Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note: updated version of arXiv:gr-qc/050809

Hierarchical Modeling of Activation Mechanisms in the ABL and EGFR Kinase Domains: Thermodynamic and Mechanistic Catalysts of Kinase Activation by Cancer Mutations

Structural and functional studies of the ABL and EGFR kinase domains have recently suggested a common mechanism of activation by cancer-causing mutations. However, dynamics and mechanistic aspects of kinase activation by cancer mutations that stimulate conformational transitions and thermodynamic stabilization of the constitutively active kinase form remain elusive. We present a large-scale computational investigation of activation mechanisms in the ABL and EGFR kinase domains by a panel of clinically important cancer mutants ABL-T315I, ABL-L387M, EGFR-T790M, and EGFR-L858R. We have also simulated the activating effect of the gatekeeper mutation on conformational dynamics and allosteric interactions in functional states of the ABL-SH2-SH3 regulatory complexes. A comprehensive analysis was conducted using a hierarchy of computational approaches that included homology modeling, molecular dynamics simulations, protein stability analysis, targeted molecular dynamics, and molecular docking. Collectively, the results of this study have revealed thermodynamic and mechanistic catalysts of kinase activation by major cancer-causing mutations in the ABL and EGFR kinase domains. By using multiple crystallographic states of ABL and EGFR, computer simulations have allowed one to map dynamics of conformational fluctuations and transitions in the normal (wild-type) and oncogenic kinase forms. A proposed multi-stage mechanistic model of activation involves a series of cooperative transitions between different conformational states, including assembly of the hydrophobic spine, the formation of the Src-like intermediate structure, and a cooperative breakage and formation of characteristic salt bridges, which signify transition to the active kinase form. We suggest that molecular mechanisms of activation by cancer mutations could mimic the activation process of the normal kinase, yet exploiting conserved structural catalysts to accelerate a conformational transition and the enhanced stabilization of the active kinase form. The results of this study reconcile current experimental data with insights from theoretical approaches, pointing to general mechanistic aspects of activating transitions in protein kinases

Characteristic Evolution and Matching

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black spacetime. A prime application of characteristic evolution is to compute waveforms via Cauchy-characteristic matching, which is also reviewed.Comment: Published version http://www.livingreviews.org/lrr-2005-1

Exploring new physics frontiers through numerical relativity

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society

Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model

We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO’s second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h95%0=3.47×10−25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering