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- ItemDistribution of Cracks in a Chain of Atoms at Low Temperature(Cham (ZG) : Springer International Publishing AG, 2021) Jansen, Sabine; König, Wolfgang; Schmidt, Bernd; Theil, FlorianWe consider a one-dimensional classical many-body system with interaction potential of Lennard–Jones type in the thermodynamic limit at low temperature 1/β∈(0,∞). The ground state is a periodic lattice. We show that when the density is strictly smaller than the density of the ground state lattice, the system with N particles fills space by alternating approximately crystalline domains (clusters) with empty domains (voids) due to cracked bonds. The number of domains is of the order of Nexp(−βesurf/2) with esurf>0 a surface energy. For the proof, the system is mapped to an effective model, which is a low-density lattice gas of defects. The results require conditions on the interactions between defects. We succeed in verifying these conditions for next-nearest neighbor interactions, applying recently derived uniform estimates of correlations.
- ItemSurface Energy and Boundary Layers for a Chain of Atoms at Low Temperature(Berlin ; Heidelberg : Springer, 2021) Jansen, Sabine; König, Wolfgang; Schmidt, Bernd; Theil, FlorianWe analyze the surface energy and boundary layers for a chain of atoms at low temperature for an interaction potential of Lennard–Jones type. The pressure (stress) is assumed to be small but positive and bounded away from zero, while the temperature β- 1 goes to zero. Our main results are: (1) As β→ ∞ at fixed positive pressure p> 0 , the Gibbs measures μβ and νβ for infinite chains and semi-infinite chains satisfy path large deviations principles. The rate functions are bulk and surface energy functionals E¯ bulk and E¯ surf. The minimizer of the surface functional corresponds to zero temperature boundary layers; (2) The surface correction to the Gibbs free energy converges to the zero temperature surface energy, characterized with the help of the minimum of E¯ surf; (3) The bulk Gibbs measure and Gibbs free energy can be approximated by their Gaussian counterparts; (4) Bounds on the decay of correlations are provided, some of them uniform in β. © 2020, The Author(s).
- ItemSeismological and Geophysical Signatures of the Deep Crustal Magma Systems of the Cenozoic Volcanic Fields Beneath the Eifel, Germany(Hoboken, NJ [u.a.] : Wiley, 2020) Dahm, Torsten; Stiller, Manfred; Mechie, James; Heimann, Sebastian; Hensch, Martin; Woith, Heiko; Schmidt, Bernd; Gabriel, Gerald; Weber, MichaelThe Quaternary volcanic fields of the Eifel (Rhineland-Palatinate, Germany) had their last eruptions less than 13,000 years ago. Recently, deep low-frequency (DLF) earthquakes were detected beneath one of the volcanic fields showing evidence of ongoing magmatic activity in the lower crust and upper mantle. In this work, seismic wide- and steep-angle experiments from 1978/1979 and 1987/1988 are compiled, partially reprocessed and interpreted, together with other data to better determine the location, size, shape, and state of magmatic reservoirs in the Eifel region near the crust-mantle boundary. We discuss seismic evidence for a low-velocity gradient layer from 30–36 km depth, which has developed over a large region under all Quaternary volcanic fields of the Rhenish Massif and can be explained by the presence of partial melts. We show that the DLF earthquakes connect the postulated upper mantle reservoir with the upper crust at a depth of about 8 km, directly below one of the youngest phonolitic volcanic centers in the Eifel, where CO2 originating from the mantle is massively outgassing. A bright spot in the West Eifel between 6 and 10 km depth represents a Tertiary magma reservoir and is seen as a model for a differentiated reservoir beneath the young phonolitic center today. We find that the distribution of volcanic fields is controlled by the Variscan lithospheric structures and terrane boundaries as a whole, which is reflected by an offset of the Moho depth, a wedge-shaped transparent zone in the lower crust and the system of thrusts over about 120 km length. ©2020. The Authors.
- ItemSurface energy and boundary layers for a chain of atoms at low temperature(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Jansen, Sabine; König, Wolfgang; Schmidt, Bernd; Theil, FlorianWe analyze the surface energy and boundary layers for a chain of atoms at low temperature for an interaction potential of Lennard-Jones type. The pressure (stress) is assumed small but positive and bounded away from zero, while the temperature goes to zero. Our main results are: (1) As _x000C_ the temperature goes to zero and at fixed positive pressure, the Gibbs measures _x0016__x000C_for infinite chains and semi-infinite chains satisfy path large deviations principles. The rate functions are bulk and surface energy functionals. The minimizer of the surface functional corresponds to zero temperature boundary layers. (2) The surface correction to the Gibbs free energy converges to the zero temperature surface energy, characterized with the help of the minimum of the surface energy functional. (3) The bulk Gibbs measure and Gibbs free energy can be approximated by their Gaussian counterparts. (4) Bounds on the decay of correlations are provided, some of them uniform in _x000C_the inverse temperature.
- ItemDistribution of cracks in a chain of atoms at low temperature(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Jansen, Sabine; König, Wolfgang; Schmidt, Bernd; Theil, FlorianWe consider a one-dimensional classical many-body system with interaction potential of Lennard--Jones type in the thermodynamic limit at low temperature 1/β ∈ (0, ∞). The ground state is a periodic lattice. We show that when the density is strictly smaller than the density of the ground state lattice, the system with N particles fills space by alternating approximately crystalline domains (clusters) with empty domains (voids) due to cracked bonds. The number of domains is of the order of N exp(-β e surf /2) with e surf > 0 a surface energy.