3D Force Research Articles

A Soft 3-dimensional Force Sensor For Measuring Head Impacts In Football Helmets

Three-dimensional (3D) force data from head impacts in football is important for understanding traumatic brain injuries (TBIs). Football helmets have not yet been instrumented with true 3D force sensors compelling the development of soft 3D force sensors that could be seamlessly integrated into existing helmet padding. PURPOSE: To develop and determine the accuracy and reliability of an in-helmet soft 3D force sensor in comparison to force plate data. METHODS: A force sensor was fabricated by embedding magnetic powder within a cylindrical rubber cushion which was affixed to a magnetometer. Prior to integration in a helmet, known compressive forces were slowly applied to the sensor to assess performance in a controlled setting. The sensor was then inserted and fixed into a cavity created on the forehead pad of a football helmet. The sensor was controlled by a microcontroller, which communicated data wirelessly to a nearby computer at a sampling rate of 29 Hz. Thirteen trials were performed in which the helmet, while being worn, impacted a vertically mounted 3D force plate from different angles. The reliability of the helmet sensor in relation to the force plate was assessed by the interclass correlation coefficient (ICC) of the peak force measured in the primary axis of the impact (i.e. z-axis for a straight impact, x-axis for an angled impact) from the helmet sensor and the force plate. RESULTS: The magnetometer’s measurements of magnetic field strength exhibited a strong second order correlation to the force applied to the sensor (r2 = 0.995). For the helmet-force plate impacts, the force vectors were clearly observable for all trials by analyzing the force-time curves of each of the three axes of the helmet sensor. The helmet sensor displayed excellent agreement with the force plate for peak force (ICC = 0.981). In addition, peak forces for 8 of 13 impacts exhibited moderately low error (1-13%) when compared to the force plate, but the rest of the impacts had larger errors (25-51%). CONCLUSIONS: The sensor performed excellent in controlled studies and had high agreement with the force plate according to the ICC. Most impacts were accurately measured, but a higher sampling rate is needed for consistent and accurate quantification of impacts that contain higher frequency components.

Three-dimensional imaging of electron spin resonance-magnetic resonance force microscopy at room temperature

In this study, we demonstrated the three-dimensional (3D) imaging by magnetic resonance force microscopy (MRFM) based on electron spin resonance (ESR) measurements at room temperature. For a microsample containing radicals, the 3D force distribution was obtained using a custom-made Si nanowire and a permanent magnetic particle. Calculation using precise values of the magnetic field distribution is required to define an accurate response function for the 3D deconvolution processing of the spin density distribution. A symmetric resonance magnetic field produces good periodic force maps using a spherical micromagnet, which simplifies the deconvolution processing with resonant slice systems. In addition, the 3D imaging method was processed in the wavenumber space by a Fourier transform that used a simple convolution with noise parameters in the response function. After the reconstruction of the distribution of electron spins (radicals), the shape of the sample agreed with that of the optical image; thus, the accuracy of the internal density structure was verified. We believe that the combination of a Si nanowire and a spherical magnetic particle used for magnetic resonance detection is a good candidate for Fourier transform 3D deconvolution in multiple MRFM applications.

Targeted capture sequencing identifies genetic variations of GRK4 and RDH8 in Han Chinese with essential hypertension in Xinjiang.

Essential hypertension is a common cardiovascular disease with complex etiology, closely related to genetic and environmental factors. The pathogenesis of hypertension involves alteration in vascular resistance caused by sympathetic nervous system (SNS) and renin angiotensin system (RAS). Susceptibility factors of hypertension vary with regions and ethnicities. In this study, we conducted target capture sequencing on 54 genes related to SNS and RAS derived from a collection of Han nationality, consisting of 151 hypertension patients and 65 normal subjects in Xinjiang, China. Six non-synonymous mutations related to hypertension were identified, including GRK4 rs1644731 and RDH8 rs1801058, Mutations are predicted to affect 3D conformation, force field, transmembrane domain and RNA secondary structure of corresponding genes. Based on protein interaction network and pathway enrichment, GRK4 is predicted to participate in hypertension by acting on dopaminergic synapse, together with interacting components. RDH8 is involved in vitamin A (retinol) metabolism and consequent biological processes related to hypertension. Thus, GRK4 and RDH8 may serve as susceptibility genes for hypertension. This finding provides new genetic evidence for elucidating risk factors of hypertension in Han nationality in Xinjiang, which in turn, enriches genetic resource bank of hypertension susceptibility genes.

