Multilevel frames for sparse tensor product spaces

For Au = f with an elliptic differential operator and stochastic data f, the m-point correlation function of the random solution u satisfies a deterministic equation with the m-fold tensor product operator A ^(m) of A. Sparse tensor products of hierarchic FE-spaces in are known to allow for approximations to which converge at essentially the rate as in the case m = 1, i.e. for the deterministic problem. They can be realized by wavelet-type FE bases (von Petersdorff and Schwab in Appl Math 51(2):145–180, 2006; Schwab and Todor in Computing 71:43–63, 2003). If wavelet bases are not available, we show here how to achieve the fast computation of sparse approximations of for Galerkin discretizations of A by multilevel frames such as BPX or other multilevel preconditioners of any standard FEM approximation for A. Numerical examples illustrate feasibility and scope of the method.     

Ephedrine-based diselenide: a promiscuous catalyst suitable to mimic the enzyme glutathione peroxidase (GPx) and to promote enantioselective C-C coupling reactions

The ephedrine-based diselenide appears as a new promiscuous catalyst, able to generate optically active alcohols by addition of organozinc to aldehydes (up to 97% ee), and shows powerful GPx like activity, reducing H(2)O(2) to water in only 16.33 min (eleven times faster than PhSeSePh).     

hp‐FEM for second moments of elliptic PDEs with stochastic data. I. Analytic regularity

For a linear second order elliptic partial differential operator A : V → V′, we consider the boundary value problems Au = f with stationary Gaussian random data f over the dual V′ of the separable Hilbert space V in which the solution u is sought. The operator A is assumed to be deterministic and bijective. The unique solution u = A^?1f is a Gaussian random field over V. It is characterized by its mean field E_u and its covariance C_u ∈ V ? V. For a class of Gaussian data f with piecewise analytic covariance kernels C_f ∈ V′ ? V′, we characterize analytic regularity of the covariance C_u of the Gaussian solution u in families of countably normed, weighted Sobolev spaces. To this end, we investigate shift theorems for the (nonhypoelliptic) deterministic tensor PDEs (A ? A)C_u = C_f proposed by Schwab and Todor, (Numer Math 95 (2003), 707–734) for the computation of covariance C_u of the random solution u. The nonhypoelliptic nature of A ? A implies that sing supp(C_u) is in general strictly larger than sing supp(C_f). For a model problem, analyticity and singular support of the solution is characterized completely. Based on our regularity results, we outline an hp‐finite element strategy (Pentenrieder, Ph.D thesis, ETHZurich, Dissertation No. 18729, 2009; Pentenrieder and Schwab, Research Report 2010‐08, Seminar for Applied Mathematics, ETH Zürich, Submitted) to approximate C_u stemming from covariances of stationary Gaussian data f. In the second part (Pentenrieder and Schwab, Research Report 2010–08, Seminar for Applied Mathematics, ETH Zürich, Submitted) of this work, we prove that this discretization gives exponential rates of convergence of the FE approximations, in terms of the number of degrees of freedom. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012     

In-medium effects on phase space distributions of antikaons measured in proton-nucleus collisions

Differential production cross sections of K+/- mesons have been measured in p + C and p + Au collisions at 1.6, 2.5, and 3.5 GeV proton beam energy. At beam energies close to the production threshold, the K- multiplicity is strongly enhanced with respect to proton-proton collisions. According to microscopic transport calculations, this enhancement is caused by two effects: the strangeness exchange reaction NY --> K- NN and an attractive in-medium K- N potential at saturation density.     

p-Carborane: a new cage spacer for photoactive metal polypyridine dyads

The first example of a binuclear ruthenium complex involving the p-carborane framework in the bridging ligand is reported. The bridging ligand is a symmetric linear array comprising a central p-carborane unit, two p-phenylene spacers, and two 5-yl-2,2'-bipyridine coordinating units. A homobinuclear Ru(II) complex, with 2,2'-bipyridine as peripheral ligands, was synthesized and characterized. The Ru(II)-Ru(III) mixed-valence species, obtained by partial oxidation, has been investigated with steady-state and time-resolved techniques in CH3CN. The rate of photoinduced electron transfer is 2.3 x 10(8) s(-1).     

Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions

We extend the multi-level Monte Carlo (MLMC) in order to quantify uncertainty in the solutions of multi-dimensional hyperbolic systems of conservation laws with uncertain initial data. The algorithm is presented and several issues arising in the massively parallel numerical implementation are addressed. In particular, we present a novel load balancing procedure that ensures scalability of the MLMC algorithm on massively parallel hardware. A new code is described and applied to simulate uncertain solutions of the Euler equations and ideal magnetohydrodynamics (MHD) equations. Numerical experiments showing the robustness, efficiency and scalability of the proposed algorithm are presented.