Short Length Scales Research Articles

Theoretical framework for the response of barotropic shelf current to along-shelf bathymetric perturbations

Abstract The mechanism underlying the response of barotropic shelf current to along-shelf bathymetric perturbations is rationalized by a one-dimensional vorticity equation. Fourier analysis of the equation in the wavenumber domain suggests that bathymetric features with relatively short length scales in the alongshore direction drive steady cross-shelf velocity undulations when the shelf circulation is against the direction of Kelvin wave propagation (upwelling regime). In contrast, much weaker and non-oscillatory cross-shelf velocity is expected when the shelf circulation is in alignment with propagating Kelvin waves (downwelling regime). The velocity undulations in the upwelling regime result from a positive feedback mechanism associated with potential vorticity (PV) advection; however, the presence of bottom friction restricts such undulations within a few wavelengths. The characteristic wavelength of undulations is determined by when the normalized drag coefficient , where u is the along-shelf mean flow speed, Hs is shelf depth, αs is the bottom slope, f is the Coriolis parameter, and r is the linear drag coefficient. Using this formula, a scale of the cross-shelf displacement distance Yt is proposed, aligning with one-layer barotropic simulations over a large parameter space. The study provides a framework for investigating barotropic cross-shelf exchange caused by shelf circulation over irregular bottom bathymetries.

Closure to the PRISM equation derived from nonlinear response theory.

Nonlinear response theory is employed to derive a closure to the polymer reference interaction site model equation. The closure applies to a liquid of neutral polymers at melt densities. It can be considered a molecular generalization of the mean spherical approximation (MSA) closure of Lebowitz and Percus to the atomic Ornstein-Zernike (OZ) equation and is similar in some aspects to the reference "molecular" MSA (R-MMSA) closure of Schweizer and Yethiraj to PRISM. For a model binary blend of freely-jointed chains, the new closure predicts an unmixing critical temperature, Tc, via the susceptibility route that scales linearly with molecular weight, N, in agreement with Flory theory. Predictions for Tc of the new closure differ greatest from those of the R-MMSA at intermediate N, the latter being about 40% higher than the former there, but at large N, both theories give about the same values. For an isotopic blend of polyethylene, the new and R-MMSA closures predict a Tc about 25% higher than the experimental value, which is only moderately less accurate than the prediction of atomic OZ-MSA theory for Tc of methane. In this way, the derivation and its consequences help to identify the ingredients in a theory needed to properly model the equilibrium properties of a polymeric liquid at both short and long lengthscales.

The tectonic development of the Central African Plateau: evidence from shear-wave splitting

SUMMARY The Central African Plateau comprises a mosaic of numerous Archean terranes—the Congo, Bangweulu and Kalahari Cratons—sutured in a series of Proterozoic to early Cambrian orogenic events. Major upper-crustal deformation and complex craton margin fault zones reflect the region’s diverse tectonic history: rifting during the Neoproterozoic, collision during the Pan-African orogeny, and more recently, Permo-Triassic Karoo rifting and the Pliocene development of the Southwestern branch of the East African Rift. The tectonic evolution and extent to which the lithospheric mantle has been re-worked by each tectonic event is poorly understood. New seismograph networks across the Plateau provide fresh opportunity to place constraints on the plate-scale Precambrian-to-Phanerozoic processes that have acted across the region. Utilizing data from seismograph deployments across the Central African Plateau, including the new Copper Basin Exploration Science network—a NW–SE-trending, 750-km-long profile of 35 broad-band stations—we explore lithospheric deformation fabrics associated with past and present tectonic events via a shear-wave splitting study of mantle seismic anisotropy. Results reveal short length-scale variations in splitting parameters (fast direction: $\phi$, delay time: $\delta$t), suggestive of a fossil lithospheric fabric cause for the observed anisotropy. A lack of fault-parallel $\phi$ across the Mwembeshi shear zone, suggests it may be too narrow at mantle depths, a thin-skinned, crustal-scale feature, and/or did not experience sufficient fault parallel shear-strain during its last active phase to form a lithospheric deformation fabric discernible via teleseismic shear-wave splitting. In the heart of the Lufilian Arc, we observe abrupt changes in splitting parameters with NE–SW, N–S and NW–SE $\phi$ and 0.5 s $< $$\delta$t$< $ 1.2 s evident at short length-scales: no single, uniform, anisotropic lattice preferred orientation (LPO) fabric defines the entire region. This is consistent with the view that multiple episodes of deformation shaped the Lufilian Arc, or perhaps that pre-existing fabrics, relating to Neoproterozoic Katangan Basin development, have failed to be completely overprinted by the Pan-African orogeny. Near the Domes, where most intense crustal re-working is thought to have taken place during the Pan-African orogeny, there is a cluster of null and low $\delta$t splits which likely reflects the lack of organized LPO fabrics, perhaps due to the presence of depth-dependent anisotropy. The neighbouring Congo Craton margin is marked by consistently weak anisotropy ($\delta$t$\lt $ 0.7 s) indicating a weak horizontal alignment of olivine at mantle lithospheric depths, typical of several Archean terranes worldwide.