Programmable DNA-augmented hydrogels for controlled activation of human lymphocytes

Contractile forces within the planar interface between T cell and antigen-presenting surface mechanically stimulate T cell receptors (TCR) in the mature immune synapses. However, the origin of mechanical stimulation during the initial, i.e., presynaptic, microvilli-based TCR activation in the course of immune surveillance remains unknown and new tools to help address this problem are needed. In this work, we develop nucleic acid nanoassembly (NAN)-based technology for functionalization of hydrogels using isothermal toehold-mediated reassociation of RNA/DNA heteroduplexes. Resulting platform allows for regulation with NAN linkers of 3D force momentum along the TCR mechanical axis, whereas hydrogels contribute to modulation of 2D shear modulus. By utilizing different lengths of NAN linkers conjugated to polyacrylamide gels of different shear moduli, we demonstrate an efficient capture of human T lymphocytes and tunable activation of TCR, as confirmed by T-cell spreading and pY foci.

Sexual dimorphisms in three-dimensional masticatory muscle attachment morphometry regulates temporomandibular joint mechanics

Temporomandibular joint (TMJ) disorders disproportionally affect females, with female to male prevalence varying from 3:1 to 8:1. Sexual dimorphisms in masticatory muscle attachment morphometry and association with craniofacial size, critical for understanding sex-differences in TMJ function, have not been reported. The objective of this study was to determine sex-specific differences in three-dimensional (3D) TMJ muscle attachment morphometry and craniofacial sizes and their impact on TMJ mechanics. Human cadaveric TMJ muscle attachment morphometry and craniofacial anthropometry (10Males; 11Females) were determined by previously developed 3D digitization and imaging-based methods. Sex-differences in muscle attachment morphometry and craniofacial anthropometry, and their correlation were determined, respectively using multivariate general linear and linear regression statistical models. Subject-specific musculoskeletal models of the mandible were developed to determine effects of sexual dimorphisms in mandibular size and TMJ muscle attachment morphometry on joint loading during static biting. There were significant sex-differences in craniofacial size (p = 0.024) and TMJ muscle attachment morphometry (p < 0.001). TMJ muscle attachment morphometry was significantly correlated with craniofacial size. TMJ contact forces estimated from biomechanical models were significantly, 23% on average (p < 0.001), greater for females compared to those for males when generating the same bite forces. There were significant linear correlations between TMJ contact force and both 3D mandibular length (R2 = 0.48, p < 0.001) and muscle force moment arm ratio (R2 = 0.68, p < 0.001). Sexual dimorphisms in masticatory muscle morphology and craniofacial sizes play critical roles in subject-specific TMJ biomechanics. Sex-specific differences in the TMJ mechanical environment should be further investigated concerning mechanical fatigue of TMJ discs associated with TMJ disorders.

Forces inside the nucleon on the light front from 3D Breit frame force distributions: Abel tomography case

We derive simple relations which express 2D light front force distributions in terms of 3D Breit frame pressure and shear force distributions. Mathematically the relations correspond to invertible Abel transformation and they establish one-to-one mathematical equivalence of 3D Breit frame force distributions and 2D light front ones. The beauty and simplicity of the Abel transformations allow us to derive a number of new relations for light front force distributions. Any knowledge (model calculation, experimental measurement, etc.) about pressure and shear force distributions in Breit frame can be unambiguously transformed into light front force distributions with the help of Abel transformation. Due to the positivity property of the Abel transformation we obtain an important result---the 2D local stability conditions are satisfied automatically if the corresponding 3D stability conditions are fulfilled. In this way we established not only mathematical equivalence of 2D and 3D forces distributions but also their physics equivalence in terms of stability. As an illustration of how the relations work, we calculated the light front force distributions for a large nucleus as a liquid drop, and for large ${N}_{c}$ nucleon as a chiral soliton.

