Length Scales Research Articles

Anti-plane Yoffe-type crack in flexoelectric material

This work investigates the deformation and polarization fields around a finite anti-plane shear (mode III) crack growing dynamically under steady-state conditions. The leading tip of this finite crack breaks the material while the trailing tip heals it. This fast moving finite crack (referred to as a rupture “pulse” in the geophysics literature) propagates with a constant velocity and with the mechanical and the electrical fields that remain invariant with respect to an observer moving with the crack-tips. This problem belongs to the first type of steady state crack growth problems according to the classification of Freund. The “prototype” problem which refers to an isotropic, body subjected to fracture under tensile loading was first proposed and solved by Yoffe, while finite cracks (or shear pulses) were also analyzed by Freund and by Rice. In the above cases the material was assumed to be linear elastic. Our analysis extends these studies to flexoelectric materials, and it is both theoretical and numerical. It discusses the asymptotic structure of the crack-tip displacement and the polarization fields; it calculates the dynamic energy release rate and presents their dependence on crack-tip velocity. Comparisons are made to the available, classical, elasto-dynamic solutions and to the static case. The influence of the electrical properties of the material on strengthening is also analyzed. Dynamic fracture of flexoelectric materials is of relevance to both the study of earthquake source mechanics and to the analysis of the reliability of micro-electronic devices. This is because both rocks and ceramics are flexoelectric. Indeed, during earthquake rupture processes, dynamic, in-plane shear (Mode-II) and out of plane shear (Mode-III), cracks propagate along faults and exhibit both mechanical and electrical polarization signatures. At an entirely different length scale, flexoelectric ceramics are currently used as sensors and transducers and can experience dynamic shear failure along interfaces when subjected to dynamic loading (e.g. impact.). Failure by dynamic fracture can be detrimental to both their mechanical reliability and electrical functionality.

Buffeting performance of long-span bridges with different span affected by parametric typhoon wind

Currently, typhoon-related performance of long span bridges usually focus on a specific wind record such as wind speed and turbulence intensity during a full typhoon, however, the inter-correlation among wind characteristic parameters under typhoon wind climate is ignored. The existing investigation about structural responses during typhoon attacks are still limited at case-study analysis, and hardly provide a generalized framework to evaluate the structural performance especially for typhoon landing whole process. This study utilizes the measured wind speeds of the strong typhoon "Hagupit" to establish a unified typhoon parametric model, during which the correlation of typhoon wind parameters including angle of attack (AoA), turbulence intensity, integral length scale and mean wind speed were taken into consideration. The measured typhoon process charactered with center-through effect with M-type average wind speed curve. Furthermore, the structural performance of long-span bridges with different spans from 1500 m to 2500 m main span was systematically studied. The aerodynamic parameters of the bridge deck section, including the aerostatic coefficients, flutter derivatives at different AoAs, and aerodynamic admittance under different oncoming flow conditions were identified through wind tunnel tests. Finally, the wind-induced buffeting performance was calculated by the buffeting frequency domain algorithm, showing various structural wind effect characteristics during the typhoon landing whole process. The maximal buffeting response is not necessarily related with the wind speed, and other wind characteristics especially turbulence intensity and AoA, etc. also affect on the results.

Scalable Macroscopic Engineering from Polymer-Based Nanoscale Building Blocks: Existing Challenges and Emerging Opportunities.

Natural materials exhibit exceptional properties due to their hierarchical structures spanning from the nano- to the macroscale. Replicating these intricate spatial arrangements in synthetic materials presents a significant challenge as it requires precise control of nanometric features within large-scale structures. Addressing this challenge depends on developing methods that integrate assembly techniques across multiple length scales to construct multiscale-structured synthetic materials in practical, bulk forms. Polymers and polymer-hybrid nanoparticles, with their tunable composition and structural versatility, are promising candidates for creating hierarchically organized materials. This review highlights advances in scalable techniques for nanoscale organization of polymer-based building blocks within macroscopic structures, including block copolymer self-assembly with additive manufacturing, polymer brush nanoparticles capable of self-assembling into larger, ordered structures, and direct-write colloidal assembly. These techniques offer promising pathways toward the scalable fabrication of materials with emergent properties suited for advanced applications such as bioelectronic interfaces, artificial muscles, and other biomaterials.

Scaling Effects of the Weissenberg Number in Electrokinetic Oldroyd-B Fluid Flow Within a Microchannel.

