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We study the accuracy of excited state (ES) geometries using optimally tuned LC-PBE functionals with tuning based on GW quasiparticle energies. We compare the results obtained with the PBE, PBE0, non-tuned, and tuned LC-PBE functionals with available high-level CC reference values as well as experimental data. First, we compare ES geometrical parameters obtained for three different types of systems: molecules composed of a few atoms, 4-(dimethylamino)benzonitrile (DMABN), and conjugated dyes. To this end, we used wave-function results as benchmarks. Next, we evaluate the accuracy of the theoretically simulated spectra as compared to the experimental ones for five large dyes. Our results show that, besides small compact molecules for which tuning LC-PBE does not allow obtaining geometries more accurate than those computed with standard functionals, tuned range-separated functionals are clearly to be favored, not only for ES geometries but also for 0–0 energies, band shapes, and intensities for absorption and emission spectra. In particular, the results indicate that GW-tuned LC-PBE functionals provide improved matching with experimental spectra as compared to conventionally tuned functionals. It is an open question whether TD-DFT with GW-tuned functionals can qualitatively mimic the actual many-body Bethe–Salpeter (BSE/GW) formalism for which analytic ionic gradients remain to be developed. [ABSTRACT FROM AUTHOR]

31P nuclear magnetic resonance (NMR) chemical shifts were shown to be very sensitive to the basis set used at the geometry optimization stage. Commonly used energy-optimized basis sets for a phosphorus atom containing only one polarization d-function were shown to be unable to provide correct equilibrium geometries for the calculations of phosphorus chemical shifts. The use of basis sets with at least two polarization d-functions on a phosphorus atom is strongly recommended. In this paper, an idea of creating the basis sets purposed for the geometry optimization that provide the least possible error coming from the geometry factor of accuracy in the resultant NMR shielding constants is proposed. The property-energy consisted algorithm with the target function in the form of the molecular energy gradient relative to P–P bond lengths was applied to create new geometry-oriented pecG-n (n = 1, 2) basis sets for a phosphorus atom. New basis sets have demonstrated by far superior performance as compared to the other commonly used energy-optimized basis sets in massive calculations of 31P NMR chemical shifts carried out at the gauge-including atomic orbital-coupled cluster singles and doubles/pecS-2 level of the theory by taking into account solvent, vibrational, and relativistic corrections. [ABSTRACT FROM AUTHOR]

Exploring the structures and spectral features of proteins with advanced quantum chemical methods is an uphill task. In this work, a fragment-based molecular tailoring approach (MTA) is appraised for the CAM-B3LYP/aug-cc-pVDZ-level geometry optimization and vibrational infrared (IR) spectra calculation of ten real proteins containing up to 407 atoms and 6617 basis functions. The use of MTA and the inherently parallel nature of the fragment calculations enables a rapid and accurate calculation of the IR spectrum. The applicability of MTA to optimize the protein geometry and evaluate its IR spectrum employing a polarizable continuum model with water as a solvent is also showcased. The typical errors in the total energy and IR frequencies computed by MTA vis-à-vis their full calculation (FC) counterparts for the studied protein are 5–10 millihartrees and 5 cm−1, respectively. Moreover, due to the independent execution of the fragments, large-scale parallelization can also be achieved. With increasing size and level of theory, MTA shows an appreciable advantage in computer time as well as memory and disk space requirement over the corresponding FCs. The present study suggests that the geometry optimization and IR computations on the biomolecules containing ∼1000 atoms and/or ∼15 000 basis functions using MTA and HPC facility can be clearly envisioned in the near future. [ABSTRACT FROM AUTHOR]

AgPd nanoalloys often undergo structural evolution during catalytic reactions; the mechanism underlying such restructuring remains largely unknown due to the use of oversimplified interatomic potentials in simulations. Herein, a deep-learning potential is developed for AgPd nanoalloys based on a multiscale dataset spanning from nanoclusters to bulk configurations, exhibits precise predictions of mechanical properties and formation energies with near-density functional theory accuracy, calculates the surface energies closer to experimental values compared to those obtained by Gupta potentials, and is applied to investigate the shape reconstruction of single-crystalline AgPd nanoalloys from cuboctahedron (Oh) to icosahedron (Ih) geometries. The Oh to Ih shape restructuring is thermodynamically favorable and occurs at 11 and 92 ps for Pd55@Ag254 and Ag147@Pd162 nanoalloys, respectively. During the shape reconstruction of Pd@Ag nanoalloys, concurrent surface restructuring of the (100) facet and internal multi-twinned phase change are observed with collaborative displacive characters. The presence of vacancies can influence the final product and reconstructing rate of Pd@Ag core–shell nanoalloys. The Ag outward diffusion on Ag@Pd nanoalloys is more pronounced in Ih geometry compared to Oh geometry and can be further accelerated by the Oh to Ih deformation. The deformation of single-crystalline Pd@Ag nanoalloys is characterized by a displacive transformation involving the collaborative displacement of a large number of atoms, distinguishing it from the diffusion-coupled transformation of Ag@Pd nanoalloys. [ABSTRACT FROM AUTHOR]

