Discrete Surface Research Articles

Three-Dimensional Photoengraving of Monolithic, Multifaceted Metasurfaces.

Metasurfaces present a potent platform to manipulate light by the spatial arrangement of sub-wavelength patterns with well-defined sizes and geometries, in thin films. Metasurfaces by definition are planar. However, it would be highly desirable to integrate metasurfaces with diverse, spatially programmed sub-wavelength features into a 3D monolith, to manipulate light within a compact 3D space. Here, a 3D photoengraving strategy is presented; that is, generation of such composite metasurfaces from a single microstructure via the irradiation of multiple interference laser beams onto different facets of the parent azopolymeric microstructure. Through "photofluidization,"thistechnique enables independent inscription and erasing of metasurfaces onto and from individual facets of 3D monoliths with arbitrary shapes and dimensions, in a high-throughput fashion (over approximately a few cm2 at a time). By engraving discrete sub-wavelength 1D surface relief gratings of different pitches on different facets of an inverse pyramidal array, a multiplexing structure-color filter is demonstrated.

Spectrophotometric loop flow analyzer for high-precision measurement of seawater pH

Automated instrument for long-term measurement of seawater pH is important for documenting the changes of the marine carbonate system and the impacts of ocean acidification. An automated pH analyzer based on loop flow analysis (LFA-pH) was developed to achieve precise and accurate measurements of seawater pH. The circulating loop allows complete mixing of an indicator and seawater, constant mixing volume of two solutions, and correcting indicator perturbation for each measurement. During laboratory testing, the LFA-pH precision achieved 0.0004, and the accuracy was 0.0017 ± 0.0038 compared with the certified standard buffer at different temperatures. During the 59 day underway measurement across the mid and high latitudes, more than 2500 pH measurements were carried out. LFA-pH showed good stability with high temperature and salinity changes, and measurement results were consistent with the discrete surface seawater pH measurement data. In situ testing of two LFA-pHs was completed near the Zhongyuan pier in Qingdao. The average pH offset between the two LFA-pHs was 0.0010 ± 0.0032 (n = 788), with the accuracies of the two LFA-pHs of 0.0012 ± 0.0033 and 0.0005 ± 0.0035 compared to discrete measurements. For continuous measurement, the average power consumption is 3.6 W at a 10 min measurement frequency. Given its low power consumption, high precision, and accuracy, FLA-pH could be adapted for underway and in situ measurements of ocean acidification observations.

Boundary Layer Transition Preflight Experiments in a Mach-6 Quiet Tunnel

Experiments on a subscale model of the U.S. Air Force Office of Scientific Research Boundary Layer Transition flight experiment were made in the Boeing/Air Force Office of Scientific Research Mach-6 Quiet Tunnel. Infrared thermography and temperature-sensitive paint were used to measure the surface temperature and heat transfer and provide images of streamwise streaks with the model at 0, 2, and 4 deg angle of attack. Variations in heating patterns were measured for yaw and roll angles. All smooth body cases remained laminar under quiet flow, but symmetric turbulent wedges were seen in noisy flow. Discrete surface pressure sensors measured possible instabilities on the model surface at locations that correspond to computed instability growth. It was discovered that the geometry was sensitive to forward- and rearward-facing steps near the swept leading edges. Controlled forward- and rearward-facing steps were created and tested. No transition was measured under quiet flow for any rearward-facing step at 0 deg angle of attack. Early transition was measured for the forward-facing steps, and correlations were developed for scaling step effects to the flight vehicle.

