Non-linear axisymmetric pulsations of rotating relativistic stars in the conformal flatness approximation

We study non-linear axisymmetric pulsations of rotating relativistic stars using a general relativistic hydrodynamics code under the assumption of a conformal flatness. We compare our results to previous simulations where the spacetime dynamics was neglected. The pulsations are studied along various sequences of both uniformly and differentially rotating relativistic polytropes with index N = 1. We identify several modes, including the lowest-order l = 0, 2, and 4 axisymmetric modes, as well as several axisymmetric inertial modes. Differential rotation significantly lowers mode frequencies, increasing prospects for detection by current gravitational wave interferometers. We observe an extended avoided crossing between the l = 0 and l = 4 first overtones, which is important for correctly identifying mode frequencies in case of detection. For uniformly rotating stars near the mass-shedding limit, we confirm the existence of the mass-shedding-induced damping of pulsations, though the effect is not as strong as in the Cowling approximation. We also investigate non-linear harmonics of the linear modes and notice that rotation changes the pulsation frequencies in a way that would allow for various parametric instabilities between two or three modes to take place. We assess the detectability of each obtained mode by current gravitational wave detectors and outline how the empirical relations that have been constructed for gravitational wave asteroseismology could be extended to include the effects of rotation.Comment: 24 pages, 20 figures; minor corrections, added extended discussion and one figure in one subsectio

Wearing a single DNA molecule with an AFM tip

While the fundamental limit on the resolution achieved in an atomic force microscope (AFM) is clearly related to the tip radius, the fact that the tip can creep and/or wear during an experiment is often ignored. This is mainly due to the difficulty in characterizing the tip, and in particular a lack of reliable methods that can achieve this in situ. Here, we provide an in situ method to characterize the tip radius and monitor tip creep and/or wear and biomolecular sample wear in ambient dynamic AFM. This is achieved by monitoring the dynamics of the cantilever and the critical free amplitude to observe a switch from the attractive to the repulsive regime. The method is exemplified on the mechanically heterogeneous sample of single DNA molecules bound to mica mineral surfaces. Simultaneous monitoring of apparent height and width of single DNA molecules while detecting variations in the tip radius R as small as one nanometer are demonstrated. The yield stress can be readily exceeded for sharp tips (R10nm). The ability to know the AFM tip radius in situ and in real-time opens up the future for quantitative nanoscale materials properties determination at the highest possible spatial resolution.Comment: 26 pages, 6 figure

Nonlinear r-modes in Rapidly Rotating Relativistic Stars

The r-mode instability in rotating relativistic stars has been shown recently to have important astrophysical implications (including the emission of detectable gravitational radiation, the explanation of the initial spins of young neutron stars and the spin-distribution of millisecond pulsars and the explanation of one type of gamma-ray bursts), provided that r-modes are not saturated at low amplitudes by nonlinear effects or by dissipative mechanisms. Here, we present the first study of nonlinear r-modes in isentropic, rapidly rotating relativistic stars, via 3-D general-relativistic hydrodynamical evolutions. Our numerical simulations show that (1) on dynamical timescales, there is no strong nonlinear coupling of r-modes to other modes at amplitudes of order one -- unless nonlinear saturation occurs on longer timescales, the maximum r-mode amplitude is of order unity (i.e., the velocity perturbation is of the same order as the rotational velocity at the equator). An absolute upper limit on the amplitude (relevant, perhaps, for the most rapidly rotating stars) is set by causality. (2) r-modes and inertial modes in isentropic stars are predominantly discrete modes and possible associated continuous parts were not identified in our simulations. (3) In addition, the kinematical drift associated with r-modes, recently found by Rezzolla, Lamb and Shapiro (2000), appears to be present in our simulations, but an unambiguous confirmation requires more precise initial data. We discuss the implications of our findings for the detectability of gravitational waves from the r-mode instability.Comment: 4 pages, 4 eps figures, accepted in Physical Review Letter

Cantilever dynamics in amplitude modulation AFM: continuous and discontinuous transitions

Transitions between the attractive and the repulsive force regimes for amplitude modulation atomic force microscopy (AFM) can be either discontinuous, with a corresponding jump in amplitude and phase, or continuous and smooth. During the transitions, peak repulsive and average forces can be up to an order of magnitude higher when these are discrete. Under certain circumstances, for example, when the tip radius is relatively large (e.g. R > 20–30 nm) and for high cantilever free amplitudes (e.g. A0 > 40–50 nm), the L state can be reached with relatively low set-points only (e.g. Asp/A0 < 0.30). We find that these cases do not generally lead to higher resolution but increase the background noise instead. This is despite the fact that the imaging can be non-contact under these conditions. The appearance of background noise is linked to increasing cantilever mean deflection and tip–surface proximity with increasing free amplitude in the L state. Cantilever dynamics in amplitude modulation AFM: Continuous and discontinuous transitions (PDF Download Available). Available from: https://www.researchgate.net/publication/231025693_Cantilever_dynamics_in_amplitude_modulation_AFM_Continuous_and_discontinuous_transitions [accessed Mar 27, 2017].Peer ReviewedPostprint (author's final draft