Slab expansion (SLABEX) tests are conducted to validate a process for calibrating the detonation products equation of state (EOS) of a high explosive (HE). The SLABEX tests use rectangular slabs of PBX 9502, a polymer-bonded HE formulation consisting of 95 wt.% 1,3,5-triamino-2,4,6-trinitrobenzene bound with Kel F-800, a co-polymer of chlorotrifluoroethylene and vinylidene-fluoride. Three PBX 9502 slab thicknesses are examined, each confined symmetrically by two rectangular copper (Cu) plates approximately one-tenth the thickness of the HE slab. For the duration of each experiment, the detonation flow along the central axis of the PBX 9502 slab remains two-dimensional. The lateral flow velocity component of the outer surfaces of the expanding Cu plates is measured, along with the steady axial detonation speed along the central axis of the SLABEX. Hydrodynamic simulations of the Cu plate expansion in the SLABEX geometry, driven by the energy stored in the detonation products by the detonation combustion event, are conducted using a Jones–Wilkins–Lee EOS for the detonation products. This EOS form was recently parameterized for PBX 9502 in the cylinder expansion test geometry using a newly developed calibration technique [Voelkel et al., Combust. Flame 246, 112373 (2022)]. Good agreement between the experiment and prediction is found in each SLABEX test, demonstrating that the detonation product EOS calibration technique produces EOSs that are predictive when applied to other geometries. [ABSTRACT FROM AUTHOR]

In this work, we propose a theoretical finite element description of the ionic profiles of a general mixture of n species of spherical charged particles dissolved in an implicit solvent, with arbitrary size and charge asymmetries, neutralizing a spherical macroion. This approach aims to close the gap between the nano- and the micro-scales in macroion solutions, taking into account the ion correlations and ionic excluded volume effects consistently. When these last two features are neglected, the classical non-linear Poisson–Boltzmann theory for n ionic species—with different ionic closest approach distances to the colloidal surface—is recovered as a limit case. As a proof of concept, we study the electrical double layer of an electroneutral mixture of oppositely charged colloids and small microions, with an asymmetry 1:333 in size and 1:10 in valence, in salt-free and added salt environments. Our theoretical approach displays a good agreement regarding the ionic profiles, the integrated charge, and the mean electrostatic potential obtained from molecular dynamics simulations with explicit-sized microions. Although the non-linear Poisson–Boltzmann colloid–colloid and colloid–microion profiles differ notably from those obtained via molecular dynamics simulations with explicit small-sized ions, the associated mean electrostatic potential agrees well with the corresponding explicit microion simulations. [ABSTRACT FROM AUTHOR]

Thermal metamaterials have garnered significant attention for their potential to manipulate heat flow, leading to the development of various thermal metadevices such as thermal cloaks, concentrators, and rotators. However, the theoretical study of thermal metadevices with nonconformal geometry remains limited due to design and fabrication challenges. This letter proposes a method for designing and manufacturing nonconformal thermal metamaterials using the conformal discrete theory to simplify the anisotropic thermal conductivity tensors. The method involves 3D printing three thermal metadevices (a thermal cloak, concentrator, and rotator) with complex nonconformal geometry. Simulation and experimental results demonstrate the successful implementation of cloaking, concentrating, and rotating functionalities. Moreover, the thermal metadevices still maintained thermal functionality well under the condition of omnidirectional heat flow. This work provides guidance for the design and manufacture of nonconformal thermal metamaterials, as well as their potential applications in other fields such as electrics/magnetics, electromagnetics/optics, and acoustics. [ABSTRACT FROM AUTHOR]

