Regions Of High Curvature Research Articles

High-Visibility Edge-Highlighting Visualization of 3D Scanned Point Clouds Based on Dual 3D Edge Extraction

Recent advances in 3D scanning have enabled the digital recording of complex objects as large-scale point clouds, which require clear visualization to convey their 3D shapes effectively. Edge-highlighting visualization is used to improve the comprehensibility of complex 3D structures by enhancing the 3D edges and high-curvature regions of the scanned objects. However, traditional methods often struggle with real-world objects due to inadequate representation of soft edges (i.e., rounded edges) and excessive line clutter, impairing resolution and depth perception. To address these challenges, we propose a novel visualization method for 3D scanned point clouds based on dual 3D edge extraction and opacity–color gradation. Dual 3D edge extraction separately identifies sharp and soft edges, integrating both into the visualization. Opacity–color gradation enhances the clarity of fine structures within soft edges through variations in color and opacity, while also creating a halo effect that improves both resolution and depth perception of the visualized edges. Computation times required for dual 3D edge extraction are comparable to conventional binary statistical edge-extraction methods. Visualizations with opacity–color gradation are executable at interactive rendering speeds. The effectiveness of the proposed method is demonstrated using 3D scanned point cloud data from high-value cultural heritage objects.

Infrared Spectroscopy of Live Cells Using High-Aspect-Ratio Metal-on-Dielectric Metasurfaces.

Fourier transform infrared (FTIR) spectroscopy is widely used for molecular analysis. However, for the materials situated in an aqueous environment, a precondition for live biological objects such as cells, transmission-based FTIR is prevented by strong water absorption of mid-infrared (MIR) light. Reflection-based cellular assays using internal reflection elements (IREs) such as high-index prisms or flat plasmonic metasurfaces mitigate these issues but suffer from a shallow probing volume localized near the plasma membrane. Inspired by the recent introduction of high-aspect-ratio nanostructures as a novel platform for manipulating cellular behavior, we demonstrate that the integration of plasmonic metasurfaces with tall dielectric nanostructures dramatically enhances the sensing capabilities of FTIR spectroscopy. We also demonstrate the ability of a metal-on-dielectric metasurface to transduce intracellular processes, such as protein translocation to high-curvature membrane regions during cell adhesion, into interpretable spectral signatures of the reflected light.

Delayed rejection Hamiltonian Monte Carlo for sampling multiscale distributions

The efficiency of Hamiltonian Monte Carlo (HMC) can suffer when sampling a distribution with a wide range of length scales, because the small step sizes needed for stability in high-curvature regions are inefficient elsewhere. To address this we present a delayed rejection (DR) variant: if an initial HMC trajectory is rejected, we make one or more subsequent proposals each using a step size geometrically smaller than the last. To reduce the cost of DR approaches, we extend the standard delayed rejection to a probabilistic framework wherein we do not make multiple proposals at every rejection, but allow the probability of a retry to depend on the probability of accepting the previous proposal. We test the scheme in several sampling tasks, including statistical applications and multiscale model distributions such as Neal’s funnel. Delayed rejection enables sampling multiscale distributions for which standard approaches such as HMC fail to explore the tails, and improves performance five-fold over optimally-tuned HMC as measured by effective sample size per gradient evaluation. Even for simpler distributions, delayed rejection provides increased robustness to step size misspecification.

Energy-Momentum Squared Gravity: A Brief Overview

In this work, we present a review of Energy-Momentum Squared Gravity (EMSG)—more specifically, f(R,TμνTμν) gravity, where R represents the Ricci scalar and Tμν denotes the energy-momentum tensor. The inclusion of quadratic contributions from the energy-momentum components has intriguing cosmological implications, particularly during the Universe’s early epochs. These effects dominate under high-energy conditions, enabling EMSG to potentially address unresolved issues in General Relativity (GR), such as the initial singularity and aspects of big-bang nucleosynthesis in certain models. The theory’s explicit non-minimal coupling between matter and geometry leads to the non-conservation of the energy-momentum tensor, which prompts the investigation of cosmological scenarios through the framework of irreversible thermodynamics of open systems. By employing this formalism, we interpret the energy-balance equations within EMSG from a thermodynamic perspective, viewing them as descriptions of irreversible matter creation processes. Since EMSG converges to GR in a vacuum and differences emerge only in the presence of an energy-momentum distribution, these distinctions become significant in high-curvature regions. Therefore, deviations from GR are expected to be pronounced in the dense cores of compact objects. This review delves into these facets of EMSG, highlighting its potential to shed light on some of the fundamental questions in modern cosmology and gravitational theory.

