45 research outputs found
Analysis and Applications of Smoothed Particle Magnetohydrodynamics
Smoothed Particle Hydrodynamics (SPH) is analysed as the weighted residual method. In particular the analysis focuses on the collocation aspect of the method. Using Monte Carlo experiments we demonstrate that SPH is highly sensitive to node disorder, especially in its symmetrised energy and momentum conserving form. This aspect of the method is related to low [Beta] MHD instabilities observed by other authors. A remedy in the form of the Weighted Differences Method is suggested, which addresses this problem to some extent, but at a cost of losing automatic conservation of energy and momentum. ¶ The Weighted Differences Method is used to simulate propagation of Alfven and magnetosonic wave fronts in [Beta] = 0 plasma, and the results are compared with data obtained with the NCSA Zeus3D code with the Method of Characteristics (MOC) module. ¶ SPH is then applied to two interesting astrophysical situations: accretion on to a white dwarf in a compact binary system, which results in a formation of an accretion disk, and gravitational collapse of a magnetised vortex. Both models are 3 dimensional. ¶ ..
Rola białek HP1 i fosforylacji histonu H3 w regulacji struktury heterochromatyny okołocentromerowej we wczesnym rozwoju zarodkowym myszy
Wyniki przedstawione przeze mnie w rozprawie doktorskiej pokazują, że pojawienie się białka HP1α podlega specyficznej i odmiennej niż w komórkach somatycznych regulacji. Wraz z danymi literaturowymi sugerują one, że pomimo braku zaburzeń w rozwoju przedimplantacyjnym zarodków z obniżonym poziomem białka HP1α, białko to może w tym czasie pełnić istotne funkcje, których efekty można obserwować dopiero w rozwoju poimplantacyjnym. Możliwe również, że białko HP1β lub inne białka mogą przynajmniej częściowo kompensować brak białka HP1α w zarodkach
Inviscid SPH
In smooth-particle hydrodynamics (SPH), artificial viscosity is necessary for
the correct treatment of shocks, but often generates unwanted dissipation away
from shocks. We present a novel method of controlling the amount of artificial
viscosity, which uses the total time derivative of the velocity divergence as
shock indicator and aims at completely eliminating viscosity away from shocks.
We subject the new scheme to numerous tests and find that the method works at
least as well as any previous technique in the strong-shock regime, but becomes
virtually inviscid away from shocks, while still maintaining particle order. In
particular sound waves or oscillations of gas spheres are hardly damped over
many periods.Comment: 14 pages (15 in arXiv), 15 figures, accepted for publication in MNRA
On the convergence of the critical cooling timescale for the fragmentation of self-gravitating discs
We carry out simulations of gravitationally unstable discs using a Smoothed
Particle Hydrodynamics (SPH) code and a grid-based hydrodynamics code, FARGO,
to understand the previous non-convergent results reported by Meru & Bate
(2011a). We obtain evidence that convergence with increasing resolution occurs
with both SPH and FARGO and in both cases we find that the critical cooling
timescale is larger than previously thought. We show that SPH has a first-order
convergence rate while FARGO converges with a second-order rate. We show that
the convergence of the critical cooling timescale for fragmentation depends
largely on the numerical viscosity employed in both SPH and FARGO. With SPH,
particle velocity dispersion may also play a role. We show that reducing the
dissipation from the numerical viscosity leads to larger values of the critical
cooling time at a given resolution. For SPH, we find that the effect of the
dissipation due to the numerical viscosity is somewhat larger than had
previously been appreciated. In particular, we show that using a quadratic term
in the SPH artificial viscosity (beta_{SPH}) that is too low appears to lead to
excess dissipation in gravitationally unstable discs, which may affect any
results that sensitively depend on the thermodynamics, such as disc
fragmentation. We show that the two codes converge to values of the critical
cooling timescale, beta_{crit} > 20 (for a ratio of specific heats of
gamma=5/3), and perhaps even as large as beta_{crit} \approx 30. These are
approximately 3-5 times larger than has been found by most previous studies.
This is equivalent to a maximum gravitational stress that a disc can withstand
without fragmenting of alpha_{GI,crit} \approx 0.013-0.02, which is much
smaller than the values typically used in the literature. It is therefore
easier for self-gravitating discs to fragment than has been concluded from most
past studies.Comment: Accepted for publication by MNRAS. 26 pages, 17 figure
SPHS: Smoothed Particle Hydrodynamics with a higher order dissipation switch
We present a novel implementation of Smoothed Particle Hydrodynamics (SPHS)
that uses the spatial derivative of the velocity divergence as a higher order
dissipation switch. Our switch -- which is second order accurate -- detects
flow convergence before it occurs. If particle trajectories are going to cross,
we switch on the usual SPH artificial viscosity, as well as conservative
dissipation in all advected fluid quantities (for example, the entropy). The
viscosity and dissipation terms (that are numerical errors) are designed to
ensure that all fluid quantities remain single-valued as particles approach one
another, to respect conservation laws, and to vanish on a given physical scale
as the resolution is increased. SPHS alleviates a number of known problems with
`classic' SPH, successfully resolving mixing, and recovering numerical
convergence with increasing resolution. An additional key advantage is that --
treating the particle mass similarly to the entropy -- we are able to use
multimass particles, giving significantly improved control over the refinement
strategy. We present a wide range of code tests including the Sod shock tube,
Sedov-Taylor blast wave, Kelvin-Helmholtz Instability, the `blob test', and
some convergence tests. Our method performs well on all tests, giving good
agreement with analytic expectations.Comment: 21 pages; 15 Figures. Submitted to MNRAS. Comments welcom
Smoothed Particle Magnetohydrodynamics III. Multidimensional tests and the div B = 0 constraint
In two previous papers (Price & Monaghan 2004a,b) (papers I,II) we have
described an algorithm for solving the equations of Magnetohydrodynamics (MHD)
using the Smoothed Particle Hydrodynamics (SPH) method. The algorithm uses
dissipative terms in order to capture shocks and has been tested on a wide
range of one dimensional problems in both adiabatic and isothermal MHD. In this
paper we investigate multidimensional aspects of the algorithm, refining many
of the aspects considered in papers I and II and paying particular attention to
the code's ability to maintain the div B = 0 constraint associated with the
magnetic field. In particular we implement a hyperbolic divergence cleaning
method recently proposed by Dedner et al. (2002) in combination with the
consistent formulation of the MHD equations in the presence of non-zero
magnetic divergence derived in papers I and II. Various projection methods for
maintaining the divergence-free condition are also examined. Finally the
algorithm is tested against a wide range of multidimensional problems used to
test recent grid-based MHD codes. A particular finding of these tests is that
in SPMHD the magnitude of the divergence error is dependent on the number of
neighbours used to calculate a particle's properties and only weakly dependent
on the total number of particles. Whilst many improvements could still be made
to the algorithm, our results suggest that the method is ripe for application
to problems of current theoretical interest, such as that of star formation.Comment: Here is the latest offering in my quest for a decent SPMHD algorithm.
