Shape Gradient Research Articles

Simulation of topographic effects on soil erosion and deposition in a small watershed of loess hilly region

AbstractTopography plays a critical role in soil migration and redistribution, but few studies have been conducted to quantify its effects on sediment deposition. In this study, we established a physical simulation and analysis framework to investigate the erosional and depositional impacts of two‐dimensional slope terrain, specifically applied to Xiannangou small watershed in the loess hilly region. The results showed that the slope gradient, slope length, and slope shape have significantly influence the distribution of soil erosion and deposition. The magnitude of the erosion/deposition rate (Yr) determines the relative intensity of slope erosion and deposition, where Yr < 0 indicates erosion and Yr > 0 signifies deposition. The erosion rate on straight slope exhibited a positive correlation with slope length, while the erosion/deposition rate on concave and convex slopes exhibited fluctuations with slope length. Soil erosion predominantly occurred along the main flow line and the middle slope, aligning with the observed distribution of gully and slope erosion in the field. The sediment deposition was primarily concentrated on the lower slope or the lowest outlet of the basin, notably in gullies and gentle slopes where the terrain slows, especially during transition from steep to gradual slopes. These results can effectively predict the relative erosion/sedimentation rate of two‐dimensional slopes, significantly contributing to a comprehensive understanding of how topography influences soil erosion and deposition. This study thoroughly considers the role of sediment deposition in the soil erosion process, providing a more accurate reflection of soil erosion/deposition in small watersheds. It addresses the existing deficiency in sediment consideration within soil erosion evaluation and supports the enhancement of soil erosion model.

Wettability and/or shape gradient induced spontaneous droplet motion on solid surfaces

This research investigates the dynamics of spontaneous droplet motion induced by wettability and shape gradients on microscale substrates. The study compares and analyzes the effects of different driving sources, including wettability gradient, shape gradient, and their combination. Findings reveal that the combination of wettability and shape gradients on a wedge-shaped track produces unique droplet motion patterns. Results demonstrate that, despite a slower initial acceleration, the combined driving force on the wedge-shaped track leads to a larger peak velocity compared to tracks with individual gradients. Additionally, the study explores the impact of track end contact angle and wedge angle on droplet motion. It highlights the preference for uniform wettability tracks for faster droplet motion, emphasizing the role of overall contact angle and wetting area. The research concludes that track size influences droplet motion, with larger wedge angles promoting faster and more stable motion. Overall, the study provides valuable insights into controlling and understanding droplet dynamics on structured surfaces.

Urban intensity gradients shape community structure, life‐history traits and performance in a multitrophic system

Abstract Urban ecosystems are formed by pronounced socio‐ecological gradients, which are distinct from other ecosystems and can simultaneously filter and promote taxa, ultimately affecting their interactions. However, the strength of the effect of filtering and facilitation across the different trophic levels could vary among biotic and abiotic factors. Here, we investigate the effects of habitat amount, temperature and host‐enemy biotic interactions in shaping communities of cavity‐nesting bees and wasps and their natural enemies. We installed trap‐nests in 80 sites distributed along urban intensity gradients in five European cities (Antwerp, Paris, Poznan, Tartu and Zurich). We quantified the species richness and abundance of hosts and their natural enemies, as well as two performance traits (survival and parasitism) and two life‐history traits (sex ratio and number of offspring per nest for the hosts). We analysed the importance of the abiotic and biotic variables using generalised linear models and multi‐model inference. We found that habitat amount was the main driver of multiple host responses, with larger habitat amounts resulting in higher species richness and abundance for hosts and natural enemies, as well as a larger probability of survival and a larger number of brood cells for hosts. Local resources proxies shaped both bees and wasps and indicate different uses of existing vegetation between bees and wasps. Temperature proxies had a minor role in shaping host and natural enemies. Biotic interactions were a main driver of host and enemy community structure, with natural enemies being strongly affected by host availability, that is, with direct density‐dependence between hosts and their natural enemies. Overall, our study highlights the importance of habitat amount and temperature in shaping urban food webs, as well as on biotic interactions through direct effects on hosts responses and the subsequent consequences for their natural enemies. As cities prepare to tackle the consequences of global change, strategies that make it possible to maintain habitat and mitigate urban overheating emerge as a key urban adaptation for biodiversity conservation.

