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Merging neutron stars offer an excellent laboratory for simultaneously studying strong-field gravity and matter in extreme environments. We establish the physical association of an electromagnetic counterpart (EM170817) with gravitational waves (GW170817) detected from merging neutron stars. By synthesizing a panchromatic data set, we demonstrate that merging neutron stars are a long-sought production site forging heavy elements by r-process nucleosynthesis. The weak gamma rays seen in EM170817 are dissimilar to classical short gamma-ray bursts with ultrarelativistic jets. Instead, we suggest that breakout of a wide-angle, mildly relativistic cocoon engulfing the jet explains the low-luminosity gamma rays, the high-luminosity ultraviolet-optical-infrared, and the delayed radio and x-ray emission. We posit that all neutron star mergers may lead to a wide-angle cocoon breakout, sometimes accompanied by a successful jet and sometimes by a choked jet.

We investigate the synchronization and decoherence of a self-excited inertia wheel multiple rigid-body dynamical system. We employ an Euler–Lagrange formulation to derive a nondimensional state space that governs the dynamics of a coupled pendula array where each element incorporates an inertia wheel. The dynamical system exhibits multiple equilibria, periodic limit-cycle oscillations, quasiperiodic, and chaotic oscillations and rotations. We make use of a combined approach including a singular perturbation multiple time scale and numerical bifurcation methodologies to determine the existence of synchronized and decoherent solutions in both weakly and strongly nonlinear regimes, respectively. The analysis reveals that synchronous oscillations are in-phase, whereas quasiperiodic oscillations are anti-phase. Furthermore, the non-stationary rotations are found to exhibit combinations of oscillations and rotations of the individual elements that are asynchronous. A Kuramoto order parameter analysis of representative solutions in various bifurcation regimes reveals the existence of chimera-like solutions where two elements are synchronized, whereas the third is desynchronized. Moreover, synchronous solutions were found to coexist with stable chimera solutions with a constant phase difference between the oscillators. [ABSTRACT FROM AUTHOR]

Author(s): K. P. Mooley (corresponding author) [1, 2, 3]; E. Nakar [4]; K. Hotokezaka [5]; G. Hallinan [3]; A. Corsi [6]; D. A. Frail [2]; A. Horesh [7]; T. Murphy [...]

In this paper, we develop and implement a nonlinear model based procedure for the estimation of rigid-body motion via an indirect measurement of an elastic appendage. We demonstrate the procedure by motion analysis of a compound planar pendulum from indirect optoelectronic measurements of markers attached to an elastic appendage that is constrained to slide along the rigid-body axis. We implement a Lagrangian approach to derive a theoretical nonlinear model that consistently incorporates several generalized forces acting on the system. Identification of the governing linear and nonlinear system parameters is obtained by analysis of frequency and damping backbone curves from controlled experiments of the decoupled system elements. The accuracy of the proposed model based procedures is evaluated and its results are compared with those of a previously reported point cluster estimation procedure. Two cases are investigated to yield 1.7% and 3.4% errors between measured motion and its model based estimation for experimental configurations, with a slider mass to pendulum frequency ratios of 12.8 and 2.5, respectively. Motion analysis of system dynamics with the point cluster method reveals a noisy signal with a maximal error of 3.9%. Thus, the proposed model based estimation procedure enables accurate evaluation of linear and nonlinear system parameters that are not directly measured. [DOI: 10.1115/1.4000465] Keywords: coupled nonlinear elastic-rigid-body dynamical system, marker-based motion analysis, nonlinear model based estimation

Finite amplitude dynamics of ships in head seas due to parametric instabilities is a subject of renewed interest with an increasing demand of operation in severe and variable environmental conditions. In this current study we investigate the nonlinear dynamics and internal resonances of a ship with a rectangular cross-section in head seas. We employ an asymptotic averaging method to obtain the slowly varying system evolution dynamics for the weakly nonlinear response, complemented by numerical integration in the strongly nonlinear regime. A weakly nonlinear frequency response is obtained analytically for a principal parametric resonance and a 1:1 roll--pitch internal resonance. Comparison of results with three degrees of freedom numerical simulations reveals a good fit. A strongly nonlinear numerical analysis reveals that beyond the stability thresholds, the system's responses included quasiperiodic dynamics. This combined approach resolves both parametric instabilities and internal resonances induced for both weak and finite nonlinear interactions, and culminates with criteria for orbital stability thresholds describing the onset of quasiperiodic response and magnification of energy transfer between coupled pitch-heave and ship roll. [DOI: 10.1115/1.3160532] Keywords: nonlinear ship dynamics, head seas, parametric roll, internal resonance, slowly varying evolution system, bifurcation thresholds, quasiperiodic response

