Growth and long-run stability

This paper analyses the implications of persistent growth upon the stability properties of dynamic models. Besides the traditional concept of asymptotic stability, new stability criteria-strong/weak absolute, strong/weak relative, strong/weak logarithmic stability-are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow.     

Synthetic protocols and building blocks for molecular electronics

Simple and readily accessible aryl bromides are useful building blocks for thiol end-capped molecular wires. Thus, 4-bromophenyl tert-butyl sulfide and 1-bromo-4-(methoxymethyl)benzene serve as precursors for a variety of oligo(phenylenevinylene) and oligo(phenyleneethynylene) wires via efficient synthetic transformations as presented in this paper.     

Selective Halogen-Lithium Exchange Reaction of Bromine-Substituted 25,26,27,28-Tetrapropoxycalix[4]arene

Methods are described for the selective bromine-lithium exchange reaction of bromine-substituted calix[4]arenes with either n-BuLi or t-BuLi in THF. Quenching of the lithiated calix[4]arenes with MeOH, D(2)O, CH(3)SSCH(3), B(OCH(3))(3), DMF, or CO(2) as electrophiles resulted in 5-monosubstituted, 5,17-disubstituted, or 5,11,17,23-tetrasubstituted calix[4]arenes with H, D, SCH(3), B(OH)(2), CHO, or COOH functionalities.     

Mono‐ and Bis(pyrrolo)tetrathiafulvalene Derivatives Tethered to C60: Synthesis,Photophysical Studies,and Self‐Assembled Monolayers

A series of mono‐ (MPTTF) and bis(pyrrolo)tetrathiafulvalene (BPTTF) derivatives tethered to one or two C₆₀ moieties was synthesized and characterized. The synthetic strategy for these dumbbell‐shaped compounds was based on a 1,3‐dipolar cycloaddition reaction between aldehyde‐functionalized MPTTF/BPTTF derivatives, two different tailor‐made amino acids, and C₆₀. Electronic communication between the MPTTF/BPTTF units and the C₆₀ moieties was studied by a variety of techniques including cyclic voltammetry and absorption spectroscopy. These solution‐based studies indicated no observable electronic communication between the MPTTF/BPTTF units and the C₆₀ moieties. In addition, femtosecond and nanosecond transient absorption spectroscopy revealed, rather surprisingly, that no charge transfer from the MPTTF/BPTTF units to the C₆₀ moieties takes place on excitation of the fullerene moiety. Finally, it was shown that the MPTTF–C₆₀ and C₆₀–BPTTF‐C₆₀ dyad and triad molecules formed self‐assembled monolayers on a Au(111) surface by anchoring to C₆₀.     

Solar Thermal Energy Storage in a Photochromic Macrocycle

The conversion and efficient storage of solar energy is recognized to hold significant potential with regard to future energy solutions. Molecular solar thermal batteries based on photochromic systems exemplify one possible technology able to harness and apply this potential. Herein is described the synthesis of a macrocycle based on a dimer of the dihydroazulene/vinylheptafulvene (DHA/VHF) photo/thermal couple. By taking advantage of conformational strain, this DHA–DHA macrocycle presents an improved ability to absorb and store incident light energy in chemical bonds (VHF–VHF). A stepwise energy release over two sequential ring‐closing reactions (VHF→DHA) combines the advantages of an initially fast discharge, hypothetically addressing immediate energy consumption needs, followed by a slow process for consistent, long‐term use. This exemplifies another step forward in the molecular engineering and design of functional organic materials towards solar thermal energy storage and release.     

Tip splittings and phase transitions in the dielectric breakdown model: mapping to the diffusion-limited aggregation model

We show that the fractal growth described by the dielectric breakdown model exhibits a phase transition in the multifractal spectrum of the growth measure. The transition takes place because the tip splitting of branches forms a fixed angle. This angle is eta dependent but it can be rescaled onto an "effectively" universal angle of the diffusion-limited aggregation branching process. We derive an analytic rescaling relation which is in agreement with numerical simulations. The dimension of the clusters decreases linearly with the angle and the growth becomes non-ractal at an angle close to 74 degrees (which corresponds to eta = 4.0+/-0.3).     

Size of the light-emitting region in a sonoluminescing bubble

The size of the light-emitting region is a key parameter toward understanding the light-emitting processes in a sonoluminescing bubble. Here we present measurements of interference effects from particles with a diameter of approximately 2 microm situated 6-10 microm from a sonoluminescing bubble. From the angular size of the pattern and from an estimated distance to the particles we conclude that the light-emitting region of a sonoluminescing bubble is smaller than commonly believed [see, e.g., Nature (London) 398, 402 (1999)]. We argue that an upper limit of the size of the light-emitting region is approximately 200 nm.     

New air-stable planar chiral ferrocenyl monophosphine ligands: Suzuki cross-coupling of aryl chlorides and bromides

[reaction: see text] A novel class of planar chiral electron-rich monophosphine ligands has been developed. The modular design allows a short and efficient synthesis of an array of aryl-ferrocenyl derivatives carrying the donating bis(dicyclohexyl)phosphino moiety. These new ligands have successfully been applied in the palladium-catalyzed Suzuki cross-coupling of activated as well as nonactivated aryl chlorides at room temperature. The asymmetric coupling of an aryl bromide and an aryl boronic acid was also tested, giving ees up to 54%.