Two Connections Between Random Systems and Non-Gibbsian Measures

In this contribution we discuss the role disordered (or random) systems have played in the study of non-Gibbsian measures. This role has two main aspects, the distinction between which has not always been fully clear: 1) From disordered systems: Disordered systems can be used as a tool; analogies with, as well as results and methods from the study of random systems can be employed to investigate non-Gibbsian properties of a variety of measures of physical and mathematical interest. 2) Of disordered systems: Non-Gibbsianness is a property of various (joint) measures describing quenched disordered systems. We discuss and review this distinction and a number of results related to these issues. Moreover, we discuss the mean-field version of the non-Gibbsian property, and present some ideas how a Kac limit approach might connect the finite-range and the mean-field non-Gibbsian properties.     

Thermal decomposition of trimethylgallium Ga(CH3)3: a shock-tube study and first-principles calculations

The thermal decomposition of Ga(CH3)3 has been studied both experimentally in shock-heated gases and theoretically within an ab-initio framework. Experiments for pressures ranging from 0.3 to 4 bar were performed in a shock tube equipped with atomic resonance absorption spectroscopy (ARAS) for Ga atoms at 403.3 nm. Time-resolved measurements of Ga atom concentrations were conducted behind incident waves as well as behind reflected shock waves at temperatures between 1210 and 1630 K. The temporal variation in Ga-atom concentration was described by a reaction mechanism involving the successive abstraction of methyl radicals from Ga(CH3)3 (R1), Ga(CH3)2 (R2), and GaCH3 (R3), respectively, where the last reaction is the rate-limiting step leading to Ga-atom formation. The rate constant of this reaction (R3) was deduced from a simulation of the measured Ga-atom concentration profiles using thermochemical data from ab-initio calculations for the reactions R1 and R2 as input. The Rice-Ramsperger-Kassel-Marcus (RRKM) method including variational transition state theory was applied for reaction R3 assuming a loose transition state. Structural parameters and vibrational frequencies of the reactant and transition state required for the RRKM calculations were obtained from first-principles simulations. The energy barrier E3(0) of reaction R3, which is the most sensitive parameter in the calculation, was adjusted until the RRKM rate constant matched the experimental one and was found to be E(0) = 288 kJ/mol. This value is in a good agreement with the corresponding ab-initio value of 266 kJ/mol. The rate constant of reaction R3 was found to be k 3/(cm(3) mol(-1)s(-1)) = 2.34 x 10(11) exp[-23330(K/ T)].     

Synthesis of fluorescent oligonucleotide--EYFP conjugate: towards supramolecular construction of semisynthetic biomolecular antennae

A novel species of DNA--protein conjugate was synthesized by chemically linking DNA oligonucleotides to Aequorea victoria green fluorescent protein mutant EYFP. An additional cysteine was added to the C-terminus of the EYFP by genetic engineering and used to covalently attach amino-modified oligonucleotide with the aid of the heterobifunctional crosslinker sSMCC. EYFP maintained its fluorescence upon conjugation. The oligonucleotide provides an additional binding site to the fluorescent protein, and hence, the EYFP conjugate could be specifically hybridized with both complementary DNA-protein conjugates in-solution as well as immobilized at capture oligonucleotides attached to a solid substrate. These studies are paving the way for future applications in the self-assembly of photoactive supramolecular complexes, such as artificial light-harvesting systems.     

Ab initio molecular dynamics simulation of a medium-sized water cluster anion: from an interior to a surface-located excess electron via a delocalized state

We present a computational study of the structure and dynamics of an excess electron in a medium-sized water cluster aimed at addressing the question of interior vs exterior solvation. Ab initio Born-Oppenheimer molecular dynamics simulations were performed within the DFT framework, employing a hybrid Gaussian and plane-wave formalism together with the PBE exchange-correlation functional and norm-conserving pseudopotentials. Analysis of a 15-ps trajectory allowed us to reach the following conclusions: (i) the excess electron is predominantly located at the cluster surface (even if it is initially placed in the interior), (ii) the computed electron binding energies correlate with the electron localization rather than with its bulk vs surface location, and (iii) a dynamical interconversion between two different H-bond patterns around the electron occurs. The computed electron binding energies and the most relevant features of the IR spectrum are in a very good agreement with results of previous experimental studies.     

Growth Mechanism of Metal–Organic Frameworks: Insights into the Nucleation by Employing a Step‐by‐Step Route

One step at a time : The in situ monitoring of the step‐by‐step formation of metal–organic frameworks (MOFs) by using surface plasmon resonance (SPR), allows the nucleation process and the formation of the secondary building units to be investigated. Growth rates on functionalized organic surfaces with different crystallographic orientations can also be studied.

     

Post-synthetic modification of epitaxially grown, highly oriented functionalized MOF thin films

Thin films of MOFs grown on solid substrates offer a huge potential with regard to tailoring the properties of a surface, in particular if used in connection with post-synthesis modification (PSM). Here, we report on the PSM of surface-supported crystalline MOFs, with target molecules using an amine-based coupling strategy.     

Illustration of transition path theory on a collection of simple examples

Transition path theory (TPT) has been recently introduced as a theoretical framework to describe the reaction pathways of rare events between long lived states in complex systems. TPT gives detailed statistical information about the reactive trajectories involved in these rare events, which are beyond the realm of transition state theory or transition path sampling. In this paper the TPT approach is outlined, its distinction from other approaches is discussed, and, most importantly, the main insights and objects provided by TPT are illustrated in detail via a series of low dimensional test problems.     

Logarithmic lower bounds for Néel walls

Most mathematical models for interfaces and transition layers in materials science exhibit sharply localized and rapidly decaying transition profiles. We show that this behavior can largely change when non-local interactions dominate and internal length scales fail to be determined by dimensional analysis: we consider a reduced model for Néel walls, micromagnetic transition layers which are observed in a suitable thin-film regime. The typical phenomenon associated with this wall type is the very long logarithmic tail of transition profiles. Recently, we derived logarithmic upper bounds. Here, we prove that the latter result is indeed optimal. In particular, we show that Néel wall profiles are supported by explicitly known comparison profiles that minimize relaxed variational principles and exhibit logarithmic decay behavior. This lower bound is established by a comparison argument based on a global maximum principle for the non-local field operator and the qualitative decay behavior of comparison profiles.Received: 17 June 2003, Accepted: 18 November 2003, Published online: 25 February 2004Mathematics Subject Classification (2000): 78A30, 49S05, 45G15, 35B25     

Scattering spherical voids in nanocrystalline TiO2- enhancement of efficiency in dye-sensitized solar cells

Spherical voids as light scattering centers in nanocrystalline TiO2 films were realized with polystyrene particles of diameter 400 nm, thus enhancing the photovoltaic performance by 25% on large areas, as well as providing an indication that these films can be used with electrolytes of higher viscosity.