This work presents a hybrid shear‐flexible beam‐element, capable of capturing arbitrarily large inelastic displacements and rotations of planar frame structures with just one element per member. Following Reissner's geometrically exact theory, the finite element problem is herein formulated within nonlinear programming principles, where the total potential energy is treated as the objective function and the exact strain‐displacement relations are imposed as kinematic constraints. The approximation of integral expressions is conducted by an appropriate quadrature, and by introducing Lagrange multipliers, the Lagrangian of the minimization program is formed and solutions are sought based on the satisfaction of necessary optimality conditions. In addition to displacement degrees of freedom at the two element edge nodes, strain measures of the centroid act as unknown variables at the quadrature points, while only the curvature field is interpolated, to enforce compatibility throughout the element. Inelastic calculations are carried out by numerical integration of the material stress‐strain law at the cross‐section level. The locking‐free behavior of the element is presented and discussed, and its overall performance is demonstrated on a set of well‐known numerical examples. Results are compared with analytical solutions, where available, and outcomes based on flexibility‐based beam elements and quadrilateral elements, verifying the efficiency of the formulation.
Extracting quadrilateral layouts from surface triangulations is an important step in texture mapping, semi-structured quadrilateral meshing for traditional analysis and spline reconstruction for isogeometric analysis. Current methods struggle to yield high-quality layouts with appropriate connectivity between singular nodes (known as “extraordinary points” for spline representations) without resorting to either mixed-integer optimization or manual constraint prescription. The first of these is computationally expensive and comes with no guarantees, while the second is laborious and error-prone. In this work, we rigorously characterize curves in a quadrilateral layout up to homotopy type and use this information to quickly define high-quality connectivity constraints between singular nodes. The mathematical theory is accompanied by appropriate computational algorithms. The efficacy of the proposed method is demonstrated in generating quadrilateral layouts on the United States Army’s DEVCOM Generic Hull vehicle and parts of a bilinear quadrilateral finite element mesh (with some linear triangles) of a 1996 Dodge Neon.
more » « less- NSF-PAR ID:
- 10385306
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Journal of Mechanics
- Volume:
- 38
- ISSN:
- 1811-8216
- Page Range / eLocation ID:
- p. 128-155
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract The analysis of time‐varying activity and connectivity patterns (i.e., the chronnectome) using resting‐state magnetic resonance imaging has become an important part of ongoing neuroscience discussions. The majority of previous work has focused on variations of temporal coupling among fixed spatial nodes or transition of the dominant activity/connectivity pattern over time. Here, we introduce an approach to capture spatial dynamics within functional domains (FDs), as well as temporal dynamics within and between FDs. The approach models the brain as a hierarchical functional architecture with different levels of granularity, where lower levels have higher functional homogeneity and less dynamic behavior and higher levels have less homogeneity and more dynamic behavior. First, a high‐order spatial independent component analysis is used to approximate functional units. A functional unit is a pattern of regions with very similar functional activity over time. Next, functional units are used to construct FDs. Finally, functional modules (FMs) are calculated from FDs, providing an overall view of brain dynamics. Results highlight the spatial fluidity within FDs, including a broad spectrum of changes in regional associations, from strong coupling to complete decoupling. Moreover, FMs capture the dynamic interplay between FDs. Patients with schizophrenia show transient reductions in functional activity and state connectivity across several FDs, particularly the subcortical domain. Activity and connectivity differences convey unique information in many cases (e.g., the default mode) highlighting their complementarity information. The proposed hierarchical model to capture FD spatiotemporal variations provides new insight into the macroscale chronnectome and identifies changes hidden from existing approaches.