We present efficient analytical gradients of property-based diabatic states and couplings using a Lagrangian formalism. Unlike previous formulations, the method achieves a computational scaling that is independent of the number of adiabatic states used to construct the diabats. The approach is generalizable to other property-based diabatization schemes and electronic structure methods as long as analytical energy gradients are available and integral derivatives with the property operator can be formed. We also introduce a scheme to phase and reorder diabats to ensure their continuity between molecular configurations. We demonstrate this for the specific case of Boys diabatic states obtained from state-averaged complete active space self-consistent field electronic structure calculations with GPU acceleration in the TeraChem package. The method is used to test the Condon approximation for the hole transfer in an explicitly solvated model DNA oligomer. [ABSTRACT FROM AUTHOR]

Self-assembly of chiral particles with an L-shape is explored by Monte-Carlo computer simulations in two spatial dimensions. For sufficiently high packing densities in confinement, a carpet-like texture emerges due to the interlocking of L-shaped particles, resembling a distorted smectic liquid crystalline layer pattern. From the positions of either of the two axes of the particles, two different types of layers can be extracted, which form distinct but complementary entangled networks. These coarse-grained network structures are then analyzed from a topological point of view. We propose a global charge conservation law by using an analogy to uniaxial smectics and show that the individual network topology can be steered by both confinement and particle geometry. Our topological analysis provides a general classification framework for applications to other intertwined dual networks. [ABSTRACT FROM AUTHOR]

We develop a linearly scaling variant of the force coupling method [K. Yeo and M. R. Maxey, J. Fluid Mech. 649, 205–231 (2010)] for computing hydrodynamic interactions among particles confined to a doubly periodic geometry with either a single bottom wall or two walls (slit channel) in the aperiodic direction. Our spectrally accurate Stokes solver uses the fast Fourier transform in the periodic xy plane and Chebyshev polynomials in the aperiodic z direction normal to the wall(s). We decompose the problem into two problems. The first is a doubly periodic subproblem in the presence of particles (source terms) with free-space boundary conditions in the z direction, which we solve by borrowing ideas from a recent method for rapid evaluation of electrostatic interactions in doubly periodic geometries [Maxian et al., J. Chem. Phys. 154, 204107 (2021)]. The second is a correction subproblem to impose the boundary conditions on the wall(s). Instead of the traditional Gaussian kernel, we use the exponential of a semicircle kernel to model the source terms (body force) due to the presence of particles and provide optimum values for the kernel parameters that ensure a given hydrodynamic radius with at least two digits of accuracy and rotational and translational invariance. The computation time of our solver, which is implemented in graphical processing units, scales linearly with the number of particles, and allows computations with about a million particles in less than a second for a sedimented layer of colloidal microrollers. We find that in a slit channel, a driven dense suspension of microrollers maintains the same two-layer structure as above a single wall, but moves at a substantially lower collective speed due to increased confinement. [ABSTRACT FROM AUTHOR]

Studies to increase the joint strength of adhesively bonded joints used in the aerospace and automotive sectors are met with interest in the field of engineering. Many different methods are used to increase the strength of the bonded joint, and one of these methods is to change the joint geometry. This study aims to increase the joint strength by changing the geometry of the joint with the same adhesive area condition. In the study, the DP460 structural adhesive was used as the adhesive, the AA2024-T3 aluminum alloy was used as the adherend, and the One Step-Lap Joint (OSLJ), Double-Strap Joint (DSJ), and Stepped Double-Strap Joint (SDSJ) was used as the joint types. The joint strengths of the joints obtained by using different step lengths and different patch lengths for these three types of joints with the same adhesive area were investigated experimentally and numerically. Firstly, the strengths of the SLJ type obtained by using four different step lengths and the DSJ type obtained by using patches of four different lengths were investigated. In the light of these investigations, the mechanical properties of the joints obtained by changing the step length and patch length in the SDSJ type, a new joint type with the same adhesive area, were obtained. As a result, compared to the OSLJ type with the same adhesive area, the joint strength of the DSJ type increases by approximately 45% to 67%. In addition, while the strength of the new type of joint (SDSJ) obtained in the presented study increases between 7% and 35% according to the DSJ type, it increases between 56% and 126% according to the OSLJ type. These increases in the joint strength vary according to the bonding area. Additionally, in the presented study, experimental data were compared with numerical analysis, and it was observed that the data were quite consistent with each other. [ABSTRACT FROM AUTHOR]

