A robust and low frequency stable time domain PMCHWT equation

The time domain PMCHWT equation models transient scattering by piecewise homogeneous dielectrics. After discretization, it can be solved using the marching-on-in-time algorithm. Unfortunately, the PMCHWT equation suffers from DC instability: it supports constant in time regime solutions. Upon discretization, the corresponding poles of the system response function shift into the unstable region of the complex plane, rendering the MOT algorithm unstable. Furthermore, the discrete system becomes ill-conditioned when a large time step is used. This phenomenon is termed low frequency breakdown. In this contribution, the quasi Helmholtz components of the PMCHWT equation are separated using projector operators. Judicially integrating or differentiating these components of the basis and testing functions leads to an algorithm that (i) does not suffer from unstable modes even in the presence of moderate numerical errors, (ii) remains well-conditioned for large time steps, and (iii) can be applied effectively to both simply and multiply connected geometries

How do we understand and visualize uncertainty?

Geophysicists are often concerned with reconstructing subsurface properties using observations collected at or near the surface. For example, in seismic migration, we attempt to reconstruct subsurface geometry from surface seismic recordings, and in potential field inversion, observations are used to map electrical conductivity or density variations in geologic layers. The procedure of inferring information from indirect observations is called an inverse problem by mathematicians, and such problems are common in many areas of the physical sciences. The inverse problem of inferring the subsurface using surface observations has a corresponding forward problem, which consists of determining the data that would be recorded for a given subsurface configuration. In the seismic case, forward modeling involves a method for calculating a synthetic seismogram, for gravity data it consists of a computer code to compute gravity fields from an assumed subsurface density model. Note that forward modeling often involves assumptions about the appropriate physical relationship between unknowns (at depth) and observations on the surface, and all attempts to solve the problem at hand are limited by the accuracy of those assumptions. In the broadest sense then, exploration geophysicists have been engaged in inversion since the dawn of the profession and indeed algorithms often applied in processing centers can all be viewed as procedures to invert geophysical data

A space-time mixed Galerkin marching-on-in-time scheme for the time-domain combined field integral equation

The time domain combined field integral equation (TD-CFIE), which is constructed from a weighted sum of the time domain electric and magnetic field integral equations (TD-EFIE and TD-MFIE) for analyzing transient scattering from closed perfect electrically conducting bodies, is free from spurious resonances. The standard marching-on-in-time technique for discretizing the TD-CFIE uses Galerkin and collocation schemes in space and time, respectively. Unfortunately, the standard scheme is theoretically not well understood: stability and convergence have been proven for only one class of space-time Galerkin discretizations. Moreover, existing discretization schemes are nonconforming, i.e., the TD-MFIE contribution is tested with divergence conforming functions instead of curl conforming functions. We therefore introduce a novel space-time mixed Galerkin discretization for the TD-CFIE. A family of temporal basis and testing functions with arbitrary order is introduced. It is explained how the corresponding interactions can be computed efficiently by existing collocation-in-time codes. The spatial mixed discretization is made fully conforming and consistent by leveraging both Rao-Wilton-Glisson and Buffa-Christiansen basis functions and by applying the appropriate bi-orthogonalization procedures. The combination of both techniques is essential when high accuracy over a broad frequency band is required

Nanobody technology : a versatile toolkit for microscopic imaging, protein-protein interaction analysis, and protein function exploration

Over the last two decades, nanobodies or single-domain antibodies have found their way in research, diagnostics, and therapy. These antigen-binding fragments, derived from Camelid heavy chain only antibodies, possess remarkable characteristics that favor their use over conventional antibodies or fragments thereof, in selected areas of research. In this review, we assess the current status of nanobodies as research tools in diverse aspects of fundamental research. We discuss the use of nanobodies as detection reagents in fluorescence microscopy and focus on recent advances in super-resolution microscopy. Second, application of nanobody technology in investigating protein-protein interactions is reviewed, with emphasis on possible uses in mass spectrometry. Finally, we discuss the potential value of nanobodies in studying protein function, and we focus on their recently reported application in targeted protein degradation. Throughout the review, we highlight state-of-the-art engineering strategies that could expand nanobody versatility and we suggest future applications of the technology in the selected areas of fundamental research

