The quasi-stationary method for black hole binary inspiral is an approximation for studying strong field effects while suppressing radiation reaction. In this paper we use a nonlinear scalar field toy model (i) to explain the underlying method of approximating binary motion by periodic orbits with radiation; (ii) to show how the fields in such a model are found by the solution of a boundary val...

Numerical simulations based on nonlinear partial differential equations (PDEs) using Newton-based methods require the solution of large, sparse linear systems of equations at each nonlinear iteration. Typically in large-scale parallel simulations such linear systems are solved by using preconditioned Krylov methods. In many cases, especially in time-dependent problems, the attributes of the lin...

Acoustic radiation force is a nonlinear acoustic effect caused by the transfer of wave momentum to absorbing or scattering objects. This phenomenon is exploited in modern ultrasound metrology for measurement of the acoustic power radiated by a source and is used for both therapeutic and diagnostic sources in medical applications. To calculate radiation force an acoustic hologram can be used in ...

Coupling electromagnetic waves in a cavity and mechanical vibrations via the radiation pressure of photons is a promising platform for investigations of quantum-mechanical properties of motion. A drawback is that the effect of one photon tends to be tiny, and hence one of the pressing challenges is to substantially increase the interaction strength. A novel scenario is to introduce into the set...

The quantum nonlinear regime of optomechanics is reached when nonlinear effects of the radiation pressure interaction are observed at the single-photon level. This requires couplings larger than the mechanical frequency and cavity-damping rate, and is difficult to achieve experimentally. Here we show how to exponentially enhance the single-photon optomechanical coupling strength using only addi...

We study fully nonlinear and perturbative evolutions of nonrotating black holes with odd-parity distortions. Perturbative methods proved to be useful in order to interpret the nonlinear results. In particular, they provided insight on the nonlinear dependence of the wave forms with the distortion parameter Q0, explaining it in terms of the multipole coupling. We also found an increase in the fr...

A theory of time-dependent nonlinear dispersive equations of the Schrödinger or Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear master equations (NLME), governing the evolution of the mode powers, and by a novel multitime scale analysis of these equations. The scattering theory is developed and coherent resonance ph...

The nonlinear interaction between Near-Infrared (NIR) and Terahertz pulses is principally investigated as a means for the detection of radiation in the hardly accessible THz spectral region. Most studies have targeted second-order nonlinear processes, given their higher efficiencies, and only a limited number have addressed third-order nonlinear interactions, mainly investigating four-wave mixi...

An improved nonlinear least-square method is presented in this paper. This method changes the traditional least-square method’s shortness of being sensitive to its initial conditions. Pattern synthesis for concentric circular arrays using nonlinear least-square method is introduced. The excitation amplitudes and phases of the array elements are optimized. This method can make the design of the ...