Relativistic simulations of rotational core collapse. I. Methods, initial models, and code tests

We describe an axisymmetric general relativistic code for rotational core collapse. The code evolves the coupled system of metric and fluid equations using the ADM 3+1 formalism and a conformally flat metric approximation of the Einstein equations. The relativistic hydrodynamics equations are formulated as a first-order flux-conservative hyperbolic system and are integrated using high-resolution shock-capturing schemes based on Riemann solvers. We assess the quality of the conformally flat metric approximation for relativistic core collapse and present a comprehensive set of tests which the code successfully passed. The tests include relativistic shock tubes, the preservation of the rotation profile and of the equilibrium of rapidly and differentially rotating neutron stars (approximated as rotating polytropes), spherical relativistic core collapse, and the conservation of rest-mass and angular momentum in dynamic spacetimes. The application of the code to relativistic rotational core collapse, with emphasis on the gravitational waveform signature, is presented in an accompanying paper.Comment: 18 pages, 12 figure

Relativistic gravitational collapse in comoving coordinates: The post-quasistatic approximation

A general iterative method proposed some years ago for the description of relativistic collapse, is presented here in comoving coordinates. For doing that we redefine the basic concepts required for the implementation of the method for comoving coordinates. In particular the definition of the post-quasistatic approximation in comoving coordinates is given. We write the field equations, the boundary conditions and a set of ordinary differential equations (the surface equations) which play a fundamental role in the algorithm. As an illustration of the method, we show how to build up a model inspired in the well known Schwarzschild interior solution. Both, the adiabatic and non adiabatic, cases are considered.Comment: 14 pages, 11 figures; updated version to appear in Int. J. Modern Phys.

Scalar field induced oscillations of neutron stars and gravitational collapse

We study the interaction of massless scalar fields with self-gravitating neutron stars by means of fully dynamic numerical simulations of the Einstein-Klein-Gordon perfect fluid system. Our investigation is restricted to spherical symmetry and the neutron stars are approximated by relativistic polytropes. Studying the nonlinear dynamics of isolated neutron stars is very effectively performed within the characteristic formulation of general relativity, in which the spacetime is foliated by a family of outgoing light cones. We are able to compactify the entire spacetime on a computational grid and simultaneously impose natural radiative boundary conditions and extract accurate radiative signals. We study the transfer of energy from the scalar field to the fluid star. We find, in particular, that depending on the compactness of the neutron star model, the scalar wave forces the neutron star either to oscillate in its radial modes of pulsation or to undergo gravitational collapse to a black hole on a dynamical timescale. The radiative signal, read off at future null infinity, shows quasi-normal oscillations before the setting of a late time power-law tail.Comment: 12 pages, 13 figures, submitted to Phys. Rev.

Gravitational waves from relativistic rotational core collapse

We present results from simulations of axisymmetric relativistic rotational core collapse. The general relativistic hydrodynamic equations are formulated in flux-conservative form and solved using a high-resolution shock-capturing scheme. The Einstein equations are approximated with a conformally flat 3-metric. We use the quadrupole formula to extract waveforms of the gravitational radiation emitted during the collapse. A comparison of our results with those of Newtonian simulations shows that the wave amplitudes agree within 30%. Surprisingly, in some cases, relativistic effects actually diminish the amplitude of the gravitational wave signal. We further find that the parameter range of models suffering multiple coherent bounces due to centrifugal forces is considerably smaller than in Newtonian simulations.Comment: 4 pages, 3 figure

Couplings in Asymmetric Orbifolds and Grand Unified String Models

Using the bosonic supercurrent (or covariant lattice) formalism, we review how to compute scattering amplitudes in asymmetric orbifold string models. This method is particularly useful for calculating scattering of multiple asymmetrically twisted string states, where the twisted states are rewritten as ordinary momentum states. We show how to reconstruct some of the 3-family grand unified string models in this formalism, and identify the quantum numbers of the massless states in their spectra. The discrete symmetries of these models are rather intricate. The superpotentials for the 3-family E_6 model and a closely related SO(10) model are discussed in some detail. The forms of the superpotentials of the two 3-family SU(6) models (with asymptotically-free hidden sectors SU(3) and SU(2) \otimes SU(2)) are also presented.Comment: 54 pages, Revtex 3.0 (to appear in Nucl. Phys. B