Smoothed Particle Magnetohydrodynamics II. Variational principles and variable smoothing length terms

In this paper we show how a Lagrangian variational principle can be used to derive the SPMHD (smoothed particle magnetohydrodynamics) equations for ideal MHD. We also consider the effect of a variable smoothing length in the SPH kernels after which we demonstrate by numerical tests that the consistent treatment of terms relating to the gradient of the smoothing length in the SPMHD equations significantly improves the accuracy of the algorithm. Our results complement those obtained in a companion paper (Price and Monaghan 2003a, paper I) for non ideal MHD where artificial dissipative terms were included to handle shocks.Comment: 14 pages, 4 figures, accepted to MNRA

Smoothed Particle Magnetohydrodynamics (some shocking results...)

There have been some issues in the past in attempts to simulate magnetic fields using the Smoothed Particle Hydrodynamics (SPH) method. SPH is well suited to star formation problems because of its Lagrangian nature. We present new, stable and conservative methods for magnetohydrodynamics (MHD) in SPH and present numerical tests on both waves and shocks in one dimension to show that it gives robust and accurate results.Comment: Kluwer latex, 6 pages, 3 figures; Proceedings of the International Workshop "Magnetic Fields and Star Formation: Theory vs Observations", Madrid, 21-25 April 2003. Revised version accepted to proceedings (exact solutions added, other minor changes

Controlling Artificial Viscosity in SPH simulations of accretion disks

We test the operation of two methods for selective application of Artificial Viscosity (AV) in SPH simulations of Keplerian Accretion Disks, using a ring spreading test to quantify effective viscosity, and a correlation coefficient technique to measure the formation of unwanted prograde alignments of particles. Neither the Balsara Switch nor Time Dependent Viscosity work effectively, as they leave AV active in areas of smooth shearing flow, and do not eliminate the accumulation of alignments of particles in the prograde direction. The effect of both switches is periodic, the periodicity dependent on radius and unaffected by the density of particles. We demonstrate that a very simple algorithm activates AV only when truly convergent flow is detected and reduces the unwanted formation of prograde alignments. The new switch works by testing whether all the neighbours of a particle are in Keplerian orbit around the same point, rather than calculating the divergence of the velocity field, which is very strongly affected by Poisson noise in the positions of the SPH particles.Comment: 8 pages, 5 figure

MAGMA: a 3D, Lagrangian magnetohydrodynamics code for merger applications

We present a new, completely Lagrangian magnetohydrodynamics code that is based on the SPH method. The equations of self-gravitating hydrodynamics are derived self-consistently from a Lagrangian and account for variable smoothing length (``grad-h''-) terms in both the hydrodynamic and the gravitational acceleration equations. The evolution of the magnetic field is formulated in terms of so-called Euler potentials which are advected with the fluid and thus guarantee the MHD flux-freezing condition. This formulation is equivalent to a vector potential approach and therefore fulfills the $\vec{\nabla}\cdot\vec{B}=0$-constraint by construction. Extensive tests in one, two and three dimensions are presented. The tests demonstrate the excellent conservation properties of the code and show the clear superiority of the Euler potentials over earlier magnetic SPH formulations.Comment: 18 pages, 17 Figures, a high resolution copy of the paper can be found at http://www.faculty.iu-bremen.de/srosswog/MAGMA.pd

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

Interactions between parental traits, environmental harshness and growth rate in determining telomere length in wild juvenile salmon

A larger body size confers many benefits, such as increased reproductive success, ability to evade predators and increased competitive ability and social status. However, individuals rarely maximise their growth rates, suggesting that this carries costs. One such cost could be faster attrition of the telomeres that cap the ends of eukaryotic chromosomes and play an important role in chromosome protection. A relatively short telomere length is indicative of poor biological state, including poorer tissue and organ performance, reduced potential longevity and increased disease susceptibility. Telomere loss during growth may also be accelerated by environmental factors, but these have rarely been subjected to experimental manipulation in the natural environment. Using a wild system involving experimental manipulations of juvenile Atlantic salmon Salmo salar in Scottish streams, we found that telomere length in juvenile fish was influenced by parental traits and by direct environmental effects. We found that faster-growing fish had shorter telomeres and there was a greater cost (in terms of reduced telomere length) if the growth occurred in a harsher environment. We also found a positive association between offspring telomere length and the growth history of their fathers (but not mothers), represented by the number of years fathers had spent at sea. This suggests that there may be long term consequences of growth conditions and parental life history for individual longevity

Fight to Win! Tools for Confronting Capital

activism anarchism capital as power political-economic disruption campaigns (PEDCs)Anarchists have generally rejected the idea that there is or ought to be a pure or inherently revolutionary strategy or tactic. In this chapter we make use of the capital-as-power theory of value and capital in a way that informs and supports the ad hoc perspective on struggle and fighting to win. Our primary purpose is to propose a method based on this theory as a means for social justice activists to assess political-economic disruption campaigns (PEDCs). Such an analysis is a needed component of an anarchist economics

An energy-conserving formalism for adaptive gravitational force softening in SPH and N-body codes

In this paper we describe an adaptive softening length formalism for collisionless N-body and self-gravitating Smoothed Particle Hydrodynamics (SPH) calculations which conserves momentum and energy exactly. This means that spatially variable softening lengths can be used in N-body calculations without secular increases in energy. The formalism requires the calculation of a small additional term to the gravitational force related to the gradient of the softening length. The extra term is similar in form to the usual SPH pressure force (although opposite in direction) and is therefore straightforward to implement in any SPH code at almost no extra cost. For N-body codes some additional cost is involved as the formalism requires the computation of the density via a summation over neighbouring particles using the smoothing kernel. The results of numerical tests demonstrate that, for homogeneous mass distributions, the use of adaptive softening lengths gives a softening which is always close to the `optimal' choice of fixed softening parameter, removing the need for fine-tuning. For a heterogeneous mass distribution (as may be found in any large scale N-body simulation) we find that the errors on the least-dense component are lowered by an order of magnitude compared to the use of a fixed softening length tuned to the densest component. For SPH codes our method presents a natural and elegant choice of softening formalism which makes a small improvement to both the force resolution and the total energy conservation at almost zero additional cost.Comment: 13 pages, 8 figures, accepted to MNRA

Enhancement of thrust reverser cascade performance using aerodynamic and structural integration

This paper focuses on the design of a cascade within a cold stream thrust reverser during the early, conceptual stage of the product development process. A reliable procedure is developed for the exchange of geometric and load data between a two dimensional aerodynamic model and a three dimensional structural model. Aerodynamic and structural simulations are carried out using realistic operating conditions, for three different design configurations with a view to minimising weight for equivalent or improved aerodynamic and structural performance. For normal operational conditions the simulations show that total reverse thrust is unaffected when the performance of the deformed vanes is compared to the un-deformed case. This shows that for the conditions tested, the minimal deformation of the cascade vanes has no significant affect on aerodynamic efficiency and that there is scope for reducing the weight of the cascade. The pressure distribution through a two dimensional thrust reverser section is determined for two additional cascade vane configurations and it is shown that with a small decrease in total reverse thrust, it is possible to reduce weight and eliminate supersonic flow regimes through the nacelle section. By increasing vane sections in high pressure areas and decreasing sections in low pressure areas the structural performance of the cascade vanes in the weight reduced designs, is improved with significantly reduced levels of vane displacement and stress