Design and Validation of a Device Attached to a Conventional Bicycle to Measure the Three-Dimensional Forces Applied to a Pedal.

Knowledge of the forces applied to the pedals during cycling is of great importance both from the point of view of improving sporting performance and medical analysis of injuries. The most common equipment for measuring pedal forces is usually limited to the study of forces in the sagittal plane. Equipment that measures three-dimensional forces tends to be bulky and to be incorporated into bicycles that are modified to accommodate it, which can cause the measurements taken to differ from those obtained in real pedalling conditions. This work presents a device for measuring the 3D forces applied to the pedal, attachable to a conventional bicycle and pedals, which does not alter the natural pedalling of cyclists. The equipment consists of four gauges located on the pedal axis and two on the crank, controlled by a microcontroller. Pedal forces measurements were made for six cyclists, with results similar to those shown in the literature. The correct estimation of the lateral-medial direction force is of great interest when evaluating a possible overload at the joints; it will also allow a comparison of the effectiveness index during pedalling, showing the role of this component in this index from a mechanical standpoint.

Observer-based Geometric Impedance Control of a Fully-Actuated Hexarotor for Physical Sliding Interaction with Unknown Generic Surfaces

Aerial physical interaction is a promising field for unmanned aerial vehicles in future applications. This paper presents a novel paradigm for automatic aerial contact-based sliding interaction (inspection/cleaning) tasks in aerial robotics allowing a 3D force with a constant norm to be applied on generic surfaces with unknown geometry. The interaction task is achieved by a fully-actuated hexarotor equipped with a rigidly attached end-effector under a passivity-based geometric impedance controller and a new sliding-mode extended state observer to estimate the interaction wrench. In order to increase the observer performance and reduce the estimation chattering phenomenon, the observer is innovatively incorporated with a super-twisting algorithm and a sigmoid function with a switching gain being adaptively updated by a fuzzy logic system. A detailed stability analysis for the observer is presented based on the Lyapunov stability theory. The proposed control approach is validated in several simulations in which we try to accomplish the aerial physical sliding interaction task with different types of objects under various sliding speeds.

Two Experimental Devices for Record and Playback of Tactile Data

A tactile record and playback system will progress tactileology—a new cross-disciplinary field related to tactile sensations—as it will enhance its use in the instruction, archiving, and analysis of human manipulation. In this paper, we describe two key devices for achieving tactileology: a tactile sensor capturing human tactile sense (fingernail color sensor) and a robotic tactile sensor, both of which can detect not only normal force but also tangential force. This is beneficial because people manipulate objects and tools in various ways, such as grasping, picking, and rubbing. The fingernail color sensor registers the three-dimensional (3D) force applied to a fingertip by detecting the fingernail color change caused by blood distribution under the fingernail, which can be observed with green illumination and a miniature camera. Since detecting this color change is more complicated than using a robotic sensor, the relationships between the image and 3D force are learned using a convolutional neural network (CNN). In the robotic sensor, the 3D force applied to a robotic finger transforms into a bright area using an illuminated acrylic core, a rubber robotic finger skin, and a miniature camera. We measure normal force and tangential force by the brightness and movement of the bright area, respectively. Using a force gauge or an electronic scale for measurement, we perform a series of evaluation experiments. The experimental results show that the precision of both the fingernail color sensor and the robotic tactile sensor are sufficient for our system.

