Asymptotic behavior of global entropy solutions for nonstrictly hyperbolic systems with linear damping

In this paper we investigate the large time behavior of the global weak entropy solutions to the symmetric Keyftiz-Kranzer system with linear damping. It is proved that as t tends to infinite the entropy solutions tend to zero in the L p nor

Coupling of structure to magnetic and superconducting orders in quasi-one-dimensional K2Cr3As3\text{K}_2\text{Cr}_3\text{As}_3

Quasi-one-dimensional $A_2\text{Cr}_3\text{As}_3$ (with $A = \text{K, Cs, Rb}$) is an intriguing new family of superconductors which exhibit many similar features to the cuprate and iron-based unconventional superconductor families. Yet in contrast to these systems, no charge or magnetic ordering has been observed which could provide the electronic correlations presumed necessary for an unconventional superconducting pairing mechanism - an absence which defies predictions of first principles models. We report the results of neutron scattering experiments on polycrystalline $\text{K}_2\text{Cr}_3\text{As}_3$ $(T_c \sim 7\text{K})$ which probed the low temperature dynamics near $T_c$ . Neutron diffraction data evidence a strong response of the nuclear lattice to the onset of superconductivity while inelastic scattering reveals a highly dispersive column of intensity at the commensurate wavevector $q = (00\frac{1}{2})$ which loses intensity beneath $T_c$ - indicative of short-range magnetic fluctuations. Using linear spin-wave theory we model the observed scattering and suggest a possible structure to the short-range magnetic order. These observations suggest that $\text{K}_2\text{Cr}_3\text{As}_3$ is in close proximity to a magnetic instability and that the incipient magnetic order both couples strongly to the lattice and competes with superconductivity - in direct analogy with the iron-based superconductors

On tidal forces in f(R) theories of gravity

Despite the extraordinary attention that modified gravity theories have attracted over the past decade, the geodesic deviation equation in this context has not received proper formulation thus far. This equation provides an elegant way to investigate the timelike, null and spacelike structure of spacetime geometries. In this investigation we provide the full derivation of this equation in situations where General Relativity has been extended in Robertson-Walker background spacetimes. We find that for null geodesics the contribution arising from the geometrical new terms is in general non-zero. Finally we apply the results to a well known class of f(R) theories, compare the results with General Relativity predictions and obtain the equivalent area distance relation.Comment: 9 pages, 2 figure