Hardy-Carleman Type Inequalities for Dirac Operators

General Hardy-Carleman type inequalities for Dirac operators are proved. New inequalities are derived involving particular traditionally used weight functions. In particular, a version of the Agmon inequality and Treve type inequalities are established. The case of a Dirac particle in a (potential) magnetic field is also considered. The methods used are direct and based on quadratic form techniques

Some sharp inequalities for integral operators with homogeneous kernel

One goal of this paper is to show that a big number of inequalities for functions in L-p(R+), p >= 1, proved from time to time in journal publications are particular cases of some known general results for integral operators with homogeneous kernels including, in particular, the statements on sharp constants. Some new results are also included, e.g. the similar general equivalence result is proved and applied for 0 < p < 1. Some useful new variants of these results are pointed out and a number of known and new Hardy-Hilbert type inequalities are derived. Moreover, a new Polya-Knopp (geometric mean) inequality is derived and applied. The constants in all inequalities in this paper are sharp

Array processing in cryoseismology: a comparison to network-based approaches at an Antarctic ice stream

Seismicity at glaciers, ice sheets, and ice shelves provides observational constraint on a number of glaciologi- cal processes. Detecting and locating this seismicity, specifi- cally icequakes, is a necessary first step in studying processes such as basal slip, crevassing, imaging ice fabric, and iceberg calving, for example. Most glacier deployments to date use conventional seismic networks, comprised of seismometers distributed over the entire area of interest. However, smaller- aperture seismic arrays can also be used, which are typically sensitive to seismicity distal from the array footprint and re- quire a smaller number of instruments. Here, we investigate the potential of arrays and array-processing methods to de- tect and locate subsurface microseismicity at glaciers, bench- marking performance against conventional seismic-network- based methods for an example at an Antarctic ice stream. We also provide an array-processing recipe for body-wave cryoseismology applications. Results from an array and a network deployed at Rutford Ice Stream, Antarctica, show that arrays and networks both have strengths and weaknesses. Arrays can detect icequakes from further distances, whereas networks outperform arrays in more comprehensive studies of a particular process due to greater hypocentral constraint within the network extent. We also gain new insights into seismic behaviour at the Rutford Ice Stream. The array de- tects basal icequakes in what was previously interpreted to be an aseismic region of the bed, as well as new icequake observations downstream and at the ice stream shear mar- gins, where it would be challenging to deploy instruments. Finally, we make some practical recommendations for future array deployments at glaciers

On the existence of solutions to the relativistic Euler equations in 2 spacetime dimensions with a vacuum boundary

We prove the existence of a wide class of solutions to the isentropic relativistic Euler equations in 2 spacetime dimensions with an equation of state of the form $p=K\rho^2$ that have a fluid vacuum boundary. Near the fluid vacuum boundary, the sound speed for these solutions are monotonically decreasing, approaching zero where the density vanishes. Moreover, the fluid acceleration is finite and bounded away from zero as the fluid vacuum boundary is approached. The existence results of this article also generalize in a straightforward manner to equations of state of the form $p=K\rho^\frac{\gamma+1}{\gamma}$ with $\gamma > 0$.Comment: A major revision of the second half of the pape

The Devastating 2022 M6.2 Afghanistan Earthquake: Challenges, Processes, and Implications

On June 21st, a Mw6.2 earthquake struck the Afghan-Pakistan-border-region, situated within the India-Asia collision. Thousand thirty-nine deaths were reported, making the earthquake the deadliest of 2022. We investigate the event\u27s rupture processes by combining seismological and geodetic observations, aiming to understand what made it that fatal. Our Interferometric Synthetic Aperture Radar-constrained slip-model and regional moment-tensor inversion, confirmed through field observations, reveal a sinistral rupture with maximum slip of 1.8 m at 5 km depth on a N20°E striking, sub-vertical fault. We suggest that not only external factors (event-time, building stock) but fault-specific factors made the event excessively destructive. Surface rupture was favored by the rock foliation, coinciding with the fault strike. The distribution of Peak-Ground-Velocity was governed by the sub-vertical fault. Maximum slip was large compared to other events globally and might have resulted in peak-frequencies coinciding with resonance-frequencies of the local buildings and demonstrates the devastating impact of moderate-size earthquakes

On the gravitational potential of modified Newtonian dynamics

Producción CientíficaThe mathematical structure of the Poisson equation of Modified Newtonian Dynamics (MOND) is studied. The appropriate setting turns out to be an Orlicz-Sobolev space whose Orlicz function is related to Milgrom’s μ-function, where there exists existence and uniqueness of weak solutions. Since these do not have in principle much regularity, a further study is performed where the gravitational field is not too large, where MOND is most relevant. In that case the field turns out to be H¨older continuous. Quasilinear MOND is also analyzed

Seismic Noise Interferometry and Distributed Acoustic Sensing (DAS): Inverting for the Firn Layer S ‐Velocity Structure on Rutford Ice Stream, Antarctica

Firn densification profiles are an important parameter for ice-sheet mass balance and palaeoclimate studies. One conventional method of investigating firn profiles is using seismic refraction surveys, but these are difficult to upscale to large-area measurements. Distributed acoustic sensing (DAS) presents an opportunity for large-scale seismic measurements of firn with dense spatial sampling and easy deployment, especially when seismic noise is used. We study the feasibility of seismic noise interferometry (SI) on DAS data for characterizing the firn layer at the Rutford Ice Stream, West Antarctica. Dominant seismic energy appears to come from anthropogenic noise and shear-margin crevasses. The DAS cross-correlation interferometry yields noisy Rayleigh wave signals. To overcome this, we present two strategies for cross-correlations: (a) hybrid instruments—correlating a geophone with DAS, and (b) stacking of selected cross-correlation panels picked in the tau-p domain. These approaches are validated with results derived from an active survey. Using the retrieved Rayleigh wave dispersion curve, we inverted for a high-resolution 1D S-wave velocity profile down to a depth of 100 m. The profile shows a “kink” (velocity gradient inflection) at ∼12 m depth, resulting from a change of compaction mechanism. A triangular DAS array is used to investigate directional variation in velocity, which shows no evident variations thus suggesting a lack of azimuthal anisotropy in the firn. Our results demonstrate the potential of using DAS and SI to image the near-surface and present a new approach to derive S-velocity profiles from surface wave inversion in firn studies