Synergistic effect of ZnO and TiO2 nanoparticles on the thermal stability and mechanical properties of glass fiber‐reinforced LY556 epoxy composites

AbstractThe article discusses the fabrication, mechanical characterization, and heat resistance of nano ZnO‐TiO2‐filled glass fiber‐reinforced LY556 epoxy composites, with focus on the synergistic effect of ZnO and TiO2 nanofillers. The fabrication of the composite laminates is achieved by the addition of the nanofillers in different wt% ranging from 1 to 5 wt%. The composites are prepared using simple hand layup technique followed by curing under vacuum. The 3D atomic force microscopy scans indicated even distribution of the nanofillers up to 2 wt% loading. Severe agglomeration of the nanofillers is evident for 3 to 5 wt% loading. The surface roughness, microhardness, flexural strength, tensile strength, and impact strength of the composites indicate a relationship with dispersion, wt% loading, and the wettability of the nanofiller with the LY556. In general, it is found that the incorporation of hard nanofillers favored the improvement of impact strength to a greater extent compared to tensile and flexural strengths. Detailed analysis of the obtained mechanical property values favors an optimum 2 wt% incorporation of the selected nanofillers to obtain improvement in various strength values of the fabricated composites. The thermal stability of the fabricated composites improved through the incorporation of ceramic nanofillers.

Combining Inertial Sensors and Machine Learning to Predict vGRF and Knee Biomechanics during a Double Limb Jump Landing Task.

(1) Background: Biomechanics during landing tasks, such as the kinematics and kinetics of the knee, are altered following anterior cruciate ligament (ACL) injury and reconstruction. These variables are recommended to assess prior to clearance for return to sport, but clinicians lack access to the current gold-standard laboratory-based assessment. Inertial sensors serve as a potential solution to provide a clinically feasible means to assess biomechanics and augment the return to sport testing. The purposes of this study were to (a) develop multi-sensor machine learning algorithms for predicting biomechanics and (b) quantify the accuracy of each algorithm. (2) Methods: 26 healthy young adults completed 8 trials of a double limb jump landing task. Peak vertical ground reaction force, peak knee flexion angle, peak knee extension moment, and peak sagittal knee power absorption were assessed using 3D motion capture and force plates. Shank- and thigh- mounted inertial sensors were used to collect data concurrently. Inertial data were submitted as inputs to single- and multiple- feature linear regressions to predict biomechanical variables in each limb. (3) Results: Multiple-feature models, particularly when an accelerometer and gyroscope were used together, were valid predictors of biomechanics (R2 = 0.68–0.94, normalized root mean square error = 4.6–10.2%). Single-feature models had decreased performance (R2 = 0.16–0.60, normalized root mean square error = 10.0–16.2%). (4) Conclusions: The combination of inertial sensors and machine learning provides a valid prediction of biomechanics during a double limb landing task. This is a feasible solution to assess biomechanics for both clinical and real-world settings outside the traditional biomechanics laboratory.

Optical force mapping at the single-nanometre scale

Three-dimensional (3D) information of the optical response in the nanometre scale is important in the field of nanophotonics science. Using photoinduced force microscopy (PiFM), we can visualize the nano-scale optical field using the optical gradient force between the tip and sample. Here, we demonstrate 3D photoinduced force field visualization around a quantum dot in the single-nanometre spatial resolution with heterodyne frequency modulation technique, using which, the effect of the photothermal expansion of the tip and sample in the ultra-high vacuum condition can be avoided. The obtained 3D mapping shows the spatially localized photoinduced interaction potential and force field vectors in the single nano-scale for composite quantum dots with photocatalytic activity. Furthermore, the spatial resolution of PiFM imaging achieved is ~0.7 nm. The single-nanometer scale photoinduced field visualization is crucial for applications such as photo catalysts, optical functional devices, and optical manipulation.

Local stiffness and work function variations of hexagonal boron nitride on Cu(111).