Microbial community and network responses across strong environmental gradients: How do they compare with macroorganisms?

The way strong environmental gradients shape multispecific assemblages has allowed us to examine a suite of ecological and evolutionary hypotheses about structure, regulation and community responses to fluctuating environments. But whether the highly diverse co-occurring microorganisms are shaped in similar ways as macroscopic organisms across the same gradients has yet to be addressed in most ecosystems. Here, we characterize intertidal biofilm bacteria communities, comparing zonation at both the "species" and community levels, as well as network attributes, with co-occurring macroalgae and invertebrates in the same rocky shore system. The results revealed that the desiccation gradient has a more significant impact on smaller communities, while both desiccation and submersion gradients (surge) affect the larger, macroscopic communities. At the community level, we also confirmed the existence of distinct communities within each intertidal zone for microorganisms, similar to what has been previously described for macroorganisms. But our results indicated that dominant microbial organisms along the same environmental gradient exhibited less differentiation across tidal levels than their macroscopic counterparts. However, despite the substantial differences in richness, size and attributes of co-occurrence networks, both macro- and micro-communities respond to stress gradients, leading to the formation of similar zonation patterns in the intertidal rocky shore.

Development and Validation of a 3-D Analytical Fluidic Model in Cartesian Coordinates for a Magnetic Refrigeration Application

This paper focuses on the development and validation of a three-dimensional (3-D) analytical model based on the formal resolution of the incompressible Navier-Stokes equations in Cartesian coordinates. This analytical fluidic model calculates the evolution of the fluid flow velocity for various pressure gradient shapes (i.e., square, trapezoidal, ramp, triangle, sinusoidal signals, etc.), with or without mean value, using Fourier series. The model can consider square and rectangular channels of any dimensions in terms of height, width, and depth. It allows for the study of different types of fluid flow and geometries. The introduction highlights the significance of analytical modeling, particularly in the context of Magnetic Refrigeration (MR) technologies. The model assumptions and governing equations are presented. The results obtained from the analytical model are validated and show good convergence with those obtained using the COMSOL Multiphysics® software. The comparison demonstrates a high level of agreement between the two models. The analytical model performs well in terms of computation time and accuracy. It will be coupled with an analytical thermic model and used to optimize Active Magnetic Regenerative Refrigeration (AMRR) cycles. The ultimate objective is to determine an optimal pressure gradient evolution in order to maximize heat exchange in a regenerator channel.

Two sequences of spiral galaxies with different shapes of the metallicity gradients

We considered two sequences of spiral galaxies with different shapes of the radial gas-phase oxygen abundance distributions from the galaxies in the survey Mapping Nearby Galaxies at Apache Point Observatory (MaNGA): (1) Galaxies in which the gradient is well approximated by a single linear relation across the whole disc, that is, galaxies with an S (slope) gradients, (2) galaxies in which the metallicity in the inner region of the disc is at a nearly constant level and the gradient is negative at larger radii, that is, galaxies with level-slope (LS) gradients. We also selected galaxies with a nearly uniform oxygen abundance across the whole galaxy, that is, galaxies with level (L) gradients (or O/H uniform galaxies) with a high oxygen abundance that can be the final evolutionary stage of the two galaxy sequences described above. The radial nitrogen abundance distributions in galaxies with LS oxygen abundance distributions also show breaks at radii smaller than the O/H distribution breaks. The observed behaviour of the oxygen and nitrogen abundances with radius in these galaxies can be explained by the time delay between the nitrogen and oxygen enrichment together with the variation in the star formation history along the radius. These galaxies clearly show the effect of the inside-out disc evolution model, which predicts that the galactic centre evolves more rapidly than the regions at greater galactocentric distances. We find that the shape of the radial abundance distribution in a galaxy is not related to its macroscopic characteristics (rotation velocity, stellar mass, isophotal radius, and star formation rate) and is independent of its present-day environment. The correlations between the gradient slopes and macroscopic characteristics of galaxies are weak in the sense that the scatter of the points in each diagram is large. The galaxies with different abundance distributions (S, LS, or L) in our sample are located within the main sequence of the star-forming galaxies in the diagram of star formation rate–stellar mass. We also examined the properties of the Milky Way in the context of the considered galaxy samples.