Topological effects and conformal invariance in long-range correlated random surfaces

We consider discrete random fractal surfaces with negative Hurst exponent H<0H<0. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level hh. The set of activated sites is usually denoted as the excursion set. The connected components of this set, the level clusters, define a one-parameter (HH) family of percolation models with long-range correlation in the site occupation. The level clusters percolate at a finite value h=h_ch=hc and for H\leq-\frac{3}{4}H≤−34 the phase transition is expected to remain in the same universality class of the pure (i.e. uncorrelated) percolation. For -\frac{3}{4}<H< 0−34<H<0 instead, there is a line of critical points with continously varying exponents. The universality class of these points, in particular concerning the conformal invariance of the level clusters, is poorly understood. By combining the Conformal Field Theory and the numerical approach, we provide new insights on these phases. We focus on the connectivity function, defined as the probability that two sites belong to the same level cluster. In our simulations, the surfaces are defined on a lattice torus of size M\times NM×N. We show that the topological effects on the connectivity function make manifest the conformal invariance for all the critical line H<0H<0. In particular, exploiting the anisotropy of the rectangular torus (M\neq NM≠N), we directly test the presence of the two components of the traceless stress-energy tensor. Moreover, we probe the spectrum and the structure constants of the underlying Conformal Field Theory. Finally, we observed that the corrections to the scaling clearly point out a breaking of integrability moving from the pure percolation point to the long-range correlated one.

Optimization of the coupling parameters and mixing uniformity of multiple organic hydraulic mixtures based on the discrete element method and response surface methodology

To address the mixing uniformity of multiple organic hydraulic (MOH) mixtures in a continuous mixer, three types of mixing parameters and their coupling effects were studied by the discrete element method (DEM) and response surface methodology. To achieve the research goal, only one parameter was selected for each type of parameter, and the corresponding model was established. Numerical simulations and optimization were implemented. A three-level, three-factor Box-Behnken Design method combined with response surface methodology was applied for the numerical design. The influence of the parameters on the mixing uniformity of the mixture was analyzed by analysis of variance (ANOVA). The ANOVA results show that the rotation speed, the installation angle, the filling ratio and the coupling between the rotation speed and the filling ratio have a significant effect on the mixing uniformity of the mixture, that the rotation speed and the filling ratio have the strongest effect on the response, and that of the fitting model of the mixing uniformity can fit the simulation data well. The coupling effect results show that the influence of coupling between the revolution and installation angle on the mixing uniformity is consistent with that between the filling ratio and installation angle and that the coupling effect between the rotation speed and the filling ratio is different. It is also found that the optimal parameter range under one factor is different from that under multivariable coupling. The optimization results show that when the discrete coefficient is the smallest, the optimal combination of the parameters is a revolution of 350 r/min, an installation angle of 25°, and a filling ratio of 70%. The experimental results are consistent with the optimization results, which indicate the correctness of the parameter optimization results.

On the moduli space of flat symplectic surface bundles

In this paper, we prove homological stability of symplectomorphisms and extended hamiltonians of surfaces made discrete. Similar to discrete surface diffeomorphisms [Nar17b], we construct an isomorphism from the stable homology group of symplectomorphisms and extended Hamiltonians of surfaces to the homology of certain infinite loop spaces. We use these infinite loop spaces to study characteristic classes of surface bundles whose holonomy groups are area preserving, in particular we give a homotopy theoretic proof of the main theorem in [KM07].

An Anatomical Evaluation of the Trapezium and Its Relationship to Basilar Joint Osteophytic Change.

To perform a comprehensive osteologic investigation into trapezium anatomy and investigate the relationship between anatomical factors and osteophyte formation, focusing on sex-specific differences. This was a cadaveric study involving 1233 trapezia and first metacarpals. Two subgroups ("Control" and "Main Study") were established. The "Control" cohort was used to identify features of the trapezium in specimens devoid of osteophytic change. The prevalence and severity of osteophytic change were investigated in the "Main Study" cohort. Sex differences were specifically assessed. Regression analyses were used to identify factors associated with osteophyte formation. Three discrete surface morphologies exist at the trapezium trapeziometacarpal (TM) facet: heart, quadrilateral, and bean. Controlling for height, men have a larger trapezium TM facet surface area. However, the trapezium assumes the same off-center saddle shape in both sexes. The presence of osteophytes at the basilar joint is a common finding; no differences in osteologic prevalence exist between sexes. The progression of osteophytic change complements the radiographic Eaton-Littler classification system. The trapezium TM facet increases the surface area with incremental osteophyte involvement, with the degree of surface area expansion correlated with increases in the severity of osteophytic change. Increased age, increased surface area, bean morphology, and decreased volar joint depth are associated with more severe osteophyte formation. Anatomical features of the trapezium may contribute to osteophyte development. Although the prevalence of osteophytic disease appears equal between sexes, sex differences exist in some anatomical parameters. These differences may help explain the increased prevalence of symptomatic basilar joint disease in women.