Imaging Dissolution Dynamics of Individual NaCl Nanoparticles during Deliquescence with In Situ Transmission Electron Microscopy.

Water vapor condensation on hygroscopic aerosol particles plays an important role in cloud formation, climate change, secondary aerosol formation, and aerosol aging. Conventional understanding considers deliquescence of nanosized hygroscopic aerosol particles a nearly instantaneous solid to liquid phase transition. However, the nanoscale dynamics of water condensation and aerosol particle dissolution prior to and during deliquescence remain obscure due to a lack of high spatial and temporal resolution single particle measurements. Here we use real time in situ transmission electron microscopy (TEM) imaging of individual sodium chloride (NaCl) nanoparticles to demonstrate that water adsorption and aerosol particle dissolution prior to and during deliquescence is a multistep dynamic process. Water condensation and aerosol particle dissolution was investigated for lab generated NaCl aerosols and found to occur in three distinct stages as a function of increasing relative humidity (RH). First, a < 100 nm water layer adsorbed on the NaCl cubes and caused sharp corners to dissolve and truncate. The water layer grew to several hundred nanometers with increasing RH and was rapidly saturated with solute, as evidenced by halting of particle dissolution. Adjacent cube corners displayed second-scale curvature fluctuations with no net particle dissolution or water layer thickness change. We propose that droplet solute concentration fluctuations drove NaCl transport from regions of high local curvature to regions of low curvature. Finally, we observed coexistence of a liquid water droplet and aerosol particle immediately prior to deliquescence. Particles dissolved discretely along single crystallographic directions, separated by few second lag times with no dissolution. This work demonstrates that deliquescence of simple pure salt particles with sizes in the range of 100 nm to several microns is not an instantaneous phase transition and instead involves a range of complex dissolution and water condensation dynamics.

Membrane curvature sensing and symmetry breaking of the M2 proton channel from Influenza A.

The M2 proton channel aids in the exit of mature influenza viral particles from the host plasma membrane through its ability to stabilize regions of high negative Gaussian curvature (NGC) that occur at the neck of budding virions. The channels are homo-tetramers that contain a cytoplasm-facing amphipathic helix (AH) that is necessary and sufficient for NGC generation; however, constructs containing the transmembrane spanning helix, which facilitates tetramerization, exhibit enhanced curvature generation. Here, we used all-atom molecular dynamics (MD) simulations to explore the conformational dynamics of M2 channels in lipid bilayers revealing that the AH is dynamic, quickly breaking the fourfold symmetry observed in most structures. Next, we carried out MD simulations with the protein restrained in four- and twofold symmetric conformations to determine the impact on the membrane shape. While each pattern was distinct, all configurations induced pronounced curvature in the outer leaflet, while conversely, the inner leaflets showed minimal curvature and significant lipid tilt around the AHs. The MD-generated profiles at the protein-membrane interface were then extracted and used as boundary conditions in a continuum elastic membrane model to calculate the membrane-bending energy of each conformation embedded in different membrane surfaces characteristic of a budding virus. The calculations show that all three M2 conformations are stabilized in inward-budding, concave spherical caps and destabilized in outward-budding, convex spherical caps, the latter reminiscent of a budding virus. One of the C2-broken symmetry conformations is stabilized by 4 kT in NGC surfaces with the minimum energy conformation occurring at a curvature corresponding to 33 nm radii. In total, our work provides atomistic insight into the curvature sensing capabilities of M2 channels and how enrichment in the nascent viral particle depends on protein shape and membrane geometry.

