ERC FUNDED PROJECTS

The purpose of this project is to develop new methods for solving boundary value problems (BVPs) for nonlinear integrable partial differential equations (PDEs). Integrable PDEs can be analyzed by means of the Inverse Scattering Transform, whose introduction was one of the most important developments in the theory of nonlinear PDEs in the 20th century. Until the 1990s the inverse scattering methodology was pursued almost entirely for pure initial-value problems. However, in many laboratory and field situations, the solution is generated by what corresponds to the imposition of boundary conditions rather than initial conditions. Thus, an understanding of BVPs is crucial. In an exciting sequence of events taking place in the last two decades, new tools have become available to deal with BVPs for integrable PDEs. Although some important issues have already been resolved, several major problems remain open. The aim of this project is to solve a number of these open problems and to find solutions of BVPs which were heretofore not solvable. More precisely, the proposal has eight objectives: 1. Develop methods for solving problems with time-periodic boundary conditions. 2. Answer some long-standing open questions raised by series of wave-tank experiments 35 years ago. 3. Develop a new approach for the study of space-periodic solutions. 4. Develop new approaches for the analysis of BVPs for equations with 3 x 3-matrix Lax pairs. 5. Derive new asymptotic formulas by using a nonlinear version of the steepest descent method. 6. Construct disk and disk/black-hole solutions of the stationary axisymmetric Einstein equations. 7. Solve a BVP in Einstein's theory of relativity describing two colliding gravitational waves. 8. Extend the above methods to BVPs in higher dimensions.

2 000 000 €

Start date: 2016-05-01, End date: 2021-04-30

We propose to carry out a project which will produce a decisive step towards improving the accuracy of the Hubble constant as determined from the Cepheid-SN Ia method to 1%, by using 28 extremely rare eclipsing binary systems in the LMC which offer the potential to determine their distances to 1%. To achieve this accuracy we will reduce the main error in the binary method by interferometric angular diameter measurements of a sample of red clump stars which resemble the stars in our binary systems. We will check on our calibration with similar binary systems close enough to determine their orbits from interferometry. We already showed the feasibility of our method which yielded the best-ever distance determination to the LMC of 2.2% from 8 such binary systems. With 28 systems and the improved angular diameter calibration we will push the LMC distance uncertainty down to 1% which will allow to set the zero point of the Cepheid PL relation with the same accuracy using the large available LMC Cepheid sample. We will determine the metallicity effect on Cepheid luminosities by a) determining a 2% distance to the more metal-poor SMC with our binary method, and by b) measuring the distances to LMC and SMC with an improved Baade-Wesselink (BW) method. We will achieve this improvement by analyzing 9 unique Cepheids in eclipsing binaries in the LMC our group has discovered which allow factor- of-ten improvements in the determination of all basic physical parameters of Cepheids. These studies will also increase our confidence in the Cepheid-based H0 determination. Our project bears strong synergy to the Gaia mission by providing the best checks on possible systematic uncertainties on Gaia parallaxes with 200 binary systems whose distances we will measure to 1-2%. We will provide two unique tools for 1-3 % distance determinations to individual objects in a volume of 1 Mpc, being competitive to Gaia already at a distance of 1 kpc from the Sun.

2 360 500 €

Start date: 2016-11-01, End date: 2021-10-31

The origin and evolution of sexual reproduction and sex differences represents one of the major unsolved problems in evolutionary biology, and although much progress had been made both via theory and empirical research, recent data suggest that sex chromosome evolution may be more complex than previously thought. The concept of sexual antagonism (when there is a positive intersexual genetic correlation in trait expression but opposite fitness effects of the trait(s) in males and females) has become essential to our understanding of sex chromosome evolution. The goal of this proposal is to understand how the interacting effects of sexual antagonism, sex-linked genetic variation, and sex-specific selection shape the genetic architecture of complex traits. I will test the hypotheses that: 1) individual sexually antagonistic loci are common in the genome, both in separate-sexed species and in hermaphrodites, and drive patterns of sexual antagonism often seen on the trait level. 2) That the response to sex-specific selection in sex-linked loci is usually due to standing sexually antagonistic genetic variation. 3) That sexually antagonistic variation is primarily non-additive in nature. To accomplish this, I will use a combination of approaches, including sex-limited experimental evolution of the X chromosome and reciprocal sex chromosome introgression among distantly related populations of Drosophila, quantitative genetic analysis and experimental evolution mimicking the creation of a novel sex chromosome in the hermaphroditic flatworm Macrostomum, and analytical and simulation modeling. This project will serve to confirm or refute the assumption that trait-level sexual antagonism reflects the contributions of many individual sexually antagonistic loci, increase our understanding of the contribution of coevolution of the sex chromosomes to population divergence, and help provide us with a better general understanding of how genotype maps to phenotype.

1 492 011 €

Start date: 2016-05-01, End date: 2021-04-30

Atmospheric aerosol particles play a key role in regulating the climate, and particulate matter is responsible for most of the 7 million deaths per year attributed to air pollution. Lack of understanding of aerosol processes, especially the formation of ice crystals and secondary particles from condensable trace gases, hampers the development of air quality modelling, and remains one of the major uncertainties in predicting climate. The purpose of this project is to achieve a comprehensive understanding of atmospheric nanocluster and ice crystal formation based on fundamental physico-chemical principles. We will use a wide palette of theoretical methods including quantum chemistry, reaction kinetics, continuum solvent models, molecular dynamics, Monte Carlo simulations, Markov chain Monte Carlo methods, computational fluid dynamics, cluster kinetic and thermodynamic models. We will study non-equilibrium effects and kinetic barriers in atmospheric clustering, and use these to build cluster distribution models with genuine predictive capacity. Chemical ionization mass spectrometers can, unlike any other instruments, detect the elemental composition of many of the smallest clusters at ambient low concentrations. However, the charging process and the environment inside the instrument change the composition of the clusters in hitherto unquantifiable ways. We will solve this problem by building an accurate model for the fate of clusters inside mass spectrometers, which will vastly improve the amount and quality of information that can be extracted from mass spectrometric measurements in atmospheric science and elsewhere. DAMOCLES will produce reliable and consistent models for secondary aerosol and ice particle formation and growth. This will lead to improved predictions of aerosol concentrations and size distributions, leading to improved air quality forecasting, more accurate estimates of aerosol indirect climate forcing and other aerosol-cloud-climate interactions.

2 390 450 €

Start date: 2016-06-01, End date: 2021-05-31