GPU Acceleration of Partial Differential Equation Solvers

Differential equations are often directly solvable by analytical means only in their one dimensional version. Partial differential equations are generally not solvable by analytical means in two and three dimensions, with the exception of few special cases. In all other cases, numerical approximation methods need to be utilized. One of the most popular methods is the finite element method. The main areas of focus, here, are the Poisson heat equation and the plate bending equation. The purpose of this paper is to provide a quick walkthrough of the various approaches that the authors followed in pursuit of creating optimal solvers, accelerated with the use of graphical processing units, and comparing them in terms of accuracy and time efficiency with existing or self-made non-accelerated solvers.

Emotional insecurity in the family and community and youth delinquency in Northern Ireland: A person-oriented analysis across five-waves

Background: Over one billion children are exposed worldwide to political violence and armed conflict. Currently, conclusions about bases for adjustment problems are qualified by limited longitudinal research from a process-oriented, social-ecological perspective. In this study, we examined a theoretically-based model for the impact of multiple levels of the social ecology (family, community) on adolescent delinquency. Specifically, this study explored the impact of children’s emotional insecurity about both the family and community on youth delinquency in Northern Ireland. Methods: In the context of a five-wave longitudinal research design, participants included 999 mother-child dyads in Belfast (482 boys, 517 girls), drawn from socially-deprived, ethnically-homogenous areas that had experienced political violence. Youth ranged in age from 10 to 20 and were 12.18 (SD = 1.82) years old on average at Time 1. Findings: The longitudinal analyses were conducted in hierarchical linear modeling (HLM), allowing for the modeling of inter-individual differences in intra-individual change. Intra-individual trajectories of emotional insecurity about the family related to children’s delinquency. Greater insecurity about the community worsened the impact of family conflict on youth’s insecurity about the family, consistent with the notion that youth’s insecurity about the community sensitizes them to exposure to family conflict in the home. Conclusions: The results suggest that ameliorating children’s insecurity about family and community in contexts of political violence is an important goal toward improving adolescents’ well-being, including reduced risk for delinquency.

Turbulent amplification of magnetic fields in laboratory laser-produced shock waves

X-ray and radio observations of the supernova remnant Cassiopeia A reveal the presence of magnetic fields about 100 times stronger than those in the surrounding interstellar medium. Field coincident with the outer shock probably arises through a nonlinear feedback process involving cosmic rays. The origin of the large magnetic field in the interior of the remnant is less clear but it is presumably stretched and amplified by turbulent motions. Turbulence may be generated by hydrodynamic instability at the contact discontinuity between the supernova ejecta and the circumstellar gas9. However, optical observations of Cassiopeia A indicate that the ejecta are interacting with a highly inhomogeneous, dense circumstellar cloud bank formed before the supernova explosion. Here we investigate the possibility that turbulent amplification is induced when the outer shock overtakes dense clumps in the ambient medium. We report laboratory experiments that indicate the magnetic field is amplified when the shock interacts with a plastic grid. We show that our experimental results can explain the observed synchrotron emission in the interior of the remnant. The experiment also provides a laboratory example of magnetic field amplification by turbulence in plasmas, a physical process thought to occur in many astrophysical phenomena.

Nonlinear hydrodynamic Langmuir waves in fully degenerate relativistic plasma

The combined effect of special relativity and electron degeneracy on Langmuir waves is analyzed by utilizing a rigorous fully relativistic hydrodynamic model. Assuming a traveling wave solution form, a set of conservation laws is identified, together with a pseudo-potential function depending on the relativistic parameter p<inf>F</inf>/(m c) (where p<inf>F</inf> is the Fermi momentum, m is the mass of the charge carriers and c the speed of light), as well as on the amplitude of the electrostatic energy perturbation.

Energy and energy flux in axisymmetric slow and fast waves

Aims: We aim to calculate the kinetic, magnetic, thermal, and total energy densities and the flux of energy in axisymmetric sausage modes. The resulting equations should contain as few parameters as possible to facilitate applicability for different observations. 

Methods: The background equilibrium is a one-dimensional cylindrical flux tube model with a piecewise constant radial density profile. This enables us to use linearised magnetohydrodynamic equations to calculate the energy densities and the flux of energy for axisymmetric sausage modes. 

Results: The equations used to calculate the energy densities and the flux of energy in axisymmetric sausage modes depend on the radius of the flux tube, the equilibrium sound and Alfvén speeds, the density of the plasma, the period and phase speed of the wave, and the radial or longitudinal components of the Lagrangian displacement at the flux tube boundary. Approximate relations for limiting cases of propagating slow and fast sausage modes are also obtained. We also obtained the dispersive first-order correction term to the phase speed for both the fundamental slow body mode under coronal conditions and the slow surface mode under photospheric conditions.