Exploring intrusive processes through the crystal cargo of volcanic rocks: The case of lava flows from Taranaki volcano, New Zealand

The present-day edifice of Taranaki volcano, New Zealand, is largely made up of lava flows extruded over approximately the last 8 kyr. The crystal cargo of plagioclase, pyroxene and amphibole in these lavas displays varied major, minor, and trace element zoning patterns, pointing to long and complex crystal growth histories. Crystal zoning patterns do not vary systematically between stratigraphic units, and multiple patterns are seen within the same sample over very short length scales. Intracrystalline elemental variations reveal mineral-melt interactions, which result in repeated resorption and recrystallisation in varied environments. Variable degrees of undercooling are evidenced by clinopyroxenes, with most crystals displaying sector zoning (ΔT < 50 K), while others only show concentric zoning, which suggests very low ΔT. The common occurrence of resorbed cores within the crystals and the prevalence of glomerocrysts indicate antecrystic and/or xenocrystic origins and crystal aggregation processes. We hypothesise that the repeated intrusion of melts into the crustal basement of Taranaki volcano has resulted in the formation of a heterogeneous subsolidus plutonic to supersolidus mushy (∼15–55 vol% crystals) system that interacts with intruding melts from the mantle. These interactions result in disaggregation of crystal clots from the plutonic intrusives and remobilization of the crystals through various sub-environments of small ephemeral mush pockets. Eruption-triggering injections of melt then pick up these crystals with varied growth histories to be extruded.

Inexpensive high fidelity melt pool models in additive manufacturing using generative deep diffusion

Defects in Laser Powder Bed Fusion (L-PBF) parts often result from the meso-scale dynamics of the molten alloy near the laser, known as the melt pool. Experimental in-situ monitoring of the three-dimensional melt pool physical fields is challenging, due to the short length and time scales involved in the process. Multi-physics simulation methods can describe the three-dimensional dynamics of the melt pool, but are computationally expensive at the mesh refinement required for accurate predictions of complex effects. Therefore, we develop a generative deep learning model based on the probabilistic diffusion framework to map low-fidelity simulation information to the high-fidelity counterpart. By doing so, we bypass the computational expense of conducting multiple high-fidelity simulations for analysis by upscaling lightweight coarse mesh simulations. We demonstrate the preservation of key metrics of the melting process between the ground truth simulation data and the diffusion model output, such as the temperature field, the melt pool dimensions and the variability of the keyhole vapor cavity. We predict the melt pool depth within 3 μm based on low-fidelity input data 4× coarser than the high-fidelity simulations, reducing analysis time by two orders of magnitude.

Fundamental properties of ideal and resistive infernal modes in tokamaks

Infernal modes are unstable in regions of weak magnetic shear and significant pressure gradients. These modes comprise a broad class of instabilities, encompassing interchange modes and kink modes, with both short and long length scales. Toroidal effects and fully electromagnetic fields are of crucial importance for their description. The role of resistive diffusion and compressibility are also critical. In order to investigate this awkward problem while still enabling fundamental physics interpretation, a new resistive MHD eigensolver has been developed. An outcome of this study is the identification of an unstable spectrum of resistive infernal modes in regions of the plasma with weak average curvature, and in regions where the average curvature is destabilising. These fast growing modes may be collectively important for our understanding of global reconnection events, stochastic magnetic fields states, and neighbouring supercritical bifurcations.

