Effect Of Geometric Constraints Research Articles

On the symmetric transformation with geometric constraints

ABSTRACT Coordinate transformation is a fundamental issue in the related studies of measurement. However, existing methodologies often need to pay more attention to the available spatial information, leading to suboptimal results. This paper addresses this issue by incorporating geometric constraints into the symmetric coordinate transformation. We propose the so-called geo-constrained transformation method based on the joint adjustment of the coordinate transformation in conjunction with the geometric constraints over a set of points. By formulating the geometric constraints as the conditional model, we analyze the effects of geometric constraints on the estimated transformation parameters and point locations. By removing such effects during the symmetric transformation algorithm, the results show better statistical performance and satisfy geometric constraints. Two numerical examples are given to demonstrate the expected improvement in the statistical accuracy. It is shown that the improvement of the point determination accuracy can go beyond 50%.

Phase Reentrances and Solid Deformations in Confined Colloidal Crystals.

A simple geometric constraint often leads to novel, complex crystalline phases distinct from the bulk. Using thin-film charge colloidal crystals, a model system with tunable interactions, we study the effects of geometric constraints. Through a combination of experiments and simulations, we systematically explore phase reentrances and solid deformation modes concerning geometrical confinement strength, identifying two distinct categories of phase reentrances below a characteristic layer number, N_{c}: one for bcc bulk-stable and another for fcc bulk-stable systems. We further verify that the dominant thermodynamic origin is the nonmonotonic dependence of solids' free energy on the degree of spatial confinement. Moreover, we discover transitions in solid deformation modes between interface-energy and bulk-energy dominance: below a specific layer number, N_{k}, geometric constraints generate unique soft deformation modes adaptive to confinement. These findings on the N-dependent thermodynamic and kinetic behaviors offer fresh insights into understanding and manipulating thin-film crystal structures.

The effects of geometric and metallurgical constraints on ultra-high strength steel weldments

The effect of geometric and metallurgical constraints on the ultimate capacity of weldments manufactured from direct-quenched (DQ) ultra-high strength steel (UHSS) is studied using numerical calculations. In addition, experimental tests are conducted to prove the phenomena in practice. DQ steels behave differently under static loading, especially their weldments, compared to the same-strength class steels, which are manufactured using different alloying and fabrication techniques. In these steels welding generates a distinct softened region at the heat-affected zone (HAZ), which, in certain conditions, can influence the ultimate load-carrying and elongation capacity of the weldment. Metallurgical constraints can form in welds where the soft zone is adjacent to zones with higher strength. Moreover, the current study shows that not only metallurgical constraints, but also geometric ones, can strengthen weldments depending on the joint type. Removing the geometrical constraints from weldments slightly reduces the ultimate load-carrying capacity, while a remarkable reduction is seen in the elongation capacity of the joint. Numerical analysis conducted for non-load carrying X-joints indicates that as the width of the soft zone increases, the effect of the geometric constraint diminishes. Thus, it appears that geometric constraints can, in certain cases, prevent the detrimental effect of strain localization from occurring in the soft regions in at the HAZ. This mechanism seems to increase both the ultimate load-carrying capacity and ultimate elongation of weldments.

Selective area epitaxy of GaAs: the unintuitive role of feature size and pitch

Selective area epitaxy (SAE) provides the path for scalable fabrication of semiconductor nanostructures in a device-compatible configuration. In the current paradigm, SAE is understood as localized epitaxy, and is modelled by combining planar and self-assembled nanowire growth mechanisms. Here we use GaAs SAE as a model system to provide a different perspective. First, we provide evidence of the significant impact of the annealing stage in the calculation of the growth rates. Then, by elucidating the effect of geometrical constraints on the growth of the semiconductor crystal, we demonstrate the role of adatom desorption and resorption beyond the direct-impingement and diffusion-limited regime. Our theoretical model explains the effect of these constraints on the growth, and in particular why the SAE growth rate is highly sensitive to the pattern geometry. Finally, the disagreement of the model at the largest pitch points to non-negligible multiple adatom recycling between patterned features. Overall, our findings point out the importance of considering adatom diffusion, adsorption and desorption dynamics in designing the SAE pattern to create pre-determined nanoscale structures across a wafer. These results are fundamental for the SAE process to become viable in the semiconductor industry.