Influences of Weld Nugget Shape and Material Gradient on the Shear Strength of Resistance Spot‐Welded Joints

Resistance spot‐welded joints containing press‐hardened steels are seen to exhibit a fracture mode called total dome failure, where the weld nugget completely separates from one steel sheet along the weld nugget edge. The effect of weld nugget shape and material property gradients is studied based on damage mechanics modeling and experimental validation to shed light on the underlying influencing factors. For a three‐steel‐sheet spot‐welded joint combining DP600 (1.5 mm)–CR1900T (1.0 mm)–CR1900T (1.0 mm), experiments under shear loading reveal that fracture occurs in the DP600 sheet along the weld nugget edge. In subsequent numerical simulation studies with damage mechanics models whose parameters are independently calibrated for every involved material configuration, three variations of the geometrical joint configuration are considered—an approximation of the real joint, one variation with a steeper weld nugget shape, and one variation with a less pronounced gradient between weld nugget material and heat‐affected zone material properties. The results of the finite‐element simulations show that a shallower weld nugget and a more pronounced material gradient lead to a faster increase of plastic strain at the edge of the weld nugget and promote the occurrence of total dome failure.

A Method for Estimating the Hydrodynamic Values of Anastomosing Rivers: The Expression of Channel Morphological Parameters

An anastomosing river is a stable multiple-channel system separated by inter-channel wetlands, and there are serious difficulties in observing the hydrodynamics of such river patterns in situ. Therefore, there are few reports on the hydrodynamic data of such rivers, for example, the upper Columbia and Pearl Rivers. In order to obtain the hydrodynamic parameter values at flow cross-sections of anastomosing rivers, without having to observe hydraulic radius, this study proposes a method called the Expression of Channel Morphological Parameters (ECMP) for hydrodynamic estimation. The calculation formula of the ECMP method is based on the shape factor (width–depth ratio), scale factor (mean depth), and gradient factor of the channel cross-sections of anastomosing rivers below a given water level as independent variables. This method can be used to calculate the mean velocity, discharge, specific stream power, and gross stream power of the flow cross-section at different water levels, only requiring the measurements of channel morphological parameters such as the mean depth, width–depth ratio, and gradient at the channel cross-section below the corresponding water level. The applicability of the ECMP method was verified using measured hydrological data. The results showed that the ECMP method is a practical estimation method with higher accuracy that is convenient for calculating the hydrodynamic parameters of anastomosing rivers. It can also be used to reconstruct ancient anastomosing rivers using the channel morphological parameters revealed from the fill sediments in ancient channels.

Soil toxicity and species dominance rather than nutrient availability drive plant species richness in swamp forests of Central Europe

AbstractAimA resource based conceptual model of plant diversity (RBCM) assumes direct relationships between resource supply and the diversity of a local plant assembly. However, the RBCM largely ignores variation in soil toxicity imposed by climatic effects. Both soil limiting resources and soil toxicity vary along climatic gradients but their net and interactive effects on plant species diversity remain unknown. We asked how climatic gradients shape resource availability, soil toxicity and dominance of herb‐layer graminoids, and how these predictors control local species diversity of herbs and bryophytes.LocationSwamp forests, Central Europe.TaxonVascular plants, bryophytes.MethodsAlpha taxonomic diversity of vascular plants and bryophytes was counted for 101 vegetation plots sampled in temperate swamp forests distributed along an 800‐km geographical gradient across the Continental, Alpine and Pannonian biogeographical regions. Path analysis (structural equation modelling) was used to quantify the direct and indirect effects of climatic variable (potential evapotranspiration; PET), limiting resources (soil N/P, Ca, C/N, proxies for light and water availability) and soil toxicity (Mn) on graminoid dominance and community diversity.ResultsPET negatively influenced species richness of both groups analysed either directly or indirectly through its positive effect on the cover of graminoid species. Alpha diversity of herbs was additionally reduced by soil toxicity (Mn). Limiting resources correlated either with species dominance (canopy shading, soil Ca) or with PET (soil N/P ratio), but they did not control species richness pattern.Main ConclusionsClimate, soil toxicity and species dominance determined alpha diversity instead of the expected importance of soil limiting resources. These results are key to advancing the theoretical framework of the RBCM. Increased soil toxicity (Mn) in well‐watered regions favours the dominance of plant competitors at the expense of less tolerant species. This implies a potential threat to wetland diversity under ongoing climate change.

