arXiv subjects

Matthew Anderson

Publications and source records attributed to Matthew Anderson.

At least 37 records · Page 2Linked to original sources

arXiv2015

Relativistic Hydrodynamics with Wavelets

Methods to solve the relativistic hydrodynamic equations are a key computational kernel in a large number of astrophysics simulations and are crucial to understanding the electromagnetic signals that originate from the merger of astrophysical compact objects. Because of the many physical length scales present when simulating such mergers, these methods must be highly adaptive and capable of automatically resolving numerous localized features and instabilities that emerge throughout the computational domain across many temporal scales. While this has been historically accomplished with adaptive mesh refinement (AMR) based methods, alternatives based on wavelet bases and the wavelet transformation have recently achieved significant success in adaptive representation for advanced engineering applications. This work presents a new method for the integration of the relativistic hydrodynamic equations using iterated interpolating wavelets and introduces a highly adaptive implementation for multidimensional simulation. The wavelet coefficients provide a direct measure of the local approximation error for the solution and place collocation points that naturally adapt to the fluid flow while providing good conservation of fluid quantities. The resulting implementation, OAHU, is applied to a series of demanding one- and two-dimensional problems which explore high Lorentz factor outflows and the formation of several instabilities, including the Kelvin-Helmholtz instability and the Rayleigh-Taylor instability.

astro-ph.IM↗

arXiv2015

Identity Testing and Lower Bounds for Read-$k$ Oblivious Algebraic Branching Programs

Read-$k$ oblivious algebraic branching programs are a natural generalization of the well-studied model of read-once oblivious algebraic branching program (ROABPs). In this work, we give an exponential lower bound of $\exp(n/k^{O(k)})$ on the width of any read-$k$ oblivious ABP computing some explicit multilinear polynomial $f$ that is computed by a polynomial size depth-$3$ circuit. We also study the polynomial identity testing (PIT) problem for this model and obtain a white-box subexponential-time PIT algorithm. The algorithm runs in time $2^{\tilde{O}(n^{1-1/2^{k-1}})}$ and needs white box access only to know the order in which the variables appear in the ABP.

cs.CC↗

arXiv2014

The Mass of the Central Black Hole in the Nearby Seyfert Galaxy NGC5273

We present the results of a reverberation-mapping program targeting NGC5273, a nearby early-type galaxy with a broad-lined active galactic nucleus. Over the course of the monitoring program, NGC5273 showed strong variability that allowed us to measure time delays in the responses of the broad optical recombination lines to changes in the continuum flux. A weighted average of these measurements results in a black hole mass determination of $M_{\rm BH} = (4.7 \pm 1.6) \times 10^6$ M$_{\odot}$. An estimate of the size of the black hole sphere of influence in NGC5273 puts it just at the limit of the resolution achievable with current ground-based large aperture telescopes. NGC5273 is therefore an important future target for a black hole mass determination from stellar dynamical modeling, especially because it is the only nearby early-type galaxy hosting an AGN with a reverberation-based mass, allowing the best comparison for the masses determined from these two techniques.

astro-ph.GA↗

arXiv2014

Magnetized Neutron Stars With Realistic Equations of State and Neutrino Cooling

We incorporate realistic, tabulated equations of state into fully relativistic simulations of magnetized neutron stars along with a neutrino leakage scheme which accounts for cooling via neutrino emission. Both these improvements utilize open-source code (GR1D) and tables from http://stellarcollapse.org. Our implementation makes use of a novel method for the calculation of the optical depth which simplifies its use with distributed adaptive mesh refinement. We present various tests with and without magnetization and preliminary results both from single stars and from the merger of a binary system.

