Estimation of poroelastic parameters from seismograms using Biot theory

We investigate the possibility to extract information contained in seismic waveforms propagating in fluid-filled porous media by developing and using a full waveform inversion procedure valid for layered structures. To reach this objective, we first solve the forward problem by implementing the Biot theory in a reflectivity-type simulation program. We then study the sensitivity of the seismic response of stratified media to the poroelastic parameters. Our numerical tests indicate that the porosity and consolidation parameter are the most sensitive parameters in forward and inverse modeling, whereas the permeability has only a very limited influence on the seismic response. Next, the analytical expressions of the sensitivity operators are introduced in a generalized least-square inversion algorithm based on an iterative modeling of the seismic waveforms. The application of this inversion procedure to synthetic data shows that the porosity as well as the fluid and solid parameters can be correctly reconstructed as long as the other parameters are well known. However, the strong seismic coupling between some of the model parameters makes it difficult to fully characterize the medium by a multi-parameter inversion scheme. One solution to circumvent this difficulty is to combine several model parameters according to rock physics laws to invert for composite parameters. Another possibility is to invert the seismic data for the perturbations of the medium properties, such as those resulting from a gas injection

Computing faithful representations for nilpotent Lie algebras

We describe three methods to determine a faithful representation of small dimension for a finite-dimensional nilpotent Lie algebra over an arbitrary field. We apply our methods in finding bounds for the smallest dimension \mu(\Lg) of a faithful \Lg-module for some nilpotent Lie algebras \Lg. In particular, we describe an infinite family of filiform nilpotent Lie algebras \Lf_n of dimension $n$ over \Q and conjecture that \mu(\Lf_n) > n+1. Experiments with our algorithms suggest that \mu(\Lf_n) is polynomial in $n$.Comment: 14 page

Regular subalgebras and nilpotent orbits of real graded Lie algebras

For a semisimple Lie algebra over the complex numbers, Dynkin (1952) developed an algorithm to classify the regular semisimple subalgebras, up to conjugacy by the inner automorphism group. For a graded semisimple Lie algebra over the complex numbers, Vinberg (1979) showed that a classification of a certain type of regular subalgebras (called carrier algebras) yields a classification of the nilpotent orbits in a homogeneous component of that Lie algebra. Here we consider these problems for (graded) semisimple Lie algebras over the real numbers. First, we describe an algorithm to classify the regular semisimple subalgebras of a real semisimple Lie algebra. This also yields an algorithm for listing, up to conjugacy, the carrier algebras in a real graded semisimple real algebra. We then discuss what needs to be done to obtain a classification of the nilpotent orbits from that; such classifications have applications in differential geometry and theoretical physics. Our algorithms are implemented in the language of the computer algebra system GAP, using our package CoReLG; we report on example computations

Diffusive spreading and mixing of fluid monolayers

The use of ultra-thin, i.e., monolayer films plays an important role for the emerging field of nano-fluidics. Since the dynamics of such films is governed by the interplay between substrate-fluid and fluid-fluid interactions, the transport of matter in nanoscale devices may be eventually efficiently controlled by substrate engineering. For such films, the dynamics is expected to be captured by two-dimensional lattice-gas models with interacting particles. Using a lattice gas model and the non-linear diffusion equation derived from the microscopic dynamics in the continuum limit, we study two problems of relevance in the context of nano-fluidics. The first one is the case in which along the spreading direction of a monolayer a mesoscopic-sized obstacle is present, with a particular focus on the relaxation of the fluid density profile upon encountering and passing the obstacle. The second one is the mixing of two monolayers of different particle species which spread side by side following the merger of two chemical lanes, here defined as domains of high affinity for fluid adsorption surrounded by domains of low affinity for fluid adsorption.Comment: 12 pages, 3 figure

Quasiconformality and mass

We identify universal quasiconformal (walking) behaviour in non-Abelian gauge field theories based on the mass-dependent all-order beta-function introduced in arXiv:0908.1364. We find different types of walking behaviour in the presence of (partially) massive species. We employ our findings to the construction of candidate theories for dynamical electroweak symmetry breaking by walking technicolour.Comment: 16 pages, 8 figures

A Simple Geometrical Model for Solid Friction

We present a simple model for the friction of two solid bodies moving against each other. In a self consistent way we can obtain the dependence of the macroscopic friction force as a function of the driving velocity, the normal force and the ruggedness of the surfaces in contact. Our results are discussed in the context of friction laws used in earthquake models.Comment: 9 pages, plain TeX, preprint HLRZ 24/9

Competition of languages in the presence of a barrier

Using the Schulze model for Monte Carlo simulations of language competition, we include a barrier between the top half and the bottom half of the lattice. We check under which conditions two different languages evolve as dominating in the two halves.Comment: 6 pages including 3 figure