1,249 research outputs found
A rigorous formulation of the cosmological Newtonian limit without averaging
We prove the existence of a large class of one-parameter families of
cosmological solutions to the Einstein-Euler equations that have a Newtonian
limit. This class includes solutions that represent a finite, but otherwise
arbitrary, number of compact fluid bodies. These solutions provide exact
cosmological models that admit Newtonian limits but, are not, either implicitly
or explicitly, averaged
Density of critical points for a Gaussian random function
Critical points of a scalar quantitiy are either extremal points or saddle
points. The character of the critical points is determined by the sign
distribution of the eigenvalues of the Hessian matrix. For a two-dimensional
homogeneous and isotropic random function topological arguments are sufficient
to show that all possible sign combinations are equidistributed or with other
words, the density of the saddle points and extrema agree. This argument breaks
down in three dimensions. All ratios of the densities of saddle points and
extrema larger than one are possible. For a homogeneous Gaussian random field
one finds no longer an equidistribution of signs, saddle points are slightly
more frequent.Comment: 11 pages 1 figure, changes in list of references, corrected typo
MRI of "diffusion" in the human brain: New results using a modified CE-FAST sequence.
“Diffusion-weighted” MRI in the normal human brain and in a patient with a cerebral metastasis is demonstrated. The method employed was a modified CE-FAST sequence with imaging times of only 6-10 s using a conventional 1.5-T whole-body MRI system (Siemens Magnetom). As with previous phantom and animal studies, the use of strong gradients together with macroscopic motions in vivo causes unavoidable artifacts in diffusion-weighted images of the human brain. While these artifacts are shown to be considerably reduced by averaging of 8-16 images, the resulting diffusion contrast is compromised by unknown signal losses due to motion
Dynamical elastic bodies in Newtonian gravity
Well-posedness for the initial value problem for a self-gravitating elastic
body with free boundary in Newtonian gravity is proved. In the material frame,
the Euler-Lagrange equation becomes, assuming suitable constitutive properties
for the elastic material, a fully non-linear elliptic-hyperbolic system with
boundary conditions of Neumann type. For systems of this type, the initial data
must satisfy compatibility conditions in order to achieve regular solutions.
Given a relaxed reference configuration and a sufficiently small Newton's
constant, a neigborhood of initial data satisfying the compatibility conditions
is constructed
Spatial Structure of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas
We investigate analytically and numerically the spatial structure of the
non-equilibrium stationary states (NESS) of a point particle moving in a two
dimensional periodic Lorentz gas (Sinai Billiard). The particle is subject to a
constant external electric field E as well as a Gaussian thermostat which keeps
the speed |v| constant. We show that despite the singular nature of the SRB
measure its projections on the space coordinates are absolutely continuous. We
further show that these projections satisfy linear response laws for small E.
Some of them are computed numerically. We compare these results with those
obtained from simple models in which the collisions with the obstacles are
replaced by random collisions.Similarities and differences are noted.Comment: 24 pages with 9 figure
Existence of axially symmetric static solutions of the Einstein-Vlasov system
We prove the existence of static, asymptotically flat non-vacuum spacetimes
with axial symmetry where the matter is modeled as a collisionless gas. The
axially symmetric solutions of the resulting Einstein-Vlasov system are
obtained via the implicit function theorem by perturbing off a suitable
spherically symmetric steady state of the Vlasov-Poisson system.Comment: 32 page
Computing domains of attraction for planar dynamics
In this note we investigate the problem of computing the
domain of attraction of a
ow on R2 for a given attractor. We consider
an operator that takes two inputs, the description of the
ow and a cover
of the attractors, and outputs the domain of attraction for the given
attractor. We show that: (i) if we consider only (structurally) stable
systems, the operator is (strictly semi-)computable; (ii) if we allow all
systems de ned by C1-functions, the operator is not (semi-)computable.
We also address the problem of computing limit cycles on these systems
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