Numerical study on the fluid-structure interaction in a model aquatic canopy flow

This work presents numerical simulations and selected results of the flow over aquatic canopies, consisting of artificial flexible rectangular blades, arranged in a well-defined order. The results obtained with three different Reynolds and Cauchy numbers are compared with experimental data achieving good agreement. The considered range of Cauchy numbers represents three different types of canopies ranging from rigid up to highly flexible plants. The transient flow data and blade positions are statistically analyzed to gain deeper understanding of the complex physical processes for this kind of fluid structure interaction. For example, the correlation of role of large scale motion of the flexible blades in conjunction with coherent vortex structures of the flow is addressed. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fast Diffusion to Self-Similarity: Complete Spectrum,Long-Time Asymptotics,and Numerology

The complete spectrum is determined for the operator on the Sobolev space W^1,2(Rⁿ) formed by closing the smooth functions of compact support with respect to the norm Here the Barenblatt profile is the stationary attractor of the rescaled diffusion equation in the fast, supercritical regime m the same diffusion dynamics represent the steepest descent down an entropy E(u) on probability measures with respect to the Wasserstein distance d₂. Formally, the operator H=HessE is the Hessian of this entropy at its minimum , so the spectral gap H:=2–n(1–m) found below suggests the sharp rate of asymptotic convergence: from any centered initial data 0u(0,x)L¹(Rⁿ) with second moments. This bound improves various results in the literature, and suggests the conjecture that the self-similar solution u(t,x)=R(t)^–n(x/R(t)) is always slowest to converge. The higher eigenfunctions – which are polynomials with hypergeometric radial parts – and the presence of continuous spectrum yield additional insight into the relations between symmetries of Rⁿ and the flow. Thus the rate of convergence can be improved if we are willing to replace the distance to with the distance to its nearest mass-preserving dilation (or still better, affine image). The strange numerology of the spectrum is explained in terms of the number of moments of .Dedicated to Elliott H. Lieb on the occasion of his 70th birthday.     

Some new results on the well-posedness of hyperbolic evolution equations

We summarize some recently obtained results on the well-posedness of hyperbolic linear evolution equations. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

PROCOS: computational analysis of protein-protein complexes

One of the main challenges in protein-protein docking is a meaningful evaluation of the many putative solutions. Here we present a program (PROCOS) that calculates a probability-like measure to be native for a given complex. In contrast to scores often used for analyzing complex structures, the calculated probabilities offer the advantage of providing a fixed range of expected values. This will allow, in principle, the comparison of models corresponding to different targets that were solved with the same algorithm. Judgments are based on distributions of properties derived from a large database of native and false complexes. For complex analysis PROCOS uses these property distributions of native and false complexes together with a support vector machine (SVM). PROCOS was compared to the established scoring schemes of ZRANK and DFIRE. Employing a set of experimentally solved native complexes, high probability values above 50% were obtained for 90% of these structures. Next, the performance of PROCOS was tested on the 40 binary targets of the Dockground decoy set, on 14 targets of the RosettaDock decoy set and on 9 targets that participated in the CAPRI scoring evaluation. Again the advantage of using a probability-based scoring system becomes apparent and a reasonable number of near native complexes was found within the top ranked complexes. In conclusion, a novel fully automated method is presented that allows the reliable evaluation of protein-protein complexes.     

From hetero- to homochiral bis(metallahelicene)s based on a Pt(III)-Pt(III) bonded scaffold: isomerization, structure, and chiroptical properties

Hetero- and homochiral diastereomeric bis(metallahelicene)s have been synthesized. They possess a rare Pt(III)-Pt(III) scaffold bridged by benzoato ligands. It is shown that heterochiral (P,M)-bis(Pt(III)-[6]helicene) can isomerize into the homochiral (P,P)- and (M,M)-bis(Pt(III)-[6]helicene). A theoretical study shows a unique σ-π conjugation between the two π-helices and the σ-Pt(III)-Pt(III) scaffold that impacts the strong chiroptical properties.     

Impact of sugar stereochemistry on natural killer T cell stimulation by bacterial glycolipids

Natural killer T (NKT) cells recognize glycolipids produced by Sphingomonas bacteria, and these glycolipids contain C6-oxidized sugars, either glucuronic acid or galacturonic acid, linked to ceramides. Glycolipids with gluco stereochemistry are the most prevalent. Multiple studies have demonstrated that galactosylceramides are more potent stimulators of NKT cells than their glucose isomers. To determine if this stereoselectivity is retained in the context of the C6-oxidized sugars found in bacterial glycolipids, we prepared two sets of gluco and galacto-glycolipids oxidized at their C6 positions and compared their NKT stimulatory properties. In the context of carboxylic acid groups at C6, gluco stereochemistry gave the more potent responses. We also prepared bacterial glycolipids containing more complex ceramide groups to determine if these chains impact NKT cell responses.     

Tame linear extension operators for smooth Whitney functions

For a compact set K⊆Rd we present a rather easy construction of a linear extension operator E:E(K)→C^∞(Rd) for the space of Whitney jets E(K) which satisfies linear tame continuity estimates , where ‖⋅s_‖ denotes the s-th Whitney norm. The construction turns out to be possible if and only if the local Markov inequality LMI(s) introduced by Bos and Milman holds for every s>r on K. In particular, E(K) admits a tame linear extension operator if and only if the local Markov inequality LMI(s) holds on K for some s?1.     

A partition-based relaxation for Steiner trees

The Steiner tree problem is a classical NP-hard optimization problem with a wide range of practical applications. In an instance of this problem, we are given an undirected graph G = (V, E), a set of terminals \({R\subseteq V}\) , and non-negative costs c _e for all edges \({e \in E}\) . Any tree that contains all terminals is called a Steiner tree; the goal is to find a minimum-cost Steiner tree. The vertices \({V \backslash R}\) are called Steiner vertices. The best approximation algorithm known for the Steiner tree problem is a greedy algorithm due to Robins and Zelikovsky (SIAM J Discrete Math 19(1):122–134, 2005); it achieves a performance guarantee of \({1+\frac{\ln 3}{2}\approx 1.55}\) . The best known linear programming (LP)-based algorithm, on the other hand, is due to Goemans and Bertsimas (Math Program 60:145–166, 1993) and achieves an approximation ratio of 2?2/|R|. In this paper we establish a link between greedy and LP-based approaches by showing that Robins and Zelikovsky’s algorithm can be viewed as an iterated primal-dual algorithm with respect to a novel LP relaxation. The LP used in the first iteration is stronger than the well-known bidirected cut relaxation. An instance is b-quasi-bipartite if each connected component of \({G \backslash R}\) has at most b vertices. We show that Robins’ and Zelikovsky’s algorithm has an approximation ratio better than \({1+\frac{\ln 3}{2}}\) for such instances, and we prove that the integrality gap of our LP is between \({\frac{8}{7}}\) and \({\frac{2b+1}{b+1}}\) .