ENG: Mechanical Engineering: Scholarly Papers

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How retroactivity affects the behavior of incoherent feedforward loops
(Elsevier BV, 2020-12-18) Wang, Junmin; Belta, Calin; Isaacson, Samuel A.
An incoherent feedforward loop (IFFL) is a network motif known for its ability to accelerate responses and generate pulses. It remains an open question to understand the behavior of IFFLs in contexts with high levels of retroactivity, where an upstream transcription factor binds to numerous downstream binding sites. Here we study the behavior of IFFLs by simulating and comparing ODE models with different levels of retroactivity. We find that increasing retroactivity in an IFFL can increase, decrease, or keep the network's response time and pulse amplitude constant. This suggests that increasing retroactivity, traditionally considered an impediment to designing robust synthetic systems, could be exploited to improve the performance of IFFLs. In contrast, we find that increasing retroactivity in a negative autoregulated circuit can only slow the response. The ability of an IFFL to flexibly handle retroactivity may have contributed to its significant abundance in both bacterial and eukaryotic regulatory networks.
On the three-dimensional correlation between myofibroblast shape and contraction
(ASME International, 2021-09-01) Khang, Alex; Lejeune, Emma; Abbaspour, Ali; Howsmon, Daniel P.; Sacks, Michael S.
Myofibroblasts are responsible for wound healing and tissue repair across all organ systems. In periods of growth and disease, myofibroblasts can undergo a phenotypic transition characterized by an increase in extracellular matrix (ECM) deposition rate, changes in various protein expression (e.g., alpha-smooth muscle actin (αSMA)), and elevated contractility. Cell shape is known to correlate closely with stress-fiber geometry and function and is thus a critical feature of cell biophysical state. However, the relationship between myofibroblast shape and contraction is complex, even as well in regards to steady-state contractile level (basal tonus). At present, the relationship between myofibroblast shape and basal tonus in three-dimensional (3D) environments is poorly understood. Herein, we utilize the aortic valve interstitial cell (AVIC) as a representative myofibroblast to investigate the relationship between basal tonus and overall cell shape. AVICs were embedded within 3D poly(ethylene glycol) (PEG) hydrogels containing degradable peptide crosslinkers, adhesive peptide sequences, and submicron fluorescent microspheres to track the local displacement field. We then developed a methodology to evaluate the correlation between overall AVIC shape and basal tonus induced contraction. We computed a volume averaged stretch tensor ⟨U⟩ for the volume occupied by the AVIC, which had three distinct eigenvalues (λ1,2,3=1.08,0.99, and 0.89), suggesting that AVIC shape is a result of anisotropic contraction. Furthermore, the direction of maximum contraction correlated closely with the longest axis of a bounding ellipsoid enclosing the AVIC. As gel-imbedded AVICs are known to be in a stable state by 3 days of incubation used herein, this finding suggests that the overall quiescent AVIC shape is driven by the underlying stress-fiber directional structure and potentially contraction level.
Learning mechanically driven emergent behavior with message passing neural networks
(Elsevier BV, 2022-10) Prachaseree, Peerasait; Lejeune, Emma
Towards out of distribution generalization for problems in mechanics
(Elsevier BV, 2022-10) Yuan, Lingxiao; Park, Harold S.; Lejeune, Emma
Enhancing mechanical metamodels with a generative model-based augmented training dataset
(ASME International, 2022-12-01) Kobeissi, Hiba; Mohammadzadeh, Saeed; Lejeune, Emma
Modeling biological soft tissue is complex in part due to material heterogeneity. Microstructural patterns, which play a major role in defining the mechanical behavior of these tissues, are both challenging to characterize and difficult to simulate. Recently, machine learning (ML)-based methods to predict the mechanical behavior of heterogeneous materials have made it possible to more thoroughly explore the massive input parameter space associated with heterogeneous blocks of material. Specifically, we can train ML models to closely approximate computationally expensive heterogeneous material simulations where the ML model is trained on datasets of simulations with relevant spatial heterogeneity. However, when it comes to applying these techniques to tissue, there is a major limitation: the number of useful examples available to characterize the input domain under study is often limited. In this work, we investigate the efficacy of both ML-based generative models and procedural methods as tools for augmenting limited input pattern datasets. We find that a style-based generative adversarial network with an adaptive discriminator augmentation mechanism is able to successfully leverage just 1000 example patterns to create authentic generated patterns. In addition, we find that diverse generated patterns with adequate resemblance to real patterns can be used as inputs to finite element simulations to meaningfully augment the training dataset. To enable this methodological contribution, we have created an open access finite element analysis simulation dataset based on Cahn-Hilliard patterns. We anticipate that future researchers will be able to leverage this dataset and build on the work presented here.
