14,444 research outputs found
A solution to the overdamping problem when simulating dust-gas mixtures with smoothed particle hydrodynamics
We present a fix to the overdamping problem found by Laibe & Price (2012)
when simulating strongly coupled dust-gas mixtures using two different sets of
particles using smoothed particle hydrodynamics. Our solution is to compute the
drag at the barycentre between gas and dust particle pairs when computing the
drag force by reconstructing the velocity field, similar to the procedure in
Godunov-type solvers. This fixes the overdamping problem at negligible
computational cost, but with additional memory required to store velocity
derivatives. We employ slope limiters to avoid spurious oscillations at shocks,
finding the van Leer Monotonized Central limiter most effective.Comment: 6 pages, 5 figures, accepted to MNRA
Dusty gas with one fluid in smoothed particle hydrodynamics
In a companion paper we have shown how the equations describing gas and dust
as two fluids coupled by a drag term can be reformulated to describe the system
as a single fluid mixture. Here we present a numerical implementation of the
one-fluid dusty gas algorithm using Smoothed Particle Hydrodynamics (SPH). The
algorithm preserves the conservation properties of the SPH formalism. In
particular, the total gas and dust mass, momentum, angular momentum and energy
are all exactly conserved. Shock viscosity and conductivity terms are
generalised to handle the two-phase mixture accordingly. The algorithm is
benchmarked against a comprehensive suit of problems: dustybox, dustywave,
dustyshock and dustyoscill, each of them addressing different properties of the
method. We compare the performance of the one-fluid algorithm to the standard
two-fluid approach. The one-fluid algorithm is found to solve both of the
fundamental limitations of the two- fluid algorithm: it is no longer possible
to concentrate dust below the resolution of the gas (they have the same
resolution by definition), and the spatial resolution criterion h < csts,
required in two-fluid codes to avoid over-damping of kinetic energy, is
unnecessary. Implicit time stepping is straightforward. As a result, the
algorithm is up to ten billion times more efficient for 3D simulations of small
grains. Additional benefits include the use of half as many particles, a single
kernel and fewer SPH interpolations. The only limitation is that it does not
capture multi-streaming of dust in the limit of zero coupling, suggesting that
in this case a hybrid approach may be required.Comment: Accepted for publication in MNRAS. Numerical code and input files for
dustybox, wave and shock tests available from
http://users.monash.edu.au/~dprice/ndspmhd
Stability and roughness of interfaces in mechanically-regulated tissues
Cell division and death can be regulated by the mechanical forces within a
tissue. We study the consequences for the stability and roughness of a
propagating interface, by analysing a model of mechanically-regulated tissue
growth in the regime of small driving forces. For an interface driven by
homeostatic pressure imbalance or leader-cell motility, long and
intermediate-wavelength instabilities arise, depending respectively on an
effective viscosity of cell number change, and on substrate friction. A further
mechanism depends on the strength of directed motility forces acting in the
bulk. We analyse the fluctuations of a stable interface subjected to cell-level
stochasticity, and find that mechanical feedback can help preserve
reproducibility at the tissue scale. Our results elucidate mechanisms that
could be important for orderly interface motion in developing tissues.Comment: Final author version, In press at Phys. Rev. Lett., supplement is
available at:
https://www.dropbox.com/s/p5mwzdxlw40eglv/supplement_28Nov.pdf?dl=0 or
contact author
Dust and gas mixtures with multiple grain species - a one-fluid approach
GL acknowledges funding from the European Research Council for the FP7 ERC advanced grant project ECOGAL. DJP is very grateful for funding via an ARC Future Fellowship, FT130100034, and Discovery Project grant DP130102078.We derive the single-fluid evolution equations describing a mixture made of a gas phase and an arbitrary number of dust phases, generalizing the approach developed by Laibe & Price. A generalization for continuous dust distributions as well as analytic approximations for strong drag regimes is also provided. This formalism lays the foundation for numerical simulations of dust populations in a wide range of astrophysical systems while avoiding limitations associated with a multiple-fluid treatment. The usefulness of the formalism is illustrated on a series of analytical problems, namely the DUSTYBOX, DUSTYSHOCK and DUSTYWAVE problems as well as the radial drift of grains and the streaming instability in protoplanetary discs. We find physical effects specific to the presence of several dust phases and multiple drag time-scales, including non-monotonic evolution of the differential velocity between phases and increased efficiency of the linear growth of the streaming instability. Interestingly, it is found that under certain conditions, large grains can migrate outwards in protoplanetary discs. This may explain the presence of small pebbles at several hundreds of astronomical units from their central star.Publisher PDFPeer reviewe
A local fluctuation theorem for large systems
The fluctuation theorem characterizes the distribution of the dissipation in
nonequilibrium systems and proves that the average dissipation will be
positive. For a large system with no external source of fluctuation,
fluctuations in properties will become unobservable and details of the
fluctuation theorem are unable to be explored. In this letter, we consider such
a situation and show how a fluctuation theorem can be obtained for a small open
subsystem within the large system. We find that a correction term has to be
added to the large system fluctuation theorem due to correlation of the
subsystem with the surroundings. Its analytic expression can be derived
provided some general assumptions are fulfilled, and its relevance it checked
using numerical simulations.Comment: 5 pages, 5 figures; revised and supplementary material include
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