This study attempts to extend previous research on electrokinetic turbulence (EKT) in Oldroyd-B fluid by investigating the relationship between the Weissenberg number ( ) and the second-order velocity structure function ( ) under applied electric fields. Inspired by Sasmal's demonstration in Sasmal (2022) of how heterogeneous zeta potentials induce turbulence above a critical , we develop a mathematical framework linking to turbulent phenomena. Our analysis incorporates recent findings on AC (Zhao & Wang, 2017) and DC (Zhao & Wang 2019) EKT, which have defined scaling laws for velocity and scalar structure functions in the forced cascade region. Our finding shows that and , for a length scale , and , where is a velocity fluctuations quantity and denotes the time relaxation parameter. This work establishes a positive correlation between and turbulent flow phenomena through a rigorous analysis of velocity structure functions, thereby offering a mathematical foundation for building the design and optimization of EKT-based microfluidicdevices.

Untangling stellar components of galaxies: Evaluation of dynamical decomposition methods in simulated galaxies with GalaxyChop

Galaxy formation is intrinsically connected to the distinct evolutionary processes of disk and spheroidal systems, which are the fundamental stellar components of galaxies. Understanding the mutual, dynamical interplay and co-evolution of these components requires a detailed dynamical analysis to allow for disentanglement of these systems. We introduce JEHistogram, a new method for the dynamical decomposition of simulated galaxies into disk and spheroidal stellar components that utilizes the angular momentum and energy of star particles. We evaluate its performance against five previously established methods using a sample of equilibrium galaxies with stellar masses in the range $10^ M_ gal /M_ $. Our assessment involves several metrics, including the completeness and purity of stellar particle classification, scale lengths, mass density profiles, velocity dispersion, and rotational velocity profiles. While all methods approximate the properties of the original components, such as mass fractions and density or velocity profiles, JEHistogram demonstrates a better accuracy, particularly in the inner regions of galaxies where component overlap complicates separation. Additionally, we apply JEHistogram to a Milky Way-like galaxy from the IllustrisTNG cosmological simulations, showcasing its capability to derive properties such as the size, mass, velocity, color, and age of dynamically defined disk and spheroidal components. All the dynamical decomposition methods we analyzed are publicly accessible through the Python package GalaxyChop

Studies on the retarded recrystallization of tungsten in CIMPLE-PSI exposed under very-high target temperature and long He+-fluence

Abstract Experiments are carried out in CIMPLE-PSI, to understand the recrystallization behavior of tungsten (W) exposed under very-high target temperature and ITER relevant long He+-fluence. The effect of helium bubbles on possible retardation of the recrystallization process is also studied. W samples are simultaneously exposed under He plasma and annealed by the plasma heat-load, in contrast to previously reported experiments in literature, which were carried out sequentially. Exposed samples are characterized by field emission scanning electron microscopy (FESEM), Vickers surface micro-hardness, nano-hardness and electron backscattered diffraction (EBSD). It is observed that the sample exposed to plasma under the highest temperature (1866 K) suffered acute retarded grain growth. This also contained small, unrecovered grains on the exposed surface. FESEM imaging of the cross-sections confirm relatively smaller helium bubbles still form even at the very high temperature conditions, which can impede the grain growth locally, whenever they are forming right on the grain boundaries. This results in an inhomogeneous mixture of surface grains with sizes from few micrometer to few tens of micrometer. EBSD estimates that the plasma exposed surface was only 34% recrystallized. The second sample exposed at a lower temperature (1699 K) but for three times higher fluence (ion fluence: 1.19×1027 m-2) was almost fully recrystallized, which shows retardation diminishes very fast with the duration of the exposure. Hardness measurements were undertaken to understand the variation with plasma exposure/annealing temperature and the extent of recrystallization, with three different probing length scales, spanning from few hundreds of nanometer to several micrometers. Both helium plasma exposed W samples are observed to undergo retarded softening up to a depth of few hundred nanometers from the surface, compared to when the metal may be recrystallized by simple heating, without any plasma exposure.