The cusp plasma imaging detector (CuPID) cubesat observatory: instrumentation
(AIP Publishing, 2022-06-01) Atz, Emil A.; Walsh, Brian; O'Brien, Connor; Collier, Michael; Berman, Ariel; Billingsley, Lisa; Blake, J. Bernard; Broll, Jeffrey M.; Chornay, Dennis; Crain, William; Cragwell, Thompson; Dobson, Norman; Kujawski, Joseph; Kuntz, Kip; Naldoza, Van; Nutter, Rousseau; Porter, F. Scott; Sibeck, David; Simms, Kenneth; Thomas, Nicholas; Turner, Drew; Weatherwax, Allan; Yousuff, Ajmal; Zosuls, Aleks
The Cusp Plasma Imaging Detector (CuPID) CubeSat observatory is a 6U CubeSat designed to observe solar wind charge exchange in magnetospheric cusps to test competing theories of magnetic reconnection at the Earth's magnetopause. The CuPID is equipped with three instruments, namely, a wide field-of-view (4.6° × 4.6°) soft x-ray telescope, a micro-dosimeter suite, and an engineering magnetometer optimized for the science operation. The instrument suite has been tested and calibrated in relevant environments, demonstrating successful design. The testing and calibration of these instruments produced metrics and coefficients that will be used to create the CuPID mission's data product.
Plasma Imaging, LOcal Measurement, and Tomographic experiment (PILOT): a mission concept for transformational multi-scale observations of mass and energy flow dynamics in Earth’s magnetosphere
(Frontiers Media SA, 2022-06-17) Malaspina, David; Ergun, Robert; Goldstein, Jerry; Spittler, Constance; Andersson, Laila; Borovsky, Joseph; Chu, Xiangning; De Moudt, Lauren; Gallagher, Dennis; Jordanova, Vania; Lejosne, Solène; Link, Jason; Maruyama, Naomi; Parker, Jeffery; Thaller, Scott; Unruh, Bryce; Walsh, Brian
We currently do not understand the fundamental physical processes that govern mass and energy flow through the Earth’s magnetosphere. Knowledge of these processes is critical to understanding the mass loss rate of Earth’s atmosphere, as well as for determining the role that a planetary magnetic field plays in atmospheric retention, and therefore habitability, for Earth-like planets beyond the solar system. Mass and energy flow processes are challenging to determine at Earth in part because Earth’s planetary magnetic field creates a complex “system of systems” composed of interdependent plasma populations and overlapping spatial regions that perpetually exchange mass and energy across a broad range of temporal and spatial scales. Further, the primary mass carrier in the magnetosphere is cold plasma (as cold as ∼0.1 eV), which is invisible to many space-borne instruments that operate in the inner magnetosphere. The Plasma Imaging LOcal and Tomographic experiment (PILOT) mission concept, described here, provides the transformational multi-scale observations required to answer fundamental open questions about mass and energy flow dynamics in the Earth’s magnetosphere. PILOT uses a constellation of spacecraft to make radio tomographic, remote sensing, and in-situ measurements simultaneously, fully capturing cold plasma mass dynamics and its impact on magnetospheric systems over an unprecedented range of spatial and temporal scales. This article details the scientific motivation for the PILOT mission concept as well as a potential mission implementation.