Alfvén Waves in Simulations of Solar Photospheric Vortices

Using advanced numerical magneto-hydrodynamic simulations of the magnetized solar photosphere, including non-gray radiative transport and a non-ideal equation of state, we analyze plasma motions in photospheric magnetic vortices. We demonstrate that apparent vortex-like motions in photospheric magnetic field concentrations do not exhibit "tornado"-like behavior or a "bath-tub" effect. While at each time instance the velocity field lines in the upper layers of the solar photosphere show swirls, the test particles moving with the time-dependent velocity field do not demonstrate such structures. Instead, they move in a wave-like fashion with rapidly changing and oscillating velocity field, determined mainly by magnetic tension in the magnetized intergranular downflows. Using time-distance diagrams, we identify horizontal motions in the magnetic flux tubes as torsional Alfvén perturbations propagating along the nearly vertical magnetic field lines with local Alfvén speed.

Rational Partial Choice Functions and Their Application to Belief Revision.

Necessary and sufficient conditions for choice functions to be rational have been intensively studied in the past. However, in these attempts, a choice function is completely specified. That is, given any subset of options, called an issue, the best option over that issue is always known, whilst in real-world scenarios, it is very often that only a few choices are known instead of all. In this paper, we study partial choice functions and investigate necessary and sufficient rationality conditions for situations where only a few choices are known. We prove that our necessary and sufficient condition for partial choice functions boils down to the necessary and sufficient conditions for complete choice functions proposed in the literature. Choice functions have been instrumental in belief revision theory. That is, in most approaches to belief revision, the problem studied can simply be described as the choice of possible worlds compatible with the input information, given an agent’s prior belief state. The main effort has been to devise strategies in order to infer the agents revised belief state. Our study considers the converse problem: given a collection of input information items and their corresponding revision results (as provided by an agent), does there exist a rational revision operation used by the agent and a consistent belief state that may explain the observed results?

The Ultraviolet-Bright, Slowly Declining Transient PS1-11af as a Partial Tidal Disruption Event

We present the Pan-STARRS1 discovery of the long-lived and blue transient PS1-11af, which was also detected by Galaxy Evolution Explorer with coordinated observations in the near-ultraviolet (NUV) band. PS1-11af is associated with the nucleus of an early type galaxy at redshift z = 0.4046 that exhibits no evidence for star formation or active galactic nucleus activity. Four epochs of spectroscopy reveal a pair of transient broad absorption features in the UV on otherwise featureless spectra. Despite the superficial similarity of these features to P-Cygni absorptions of supernovae (SNe), we conclude that PS1-11af is not consistent with the properties of known types of SNe. Blackbody fits to the spectral energy distribution are inconsistent with the cooling, expanding ejecta of a SN, and the velocities of the absorption features are too high to represent material in homologous expansion near a SN photosphere. However, the constant blue colors and slow evolution of the luminosity are similar to previous optically selected tidal disruption events (TDEs). The shape of the optical light curve is consistent with models for TDEs, but the minimum accreted mass necessary to power the observed luminosity is only 0.002 M, which points to a partial disruption model. A full disruption model predicts higher bolometric luminosities, which would require most of the radiation to be emitted in a separate component at high energies where we lack observations. In addition, the observed temperature is lower than that predicted by pure accretion disk models for TDEs and requires reprocessing to a constant, lower temperature. Three deep non-detections in the radio with the Very Large Array over the first two years after the event set strict limits on the production of any relativistic outflow comparable to Swift J1644+57, even if off-axis.

Partial Cooperation in Strategic Decision Situations

We consider a normal form game in which there is a single exogenously given coalition of cooperating players that can write a binding agreement on pre-selected actions. These collective actions typically represent a certain number of dimensions in the players’ strategy space. The actions represented by the other dimensions of the strategy space remain under the complete, individual control of the players.
We consider a standard extension of the Nash equilibrium concept denoted as a partial cooperative equilibrium as well as an equilibrium concept in which the coalition of cooperators has a leadership position. Existence results are developed for these new equilibrium concepts. We identify conditions on these partial cooperative games under which the various equilibrium concepts are equivalent.
We apply this game theoretic framework to existing models of multi-market oligopolies and international pollution abatement. In a multi-market oligopoly typically a merger paradox emerges in the partial cooperative equilibrium, which vanishes if the cartel of collaborators exploits its leadership position. Our application to international pollution abatement treaties shows that cooperation by a sufficiently large group of countries results in a Pareto improvement over the standard tragedy of the commons outcome described by the Nash equilibrium.

