Conjectured set of exact bootstrap equations

A set of exact bootstrop equations is conjectured, consisting of two coupled homogeneous equations for the vertex function and the propagator from which any n-legged amplitude can be constructed. One equation is analogous to the vanishing of vertex renormalization constants (Z=0); the second equation expresses "duality". All graphs can be reduced to the simple tree diagram. Amplitudes, if solutions exist, will be crossing symmetric and will have at least all the necessary singularities making unitarity plausible but not proved

Method for the Self-Consistent Determination of Regge Pole Parameters

A method is suggested for approximately bootstrapping Regge trajectories, thereby avoiding the cutoff problems of the usual bootstrap calculation. The method is based on dispersion relations for Regge trajectories and on unitarity applied at l=α. Successively more realistic approximations are described which bring in more information on the potential, and more trajectories. The approximate Regge parameters are guaranteed to have the desired threshold and asymptotic properties

The Geophysical Model Generator: a tool to unify and interpret geophysical datasets

Geophysical datasets and their interpretations form the basis of geodynamic simulations of the Earth’s mantle and lithosphere. Yet, going from data to models is often non-trivial, particularly in complex regions such as the Alps. This is because creating consistent three-dimensional models from these datasets is often challenging due to technical discrepancies such as different data set formats, different spatial resolutions or discrepancies between different data sets. At the same time, the different datasets obtained through initiatives such as AlpArray contain a wealth of data that can help to constrain subsurface models to an unprecedented extent. Yet interpreting these different data still involves subjective steps and ideally different datasets are combined in the process. To facilitate the joint interpretation of these datasets and the generation of geodynamic model setups, we therefore developed an open-source package - the Geophysical Model Generator (GMG) - to assist with unifying these datasets in a common data format that can then be further used to visualize, compare and interpret data. Within this package, we provide a set of routines to import different datasets, convert them to a common data format and to process them further (e.g., to create vote maps from different tomographies). These unified datasets can then be exported as vtk-files for further 3D visualization (e.g., Paraview). Moreover, with the Geophysical Model Generator it is also possible to create model setups for numerical models (such as the 3D geodynamic code LaMEM). This package thus covers the entire workflow from data import to numerical model generation. Key features of the Geophysical Model Generator include 1) the creation of 3D volumes from seismic tomography models, 2) the import of 2D data (e.g., surface or Moho topography or screenshots from published papers) and 3) the incorporation of point data such as earthquake locations or GPS measurements. Both scalar and vector data can be handled. With these tools, one can then create a consistent overview of the entire data available for a given region. The package is written in Julia and hosted as a public open-source repository on GitHub (https://github.com/JuliaGeodynamics/GeophysicalModelGenerator.jl). To assist the joint interpretation of different geophysical datasets, we furthermore provide a graphical user interface that allows to view and compare them (https://github.com/JuliaGeodynamics/DataPicker). The GUI works provides an interactive webpage, allows loading different datasets and facilitates the manual interpretation of different structures (such as subducting slabs) along profiles and visualize them in 3D while taking different data into account. An example of the current version is given in Figure 1

Numerical modelling of magma dynamics coupled to tectonic deformation of lithosphere and crust

Many unresolved questions in geodynamics revolve around the physical behaviour of the two-phase system of a silicate melt percolating through and interacting with a tectonically deforming host rock. Well-accepted equations exist to describe the physics of such systems and several previous studies have successfully implemented various forms of these equations in numerical models. To date, most such models of magma dynamics have focused on mantle flow problems and therefore employed viscous creep rheologies suitable to describe the deformation properties of mantle rock under high temperatures and pressures. However, the use of such rheologies is not appropriate to model melt extraction above the lithosphere-asthenosphere boundary, where the mode of deformation of the host rock transitions from ductile viscous to brittle elasto-plastic. Here, we introduce a novel approach to numerically model magma dynamics, focusing on the conceptual study of melt extraction from an asthenospheric source of partial melt through the overlying lithosphere and crust. To this end, we introduce an adapted set of two-phase flow equations, coupled to a visco-elasto-plastic rheology for both shear and compaction deformation of the host rock in interaction with the melt phase. We describe in detail how to implement this physical model into a finite-element code, and then proceed to evaluate the functionality and potential of this methodology using a series of conceptual model setups, which demonstrate the modes of melt extraction occurring around the rheological transition from ductile to brittle host rocks. The models suggest that three principal regimes of melt extraction emerge: viscous diapirism, viscoplastic decompaction channels and elasto-plastic dyking. Thus, our model of magma dynamics interacting with active tectonics of the lithosphere and crust provides a novel framework to further investigate magmato-tectonic processes such as the formation and geometry of magma chambers and conduits, as well as the emplacement of plutonic rock complexe

Neutrino oscillations in matter of varying density

We consider two-family neutrino oscillations in a medium of continuously-varying density as a limit of the process in a series of constant-density layers. We construct analytic expressions for the conversion amplitude at high energies within a medium with a density profile that is piecewise linear. We compare some cases to understand the type of effects that depend on the order of the material traversed by a neutrino beam.Comment: 10 page

Field-theoretic formulation of the bootstrap hypothesis

A precise statement of the bootstrap theory in the language of conventional Lagrangian field theory is given. Under no further assumptions than the Mandelstam representation, it is shown that this closed-form theory is equivalent to the more usual S-matrix formulation in terms of Regge trajectories. The assumptions of the bootstrap theory are stated in terms of the vanishing of well-defined renormalization constants Z. All standard results and approximation methods in the bootstrap theory are shown to follow directly from the Z=0 conditions