26 pages, 15 figures, accepted for publication in MNRAS. Version with high
res figures available from
http://www.astro.ex.ac.uk/people/dprice/pubs/spmhd/spmhdpaper3.pd
Newtonian Hydrodynamics of the Coalescence of Black Holes with Neutron Stars I: Tidally locked binaries with a stiff equation of state
We present a detailed study of the hydrodynamical interactions in a Newtonian
black hole-neutron star binary during the last stages of inspiral. We consider
close binaries which are tidally locked, use a stiff equation of state (with an
adiabatic index Gamma=3) throughout, and explore the effect of different
initial mass ratios on the evolution of the system. We calculate the
gravitational radiation signal in the quadrupole approximation. Our
calculations are carried out using a Smooth Particle Hydrodynamics (SPH) code.Comment: Replaces previous version which had figures separate from the text of
the paper. Now 47 pages long with 19 embedded figures (the figures are the
same, they were renumbered) Uses aaspp4.st
How initial and boundary conditions affect protoplanetary migration in a turbulent sub-Keplerian accretion disc: 2D non viscous SPH simulations
Current theories on planetary formation establish that giant planet formation
should be contextual to their quick migration towards the central star due to
the protoplanets-disc interactions on a timescale of the order of years,
for objects of nearly 10 terrestrial masses. Such a timescale should be smaller
by an order of magnitude than that of gas accretion onto the protoplanet during
the hierarchical growing-up of protoplanets by collisions with other minor
objects. These arguments have recently been analysed using N-body and/or
fluid-dynamics codes or a mixing of them. In this work, inviscid 2D simulations
are performed, using the SPH method, to study the migration of one protoplanet,
to evaluate the effectiveness of the accretion disc in the protoplanet dragging
towards the central star, as a function of the mass of the planet itself, of
disc tangential kinematics. To this purpose, the SPH scheme is considered
suitable to study the roles of turbulence, kinematic and boundary conditions,
due to its intrinsic advective turbulence, especially in 2D and in 3D codes.
Simulations are performed both in disc sub-Keplerian and in Keplerian kinematic
conditions as a parameter study of protoplanetary migration if moderate and
consistent deviations from Keplerian Kinematics occur. Our results show
migration times of a few orbital periods for Earth-like planets in
sub-Keplerian conditions, while for Jupiter-like planets estimates give that
about orbital periods are needed to half the orbital size. Timescales of
planet migration are strongly dependent on the relative position of the planet
with respect to the shock region near the centrifugal barrier of the disc flow.Comment: 12 pages, 18 figures, under review by MNRA
An approach for solving the boundary free edge difficulties in SPH modelling: application to a viscous accretion disc in close binaries
In this work, we propose a SPH interpolating Kernel reformulation suitable
also to treat free edge boundaries in the computational domain. Application to
both inviscid and viscous stationary low compressibility accretion disc models
in Close Binaries (CB) are shown. The investigation carried out in this paper
is a consequence of the fact that a low compressibility modelling is crucial to
check numerical reliability.
Results show that physical viscosity supports a well-bound accretion disc
formation, despite the low gas compressibility, when a Gaussian-derived Kernel
(from the Error Function) is assumed, in extended particle range - whose Half
Width at Half Maximum (HWHM) is fixed to a constant value - without any
spatial restrictions on its radial interaction (hereinafter GASPHER). At the
same time, GASPHER ensures adequate particle interpolations at the boundary
free edges. Both SPH and adaptive SPH (hereinafter ASPH) methods lack accuracy
if there are not constraints on the boundary conditions, in particular at the
edge of the particle envelope: Free Edge (FE) conditions. In SPH, an
inefficient particle interpolation involves a few neighbour particles; instead,
in the second case, non-physical effects involve both the boundary layer
particles themselves and the radial transport.
Either in a regime where FE conditions involve the computational domain, or
in a viscous fluid dynamics, or both, a GASPHER scheme can be rightly adopted
in such troublesome physical regimes. Despite the applied low compressibiity
condition, viscous GASPHER model shows clear spiral pattern profiles
demonstrating the better quality of results compared to SPH viscous ones.
Moreover a successful comparison of results concerning GASPHER 1D inviscid
shock tube with analytical solution is also reported.Comment: 18 pages, 12 figure