16,052 research outputs found
Flux surface shaping effects on tokamak edge turbulence and flows
Shaping of magnetic flux surfaces is found to have a strong impact on
turbulence and transport in tokamak edge plasmas. A series of axisymmetric
equilibria with varying elongation and triangularity, and a divertor
configuration are implemented into a computational gyrofluid turbulence model.
The mechanisms of shaping effects on turbulence and flows are identified.
Transport is mainly reduced by local magnetic shearing and an enhancement of
zonal shear flows induced by elongation and X-point shaping.Comment: 10 pages, 11 figures. Submitted to Physics of Plasma
Riemann solvers and undercompressive shocks of convex FPU chains
We consider FPU-type atomic chains with general convex potentials. The naive
continuum limit in the hyperbolic space-time scaling is the p-system of mass
and momentum conservation. We systematically compare Riemann solutions to the
p-system with numerical solutions to discrete Riemann problems in FPU chains,
and argue that the latter can be described by modified p-system Riemann
solvers. We allow the flux to have a turning point, and observe a third type of
elementary wave (conservative shocks) in the atomistic simulations. These waves
are heteroclinic travelling waves and correspond to non-classical,
undercompressive shocks of the p-system. We analyse such shocks for fluxes with
one or more turning points.
Depending on the convexity properties of the flux we propose FPU-Riemann
solvers. Our numerical simulations confirm that Lax-shocks are replaced by so
called dispersive shocks. For convex-concave flux we provide numerical evidence
that convex FPU chains follow the p-system in generating conservative shocks
that are supersonic. For concave-convex flux, however, the conservative shocks
of the p-system are subsonic and do not appear in FPU-Riemann solutions
Magnetic models on Apollonian networks
Thermodynamic and magnetic properties of Ising models defined on the
triangular Apollonian network are investigated. This and other similar networks
are inspired by the problem of covering an Euclidian domain with circles of
maximal radii. Maps for the thermodynamic functions in two subsequent
generations of the construction of the network are obtained by formulating the
problem in terms of transfer matrices. Numerical iteration of this set of maps
leads to exact values for the thermodynamic properties of the model. Different
choices for the coupling constants between only nearest neighbors along the
lattice are taken into account. For both ferromagnetic and anti-ferromagnetic
constants, long range magnetic ordering is obtained. With exception of a size
dependent effective critical behavior of the correlation length, no evidence of
asymptotic criticality was detected.Comment: 21 pages, 5 figure
Diffusion and spectral dimension on Eden tree
We calculate the eigenspectrum of random walks on the Eden tree in two and
three dimensions. From this, we calculate the spectral dimension and the
walk dimension and test the scaling relation (
for an Eden tree). Finite-size induced crossovers are observed, whereby the
system crosses over from a short-time regime where this relation is violated
(particularly in two dimensions) to a long-time regime where the behavior
appears to be complicated and dependent on dimension even qualitatively.Comment: 11 pages, Plain TeX with J-Phys.sty style, HLRZ 93/9
Multiple Invaded Consolidating Materials
We study a multiple invasion model to simulate corrosion or intrusion
processes. Estimated values for the fractal dimension of the invaded region
reveal that the critical exponents vary as function of the generation number
, i.e., with the number of times the invasion process takes place. The
averaged mass of the invaded region decreases with a power-law as a
function of , , where the exponent . We
also find that the fractal dimension of the invaded cluster changes from
to . This result confirms that the
multiple invasion process follows a continuous transition from one universality
class (NTIP) to another (optimal path). In addition, we report extensive
numerical simulations that indicate that the mass distribution of avalanches
has a power-law behavior and we find that the exponent
governing the power-law changes continuously as a
function of the parameter . We propose a scaling law for the mass
distribution of avalanches for different number of generations .Comment: 8 pages and 16 figure
Gaussian model of explosive percolation in three and higher dimensions
The Gaussian model of discontinuous percolation, recently introduced by
Ara\'ujo and Herrmann [Phys. Rev. Lett., 105, 035701 (2010)], is numerically
investigated in three dimensions, disclosing a discontinuous transition. For
the simple-cubic lattice, in the thermodynamic limit, we report a finite jump
of the order parameter, . The largest cluster at the
threshold is compact, but its external perimeter is fractal with fractal
dimension . The study is extended to hypercubic lattices up
to six dimensions and to the mean-field limit (infinite dimension). We find
that, in all considered dimensions, the percolation transition is
discontinuous. The value of the jump in the order parameter, the maximum of the
second moment, and the percolation threshold are analyzed, revealing
interesting features of the transition and corroborating its discontinuous
nature in all considered dimensions. We also show that the fractal dimension of
the external perimeter, for any dimension, is consistent with the one from
bridge percolation and establish a lower bound for the percolation threshold of
discontinuous models with finite number of clusters at the threshold
On the Shape of the Tail of a Two Dimensional Sand Pile
We study the shape of the tail of a heap of granular material. A simple
theoretical argument shows that the tail adds a logarithmic correction to the
slope given by the angle of repose. This expression is in good agreement with
experiments. We present a cellular automaton that contains gravity, dissipation
and surface roughness and its simulation also gives the predicted shape.Comment: LaTeX file 4 pages, 4 PS figures, also available at
http://pmmh.espci.fr
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