Combined scanning tunnelling and atomic force microscopy using a qPlus sensor enables the measurement of electronic and mechanic properties of two-dimensional materials at the nanoscale. In this work, we study hexagonal boron nitride (h-BN), an atomically thin 2D layer, that is van der Waals-coupled to a Cu(111) surface. The system is of interest as a decoupling layer for functional 2D heterostructures due to the preservation of the h-BN bandgap and as a template for atomic and molecular adsorbates owing to its local electronic trapping potential due to the in-plane electric field. We obtain work function (Φ) variations on the h-BN/Cu(111) superstructure of the order of 100 meV using two independent methods, namely the shift of field emission resonances and the contact potential difference measured by Kelvin probe force microscopy. Using 3D force profiles of the same area we determine the relative stiffness of the Moiré region allowing us to analyse both electronic and mechanical properties of the 2D layer simultaneously. We obtain a sheet stiffness of 9.4 ± 0.9 N·m−1, which is one order of magnitude higher than the one obtained for h-BN/Rh(111). Using constant force maps we are able to derive height profiles of h-BN/Cu(111) showing that the system has a corrugation of 0.6 ± 0.2 Å, which helps to demystify the discussion around the flatness of the h-BN/Cu(111) substrate.

Comparison of the Effect of Insole Correction on Three-Dimensional Knee Joint Moments during Gait in Standing Workers with Leg Length Discrepancy

Background Few studies have been performed to investigate the correction of leg length discrepancy (LLD) on the kinetic characteristics of the knee joint using a shoe insole during gait among those who must stand while working. Purpose To verify three-dimensional (3D) knee joint moments using a 3D motion capture system and force platforms with and without insoles during gait in standing workers with LLD. Study design This was a repeated-measures design. Methods Twenty-seven standing workers with LLD participated in this study. Kinetic data of the knee joint were collected using a motion analysis system and two force platforms. The participants were asked to walk freely along a 6-m walkway wearing a standard pair of shoes or standard shoes with an LLD-corrected insole. Repeated-measures analysis of variance (ANOVA) was used to compare the knee joint moments according to shoe conditions and limb sides. Results There were significant differences in most moment variables related to the knee joint in participants with LLD-corrected insoles worn on the short limb except for the knee moments of adduction, abduction, and internal rotation (<italic>p</italic>&lt;0.05). Significant differences were shown in the maximal moment of knee adduction, abduction, internal rotation, and external rotation between the long and short legs when the participants wore standard shoes only during gait (<italic>p</italic>&lt;0.05). Conclusions The results demonstrated a significant association between the imbalance of the knee moments and LLD among retail staff who must stand while working. Therefore, the results of this study will be useful in explaining the incidence and biomechanical characteristics of knee osteoarthritis in standing workers with LLD.

Effect of Muscle-Specific Fatigue on the Risk of Anterior Cruciate Ligament Injury in Females

The aim of our study was to investigate the effect of muscle-specific fatigue of the quadriceps and hamstring muscles on the biomechanical factors of anterior cruciate ligament (ACL) injury using musculoskeletal modeling techniques during directional diversion maneuver. Fifteen female subjects performed a directional diversion maneuver under three treatment conditions (quadriceps fatigue, hamstring fatigue, and control gait). Data from the 3D motion capture system and force platform were used to extract anterior/posterior ACL forces using the two-bundle ACL musculoskeletal modeling approach. A decrease in maximum extension (51.3%) and flexion (50.7%) torque after fatigue was observed. After quadriceps fatigue, the extension (p = 0.041) and adduction moments (p = 0.046) of the knee joint and the mean anterior bundle of ACL force (p = 0.021) decreased significantly. The knee flexion angle (p = 0.003), knee valgus angle (p = 0.013), and shear force (p = 0.043) decreased significantly after hamstring fatigue. The decrease in ACL force after quadriceps fatigue confirms its significant role in causing an ACL injury. However, no significant differences in ACL load after hamstring fatigue leads us to speculate that the antagonist muscle group, i.e., the hamstring, might not have a preventive mechanism against ACL injury.

