Vertical Mode Research Articles

Gate-Tunable Multiband van der Waals Photodetector and Polarization Sensor.

A single photodetector with tunable detection wavelengths and polarization sensitivity can potentially be harnessed for diverse optical applications ranging from imaging and sensing to telecommunications. Such a device will require the combination of multiple material systems with different structures, band gaps, and photoelectrical responses, which is extremely difficult to engineer using traditional epitaxial films. Here, we develop a multifunctional and high-performance photosensor using all van der Waals materials. The device features a gate-tunable spectral response that is switchable between near-infrared/visible and short-/midwave infrared, as well as broad-band operation, at room temperature. The linear polarization sensitivity in the telecommunication O-band can also be directly modulated between horizontal, vertical, and nonpolarizing modes. These effects originate from the balance of photocurrent generation in two of the active layers that can be manipulated by an electric field. The photodetector features high detectivity (>109 cmHz1/2W-1) together with fast operation speed (∼1 MHz) and can be further exploited for dual visible and infrared imaging.

Recovering Quasi-Biennial Oscillations from Chaos

Abstract The Quasi-Biennial Oscillation (QBO) is understood to result from wave-mean-flow interactions, but the reasons for its relative stability remain a subject of ongoing debate. In addition, consensus has yet to be reached regarding the respective roles of different equatorial wave types in shaping the QBO’s characteristics. Here we employ Holton-Lindzen-Plumb’s quasilinear model to shed light on the robustness of periodic behavior in the presence of multiple wave forcings. A comprehensive examination of the various dynamical regimes in this model reveals that increased vertical wave propagation at higher altitudes favors periodicity. In the case of single standing wave forcing, enhanced vertical propagation is controlled by the wave attenuation length scale. The occurrence of non-periodic states at high forcing amplitudes is explained by the excitation of high vertical unstable modes. Increasing the attenuation length scale prevents the emergence of such modes. When multiple wave forcing is considered, the mean flow generated by a dominant primary wave facilitates greater vertical propagation of a perturbation wave. Raising the altitude where most of the wave damping occurs favors periodicity by preventing the development of secondary jets responsible for the aperiodic behavior. This mechanism underscores the potential role of internal gravity waves in supporting the periodicity of a QBO primarily driven by planetary waves.

Numerical Study of Air Distribution and Thermal Environment in Attached Ventilation Mode in the Generator Layer of a Hydropower Station

Because they are in enclosed underground buildings, the generator layers of hydropower stations have limited ventilation. In order to reduce the influence of a hot and humid environment on equipment and staff health and create a good thermal environment with good air quality for underground buildings, in this paper, vertical wall-attached ventilation was combined with the generator layer of a hydropower station to replace traditional ventilation. The influence of air supply velocity, air supply outlet position, and the opening mode of the generator layer on indoor velocity and temperature field distribution were analyzed via numerical simulation, and the evaluation indices of different cases were also compared. In the single-sided vertical wall-attached ventilation mode, when the velocity was increased from 4 m/s to 8 m/s, the maximum increment in the energy utilization coefficient was 41%, and the maximum reduction in the velocity non-uniformity coefficient was 9.5%. The results show that the single-sided mode can offer a higher ventilation efficiency than the double-sided mode, with a higher energy efficiency and a more uniform air distribution. Based on the mean temperature and velocity, and the key evaluation indices (head-foot temperature difference, percentage of dissatisfaction, non-uniformity coefficient, energy utilization coefficient, and air diffusion performance index), it is suggested that the single-sided air supply mode should be adopted for this kind of tall building, with an air supply velocity of v = 6 m/s and two open air supply outlets at each interval.