Elevational range size patterns of vascular plants in the Himalaya contradict Rapoport's rule

Abstract Elevational range size patterns reflect ecological and evolutionary processes, but they are also affected by geometric constraints. The confounding effect of these constraints led to an ongoing controversy about the elevational Rapoport's rule, which postulates a positive association between the range size and elevation, and about the plausibility of the climate variability hypotheses as its causal explanation. Here we used an advanced null modelling approach to disentangle the interacting effects of geometric constraints and species richness gradients on the elevational range size of vascular plants. We collected extensive field data on elevational distribution for 728 vascular plant species occurring in the Ladakh region, Western Himalaya. We supplied these regional data with subcontinental elevational ranges extracted from the literature. Moreover, we used in situ measured temperatures to quantify temperature variability along an elevational gradient to test the climate variability hypothesis. Observed range size patterns were sensitive to methods used to quantify the average range size. Range truncation disproportionately affected regional ranges of low‐elevation species and resulted in spurious support of elevational Rapoport's rule. However, when the confounding effects of domain boundaries and richness gradient were controlled, our null models revealed only slight deviations from the random expectations of elevational range size patterns, contrasting with the prediction of the Rapoport's rule. In line with these findings, seasonal and diurnal temperature variability did not change with elevation. Synthesis. Geometric constraints combined with underlying species richness gradient create range size patterns seemingly supporting Rapoport's elevational rule. However, null models accounting for these effects indicate that the range size of vascular plants in the Himalayas does not increase with elevation. Given the universality of the geometric constraints and species richness gradient, our results suggest that these confounding factors must be controlled when testing Rapoport's rule. The null model approach described here provides an efficient tool to do that.

Effect of geometric constraint caused by nearby particles on the detachment from the particle-laden interface

The bubble-particle detachment interaction is critical to the flotation of coarse (composite) particles which has attracted significant research interest in recent years. It is principally controlled by the capillary forces arising from the deformation of the air–water interface that has been quantified employing the single-particle models. However, these single-particle models can be far away from the detachment in the actual flotation process in which the bubble surface is covered by many attached particles. Here, we investigate the effect of the presence of nearby (attached) particles on the interfacial deformation, thereby influencing the particle detachment from the laden interface. Specifically, the detaching force and the deformed interface shape were simultaneously recorded for a floating sphere at the center of a hexagonal lattice unit that comprised six spheres fixed at an initially planar air–water interface. The 3-dimensional Young–Laplace equation was numerically solved to determine the interface deformation, quantify the detachment process, and validate the model prediction for the detaching force. The results show that the effect of nearby particles called the constraint effect on the interface deformation and the detaching force is significant. The nearby particles confine the interface deformation around the test particle, thereby restricting the movement of the three-phase contact line (TPCL) on the particle surface, leading to smaller changes in the TPCL radius and displacement into the liquid phase during the detachment interaction than those in the absence of nearby particles. However, the change in the contact angle and polar angle of TPCL on the test particle is insignificant. The constraint effect reduces the tenacity which is critical to the stability of bubble-particle aggregates and was not expected. The results of this work provide useful details about the detachment and floatability of particles at the particle-laden interface, which is relevant in many industrial applications, including flotation separation.

Effect of the Geometrical Constraints to the Wenner Four-Point Electrical Resistivity Test of Reinforced Concrete Slabs.

