15,698 research outputs found
Proceedings for the ICASE Workshop on Heterogeneous Boundary Conditions
Domain Decomposition is a complex problem with many interesting aspects. The choice of decomposition can be made based on many different criteria, and the choice of interface of internal boundary conditions are numerous. The various regions under study may have different dynamical balances, indicating that different physical processes are dominating the flow in these regions. This conference was called in recognition of the need to more clearly define the nature of these complex problems. This proceedings is a collection of the presentations and the discussion groups
Order out of Randomness : Self-Organization Processes in Astrophysics
Self-organization is a property of dissipative nonlinear processes that are
governed by an internal driver and a positive feedback mechanism, which creates
regular geometric and/or temporal patterns and decreases the entropy, in
contrast to random processes. Here we investigate for the first time a
comprehensive number of 16 self-organization processes that operate in
planetary physics, solar physics, stellar physics, galactic physics, and
cosmology. Self-organizing systems create spontaneous {\sl order out of chaos},
during the evolution from an initially disordered system to an ordered
stationary system, via quasi-periodic limit-cycle dynamics, harmonic mechanical
resonances, or gyromagnetic resonances. The internal driver can be gravity,
rotation, thermal pressure, or acceleration of nonthermal particles, while the
positive feedback mechanism is often an instability, such as the
magneto-rotational instability, the Rayleigh-B\'enard convection instability,
turbulence, vortex attraction, magnetic reconnection, plasma condensation, or
loss-cone instability. Physical models of astrophysical self-organization
processes involve hydrodynamic, MHD, and N-body formulations of Lotka-Volterra
equation systems.Comment: 61 pages, 38 Figure
Wave modelling - the state of the art
This paper is the product of the wave modelling community and it tries to make a picture of the present situation in this branch of science, exploring the previous and the most recent results and looking ahead towards the solution of the problems we presently face. Both theory and applications are considered.
The many faces of the subject imply separate discussions. This is reflected into the single sections, seven of them, each dealing with a specific topic, the whole providing a broad and solid overview of the present state of the art. After an introduction framing the problem and the approach we followed, we deal in sequence with the following subjects: (Section) 2, generation by wind; 3, nonlinear interactions in deep water; 4, white-capping dissipation; 5, nonlinear interactions in shallow water; 6, dissipation at the sea bottom; 7, wave propagation; 8, numerics. The two final sections, 9 and 10, summarize the present situation from a general point of view and try to look at the future developments
A delay differential model of ENSO variability: Parametric instability and the distribution of extremes
We consider a delay differential equation (DDE) model for El-Nino Southern
Oscillation (ENSO) variability. The model combines two key mechanisms that
participate in ENSO dynamics: delayed negative feedback and seasonal forcing.
We perform stability analyses of the model in the three-dimensional space of
its physically relevant parameters. Our results illustrate the role of these
three parameters: strength of seasonal forcing , atmosphere-ocean coupling
, and propagation period of oceanic waves across the Tropical
Pacific. Two regimes of variability, stable and unstable, are separated by a
sharp neutral curve in the plane at constant . The detailed
structure of the neutral curve becomes very irregular and possibly fractal,
while individual trajectories within the unstable region become highly complex
and possibly chaotic, as the atmosphere-ocean coupling increases. In
the unstable regime, spontaneous transitions occur in the mean ``temperature''
({\it i.e.}, thermocline depth), period, and extreme annual values, for purely
periodic, seasonal forcing. The model reproduces the Devil's bleachers
characterizing other ENSO models, such as nonlinear, coupled systems of partial
differential equations; some of the features of this behavior have been
documented in general circulation models, as well as in observations. We
expect, therefore, similar behavior in much more detailed and realistic models,
where it is harder to describe its causes as completely.Comment: 22 pages, 9 figure
The Self-Regulated Winds of Long Period Variable Stars
Numerical models of the extended atmospheres of long period variable or Mira
stars have shown that their winds have a very simple, power law structure when
averaged over the pulsation cycle. This structure is stable and robust despite
the pulsational wave disturbances, and appears to be strongly self-regulated.
Observational studies support these conclusions. The models also show that
dust-free winds are nearly adiabatic, with little heating or cooling. The
classical, steady, adiabatic wind solution to the hydrodynamic equations fails
to account for an extensive region of nearly constant outflow velocity. We
investigate analytic solutions which include the effects of wave pressure,
heating, and the resulting entropy changes. Wave pressure is represented by a
term like that in the Reynolds turbulence equation for the mean velocity.
Although the pressure from individual waves is modest, the waves are likely the
primary agent of self-regulation of dust-free winds. In models of dusty winds,
the gas variables also adopt a power law dependence on radius. Heating is
required at all radii to maintain this flow, and grain heating and heat
transfer to the gas are significant. Both hydrodynamic and gas/grain thermal
feedbacks transform the flow towards self-regulated forms. (Abridged)Comment: 14 pgs., 3 figures, accepted for MNRAS, 200
Global Stabilization of the Navier-Stokes-Voight and the damped nonlinear wave equations by finite number of feedback controllers
In this paper we introduce a finite-parameters feedback control algorithm for
stabilizing solutions of the Navier-Stokes-Voigt equations, the strongly damped
nonlinear wave equations and the nonlinear wave equation with nonlinear damping
term, the Benjamin-Bona-Mahony-Burgers equation and the KdV-Burgers equation.