Towards more valid simulations of slopestyle and big air jumps: Aerodynamics during in-run and flight phase

ObjectivesThis study aimed to investigate air drag and lift during the in-run and flight phase of ski and snowboard slopestyle and big air, to allow more valid modeling of jumps and hence reduce injury risk. DesignWe present an experimental, multiple single athlete study based on wind tunnel measurements of 4 skiers and 3 snowboarders. MethodsMeasurements were carried out in a closed loop wind tunnel, measuring airflow speed and 3D forces acting on the athletes. Athletes performed trials in typical postures at 35, 60 and 85 km/h wearing slim-, regular- and wide fit apparel. Drag and lift area (cDA; cLA) were calculated and analyzed using linear and multiple regression to describe their dependencies on posture, apparel and speed. ResultscDA values were higher than earlier assumed and ranged from 0.3 to 0.95 m2 for skiers and from 0.35 to 0.55 m2 for snowboarders, primarily dominated by posture, and followed by apparel. cLA ranged from −0.1 to 0.45 m2 for skiers and from 0.04 to 0.17 m2 for snowboarders. To facilitate more valid jump modeling posture- and apparel-dependent formulations for air drag coefficients were provided and the consequences of sport specific differences on modeling were highlighted. ConclusionsApplying the air drag coefficients and relationships determined in this study will help to improve validity of jump modeling in big air and slopestyle. The variability in aerodynamic forces in slopestyle and big air is caused by differences between sports, posture and apparel.

Large-deformation instability behaviors of 3D beams supported with 3D hinge joints subjected to axial and torsional loadings

In this paper, an instability analysis of three-dimensional (3D) beams supported with 3D hinges under axial and torsional loadings is presented in the large displacement and rotation regime. An exact displacement field is proposed based on the central line and orientation of the cross section consisting of nine parameters corresponding to 3D centroid movements and rotations. The Cauchy–Green deformation tensor is derived in the local coordinate system according to the proposed displacement field. The deformation tensor and a normal-shear constitutive model with highly polynomial nonlinearity are developed based on continuum mechanics. A finite element formulation is then established based on the higher-order shape functions to avoid shear and membrane locking issues. The elemental governing equations of equilibrium as well as 3D nodal forces and moments are obtained using the Hamiltonian principle. To solve the final nonlinear equilibrium equations, Newton–Raphson and Riks techniques by an incremental-iterative scheme are implemented. The numerical results are presented to assess instability behaviors of beams with different cross sections and various 3D boundary conditions. The effects of 3D hinge joints on the stability of beams under axial and torsional loadings are studied for the first time. The numerical results reveal instability in bending and lateral-torsional buckling for beams supported by 3D hinge joints. This phenomenon is proved by both the finite strain model and its linearization for small deformations. The numerical results show that the present finite element formulation is robust, reliable as well as simple and easy to model instability of 3D beams in the large displacement regime.

High‐Density Force and Temperature Sensing Skin Using Micropillar Array with Image Sensor

Driving toward the goal of gaining a high level of intelligence and agility that mimics or surpasses that of humans, sensing systems have been widely investigated. As a complex network, tactile sense converts environmental stimuli into electrical impulses through various sensory receptors, which has been exploited in a large number of revolutionary applications, including robotics, prosthetics, and health‐monitoring devices. However, it remains significantly difficult to mimic all the functionalities of human skin. Herein, a machine tactile sensing system is proposed based on machine vision, which is commonly referred to as “electronic skin” or “e‐skin.” With a high density of 625 sensing points per square centimeter similar to that of human skin, the proposed sensing system can successfully measure 3D force and temperature distribution simultaneously. Based on this information, the shape, weight, texture, stiffness, and viscosity of objects can be obtained, comprehensively mimicking the human tactile system. Moreover, the experimental results show that the proposed e‐skin achieves excellent repeatability, reproducibility, and stability compared to those based on other principles such as the piezoresistive effect and capacitive effect.