КОНСТРУЮВАННЯ ДИСКРЕТНИХ СІТОК ТА ПОВЕРХОНЬ НА ОСНОВІ ІЗОТРОПНИХ В-СПЛАЙНІВ

Modeling geometric objects in isotropic space allows us to simplify a number of calculations related to the calculation of differential characteristics. To create the ability to control the curved contours of objects, it is advisable to apply parametric curves based on characteristic polygons. For each type of such curves, there are limitations to the calculation of coordinates and lengths in isotropic space. Studies on modeling isotropic B-splines and based on them grids and surfaces are local in nature and require more detailed consideration. The paper proposes to model isotropic B-splines based on the recursive Cox de Boer formulas. The coordinates of the points for the spline are calculated based on the equal to zero side lengths of the characteristic polygons. Examples of constructed splines for different types of nodal vectors are given. It is shown that some types of nodal vectors do not allow the curve to pass through the start and end points of polygons. In this case, it is necessary to carry out adjustments to the nodal vector. The authors of the work developed an algorithm for modeling discrete grids and surfaces based on B-splines. All calculations are made in a complex space. When displaying geometric objects, the selection of the real part and the transition to the real space are carried out. As an example, visualization of the grid and surface based on an open uniform nodal vector is given. To research isotropic discrete curves, grids and surfaces based on B-splines, C # software was created for the .Net Core platform. Further research is related to the study of the influence of nodal vectors on the basis of an isotropic B-spline and surfaces. Keywords: isotropic curve, B-spline, discrete grids, discrete surfaces based on isotropic splines.

Equivalence between Digital Well-Composedness and Well-Composedness in the Sense of Alexandrov on n-D Cubical Grids

Among the different flavors of well-composednesses on cubical grids, two of them, called, respectively, digital well-composedness (DWCness) and well-composedness in the sense of Alexandrov (AWCness), are known to be equivalent in 2D and in 3D. The former means that a cubical set does not contain critical configurations, while the latter means that the boundary of a cubical set is made of a disjoint union of discrete surfaces. In this paper, we prove that this equivalence holds in n-D, which is of interest because today images are not only 2D or 3D but also 4D and beyond. The main benefit of this proof is that the topological properties available for AWC sets, mainly their separation properties, are also true for DWC sets, and the properties of DWC sets are also true for AWC sets: an Euler number locally computable, equivalent connectivities from a local or global point of view. This result is also true for gray-level images thanks to cross section topology, which means that the sets of shapes of DWC gray-level images make a tree like the ones of AWC gray-level images.

Generating Logistic Characteristic Curves using Discrete Event Simulation and Response Surface Models

Generating Logistic Characteristic Curves using Discrete Event Simulation and Response Surface Models

Statistical regularization for trend detection: an integrated approach for detecting long-term trends from sparse tropospheric ozone profiles

