ERC FUNDED PROJECTS

A wide variety of materials including coatings and adhesives, emerging materials for nanotechnology products, as well as everyday food products are processed or delivered as suspensions. The flow properties of such suspensions must be finely adjusted according to the demands of the respective processing techniques, even for the feel of cosmetics and the perception of food products is highly influenced by their rheological properties. The recently developed capillary suspensions concept has the potential to revolutionize product formulations and material design. When a small amount (less than 1%) of a second immiscible liquid is added to the continuous phase of a suspension, the rheological properties of the mixture are dramatically altered from a fluid-like to a gel-like state or from a weak to a strong gel and the strength can be tuned in a wide range covering orders of magnitude. Capillary suspensions can be used to create smart, tunable fluids, stabilize mixtures that would otherwise phase separate, significantly reduce the amount organic or polymeric additives, and the strong particle network can be used as a precursor for the manufacturing of cost-efficient porous ceramics and foams with unprecedented properties. This project will investigate the influence of factors determining capillary suspension formation, the strength of these admixtures as a function of these aspects, and how capillary suspensions depend on external forces. Only such a fundamental understanding of the network formation in capillary suspensions on both the micro- and macroscopic scale will allow for the design of sophisticated new materials. The main objectives of this proposal are to quantify and predict the strength of these admixtures and then use this information to design a variety of new materials in very different application areas including, e.g., porous materials, water-based coatings, ultra low fat foods, and conductive films.

1 489 618 €

Start date: 2013-08-01, End date: 2018-07-31

"The finite element method is one of the most successful techniques for designing numerical methods for systems of partial differential equations (PDEs). It is not only a methodology for developing numerical algorithms, but also a mathematical framework in which to explore their behavior. The finite element exterior calculus (FEEC) provides a new structure that produces a deeper understanding of the finite element method and its connections to the partial differential equation being approximated. The goal is to develop discretizations which are compatible with the geometric, topological, and algebraic structures which underlie well-posedness of the partial differential equation. The phrase FEEC was first used in a paper the PI wrote for Acta Numerica in 2006, together with his coworkers, D.N. Arnold and R.S. Falk. The general philosophy of FEEC has led to the design of new algorithms and software developments, also in areas beyond the direct application of the theory. The present project will be devoted to further development of the foundations of FEEC, and to direct or indirect use of FEEC in specific applications. The ambition is to set the scene for a nubmer of new research directions based on FEEC by giving ground-braking contributions to its foundation. The aim is also to use FEEC as a tool, or a guideline, to extend the foundation of numerical PDEs to a variety of problems for which this foundation does not exist. The more application oriented parts of the project includes topics like numerical methods for elasticity, its generalizations to more general models in materials science such as viscoelasticity, poroelasticity, and liquid crystals, and the applications of these models to CO2 storage and deformations of the spinal cord."

2 059 687 €

Start date: 2014-02-01, End date: 2019-01-31

"The rate at which research labs, enterprises and governments accumulate data is high and fast increasing. Often, these data are collected for no specific purpose, or they turn out to be useful for unanticipated purposes: Companies constantly look for new ways to monetize their customer databases; Governments mine various databases to detect tax fraud; Security agencies mine and cross-associate numerous heterogeneous information streams from publicly accessible and classified databases to understand and detect security threats. The objective in such Exploratory Data Mining (EDM) tasks is typically ill-defined, i.e. it is unclear how to formalize how interesting a pattern extracted from the data is. As a result, EDM is often a slow process of trial and error. During this fellowship we aim to develop the mathematical principles of what makes a pattern interesting in a very subjective sense. Crucial in this endeavour will be research into automatic mechanisms to model and duly consider the prior beliefs and expectations of the user for whom the EDM patterns are intended, thus relieving the users of the complex task to attempt to formalize themselves what makes a pattern interesting to them. This project will represent a radical change in how EDM research is done. Currently, researchers typically imagine a specific purpose for the patterns, try to formalize interestingness of such patterns given that purpose, and design an algorithm to mine them. However, given the variety of users, this strategy has led to a multitude of algorithms. As a result, users need to be data mining experts to understand which algorithm applies to their situation. To resolve this, we will develop a theoretically solid framework for the design of EDM systems that model the user's beliefs and expectations as much as the data itself, so as to maximize the amount of useful information transmitted to the user. This will ultimately bring the power of EDM within reach of the non-expert."

1 549 315 €

Start date: 2014-05-01, End date: 2019-04-30

The current theory of cosmic inflation is largely based on classical physics. This undermines its predictivity in a world that is fundamentally quantum mechanical. With this project we will develop a novel approach towards a quantum theory of inflation. We will do this by introducing holographic techniques in cosmology. The notion of holography is the most profound conceptual breakthrough that has emerged form fundamental high-energy physics in recent years. It postulates that (quantum) gravitational systems such as the universe as a whole have a precise `holographic’ description in terms of quantum field theories defined on their boundary. Our aim is to develop a holographic framework for quantum cosmology. We will then apply this to three areas of theoretical cosmology where a quantum approach is of critical importance. First, we will put forward a holographic description of inflation that clarifies its microphysical origin and is rigorously predictive. Using this we will derive the distinct observational signatures of novel, truly holographic models of the early universe where inflation has no description in terms of classical cosmic evolution. Second, we will apply holographic cosmology to improve our understanding of eternal inflation. This is a phase deep into inflation where quantum effects dominate the evolution and affect the universe’s global structure. Finally we will work towards generalizing our holographic models of the primordial universe to include the radiation, matter and vacuum eras. The resulting unification of cosmic history in terms of a single holographic boundary theory may lead to intriguing predictions of correlations between early and late time observables, tying together the universe’s origin with its ultimate fate. Our project has the potential to revolutionize our perspective on cosmology and to further deepen the fruitful interaction between cosmology and high-energy physics.

1 995 900 €

Start date: 2014-08-01, End date: 2019-07-31