The main objectives of this study are to evaluate the effect of geometrical constraints of plain concrete and reinforced concrete slabs on the Wenner four-point concrete electrical resistivity (ER) test through numerical and experimental investigation and to propose measurement recommendations for laboratory and field specimens. First, a series of numerical simulations was performed using a 3D finite element model to investigate the effects of geometrical constraints (the dimension of concrete slabs, the electrode spacing and configuration, and the distance of the electrode to the edges of concrete slabs) on ER measurements of concrete. Next, a reinforced concrete slab specimen (1500 mm (width) by 1500 mm (length) by 300 mm (thickness)) was used for experimental investigation and validation of the numerical simulation results. Based on the analytical and experimental results, it is concluded that measured ER values of regularly shaped concrete elements are strongly dependent on the distance-to-spacing ratio of ER probes (i.e., distance of the electrode in ER probes to the edges and/or the bottom of the concrete slabs normalized by the electrode spacing). For the plain concrete, it is inferred that the thickness of the concrete member should be at least three times the electrode spacing. In addition, the distance should be more than twice the electrode spacing to make the edge effect almost negligible. It is observed that the findings from the plain concrete are also valid for the reinforced concrete. However, for the reinforced concrete, the ER values are also affected by the presence of reinforcing steel and saturation of concrete, which could cause disruptions in ER measurements.

Geometry effects on mode I brittle fracture in U‐notched specimens

AbstractThe effects of geometrical constraints on the fracture initiation location and the fracture strength are evaluated in U‐notched specimens using theoretical and experimental analyses. It is proven that high geometrical constraints in pure mode I loading of geometrically symmetric U‐notched specimens can result in occurrence of the maximum tangential stress (MTS) at two symmetric points on both sides of the notch bisector line. The experiments also indicated that the fracture takes place from a direction that is not along the notch bisector line. The experimental results are then examined theoretically through a stress‐based brittle fracture criterion. Because the conventional MTS criterion was poor to predict the onset of fracture properly, an attempt is made to use the generalized MTS (GMTS) criterion by considering the higher order terms in the fracture model. It is shown that the GMTS criterion gives very good predictions for experimentally obtained values of crack initiation angle and notch fracture resistance.

Spatial and climatic variables independently drive elevational gradients in ant species richness in the Eastern Himalaya.

Elevational gradients are considered important for understanding causes behind gradients in species richness due to the large variation in climate and habitat within a small spatial extent. Geometric constraints are thought to interact with environmental variables and influence elevational patterns in species richness. However, the geographic setting of most mountain ranges, particularly continuity with low elevation areas may reduce the effect of geometric constraints at lower elevations. In the present study, we test the effects of climatic gradients and continuity with the low elevation plains of the eastern Himalayan mountain range on patterns of species richness. We studied species richness of ants (Hymenoptera: Formicidae) on an elevational gradient between 600m and 2400m in the Eastern Himalaya–part of Himalaya biodiversity hotspot. Ants were sampled in nine elevational bands of 200m with four transects in each band using pitfall and Winkler traps. We used regression models to identify the most important environmental variables that predict species richness and used constrained null models to test the effects of contiguity between the mountain range and plains. We find a monotonic decline in species richness of ants with elevation. Temperature was a more important predictor of species richness than habitat complexity. Geometric constraints model weighted by temperature with a soft lower boundary and hard upper boundary best explained the species richness pattern. This suggests that a combination of climate and geometric constraints drive the elevational species richness patterns of ants.

About Compression Fracture

The paper discusses fracture processes occurring under compressive loads. The processes are considered from two points of view: (i) compression fracture mechanisms and their effect on the strength and fracture resistance of the material, and (ii) the effect of geometric constraints on the stress-strain state and fracture conditions of bodies (natural objects) with cracks and crack-like defects. These are particularly the effects associated with crack surface contact, friction, and loading history. Fracture structures are described which form in the conditions of high-rate compression under extreme loads typical of tectonic processes and deep hydrocarbon production. The structures include crack-like compaction regions in highly porous brittle materials (rocks) formed under compression, which present a new form of quasi-brittle mode I fracture (a compression crack). A method is proposed for estimating the effective strength of compressed bodies with one dimension (thickness) being much smaller than the other two and that have through-thickness variable properties and/or composition. As an example, the ice cover strength with respect to longitudinal compression is considered taking into account a partial loss of the ice bearing capacity. The influence of geometric constraints on the fracture mechanisms in fractured thin bodies is discussed. It is shown that the compression fracture of bodies with elongated through holes (or crack-like defects), whose length is much larger than the body thickness, occurs by a mechanism induced by the overlapping of crack surfaces.