We analyse 13 yr of Fermi Large Area Telescope Pass 8 events from 127 gamma-ray emitting millisecond pulsars (MSPs) in the energy range 0.1–100 GeV and significantly detect 118 MSPs. We fit the stacked emission with a log parabola (LP) spectral model that we show is preferred to two previously published models. We consider the influence of pulsar properties and observed geometric effects on spectral features by defining energy flux colours for both the individual MSPs, and our stacked model as a baseline. There is no correlation of colours with pulsar luminosity, |$\dot{E}$|⁠ , surface magnetic field, or magnetic impact angle. We also find that pulsar geometry has little effect on the observed gamma-ray spectrum, which is in tension with previous modelling of gamma-ray emission with respect to pulsar geometry. Our LP MSP model is applicable to problems where an ensemble of gamma-ray MSPs is considered, such as that of the Galactic Centre excess or in the case of emission from globular clusters. [ABSTRACT FROM AUTHOR]

In this paper, we study, for functionals having a minimax geometry on a constraint, the existence of bounded Palais-Smale sequences carrying Morse index type information. [ABSTRACT FROM AUTHOR]

The maximum function, on vectors of real numbers, is not differentiable. Consequently, several differentiable approximations of this function are popular substitutes. We survey three smooth functions which approximate the maximum function and analyze their convergence rates. We interpret these functions through the lens of tropical geometry, where their performance differences are geometrically salient. As an application, we provide an algorithm which computes the max-convolution of two integer vectors in quasi-linear time. We show this algorithm's power in computing adjacent sums within a vector as well as computing service curves in a network analysis application. [ABSTRACT FROM AUTHOR]

Polycrystalline diamond compacts (PDC) with three different substrate geometries and trimodal diamond particle formulation were fabricated. The properties of prepared PDC including Vickers hardness, toughness, wear performance, and thermal stability were evaluated. The microscopic features including morphology, elemental and phase composition, and residual stress state were systematically investigated. The optimal substrate contributing to best comprehensive properties of PDC was singled out. Discrepancies in the properties of PDCs with different substrate geometries were mainly in fracture toughness and impact toughness, with maximum and minimum values of 6.54 MPa m1/2/3120 J and 5 MPa m1/2/1680 J, respectively. The best wear performance was 5.88 mm2/60P. The results showed that the tendency of wear performance was consistent with toughness and thermal stability, showing a strong correlation. The substrate geometry affected the morphology and composition of the cobalt transition layer in the interface, which had a significant impact on its toughness. Differences in residual stress states induced by the interfacial geometries were also important determining PDC's impact toughness. [ABSTRACT FROM AUTHOR]

Let r and s be positive integers such that r ⩾ 2. Let U and V be vector spaces over fields F and K , respectively, such that dim ⁡ U ⩾ 3 and F has at least r + 1 elements. In this paper, we characterize surjective maps ψ : S r U → S s V preserving adjacency in both directions on symmetric tensors of finite order, which generalizes Hua's fundamental theorem of geometry of symmetric matrices. We give examples showing the indispensability of the assumptions dim ⁡ U ⩾ 3 and the cardinality | F | ⩾ r + 1 in our result. [ABSTRACT FROM AUTHOR]

The proper scheduling of track maintenance and renewal operations is dependent on the accuracy of predictive maintenance outputs which, in turn, rely on the appropriate modelling of the track geometry degradation process. This paper explores the incidence and representativeness of the alerts generated due to local defects of track geometry and the modelling of their degradation rates between consecutive tamping operations. A software tool was developed and used to process track inspection data collected over 12 years of operation of the main Portuguese line (Lisbon-Porto) on a total of 727 km of single-track lines where speeds vary between 30 and 220 km/h. Linear regressions are found to be suitable to model the degradation rates of local defects of longitudinal levelling, alignment and twist in the vast majority of cases, although 20–30% of the time degradation patterns prove to be non-linear even in the short term. The local defects of alignment degrade more rapidly and trigger 80% of the unplanned maintenance needs. Modelling the evolution of local defects, and not only the standard deviation on sections 200 m long, allows us to anticipate unplanned maintenance and tackle unavailability costs. [ABSTRACT FROM AUTHOR]

Phononic crystals are renowned for their distinctive wave propagation characteristics, notably bandgaps that offer precise control over vibration phenomena, positioning them as a critical material in advanced vibro-elastic engineering and design. We investigate how pore shapes influence the bandgap in continuum two-dimensional phononic crystals made from a single material. Using the square lattice and unit cells with fourfold symmetry, our numerical analyses reveal that the normalized gap size is highly dependent on the minimum ligament width in the structure. Additionally, we find that fine geometric features represented by higher-order Fourier coefficients decrease the gap size. This study offers insight into the design of phononic crystals and vibro-elastic metamaterials for precise wave control through void patterning. [ABSTRACT FROM AUTHOR]

