Collective modes across the soliton-droplet crossover in binary Bose mixtures

We study the collective modes of a binary Bose mixture across the soliton to droplet crossover in a quasi one dimensional waveguide with a beyond-mean-field equation of state and a variational Gaussian ansatz for the scalar bosonic field of the corresponding effective action. We observe a sharp difference in the collective modes in the two regimes. Within the soliton regime modes vary smoothly upon the variation of particle number or interaction strength. On the droplet side collective modes are inhibited by the emission of particles. This mechanism turns out to be dominant for a wide range of particle numbers and interactions. In a small window of particle number range and for intermediate interactions we find that monopole frequency is likely to be observed. In the last part we focus on the spin-dipole modes for the case of equal intraspecies interactions and equal equilibrium particle numbers in the presence of a weak longitudinal confinement. We found that such modes might be unobservable in the real-time dynamics close to the equilibrium as their frequency is higher than the particle emission spectrum by at least one order of magnitude in the droplet phase. Our results are relevant for experiments with two-component BECs for which we provide realistic parameters.Comment: Accepted for Publication in PR

Thermal Fluctuations: Modes versus the Continuum

The thermal fluctuation spectrum of the signal received on a patch electrode is examined and it is shown that the spectrum shows both the modes of the plasma and a continuous spectrum related to the independent-particle motions of plasma electrons. Modes whose axial phase velocity are more than 3–4 times the electron thermal speed are lightly Landau-damped and are clearly separated from the continuum. Long wavelength modes are "acoustic" in nature. If the axial phase velocity of a mode becomes less than 1–2 times the electron thermal speed, then the mode becomes strongly Landau-damped and it merges into the continuum. The mode velocities are of the order of wpa , where a is the plasma radius, so that the plasma radius must be at least several deBye lengths in order to have lightly damped modes. In general, the spectrum is a mixture of a continuous spectrum together with a finite number of modes which are Landau-damped by varying amounts, depending on their phase velocity relative to the electron thermal speed. Only in the extreme limit, wpa << vth does the continuous spectrum tend to a Gaussian of width k vth, characteristic of independent particles. The effect of the "load impedance" on the measurements is also discussed

Directivity Modes of Earthquake Populations with Unsupervised Learning

We present a novel approach for resolving modes of rupture directivity in large populations of earthquakes. A seismic spectral decomposition technique is used to first produce relative measurements of radiated energy for earthquakes in a spatially compact cluster. The azimuthal distribution of energy for each earthquake is then assumed to result from one of several distinct modes of rupture propagation. Rather than fitting a kinematic rupture model to determine the most likely mode of rupture propagation, we instead treat the modes as latent variables and learn them with a Gaussian mixture model. The mixture model simultaneously determines the number of events that best identify with each mode. The technique is demonstrated on four datasets in California, each with compact clusters of several thousand earthquakes with comparable slip mechanisms. We show that the datasets naturally decompose into distinct rupture propagation modes that correspond to different rupture directions, and the fault plane is unambiguously identified for all cases. We find that these small earthquakes exhibit unilateral ruptures 63–73% of the time on average. The results provide important observational constraints on the physics of earthquakes and faults

Directivity Modes of Earthquake Populations with Unsupervised Learning

We present a novel approach for resolving modes of rupture directivity in large populations of earthquakes. A seismic spectral decomposition technique is used to first produce relative measurements of radiated energy for earthquakes in a spatially compact cluster. The azimuthal distribution of energy for each earthquake is then assumed to result from one of several distinct modes of rupture propagation. Rather than fitting a kinematic rupture model to determine the most likely mode of rupture propagation, we instead treat the modes as latent variables and learn them with a Gaussian mixture model. The mixture model simultaneously determines the number of events that best identify with each mode. The technique is demonstrated on four datasets in California, each with compact clusters of several thousand earthquakes with comparable slip mechanisms. We show that the datasets naturally decompose into distinct rupture propagation modes that correspond to different rupture directions, and the fault plane is unambiguously identified for all cases. We find that these small earthquakes exhibit unilateral ruptures 63–73% of the time on average. The results provide important observational constraints on the physics of earthquakes and faults