Hydrogen informed Gurson model for hydrogen embrittlement simulation

Hydrogen-microvoid interactions were studied via unit cell analyses with different hydrogen concentrations. The absolute failure strain decreases with hydrogen concentration, but the failure loci were found to follow the same trend dependent only on stress triaxiality, in other words, the effects of geometric constraint and hydrogen on failure are decoupled. Guided by the decoupling principle, a hydrogen informed Gurson model is proposed. This model is the first practical hydrogen embrittlement simulation tool based on the hydrogen enhanced localized plasticity (HELP) mechanism. It introduces only one additional hydrogen related parameter into the Gurson model and is able to capture hydrogen enhanced internal necking failure of microvoids with accuracy; its parameter calibration procedure is straightforward and cost efficient for engineering purpose.

Swimming of ciliates under geometric constraints

The habitat of ciliates is widely spread and encompasses the ocean, soil, and digestive tract of mammals. Some ciliates live on surfaces; however, the effect of geometric constraints on their behavior and habitat is still largely a mystery. In this article, we discuss the behavior of swimming ciliates under various geometric constraints. To gain insight, we first calculated the lubrication forces exerted on a cell under various geometric constraints, where the cell was modeled as a squirmer. We then examined the behavior of cells near a free surface, a rigid wall, and in complex geometries. Our results show that cell behavior was strongly dependent on the geometric constraints and swimmer type; for example, some cells became entrapped, whereas others were able to escape. The mechanism underlying the behavior was well represented by the derived lubrication forces, providing a better understanding of cell behavior in natural and industrial environments. In addition, this article provides a brief overview of the field and the outlook for future research in this area.

Zoogeographic patterns of pelagic oceanic cephalopods along the eastern Pacific Ocean

AbstractAimTo analyse the diversity and distribution of oceanic pelagic cephalopods along the eastern Pacific Ocean assessing the existence of biogeographic structuring, and the role of physical variables in generating geographical patterns. We hypothesized that the control by environmental factors, and the effect of geometric constraints, determine the range size and limits of distribution of oceanic cephalopods along the eastern Pacific Ocean, generating a latitudinal gradient in species richness.LocationEastern Pacific Ocean (60°N – 60°S), from the Gulf of Alaska to the Southern Ocean.MethodsBased on a literature review and >5,000 records obtained from collections, we constructed a presence–absence matrix including 61 latitudinal bands (2° each) along the Eastern Pacific, and estimated species richness and range endpoints at each band. Biogeographic units were determined by means of multivariate analyses. Species richness was compared with null model predictions in order to test for the existence of geometric constraints using the Mid‐Domain Null model. The effects on species richness of environmental variables (temperature, salinity and oxygen) were evaluated separately for surface and depth (0–1,000 m) data, by means of ordinary least squares regression and simultaneous autoregressive models. Rapoport's pattern was assessed by applying the Stevens’ method and the range midpoint method.ResultsSpecies richness was high across the tropics and decreased towards the both poles. We identified five biogeographic units, highlighting two major distribution breaks at 40°N and 42°S. Species richness was strongly related with environmental variables, although the combined variables accounted for a large fraction of the variance between 0 and 1,000 m (R2 = 0.99), while temperature was the best single predictor at the surface (R2 = 0.98). Species richness curves showed a mid‐domain effect (MDE), and the mean latitudinal range was higher in the tropics and at warm latitudes, generating an inverse Rapoport's pattern.Main conclusionsAlong the eastern Pacific Ocean oceanic cephalopods exhibit both a clear biogeographic patterning and an interhemispheric (poleward decreasing) diversity gradient, which appear strongly related with physical factors and external forcing, as well as with a MDE as a seemingly consequence of the naturally bounded domain of the Eastern Pacific.

