Project acronym CONDMATH
Project Mathematical Problems in Superconductivity and Bose-Einstein Condensation
Researcher (PI) Soeren Fournais
Host Institution (HI) AARHUS UNIVERSITET
Call Details Starting Grant (StG), PE1, ERC-2007-StG
Summary This project in mathematical physics is concerned with the mathematical understanding of superconductivity and Bose-Einstein condensation. These physical phenomena are the subject of intense research activity both in the experimental and theoretical physics communities and in mathematics. However, despite a lot of effort, many key questions lack a mathematically rigorous answer. The ambition of the present project is to improve this situation. I plan to analyze both the effective models and the underlying microscopic description of superconductivity and Bose-Einstein condensation. The effective models are (systems of) non-linear partial differential equations, and I will apply recently developed mathematical techniques for their analysis. To mention an important specific problem in this part of the project, I am interested in the appearance of regular (Abrikosov) lattices of vortices. For superconductivity, which I will treat in the Ginzburg-Landau model, it is an experimental fact that this happens when an exterior magnetic field comes close to a critical value. For rotating Bose-Einstein condensates, in the Gross-Pitaevskii model, a similar phenomenon occurs for sufficiently large rotations. However, as yet we are unable to derive these lattices directly from the relevant equations. Even more fundamental are the questions about the microscopic models. The aim here is to prove that the desired condensation actually occurs under conditions relevant to experiment, i.e. to prove that the condensation phenomena are correctly described by our fundamental equations of Nature. The microscopic models are systems with a large number of variables and developing the mathematical techniques necessary for the analysis of such systems is an important question in current research in Mathematics.
Summary
This project in mathematical physics is concerned with the mathematical understanding of superconductivity and Bose-Einstein condensation. These physical phenomena are the subject of intense research activity both in the experimental and theoretical physics communities and in mathematics. However, despite a lot of effort, many key questions lack a mathematically rigorous answer. The ambition of the present project is to improve this situation. I plan to analyze both the effective models and the underlying microscopic description of superconductivity and Bose-Einstein condensation. The effective models are (systems of) non-linear partial differential equations, and I will apply recently developed mathematical techniques for their analysis. To mention an important specific problem in this part of the project, I am interested in the appearance of regular (Abrikosov) lattices of vortices. For superconductivity, which I will treat in the Ginzburg-Landau model, it is an experimental fact that this happens when an exterior magnetic field comes close to a critical value. For rotating Bose-Einstein condensates, in the Gross-Pitaevskii model, a similar phenomenon occurs for sufficiently large rotations. However, as yet we are unable to derive these lattices directly from the relevant equations. Even more fundamental are the questions about the microscopic models. The aim here is to prove that the desired condensation actually occurs under conditions relevant to experiment, i.e. to prove that the condensation phenomena are correctly described by our fundamental equations of Nature. The microscopic models are systems with a large number of variables and developing the mathematical techniques necessary for the analysis of such systems is an important question in current research in Mathematics.
Max ERC Funding
749 571 €
Duration
Start date: 2008-09-01, End date: 2013-08-31
Project acronym HPAH
Project Hydrogen interaction with polycyclic aromatic hydrocarbons – from interstellar catalysis to hydrogen storage
Researcher (PI) Liv Hornekaer
Host Institution (HI) AARHUS UNIVERSITET
Call Details Starting Grant (StG), PE4, ERC-2007-StG
Summary In a truly cross-disciplinary research project encompassing surface science, astrophysics and chemistry we aim to address two of the major outstanding questions in the field of astrochemistry, namely i) how molecular hydrogen, the most abundant molecule in the interstellar medium, form, and ii) whether it is possible to identify specific Polycyclic Aromatic Hydrocarbon (PAH) species in interstellar spectra. The insights gained from the experimental investigations may revolutionize our current understanding of astrochemistry and will have impact even beyond the field. Special emphasis will be placed on the impact our findings will have on ascertaining the suitability of PAHs as a hydrogen storage medium. By combining scanning tunneling microscopy, thermal desorption spectroscopy, laser-induced thermal desorption time-of-flight mass spectrometry, fluorescence spectroscopy experiments and density functional theory calculations we will map out the interaction of atomic hydrogen with PAHs. The goal of the investigation is to obtain atomic level understanding of the atomic hydrogen – PAH interaction in order to i) ascertain whether interstellar molecular hydrogen formation, contrary to present belief but in accordance with our recent calculations, could occur predominantly via interaction with PAHs, ii) measure the adsorption/emission spectrum of Hydrogen-PAH complexes and thereby facilitate observational detection of these complexes in the interstellar medium, iii) determine whether PAHs are a promising medium for hydrogen storage and iv) ascertain whether the hydrogen storage properties of PAHs are tunable by electro-magnetic radiation. This ambitious and cross-disciplinary research project will predominantly take place at the newly established Surface Dynamics Laboratory at the University of Aarhus, headed by the applicant, but will also benefit from fruitful collaborations already initiated with local, national and international colleagues.
Summary
In a truly cross-disciplinary research project encompassing surface science, astrophysics and chemistry we aim to address two of the major outstanding questions in the field of astrochemistry, namely i) how molecular hydrogen, the most abundant molecule in the interstellar medium, form, and ii) whether it is possible to identify specific Polycyclic Aromatic Hydrocarbon (PAH) species in interstellar spectra. The insights gained from the experimental investigations may revolutionize our current understanding of astrochemistry and will have impact even beyond the field. Special emphasis will be placed on the impact our findings will have on ascertaining the suitability of PAHs as a hydrogen storage medium. By combining scanning tunneling microscopy, thermal desorption spectroscopy, laser-induced thermal desorption time-of-flight mass spectrometry, fluorescence spectroscopy experiments and density functional theory calculations we will map out the interaction of atomic hydrogen with PAHs. The goal of the investigation is to obtain atomic level understanding of the atomic hydrogen – PAH interaction in order to i) ascertain whether interstellar molecular hydrogen formation, contrary to present belief but in accordance with our recent calculations, could occur predominantly via interaction with PAHs, ii) measure the adsorption/emission spectrum of Hydrogen-PAH complexes and thereby facilitate observational detection of these complexes in the interstellar medium, iii) determine whether PAHs are a promising medium for hydrogen storage and iv) ascertain whether the hydrogen storage properties of PAHs are tunable by electro-magnetic radiation. This ambitious and cross-disciplinary research project will predominantly take place at the newly established Surface Dynamics Laboratory at the University of Aarhus, headed by the applicant, but will also benefit from fruitful collaborations already initiated with local, national and international colleagues.
Max ERC Funding
1 499 810 €
Duration
Start date: 2008-07-01, End date: 2013-06-30