The substantial data volume within dynamic point clouds representing three-dimensional moving entities necessitates advancements in compression techniques. Motion estimation (ME) is crucial for reducing point cloud temporal redundancy. Standard block-based ME schemes, which typically utilize the previously decoded point clouds as inter-reference frames, often yield inaccurate and translation-only estimates for dynamic point clouds. To overcome this limitation, we propose an advanced patch-based affine ME scheme for dynamic point cloud geometry compression. Our approach employs a forward-backward jointing ME strategy, generating affine motion-compensated frames for improved inter-geometry references. Before the forward ME process, point cloud motion analysis is conducted on previous frames to perceive motion characteristics. Then, a point cloud is segmented into deformable patches based on geometry correlation and motion coherence. During the forward ME process, affine motion models are introduced to depict the deformable patch motions from the reference to the current frame. Later, affine motion-compensated frames are exploited in the backward ME process to obtain refined motions for better coding performance. Experimental results demonstrate the superiority of our proposed scheme, achieving an average 6.28% geometry bitrate gain over the inter codec anchor. Additional results also validate the effectiveness of key modules within the proposed ME scheme. [ABSTRACT FROM AUTHOR]

This paper discusses the relevance of using physical situations to introduce the concept of angles at elementary school. We compare the effectiveness of two geometry teaching sequences. In the first one (physical sequence), the pupils learned the angle concept by experimenting on the playground (i.e. mesospace) and then modelling the situation. In the second one (paper-and-pencil sequence), the pupils worked solely in the space of a sheet of paper (i.e. microspace). In both sequences, pupils compared areas of space delineated by an angle between two directions. Pupils in two Grade 3 classes were exposed to one of the two teaching sequences. The unfolding of these sequences was videotaped and analyzed, and the pupils were tested individually, before and after teaching, to measure each sequence's effectiveness. Results showed that both sequences are effective to grasp the angle concept: Most pupils overcame the common erroneous conception of comparing angles' sides' lengths instead of angle openness. The comparison of areas of space delineated by an angle between two infinite directions, which is the two sequences' common core, seems to be the key factor underlying angle conceptualization. This paper ends with a discussion of these results' teaching implications and the merits of each sequence. [ABSTRACT FROM AUTHOR]

We study the geometry of smooth projective surfaces defined by Frobenius forms, a class of homogenous polynomials in prime characteristic recently shown to have minimal possible F-pure threshold among forms of the same degree. We call these surfaces extremal surfaces , and show that their geometry is reminiscent of the geometry of smooth cubic surfaces, especially non-Frobenius split cubic surfaces. For instance, extremal surfaces have many lines but no triangles, hence many "star points" analogous to Eckardt points on a cubic surface. We generalize the classical notion of a double six for cubic surfaces to a double 2 d on an extremal surface of degree d. We show that, asymptotically in d , smooth extremal surfaces have at least 1 16 d 14 double 2 d 's. A key element of the proofs is the large automorphism group of an extremal surface, which we show to act transitively on many associated sets, such as the set of triples of skew lines on the extremal surface. [ABSTRACT FROM AUTHOR]

This study explores the application of abrasive waterjet drilling (AWJD) for varied patterns of GF/Al mesh hybrid composites (neat glass NG, AG: Al in the exterior surface, and GA: Al in the center). Key parameters such as jet pressure (P), standoff distance (S), and traverse speed (V) are systematically varied, influencing material removal rate (MRR), hole taper ratio (Tr), and roundness error (Re). Employing a Taguchi approach with an L9 design. It was indicated that the optimal conditions for maximum MRR are (P: 150 MPa, S: 2 mm, and V: 900 mm/min). V and S are the main influential parameters on Tr and Re. Gray relational analysis (GRA) is employed for simultaneous optimization, enhancing drilling performance. The optimal parameters P of 150 MPa, S of 2 mm, and V of 300 mm/min are determined. Validation trials confirm the effectiveness of the determined parameters. A robust multiple regression equation is formulated, providing a predictive model that aligns closely with experimental observations. Highlights: The hybrid composites were drilled via a nontraditional process.The attributes of the hole geometry and the material removal impacts were studied.Operation parameters were optimized to improve MRR, Re, and Tr.A multiple regression model and a confirmation test were performed and validated. [ABSTRACT FROM AUTHOR]

