Equilibrium thermodynamics and thermodynamic processes in nonlinear systems

A general method for the calculation of thermodynamic quasi-equilibrium processes by molecular dynamics (MD) simulation in canonical ensemble is developed. The method is suitable for classical systems with arbitrary interaction potentials. Though this MD method does not allow to calculate directly partition function and entropy, it is possible to calculate necessary partial derivatives which enter into the expressions for the full derivatives dT/dV and d β/dV for adiabitic and isobaric processes. Namely the solutions of these ordinary differential equations define the corresponding thermodynamic processes. The adiabatic process for the 1D Toda lattice is analyzed in details. The usage of the Toda potential allows to perform all analytical calculus up to accurate answers and to compare numerical and analytical results. Exact analytical expressions for the thermodynamics of 1D lattices with few types of nearest neighbor interactions are obtained as a necessary interim solutions. MD-simulation of quasi equilibrium processes in canonical ensemble demands the achievement of thermodynamic equilibrium, thus the thermalization kinetics is briefly discussed.     

Poincaré series and monodromy of the simple and unimodal boundary singularities

A boundary singularity is a singularity of a function on a manifold with boundary. The simple and unimodal boundary singularities were classified by V.I. Arnold and V.I. Matov. The McKay correspondence can be generalized to the simple boundary singularities. We consider the monodromy of the simple, parabolic, and exceptional unimodal boundary singularities. We show that the characteristic polynomial of the monodromy is related to the Poincaré series of the coordinate algebra of the ambient singularity.     

Aromatic Xanthates and Dithiocarbamates for the Polymerization of Ethylene through Reversible Addition–Fragmentation Chain Transfer (RAFT)

Aromatic xanthates and dithiocarbamates were used as chain‐transfer agents (CTAs) in reversible addition–fragmentation chain‐transfer (RAFT) polymerizations of ethylene under milder conditions (≤80 °C, ≤200 bar). While detrimental side fragmentation of the intermediate radical leading to loss of living chain‐ends was observed before with alkyl xanthate CTAs, this was absent for the aromatic CTAs. The loss of living chain‐ends was nevertheless detected for the aromatic xanthates via a different mechanism based on cross‐termination. Narrow molar‐mass distributions with dispersities between 1.2 and 1.3 were still obtained up to number average molar masses M_n of 1000 g mol^?1. The loss of chain‐ends was minor for dithiocarbamates, yielding polyethylene up to M_n=3000 g mol^?1 with dispersities between 1.4 and 1.8. While systems investigated showed significant rate retardation, the dithiocarbamates are the first CTAs giving polyethylene with a high livingness via RAFT polymerization.     

Quantenstatistik des Hochtemperatur-Plasmas im thermodynamischen Gleichgewicht

High temperature plasmas are investigated on the basis of quantum theory. A new method for the calculation of the thermodynamic properties is developed. According to the method of Morita effective potentials are introduced. They permit the evaluation of the partition function with the well-known formalism of classical statistical mechanics. The first corrections added to Debye's limiting law of the free energy are expressed by the two particle Slater sum S₂(r). A Bloch equation for S₂(r) is derived and is solved in the Fourier representation by a development according to the interaction parameter ζ = e²/kTλ, λ being the thermal wavelength. The effects of symmetry are taken into account. The free energy is calculated explicitely up to the order of ζ². In the case of small concentrations our results agrees with that derived by Trubnikow and Elesin. Effects of symmetry neglected, up to the order of ζ² the formula of DeWitt is obtained.     

Radial Index and Euler Obstruction of a 1-Form on a Singular Variety

A notion of the radial index of an isolated singular point of a 1-form on a singular (real or complex) variety is discussed. For the differential of a function it is related to the Euler characteristic of the Milnor fibre of the function. A connection between the radial index and the local Euler obstruction of a 1-form is described. This gives an expression for the local Euler obstruction of the differential of a function in terms of Euler characteristics of some Milnor fibres.Mathematics Subject Classifications (2000). 14B05, 32S60, 58A10*Partially supported by the DFG-programme “Global methods in complex geometry” (Eb 102/4–2), grants RFBR–04–01–00762, NSh–1972.2003.1     

Stochastic Theory of Nucleation in Nonequilibrium Bistable Reaction Systems

Nucleation is one of the fundamental types of forming stable dissipative nonequilibrium structures in metastable initial states. The nucleation process of a bistable chemical reaction system is investigated. First a microdroplet with radius R₀ of the new state imbedded in the parent one is formed by a local particle number fluctuation. The radius of the microdroplet R(t) fluctuates due to the interference of reaction and diffusion. If R(t) considerably exceeds a critical value R_k the droplet starts to grow deterministically. The mean nucleation time of one droplet in weakly supersaturated systems is calculated using the concept of the mean first passage time.     

Chloropalladated propargyl amine: a highly efficient phosphine-free catalyst precursor for the Heck reaction

[reaction: see text] The palladacycle (Pd[k(1)-C, k(1)-N-C=(C(6)H(5))C(Cl)CH(2)NMe(2)](mu-Cl))(2) 1 derived from the chloropalladation of 3-(dimethylamino)-1-phenyl-1-propyne promotes the arylation of olefins under relatively mild reaction conditions. The coupling of iodoarenes and activated bromoarenes with n-butylacrylate and styrene occurs at room temperature. Turnover numbers of up to 85 000 have been achieved with deactivated bromoarenes and up to 1000 for activated chloroarenes at higher temperatures (80-150 degrees C).