Contact-force-based closed-loop control of shell structure additive manufacturing with continuous-fiber-reinforced polymer composites

Additive manufacturing (AM) is an automated process for fabricating complex structures, especially for continuous fiber-reinforced polymer (CFRP) composites with exceptional mechanical performance and reduced weight. The extrusion-based CFRP-AM process has been widely adopted but faces challenges with insufficient impregnation/adhesion and lack of geometrical accuracy. Existing research efforts exploit various mechatronics approaches and printing parameter adjustment techniques to enhance CFRP quality. Nevertheless, most of them are static or slow-varying; thus, they cannot dynamically adjust to local geometrical features and faults, which are particularly representative of the CFRP-AM process in high-curvature regions. To enable dynamic and rapid adjustment, this study exploits contact forces as major real-time feedback signals to dynamically control the feed velocity, layer height, and fiber extrusion rate. To create a continuous feedback control environment for dynamic adjustment, the study also proposes a novel helical CFRP-AM printing trajectory generation method for closed shell structures, such that the helical angles indirectly adjust the layer height of the parts. A material extrusion CFRP-AM platform combining a co-extrusion nozzle, an industrial robot, a six-degree-of-freedom load cell, and a real-time closed-loop control system is built to verify the proposed control framework. Three representative case studies are introduced to show the enhancements of the closed-loop CFRP-AM process, particularly in layer height adjustment, high-speed printing, and large curvature regions.

Hemodynamic Characteristics of a Tortuous Microvessel Using High-Fidelity Red Blood Cell Resolved Simulations.

Tortuous microvessels are characteristic of microvascular remodeling associated with numerous physiological and pathological scenarios. Three-dimensional (3D) hemodynamics in tortuous microvessels influenced by red blood cells (RBCs), however, are largely unknown, and important questions remain. Is blood viscosity influenced by vessel tortuosity? How do RBC dynamics affect wall shear stress (WSS) patterns and the near-wall cell-free layer (CFL) over a range of conditions? The objective of this work was to parameterize hemodynamic characteristics unique to a tortuous microvessel. RBC-resolved simulations were performed using an immersed boundary method-based 3D fluid dynamics solver. A representative tortuous microvessel was selected from a stimulated angiogenic network obtained from imaging of the rat mesentery and digitally reconstructed for the simulations. The representative microvessel was a venule with a diameter of approximately 20 μm. The model assumes a constant diameter along the vessel length and does not consider variations due to endothelial cell shapes or the endothelial surface layer. Microvessel tortuosity was observed to increase blood apparent viscosity compared to a straight tube by up to 26%. WSS spatial variations in high curvature regions reached 23.6 dyne/cm2 over the vessel cross-section. The magnitudes of WSS and CFL thickness variations due to tortuosity were strongly influenced by shear rate and negligibly influenced by tube hematocrit levels. New findings from this work reveal unique tortuosity-dependent hemodynamic characteristics over a range of conditions. The results provide new thought-provoking information to better understand the contribution of tortuous vessels in physiological and pathological processes and help improve reduced-order models.

Fringe-based depth segmentation via minimum-fringe-period-based singular points extraction

In the field of machine vision, depth segmentation plays a crucial role in dividing targets into different regions based on abrupt changes in depth. Phase-shifting depth segmentation is a technique that extracts singular points to form segmentation lines by leveraging the phase-shifting invariance of singular points in different wrapped phase maps. This makes it immune to color, texture, and camera exposure. However, current phase-shifting depth segmentation techniques face challenges in the precision of segmentation. To overcome this issue, this paper proposes a singular points extraction technique by constructing a more comprehensive threshold with the help of the minimum period of the phase map. Taking full advantage of the proposed technique, mean-value points and order singular points are accurately filtered out, and the integrity of segmentation lines in high-curvature regions can be guaranteed. During optimization processing, the precision of segmentation is improved by employing a low-cost morphology-based optimization model. Simulation results demonstrate the segmentation accuracy reaches up to 98.58% even in a noisy condition. Experimental results on different objects indicate that the proposed method exhibits good generalization and robustness.