The linkage between spatial and temporal variations in epifaunal and primary producer communities in eelgrass (Zostera marina) beds

Environmental variability within estuaries and lagoons creates environmental gradients. Spatial variations in environments associated with environmental gradients shape spatial variations in primary producer and invertebrate communities. However, whether larger spatial variations are linked to greater temporal variations in the communities remained unclear. To understand the linkage between spatial and temporal variations in the communities and the factors shaping these variations, we targeted various functional groups of primary producers and invertebrates (epifauna) in eelgrass (Zostera marina) ecosystems in lagoons with and without distinct salinity gradients. We tested the following hypotheses: 1) larger spatial variation in the primary producer biomasses and epifaunal community structures (abundance, biomass, and species richness) are associated with greater temporal variation in the structures, and 2) salinity would be a more pronounced factor than water temperature and biomasses of primary producers in shaping the community structures in the lagoon with a salinity gradient. Our results showed that temporal and spatial variations in the primary producer biomasses and community structures of epifauna were larger in the lagoon with a salinity gradient. Moreover, salinity, water temperature, and the biomasses of primary producers affected the spatio-temporal variations in the community structures of epifauna, regardless of the presence of the gradients. We present from these results the connection between spatial and temporal variations of the primary producer and epifaunal community structures and the effects of abiotic and biotic factors shaping the communities.

Study on the optimization of the integration path between animation design and cultural and creative industries in the information era

Abstract This paper aims to promote the integration of animation design and cultural and creative industries. The shape gradient algorithm is used to analyze the features of the animated shapes. The corresponding interval distance of anime shapes is determined by calculating the curve sampling points of anime feature points. The deformation framework is created, and a sequence of anime shapes is generated using the linear interpolation method. In the deformation of anime design, the role of three algorithms, namely image segmentation module, association map of attributes, and mathematical description of EMD, on its generation is focused on the analysis. The results show that anime users from post-00 and post-10 are more inclined to anime peripherals, accounting for 30% and 35%, respectively. The annual growth rate of anime peripheral is 90.2%, and the annual growth rate of the overseas anime market is also gradually increasing, reaching a growth rate of 103.1%. A successful anime IP will certainly influence the development of its anime and cultural creation industry. The research in this paper is conducive to promoting better integration of animation design and cultural and creative industries and promoting the development of an innovation economy.

Convergent evolving finite element approximations of boundary evolution under shape gradient flow

Abstract As a specific type of shape gradient descent algorithm, shape gradient flow is widely used for shape optimization problems constrained by partial differential equations. In this approach, the constraint partial differential equations could be solved by finite element methods on a domain with a solution-driven evolving boundary. Rigorous analysis for the stability and convergence of such finite element approximations is still missing from the literature due to the complex nonlinear dependence of the boundary evolution on the solution. In this article, rigorous analysis of numerical approximations to the evolution of the boundary in a prototypical shape gradient flow is addressed. First-order convergence in time and $k$th order convergence in space for finite elements of degree $k\geqslant 2$ are proved for a linearly semi-implicit evolving finite element algorithm up to a given time. The theoretical analysis is consistent with the numerical experiments, which also illustrate the effectiveness of the proposed method in simulating two- and three-dimensional boundary evolution under shape gradient flow. The extension of the formulation, algorithm and analysis to more general shape density functions and constraint partial differential equations is also discussed.