gr-qc↗

arXiv2014

On Symmetric Circuits and Fixed-Point Logics

We study properties of relational structures such as graphs that are decided by families of Boolean circuits. Circuits that decide such properties are necessarily invariant to permutations of the elements of the input structures. We focus on families of circuits that are symmetric, i.e., circuits whose invariance is witnessed by automorphisms of the circuit induced by the permutation of the input structure. We show that the expressive power of such families is closely tied to definability in logic. In particular, we show that the queries defined on structures by uniform families of symmetric Boolean circuits with majority gates are exactly those definable in fixed-point logic with counting. This shows that inexpressibility results in the latter logic lead to lower bounds against polynomial-size families of symmetric circuits.

cs.CC↗

arXiv2013

Linking electromagnetic and gravitational radiation in coalescing binary neutron stars

We expand on our study of the gravitational and electromagnetic emissions from the late stage of an inspiraling neutron star binary as presented in Ref. \cite{Palenzuela:2013hu}. Interactions between the stellar magnetospheres, driven by the extreme dynamics of the merger, can yield considerable outflows. We study the gravitational and electromagnetic waves produced during the inspiral and merger of a binary neutron star system using a full relativistic, resistive MHD evolution code. We show that the interaction between the stellar magnetospheres extracts kinetic energy from the system and powers radiative Poynting flux and heat dissipation. These features depend strongly on the configuration of the initial stellar magnetic moments. Our results indicate that this power can strongly outshine pulsars in binaries and have a distinctive angular and time-dependent pattern. Our discussion provides more detail than Ref. \cite{Palenzuela:2013hu}, showing clear evidence of the different effects taking place during the inspiral. Our simulations include a few milliseconds after the actual merger and study the dynamics of the magnetic fields during the formation of the hypermassive neutron star. We also briefly discuss the possibility of observing such emissions.

gr-qc↗

arXiv2013

Gravitational and electromagnetic outputs from binary neutron star mergers

The late stage of an inspiraling neutron star binary gives rise to strong gravitational wave emission due to its highly dynamic, strong gravity. Moreover, interactions between the stellar magnetospheres can produce considerable electromagnetic radiation. We study this scenario using fully general relativistic, resistive magneto-hydrodynamics simulations. We show that these interactions extract kinetic energy from the system, dissipate heat, and power radiative Poynting flux, as well as develop current sheets. Our results indicate that this power can: (i) outshine pulsars in binaries, (ii) display a distinctive angular- and time-dependent pattern, and (iii) radiate within large opening angles. These properties suggest that some binary neutron star mergers are ideal candidates for multimessenger astronomy.

gr-qc↗

arXiv2013

Maximum Matching and Linear Programming in Fixed-Point Logic with Counting

We establish the expressibility in fixed-point logic with counting (FPC) of a number of natural polynomial-time problems. In particular, we show that the size of a maximum matching in a graph is definable in FPC. This settles an open problem first posed by Blass, Gurevich and Shelah, who asked whether the existence of perfect matchings in general graphs could be determined in the more powerful formalism of choiceless polynomial time with counting. Our result is established by showing that the ellipsoid method for solving linear programs can be implemented in FPC. This allows us to prove that linear programs can be optimised in FPC if the corresponding separation oracle problem can be defined in FPC. On the way to defining a suitable separation oracle for the maximum matching problem, we provide FPC formulas defining maximum flows and canonical minimum cuts in capacitated graphs.

cs.LO↗

arXiv2013

Independent Vector Analysis: Identification Conditions and Performance Bounds

Recently, an extension of independent component analysis (ICA) from one to multiple datasets, termed independent vector analysis (IVA), has been the subject of significant research interest. IVA has also been shown to be a generalization of Hotelling's canonical correlation analysis. In this paper, we provide the identification conditions for a general IVA formulation, which accounts for linear, nonlinear, and sample-to-sample dependencies. The identification conditions are a generalization of previous results for ICA and for IVA when samples are independently and identically distributed. Furthermore, a principal aim of IVA is the identification of dependent sources between datasets. Thus, we provide the additional conditions for when the arbitrary ordering of the sources within each dataset is common. Performance bounds in terms of the Cramer-Rao lower bound are also provided for the demixing matrices and interference to source ratio. The performance of two IVA algorithms are compared to the theoretical bounds.