Smart composites embedded with Fiber Bragg Grating (FBG) sensors are getting increasingly popular in aircraft structures due to their self‐sensing and monitoring capability. However, a resin pocket around the FBG sensor would be formed in the manufacturing process, which strongly impacts the mechanical properties of the composite host. Therefore, the influence of primary processing parameters (FBG orientation angle, preforming temperature, and preforming pressure) on the formation of resin pockets was investigated in this work. It is found that there is a sinusoidal relation between the resin pocket geometry and the FBG orientation angle. A negative linear relation is noted between the resin pocket geometry and the preforming temperature and pressure. A prediction model based on the backpropagation neural network (BPNN) was established, which was able to quickly and accurately predict resin pocket geometry subjected to given processing parameters. This work provides useful guidance for the processing control of smart composites embedded with FBG sensors. Highlights: Resin pocket geometry was formed primarily in the preforming stage.Effect of processing parameters on resin pocket geometry was characterized.A BPNN model was established for the fast prediction of resin pocket geometry. [ABSTRACT FROM AUTHOR]

In conjunction with theoretical calculations, the in vitro and in vivo uranyl binding capabilities of a bidentate picolinate (Pic) ligand and its pentadentate derivative (H2dpa) are investigated. The planar N3O2-donor configuration of H2dpa matches the typical pentagonal-bipyramid coordination geometry of uranyl, demonstrating a remarkable removal preference for uranyl in the kidneys. [ABSTRACT FROM AUTHOR]

The Hilbert scheme Hilb n ℂ 3 of n points on ℂ 3 can be expressed as the critical locus of a regular function on a smooth variety . Recent development in birational geometry suggests a study of singularities of the pair (, Hilb n ℂ 3) using jet schemes. In this paper, we use a comparison between Hilb n ℂ 3 and the scheme C 3 , n of three commuting n × n matrices to estimate the log canonical threshold of (, Hilb n ℂ 3). As a consequence, we see that although both dim and dim Hilb n ℂ 3 have asymptotic growth O (n 2) , the largest multiplicity of any points on Hilb n ℂ 3 has at most linear growth O (n). [ABSTRACT FROM AUTHOR]

A hybrid satellite–terrestrial relay network is a simple and flexible solution that can be used to improve the performance of land mobile satellite systems, where the communication links between satellite and mobile terrestrial users can be unstable due to the multipath effect, obstacles, as well as the additional atmospheric losses. Motivated by these facts, in this paper, we analyze a system where the satellite–terrestrial links undergo shadowed Rice fading, and, following this, terrestrial relay applies the selection relaying protocol and forwards the information to the final destination using the communication link subjected to Nakagami-m fading. For the considered relaying protocol, we derive the exact closed-form expressions for the outage probability, outage capacity, and ergodic capacity, presented in polynomial–exponential form for the integer-valued fading parameters. The presented numerical results illustrate the usefulness of the selection relaying for various propagation scenarios and system geometry parameters. The obtained analytical results are corroborated by an independent simulation method, based on the originally developed fading simulator. [ABSTRACT FROM AUTHOR]

Shape‐conveying line drawings generated from 3D models normally create closed regions in image space. These lines and regions can be stylized to mimic various artistic styles, but for complex objects, the extracted topology is unnecessarily dense, leading to unappealing and unnatural results under stylization. Prior works typically simplify line drawings without considering the regions between them, and lines and regions are stylized separately, then composited together, resulting in unintended inconsistencies. We present a method for joint simplification of lines and regions simultaneously that penalizes large changes to region structure, while keeping regions closed. This feature enables region stylization that remains consistent with the outline curves and underlying 3D geometry. [ABSTRACT FROM AUTHOR]

Side‐scan sonar is a lightweight acoustic sensor that is frequently deployed on autonomous underwater vehicles (AUVs) to provide high‐resolution seafloor images. However, using side‐scan images to perform simultaneous localization and mapping (SLAM) remains a challenge when there is a lack of 3D bathymetric information and discriminant features in the side‐scan images. To tackle this, the authors propose a feature‐based SLAM framework using side‐scan sonar, which is able to automatically detect and robustly match keypoints between paired side‐scan images. The authors then use the detected correspondences as constraints to optimise the AUV pose trajectory. The proposed method is evaluated on real data collected by a Hugin AUV, using as a ground truth reference both manually‐annotated keypoints and a 3D bathymetry mesh from multibeam echosounder (MBES). Experimental results demonstrate that this approach is able to reduce drifts from the dead‐reckoning system. The framework is made publicly available for the benefit of the community. [ABSTRACT FROM AUTHOR]