Analysis of Nonlinear Flow and Heat Transfer Issues in Nanofluid by Using RK-4th Order Method

Nanofluids, composed of a base fluid with dispersed nanoparticles, have gained significant attention due to their unique thermal and flow characteristics. Understanding the nonlinear flow and heat transfer phenomena in nanofluids is crucial for optimizing their performance in engineering applications. In this study, we propose using the Runge-Kutta 4th order (RK-4) numerical method to analyze these issues. The RK-4 method is known for its accuracy and efficiency in solving ordinary differential equations. By applying this method to the governing equations of fluid flow and heat transfer, we can accurately capture the nonlinear behavior of nanofluids. We investigate various nonlinear phenomena, such as boundary layer separation, flow instability, and heat transfer enhancement, considering factors like nanoparticle concentration, size, shape, fluid properties, Reynolds number, and temperature gradient. The RK-4 method provides accurate solutions, revealing critical parameters that affect flow and heat transfer behavior. Comparisons with experimental data and other numerical methods validate the approach, demonstrating its reliability. Parametric studies are conducted to optimize nanofluid characteristics for improved heat transfer and fluid flow. This research enhances our understanding of nonlinear flow and heat transfer in nanofluids and enables efficient numerical analysis, opening new avenues for improving nanofluid-based systems.

Environmental gradients shape microbiome assembly and stability in the East China sea

Microbiomes play a key role in marine ecosystem functioning and sustainability. Their organization and stability in coastal areas, particularly in anthropogenic-influenced regions, however, remains unclear compared with an understanding of how microbial community shifts respond to marine environmental gradients. Here, the assembly and community associations across vertical and horizontal gradients in the East China Sea are systematically researched. The seawater microbial communities possessed higher robustness and lower fragmentation and vulnerability compared to the sediment microbiomes. Spatial gradients act as a deterministic filtering factor for microbiome organization. Microbial communities had lower phylogenetic distance and higher niche breadth in the nearshore and offshore areas compared to intermediate areas. The phylogenetic distance of microbiomes decreased from the surface to the bottom but the niche breadth was enhanced in surface and bottom environments. Vertical gradients destabilized microbial associations, while the community diversity was enhanced. Multivariate regression tree analysis and canonical correspondence analysis indicated that depth, distance from shore, nutrient availability, temperature, salinity, and chlorophyll a, affected the distribution and co-occurrence of microbial groups. Our results highlight the crucial roles of environmental gradients in determining microbiome association and stability. These results improve our understanding of the survival strategies/adaptive mechanisms of microbial communities in response to environmental variation and provide new insights for protecting the ecosystems and maintaining the sustainability of ecological functions.

MaNGA DynPop – II. Global stellar population, gradients, and star-formation histories from integral-field spectroscopy of 10K galaxies: link with galaxy rotation, shape, and total-density gradients

ABSTRACT This is the second paper of the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) Dynamics and stellar Population (DynPop) series, which analyses the global stellar population, radial gradients, and non-parametric star-formation history of ∼10K galaxies from the MaNGA Survey final data release 17 and relates them with dynamical properties of galaxies. We confirm the correlation between the stellar population properties and the stellar velocity dispersion σe, but also find that younger galaxies are more metal-poor at fixed σe. Stellar age, metallicity, and mass-to-light ratio (M*/L) all decrease with increasing galaxy rotation, while their radial gradients become more negative (i.e. lower value at the outskirts). The exception is the slow rotators, which also appear to have significantly negative metallicity gradients, confirming the mass–metallicity gradient correlation. Massive disc galaxies in the green valley, on the $(\sigma _{\rm e},\rm age)$ plane, show the most negative age and metallicity gradients, consistent with their old central bulges surrounded by young star-forming discs and metal-poor gas accretion. Galaxies with high σe, steep total mass-density slope, low dark matter fraction, high M*/L, and high metallicity have the highest star-formation rate at earlier times, and are currently quenched. We also discover a population of low-mass star-forming galaxies with low rotation but physically distinct from the massive slow rotators. A catalogue of these stellar population properties is provided publicly.

PH Gradients in Spatially Non-Uniform AC Electric Fields around the Charging Frequency; A Study of Two Different Geometries and Electrode Passivation.

