Patchy worm-like micelles: solution structure studied by small-angle neutron scattering

Triblock terpolymers exhibit a rich self-organization behavior including the formation of fascinating cylindrical core-shell structures with a phase separated corona. After crystallization-induced self-assembly of polystyrene-block-polyethylene-block-poly(methyl methacrylate) triblock terpolymers (abbreviated as SEMs = Styrene-Ethylene-Methacrylates) from solution, worm-like core-shell micelles with a patchy corona of polystyrene and poly(methyl methacrylate) were observed by transmission electron microscopy. However, the solution structure is still a matter of debate. Here, we present a method to distinguish in situ between a Janus-type (two faced) and a patchy (multiple compartments) configuration of the corona. To discriminate between both models the scattering intensity must be determined mainly by one corona compartment. Contrast variation in small-angle neutron scattering enables us to focus on one compartment of the worm-like micelles. The results validate the existence of the patchy structure also in solution.     

Nonholonomic Mechanical Systems and Kaluza–Klein Theory

In the first part of the paper we present a new point of view on the geometry of nonholonomic mechanical systems with linear and affine constraints. The main geometric object of the paper is the nonholonomic connection on the distribution of constraints. By using this connection and adapted frame fields, we obtain the Newton forms of Lagrange–d’Alembert equations for nonholonomic mechanical systems with linear and affine constraints. In the second part of the paper, we show that the Kaluza–Klein theory is best presented and explained by using the framework of nonholonomic mechanical systems. We show that the geodesics of the Kaluza–Klein space, which are tangent to the electromagnetic distribution, coincide with the solutions of Lagrange–d’Alembert equations for a nonholonomic mechanical system with linear constraints, and their projections on the spacetime are the geodesics from general relativity. Any other geodesic of the Kaluza–Klein space that is not tangent to the electromagnetic distribution is also a solution of Lagrange–d’Alembert equations, but for affine constraints. In particular, some of these geodesics project exactly on the solutions of the Lorentz force equations of the spacetime.     

Synthesis and physico-chemical properties of a novel series of aromatic electron acceptors based on N-heterocycles

The synthesis of a novel series of N-based heterocyclic salts using a simple and efficient N-alkylation of 1,2-bis(4-pyridyl)ethane with reactive halides is reported. These compounds can be transformed into the corresponding pyridinium methylides by addition of a base. The former exhibit an unstable absorption bands at 395–410 nm. The structures of the salts were fully characterized by UV–vis, IR, NMR and MS spectroscopy and elemental analysis. The pK values of selected compounds were also determined and the acid–basic equilibrium was investigated by UV–vis spectrophotometry. The thermal stability of all species was determined by thermogravimetric analysis.     

Viability property for a backward stochastic differential equation and applications to partial differential equations

In the present paper, we study conditions under which the solutions of a backward stochastic differential equation remains in a given set of constraints. This property is the so-called “viability property”. In a separate section, this condition is translated to a class of partial differential equations. Received: 23 April 1998 / Published online: 14 February 2000     

A self-compensating optical delay stage

Using a retro-reflecting prism and a mirror to form a two-fold optical delay yields very useful characteristics: long optical delay, self-compensation for deviations of the motion of the delay stage, easy adjustment and no influence on polarization of the beam. Such a delay stage is described, and the advantages of the set-up explained.     

Temperature dependence of the single-particle spectrum in sodium clusters

We show that the electronic density of states of small sodium clusters is strongly affected by both thermal fluctuations about the ground state ionic configuration and transitions between different shape isomers as the temperature of the cluster is increased. Contrary to common expectations, the clusters undergo a sharp transition in the temperature range of 100K to 150 K, after which the single-particle level distributions become bimodal. At even higher temperatures the signature of the ground state configuration disappears, and the density of states is dominated by higher energy isomers. We also discuss the implications of these findings for the interpretation of the photoelectron spectra of these systems.     

Martin compactification for discrete potential theory and the mean value property

A converse of the well-known theorem on themean value property of harmonic functions is given. It is shown that a positive measurable function is harmonic if it possesses arestricted mean value property. Earlier proofs obtained using the probabilistic techniques were given by Veech, Heath and Baxter. Our approach is based on a Martin type compactification built up with the help of some quite elementarya priori inequalities foraveraging kernels.     

The effect of delayed feedback information on network performance

The performance of a network subject to either state dependent or state independent flow control is investigated. In the state dependent case, the flow control policy is a function of the total number of packets for which the controller has not yet received an acknowledgment. In this case it is shown that the optimal flow control is a sliding window mechanism. The effect of the delayed feedback on the network performance as well as the size of the window are studied. The state independent optimal rate is also derived. The performance of the state dependent and state independent flow control policies are compared. Conditions for employing one of the two types of flow control policies for superior end-to-end network performance are discussed. All the results obtained are demonstrated using simple examples.