We study hypersurfaces of the four‐dimensional Thurston geometry Sol04$\mathrm{Sol}^4_0$, which is a Riemannian homogeneous space and a solvable Lie group. In particular, we give a full classification of hypersurfaces whose second fundamental form is a Codazzi tensor—including totally geodesic hypersurfaces and hypersurfaces with parallel second fundamental form—and of totally umbilical hypersurfaces of Sol04$\mathrm{Sol}^4_0$. We also give a closed expression for the Riemann curvature tensor of Sol04$\mathrm{Sol}^4_0$, using two integrable complex structures. [ABSTRACT FROM AUTHOR]

It is shown that the two‐dimensional Mullins–Sekerka problem is well‐posed in all subcritical Sobolev spaces Hr(R)$H^r({\mathbb {R}})$ with r∈(3/2,2)$r\in (3/2,2)$. This is the first result, where this issue is established in an unbounded geometry. The novelty of our approach is the use of the potential theory to formulate the model as an evolution problem with nonlinearities expressed by singular integral operators. [ABSTRACT FROM AUTHOR]

In a typical semiconductor material, the majority of the heat is carried by long-wavelength, long-mean-free-path phonons. Nanostructuring strategies to reduce thermal conductivity, a promising direction in the field of thermoelectrics, place scattering centers of size and spatial separation comparable to the mean free paths of the dominant phonons to selectively scatter them. The resultant thermal conductivity is in most cases well predicted using Matthiessen's rule. In general, however, long-wavelength phonons are not as effectively scattered as the rest of the phonon spectrum. In this work, using large-scale molecular-dynamics simulations, non-equilibrium Green's function simulations, and Monte Carlo simulations, we show that specific nanoporous geometries that create narrow constrictions in the passage of phonons lead to anticorrelated heat currents in the phonon spectrum. This effect results in super-suppression of long-wavelength phonons due to heat trapping and reductions in the thermal conductivity to values well below those predicted by Matthiessen's rule. [ABSTRACT FROM AUTHOR]

MMC is one of the topology optimization methods that provides explicit boundary description of the optimized topology. However, due to the inherent nature of MMC, the obtained geometry could exhibit distinct local singularities. To cope with this issue, a non-parametric geometry patching technique for MMC is developed. A moving node patching technique for both 2D and 3D cases is developed in conjunction with MMC to obtain structures with smooth boundaries. Numerical examples in 2D and 3D are presented to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

To facilitate the transition of quantum effects from the controlled laboratory environment to practical real-world applications, there is a pressing need for scalable platforms. One promising strategy involves integrating thermal vapors with nanostructures designed to manipulate atomic interactions. In this tutorial, we aim to gain deeper insights into this by examining the behavior of thermal vapors that are confined within nanocavities or waveguides and exposed to near-resonant light. We explore the interactions between atoms in confined dense thermal vapors. Our investigation reveals deviations from the predictions of continuous electrodynamics models, including density-dependent line shifts and broadening effects. In particular, our results demonstrate that by carefully controlling the saturation of single atoms and the interactions among multiple atoms using nanostructures, along with controlling the geometry of the atomic cloud, it becomes possible to manipulate the effective optical nonlinearity of the entire atomic ensemble. This capability renders the hybrid thermal atom-nanophotonic platform a distinctive and valuable one for manipulating the collective effect and achieving substantial optical nonlinearities. [ABSTRACT FROM AUTHOR]

Middle Cerebral Artery Bifurcation Aneurysm (MbifA) is associated with a high risk of rupture and poor overall prognosis in patients once it ruptures. Morphological, geometric, and hemodynamic parameters have been identified as factors contributing to the rupture of intracranial aneurysms. However, there are no studies that combine these 3 types of parameters to specifically target MbifA rupture. This study enrolled all patients with MbifAs diagnosed at our treatment center from 1 April 2021 to 31 July 2023 who met the study criteria. All patients underwent digital subtraction angiography examination to obtain 3D rotational angiography data. We imported the complete image data into the Aneurysm/Artery Reconstruction and Analysis machine to obtain 13 morphological parameters (D neck , D dome , Height, D max , D artery , aspect ratio [AR], size ratio, dome-neck-ratio [DNR], height-artery-ratio, bottleneck factor, Inflow Angle, Incline Angle, Arterial Angle), 5 geometric parameters (V,S,undulation index [UI], ellipticity index [EI],nonsphericity index [NSI]), and 5 hemodynamic parameters (wall shear stress [WSS], the maximum WSS, the parent artery WSS, the normalized WSS [NWSS], oscillatory shear index [OSI]). All the above significant parameters were tested by univariate and multivariate analyses to find out the independent discriminatory factors. A total of 49 MbifAs (16 ruptured and 33 unruptured) from 44 patients were included in the study. Height (P = 0.033), AR (P = 0.007), DNR (P = 0.011), EI (P = 0.042), NSI(P = 0.030), UI(P = 0.027), WSS(P = 0.033), and NWSS(P = 0.002) were all associated with MbifA rupture in univariate analyses, but only NWSS was an independent risk factor (P = 0.036, OR = 0.046, 95% CI: 0.003–0.815) in multivariate logistic regression analysis. Height, AR, DNR, EI, UI, NSI, WSS, and NWSS may be correlated with MbifA rupture, but only NWSS was an independent risk factor. A lower NWSS was associated with a higher risk of MbifA rupture. No significant differences were observed in the angle parameters, including the Inflow Angle, between ruptured and unruptured MbifAs. OSI was significantly increased at the dome of the aneurysm but the mean OSI was not found to be associated with MbifA rupture. [ABSTRACT FROM AUTHOR]