Sensitivity Analysis of One-Dimensional Multiphysics Simulation of CO2 Electrolysis Cell.

Electrochemical (EC) carbon dioxide (CO2) reduction, where CO2 is converted to value-added products such as fuel precursors, plays a key role in helping the world's energy system reach net-zero carbon emissions. Simulations of EC cells provide valuable insight into their operation since detailed experimental results on short length and time scales are difficult to obtain. In this work, we construct a 1D simulation of a membrane-electrode-assembly EC cell for CO2 reduction, using a porous silver gas diffusion cathode. We run the simulation under different electrolyte conditions, showing how the cell performance is affected. We then perform a sensitivity analysis of all input parameters to the simulation, which has not been presented before in the literature. We show that the CO partial current density (i CO) is significantly affected by each input parameter of the simulation. i CO is most sensitive to EC kinetic parameters (i 0/α) of all EC reactions, with a 1% change in α resulting in up to 6% change in i CO. Since there is uncertainty associated with the value of each input parameter, this indicates that infidelity between experiment and simulation is likely, and thus, caution should be practiced when comparing experimental results to simulation results. Further, we show that the large range of conditions simulated in literature helps to explain the large variance in reported values of i 0 and α. The results of this paper demonstrate the potential of sensitivity analysis methods to quickly optimize aspects of cell performance (CO2 utilization, Faradaic efficiency, etc.).

Using PFG‐NMR and iGC to Study Diffusion and Adsorption in Heterogeneous Catalysts

AbstractMass transport in porous systems is inherently complex, but at the same also of utmost importance for large‐scale industrial processes such as heterogeneous catalysis. For each of the different length scales of diffusive motion potentially involved or relevant, specific characterization techniques have been developed and successfully applied over the years – including, but not limited to pulsed field gradient nuclear magnetic resonance (PFG‐NMR) spectroscopy, zero length column (ZLC) measurements and inverse gas chromatography (iGC). While each of these methods can deliver detailed information on certain types of diffusion, none of them are capable of delivering a full picture of mass transport across multiple length scales alone. In this context, the goal of the present work was to evaluate the technical feasibility and characterization potential of the hyphenated combination of PFG‐NMR and iGC in a coupled experimental setup. Challenges, advantages, and limitations of this approach are discussed using the example of propane adsorption and diffusion in two different zeolite catalysts (Mg(H)‐ZSM‐5 and Silicalite‐1). It is shown that the simultaneous detection of self‐diffusion on short length scales (as probed by PFG‐NMR) and transport diffusion covering longer distances (detectable by iGC) cannot be realized under the used conditions, essentially due to the lack of kinetic control at higher reactant loadings. The key advantage of the developed coupled setup is the ability of the iGC instrument to provide defined and readily variable levels of catalyst loading, which enables advanced pore connectivity studies by PFG‐NMR and yields thermodynamic data on reactant adsorption at the same time.

Approaching Maximum Resolution in Structured Illumination Microscopy via Accurate Noise Modeling.

Biological images captured by microscopes are characterized by heterogeneous signal-to-noise ratios (SNRs) due to spatially varying photon emission across the field of view convoluted with camera noise. State-of-the-art unsupervised structured illumination microscopy (SIM) reconstruction algorithms, commonly implemented in the Fourier domain, do not accurately model this noise and suffer from high-frequency artifacts, user-dependent choices of smoothness constraints making assumptions on biological features, and unphysical negative values in the recovered fluorescence intensity map. On the other hand, supervised methods rely on large datasets for training, and often require retraining for new sample structures. Consequently, achieving high contrast near the maximum theoretical resolution in an unsupervised, physically principled, manner remains an open problem. Here, we propose Bayesian-SIM (B-SIM), an unsupervised Bayesian framework to quantitatively reconstruct SIM data, rectifying these shortcomings by accurately incorporating known noise sources in the spatial domain. To accelerate the reconstruction process, we use the finite extent of the point-spread-function to devise a parallelized Monte Carlo strategy involving chunking and restitching of the inferred fluorescence intensity. We benchmark our framework on both simulated and experimental images, and demonstrate improved contrast permitting feature recovery at up to 25% shorter length scales over state-of-the-art methods at both high- and low-SNR. B-SIM enables unsupervised, quantitative, physically accurate reconstruction without the need for labeled training data, democratizing high-quality SIM reconstruction and expands the capabilities of live-cell SIM to lower SNR, potentially revealing biological features in previously inaccessible regimes.