Thermal Fluid Modeling Approaches in SAM for High Temperature Gas-Cooled Reactor Applications

This paper provides an overview of the unique modeling and simulation challenges and needs in the system and safety analysis of two common types of High Temperature Gas-cooled Reactor (HTGR) designs. The challenges are associated with the complex core geometry configurations and the change of the dominant heat removal mechanisms between normal operating conditions and decay heat removal transients. This requires that simulation tools utilize models with reasonable length scales and capture both the localized heat transfer and the core-scale heat transfer at the same time. To meet such analysis needs, different methodologies were developed. This includes adopting existing methods and further developing/improving them, as well as proposing innovative methods that leverage advanced computational frameworks such as the Multiphysics Object Oriented Simulation Environment (MOOSE).

The Unique Behavior of Vertical Velocity in Developing Deep Convection

AbstractWhen daytime tropical convection develops away from mesoscale disturbances, it typically transitions gradually from dry to shallow to deep convection on hourly timescales. The transition is commonly associated with the formation of larger horizontal boundary‐layer structures and an increasing level of cloud organization aloft. This study demonstrates that a spectral analysis of the resolved high‐resolution sub‐cloud flow features allows for a robust identification of dominant length scales and the quantification of their growth rates during the transition. Furthermore, it is shown that temperature, moisture, and horizontal winds develop multiple length scales with the largest ones growing up to several kilometers in magnitude. However, the vertical velocity behaves in a distinct manner developing significantly smaller values, comparable over land and ocean. This indicates stronger inherent limits of vertical velocity to self‐organize by size.

Solvent-adaptive hydrogels with lamellar confinement cellular structure for programmable multimodal locomotion

Biological organisms can perform flexible and controllable multimodal motion under external stimuli owing to the hierarchical assembly of anisotropic structures across multiple length scales. However, artificial soft actuators exhibit the limited response speed, deformation programmability and movement capability especially in harsh environments because of insufficient anisotropic hierarchy and precision in structural design. Here, we report a programmed assembly directed confinement polymerization method for the fabrication of environmentally tolerant and fast responsive hydrogels with lamellar assembly-confined cellular structure interpenetrated with highly aligned nanopillars by the directional freezing-assisted polymerization in the predesigned anisotropic laminar scaffold. The obtained hydrogel exhibits ultrafast responsiveness and anisotropic deformation exposed to temperature/light/solvent stimulation, maintaining highly consistent responsive deformation capability in all-polarity solvents over 100 days of soaking. Moreover, the hydrogels implement photoactive programmable multi-gait locomotion whose amplitude and directionality are precisely regulated by the intrinsic structure, including controlled crawling and rotation in water and non-polar solvents, and 3D self-propulsion floating and swimming in polar solvents. Thus, this hydrogel with hierarchically ordered structure and dexterous locomotion may be suitable for flexible intelligent actuators serving in harsh solvent environments.

X‐Raying Neutral Density Disturbances in the Mesosphere and Lower Thermosphere Induced by the 2022 Hunga‐Tonga Volcano Eruption‐Explosion

AbstractWe present X‐ray observations of the upper atmospheric density disturbance caused by the explosive eruption of the Hunga Tonga‐Hunga Ha'apai (HTHH) volcano on 15 January 2022. From 14 January to 16 January, the Chinese X‐ray astronomy satellite, Insight‐HXMT, was observing the supernova remnant Cassiopeia A. The X‐ray data obtained during Earth's atmospheric occultations allowed us to measure neutral densities in the altitude range of 90–150 km. The density profiles above 110 km altitude obtained before the major eruption are in reasonable agreement with expectations by both GAIA and NRLMSIS 2.0 models. In contrast, after the HTHH eruption, a severe density depletion was found up to 1,000 km away from the epicenter, and a relatively weak depletion extending up to km for over 8 hr after the eruption. In addition, density profiles showed wavy structures with a typical length scale of either 20 km (vertical) or 1,000 km (horizontal). This may be caused by Lamb waves or gravity waves triggered by the volcanic eruption.

