Shape dependence of correlation times in chaos-induced diffusion

A one-dimensional discrete-time chaotic system generating a diffusive process with strong correlations between successive steps is considered, as realized in brownian motion with directional persistence (observed e.g. for the motion of infusoriae). The resulting intermittency-like behavior without $\text{1}\text{?}$ spectrum may be found in many nonlinear systems with two metastable states.     

Diffusion and trapping on a nested fractal structure

We consider the spreading of an ensemble of phase points on a nested hierarchy of levels whose spatial extension scales self-similar. In order to model turbulent pair separation, a deterministic dynamical law is defined that maps a given scale to all (infinitely many) smaller scales and also to the next larger scale. The model can be solved analytically. We find anomalous diffusion (exponential increase of the variance) or trapping (finite limiting value of low order moments) depending on the dominance of level-up or level-down mapping.Supported in part by the Deutsche Forschungsgemeinschaft through Sonderforschungsbereich 123 Statistical Mathematical Models     

Trajectory based non-markovian dissipative tunneling

The influence of a dissipative environment on scattering of a particle by a barrier is investigated by using the recently introduced bohmian mechanics with complex action [J. Chem. Phys. 125, 231103 (2006)]. An extension of this complex trajectory based formalism to include the interaction of the tunneling particle with an environment of harmonic oscillators with a continuous spectral density and at a certain finite temperature allows us to calculate transmission probabilities beyond the weak system bath coupling regime. The results display an increasing tunneling probability for energies below the barrier and a decreased transmission above the barrier due to the coupling. Furthermore, we demonstrate that solutions of a markovian master equation fail to do so in general.     

Using regularization and second order information in outer approximation for convex MINLP

Mathematical Programming - In this paper, we present two new methods for solving convex mixed-integer nonlinear programming problems based on the outer approximation method. The first method is...     

Comparison principles applied to obstacle problems with penalties

Penalty methods form a well known technique to embed elliptic variational inequality problems into a family of variational equations (cf. [6], [13], [17]). Using the specific inverse monotonicity properties of these problems L _∞-bounds for the convergence can be derived by means of comparison solutions. Lagrange duality is applied to estimate parameters involved.

For piecewise linear finite elements applied on weakly acute triangulations in combination with mass lumping the inverse monotonicity of the obstacle problems can be transferred to its discretization. This forms the base of similar error estimations in the maximum norm for the penalty method applied to the discrete problem.

The technique of comparison solutions combined with the uniform boundedness of the Lagrange multipliers leads to decoupled convergence estimations with respect to the discretization and penalization parameters.     

Ring-expansion approaches for the total synthesis of salimabromide

We describe the evolution of a synthetic strategy for the construction of the marine polyketide salimabromide. Combining a bicyclo[3.1.0]hexan-2-one ring-expansion to build up a functionalized naphthalene and an unprecedented rearrangement/cyclization cascade, enabled synthesis of a dearomatized tricyclic subunit of the target compound. Alternatively, an intramolecular keteniminium [2 + 2]-cycloaddition and subsequent Baeyer–Villiger ring-expansion gave access to the sterically encumbered architecture of salimabromide. Sequential oxidation of the carbon framework finally enabled the total synthesis of this unusual natural product.     

Competitive Metal Coordination of Hexaaminotriphenylene on Cu(111) by Intrinsic Copper Versus Extrinsic Nickel Adatoms

The interplay between the self-assembly and surface chemistry of 2,3,6,7,10,11-hexaaminotriphenylene (HATP) on Cu(111) was complementarily studied by high-resolution scanning tunneling microscopy (STM) and X-ray photoelectron spectroscopy (XPS) under ultra-high vacuum conditions. To shed light on the competitive metal coordination, comparative experiments were carried out on pristine and nickel-covered Cu(111). Directly after room-temperature deposition of HATP onto pristine Cu(111), self-assembled aggregates were observed by STM, and XPS results indicated still protonated amino groups. Annealing up to 200 °C activated the progressive single deprotonation of all amino groups as indicated by chemical shifts of both the N 1s and C 1s core levels in the XP spectra. This enabled the formation of topologically diverse π–d conjugated coordination networks with intrinsic copper adatoms. The basic motif of these networks was a metal–organic trimer, in which three HATP molecules were coordinated by Cu₃ clusters, as corroborated by the accompanying density functional theory (DFT) simulations. Additional deposition of more reactive nickel atoms resulted in both chemical and structural changes with deprotonation and formation of bis(diimino)–Ni bonded networks already at room temperature. Even though fused hexagonal metal-coordinated pores were observed, extended honeycomb networks remained elusive, as tentatively explained by the restricted reversibility of these metal–organic bonds.     

Optimizing control of simulated moving bed separations of mixtures subject to the generalized Langmuir isotherm

Simulated moving bed (SMB) is a cost-efficient separation technique that offers high productivity and low solvent consumption. SMB has gained importance in the pharmaceutical and fine chemical industry to perform complex separation tasks. However, an open and challenging problem is the optimal, robust operation of the SMB process. We have developed a control scheme that integrates the optimization and control of the SMB unit. A significant feature of the controller is that only minimal information of the system has to be provided, i.e. the linear adsorption behavior of the mixture to be separated and the average void fraction of the columns. Therefore, a full characterization of the adsorption behavior of the mixture and the columns is no longer required. In this ‘cycle to cycle’ control scheme, the measurements, optimization and control actions are performed once in every cycle. This paper presents simulation results of the control scheme applied to the separation of binary mixtures characterized by generalized Langmuir isotherms. The results are presented and analyzed in the frame of the triangle theory that has been recently extended to encompass these types of isotherms. Besides, online optimum performance of the SMB unit is compared with off-line optimization carried out using genetic algorithm. The results show that the controller fulfills the product and process specifications while operating the SMB unit optimally, regardless of the different types of Langmuir isotherms that the systems exhibit.     

The synthesis of azadirachtin: a potent insect antifeedant

We describe in full the first synthesis of the potent insect antifeedant azadirachtin through a highly convergent approach. An O-alkylation reaction is used to unite decalin ketone and propargylic mesylate fragments, after which a Claisen rearrangement constructs the central C8-C14 bond in a stereoselective fashion. The allene which results from this sequence then enables a second critical carbon-carbon bond forming event whereby the [3.2.1] bicyclic system, present in the natural product, is generated via a 5-exo-radical cyclisation process. Finally, using knowledge gained through our early studies into the reactivity of the natural product, a series of carefully designed steps completes the synthesis of this challenging molecule.