13,400 research outputs found
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 over \Q and conjecture that \mu(\Lf_n) > n+1.
Experiments with our algorithms suggest that \mu(\Lf_n) is polynomial in .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
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