Dielectrophoresis (DEP), a precision nonlinear electrokinetic tool utilized within microfluidic devices, can induce bioparticle polarization that manifests as motion in the electric field; this phenomenon has been leveraged for phenotypic cellular and biomolecular detection, making DEP invaluable for diagnostic applications. As device operation times lengthen, reproducibility and precision decrease, which has been postulated to be caused by ion gradients within the supporting electrolyte medium. This research focuses on characterizing pH gradients above, at, and below the electrode charging frequency (0.2-1.4 times charging frequency) in an aqueous electrolyte solution in order to extend the parameter space for which microdevice-imposed artifacts on cells in clinical diagnostic devices have been characterized. The nonlinear alternating current (AC) electric fields (0.07 Vpp/μm) required for DEP were generated via planar T-shaped and star-shaped microelectrodes overlaid by a 70 μm high microfluidic chamber. The experiments were designed to quantify pH changes temporally and spatially in the two microelectrode geometries. In parallel, a 50 nm hafnium oxide (HfO2) thin film on the microelectrodes was tested to provide insights into the role of Faradaic surface reactions on the pH. Electric field simulations were conducted to provide insights into the gradient shape within the microelectrode geometries. Frequency dependence was also examined to ascertain ion electromigration effects above, at, and below the electrode charging frequency. The results revealed Faradaic reactions above, at, and below the electrode charging frequency. Comparison experiments further demonstrated that pH changes caused by Faradaic reactions increased inversely with frequency and were more pronounced in the star-shaped geometry. Finally, HfO2 films demonstrated frequency-dependent properties, impeding Faradaic reactions.

Distorted dynamic similitude of sandwich FGM plates and shells in high-temperature environments

Limit to the size of the experimental platform, scaled-down model test is a reliable mean to study the dynamic of sandwich functionally graded material (FGM) structures in high-temperature environments. However, due to the complexity of material composition and impact of high-temperature environments, relevant parameters cannot be scaled with traditional similitude methods, resulting in the similitude distortion. For the first time, the present work studies the distorted dynamic similitude of sandwich FGM plates and shells in high-temperature environments. Based on the Energy Similitude Correction Method proposed by the author in recent years, the similitude distortion derived from the non-scalability of material properties and thermal effects is solved. More importantly, the application object of this method is extended for the first time from plates to shells of various shapes, including cylindrical shells, conical shells and double curved shells. Meanwhile, heat conduction, thermal expansion and temperature-dependent material properties are taken into account for the impact of high-temperature environments. Various numerical examples are verified with different gradient coefficients, thicknesses, temperature conditions and shapes of shells. The results of high-precision similitude show that the prediction approach is correct and widely applicable.

Effect of phase change heat storage tank with gradient fin structure on solar energy storage: A numerical study

In this paper, the heat storage process of a latent heat thermal energy storage (LHTES) tank is studied numerically. A new type of gradient fin is added to the heat storage process in a latent heat storage tank to improve the heat transfer performance of the internal phase change material (PCM). The numerical model is verified by the experimental data. The influences of different structures on the melting rate, temperature distribution, velocity distribution, and maximum melting rate of PCM in LHTES tank are investigated, and the influence of natural convection on the energy storage system is further quantified. The results show that the melting time can be significantly reduced by 16.9% by using the four straight fins with gradient shape, and the melting time can be further reduced by 41.1% by reconstruction of the gradient fin position. The deformation in the opposite direction will slow down the melting speed and extend the melting time by more than 4.66 times. The convection criterion for judging the buoyancy convection of the melt in this paper shows that natural convection is dominant in both the upper and lower part of the melt. The closer the convection coefficient is to the overall heat transfer coefficient, the better the melting efficiency and energy efficiency will be.

A discontinuous Galerkin level set method using distributed shape gradient and topological derivatives for multi-material structural topology optimization

A discontinuous Galerkin level set method using distributed shape gradient and topological derivatives for multi-material structural topology optimization

Lagrangian approach and shape gradient for inverse problem of breaking line identification in solid: contact with adhesion

A class of inverse identification problems constrained by variational inequalities is studied with respect to its shape differentiability. The specific problem appearing in failure analysis describes elastic bodies with a breaking line subject to simplified adhesive contact conditions between its faces. Based on the Lagrange multiplier approach and smooth Lavrentiev penalization, a semi-analytic formula for the shape gradient of the Lagrangian linearized on the solution is proved, which contains both primal and adjoint states. It is used for the descent direction in a gradient algorithm for identification of an optimal shape of the breaking line from boundary measurements. The theoretical result is supported by numerical simulation tests of destructive testing in 2D configuration with and without contact.