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Register a new userA mode parabolic equations method with the resonant mode interaction
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A mode parabolic equation method for resonantly interacted modes was developed. The flow of acoustic energy is conserved for the derived equations with an accuracy adequate to the used approximation. The testing calculations were done for ASA wedge benchmark and proved excellent agreement with COUPLE program.
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We present a complete analytical derivation of the equations used for stationary and nonstationary wave systems regarding resonant sound transmission and reflection described by the phenomenological Coupled-Mode Theory. We calculate the propagating and coupling parameters used in Coupled-Mode Theory directly by utilizing the generalized eigenwave-eigenvalue problem from the Hamiltonian of the sound wave equations. This Hamiltonian formalization can be very useful since it has the ability to describe mathematically a broad range of acoustic wave phenomena. We demonstrate how to use this theory as a basis for perturbative analysis of more complex resonant scattering scenarios. In particular, we also form the effective Hamiltonian and coupled-mode parameters for the study of sound resonators with background moving media. Finally, we provide a comparison between Coupled-Mode theory and full-wave numerical examples, which validate the Hamiltonian approach as a relevant model to compute the scattering characteristics of waves by complex resonant systems.
We consider a class of time dependent second order partial differential equations governed by a decaying entropy. The solution usually corresponds to a density distribution, hence positivity (non-negativity) is expected. This class of problems covers important cases such as Fokker-Planck type equations and aggregation models, which have been studied intensively in the past decades. In this paper, we design a high order discontinuous Galerkin method for such problems. If the interaction potential is not involved, or the interaction is defined by a smooth kernel, our semi-discrete scheme admits an entropy inequality on the discrete level. Furthermore, by applying the positivity-preserving limiter, our fully discretized scheme produces non-negative solutions for all cases under a time step constraint. Our method also applies to two dimensional problems on Cartesian meshes. Numerical examples are given to confirm the high order accuracy for smooth test cases and to demonstrate the effectiveness for preserving long time asymptotics.
Magnetic interaction between photons and dipoles is essential in electronics, sensing, spectroscopy, and quantum computing. However, its weak strength often requires resonators to confine and store the photons. Here, we present mode engineering techniques to create resonators with ultrasmall mode volume and ultrahigh quality factor. In particular, we show that it is possible to achieve an arbitrarily small mode volume only limited by materials or fabrication with minimal Q degradation. We compare mode-engineered cavities in a trade-off space and show that the magnetic interaction can be strengthened more than $10^{16}$ times compared to free space. These methods enable new applications from high-cooperativity microwave-spin coupling in quantum computing or compact electron paramagnetic resonance (EPR) sensors to fundamental science such as dark matter searches.
We consider an optomechanical system comprising a single cavity mode and a dense spectrum of acoustic modes and solve for the quantum dynamics of initial cavity mode Fock (i.e., photon number) superposition states and thermal acoustic states. The optomechanical interaction results in dephasing without damping and bears some analogy to gravitational decoherence. For a cavity mode locally coupled to a one-dimensional (1D) elastic string-like environment or two-dimensional (2D) elastic membrane-like environment, we find that the dephasing dynamics depends respectively on the string length and membrane area--a consequence of an infrared divergence in the limit of an infinite-sized string or membrane. On the other hand, for a cavity mode locally coupled to a three-dimensional (3D) bulk elastic solid, the dephasing dynamics is independent of the solid volume (i.e., is infrared finite), but dependent on the local geometry of the coupled cavity--a consequence of an ultraviolet divergence in the limit of a pointlike coupled cavity. We consider as possible respective realizations for the cavity-coupled-1D and 2D acoustic environments, an LC oscillator capacitively coupled to a partially metallized strip and a cavity light mode interacting via light pressure with a membrane.
We describe an atom interferometric gravitational wave detector design that can operate in a resonant mode for increased sensitivity. By oscillating the positions of the atomic wavepackets, this resonant detection mode allows for coherently enhanced, narrow-band sensitivity at target frequencies. The proposed detector is flexible and can be rapidly switched between broadband and narrow-band detection modes. For instance, a binary discovered in broadband mode can subsequently be studied further as the inspiral evolves by using a tailored narrow-band detector response. In addition to functioning like a lock-in amplifier for astrophysical events, the enhanced sensitivity of the resonant approach also opens up the possibility of searching for important cosmological signals, including the stochastic gravitational wave background produced by inflation. We give an example of detector parameters which would allow detection of inflationary gravitational waves down to $Omega_text{GW} sim 10^{-14}$ for a two satellite space-based detector.
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