MMS observations of storm‐time magnetopause boundary layers in the vicinity of the Southern cusp
(American Geophysical Union (AGU), 2022-12-28) Burkholder, Brandon L.; Chen, Li‐Jen; Fuselier, Stephen; Gershman, Daniel; Schiff, Conrad; Shuster, Jason; Zou, Ying; Walsh, Brian M.; Reiff, Patricia; Petrinec, Steve; Sciola, Anthony
The spatial extent of magnetopause magnetic reconnection from in situ THEMIS measurements
(American Geophysical Union (AGU), 2022-12) Atz, Emil A.; Walsh, Brian M.; Broll, Jeffrey M.; Zou, Ying
An optimal transmission line switching and bus splitting heuristic incorporating AC and N-1 contingency constraints
(Elsevier BV, 2021-12) Heidarifar, Majid; Andrianesis, Panagiotis; Ruiz, Pablo; Caramanis, Michael C.; Paschalidis, Ioannis Ch.
Optimal transmission line switching and/or bus splitting is shown to contribute in relieving congestion and reducing the operation cost by rerouting power flows throughout the network. Although bus splitting may be as powerful as line switching in congestion mitigation and is typically considered a smaller disturbance compared with line switching, it has received less attention in the literature in part due to the more complicated node-breaker modeling requirement. In this paper, an optimal transmission line switching and bus splitting heuristic is presented to minimize the operation cost while respecting AC and N-1 contingency constraints. We present a two-level solution method where switching decisions are made in the upper level problem formulated as a mixed integer second order cone programming master problem, while the resulting network topology is checked against AC and N-1 contingency constraints in lower level subproblems. Line switching and bus splitting are modeled as switching actions assuming double-bus double-breaker substation arrangements where all elements at a substation, including generators, loads, lines and shunt elements, are given switches to connect to either of the busbars if the respective substation is split. We also introduce additional constraints to model a breaker-and-a-half substation scheme. Furthermore, a pre-screening step is presented to limit the search space of the problem, thus accelerating the solution process. We demonstrate the application of the proposed method on IEEE standard test systems.
Probability calculations within stochastic electrodynamics
(Frontiers Media SA, 2021-04-12) Cole, Daniel C.
Several stochastic situations in stochastic electrodynamics (SED) are analytically calculated from first principles. These situations include probability density functions, as well as correlation functions at multiple points of time and space, for the zero-point (ZP) electromagnetic fields, as well as for ZP plus Planckian (ZPP) electromagnetic fields. More lengthy analytical calculations are indicated, using similar methods, for the simple harmonic electric dipole oscillator bathed in ZP as well as ZPP electromagnetic fields. The method presented here makes an interesting contrast to Feynman’s path integral approach in quantum electrodynamics (QED). The present SED approach directly entails probabilities, while the QED approach involves summing weighted paths for the wave function.
Trajectory optimization for thermally-actuated soft planar robot limbs
(IEEE, 2022-04-04) Wertz, Anthony; Sabelhaus, Andrew P.; Majidi, Carmel
Practical use of robotic manipulators made from soft materials requires generating and executing complex motions. We present the first approach for generating trajectories of a thermally-actuated soft robotic manipulator. Based on simplified approximations of the soft arm and its antagonistic shape-memory alloy actuator coils, we justify a dynamics model of a discretized rigid manipulator with joint torques proportional to wire temperature. Then, we propose a method to calibrate this model from experimental data and demonstrate that the simulation aligns well with a hardware test. Finally, we use a direct collocation optimization with the robot's nonlinear dynamics to generate feasible state-input trajectories from a desired reference. Three experiments validate our approach for a single-segment robot in hardware: first using a hand-derived reference trajectory, then with two teach-and-repeat tests. The results show promise for both open-loop motion generation as well as for future applications with feedback.
Power markets with information-aware self-scheduling electric vehicles
(Springer Science and Business Media LLC, 2020-12) Yanikara, F. Selin; Andrianesis, Panagiotis; Caramanis, Michael
We consider multi-period (24-h day-ahead) multi-commodity (energy and regulation reserves) decentralized electricity transmission and distribution (T&D) market designs. Whereas conventional centralized generators with uniform price quantity offers are scheduled by a transmission system operator, low-voltage network-connected distributed energy resources (DERs) with complex preferences and requirements, such as electric vehicles (EVs), are allowed to self-schedule adapting to spatiotemporal marginal cost-based prices. We model the salient characteristics of interconnected T&D networks, and we consider self-scheduling DER responses under alternative distribution network information-aware or information-unaware market designs. Moreover, we consider a single (EV load aggregator) network information-aware scheduler market design. Our contribution is the characterization and comparative analysis—analytic as well as numerical—of equilibria, using game-theoretical approaches to prove existence and uniqueness, and the investigation of the role of information on self-scheduling and EV aggregator coordinated EV scheduling. Finally, we derive conclusions on the impact to social welfare and distributional equity of information-aware/information-unaware self-scheduling as well as single EV aggregator scheduling and implications that are relevant to market design and policy considerations.
