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It had been previously shown that an idealized version of the two-wave-vector extension of the NMR pulsed-field-gradient spin echo diffusion experiment can be used to determine the apparent radius of geometries with restricted diffusion. In the present work, the feasibility of the experiment was demonstrated in an NMR imaging experiment, in which the apparent radius of axons in white matter tissue was determined. Moreover, numerical simulations have been carried out to determine the reliability of the results. For small diffusion times, the radius is systematically underestimated. Larger gradient area, finite length gradient pulses, and a statistical distribution of radii within a voxel all have a minor influence on the estimated radius. Pulsed-field-gradient spin echo (PGSE) NMR experiments have been used to measure apparent diffusion in liquids and biological tissue (1,2). In the narrow gradient pulse limit (i.e., using infinitely short pulses), the signal obtained with the PGSE experiment corresponds to the Fourier transform of the diffusion propagator (3,4). Using this so-called q-space imaging technique, the evolution of the diffusion propagator can be measured by acquiring images or spectra with increasing delays between the pulsed diffusion gradients (5,6) and has been used to characterize the diffusion propagator in liquids (6), red blood cells (7,8), and nerve cells (5). The shape of the diffusion propagator carries information about the microstructure of the sample (e.g., biological tissue) and allows the study of compartments that are much smaller than typical sizes that can be resolved by morphological MRI methods (6,9,10).A two-wave-vector extension to the standard PGSE experiment using two pairs of pulsed gradients in a double spin echo, a so called two-wave-vector exper- iment, has been used to study flow effects in more detail than possible with a single gradient pair (11). In general, two-wave-vector experiments carry more details than obtainable through a one wave vector experiment. For example, a two-wave-vector experiment can distinguish between diffusion in different compartments and diffraction-like behavior which is caused by restricted diffusion (12).In the case of restricted diffusion, theoretical calculations by Mitra have shown that the two-wave-vector experiment can be used to determine the radius of gyration of pores using several approximations (12). The same is true for any geometry with restricted diffusion. Potential applications of this theoretical work include the measurement of the size of microscopic structures in biological tissue, as for example done in (13)(14)(15).In the present work, the theory (12) has been successfully applied to quantify the apparent cell radius in an NMR imaging experiment of biological tissue. Furthermore, it has been investigated how deviations from the idealized assumptions affect the apparent radius. Among the effects studied are finite widths of gradient pulses and radius distributions. The term apparent refers to the fact that the determination...

We describe a criterion for particles suspended in a randomly moving fluid to aggregate. Aggregation occurs when the expectation value of a random variable is negative. This variable evolves under a stochastic differential equation. We analyse this equation in detail in the limit where the correlation time of the velocity field of the fluid is very short, such that the stochastic differential equation is a Langevin equation.

All-dielectric metasurfaces supporting photonic bound states in the continuum (BICs) are an exciting toolkit for achieving resonances with ultranarrow linewidths. However, the transition from theory to experimental realization can significantly reduce the optical performance of BIC-based nanophotonic systems, severely limiting their application potential. Here, we introduce a combined numerical/experimental methodology for predicting how unavoidable tolerances in nanofabrication such as random geometrical variations affect the performance of different BIC metasurface designs. We compare several established all-dielectric BIC unit cell geometries with broken in-plane inversion symmetry including tilted ellipses, asymmetric double rods, and split rings. Significantly, even for low fabrication-induced geometrical changes, both the BIC resonance amplitude and its quality factor (Q-factor) are significantly reduced. We find that the all-dielectric ellipses maintain the highest Q-factors throughout the geometrical variation range, whereas the rod and split ring geometries fall off more quickly. The same behavior is confirmed experimentally, where geometrical variation values are derived from automated processing of sets of scanning electron microscopy (SEM) images. Our methodology provides crucial insights into the performance degradation of BIC metasurfaces when moving from simulations to fabricated samples and will enable the development of robust, high-Q, and easy to manufacture nanophotonic platforms for applications ranging from biomolecular sensing to higher harmonic generation.