Effect of geometrical constraints on human pluripotent stem cell nuclei in pluripotency and differentiation.

Mechanical stimuli and geometrical constraints transmitted across the cytoskeleton to the nucleus affect the nuclear morphology and cell function. Human pluripotent stem cells (hPSCs) represent an effective tool for evaluating transitions in nuclear deformability from the pluripotent to differentiated stage, and for deciphering the underlying mechanisms. We report the first study that investigates the nuclear deformability induced by geometrical constraints of hPSCs both in the pluripotent stage and during early germ layer specification. We specifically developed micro-structured surfaces coupled with high-content imaging analysis algorithms to quantitatively characterize nuclear deformability. Our results show that hPSCs possess high nuclear deformability, which does not alter pluripotency. We observed nuclear deformability transition along early germ layer specification: during early ectoderm differentiation nuclear deformability is strongly reduced, during early endoderm differentiation nuclei keep a deformed shape and during early mesoderm specification they show an intermediate behaviour. Different mRNA expressions between hPSCs differentiated on flat and micro-structured surfaces have been observed along early mesoderm and early endoderm specification. In order to better understand the mechanisms of the nuclear deformability transition observed during early ectoderm differentiation, we also employed cytoskeletal and nuclear protein inhibitors to evaluate their role in determining the nuclear shape. Actin and nesprin are essential for maintaining deformed nuclei, while lamin A/C and intermediate filaments confer rigidity to the nucleus. This study suggests that nuclear deformability is highly regulated during differentiation.

Patterns of an elevational gradient affecting moths across the South Korean mountains: effects of geometric constraints, plants, and climate

AbstractWe investigated elevational richness patterns of three moth groups (Erebidae, Geometridae, and Noctuidae) along four elevational gradients located on one northern and three southern mountains in South Korea, as well as the effects of plants and climatic factors on the diversity patterns of moths. Moths were collected with an ultraviolet light trap at 32 sites from May through October, 2013. Plant species richness and mean temperatures for January and June were acquired. Observed and estimated moth species richness was calculated and the diversity patterns with null models were compared. Species richness along four elevational gradients peaked at mid‐elevations, whereas deviations occurred at elevations below mid‐peak in the southern mountains and elevations higher than mid‐peak on the northern mountain. Species richness curves of three moth groups also peaked at mid‐elevations throughout South Korea. However, the species richness curves for Erebidae were positively skewed, indicating that a preference for lowlands, whereas curves of the Geometridae were negatively skewed, indicating a preference for highlands. The mid‐peak diversity pattern between plants and moths on the Korean mountains showed an elevational breadth that overlapped between 800 and 900 m. Multiple regression analysis revealed that plant species richness and January mean temperature significantly influenced moth species richness and abundance. The rapid increase in mean annual temperature in the Korean peninsula and the unimodal elevational gradients of moths across the country suggest that an uphill shift in peak optimum elevation and changes in the highest peak of the curve will occur in the future.

