Implementation of intermittent renewable energy sources in the energy grid will require the use of large-scale energy storage to mitigate the discrepancies between energy production and demand. Non-aqueous organic redox flow batteries from abundant all-carbon based materials can provide a sustainable solution. Flow batteries decouple storage capacity from power output, allowing for independently scalable, cheap and massive energy storage. However, current technology has not reached a mature enough level and many scientific questions still need to be answered. Specifically, new active materials need to be developed that simultaneously deliver high cell voltages and energy density in combination with good cyclability and stability. Here the development of a new class of molecules is proposed that is expected to meet these requirements, advancing the state-of-the-art of this technology. This will be achieved by a unique interdisciplinary approach, combining organic synthesis, electrochemistry, device engineering and device physics. The use of ambipolar redox active materials comprised of electron rich and electron poor groups (donor-acceptor strategy) is proposed to generate molecules with tuneable redox potentials. This allows their implementation on both the positive as negative half-cell of the battery, avoiding capacity loss by crossover. An iterative design strategy will be used to build a library of compounds that will be screened for reversible redox chemistry and stability. New membranes separating the half cells will be developed and matched with redox materials that passed the first screening, testing for compatibility and crossover rates. Finally, all components will be combined and studied in prototype flow batteries. Results from these studies will be used as input for computational modelling in order to predict a new generation of redox compounds and improved membrane design. This ultimately leads to a detailed understanding on their structure-property relations and development of materials that can be used for large-scale energy storage.

Many problems in computer science naturally require finding some optimum structure in discrete objects like strings, graphs and circuits. Discrete optimization is the study of such computational problems, and it plays a key role in various applied areas like logistics, bioinformatics, chip design, and machine learning. One of the most successful approaches for solving such problems is via continuous methods. Here, one first considers a tractable “continuous relaxation” for the discrete problem, and then uses some “rounding technique”, often based on geometry or probability, to extract a good discrete solution from the continuous information. Despite much progress, our understanding of these methods is still quite limited: (i) most rounding approaches are problem-specific, and we lack a unified theory and methodology, (ii) the strength and applicability of powerful new relaxation approaches is barely understood, and (iii) for several fundamental optimization problems, large gaps exist between the known upper and lower bounds on how well they can be solved. Here, we propose several promising new ideas and directions for future progress, based on our recent work and other impressive developments in the field at interface between discrete and continuous mathematics. In particular, we will develop new unified rounding techniques that are applicable to a wide class of problems, by building on the connections between rounding and discrepancy theory. The area of algorithmic discrepancy, initiated by us, and has already led to several breakthrough results. We also explore several very powerful recent approaches for relaxations based on hierarchies, stable polynomials and matrix norms. We will develop techniques to use them in novel ways to resolve several long-standing questions, and problems arising in new emerging applications in theoretical computer science and discrete optimization, where the current approaches fail.