12,942 research outputs found
The Sun's Supergranulation
Supergranulation is a fluid-dynamical phenomenon taking place in the solar
photosphere, primarily detected in the form of a vigorous cellular flow pattern
with a typical horizontal scale of approximately 30--35~megameters, a dynamical
evolution time of 24--48~h, a strong 300--400~m/s (rms) horizontal flow
component and a much weaker 20--30~m/s vertical component. Supergranulation was
discovered more than sixty years ago, however, explaining its physical origin
and most important observational characteristics has proven extremely
challenging ever since, as a result of the intrinsic multiscale, nonlinear
dynamical complexity of the problem concurring with strong observational and
computational limitations. Key progress on this problem is now taking place
with the advent of 21st-century supercomputing resources and the availability
of global observations of the dynamics of the solar surface with high spatial
and temporal resolutions. This article provides an exhaustive review of
observational, numerical and theoretical research on supergranulation, and
discusses the current status of our understanding of its origin and dynamics,
most importantly in terms of large-scale nonlinear thermal convection, in the
light of a selection of recent findings.Comment: Major update of 2010 Liv. Rev. Sol. Phys. review. Addresses many new
theoretical, numerical and observational developments. All sections,
including discussion, revised extensively. Also includes previously
unpublished results on nonlinear dynamics of convection in large domains, and
lagrangian transport at the solar surfac
Dynamics of Simple Balancing Models with State Dependent Switching Control
Time-delayed control in a balancing problem may be a nonsmooth function for a
variety of reasons. In this paper we study a simple model of the control of an
inverted pendulum by either a connected movable cart or an applied torque for
which the control is turned off when the pendulum is located within certain
regions of phase space. Without applying a small angle approximation for
deviations about the vertical position, we see structurally stable periodic
orbits which may be attracting or repelling. Due to the nonsmooth nature of the
control, these periodic orbits are born in various discontinuity-induced
bifurcations. Also we show that a coincidence of switching events can produce
complicated periodic and aperiodic solutions.Comment: 36 pages, 12 figure
Explicit solution for vibrating bar with viscous boundaries and internal damper
We investigate longitudinal vibrations of a bar subjected to viscous boundary
conditions at each end, and an internal damper at an arbitrary point along the
bar's length. The system is described by four independent parameters and
exhibits a variety of behaviors including rigid motion, super
stability/instability and zero damping. The solution is obtained by applying
the Laplace transform to the equation of motion and computing the Green's
function of the transformed problem. This leads to an unconventional
eigenvalue-like problem with the spectral variable in the boundary conditions.
The eigenmodes of the problem are necessarily complex-valued and are not
orthogonal in the usual inner product. Nonetheless, in generic cases we obtain
an explicit eigenmode expansion for the response of the bar to initial
conditions and external force. For some special values of parameters the system
of eigenmodes may become incomplete, or no non-trivial eigenmodes may exist at
all. We thoroughly analyze physical and mathematical reasons for this behavior
and explicitly identify the corresponding parameter values. In particular, when
no eigenmodes exist, we obtain closed form solutions. Theoretical analysis is
complemented by numerical simulations, and analytic solutions are compared to
computations using finite elements.Comment: 29 pages, 6 figure
Aspects of Bifurcation Theory for Piecewise-Smooth, Continuous Systems
Systems that are not smooth can undergo bifurcations that are forbidden in
smooth systems. We review some of the phenomena that can occur for
piecewise-smooth, continuous maps and flows when a fixed point or an
equilibrium collides with a surface on which the system is not smooth. Much of
our understanding of these cases relies on a reduction to piecewise linearity
near the border-collision. We also review a number of codimension-two
bifurcations in which nonlinearity is important.Comment: pdfLaTeX, 9 figure
Phase Separation in Binary Fluid Mixtures with Continuously Ramped Temperature
We consider the demixing of a binary fluid mixture, under gravity, which is
steadily driven into a two phase region by slowly ramping the temperature. We
assume, as a first approximation, that the system remains spatially isothermal,
and examine the interplay of two competing nonlinearities. One of these arises
because the supersaturation is greatest far from the meniscus, creating
inversion of the density which can lead to fluid motion; although isothermal,
this is somewhat like the Benard problem (a single-phase fluid heated from
below). The other is the intrinsic diffusive instability which results either
in nucleation or in spinodal decomposition at large supersaturations.
Experimental results on a simple binary mixture show interesting oscillations
in heat capacity and optical properties for a wide range of ramp parameters. We
argue that these oscillations arise under conditions where both nonlinearities
are important
Experimental investigation into localized instabilities of mixed Rayleigh-BĂ©nard-Poiseuille convection
The stability of the Rayleigh-BĂ©nard-Poiseuille flow in a channel with large transverse aspect ratio (ratio of width to vertical channel height) is studied experimentally. The onset of thermal convection in the form of âtransverse rolls' (rolls with axes perpendicular to the Poiseuille flow direction) is determined in the Reynolds-Rayleigh number plane for two different working fluids: water and mineral oil with Prandtl numbers of approximately 6.5 and 450, respectively. By analysing experimental realizations of the system impulse response it is demonstrated that the observed onset of transverse rolls corresponds to their transition from convective to absolute instability. Finally, the system response to localized patches of supercriticality (in practice local âhot spots') is observed and compared with analytical and numerical results of Martinand, CarriĂšre & Monkewitz (J. Fluid Mech., vol. 502, 2004, p. 175 and vol. 551, 2006, p. 275). The experimentally observed two-dimensional saturated global modes associated with these patches appear to be of the âsteep' variety, analogous to the one-dimensional steep nonlinear modes of Pier, Huerre & Chomaz (Physica D, vol. 148, 2001, p. 49
Acceleration and collimation of relativistic MHD disk winds
We perform axisymmetric relativistic magnetohydrodynamic (MHD) simulations to
investigate the acceleration and collimation of jets and outflows from disks
around compact objects. The fiducial disk surface (respectively a slow disk
wind) is prescribed as boundary condition for the outflow. We apply this
technique for the first time in the context of relativistic jets. The strength
of this approach is that it allows us to run a parameter study in order to
investigate how the accretion disk conditions govern the outflow formation. Our
simulations using the PLUTO code run for 500 inner disk rotations and on a
physical grid size of 100x200 inner disk radii. In general, we obtain
collimated beams of mildly relativistic speed and mass-weighted half-opening
angles of 3-7 degrees. When we increase the outflow Poynting flux by injecting
an additional disk toroidal field into the inlet, Lorentz factors up to 6 are
reached. These flows gain super-magnetosonic speed and remain Poynting flux
dominated. The light surface of the outflow magnetosphere tends to align
vertically - implying three relativistically distinct regimes in the flow - an
inner sub-relativistic domain close to the jet axis, a (rather narrow)
relativistic jet and a surrounding subrelativistic outflow launched from the
outer disk surface - similar to the spine-sheath structure currently discussed
for asymptotic jet propagation and stability. The outer subrelativistic disk
wind is a promising candidate for the X-ray absorption winds that are observed
in many radio-quiet AGN.Comment: 22 pages, 15 figures; accepted for publication in ApJ; incorporates
changes according to refere
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