Suckling strategies in the pig: The Göttingen minipig as a model

Göttingen minipig (GMP) has gained importance as model animal in human medicine. However, little is known about the suckling behaviour of GMP. Suckling is considered as a fundamental behavioural trait in mammals, most important for development and survival of the individual. Understanding its development and changes due to artificial selection is important when planning selection on reproductive traits in sows. GMP is a highly valuable model for studying the suckling behaviour in the pig, because its key features are intermediate between commercial breeds (CB) and wild boar (WB), namely, similar teat number as CB, similar litter size as WB and balanced muscularity of extremities. We compared the suckling behaviour of GMP and CB based on measures of suckling stability (the probability of consecutive sucklings on the same suckling position), suckling ranges (number of teat pairs in the range of the outermost teat pairs that piglets occupied) and piglets’ distribution along the udder by use of the MDE-model (effect of geometric constraints, normally expressed as a hump-shaped distribution of organisms). We also incorporated published date on suckling preferences of WB piglets. Our study revealed alterations of suckling behaviour in piglets, wherein GMP showed intermediate suckling strategies (i.e. suckling ranges). However, there appeared to be a certain degree of behavioural conservatism. Domestic piglets maintained the tendency to prefer abdominal (middle) teats, which are anatomically posterior in WB and preferred by wild piglets. It can be suggested, that this general tendency seen in domestic piglets (GMP and CB), is not generated by geometric constraints (mid-domain effect), but appears to originate from the wild ancestor. Results of the present study suggest that the selection of CB for increasing litter size and higher number of teats might have led to imbalances between suckling behaviour, teat number and udder space availability.

Two-dimensional decaying turbulence in confined geometries

Several interesting phenomena have been observed simulating two-dimensional decaying turbulence in bounded domains. In this paper, an overview is given about our observations obtained by simulating freely decaying turbulence in different regular polygon shaped containers with no-slip walls. For these simulations the lattice Boltzmann method has been used as a numerical approach. The initial Reynolds number based on the container dimension was in the order of 10,000. The initial condition was the same in each simulation, therefore, we were able to compare the effect of geometrical constraints on the evolution of relevant physical quantities such as the kinetic energy and the enstrophy.

Effects of Geometric Constraint on Solidification Microstructural Development of Peritectic TiAl Alloys

Directional solidification of binary peritectic TiAl alloys through preforms with straight channels with spacing on the order of the dendritic tip radius were simulated using a modified solid-liquid interface tracking model. Interruption of the steady-state growth of the primary β-phase by constraint of solutal diffusion within very thin sections of ceramic preforms can lead to solidification conditions favorable for the nucleation and continued growth of the peritectic α-phase even after the growth front has exited the preform.

Two-Dimensonal Decaying Turbulence in Different Shaped Containers

Several interesting phenomena have been observed simulating two-dimensional decaying turbulence in bounded domains. In this paper an overview is given about our observations obtained by simulating freely decaying turbulence in different regular polygon shaped containers with no-slip walls. For these simulations the lattice Boltzmann method has been used as a numerical approach. The initial Reynolds number based on the container dimension was in the order of 1000. The initial condition was the same in each simulation, therefore, we were able to compare the effect of geometrical constraints on the evolution of relevant physical quantities such as the kinetic energy and the enstrophy.

A Particle Image Velocimetry-Based Investigation of the Flow Field in an Oblique Jet Impingement Configuration

Impinging jets have become an indispensable measure for cooling applications in gas turbine technology. The present study seeks to explore the flow field dynamics inside an enigine-relevant cooling passage of trapezoidal cross-section. The investigated geometry produces a highly complex flow field which was investigated employing particle image velocimetry (PIV). The experiments were accompanied by numerical simulations solving the Reynolds-averaged Navier–Stokes (RANS) equations with FLUENT using the low-Re k-ω-SST (shear stress transport) turbulence model. Additionally, time-resolved pressure measurements were performed utilizing Kulite pressure transducers. The spectral analysis of the transient pressure signal in conjunction with a proper orthogonal decomposition (POD) analysis of the PIV data allows for a detailed insight into the effects of geometric constraints on the fluid dynamic processes inside the geometry. The results are presented for a jet Reynolds number of 45,000 and display a qualitatively fair agreement between the experiments and numerical simulations. Nevertheless, the simulations predict flow features in particular regions of the geometry that are absent in the experiments. Despite the lack of conspicuous high energy modes, the flow was well suited for a POD analysis. Depending on the considered PIV plane, it could be shown that up to 25% of the flow field's total turbulent energy is contained in the first ten POD modes. Additionally, using the first 20 to 60 POD modes sufficed to reconstruct the flow fields with its governing features.