Mode Shape-Based Damage Detection of Twin Skewed Bridges Based on OMA and FE Model Updating

A comparative study of the dynamic behavior of twin single-span bridges was carried out based on operational modal analysis and a linear finite element model updating with the aim of finding a potential damage indicator. The bridges are skewed, 30 m long and with prestressed concrete girders as the main support structure, but one of them were collided and suffered damage in two of its I-shape girders. Ambient vibration tests were conducted by deploying 14 uniaxial accelerometers along the sidewalks, experimental modal parameters were identified using the COVariance-driven Stochastic Subspace Identification method (SSI-COV). Six vertical modes were clearly identified for each structure. Additionally, some extra modes with non-proportional damping were identified. It was found that the modal frequencies are sensitive to the support conditions and the overall stiffness of the bridge but not to the localized girder damage, which, on the contrary, is reflected in the discrepancy in the fundamental bending mode shape amplitude between the lateral sides of the bridge, and a so-called Continuous Symmetry Measure adopted as a symmetry index seems to be a good damage indicator for this type of straight-alignment simply supported bridges, given the symmetric nature of the bending mode shapes and the asymmetric nature of the damage.

Effective parameters on polydimethylsiloxane/graphene composite-based triboelectric nanogenerator performance

ABSTRACT This paper systematically investigates the effective parameter on the performance of polydimethylsiloxane/graphene (PDMS@Gr)-based triboelectric nanogenerators (TENGs) as well as their applications. PDMS@Gr films containing 0, 0.05, 0.5, 1, and 1.5 wt.% graphene are synthesized, and their surface characteristics, mechanical behavior, and electrical properties are characterized. Vertical contact-separation mode TENGs are fabricated, and their performance is evaluated. The results demonstrate that the surface roughness and surface charge density are the most critical parameters for the performance of PDMS@Gr-based TENGs compared to the electrical and mechanical properties of the friction layers. The PDMS@Gr-based TENG with 1 wt.% graphene shows the highest power output of 2.6 W/m2 at an optimized working condition (5 Hz and 15 N). It also exhibits stable power output until 15,000 working cycles and displays battery-free applications by powering a light-emitting diode (LED) array, a calculator, a digital watch, and a digital thermometer.

High-efficiency metal-free electro-Fenton system on oxygenated graphene-based floating electrodes

Metal-free electro-Fenton (EF) are a promising technology for environmental remediation. This paper reports a novel EF modified with oxygenated graphene aerogel used as a floating electrode for efficient degradation of bisphenol A (BPA) through improved H2O2 yield combined with activation of hydroxyl radical (·OH) production. Impressively, the floating configuration of the electrodes allowed oxygen from the air to diffuse naturally into the reaction interface, reducing additional aeration energy consumption. The current efficiency of the floating system for H2O2 production was 40 times higher than the conventional vertical mode. The pollutant degradation trend exhibited a positive correlation with the ·OH production performance of the electrode. The modified catalyst system achieved the highest ·OH yield of 76.48 μM within 60 min, which was 2.72 times greater than that of the catalyst-free (28.10 μM) and 2.06 times higher than that of the unmodified catalyst (37.19 μM). Experiments and theoretical calculations indicated that the oxygen-containing functional groups introduced the graphene skeleton created new sites for in situ activation of electrogenerated H2O2, resulting in increased ·OH production. The primary activation sites were identified as the = O and –COOH groups, with the = O edges playing a particularly significant role. This system offers long-lasting stability and avoids secondary pollution, making it ideal for green environmental remediation compared to the traditional EF process.

Total Energy-Based Control Design and Optimization for Lift-Plus-Cruise Aircraft

This paper presents a methodology for optimizing a Total Energy–based control system architecture for a lift-plus-cruise vertical takeoff and landing urban air mobility concept. The Total Energy Control System algorithm, which was originally developed for fixed-wing applications, is extended to also be applicable to hovering and transitioning flight. Control system parameters are optimized using a genetic algorithm optimization scheme, subject to constraints on dynamic stability and control response characteristics. Control system optimization and flight simulations are performed using the Modular Aircraft Dynamics and Control Algorithm Simulation Platform. Results presented include simulations of the optimized flight control system operation for maneuvering scenarios representative of hover, transition, and forward flight conditions as well as during transitions between vertical and forward flight modes. The presented results demonstrate the effectiveness of the proposed control system architecture and the demonstrated optimization methodology.

