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Bayesian Nonlocal Operator Regression (BNOR): Towards the Characterization of Uncertainty in Heterogeneous Materials.
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Coarse-graining and nonlocality
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Nonlocal modeling of the interfaces between graphene layers
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Algebraic multigrid solver for nonlocal equations
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Algebraic multigrid solver for nonlocal equations
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Scalable methods for nonlocal models
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Finite element methods for nonlocal problems - Theoretical background material for PyNucleus
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Inference of kernel parameters for nonlocal equations
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Coarse Graining Kinetic Monte Carlo into a Nonlocal Continuum Model
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Gallium Nitride Nonlocal Metasurfaces with Broken Vertical Symmetry
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Scalable methods for nonlocal models
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Chiral nonlocal metasurfaces in gallium nitride with lithographically-defined vertical symmetry breaking
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A Nonlocal Magneto-curvature Instability in a Differentially Rotating Disk
A global mode is shown to be unstable to nonaxisymmetric perturbations in a differentially rotating Keplerian disk containing either vertical or azimuthal magnetic fields. In an unstratified cylindrical disk model, using both global eigenvalue stability analysis and linear global initial-value simulations, it is demonstrated that this instability dominates at strong magnetic fields where local standard magnetorotational instability (MRI) becomes stable. Unlike the standard MRI mode, which is concentrated in the high flow shear region, these distinct global modes (with low azimuthal mode numbers) are extended in the global domain and are Alfvén-continuum-driven unstable modes. As its mode structure and relative dominance over MRI are inherently determined by the global spatial curvature as well as the flow shear in the presence of a magnetic field, we call it the magneto-curvature (magneto-spatial-curvature) instability. Consistent with the linear analysis, as the field strength is increased in the nonlinear simulations, a transition from MRI-driven turbulence to a state dominated by global nonaxisymmetric modes is obtained. This global instability could therefore be a source of nonlinear transport in accretion disks at a higher magnetic field than predicted by local models.
Nonlocal Galileons and self-acceleration
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Nonlocal plasma turbulence associated with interplanetary shocks
Regions of plasma turbulence extending several tenths of an astronomical unit upstream or downstream of interplanetary shocks have been detected by the plasma wave instrument on ISEE 3. Highly impulsive electric field bursts at 1-10 kHz were found (hours upstream of quasi-parallel interplanetary shocks) whose average and peak amplitudes occasionally increased until the shock crossing, when they were suppressed. A 0.1-1 kHz electric field component was enhanced at nearly all shocks, and persisted downstream. A smooth, high-frequency continuum near and above the local electron plasma frequency was enhanced at, and persisted downstream of, every interplanetary shock studied. While no single interplanetary shock showed every effect, the ensemble of shocks contained at least one example of each type of plasma wave found upstream of the earth's bow shock.
Nonlocal stability analysis of the MHD Kelvin-Helmholtz instability in a compressible plasma
A general stability analysis is given of the Kevin-Helmholtz instability, for the case of sheared MHD flow of finite thickness in a compressible plasma which allows for the arbitrary orientation of the magnetic field, velocity flow, and wave vector in the plane perpendicular to the velocity gradient. The stability problem is reduced to the solution of a single second-order differential equation including a gravitational term to represent the coupling between the Kelvin-Helmholtz mode and the interchange mode. Compressibility and a magnetic field component parallel to the flow are found to be stabilizing effects, with destabilization of only the fast magnetosonic mode in the transverse case, and the presence of both Alfven and slow magnetosonic components in the parallel case. Analysis results are used in a discussion of the stability of sheared plasma flow at the magnetopause boundary and in the solar wind.