DCES-PA: Deformation-controllable elastic shape model for 3D bone proliferation analysis using hand HR-pQCT images

Bone proliferation is an important pathological feature of inflammatory rheumatic diseases. Although recent advance in high-resolution peripheral quantitative computed tomography (HR-pQCT) enables physicians to study microarchitectures, physicians’ annotation of proliferation suffers from slice inconsistency and subjective variations. Also, there are only few effective automatic or semi-automatic tools for proliferation detection. In this study, by integrating pathological knowledge of proliferation formation with the advancement of statistical shape analysis theory, we present an unsupervised method, named Deformation-Controllable Elastic Shape model, for 3D bone Proliferation Analysis (DCES-PA). Unlike previous shape analysis methods that directly regularize the smoothness of the displacement field, DCES-PA regularizes the first and second-order derivative of the displacement field and decomposes these vector fields according to different deformations. For the first-order elastic metric, DCES-PA orthogonally decomposes the first-order derivative of the displacement field by shearing, scaling and bending deformation, and then penalize deformations triggering proliferation formation. For the second-order elastic metric, DCES-PA encodes both intrinsic and extrinsic surface curvatures into the second-order derivative of the displacement field to control the generation of high-curvature regions. By integrating the elastic shape metric with the varifold distances, DCES-PA achieves correspondence-free shape analysis. Extensive experiments on both simulated and real clinical datasets demonstrate that DCES-PA not only shows an improved accuracy than other state-of-the-art shape-based methods applied to proliferation analysis but also produces highly sensitive proliferation annotations to assist physicians in proliferation analysis.

Smooth extensions of black holes in loop quantum gravity

Vacuum spherically symmetric loop quantum gravity in the midi-superspace approximation using inhomogeneous horizon-penetrating slices has been studied for a decade, and it has been noted that the singularity is eliminated. It is replaced by a region of high curvature and potentially large quantum fluctuations. It was recently pointed out that the effective semiclassical metric implies the existence of a shell of matter which violates energy conditions in regions where the curvature is largest. Here, we propose an alternative way of treating the problem that is free from the shells. The ambiguity in the treatment is related with the existence of new observables in the quantum theory that characterize the area excitations, and how the counterpart of diffeomorphisms in the discrete quantum theory is mapped to the continuum semiclassical picture. The resulting spacetime in the high curvature region inside the horizon is approximated by a metric of the type of the Simpson–Visser wormhole and it connects the black hole interior to a white hole in a smooth manner.

Automated deviation-aware landmark selection for freeform product accuracy qualification in 3D printing

Landmarks are essential in non-rigid shape registration for identifying the correspondence between designs and actual products. In 3D printing, manual selection of landmarks becomes labor-intensive, due to complex product geometries and their non-uniform shape deviations. Automatic selection, however, has to pinpoint landmarks indicative of geometric regions prone to deviations for accuracy qualification. Existing automatic landmarking methods often generate clustered and redundant landmarks for prominent features with high curvatures, compromising the balance between global and local registration errors. To address these issues, we propose an automatic landmark selection method through deviation-aware segmentation and landmarking. As opposed to segmentation for semantic feature identification, deviation-aware segmentation partitions a freeform product for high-curvature region identification. Prone to deviation, these regions are generated through curvature-sensitive remeshing to extract vertices of high curvature and automatic clustering of vertices based on vertex density. Within each segment or high-curvature region, a curvature-weighted function is tailored for the Gaussian process landmarking to sequentially select landmarks with the highest local curvatures. Furthermore, we propose a new evaluation criterion to assess the effectiveness of selected landmarks through registration. The proposed approach is tested through automatic landmarking of printed dental models.

Engineering phase and density of Bose–Einstein condensates in curved waveguides with toroidal topology

We investigate the effects of ellipticity-induced curvature on atomic Bose–Einstein condensates confined in quasi-one-dimensional closed-loop waveguides. Our theoretical study reveals intriguing phenomena arising from the interplay between curvature and interactions. Density modulations are observed in regions of high curvature, but these modulations are suppressed by strong repulsive interactions. Additionally, we observe phase accumulation in regions with the lowest curvature when the waveguide with superflow has high eccentricity. Furthermore, waveguides hosting vortices exhibit dynamic transformations between states with different angular momenta. These findings provide insights into the behavior of atomic condensates in curved waveguides, with implications for fundamental physics and quantum technologies. The interplay between curvature and interactions offers opportunities for exploring novel quantum phenomena and engineering quantum states in confined geometries.