A numerical study on the oscillatory dynamics of tip vortex cavitation

In this paper, we numerically study the mechanism of the oscillatory flow dynamics associated with the tip vortex cavitation (TVC) over an elliptical hydrofoil section. Using our recently developed three-dimensional variational multiphase flow solver, we investigate the TVC phenomenon at Reynolds number $Re = 8.95 \times 10^5$ via dynamic subgrid-scale modelling and the homogeneous mixture theory. To begin, we examine the grid resolution requirements and introduce a length scale considering both the tip vortex strength and the core radius. This length scale is then employed to non-dimensionalize the spatial resolution in the tip vortex region, the results of which serve as a basis for estimation of the required mesh resolution in large eddy simulations of TVC. We next perform simulations to analyse the dynamical modes of tip vortex cavity oscillation at different cavitation numbers, and compare them with the semi-analytical solution. The breathing mode of cavity surface oscillation is extracted from the spatial-temporal evolution of the cavity's effective radius. The temporally averaged effective radius demonstrates that the columnar cavity experiences a growth region followed by decay as it progresses away from the tip. Further examination of the characteristics of local breathing mode oscillations in the growth and decay regions indicates the alteration of the cavity's oscillatory behaviour as it travels from the growth region to the decay region, with the oscillations within the growth region being characterized by lower frequencies. For representative cavitation numbers $\sigma \in [1.2,2.6]$ , we find that pressure fluctuations exhibit a shift of the spectrum towards lower frequencies as the cavitation number decreases, similar to its influence on breathing mode oscillations. The results indicate the existence of correlations between the breathing mode oscillations and the pressure fluctuations. While the low-frequency pressure fluctuations are found to be correlated with the growth region, the breathing mode oscillations within the decay region are related to higher-frequency pressure fluctuations. The proposed mechanism can play an important role in developing mitigation strategies for TVC, which can reduce the underwater radiated noise by marine propellers.

Impact of ocean vertical-mixing parameterization on Arctic sea ice and upper-ocean properties using the NEMO-SI3 model

Abstract. We evaluate the vertical turbulent-kinetic-energy (TKE) mixing scheme of the NEMO-SI3 ocean–sea-ice model in sea-ice-covered regions of the Arctic Ocean. Specifically, we assess the parameters involved in TKE mixed-layer-penetration (MLP) parameterization. This ad hoc parameterization aims to capture processes that impact the ocean surface boundary layer, such as near-inertial oscillations, ocean swells, and waves, which are often not well represented in the default TKE scheme. We evaluate this parameterization for the first time in three regions of the Arctic Ocean: the Makarov, Eurasian, and Canada basins. We demonstrate the strong effect of the scaling parameter that accounts for the presence of sea ice. Our results confirm that TKE MLP must be scaled down below sea ice to avoid unrealistically deep mixed layers. The other parameters evaluated are the percentage of energy penetrating below the mixed layer and the length scale of its decay with depth. All these parameters affect mixed-layer depth and its seasonal cycle, surface temperature, and salinity, as well as underlying stratification. Shallow mixed layers are associated with stronger stratification and fresh surface anomalies, and deeper mixed layers correspond to weaker stratification and salty surface anomalies. Notably, we observe significant impacts on sea-ice thickness across the Arctic Ocean in two scenarios: when the scaling parameter due to sea ice is absent and when the TKE mixed-layer-penetration process vanishes. In the former case, we observe an increase of several meters in mixed-layer depth, along with a reduction in sea-ice thickness ranging from 30 to 40 cm, reflecting the impact of stronger mixing. Conversely, in the latter case, we notice that a shallower mixed layer is accompanied by a moderate increase in sea-ice thickness, ranging from 10 to 20 cm, as expected from weaker mixing. Additionally, interannual variability suggests that experiments incorporating a scaling parameter based on sea-ice concentration display an increased mixed-layer depth during periods of reduced sea ice, which is consistent with observed trends. These findings underscore the influence of enhanced ocean mixing, through specific parameterizations, on the physical properties of the upper ocean and sea ice.

Immersed boundary method for dynamic simulation of polarizable colloids of arbitrary shape in explicit ion electrolytes.

We develop a computational method for modeling electrostatic interactions of arbitrarily shaped, polarizable objects on colloidal length scales, including colloids/nanoparticles, polymers, and surfactants, dispersed in explicit ion electrolytes and nonionic solvents. Our method computes the nonuniform polarization charge distribution induced in a colloidal particle by both externally applied electric fields and local electric fields arising from other charged objects in the dispersion. This leads to expressions for electrostatic energies, forces, and torques that enable efficient molecular dynamics and Brownian dynamics simulations of colloidal dispersions in electrolytes, which can be harnessed to accurately predict structural and transport properties. We describe an implementation in which colloidal particles are modeled as rigid composites of small spherical beads that tessellate the surface of the particle. The electrostatics calculations are accelerated using a spectrally accurate particle-mesh-Ewald technique implemented on a graphics processing unit and regularized such that the electrostatic calculations are well-defined even for overlapping bodies. We illustrate the effectiveness of this approach with a comprehensive set of calculations: the induced dipole moments and forces for individual, paired, and lattice configurations of spherical colloids in an electric field; the induced dipole moment and torque for anisotropic particles subjected to an electric field; the equilibrium ion distribution in the double layer surrounding charged colloids; the dynamics of charged colloids; and the behavior of ions in the double layer of a polarizable colloid under the influence of an electric field.