Partial Encryption by Randomized Zig-Zag Scanning for Video Encoding

19.Wang, Y, O’Neill, M, Kurugollu, F, Partial Encryption by Randomized Zig-Zag Scanning for Video Encoding, IEEE International Symposium on Circuits and Systems (ISCAS), Beijing, May 2013

Simulating reinforced concrete members. Part 1: partial interaction properties

Reinforced concrete members are extremely complex under loading because of localised deformations in the concrete (cracks, sliding planes) and between the reinforcement and concrete (slip). An ideal model for simulating behaviour of reinforced concrete members should incorporate both global behaviour and the localised behaviours that are seen and measured in practice; these localised behaviours directly affect the global behaviour. Most commonly used models do not directly simulate these localised behaviours that can be seen or measured in real members; instead, they overcome these limitations by using empirically or semi-empirically derived strain-based pseudo properties such as the use of effective flexural rigidities for deflection; plastic hinge lengths for strength and ductility; and energy-based approaches for both concrete softening in compression and concrete softening after tensile cracking to allow for tension stiffening. Most reinforced concrete member experimental testing is associated with deriving these pseudo properties for use in design and analysis, and this component of development is thus costly. The aim of the present research is to reduce this cost substantially. In this paper, localised material behaviours and the mechanisms they induce are described. Their incorporation into reinforced concrete member behaviour without the need for empirically derived pseudo properties is described in a companion paper.

Solar coronal magnetic fields derived using seismology techniques applied to omnipresent sunspot waves

Sunspots on the surface of the Sun are the observational signatures of intense manifestations of tightly packed magnetic field lines, with near-vertical field strengths exceeding 6,000 G in extreme cases1. It is well accepted that both the plasma density and the magnitude of the magnetic field strength decrease rapidly away from the solar surface, making high-cadence coronal measurements through traditional Zeeman and Hanle effects difficult as the observational signatures are fraught with low-amplitude signals that can become swamped with instrumental noise2, 3. Magneto-hydrodynamic (MHD) techniques have previously been applied to coronal structures, with single and spatially isolated magnetic field strengths estimated as 9–55 G (refs 4,5,6,7). A drawback with previous MHD approaches is that they rely on particular wave modes alongside the detectability of harmonic overtones. Here we show, for the first time, how omnipresent magneto-acoustic waves, originating from within the underlying sunspot and propagating radially outwards, allow the spatial variation of the local coronal magnetic field to be mapped with high precision. We find coronal magnetic field strengths of 32 ± 5 G above the sunspot, which decrease rapidly to values of approximately 1 G over a lateral distance of 7,000 km, consistent with previous isolated and unresolved estimations. Our results demonstrate a new, powerful technique that harnesses the omnipresent nature of sunspot oscillations to provide magnetic field mapping capabilities close to a magnetic source in the solar corona.

On the Source of Propagating Slow Magnetoacoustic Waves in Sunspots

Recent high-resolution observations of sunspot oscillations using simultaneously operated ground- and space-based telescopes reveal the intrinsic connection between different layers of the solar atmosphere. However, it is not clear whether these oscillations are externally driven or generated in situ. We address this question by using observations of propagating slow magnetoacoustic waves along a coronal fan loop system. In addition to the generally observed decreases in oscillation amplitudes with distance, the observed wave amplitudes are also found to be modulated with time, with similar variations observed throughout the propagation path of the wave train. Employing multi-wavelength and multi-instrument data, we study the amplitude variations with time as the waves propagate through different layers of the solar atmosphere. By comparing the amplitude modulation period in different layers, we find that slow magnetoacoustic waves observed in sunspots are externally driven by photospheric p-modes, which propagate upward into the corona before becoming dissipated.

Improved Efficiency for Partial Oxidation of Methane by Controlled Copper Deposition on Surface-Modified ZSM-5

The mono(μ-oxo) dicopper cores present in the pores of Cu-ZSM-5 are active for the partial oxidation of methane to methanol. However, copper on the external surface reduces the ratio of active, selective sites to unselective sites. More efficient catalysts are obtained by controlling the copper deposition during synthesis. Herein, the external exchange sites of ZSM-5 samples were passivated by bis(trimethylsilyl) trifluoroacetamide (BSTFA) followed by calcination, promoting selective deposition of intraporous copper during aqueous copper ion exchange. At an optimum level of 1–2 wt % SiO2, IR studies showed a 64 % relative reduction in external copper species and temperature-programmed oxidation analysis showed an associated increase in the formation of methanol compared with unmodified Cu-ZSM-5 samples. It is, therefore, reported that the modified zeolites contained a significantly higher proportion of active, selective copper species than their unmodified counterparts with activity for partial methane oxidation to methanol.