cs.LG↗

arXiv2012

Neutron Star Evolutions using Tabulated Equations of State with a New Execution Model

The addition of nuclear and neutrino physics to general relativistic fluid codes allows for a more realistic description of hot nuclear matter in neutron star and black hole systems. This additional microphysics requires that each processor have access to large tables of data, such as equations of state, and in large simulations the memory required to store these tables locally can become excessive unless an alternative execution model is used. In this work we present relativistic fluid evolutions of a neutron star obtained using a message driven multi-threaded execution model known as ParalleX. These neutron star simulations would require substantial memory overhead dedicated entirely to the equation of state table if using a more traditional execution model. We introduce a ParalleX component based on Futures for accessing large tables of data, including out-of-core sized tables, which does not require substantial memory overhead and effectively hides any increased network latency.

cs.DC↗

arXiv2011

Adaptive Mesh Refinement for Astrophysics Applications with ParalleX

Several applications in astrophysics require adequately resolving many physical and temporal scales which vary over several orders of magnitude. Adaptive mesh refinement techniques address this problem effectively but often result in constrained strong scaling performance. The ParalleX execution model is an experimental execution model that aims to expose new forms of program parallelism and eliminate any global barriers present in a scaling-impaired application such as adaptive mesh refinement. We present two astrophysics applications using the ParalleX execution model: a tabulated equation of state component for neutron star evolutions and a cosmology model evolution. Performance and strong scaling results from both simulations are presented. The tabulated equation of state data are distributed with transparent access over the nodes of the cluster. This allows seamless overlapping of computation with the latencies introduced by the remote access to the table. Because of the expected size increases to the equation of state table, this type of table partitioning for neutron star simulations is essential while the implementation is greatly simplified by ParalleX semantics.

cs.DC↗

arXiv2011

An Application Driven Analysis of the ParalleX Execution Model

Exascale systems, expected to emerge by the end of the next decade, will require the exploitation of billion-way parallelism at multiple hierarchical levels in order to achieve the desired sustained performance. The task of assessing future machine performance is approached by identifying the factors which currently challenge the scalability of parallel applications. It is suggested that the root cause of these challenges is the incoherent coupling between the current enabling technologies, such as Non-Uniform Memory Access of present multicore nodes equipped with optional hardware accelerators and the decades older execution model, i.e., the Communicating Sequential Processes (CSP) model best exemplified by the message passing interface (MPI) application programming interface. A new execution model, ParalleX, is introduced as an alternative to the CSP model. In this paper, an overview of the ParalleX execution model is presented along with details about a ParalleX-compliant runtime system implementation called High Performance ParalleX (HPX). Scaling and performance results for an adaptive mesh refinement numerical relativity application developed using HPX are discussed. The performance results of this HPX-based application are compared with a counterpart MPI-based mesh refinement code. The overheads associated with HPX are explored and hardware solutions are introduced for accelerating the runtime system.

cs.DC↗

arXiv2011

Improving the scalability of parallel N-body applications with an event driven constraint based execution model

The scalability and efficiency of graph applications are significantly constrained by conventional systems and their supporting programming models. Technology trends like multicore, manycore, and heterogeneous system architectures are introducing further challenges and possibilities for emerging application domains such as graph applications. This paper explores the space of effective parallel execution of ephemeral graphs that are dynamically generated using the Barnes-Hut algorithm to exemplify dynamic workloads. The workloads are expressed using the semantics of an Exascale computing execution model called ParalleX. For comparison, results using conventional execution model semantics are also presented. We find improved load balancing during runtime and automatic parallelism discovery improving efficiency using the advanced semantics for Exascale computing.

cs.DC↗

arXiv2010

Mergers of Magnetized Neutron Stars with Spinning Black Holes: Disruption, Accretion and Fallback