Computation of Convex Hull prices in electricity markets with non-convexities using Dantzig-Wolfe decomposition
(2020) Andrianesis, Panagiotis; Caramanis, Michael C.; Hogan, William W.
The presence of non-convexities in electricity markets has been an active research area for about two decades. The — inevitable under current marginal cost pricing — problem of guaranteeing that no market participant incurs losses in the day-ahead market is addressed in current practice through make-whole payments a.k.a. uplift. Alternative pricing rules have been studied to deal with this problem. Among them, Convex Hull (CH) prices associated with minimum uplift have attracted significant attention. Several US Independent System Operators (ISOs) have considered CH prices but resorted to approximations, mainly because determining exact CH prices is computationally challenging, while providing little intuition about the price formation rationale. In this paper, we describe the CH price estimation problem by relying on Dantzig-Wolfe decomposition and Column Generation, as a tractable, highly paralellizable, and exact method — i.e., yielding exact, not approximate, CH prices — with guaranteed finite convergence. Moreover, the approach provides intuition on the underlying price formation rationale. A test bed of stylized examples provide an exposition of the intuition in the CH price formation. In addition, a realistic ISO dataset is used to support scalability and validate the proof-of-concept.
A Riemannian optimization approach to the radial distribution network load flow problem
(Elsevier BV, 2021-07) Heidarifar, Majid; Andrianesis, Panagiotis; Caramanis, Michael
The Load Flow (LF) equations in power networks are the foundation of several applications on active and reactive power flow control, distributed and real-time control and optimization. In this paper, we formulate the LF problem in radial electricity distribution networks as an unconstrained Riemannian optimization problem, consisting of two manifolds, and we consider alternative retractions and initialization options. We introduce a Riemannian approximate Newton method tailored to the LF problem, as an exact solution method guaranteeing monotonic descent and local superlinear convergence rate. Extensive numerical comparisons on several test networks illustrate that the proposed method outperforms standard Riemannian optimization methods (Gradient Descent, Newton’s), and achieves comparable performance with the traditional Newton–Raphson method (in Euclidean coordinates), albeit besting it by a guarantee to convergence. We also consider an approximate LF solution obtained by the first iteration of the proposed method, and we show that it significantly outperforms other approximants in the LF literature. Lastly, we derive an interesting analogy with the well-known Backward–Forward Sweep (BFS) method showing that BFS iterations move on the power flow manifold, and highlighting the advantage of our method in converging under high constant impedance loading conditions, whereas BFS may diverge.
Optimal distributed energy resource coordination: a decomposition method based on distribution locational marginal costs
(Institute of Electrical and Electronics Engineers (IEEE), 2022-03) Andrianesis, Panagiotis; Caramanis, Michael; Li, Na
In this paper, we consider the day-ahead operational planning problem of a radial distribution network hosting Distributed Energy Resources (DERs) including rooftop solar and storage-like loads, such as electric vehicles. We present a novel decomposition method that is based on a centralized AC Optimal Power Flow (AC OPF) problem interacting iteratively with self-dispatching DER problems adapting to real and reactive power Distribution Locational Marginal Costs. We illustrate the applicability and tractability of the proposed method on an actual distribution feeder, while modeling the full complexity of spatiotemporal DER capabilities and preferences, and accounting for instances of non-exact AC OPF convex relaxations. We show that the proposed method achieves optimal Grid-DER coordination, by successively improving feasible AC OPF solutions, and discovers spatiotemporally varying marginal costs in distribution networks that are key to optimal DER scheduling by modeling losses, ampacity and voltage congestion, and, most importantly, dynamic asset degradation.
Emergence of structure in columns of grains and elastic loops
(2021-09-07) Guerra, Arman; Holmes, Douglas P.