Abstract. Detecting a tropospheric ozone trend from sparsely sampled ozonesonde profiles (typically once per week) is challenging due to the short-lived anomalies in the time series resulting from ozone's high temporal variability. To enhance trend detection, we have developed a sophisticated statistical approach that utilizes a geoadditive model to assess ozone variability across a time series of vertical profiles. Treating the profile time series as a set of individual time series on discrete pressure surfaces, a class of smoothing spline ANOVA (analysis of variance) models is used for the purpose of jointly modeling multiple correlated time series (on separate pressure surfaces) by their associated seasonal and interannual variabilities. This integrated fit method filters out the unstructured variation through a statistical regularization (i.e., a roughness penalty) by taking advantage of the additional correlated data points available on the pressure surfaces above and below the surface of interest. We have applied this technique to the trend analysis of the vertically correlated time series of tropospheric ozone observations from (1) IAGOS (In-service Aircraft for a Global Observing System) commercial aircraft profiles above Europe and China throughout 1994–2017 and (2) NOAA GML's (Global Monitoring Laboratory) ozonesonde records at Hilo, Hawaii, (1982–2018) and Trinidad Head, California (1998–2018). We illustrate the ability of this technique to detect a consistent trend estimate and its effectiveness in reducing the associated uncertainty in the profile data due to the low sampling frequency. We also conducted a sensitivity analysis of frequent IAGOS profiles above Europe (approximately 120 profiles per month) to determine how many profiles in a month are required for reliable long-term trend detection. When ignoring the vertical correlation, we found that a typical sampling strategy (i.e. four profiles per month) might result in 7 % of sampled trends falling outside the 2σ uncertainty interval derived from the full dataset with an associated 10 % of mean absolute percentage error. Based on a series of sensitivity studies, we determined optimal sampling frequencies for (1) basic trend detection and (2) accurate quantification of the trend. When applying the integrated fit method, we find that a typical sampling frequency of four profiles per month is adequate for basic trend detection; however, accurate quantification of the trend requires 14 profiles per month. Accurate trend quantification can be achieved with only 10 profiles per month if a regular sampling frequency is applied. In contrast, the standard separated fit method, which ignores the vertical correlation between pressure surfaces, requires 8 profiles per month for basic trend detection and 18 profiles per month for accurate trend quantification. While our method improves trend detection from sparse datasets, the key to substantially reducing the uncertainty is to increase the sampling frequency.

Geology and Geochemistry of Iroko-Granites Southwestern Nigeria: implication on provenance

The geology, geochemistry of Iroko-granites have been studied and reported in this paper. The study area has been described as of Archaean –Early Proterozoic terrain underlain by migmatite-gneiss-quartzite complex with supracustal rocks. Large number of granites which outcrops in Iroko-Ekiti represent a typical occurrence of granitoids sporadically distributed in the basement and are known to belong to the Older Granite suites, which are attributable to the Pan-African Orogeny(750± 150Ma). The rocks occur, mostly as flat and low lying within sparse vegetation. Structures common on and around the outcrops include quartz vein, veinlets, pegmatite dykes which trend North-south, discrete exfoliated surfaces and xenoliths of older rocks. This study reveals that the granites belong to calc-alkalic suites, demonstrate metaluminous nature, and exhibit characteristics of I-type granites. The granite is a distinctive type in that it is relatively highly potassic, has high FeO/(FeO + MgO) ratio, and high average Zr (299.75ppm) concentration with other high field strength elements. The trace elements study implicates pronounced fractional crystallization during evolution of the granites and thus petrogenetically discriminates as Syn-collision provenance.

Fc receptor-like 4 and 5 define human atypical memory B cells.

Atypical memory B cells accumulate in chronic infections and autoimmune conditions, and commonly express FCRL4 and FCRL5, respective IgA and IgG receptors. We characterized memory cells from tonsils on the basis of both FCRL4 and FCRL5 expression, defining three subsets with distinct surface proteins and gene expression. Atypical FCRL4+FCRL5+ memory cells had the most discrete surface protein expression and were enriched in cell adhesion pathways, consistent with functioning as tissue-resident cells. Atypical FCRL4-FCRL5+ memory cells expressed transcription factors and immunoglobulin genes that suggest poised differentiation into plasma cells. Accordingly, the FCRL4-FCRL5+ memory subset was enriched in pathways responding to endoplasmic reticulum stress and IFN-γ. We reconstructed ongoing B-cell responses as lineage trees, providing crucial in vivo developmental context. Each memory subset typically maintained its lineage, denoting mechanisms enforcing their phenotypes. Classical FCRL4-FCRL5- memory cells were infrequently detected in lineage trees, suggesting the majority were in a quiescent state. FCRL4-FCRL5+ cells were the most represented memory subset in lineage trees, indicating robust participation in ongoing responses. Together, these differences suggest FCRL4 and FCRL5 are unlikely to be passive markers but rather active drivers of human memory B-cell development and function.

