242 research outputs found
Singularity Theory for W-Algebra Potentials
The Landau potentials of -algebra models are analyzed with
algebraic-geometric methods. The number of ground states and the number of
independent perturbations of every potential coincide and can be computed. This
number agrees with the structure of ground states obtained in a previous paper,
namely, as the phase structure of the IRF models of Jimbo et al. The
singularities associated to these potentials are identified.Comment: 11 pp., LaTeX file, UVA-93-4
The exact renormalization group in Astrophysics
The coarse-graining operation in hydrodynamics is equivalent to a change of
scale which can be formalized as a renormalization group transformation. In
particular, its application to the probability distribution of a
self-gravitating fluid yields an "exact renormalization group equation" of
Fokker-Planck type. Since the time evolution of that distribution can also be
described by a Fokker-Planck equation, we propose a connection between both
equations, that is, a connection between scale and time evolution. We finally
remark on the essentially non-perturbative nature of astrophysical problems,
which suggests that the exact renormalization group is the adequate tool for
them.Comment: World Scientific style, 6 pages, presented at the 2nd Conference on
the Exact RG, Rome 200
Renormalization group irreversible functions in more than two dimensions
There are two general irreversibility theorems for the renormalization group
in more than two dimensions: the first one is of entropic nature, while the
second one, by Forte and Latorre, relies on the properties of the stress-tensor
trace, and has been recently questioned by Osborn and Shore. We start by
establishing under what assumptions this second theorem can still be valid.
Then it is compared with the entropic theorem and shown to be essentially
equivalent. However, since the irreversible function of the (corrected)
Forte-Latorre theorem is non universal (whereas the relative entropy of the
other theorem is universal), it needs the additional step of renormalization.
On the other hand, the irreversibility theorem is only guaranteed to be
unambiguous if the integral of the stress-tensor trace correlator is finite,
which happens for free theories only in dimension smaller than four.Comment: 4 pages; minor changes to improve readability; to appear in Phys.
Rev.
A non-perturbative Kolmogorov turbulence approach to the cosmic web structure
The Kolmogorov approach to turbulence is applied to the Burgers turbulence in the stochastic adhesion model of large-scale structure formation. As the perturbative approach to this model is unreliable, here a new, non-perturbative approach, based on a suitable formulation of Kolmogorov's scaling laws, is proposed. This approach suggests that the power-law exponent of the matter density two-point correlation function is in the range 1–1.33, but it also suggests that the adhesion model neglects important aspects of the gravitational dynamics
Pressure measurements on real high-speed trains travelling through tunnels
From November, 2006 to March, 2008 a series of tests were performed onboard a wide variety of trains in order to check their response to pressure waves generated while passing through tunnels. In this communication part of the experimental results are presented, showing the pressure waves generated and focusing on the differences caused by some parameters involved such as train length and shape or tunnel lengths. The results are in accordance with the train wave signature method and the one-dimensional pressure wave theory
Nonlinear spherical gravitational downfall of gas onto a solid ball: analytic and numerical results
The process of downfall of initially homogeneous gas onto a solid ball due to
the ball's gravity (relevant in astrophysical situations) is studied with a
combination of analytic and numerical methods. The initial explicit solution
soon becomes discontinuous and gives rise to a shock wave. Afterwards, there is
a crossover between two intermediate asymptotic similarity regimes, where the
shock wave propagates outwards according to two self-similar laws, initially
accelerating and eventually decelerating and vanishing, leading to a static
state. The numerical study allows one to investigate in detail this dynamical
problem and its time evolution, verifying and complementing the analytic
results on the initial solution, intermediate self-similar laws and static
long-term solution.Comment: 19 pages, 10 PS figures (some large
Anisotropy in Homogeneous Rotating Turbulence
The effective stress tensor of a homogeneous turbulent rotating fluid is
anisotropic. This leads us to consider the most general axisymmetric four-rank
``viscosity tensor'' for a Newtonian fluid and the new terms in the turbulent
effective force on large scales that arise from it, in addition to the
microscopic viscous force. Some of these terms involve couplings to vorticity
and others are angular momentum non conserving (in the rotating frame).
Furthermore, we explore the constraints on the response function and the
two-point velocity correlation due to axisymmetry. Finally, we compare our
viscosity tensor with other four-rank tensors defined in current approaches to
non-rotating anisotropic turbulence.Comment: 14 pages, RevTe
Statistics and geometry of cosmic voids
We introduce new statistical methods for the study of cosmic voids, focusing
on the statistics of largest size voids. We distinguish three different types
of distributions of voids, namely, Poisson-like, lognormal-like and Pareto-like
distributions. The last two distributions are connected with two types of
fractal geometry of the matter distribution. Scaling voids with Pareto
distribution appear in fractal distributions with box-counting dimension
smaller than three (its maximum value), whereas the lognormal void distribution
corresponds to multifractals with box-counting dimension equal to three.
Moreover, voids of the former type persist in the continuum limit, namely, as
the number density of observable objects grows, giving rise to lacunar
fractals, whereas voids of the latter type disappear in the continuum limit,
giving rise to non-lacunar (multi)fractals. We propose both lacunar and
non-lacunar multifractal models of the cosmic web structure of the Universe. A
non-lacunar multifractal model is supported by current galaxy surveys as well
as cosmological -body simulations. This model suggests, in particular, that
small dark matter halos and, arguably, faint galaxies are present in cosmic
voids.Comment: 39 pages, 8 EPS figures, supersedes arXiv:0802.038
Stochastic formulation of the renormalization group: supersymmetric structure and topology of the space of couplings
The exact or Wilson renormalization group equations can be formulated as a
functional Fokker-Planck equation in the infinite-dimensional configuration
space of a field theory, suggesting a stochastic process in the space of
couplings. Indeed, the ordinary renormalization group differential equations
can be supplemented with noise, making them into stochastic Langevin equations.
Furthermore, if the renormalization group is a gradient flow, the space of
couplings can be endowed with a supersymmetric structure a la Parisi-Sourlas.
The formulation of the renormalization group as supersymmetric quantum
mechanics is useful for analysing the topology of the space of couplings by
means of Morse theory. We present simple examples with one or two couplings.Comment: 13 pages, based on contribution to "Progress in Supersymmetric
Quantum Mechanics" (Valladolid U.), accepted in Journal of Physics
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