It is possible to build free-standing, load-bearing structures using only rocks and loops of elastic material. We investigate how these structures emerge, and find that the necessary maximum loop spacing (the critical spacing) is a function of the frictional properties of the grains and the elasticity of the confining material. We derive a model to understand both of these relationships, which depends on a simplification of the behavior of the grains at the edge of a structure. We find that higher friction leads to larger stable grain-grain and grain-loop contact angles resulting in a simple function for the frictional critical spacing, which depends linearly on friction to first order. On the other hand, a higher bending rigidity enables the loops to better contain the hydrostatic pressure of the grains, which we understand using a hydroelastic scale. These findings will illuminate the stabilization of dirt by plant roots, and potentially enable the construction of simple adhesion-less structures using only granular material and fiber.
Elastic instabilities govern the morphogenesis of the optic cup
(2021-09-24) Lee, Jeong-Ho; Park, Harold S.; Holmes, Douglas P.
Because the normal operation of the eye depends on sensitive morphogenetic processes for its eventual shape, developmental flaws can lead to wide-ranging ocular defects. However, the physical processes and mechanisms governing ocular morphogenesis are not well understood. Here, using analytical theory and nonlinear shell finite-element simulations, we show, for optic vesicles experiencing matrix-constrained growth, that elastic instabilities govern the optic cup morphogenesis. By capturing the stress amplification owing to mass increase during growth, we show that the morphogenesis is driven by two elastic instabilities analogous to the snap through in spherical shells, where the second instability is sensitive to the optic cup geometry. In particular, if the optic vesicle is too slender, it will buckle and break axisymmetry, thus, preventing normal development. Our results shed light on the morphogenetic mechanisms governing the formation of a functional biological system and the role of elastic instabilities in the shape selection of soft biological structures.
Delayed buckling of spherical shells due to viscoelastic knockdown of the critical load
(The Royal Society, 2021-09) Stein-Montalvo, Lucia; Holmes, Douglas P.; Coupier, Gwennou
We performed dynamic pressure buckling experiments on defect-seeded spherical shells made of a common silicone elastomer. Unlike in quasi-static experiments, shells buckled at ostensibly subcritical pressures, i.e. below the experimentally determined critical load at which buckling occurs elastically, often following a significant delay period from the time of load application. While emphasizing the close connections to elastic shell buckling, we rely on viscoelasticity to explain our observations. In particular, we demonstrate that the lower critical load may be determined from the material properties, which is rationalized by a simple analogy to elastic spherical shell buckling. We then introduce a model centred on empirical quantities to show that viscoelastic creep deformation lowers the critical load in the same predictable, quantifiable way that a growing defect would in an elastic shell. This allows us to capture how both the deflection at instability and the time delay depend on the applied pressure, material properties and defect geometry. These quantities are straightforward to measure in experiments. Thus, our work not only provides intuition for viscoelastic behaviour from an elastic shell buckling perspective but also offers an accessible pathway to introduce tunable, time-controlled actuation to existing mechanical actuators, e.g. pneumatic grippers.
Efficient snap-through of spherical caps by applying a localized curvature stimulus
(2022-01-13) Stein-Montalvo, Lucia; Lee, Jeong-Ho; Yang, Yi; Landesberg, Melanie; Park, Harold S.; Holmes, Douglas P.
In bistable actuators and other engineered devices, a homogeneous stimulus (e.g., mechanical, chemical, thermal, or magnetic) is often applied to an entire shell to initiate a snap-through instability. In this work, we demonstrate that restricting the active area to the shell boundary allows for a large reduction in its size, thereby decreasing the energy input required to actuate the shell. To do so, we combine theory with 1D finite element simulations of spherical caps with a non-homogeneous distribution of stimulus-responsive material. We rely on the effective curvature stimulus, i.e., the natural curvature induced by the non-mechanical stimulus, which ensures that our results are entirely stimulus-agnostic. To validate our numerics and demonstrate this generality, we also perform two sets of experiments, wherein we use residual swelling of bilayer silicone elastomers-a process that mimics differential growth-as well as a magneto-elastomer to induce curvatures that cause snap-through. Our results elucidate the underlying mechanics, offering an intuitive route to optimal design for efficient snap-through.

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