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Abstract This work reports a three‐dimensional (3D) radio frequency L−C filter network enabled by a CMOS‐compatible two‐dimensional (2D) fabrication approach, which combines inductive (L) and capacitive (C) self‐rolled‐up membrane (S‐RuM) components monolithically into a single L−C network structure, thereby greatly reducing the on‐chip area footprint. The individual L−C elements are fabricated in‐plane using standard semiconductor processing techniques, and subsequently triggered by the built‐in stress to self‐assemble and roll into cylindrical air‐core architectures. By designing the planar structure geometry and constituent layer properties to achieve a specific number of turns with a desired inner diameter when the device is rolled up, the electrical characteristics can be engineered. The network layouts of the L and C components are also reconfigurable by selecting appropriate input, output, and ground contact routing topographies. The devices demonstrated here operate over the range of ≈1−10 GHz. Their area and volume footprints are ≈0.09 mm2and ≈0.01 mm3, respectively, which are ≈10× smaller than most of the comparable conventional filter designs. These S‐RuM‐enabled 3D microtubular L−C filter networks represent significant advancement for miniaturization and integration of passive electronic components for applications in mobile connectivity and other frequency range.
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In social networks, a node’s position is, in and of itself, a form of social capital. Better-positioned members not only benefit from (faster) access to diverse information, but innately have more potential influence on information spread. Structural biases often arise from network formation, and can lead to significant disparities in information access based on position. Further, processes such as link recommendation can exacerbate this inequality by relying on network structure to augment connectivity. In this paper, we argue that one can understand and quantify this social capital through the lens of information flow in the network. In contrast to prior work, we consider the setting where all nodes may be sources of distinct information, and a node’s (dis)advantage takes into account its ability to access all information available on the network, not just that from a single source. We introduce three new measures of advantage (broadcast, influence, and control), which are quantified in terms of position in the network using access signatures – vectors that represent a node’s ability to share information with each other node in the network. We then consider the problem of improving equity by making interventions to increase the access of the least-advantaged nodes. Since all nodes are already sources of information in our model, we argue that edge augmentation is most appropriate for mitigating bias in the network structure, and frame a budgeted intervention problem for maximizing broadcast (minimum pairwise access) over the network. Finally, we propose heuristic strategies for selecting edge augmentations and empirically evaluate their performance on a corpus of real-world social networks. We demonstrate that a small number of interventions can not only significantly increase the broadcast measure of access for the least-advantaged nodes (over 5 times more than random), but also simultaneously improve the minimum influence. Additional analysis shows that edge augmentations targeted at improving minimum pairwise access can also dramatically shrink the gap in advantage between nodes (over ) and reduce disparities between their access signatures.more » « less
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Background A lack of in utero imaging data hampers our understanding of the connections in the human fetal brain. Generalizing observations from postmortem subjects and premature newborns is inaccurate due to technical and biological differences.
Purpose To evaluate changes in fetal brain structural connectivity between 23 and 35 weeks postconceptional age using a spatiotemporal atlas of diffusion tensor imaging (DTI).
Study Type Retrospective.
Population Publicly available diffusion atlases, based on 60 healthy women (age 18–45 years) with normal prenatal care, from 23 and 35 weeks of gestation.
Field Strength/Sequence 3.0 Tesla/DTI acquired with diffusion‐weighted echo planar imaging (EPI).
Assessment We performed whole‐brain fiber tractography from DTI images. The cortical plate of each diffusion atlas was segmented and parcellated into 78 regions derived from the Edinburgh Neonatal Atlas (ENA33). Connectivity matrices were computed, representing normalized fiber connections between nodes. We examined the relationship between global efficiency (GE), local efficiency (LE), small‐worldness (SW), nodal efficiency (NE), and betweenness centrality (BC) with gestational age (GA) and with laterality.
Statistical Tests Linear regression was used to analyze changes in GE, LE, NE, and BC throughout gestation, and to assess changes in laterality. The
t ‐tests were used to assess SW.P ‐values were corrected using Holm‐Bonferroni method. A correctedP ‐value <0.05 was considered statistically significant.Results Network analysis revealed a significant weekly increase in GE (5.83%/week, 95% CI 4.32–7.37), LE (5.43%/week, 95% CI 3.63–7.25), and presence of SW across GA. No significant hemisphere differences were found in GE (
P = 0.971) or LE (P = 0.458). Increasing GA was significantly associated with increasing NE in 41 nodes, increasing BC in 3 nodes, and decreasing BC in 2 nodes.Data Conclusion Extensive network development and refinement occur in the second and third trimesters, marked by a rapid increase in global integration and local segregation.
Level of Evidence 3
Technical Efficacy Stage 2