Calderon multiplicative preconditioner for the PMCHWT equation applied to chiral media

In this contribution, a Calderon preconditioned algorithm for the modeling of scattering of time harmonic electromagnetic waves by a chiral body is introduced. The construction of the PMCHWT in the presence of chiral media is revisited. Since this equation reduces to the classic PMCHWT equation when the chirality parameter tends to zero, it shares its spectral properties. More in particular, it suffers from dense grid breakdown. Based on the work in [1], [2], a regularized version of the PMCHWT equation is introduced. A discretization scheme is described. Finally, the validity and spectral properties are studied numerically. More in particular, it is proven that linear systems arising in the novel scheme can be solved in a small number of iterations, regardless the mesh parameter

Azimuthal Anisotropy From Multimode Waveform Modeling Reveals Layering Within the Antarctica Craton

The isotropic structure of the crust and upper mantle under Antarctica has been constrained by many studies. However, the depth dependence of seismic anisotropy, a powerful tool to characterize deformation and flow, is still poorly known. Here, we modeled three-dimensional (3-D) variations in azimuthal anisotropy under Antarctica using a multimode Rayleigh waveform fitting technique. We first searched the model space with a reversible-jump Markov Chain Monte Carlo approach to find path-averaged vertically polarized shear wave velocity profiles that fit fundamental and higher mode Rayleigh waveforms. We then inverted them to obtain a 3-D velocity and azimuthal anisotropy model across the region down to 600 km depth. Our results reveal that the east-west dichotomy found in other studies is not only characterized by different wave velocities but also by different anisotropy directions, likely reflecting the different deformation histories of the two blocks. Azimuthal anisotropy was found to be present in the top 300 km only and peaks at 100 - 200 km depth under the East Antarctica craton. Additionally, depth changes in fast direction were observed within the craton between 75 km and 150 km depth, suggesting layering is present. We speculate this layering relates to the formation history of the craton.submitted to Seismic

Accurate and conforming mixed discretization of the chiral Müller equation

Scattering of time-harmonic fields by chiral objects can be modeled by a second kind boundary integral equation, similar to Muller's equation for scattering by nonchiral penetrable objects. In this contribution, a mixed discretization scheme for the chiral Muller equation is introduced using both Rao-Wilton- Glisson and Buffa-Christiansen funtions. It is shown that this mixed discretization yields more accurate solutions than classical discretizations, and that they can be computed in a limited number of iterations using Krylov type solvers

Azimuthal Anisotropy From Multimode Waveform Modeling Reveals Layering Within the Antarctica Craton

The isotropic structure of the crust and upper mantle under Antarctica has been constrained by many studies. However, the depth dependence of seismic anisotropy, a powerful tool to characterize deformation and flow, is still poorly known. Here, we modeled three-dimensional (3-D) variations in azimuthal anisotropy under Antarctica using a multimode Rayleigh waveform fitting technique. We first searched the model space with a reversible-jump Markov Chain Monte Carlo approach to find path-averaged vertically polarized shear wave velocity profiles that fit fundamental and higher mode Rayleigh waveforms. We then inverted them to obtain a 3-D velocity and azimuthal anisotropy model across the region down to 600 km depth. Our results reveal that the east-west dichotomy found in other studies is not only characterized by different wave velocities but also by different anisotropy directions, likely reflecting the different deformation histories of the two blocks. Azimuthal anisotropy was found to be present in the top 300 km only and peaks at 100 - 200 km depth under the East Antarctica craton. Additionally, depth changes in fast direction were observed within the craton between 75 km and 150 km depth, suggesting layering is present. We speculate this layering relates to the formation history of the craton.submitted to Seismic