity 9: 37–45, 2004     

Bounds for non‐periodic mixtures of infinitely many materials

We prove bounds on the homogenized coefficients for general non‐periodic mixtures of an arbitrary number of isotropic materials, in the heat conduction framework. The component materials and their proportions are given through the Young measure associated to the sequence of coefficient functions. Upper and lower bounds inequalities are deduced in terms of algebraic relations between this Young measure and the eigenvalues of the H‐limit matrix. The proofs employ arguments of compensated compactness and fine properties of Young measures. When restricted to the periodic case, we recover known bounds. Copyright © 2005 John Wiley & Sons, Ltd.     

Sound propagation in the atmospheric surface layer: Comparison of experiment with FFP predictions

This paper presents a set of acoustical and meteorological data from an outdoor sound propagation experiment. This experiment was done in a farm field near Rock Springs, Pennsylvania, on 7 July 1990. Meteorological and acoustical measurements were recorded simultaneously during six different times in the day. The meteorological measurements permitted determination of the sound speed profiles during each of the measurement sessions, using a method based on surface-layer similarity scaling. The acoustical measurements allowed precise determination of the relative sound pressure levels for a frequency range up to 3150 Hz at six different distances (66, 88, 125, 175, 250 and 350 m). The results show atmospheric conditions have an important effect on sound propagation. At medium and high frequencies, variations of the relative SPL have been measured at distances as short as 62 m. These effects increased with the distances so that variations as great as 30 dB have been measured during that day. Comparisons with the fast field program predictions are also presented, and amply demonstrate the accuracies of this model, especially for the downward refraction cases.