Spatio-temporal organization of the E. coli chromosome from base to cellular length scales.

Escherichia coli has been a vital model organism for studying chromosomal structure, thanks, in part, to its small and circular genome (4.6 million base pairs) and well-characterized biochemical pathways. Over the last several decades, we have made considerable progress in understanding the intricacies of the structure and subsequent function of the E. coli nucleoid. At the smallest scale, DNA, with no physical constraints, takes on a shape reminiscent of a randomly twisted cable, forming mostly random coils but partly affected by its stiffness. This ball-of-spaghetti-like shape forms a structure several times too large to fit into the cell. Once the physiological constraints of the cell are added, the DNA takes on overtwisted (negatively supercoiled) structures, which are shaped by an intricate interplay of many proteins carrying out essential biological processes. At shorter length scales (up to about 1 kb), nucleoid-associated proteins organize and condense the chromosome by inducing loops, bends, and forming bridges. Zooming out further and including cellular processes, topological domains are formed, which are flanked by supercoiling barriers. At the megabase-scale both large, highly self-interacting regions (macrodomains) and strong contacts between distant but co-regulated genes have been observed. At the largest scale, the nucleoid forms a helical ellipsoid. In this review, we will explore the history and recent advances that pave the way for a better understanding of E. coli chromosome organization and structure, discussing the cellular processes that drive changes in DNA shape, and what contributes to compaction and formation of dynamic structures, and in turn how bacterial chromatin affects key processes such as transcription and replication.

Coordinated reset stimulation of plastic neural networks with spatially dependent synaptic connections.

Abnormal neuronal synchrony is associated with several neurological disorders, including Parkinson's disease (PD), essential tremor, dystonia, and epilepsy. Coordinated reset (CR) stimulation was developed computationally to counteract abnormal neuronal synchrony. During CR stimulation, phase-shifted stimuli are delivered to multiple stimulation sites. Computational studies in plastic neural networks reported that CR stimulation drove the networks into an attractor of a stable desynchronized state by down-regulating synaptic connections, which led to long-lasting desynchronization effects that outlasted stimulation. Later, corresponding long-lasting desynchronization and therapeutic effects were found in animal models of PD and PD patients. To date, it is unclear how spatially dependent synaptic connections, as typically observed in the brain, shape CR-induced synaptic downregulation and long-lasting effects. We performed numerical simulations of networks of leaky integrate-and-fire neurons with spike-timing-dependent plasticity and spatially dependent synaptic connections to study and further improve acute and long-term responses to CR stimulation. The characteristic length scale of synaptic connections relative to the distance between stimulation sites plays a key role in CR parameter adjustment. In networks with short synaptic length scales, a substantial synaptic downregulation can be achieved by selecting appropriate stimulus-related parameters, such as the stimulus amplitude and shape, regardless of the employed spatiotemporal pattern of stimulus deliveries. Complex stimulus shapes can induce local connectivity patterns in the vicinity of the stimulation sites. In contrast, in networks with longer synaptic length scales, the spatiotemporal sequence of stimulus deliveries is of major importance for synaptic downregulation. In particular, rapid shuffling of the stimulus sequence is advantageous for synaptic downregulation. Our results suggest that CR stimulation parameters can be adjusted to synaptic connectivity to further improve the long-lasting effects. Furthermore, shuffling of CR sequences is advantageous for long-lasting desynchronization effects. Our work provides important hypotheses on CR parameter selection for future preclinical and clinical studies.

Pattern Formation in Evaporating Polymer Solutions-Interplay between Dewetting and Decomposition.