The Ricci flow and the early universe

A framework of quantum spacetime reference frame is proposed and reviewed, in which the quantum spacetime at the Gaussian approximation is deformed by the Ricci flow. At sufficient large scale, the Ricci flow not only smooths out local small irregularities making the universe a homogeneous and isotropic Friedmann–Robertson–Walker metric, but also develops a local singularity at the physical-time origin. Due to the phenomenological suppression of the non-Gaussian primordial perturbations, we assume the validity of the Ricci flow applying to the high curvature region near the local singularity of the early universe. The no-local-collapsing theorem of Perelman ensures the existence of a canonical neighborhood around the large curvature pinching point, which resembles a gradient shrinking Ricci soliton (GSRS) solution of the Ricci flow. Without any inflaton field, the GSRS naturally reproduces an exact inflationary deSitter universe near the singularity at the leading order. Without any rolling-down behavior of inflaton, the deviation from exact deSitter described by the “slow roll parameters” can be calculated by a small deviation from the singular flow-time via the Ricci flow, and the primordial perturbations can also be studied on the GSRS background, the power spectrum of the scalar perturbation agrees with present observations, and the one of the tensor perturbation is predicted too small to be detectable than the standard inflation. The previous treatment of the cosmological constant and the effective gravity are also briefly reviewed in the framework. So we argue that the Ricci flow provides us a possible unified view and treatment of the late epoch accelerating expansion and early epoch inflation of the universe without introducing dark energy or inflaton (dark energy of the second kind).

Geometrical control of interface patterning underlies active matter invasion

Interaction between active materials and the boundaries of geometrical confinement is key to many emergent phenomena in active systems. For living active matter consisting of animal cells or motile bacteria, the confinement boundary is often a deformable interface, and it has been unclear how activity-induced interface dynamics might lead to morphogenesis and pattern formation. Here, we studied the evolution of bacterial active matter confined by a deformable boundary. We found that an ordered morphological pattern emerged at the interface characterized by periodically spaced interfacial protrusions; behind the interfacial protrusions, bacterial swimmers self-organized into multicellular clusters displaying +1/2 nematic defects. Subsequently, a hierarchical sequence of transitions from interfacial protrusions to creeping branches allowed the bacterial active drop to rapidly invade surrounding space with a striking self-similar branch pattern. We found that this interface patterning is geometrically controlled by the local curvature of the interface, a phenomenon we denote as collective curvature sensing. Using a continuum active model, we revealed that the collective curvature sensing arises from enhanced active stresses near high-curvature regions, with the active length scale setting the characteristic distance between the interfacial protrusions. Our findings reveal a protrusion-to-branch transition as a unique mode of active matter invasion and suggest a strategy to engineer pattern formation of active materials.

Imaging of the internal structure of an asteroid analogue from quasi-monostatic microwave measurement data

Context.The internal structures of small solar system bodies (SSSBs) are still poorly understood. In this paper, we find an experimental tomographic reconstruction of coarse high-contrast details inside a complex-structured target object using multipoint full-wave radar data.Aims.Our aim is to advance the development of inversion techniques to be used in potential planetary scientific radar investigations targeting SSSBs, which have complex shapes and whose internal structure is largely unknown. Finding out the structure is an important scientific objective of Solar System research in order to understand its history and evolution.Methods.This is the second part (Paper II) of a joint study considering the methods to analyse and invert quasi-monostatic microwave measurement data of an asteroid analogue. We focused on incorporating advanced, full-wave, forward simulation in time domain with experimental data obtained from multiple measurement points. In particular, this study investigates multiple scattering and multipath effect suppression (MES) to reduce artefacts in the reconstructions. MES is necessary since the high-contrast and complex-shaped target and, especially, its back wall in high curvature regions cause intense reflections that deteriorate the reconstruction quality if not treated correctly. We considered the following two approaches to obtain MES: (i) geometrical optics-based pathlength thresholding and (ii) a peak detection method to investigate whether a data-driven approach could be used. At the inversion stage, we investigated marginalisation of random effects due to modelling by splitting a larger point set into several sparse sets of measurements.Results.Based on the results, MES is crucial to localise a void inside the complex analogue target. A reconstruction can be found when the maximum signal propagation time approximately matches that of the first back-wall echo for each measurement point. The marginalisation approach allows us to find a reconstruction that is comparable in quality to the case of full data, while reducing the computation effort per subsystem, which is advantageous when inverting a large data set.

