Publications

By a well known theorem of Robbins, a graph G has a strongly connected orientation if and only if G is 2-edge-connected and it is easy to find, in linear time, either a cut edge of G or a strong orientation of G. A result of Durand de Gevigney shows that for every it is NP-hard to decide if a given graph G has a k-strong orientation. Thomassen showed that one can check in polynomial time whether a given graph has a 2-strong orientation. This implies that for a given digraph D we can determine in polynomial time whether we can reorient (=reverse) some arcs of to obtain a 2-strong digraph. This naturally leads to the question of determining the minimum number of such arcs to reverse before the resulting graph is 2-strong. In this paper we show that finding this number is NP-hard. If a 2-connected graph G has no 2-strong orientation, we may ask how many of its edges we may orient so that the resulting mixed graph is still 2-strong. Similarly, we may ask for a 2-edge-connected graph G how many of its edges we can orient such that the resulting mixed graph remains 2-arc-strong. We prove that when restricted to graphs satisfying suitable connectivity conditions, both of these problems are equivalent to finding the minimum number of edges we must double in a 2-edge-connected graph in order to obtain a 4-edge-connected graph. Using this, we show that all these three problems are NP-hard. Finally, we consider the operation of deorienting an arc uv of a digraph D meaning replacing it by an undirected edge between the same vertices. In terms of connectivity properties, this is equivalent to adding the opposite arc vu to D. We prove that for every it is NP-hard to find the minimum number of arcs to deorient in a digraph D in order to obtain an ℓ-strong digraph.

Selecting the right cathode material is a key component to achieving high-energy and long-lifespan aqueous zinc-ion batteries (AZIBs); however, the development of cathode materials still faces serious challenges due to the high polarization of Zn2+. In this work, MnV12O31&hahog;10H2O (MnVO) synthesized via a one-step hydrothermal method is proposed as a promising cathode material for AZIBs. Because the stable layered structure and hieratical morphology of MnVO provide a large layer space for rapid ion transports, this material exhibits high specific capacity (433 mAh g−1 at 0.1 A g−1), an outstanding long-term cyclability (5000 cycles at a current density of 3 A g−1), and an excellent energy density (454.65 Wh kg−1). To illustrate the intercalation mechanism, ex situ X-Ray diffraction, Fourier transform infrared spectroscopy, and X-ray photoelectron spectroscopy are adopted, uncovering an H+/Zn2+ dual-cation co-intercalation processes. In addition, density-functional theory calculation analysis shows that MnVO has a delocalized electron cloud and the diffusion energy barrier of Zn2+ in MnVO is low, which promotes the Zn2+ transport and consequently improves the reversibility of the battery upon deep cycling. The key and enlightening insights are provided in the results for designing high-performance vanadium-oxide-based cathode materials for AZIBs.

Relaxation and diffusion measurements were carried out on single and binary liquids filling the pore space of controlled porous glass Vycor with an average pore size of about 4 nm. The dispersion of the longitudinal relaxation time T1 is discussed as a means to identify liquid-surface interaction based on existing models developed for metal-free glass surfaces. In addition, the change of T1 and T2 with respect to their bulk values is discussed, in particular T2 serves as a probe for the strength of molecular interactions. As the native glass surface is polar and contains a large amount of hydroxyl groups, a pronounced interaction of polar and protic adsorbate liquids is expected; however, the T1 dispersion, and the corresponding reduction of T2, are also observed for non-polar liquids such as alkanes and cyclohexane. Deuterated liquids are employed for simplifying data analysis in binary systems, but also for separating the respective contributions of intra- and intermolecular interactions to the overall relaxation rate. Despite the lack of paramagnetic impurities in the glass material, 1H and 2H relaxation dispersions of equivalent molecules are frequently found to differ from each other, suggesting intermolecular relaxation mechanisms for the 1H nuclei. The variation of the T1 dispersion when comparing single and binary systems gives clear evidence for the preferential adsorption of one of the two liquids, suggesting complete phase separation in several cases. Measurement of the apparent tortuosity by self-diffusion experiments supports the concept of a local variation of sample composition within the porespace.

We address the feedback design problem for switched linear systems. In particular we aim to design a switched state-feedback such that the resulting closed-loop switched system is in upper triangular form. To this effect we formulate and analyse the feedback rectification problem for pairs of matrices. We present necessary and sufficient conditions for the feedback rectifiability of pairs for two subsystems and give a constructive procedure to design stabilizing state-feedback for a class of switched systems. Several examples illustrate the characteristics of the problem considered and the application of the proposed constructive procedure.

In multi-objective mixed-integer convex optimization, multiple convex objective functions need to be optimized simultaneously while some of the variables are restricted to take integer values. In this paper, we present a new algorithm to compute an enclosure of the nondominated set of such optimization problems. More precisely, we decompose the multi-objective mixed-integer convex optimization problem into several multi-objective continuous convex optimization problems, which we refer to as patches. We then dynamically compute and improve coverages of the nondominated sets of those patches to finally combine them to obtain an enclosure of the nondominated set of the multi-objective mixed-integer convex optimization problem. Additionally, we introduce a mechanism to reduce the number of patches that need to be considered in total. Our new algorithm is the first of its kind and guaranteed to return an enclosure of prescribed quality within a finite number of iterations. For selected numerical test instances we compare our new criterion space based approach to other algorithms from the literature and show that much larger instances can be solved with our new algorithm.