Multi-channel machine learning based nonlocal kinetic energy density functional for semiconductors

Abstract The recently proposed machine learning-based physically-constrained nonlocal (MPN) kinetic energy density functional (KEDF) can be used for simple metals and their alloys [Phys. Rev. B 109, 115135 (2024)]. However, the MPN KEDF does not perform well for semiconductors. Here we propose a multi-channel MPN (CPN) KEDF, which extends the MPN KEDF to semiconductors by integrating information collected from multiple channels, with each channel featuring a specific length scale in real space. The CPN KEDF is systematically tested on silicon and binary semiconductors. We find that the multi-channel design for KEDF is beneficial for machine-learning-based models in capturing the characteristics of semiconductors, particularly in handling covalent bonds. In particular, the CPN5 KEDF, which utilizes five channels, demonstrates excellent accuracy across all tested systems. These results offer a new path for generating KEDFs for semiconductors.

Unlocking self-discharge: Unveiling the mysteries of electrode-free Zn-MnO2 batteries with advanced in situ techniques in mild acid aqueous electrolytes

We introduce a novel approach to Zinc-MnO2 battery architecture utilizing a 3D network of carbon nanofibers as both current collector and electrode material, promising enhanced performance and longevity for large-scale energy storage. Employing mild aqueous electrolytes, we address the challenge of managing self-discharge, crucial for short-term energy storage. Advanced coupled characterization techniques, including in-situ EQCM (Electrochemical Quartz Crystal Microbalance) and high-resolution optical microscopy, elucidate self-discharge mechanisms across over multiple length scales. Findings reveal that the self-discharge is mainly at the zinc electrode due to concomitant dissolution of Zinc (corrosion) and HER (Hydrogen Evolution Reaction) phenomena. Interestingly, the corrosion current was estimated irrespective of charging protocol and remains consistent, indicating the independence of zinc corrosion kinetics from the length scale. Finally, the morphology of the zinc layer appears to be critical, suggesting that self-discharge is primarily a chemical process. This innovative design strategy offers the potential for high-performance Zinc-MnO2 batteries with extended cycle life to meet the requirements of large-scale energy storage applications.

Hamiltonian System-Based Symplectic Framework for Analytical Vibration Analysis of Microplates

Abstract The classical elasticity is inadequate for the dynamic analysis of microplates due to the size effect. This study incorporates a higher-order strain gradient theory into the Hamiltonian system-based symplectic framework and derives new analytical solutions for the free vibration of microplates. The analytical solutions are obtained using rigorous mathematical techniques, including separation of variables, symplectic eigen expansion, and superposition, without relying on predetermined solution forms. Hence, they are not restricted to Lévy-type boundary conditions. Using these analytical solutions, we present comprehensive vibration results for microplates and perform detailed parametric studies to explore the impact of length scale parameters on the natural frequencies. Given the growing demand for microplates in advanced engineering applications, the obtained analytical solutions are expected to facilitate their design and performance optimization.

On the Scaling of Transport Phenomena at a Monotonously Changing Hydraulic Conductivity Field

Monotonously stratified porous medium, where the layered medium changes its hydraulic conductivity with depth, is present in various systems like tilled soil and peat formation. In this study, the flow pattern within a monotonously stratified porous medium is explored by deriving a non-dimensional number, Fhp, from the macroscopic Darcian-based flow equation. The derived Fhp theoretically classifies the flow equation to be hyperbolic or parabolic, according to the hydraulic head gradient length scale, and the hydraulic conductivity slope and mean. This flow classification is explored numerically, while its effect on the transport is explored by Lagrangian particle tracking (LPT). The numerical simulations show the transition from hyperbolic to parabolic flow, which manifests in the LPT transition from advective to dispersive transport. This classification is also applied to an interpolation of tilled soil from the literature, showing that, indeed, there is a transition in the transport. These results indicate that in a monotonously stratified porous medium, very low conducting (impervious) formations may still allow unexpected contamination leakage, specifically for the parabolic case. This classification of the Fhp to the flow and transport pattern provides additional insight without solving the flow or transport equation only by knowing the hydraulic conductivity distribution.

