We present a field-theoretic framework for modeling electromagnetic energy propagation in heterogeneous media by introducing the concept of electromagnetic geodesics. Unlike traditional ray optics, which assumes either a straight-line propagation or a simple bending in refractive media, our approach formulates wave propagation as geodetic motion in a curved spatial geometry induced by variations in refractive index. Building on earlier work, we move beyond scalar refractive index analogies and instead construct a local Riemannian metric characterized by an orthogonal geometric tensor derived from the Helmholtz representation. This tensor encodes spatial anisotropy and curvature, enabling a rigorous description of energy flow through complex media. We derive the electromagnetic geodesics by formulating and solving a Lagrangian system, yielding equations of motion for wavefront trajectories, group velocity, and intensity distribution. The concept of refractive tension—the vector displacement between Euclidean and transformed positions—plays a central role in defining the transformation matrix and associated metric. Numerical simulations for a spherical inhomogeneity embedded in vacuum demonstrate the emergence of curved geodesics and localized energy redistribution, illustrating the model's potential for interpreting interstellar electromagnetic phenomena and refractive effects in astrophysical environments. In particular, it shows the spatial dispersion of a the energy flow in the vicinity of the spherical inhomogeneity.

Plain Language Summary
We propose a new way to describe how light and electromagnetic energy move through complex materials. Instead of straight or bent paths, waves follow curved “geodesics” shaped by refractive index changes. This geometric approach explains energy flow, predicts intensity patterns, and helps interpret astrophysical and interstellar phenomena.

Perylene dianhydride (PDA) hydrogels are made from highly accessible perylene diamic acid salts (PDAA salts) by a versatile protonation–hydrolysis mechanism. Very weak gels are formed initially by π-stacking of PDAAs and subsequent hydrolysis yields much stronger PDA hydrogels. Hydrogels are readily made at concentrations down to 0.5 mM, exhibit storage moduli around 600 Pa @ 1 mM and undergo significant syneresis in time.

A novel protocol for the synthesis of perylene diimides (PDIs), by reacting perylene dianhydride (PDA) with aliphatic amines is reported. Full conversions were obtained at temperatures between 20 and 60 °C, using DBU as the base in DMF or DMSO. A "green"synthesis of PDIs, that runs at higher temperatures, was developed using K2CO3 in DMSO. The reaction sequence for the imidization process, via perylene amic acid intermediates (PAAs), has been confirmed experimentally aided by the synthesis and full characterization of stable model amic acid salts and amic esters. Kinetic studies, using absorption spectroscopy, have established that PDI formation proceeds via fast amic acid formation, followed by a slow conversion to imides. Solubility of the intermediate PAA salts is found to be low and rate-limiting. Based on this finding, quantitative PDI synthesis at room temperature was achieved by diluting the reaction mixture with water, the solvent in which PAA salts have better solubility. Thus, the otherwise harsh synthesis of PDIs has been transformed into an extremely convenient functional group tolerant and highly efficient reaction that runs at room temperature.

In this paper we discuss an imaging method when the object has known support and its spatial Fourier transform is only known on a certain k-space undersampled pattern. The simple conjugate gradient least squares algorithm applied to the corresponding truncated Fourier transform equation produces reconstructions that are basically of a similar quality as reconstructions obtained by solving a standard compressed sensing problem in which support information is not taken into account. Connections with previous one-dimensional approaches are highlighted and the performance of the method for two-and three-dimensional simulated and measured incomplete spectral data sets is illustrated. Possible extensions of the method are also briefly discussed.

Synthetic-aperture (SA) imaging is a popular method to visualize the reflectivity of an object from ultrasonic reflections. The method yields an image of the (volume) contrast in acoustic impedance with respect to the embedding. Typically, constant mass density is assumed in the underlying derivation. Due to the band-limited nature of the recorded data, the image is blurred in space, which is quantified by the associated point spread function. SA volume imaging is valid under the Born approximation, where it is assumed that the contrast is weak. When objects are large with respect to the wavelength, it is questionable whether SA volume imaging should be the method-of-choice. Herein, we propose an alternative solution that we refer to as SA interface imaging. This approach yields a vector image of the discontinuities of acoustic impedance at the tissue interfaces. Constant wave speed is assumed in the underlying derivation. The image is blurred in space by a tensor, which we refer to as the interface spread function. SA interface imaging is valid under the Kirchhoff approximation, where it is assumed that the wavelength is small compared to the spatial dimensions of the interfaces. We compare the performance of volume and interface imaging on synthetic data and on experimental data of a gelatin cylinder with a radius of 75 wavelengths, submerged in water. As expected, the interface image peaks at the gelatin-water interface, while the volume image exposes a peak and trough on opposing sides of the interface.

In acoustic reflectivity imaging, we infer the internal reflectivity of an unknown object from reflected waveforms. A common assumption is that the mass density is constant and that the recorded pressure field is related to a volume contrast in the wave speed by a nonlinear volume-integral representation. This representation is typically linearized under the Born approximation and solved for the volume contrast by iterative inversion. We propose an alternative methodology, which we refer to as interface contrast imaging. In our derivation, we assume a medium with constant wave speed, which contains discontinuities of the acoustic impedance at a collection of interfaces between piecewise-homogeneous subdomains. A linear relationship is established between the recorded data and the gradient of the acoustic impedance at the interfaces, which we refer to as an interface contrast. This contrast can be solved for by iterative inversion. With this procedure, acoustic interfaces can be delineated with superior resolution compared to volume contrast imaging. Since the convergence speed is relatively fast and a reasonable image can already be obtained after a single iteration, real-time applications seem feasible. If necessary, the acoustic impedance can also be imaged by integrating the retrieved reflectivity contrast over space.

We introduce a new regularization scheme for multiparameter seismic full-waveform inversion (FWI). Using this scheme, we can constrain spatial variations of parameters which are having a weak sensitivity with the one that having a good sensitivity to the measurement, assuming that these parameters have similarities in their structures. In seismic FWI, we apply this scheme when inverting the P-wave velocity and mass density simultaneously. Results from numerical tests show that this scheme may significantly improve the reconstruction of the mass density. Since we obtain an improved mass-density distribution, the inverted P-wave velocity is also enhanced. Hence, we also obtain a better data fit. As numerical examples we show inversions of both vertical seismic profiling (VSP) and surface seismic measurements.