Multifunctional Materials Strategies for Enhanced Safety of Wireless, Skin‐Interfaced Bioelectronic Devices

AbstractMany recently developed classes of wireless, skin‐interfaced bioelectronic devices rely on conventional thermoset silicone elastomer materials, such as poly(dimethylsiloxane) (PDMS), as soft encapsulating structures around collections of electronic components, radio frequency antennas and, commonly, rechargeable batteries. In optimized layouts and device designs, these materials provide attractive features, most prominently in their gentle, noninvasive interfaces to the skin even at regions of high curvature and large natural deformations. Past studies, however, overlook opportunities for developing variants of these materials for multimodal means to enhance the safety of the devices against failure modes that range from mechanical damage to thermal runaway. This study presents a self‐healing PDMS dynamic covalent matrix embedded with chemistries that provide thermochromism, mechanochromism, strain‐adaptive stiffening, and thermal insulation, as a collection of attributes relevant to safety. Demonstrations of this materials system and associated encapsulation strategy involve a wireless, skin‐interfaced device that captures mechanoacoustic signatures of health status. The concepts introduced here can apply immediately to many other related bioelectronic devices.

Nambu-Goto dynamics of field theory cosmic string loops

We perform a detailed comparison of the dynamics of cosmic stringloops obtained in cosmological field theory simulations with their expected motion according to theNambu-Goto action. We demonstrate that these loops follow thetrajectories predicted within the NG effective theory except in regionsof high curvature where energy is emitted from the loop in the form of massiveradiation. This energy loss continues for all the loopsstudied in this simulation until they self-intersect or become small enough that they annihilateand disappear well before they complete a single oscillation. We comment on the relevance of thisinvestigation to the interpretation of the results from cosmological field theory simulationsas well as their extrapolation to a cosmological context.

Plasmoid Instability in the Multiphase Interstellar Medium

The processes controlling the complex clump structure, phase distribution, and magnetic field geometry that develop across a broad range of scales in the turbulent interstellar medium (ISM) remain unclear. Using unprecedentedly high-resolution 3D magnetohydrodynamic simulations of thermally unstable turbulent systems, we show that large current sheets unstable to plasmoid-mediated reconnection form regularly throughout the volume. The plasmoids form in three distinct environments: (i) within cold clumps, (ii) at the asymmetric interface of the cold and warm phases, and (iii) within the warm, volume-filling phase. We then show that the complex magnetothermal phase structure is characterized by a predominantly highly magnetized cold phase, but that regions of high magnetic curvature, which are the sites of reconnection, span a broad range in temperature. Furthermore, we show that thermal instabilities change the scale-dependent anisotropy of the turbulent magnetic field, reducing the increase in eddy elongation at smaller scales. Finally, we show that most of the mass is contained in one contiguous cold structure surrounded by smaller clumps that follow a scale-free mass distribution. These clumps tend to be highly elongated and exhibit a size versus internal velocity relation consistent with supersonic turbulence and a relative clump distance–velocity scaling consistent with subsonic motion. We discuss the striking similarity of cold plasmoids to observed tiny-scale atomic and ionized structures and H i fibers and consider how the presence of plasmoids will modify the motion of charged particles, thereby impacting cosmic-ray transport and thermal conduction in the ISM and other similar systems.

The dynamics of domain wall strings

We study the dynamics of domain wall solitons in (2+1)d field theories. These objects are extended along one of the spatial directions, so they also behave as strings; hence the name of domain wall strings. We show analytically and numerically that the amount of radiation from the propagation of wiggles on these objects is negligible except for regions of high curvature. Therefore, at low curvatures, the domain wall strings behave exactly as the Nambu-Goto action predicts. We show this explicitly with the use of several different numerical experiments of the evolution of these objects in a lattice. We then explore their dynamics in the presence of internal mode excitations. We do this again by performing field theory simulations and identify an effective action that captures the relevant interactions between the different degrees of freedom living on the string. We uncover a new parametric resonance instability that transfers energy from the internal mode to the position of the domain wall. We show that this instability accelerates the radiation of the internal mode energy. We also explore the possibility of exciting the internal mode of the soliton with the collision of wiggles on the domain wall. Our numerical experiments indicate that this does not happen unless the wiggles have already a wavelength of the order of the string thickness. Finally, we comment on the possible relevance of our findings to cosmological networks of defects. We argue that our results cast some doubts on the significance of the internal modes in cosmological applications beyond a brief transient period right after their formation. This, however, should be further investigated using cosmological simulations of our model.