Black hole-neutron star mergers in Einstein-scalar-Gauss-Bonnet gravity

Gravitational wave observations of black hole-neutron star binaries, particularly those where the black hole has a lower mass compared to other observed systems, have the potential to place strong constraints on modifications to general relativity that arise at small curvature length scales. Here we study the dynamics of black hole-neutron star mergers in shift-symmetric Einstein-scalar-Gauss-Bonnet gravity, a representative example of such a theory, by numerically evolving the full equations of motion. We consider quasi-circular binaries with different mass-ratios that are consistent with recent gravitational wave observations, including cases with and without tidal disruption of the star, and quantify the impact of varying the coupling controlling deviations from general relativity on the gravitational wave signal and scalar radiation. We find that the main effect on the late inspiral is the accelerated frequency evolution compared to general relativity, and that—even considering Gauss-Bonnet coupling values approaching those where the theory breaks down—the impact on the merger gravitational wave signal is mild, predominately manifesting as a small change in the amplitude of the ringdown. We compare our results to current post-Newtonian calculations and find consistency throughout the inspiral. Published by the American Physical Society 2024

Scylla. II. The Spatially Resolved Star Formation History of the Large Magellanic Cloud Reveals an Inverted Radial Age Gradient

The proximity of the Magellanic Clouds provides the opportunity to study interacting dwarf galaxies near a massive host, and spatial trends in their stellar population properties in particular, with a unique level of detail. The Scylla pure parallel program has obtained deep (80% complete to >1 mag below the ancient main-sequence turnoff), homogeneous two-filter Hubble Space Telescope imaging sampling the inner star-forming disk of the Large Magellanic Cloud (LMC), the perfect complement to shallower, contiguous ground-based surveys. We harness this imaging together with extant archival data and fit lifetime star formation histories (SFHs) to resolved color–magnitude diagrams of 111 individual fields, using three different stellar evolutionary libraries. We validate per-field recovered distances and extinctions, as well as the combined global LMC age–metallicity relation and SFH against independent estimates. We find that the present-day radial age gradient reverses from an inside-out gradient in the inner disk to an outside-in gradient beyond ∼2 disk scale lengths, supported by ground-based measurements. The gradients become relatively flatter at earlier look-back times, while the location of the inversion remains constant over an order of magnitude in look-back time, from ∼1 to 10 Gyr. This suggests at least one mechanism that predates the recent intense LMC–Small Magellanic Cloud interaction. We compare observed radial age trends to other late-type galaxies at fixed stellar mass and discuss similarities and differences in the context of potential drivers, implying strong radial migration in the LMC.

Rapidly Screening the Correlation between the Rotational Mobility and the Hydrogen Bonding Strength of Confined Water.

Automated Deuterium Relaxation-Ordered SpectroscopY in solution (ADROSYS), an automated two-dimensional deuterium NMR methodology, discriminates between D2O populations (as well as deuterium-labeled alcohol groups) whose properties differ as a result of being confined inside nanoscale volumes. In this contribution, a proof-of-principle demonstration on reverse micelles (RMs) yields the insight that as the length scale of the confinement decreases from several nanometers down to less than a nanometer, the position of the signal peak migrates through the two-dimensional (2D) spectrum, tracing out a distinctive path in the 2D space (of relaxation time vs chemical shift). The signals typically follow a relatively gentle linear path for water confined on the scale of several nanometers, before curving once the surfactants confine the water molecules to length scales smaller than 1-2 nm. The qualitative shape of this path, especially in the regime of strong confinement, can change with different choices of surfactants, i.e., a different choice of chemistry at the edges of the confining environment. An important facet of this research was to demonstrate the relatively wide applicability of these techniques by showing that both: (1) Standard modern NMR instrumentation is capable of deploying an automated measurement, even though the choice of a deuterium nucleus is nonstandard and frequently requires companion proton spectra in order to reference the chemical shifts; and (2) well-established (though underutilized) modern techniques can process the resulting signal even though it involves the somewhat unusual combination of chemical shifts along one dimension and a distribution of relaxation times along another dimension. In addition to demonstrating that this technique can be deployed across many samples of interest, detailed facts pertaining to the broadening or shifting of resulting signals upon inclusion of various guest molecules are also discussed.