Quad-mesh based isometric mappings and developable surfaces

We discretize isometric mappings between surfaces as correspondences between checkerboard patterns derived from quad meshes. This method captures the degrees of freedom inherent in smooth isometries and enables a natural definition of discrete developable surfaces. This definition, which is remarkably simple, leads to a class of discrete developables which is much more flexible in applications than previous concepts of discrete developables. In this paper, we employ optimization to efficiently compute isometric mappings, conformal mappings and isometric bending of surfaces. We perform geometric modeling of developables, including cutting, gluing and folding. The discrete mappings presented here have applications in both theory and practice: We propose a theory of curvatures derived from a discrete Gauss map as well as a construction of watertight CAD models consisting of developable spline surfaces.

Inter-surface maps via constant-curvature metrics

We propose a novel approach to represent maps between two discrete surfaces of the same genus and to minimize intrinsic mapping distortion. Our maps are well-defined at every surface point and are guaranteed to be continuous bijections (surface homeomorphisms). As a key feature of our approach, only the images of vertices need to be represented explicitly, since the images of all other points (on edges or in faces) are properly defined implicitly. This definition is via unique geodesics in metrics of constant Gaussian curvature. Our method is built upon the fact that such metrics exist on surfaces of arbitrary topology, without the need for any cuts or cones (as asserted by the uniformization theorem). Depending on the surfaces' genus, these metrics exhibit one of the three classical geometries: Euclidean, spherical or hyperbolic. Our formulation handles constructions in all three geometries in a unified way. In addition, by considering not only the vertex images but also the discrete metric as degrees of freedom, our formulation enables us to simultaneously optimize the images of these vertices and images of all other points.

Inter-surface effective electrostatic interactions in the presence of surface charge discreteness and solvent granularity

Effects of relative arrangement of discrete surface charges and solvent granularity on the effective potential of mean force (EPMF) are studied. Main conclusions are summarized as follows: (i) With consideration of the solvent granularity the EPMF always becomes more attractive, and one like charge attraction always appears even if the counter-ion is univalent. Moreover, with transition from asymmetrical to symmetrical surface charge distributions of similar surface charge compactness, attraction strength of the EPMF always rises; with increase of the counter-ion valence the EPMF attraction strength rises unless the surface charge configuration is asymmetrical and less compact and the counter-ion high-valence. (ii) Whether the surface charge distribution is asymmetrical or symmetrical, the EPMF tends to become more attractive in the compactness charge configuration than in the non-compactness charge configuration. (iii) The correlation between the EPMF attraction strength and bulk mole concentration can be positive or negative depending on the counter-ion valence, compactness of surface charge distribution, and average surface charge strength. Highly taking value of each of the three quantities helps in inducing one negative correlation and vice versa. (iv) Co-ion size has almost no influence on the EPMF, increasing or decreasing the counter-ion size inhibits or enhances the solvent granularity effect.

Coupling surface flow and subsurface flow in complex soil structures using mimetic finite differences

We explore the coupling of surface and subsurface flows on fully unstructured meshes that conform to complex soil structures. To accommodate the distorted meshes that inevitably result from explicit representation of complex soil structures, we leverage the structure of the Mimetic Finite Difference (MFD) spatial discretization scheme to couple surface and subsurface flows. The MFD method achieves second-order accuracy and maintains local mass conservation on distorted meshes. We couple the diffusion wave approximation for surface flows to the Richards equation for subsurface flow, ensuring continuity of both pressure and flux between the surface and subsurface. The MFD method is particularly convenient for this coupling because it uses face-based constraints in the subsurface system that can be expressed as face-pressure unknowns. Those unknowns are coincident with surface cell-based unknowns, thus allowing the discrete surface system to be directly substituted into the subsurface system and solved implicitly as a global system. Robust representation of the transition between wet and dry surface conditions requires upwinding of the relative permeability and is facilitated by globalization in the nonlinear solver. The approach and its implementation in the Advanced Terrestrial Simulator (ATS) are evaluated by comparison to previously published benchmarks. Using runoff from soils with patchy groundcover (duff) as an example, we show that the new method converges significantly faster in mesh convergence tests than the commonly used two-point flux approximation.