We investigate the merger of a neutron star (of compaction ratio $0.1$) in orbit about a spinning black hole in full general relativity with a mass ratio of $5:1$, allowing for the star to have an initial magnetization of $10^{12} {\rm Gauss}$. We present the resulting gravitational waveform and analyze the fallback accretion as the star is disrupted. The evolutions suggest no significant effects from the initial magnetization. We find that only a negligible amount of matter becomes unbound; $99%$ of the neutron star material has a fallback time of 10 seconds or shorter to reach the region of the central engine and that $99.99%$ of the star will interact with the central disk and black hole within 3 hours.

gr-qc↗

arXiv2009

Post-merger electromagnetic emissions from disks perturbed by binary black holes

We simulate the possible emission from a disk perturbed by a recoiling super-massive black hole. To this end, we study radiation transfer from the system incorporating bremsstrahlung emission from a Maxwellian plasma and absorption given by Kramer's opacity law modified to incorporate blackbody effects. We employ this model in the radiation transfer integration to compute the luminosity at several frequencies, and compare with previous bremsstrahlung luminosity estimations from a transparent limit (in which the emissivity is integrated over the computational domain and over all frequencies) and with a simple thermal emission model. We find close agreement between the radiation transfer results and the estimated bremsstrahlung luminosity from previous work for electromagnetic signals above $10^{14}$ Hz. For lower frequencies, we find a self-eclipsing behavior in the disk, resulting in a strong intensity variability connected to the orbital period of the disk.

astro-ph.HE↗

arXiv2009

Binary black holes' effects on electromagnetic fields

In addition to producing gravitational waves (GW), the dynamics of a binary black hole system could induce emission of electromagnetic (EM) radiation by affecting the behavior of plasmas and electromagnetic fields in their vicinity. We here study how the electromagnetic fields are affected by a pair of orbiting black holes through the merger. In particular, we show how the binary's dynamics induce a variability in possible electromagnetically induced emissions as well as a possible enhancement of electromagnetic fields during the late-merge and merger epochs. These time dependent features will likely leave their imprint in processes generating detectable emissions and can be exploited in the detection of electromagnetic counterparts of gravitational waves.

astro-ph.HE↗

arXiv2009

Perturbed disks get shocked. Binary black hole merger effects on accretion disks

The merger process of a binary black hole system can have a strong impact on a circumbinary disk. In the present work we study the effect of both central mass reduction (due to the energy loss through gravitational waves) and a possible black hole recoil (due to asymmetric emission of gravitational radiation). For the mass reduction case and recoil directed along the disk's angular momentum, oscillations are induced in the disk which then modulate the internal energy and bremsstrahlung luminosities. On the other hand, when the recoil direction has a component orthogonal to the disk's angular momentum, the disk's dynamics are strongly impacted, giving rise to relativistic shocks. The shock heating leaves its signature in our proxies for radiation, the total internal energy and bremsstrahlung luminosity. Interestingly, for cases where the kick velocity is below the smallest orbital velocity in the disk (a likely scenario in real AGN), we observe a common, characteristic pattern in the internal energy of the disk. Variations in kick velocity simply provide a phase offset in the characteristic pattern implying that observations of such a signature could yield a measure of the kick velocity through electromagnetic signals alone.

astro-ph.HE↗

arXiv2008

Magnetized Neutron Star Mergers and Gravitational Wave Signals

We investigate the influence of magnetic fields upon the dynamics of and resulting gravitational waves from a binary neutron star merger in full general relativity coupled to ideal magnetohydrodynamics (MHD). We consider two merger scenarios, one where the stars begin with initially aligned poloidal magnetic fields and one with no magnetic field. Both mergers result in a strongly differentially rotating object. In comparison to the non-magnetized scenario, the aligned magnetic fields delay the final merger of the two stars. During and after merger we observe phenomena driven by the magnetic field, including Kelvin-Helmholtz instabilities in shear layers, winding of the field lines, and transition from poloidal to toroidal fields. These effects not only produce electromagnetic radiation, but also can have a strong influence on the gravitational waves. Thus, there are promising prospects for studying such systems with both types of waves.

gr-qc↗