Traction Force Microscopy of Human Neutrophils During Critical Illness

Mapping of tractional forces produced by human neutrophils enables a precise understanding of mechanisms responsible for well-regulated cell motility. In collaboration with the Henann Lab at Brown University's Department of Solid Mechanics and the Franck Lab at University of Wisconsin's College of Engineering, we have developed a novel method of quantifying cellular force generation. Previously, Traction Force Microscopy (TFM) methods have required a 3D imaging modality to capture 3D forces. Here, we demonstrate a new method that can capture 3D forces using only a 2D imaging modality. Therefore, both forces in-plane with the substrate as well as forces out-of-plane to the substrate can now be seen with a standard epifluorescent microscope. Our technique involves embedding a single layer of fiducial markers under the surface of a soft fibronectin-coated polyacrylamide gel, followed by our previously published single particle tracking algorithm (T-PT) and a novel finite element method to quantify forces from substrate displacement. To validate this system, PMNs were obtained from healthy donors with ex vivo activation and from septic donors. Sepsis is a potentially fatal systemic inflammatory response to infection that can progress to multiorgan system failure. We hypothesize that ex vivo activation of PMNs from healthy donors and different substrate stiffnesses will lead to differential force production. On soft substrates (1kPa), when comparing PMN force generation from healthy and septic donors, we found that neutrophils from septic donors produce greater forces. However, ex vivo activation of PMNs from healthy donors with Lipopolysaccharide (LPS) had no effect, while a stimulant cocktail of LPS, Interferon Gamma (IFN-g), and Granulocyte-Macrophage Colony-Stimulating Factor (GM-CSF) decreased force generation. Further, ex vivo activation with Phorbol Myristate Acetate (PMA) and N-Formylmethionine-leucyl-phenylalanine (fMLP) increased force generation. However, on stiff substrates (10kPa) LPS, PMA, and fMLP all had no effect on force generation, while the stimulant cocktail decreased total forces. Taken together with our novel TFM technique, these findings indicate that PMNs from septic patients are abnormal in their spatiotemporal generation of 3D forces. Further, secondary stimulation leads to differential dysregulation of force generation that is also mechanosensitive to substrate stiffness. Because there is still the need to further elucidate the deleterious molecular mechanisms during PMN-mediated sepsis, our methods will help bridge the divide between understanding dysregulation both in its biochemical and its mechanical interactions with the microenvironment.

3D simulations of vertical displacement events in tokamaks: A benchmark of M3D-C1, NIMROD, and JOREK

In recent years, the nonlinear 3D magnetohydrodynamic codes JOREK, M3D-C1, and NIMROD developed the capability of modeling realistic 3D vertical displacement events (VDEs) including resistive walls. In this paper, a comprehensive 3D VDE benchmark is presented between these state-of-the-art codes. The simulated case is based on an experimental NSTX plasma but with a simplified rectangular wall. There are differences between the physics models and numerical methods, and the VDE evolution leads to sensitivities on the initial conditions that cannot be avoided as can be done in edge localized modes (ELM) and sawtooth simulations (due to the non-cyclical nature of VDEs). Nonetheless, the comparison serves to quantify the level of agreement in the relevant quantities used to characterize disruptions, such as the 3D wall forces and energy decay. The results bring confidence regarding the use of the mentioned codes for disruption studies, and they distinguish aspects that are specific to the models used (e.g., reduced vs full MHD models). The simulations show important 3D features for a NSTX plasma, such as the self-consistent evolution of the halo current and the origin of the wall forces. In contrast to other reduced MHD models based on an ordering in the aspect ratio, the ansatz-based JOREK reduced MHD model allows capturing many aspects of the 3D dynamics even in the spherical tokamak limit considered here.