Discrete Surface Ricci Flow for General Surface Meshing in Computational Electromagnetics Using Iterative Adaptive Refinement

We propose a surface meshing approach for computational electromagnetics (CEM) based on discrete surface Ricci flow (DSRF) with iterative adaptive refinement (AR) in the parametric domain for the automated generation of high-quality surface meshes of arbitrary element type, order, and count. Surfaces are conformally mapped by DSRF to a canonical parametric domain, allowing a canonical seed mesh to be mapped back to an approximation of the original surface. The new DSRF-based meshing technique provides a framework for generation of meshes with high element quality, aimed to greatly enhance the accuracy, conditioning properties, stability, robustness, and efficiency of surface integral equation CEM solutions. We demonstrate the ability of the proposed DSRF technique to produce meshes with near-optimal element corner angles for complicated, highly varied surfaces such as the NASA almond and a fighter jet model, using triangular, quadrilateral, and discontinuous quadrilateral elements. Other element types are also discussed. Where high-fidelity meshing is desired, the technique can capture fine-scale detail using very few high-order elements. Where low-fidelity meshing is desired, DSRF with AR can accurately recreate course-scale detail using standard first-order elements (e.g., flat triangular patches).

Hydro-mechanical interaction effects and channelling in three-dimensional fracture networks undergoing growth and nucleation

The flow properties of geomechanically generated discrete fracture networks are examined in the context of channelling. Fracture networks are generated by growing fractures in tension, modelling the low permeability rock as a linear elastic material. Fractures are modelled as discrete surfaces which grow quasi-statically within a three-dimensional (3D) volume. Fractures may have their locations specified as a simulation input, or be generated as a function of damage, quantified using the local variation in equivalent strain. The properties of the grown networks are shown to be a product of in situ stress, relative orientation of initial flaws, and competitive process of fracture interaction and growth. Fractures grow preferentially in the direction perpendicular to the direction of maximum tension and may deviate from this path due to mechanical fracture interaction. Flow is significantly channelled through a subset of the fractures in the full domain, consistent with observations of other real and simulated fractures. As the fracture networks grow, small changes in the geometry of the fractures lead to large changes in the locations and scale of primary flow channels. The flow variability and formation of channels are examined for two growing networks, one with a fixed amount of fractures, and another with nucleating fractures. The interaction between fractures is shown to modify the local stress field, and in turn the aperture of the fractures. Pathways for single-phase flow are the results of hydro-mechanical effects in fracture networks during growth. These are the results of changes to the topology of the network as well as the result of mechanical self-organisation which occurs during interaction leading to growth and intersection.

Time‐Lapse Seismic Imaging of Oceanic Fronts and Transient Lenses Within South Atlantic Ocean

AbstractOceanic fronts play a pivotal role in controlling water mass transfer, although little is known about deep frontal structure on appropriate temporal and spatial scales. Here, we present a sequence of calibrated time‐lapse images from a three‐dimensional seismic survey that straddles the Brazil‐Malvinas Confluence—a significant feature of the meridional overturning circulation. Eight vertical transects reveal the evolution of a major front. It is manifest as a discrete planar surface that dips at less than 2° and is traceable to 1.5–2 km depth. Its shape and surface expression are consistent with sloping isopycnal surfaces of the calculated potential density field and with coeval sea surface temperature measurements, respectively. Within the top ∼1 km, where cold fresh water subducts beneath warm salty water, a series of tilted lenses are banked up against the sharply defined front. The largest of these structures is centered at 700 m depth and is cored by cold fresh water. Time‐lapse imagery demonstrates that this tilted lens grows and decays over 9 days. It has a maximum diameter of <34±0.13 km and a maximum height of <750±10 m. Beneath 1 km, where horizontal density gradients are negligible, numerous deforming lenses and filaments on length scales of 10–100 km are being swept toward the advecting front.