3,468 research outputs found

    The Convergence of Particle-in-Cell Schemes for Cosmological Dark Matter Simulations

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    Particle methods are a ubiquitous tool for solving the Vlasov-Poisson equation in comoving coordinates, which is used to model the gravitational evolution of dark matter in an expanding universe. However, these methods are known to produce poor results on idealized test problems, particularly at late times, after the particle trajectories have crossed. To investigate this, we have performed a series of one- and two-dimensional "Zel'dovich Pancake" calculations using the popular Particle-in-Cell (PIC) method. We find that PIC can indeed converge on these problems provided the following modifications are made. The first modification is to regularize the singular initial distribution function by introducing a small but finite artificial velocity dispersion. This process is analogous to artificial viscosity in compressible gas dynamics, and, as with artificial viscosity, the amount of regularization can be tailored so that its effect outside of a well-defined region - in this case, the high-density caustics - is small. The second modification is the introduction of a particle remapping procedure that periodically re-expresses the dark matter distribution function using a new set of particles. We describe a remapping algorithm that is third-order accurate and adaptive in phase space. This procedure prevents the accumulation of numerical errors in integrating the particle trajectories from growing large enough to significantly degrade the solution. Once both of these changes are made, PIC converges at second order on the Zel'dovich Pancake problem, even at late times, after many caustics have formed. Furthermore, the resulting scheme does not suffer from the unphysical, small-scale "clumping" phenomenon known to occur on the Pancake problem when the perturbation wave vector is not aligned with one of the Cartesian coordinate axes.Comment: 29 pages, 29 figures. Accepted for publication in ApJ. The revised version includes a discussion of energy conservation in the remapping procedure, as well as some interpretive differences in the Conclusions made in response to the referee report. Results themselves are unchange

    A 4th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov-Poisson Equation

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    Numerical solutions to the Vlasov-Poisson system of equations have important applications to both plasma physics and cosmology. In this paper, we present a new Particle-in-Cell (PIC) method for solving this system that is 4th-order accurate in both space and time. Our method is a high-order extension of one presented previously [B. Wang, G. Miller, and P. Colella, SIAM J. Sci. Comput., 33 (2011), pp. 3509--3537]. It treats all of the stages of the standard PIC update - charge deposition, force interpolation, the field solve, and the particle push - with 4th-order accuracy, and includes a 6th-order accurate phase-space remapping step for controlling particle noise. We demonstrate the convergence of our method on a series of one- and two- dimensional electrostatic plasma test problems, comparing its accuracy to that of a 2nd-order method. As expected, the 4th-order method can achieve comparable accuracy to the 2nd-order method with many fewer resolution elements.Comment: 18 pages, 10 figures, submitted to SIS

    Star Cluster Formation in Turbulent, Magnetized Dense Clumps with Radiative and Outflow Feedback

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    We present three Orion simulations of star cluster formation in a 1000 Msun, turbulent molecular cloud clump, including the effects of radiative transfer, protostellar outflows, and magnetic fields. Our simulations all use self-consistent turbulent initial conditions and vary the mean mass-to-flux ratio relative to the critical value over 2, 10, and infinity to gauge the influence of magnetic fields on star cluster formation. We find, in good agreement with previous studies, that magnetic fields of typically observed strengths lower the star formation rate by a factor of 2.4 and reduce the amount of fragmentation by a factor of 2 relative to the zero-field case. We also find that the field increases the characteristic sink particle mass, again by a factor of 2.4. The magnetic field also increases the degree of clustering in our simulations, such that the maximum stellar densities in the strong field case are higher than the others by again a factor of 2. This clustering tends to encourage the formation of multiple systems, which are more common in the rad-MHD runs than the rad-hydro run. The companion frequency in our simulations is consistent with observations of multiplicity in Class I sources, particularly for the strong field case. Finally, we find evidence of primordial mass segregation in our simulations reminiscent of that observed in star clusters like the Orion Nebula Cluster.Comment: 21 pages, 17 figures, accepted by MNRA

    Representing the Process of Machine Tool Calibration in First-order Logic

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    Machine tool calibration requires a wide range of measurement techniques that can be carried out in many different sequences. Planning a machine tool calibration is typically performed by a subject expert with a great understanding of International standards and industrial best-practice guides. However, it is often the case that the planned sequence of measurements is not the optimal. Therefore, in an attempt to improve the process, intelligent computing methods can be designed for plan suggestion. As a starting point, this paper presents a way of converting expert knowledge into first-order logic that can be expressed in the PROLOG language. It then shows how queries can be executed against the logic to construct a knowledge-base of all the different measurements that can be performed during machine tool calibration

    Bodies in the Brain

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