42,648 research outputs found
Recursion relations for Double Ramification Hierarchies
In this paper we study various properties of the double ramification
hierarchy, an integrable hierarchy of hamiltonian PDEs introduced in [Bur15]
using intersection theory of the double ramification cycle in the moduli space
of stable curves. In particular, we prove a recursion formula that recovers the
full hierarchy starting from just one of the Hamiltonians, the one associated
to the first descendant of the unit of a cohomological field theory. Moreover,
we introduce analogues of the topological recursion relations and the divisor
equation both for the hamiltonian densities and for the string solution of the
double ramification hierarchy. This machinery is very efficient and we apply it
to various computations for the trivial and Hodge cohomological field theories,
and for the -spin Witten's classes. Moreover we prove the Miura equivalence
between the double ramification hierarchy and the Dubrovin-Zhang hierarchy for
the Gromov-Witten theory of the complex projective line (extended Toda
hierarchy).Comment: Revised version, to be published in Communications in Mathematical
Physics, 27 page
Mean-field expansion for spin models with medium-range interactions
We study the critical crossover between the Gaussian and the Wilson-Fisher
fixed point for general O(N)-invariant spin models with medium-range
interactions. We perform a systematic expansion around the mean-field solution,
obtaining the universal crossover curves and their leading corrections. In
particular we show that, in three dimensions, the leading correction scales as
being the range of the interactions. We compare our results with
the existing numerical ones obtained by Monte Carlo simulations and present a
critical discussion of other approaches.Comment: 49 pages, 8 figure
Linear stability analysis of magnetized relativistic jets: the nonrotating case
We perform a linear analysis of the stability of a magnetized relativistic
non-rotating cylindrical flow in the aproximation of zero thermal pressure,
considering only the m = 1 mode. We find that there are two modes of
instability: Kelvin-Helmholtz and current driven. The Kelvin-Helmholtz mode is
found at low magnetizations and its growth rate depends very weakly on the
pitch parameter. The current driven modes are found at high magnetizations and
the value of the growth rate and the wavenumber of the maximum increase as we
decrease the pitch parameter. In the relativistic regime the current driven
mode is splitted in two branches, the branch at high wavenumbers is
characterized by the eigenfunction concentrated in the jet core, the branch at
low wavenumbers is instead characterized by the eigenfunction that extends
outside the jet velocity shear region.Comment: 22 pages, 13 figures, MNRAS in pres
Linear and nonlinear evolution of current-carrying highly magnetized jets
We investigate the linear and nonlinear evolution of current-carrying jets in
a periodic configuration by means of high resolution three-dimensional
numerical simulations. The jets under consideration are strongly magnetized
with a variable pitch profile and initially in equilibrium under the action of
a force-free magnetic field. The growth of current-driven (CDI) and
Kelvin-Helmholtz (KHI) instabilities is quantified using three selected cases
corresponding to static, Alfvenic and super-Alfvenic jets.
During the early stages, we observe large-scale helical deformations of the
jet corresponding to the growth of the initially excited CDI mode. A direct
comparison between our simulation results and the analytical growth rates
obtained from linear theory reveals good agreement on condition that
high-resolution and accurate discretization algorithms are employed.