The experimental measurements of ${2D}$ 2 D micro/nanolayered dimples' dimensions (both geometry and pattern) on the published tensile fractographs of a series of austempered high-strength low-carbon bainitic steel are carried out and interpreted with the corresponding initial microstructural features and tensile mechanical responses as a function of austempering temperature. [ABSTRACT FROM AUTHOR]

We show that the Lipschitz‐free space with the Radon–Nikodým property and a Daugavet point recently constructed by Veeorg is in fact a dual space isomorphic to ℓ1$\ell _1$. Furthermore, we answer an open problem from the literature by showing that there exists a superreflexive space, in the form of a renorming of ℓ2$\ell _2$, with a Δ$\Delta$‐point. Building on these two results, we are able to renorm every infinite‐dimensional Banach space to have a Δ$\Delta$‐point. Next, we establish powerful relations between existence of Δ$\Delta$‐points in Banach spaces and their duals. As an application, we obtain sharp results about the influence of Δ$\Delta$‐points for the asymptotic geometry of Banach spaces. In addition, we prove that if X$X$ is a Banach space with a shrinking k$k$‐unconditional basis with k<2$k < 2$, or if X$X$ is a Hahn–Banach smooth space with a dual satisfying the Kadets–Klee property, then X$X$ and its dual X∗$X^*$ fail to contain Δ$\Delta$‐points. In particular, we get that no Lipschitz‐free space with a Hahn–Banach smooth predual contains Δ$\Delta$‐points. Finally, we present a purely metric characterization of the molecules in Lipschitz‐free spaces that are Δ$\Delta$‐points, and we solve an open problem about representation of finitely supported Δ$\Delta$‐points in Lipschitz‐free spaces. [ABSTRACT FROM AUTHOR]

Increasing evidence indicates the role of mitochondrial and vascular dysfunction in aging and aging-associated pathologies; however, the exact mechanisms and chronological processes remain enigmatic. High-energy demand organs, such as the brain, depend on the health of their mitochondria and vasculature for the maintenance of normal functions, therefore representing vulnerable targets for aging. This methodology article describes an analysis pipeline for three-dimensional (3-D) mitochondria-associated signal geometry of two-photon image stacks of brain vasculature. The analysis methods allow the quantification of mitochondria-associated signals obtained in real time in their physiological environment. In addition, signal geometry results will allow the extrapolation of fission and fusion events under normal conditions, during aging, or in the presence of different pathological conditions, therefore contributing to our understanding of the role mitochondria play in a variety of aging-associated diseases with vascular etiology. NEW & NOTEWORTHY Analysis pipeline for 3-D mitochondria-associated signal geometry of two-photon image stacks of brain vasculature. [ABSTRACT FROM AUTHOR]

We prove new optimal C 1 , α regularity results for obstacle problems involving evolutionary p -Laplace type operators in the degenerate regime p > 2. Our main results include the optimal regularity improvement at free boundary points in intrinsic backward p -paraboloids, up to the critical exponent, α ≤ 2 / (p − 2) , and the optimal regularity across the free boundaries in the full cylinders up to a universal threshold. Moreover, we provide an intrinsic criterion by which the optimal regularity improvement at free boundaries can be extended to the entire cylinders. An important feature of our analysis is that we do not impose any assumption on the time derivative of the obstacle. Our results are formulated in function spaces associated to what we refer to as higher order or C 1 , α intrinsic interpolative geometries. [ABSTRACT FROM AUTHOR]