This algorithm capitalizes on the fact that such infinite-dimensional
dissipative dynamical systems posses finite-dimensional long-time behavior
which is represented by, for instance, the finitely many determining parameters
of their long-time dynamics, such as determining Fourier modes, determining
volume elements, determining nodes , etc..The algorithm utilizes these finite
parameters in the form of feedback control to stabilize the relevant solutions.
For the sake of clarity, and in order to fix ideas, we focus in this work on
the case of low Fourier modes feedback controller, however, our results and
tools are equally valid for using other feedback controllers employing other
spatial coarse mesh interpolants
Relaminarisation of Re_{\tau} = 100 channel flow with globally stabilising linear feedback control
The problems of nonlinearity and high dimension have so far prevented a
complete solution of the control of turbulent flow. Addressing the problem of
nonlinearity, we propose a flow control strategy which ensures that the energy
of any perturbation to the target profile decays monotonically. The
controller's estimate of the flow state is similarly guaranteed to converge to
the true value. We present a one-time off-line synthesis procedure, which
generalises to accommodate more restrictive actuation and sensing arrangements,
with conditions for existence for the controller given in this case. The
control is tested in turbulent channel flow () using full-domain
sensing and actuation on the wall-normal velocity. Concentrated at the point of
maximum inflection in the mean profile, the control directly counters the
supply of turbulence energy arising from the interaction of the wall-normal
perturbations with the flow shear. It is found that the control is only
required for the larger-scale motions, specifically those above the scale of
the mean streak spacing. Minimal control effort is required once laminar flow
is achieved. The response of the near-wall flow is examined in detail, with
particular emphasis on the pressure and wall-normal velocity fields, in the
context of Landahl's theory of sheared turbulence
Selection theorem for systems with inheritance
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic
systems is studied. A non-linear kinetic system with conservation of supports
for distributions has generically finite-dimensional asymptotics. Such systems
are apparent in many areas of biology, physics (the theory of parametric wave
interaction), chemistry and economics. This conservation of support has a
biological interpretation: inheritance. The finite-dimensional asymptotics
demonstrates effects of "natural" selection. Estimations of the asymptotic
dimension are presented. After some initial time, solution of a kinetic
equation with conservation of support becomes a finite set of narrow peaks that
become increasingly narrow over time and move increasingly slowly. It is
possible that these peaks do not tend to fixed positions, and the path covered
tends to infinity as t goes to infinity. The drift equations for peak motion
are obtained. Various types of distribution stability are studied: internal
stability (stability with respect to perturbations that do not extend the
support), external stability or uninvadability (stability with respect to
strongly small perturbations that extend the support), and stable realizability
(stability with respect to small shifts and extensions of the density peaks).
Models of self-synchronization of cell division are studied, as an example of
selection in systems with additional symmetry. Appropriate construction of the
notion of typicalness in infinite-dimensional space is discussed, and the
notion of "completely thin" sets is introduced.
Key words: Dynamics; Attractor; Evolution; Entropy; Natural selectionComment: 46 pages, the final journal versio
Cascades and transitions in turbulent flows
Turbulence is characterized by the non-linear cascades of energy and other
inviscid invariants across a huge range of scales, from where they are injected
to where they are dissipated. Recently, new experimental, numerical and
theoretical works have revealed that many turbulent configurations deviate from
the ideal 3D/2D isotropic cases characterized by the presence of a strictly
direct/inverse energy cascade, respectively. We review recent works from a
unified point of view and we present a classification of all known transfer
mechanisms. Beside the classical cases of direct and inverse cascades, the
different scenarios include: split cascades to small and large scales
simultaneously, multiple/dual cascades of different quantities, bi-directional
cascades where direct and inverse transfers of the same invariant coexist in
the same scale-range and finally equilibrium states where no cascades are
present, including the case when a condensate is formed. We classify all
transitions as the control parameters are changed and we analyse when and why
different configurations are observed. Our discussion is based on a set of
paradigmatic applications: helical turbulence, rotating and/or stratified
flows, MHD and passive/active scalars where the transfer properties are altered
as one changes the embedding dimensions, the thickness of the domain or other
relevant control parameters, as the Reynolds, Rossby, Froude, Peclet, or Alfven
numbers. We discuss the presence of anomalous scaling laws in connection with
the intermittent nature of the energy dissipation in configuration space. An
overview is also provided concerning cascades in other applications such as
bounded flows, quantum, relativistic and compressible turbulence, and active
matter, together with implications for turbulent modelling. Finally, we present
a series of open problems and challenges that future work needs to address.Comment: accepted for publication on Physics Reports 201
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