Pattern formation during solution evaporation is common in several industrial settings and involves a complex interplay of multiple processes, including wetting/dewetting, diffusion, and rheological characteristics of the solution. Monitoring the emergence of patterns during evaporation under controlled conditions may allow deconvolution of different processes and, in turn, improve our understanding of this common yet complex phenomenon. Here, we probe the importance of initial conditions, defined by the solution concentration c 0, on the pattern formation in evaporating polymer solutions on the air-water interface. Intriguingly, the initial decrease in the lateral length scale (ξ), characterizing the patterns, takes an upturn at higher concentrations, revealing reentrant behavior. We employ a gradient dynamics model consisting of coupled evolution equations for the film height and the polymer fraction in the solution. Our simulations capture two different length scales revealing the reasons underlying the re-entrant behavior of ξ(c 0). While the long-range destabilizing interactions between suspension and water result in the dewetting of thin film solutions, the phase separation between the polymer and solvent occurs at shorter length scales. Our results demonstrate the importance of initial concentration on pattern formation and, thereby, on the resultant properties of thin polymer films.

Universal stress correlations in crystalline and amorphous packings.

We present a universal characterization of stress correlations in athermal systems, across crystalline to amorphous packings. Via numerical analysis of static configurations of particles interacting through harmonic as well as Lennard-Jones potentials, for a variety of preparation protocols and ranges of microscopic disorder, we show that the properties of the stress correlations at large lengthscales are surprisingly universal across all situations, independent of structural correlations, or the correlations in orientational order. In the near-crystalline limit, we present exact results for the stress correlations for both models, which work surprisingly well at large lengthscales, even in the amorphous phase. Finally, we study the differences in stress fluctuations across the amorphization transition, where stress correlations reveal the loss of periodicity in the structure at short lengthscales with increasing disorder.

3D Printing of Double Network Granular Elastomers with Locally Varying Mechanical Properties.

Fast advances in the design of soft actuators and robots demand for new soft materials whose mechanical properties can be changed over short length scales. Elastomers can be formulated as highly stretchable or rather stiff materials and hence, are attractive for these applications. They are most frequently cast such that their composition cannot be changed over short length scales. A method that allows to locally change the composition of elastomers on hundreds of micrometer lengths scales is direct ink writing (DIW). Unfortunately, in the absence of rheomodifiers, most elastomer precursors cannot be printed through DIW. Here, 3D printable double network granular elastomers (DNGEs) whose ultimate tensile strain and stiffness can be varied over an unprecedented range are introduced. The 3D printability of these materials is leveraged to produce an elastomer finger containing rigid bones that are surrounded by a soft skin. Similarly, the rheological properties of the microparticle-based precursors are leveraged to cast elastomer slabs with locally varying stiffnesses that deform and twist in a predefined fashion. These DNGEs are foreseen to open up new avenues in the design of the next generation of smart wearables, strain sensors, prosthesis, soft actuators, and robots.

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Garnet zoning patterns record multiple processes of chemical transfer during subduction

Subduction is the principal mechanism by which volatiles are transferred from the Earth's surface to its interior. In garnets from eclogites and blueschists formed within the subduction setting, fine-scale, oscillatory elemental zoning is a common feature, sometimes considered to record open-system fluid exchange during prograde metamorphism. We present oxygen isotope data for garnets with such zoning from five exhumed subduction zone complexes. Short length scale fluctuations in elemental and oxygen isotope zoning (which are themselves spatially decoupled) cannot be linked to open-system fluid exchange during garnet crystallization in all samples; these data do not provide evidence for a genetic relationship between elemental oscillations and fluid fluxing. However, garnets from one setting do provide clear evidence for syn-growth ingress of elementally and isotopically buffering fluids, a process that operated simultaneously with the formation of elemental oscillations. Our findings indicate multiple mechanisms of chemical transfer operate at the grain–rock scale during subduction, and that some subduction zone rocks may experience only limited interaction with external prograde fluids. These results are consistent with a picture of highly heterogenous volatile transfer during subduction, and suggest that some proportion of the fluid inventory inherited at shallow depths may be transferred to sub-arc depths.

Evidence for widespread cytoplasmic structuring into mesoscale condensates.