After the initial linear phase, the jet structure is significantly altered
and, while slowly-moving jets show increasing helical deformations, larger
velocity shear are violently disrupted on a few Alfven crossing time leaving a
turbulent flow structure. Overall, kinetic and magnetic energies are quickly
dissipated into heat and during the saturated regime the jet momentum is
redistributed on a larger surface area with most of the jet mass travelling at
smaller velocities. The effectiveness of this process is regulated by the onset
of KHI instabilities taking place at the jet/ambient interface and can be held
responsible for vigorous jet braking and entrainment.Comment: 14 pages, 11 figure
Fully Convective Magnetorotational Turbulence in Stratified Shearing Boxes
We present a numerical study of turbulence and dynamo action in stratified
shearing boxes with zero magnetic flux. We assume that the fluid obeys the
perfect gas law and has finite (constant) thermal diffusivity. We choose
radiative boundary conditions at the vertical boundaries in which the heat flux
is propor- tional to the fourth power of the temperature. We compare the
results with the corresponding cases in which fixed temperature boundary
conditions are applied. The most notable result is that the formation of a
fully convective state in which the density is nearly constant as a function of
height and the heat is transported to the upper and lower boundaries by
overturning motions is robust and persists even in cases with radiative
boundary conditions. Interestingly, in the convective regime, although the
diffusive transport is negligible the mean stratification does not relax to an
adiabatic state.Comment: 11 pages, 4 figures, accepted for publication in ApJ Letter
On the convergence of Magnetorotational turbulence in stratified isothermal shearing boxes
We consider the problem of convergence in stratified isothermal shearing
boxes with zero net magnetic flux. We present results with the highest
resolution to-date--up to 200 grid-point per pressure scale height--that show
no clear evidence of convergence. Rather, the Maxwell stresses continue to
decrease with increasing resolution. We propose some possible scenarios to
explain the lack of convergence based on multi-layer dynamo systems.Comment: 10 pages, 4 figures, accepted for publication in ApJ Letter
Magnetic Helicities and Dynamo Action in Magneto-rotationally Driven Turbulence
We examine the relationship between magnetic flux generation, taken as an
indicator of large-scale dynamo action, and magnetic helicity, computed as an
integral over the dynamo volume, in a simple dynamo. We consider dynamo action
driven by Magneto-Rotational Turbulence (MRT) within the shearing-box
approximation. We consider magnetically open boundary conditions that allow a
flux of helicity in or out of the computational domain. We circumvent the
problem of the lack of gauge invariance in open domains by choosing a
particular gauge -- the winding gauge -- that provides a natural interpretation
in terms of average winding number of pairwise field lines. We use this gauge
precisely to define and measure the helicity and helicity flux for several
realizations of dynamo action. We find in these cases, that the system as a
whole does not break reflectional symmetry and the total helicity remains small
even in cases when substantial magnetic flux is generated. We find no
particular connection between the generation of magnetic flux and the helicity
or the helicity flux through the boundaries. We suggest that this result may be
due to the essentially nonlinear nature of the dynamo processes in MRT.Comment: 26 pages, 10 figures, ApJ accepte
Quantized vortices in two dimensional solid 4He
Diagonal and off-diagonal properties of 2D solid 4He systems doped with a
quantized vortex have been investigated via the Shadow Path Integral Ground
State method using the fixed-phase approach. The chosen approximate phase
induces the standard Onsager-Feynman flow field. In this approximation the
vortex acts as a static external potential and the resulting Hamiltonian can be
treated exactly with Quantum Monte Carlo methods. The vortex core is found to
sit in an interstitial site and a very weak relaxation of the lattice positions
away from the vortex core position has been observed. Also other properties
like Bragg peaks in the static structure factor or the behavior of vacancies
are very little affected by the presence of the vortex. We have computed also
the one-body density matrix in perfect and defected 4He crystals finding that
the vortex has no sensible effect on the off-diagonal long range tail of the
density matrix. Within the assumed Onsager Feynman phase, we find that a
quantized vortex cannot auto-sustain itself unless a condensate is already
present like when dislocations are present. It remains to be investigated if
backflow can change this conclusion.Comment: 4 pages, 3 figures, LT26 proceedings, accepted for publication in
Journal of Physics: Conference Serie
Making Fanaroff-Riley I radio sources. Numerical Hydrodynamic 3D Simulations of Low Power Jets
Extragalactic radio sources have been classified into two classes,
Fanaroff-Riley I and II, which differ in morphology and radio power. Strongly
emitting sources belong to the edge-brightened FR II class, and weakly emitting
sources to the edge-darkened FR I class. The origin of this dichotomy is not
yet fully understood. Numerical simulations are successful in generating FR II
morphologies, but they fail to reproduce the diffuse structure of FR Is.
By means of hydro-dynamical 3D simulations of supersonic jets, we investigate
how the displayed morphologies depend on the jet parameters. Bow shocks and
Mach disks at the jet head, which are probably responsible for the hot spots in
the FR II sources, disappear for a jet kinetic power L_kin < 10^43 erg/s. This
threshold compares favorably with the luminosity at which the FR I/FR II
transition is observed.
The problem is addressed by numerical means carrying out 3D HD simulations of
supersonic jets that propagate in a non-homogeneous medium with the ambient
temperature that increases with distance from the jet origin, which maintains
constant pressure.
The jet energy in the lower power sources, instead of being deposited at the
terminal shock, is gradually dissipated by the turbulence. The jets spread out
while propagating, and they smoothly decelerate while mixing with the ambient
medium and produce the plumes characteristic of FR I objects.
Three-dimensionality is an essential ingredient to explore the FR I evolution
because the properties of turbulence in two and three dimensions are very
different, since there is no energy cascade to small scales in two dimensions,
and two-dimensional simulations with the same parameters lead to FRII-like
behavior.Comment: 11 pages, 12 figures, to appear on A&
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