We investigate the nonlinear dynamics and stability of a rotating system with an electromagnetic noncontact eddy-current damper. The damper is modeled by a thin nonmagnetic disk that is translating and rotating with a shaft in an air gap of a direct current electromagnet. The damper dissipates energy of the rotating system lateral vibration through induced eddy-currents. The dynamical system also includes a cubic restoring force representing nonlinear behavior of rubber o-rings supporting the shaft. The equilibrium state of the balanced rotating system with an eddy-current damper becomes unstable via a Hopf bifurcation and exact solutions for the limit cycle radius and frequency of the self-excited oscillation are obtained analytically. Forced vibration induced by the rotating system mass imbalance is also investigated analytically and numerically. System response includes periodic and quasiperiodic solutions. Stability of the periodic solutions obtained from the balanced self-excited motion and the imbalance forced response is analyzed by use of Floquet theory. This analysis enables an explanation of the nonlinear dynamics and stability phenomena documented for rotating systems controlled by electromagnetic eddy-current dampers.

We combine an averaging procedure with a Hilbert transform-based algorithm for parameter estimation of a nonlinear ocean system roll model. System backbone curves obtained from data are compared to those obtained analytically and are found to be accurate. Sensitivity of the results is tested by introducing random noise to a nonlinear model describing roll response of a small fishing boat. An example field calibration test of a small semisubmersible exhibiting nonlinear damping is also considered.

We investigate the response of a nonlinear small-body ocean-mooring system excited by finite-amplitude waves. The system is characterized by a coupled geometrically nonlinear restoring force defined by a single elastic tether. The nonlinear hydrodynamic exciting force includes both dissipative and convective terms that are not negligible in a finite wave amplitude environment. Stability of periodic motion is determined numerically and the bifurcation structure includes ultrasubharmonic and quasi-periodic response. The dissipation mechanism is found to control stability thresholds, whereas the convective nonlinearity governs the evolution to chaotic system response.

An intricate universal superstructure in bifurcation sets and routes to chaos of a nonlinear moored ocean system subjected to monochromatic wave excitations are investigated analytically and demonstrated numerically in detail herein. System nonlinearities include complex geometric restoring force and coupled fluid-system exciting forces. Primary and secondary resonance regions are identified by employing variational analysis techniques for local stability. Tangent and periodic doubling bifurcations are examined to reveal the underlying intricate superstructure. Numerical results of this complex system uncover a steady-state superstructure in the bifurcation sets that exhibit a similar bifurcation pattern of coexisting solutions in the subharmonic, ultraharmonic, and ultrasubharmonic domains. Within this superstructure it is illustrated that strange attractors appear when a period doubling sequence is infinite, and when abrupt changes in the size of an attractor occur near tangent bifurcations.

We introduce and demonstrate the applicability of a parameter identification algorithm based on the Hilbert transform to nonlinear ocean mooring systems. The mooring dynamical system consists of a submerged small body and includes a geometrically nonlinear restoring force and a nonlinear dissipation function incorporating both viscous and structural damping. By combining a recently developed methodology with a generalized averaging procedure, parameter estimation from the slowly varying envelope dynamics is enabled. System backbone curves obtained from data generated by numerical simulation are compared to those obtained analytically and are found to be accurate. An example large-scale experiment is also considered.

A phenomenological continuum model of dispersion was developed as a general three-dimensional theory to study shock wave dispersion. Testing of the model showed it predicted dispersive effects of a wave of characteristic length when a wave was propagated through a chain of springs. It also showed that if dispersive terms are present, they can cause the shock wave stress to overshoot Hugoniot stress by up to 50%, a phenomenon which could cause an underprediction of the stress failure threshold level in shock experiments.