Compartmentalization is an essential feature of eukaryotic life and is achieved both via membrane-bound organelles, such as mitochondria, and membrane-less biomolecular condensates, such as the nucleolus. Known biomolecular condensates typically exhibit liquid-like properties and are visualized by microscopy on the scale of ~1 µm (refs. 1,2). They have been studied mostly by microscopy, examining select individual proteins. So far, several dozen biomolecular condensates are known, serving a multitude of functions, for example, in the regulation of transcription3, RNA processing4 or signalling5,6, and their malfunction can cause diseases7,8. However, it remains unclear to what extent biomolecular condensates are utilized in cellular organization and at what length scale they typically form. Here we examine native cytoplasm from Xenopus egg extract on a global scale with quantitative proteomics, filtration, size exclusion and dilution experiments. These assays reveal that at least 18% of the proteome is organized into mesoscale biomolecular condensates at the scale of ~100 nm and appear to be stabilized by RNA or gelation. We confirmed mesoscale sizes via imaging below the diffraction limit by investigating protein permeation into porous substrates with defined pore sizes. Our results show that eukaryotic cytoplasm organizes extensively via biomolecular condensates, but at surprisingly short length scales.

Efficient Magnetic Vortex Acceleration by femtosecond laser interaction with long living optically shaped gas targets in the near critical density plasma regime

We introduce a novel, gaseous target optical shaping laser set-up, capable to generate short scale length, near-critical target profiles via generated colliding blast waves. These profiles are capable to maintain their compressed density for several nanoseconds, being therefore ideal for laser-plasma particle acceleration experiments in the near critical density plasma regime. Our proposed method overcomes the laser-target synchronization limitations and delivers energetic protons, during the temporal evolution of the optically shaped profile, in a time window of approximately 2.5 ns. The optical shaping of the gas-jet profiles is optimised by MagnetoHydroDynamic simulations. 3D Particle-In-Cell models, adopting the spatiotemporal profile, simulate the 45 TW femtosecond laser plasma interaction to demonstrate the feasibility of the proposed proton acceleration set-up. The optical shaping of gas-jets is performed by multiple, nanosecond laser pulse generated blastwaves. This process results in steep gradient, short scale length plasma profiles, in the near critical density regime allowing operation at high repetition rates. Notably, the Magnetic Vortex Acceleration mechanism exhibits high efficiency in coupling the laser energy into the plasma in the optically shaped targets, resulting to collimated proton beams of energies up to 14 MeV.

In Situ X-ray Scattering Reveals Coarsening Rates of Superlattices Self-Assembled from Electrostatically Stabilized Metal Nanocrystals Depend Nonmonotonically on Driving Force.

Self-assembly of colloidal nanocrystals (NCs) into superlattices (SLs) is an appealing strategy to design hierarchically organized materials with promising functionalities. Mechanistic studies are still needed to uncover the design principles for SL self-assembly, but such studies have been difficult to perform due to the fast time and short length scales of NC systems. To address this challenge, we developed an apparatus to directly measure the evolving phases in situ and in real time of an electrostatically stabilized Au NC solution before, during, and after it is quenched to form SLs using small-angle X-ray scattering. By developing a quantitative model, we fit the time-dependent scattering patterns to obtain the phase diagram of the system and the kinetics of the colloidal and SL phases as a function of varying quench conditions. The extracted phase diagram is consistent with particles whose interactions are short in range relative to their diameter. We find the degree of SL order is primarily determined by fast (subsecond) initial nucleation and growth kinetics, while coarsening at later times depends nonmonotonically on the driving force for self-assembly. We validate these results by direct comparison with simulations and use them to suggest dynamic design principles to optimize the crystallinity within a finite time window. The combination of this measurement methodology, quantitative analysis, and simulation should be generalizable to elucidate and better control the microscopic self-assembly pathways of a wide range of bottom-up assembled systems and architectures.

Proton Diffusion in Liquid 1,2,3-Triazole Studied by Incoherent Quasi-Elastic Neutron Scattering.

Improving the proton transport in polymer electrolytes impacts the performance of next-generation solid-state batteries. However, little is known about proton conductivity in nonaqueous systems due to the lack of an appropriate level of fundamental understanding. Here, we studied the proton transport in small molecules with dynamic hydrogen bonding, 1,2,3-triazole, as a model system of proton hopping in a nonaqueous environment using incoherent quasi-elastic neutron scattering. By using the jump-diffusion model, we identified the elementary jump-diffusion motion of protons at a much shorter length scale than those by nuclear magnetic resonance and impedance spectroscopy for the estimated long-range diffusion. In addition, a spatially restricted diffusive motion was observed, indicating that proton motion in 1,2,3-triazole is complex with various local correlated dynamics. These correlated dynamics will be important in elucidating the nature of the proton dynamics in nonaqueous systems.