Computational insights into diverse binding modes of the allosteric modulator and their regulation on dopamine D1 receptor

Allosteric drugs hold the promise of addressing many challenges in the current drug development of GPCRs. However, the molecular mechanism underlying their allosteric modulations remain largely elusive. The dopamine D1 receptor (DRD1), a member of Class A GPCRs, is critical for treating psychiatric disorders, and LY3154207 serves as its promising positive allosteric modulator (PAM). In the work, we utilized extensive Gaussian-accelerated molecular dynamics simulations (a total of 41μs) for the first time probe the diverse binding modes of the allosteric modulator and their regulation effects, based on the DRD1 and LY3154207 as representative. Our simulations identify four binding modes of LY3154207 (one boat mode, two metastable vertical modes and a novel cleft-anchored mode), in which the boat mode is the most stable while there three modes are similar in the stability. However, it is interesting to observed that the most stable boat mode inversely exhibits the weakest positive allosteric effect on influencing the orthosteric ligand binding and maintaining the activity of the transducer binding site. It should result from its induced weaker correlation between the allosteric site and the orthosteric site, and between the orthosteric site and the transducer binding site than the other three binding modes, as well as its weakened interaction between a crucial activation-related residue (S2025.46) and the orthosteric ligand (dopamine). Overall, the work offers atomic-level information to advance our understanding of the complex allosteric regulation on GPCRs, which is beneficial to the allosteric modulator design and development.

Polystyrene Waste-ZnO nanocomposite film for energy harvesting via hydrophobic triboelectric nanogenerator: Transforming waste into energy

This research aimed to generate electricity from polystyrene waste materials combined with zinc oxide (ZnO) nanomaterials. Developing alternative polystyrene waste materials for generating electricity in triboelectric nanogenerator (TENG) could be beneficial in a circular economy and sustainable development. With the motivation to reduce environmental pollution by using polystyrene waste, a recycled polystyrene-ZnO nanocomposite film (rPS-ZnO NF) was synthesized and served as a triboelectric material for energy harvesting applications. ZnO nanopowder was produced by a low-temperature solution immersion method in conjunction with a simple film-casting method to prepare the rPS-ZnO NF. The effects of varying amounts of toluene as a solvent medium and the immersion time in stearic acid (SA) solution treatment on the structural properties, wettability behavior, surface morphology, chemical bonding properties, surface characteristics, and TENG performance were investigated. In this work, rPS film, rPS-ZnO NF, and SA-treated rPS-ZnO NF were paired with Kapton film as the opposite triboelectric material in constructing the vertical contact-separation mode TENG. Compared to rPS TENG, the rPS-ZnO TENG exhibited a two-fold enhancement in performance (8.2 V) in output voltage and ∼4.5 fold enhancement (28.1 μW/cm2) in power density. Furthermore, following SA treatment, the triboelectric performance further improved, reaching the highest open circuit voltage of ∼8.8 V and the highest power density of 32.0 μW/cm2 for repeated 2 N-solenoid tapping force. The hydrophobic behavior was also improved with the highest water contact angle of 134.7 (when the SA treatment immersion time was 1 h). These findings demonstrate that SA-treated rPS-ZnO NF could be a promising candidate for efficient mechanical energy harvesting with high electrical output and excellent surface wettability. This research not only exhibits an excellent output performance of SA-treated rPS-ZnO TENG, but it also sheds new light on the sustainable approach of converting polystyrene waste into energy-harvesting material.

Impact of vertical girder deformations on the high-speed train operation performance

The deformation of bridge structures will cause deterioration of geometry on the rail surface during the service period, which will threaten the normal operation of train. A train–track–bridge coupling dynamics model was established. In order to simulate real operational conditions, initial geometric irregularity was taken into account, which was combined with rail irregularity caused by different vertical deformation of girder and was superimposed as external excitation. The probabilistic and statistical characteristics of operational performance indexes were analysed. The sensitivity of operational performance indexes to different deformation modes was studied. The vertical deformation thresholds of girder based on probability guarantee rate were obtained. The results show that unloading rate of wheel and wheel/track vertical force are more sensitive to single vertical rotation deformation mode. Vertical acceleration of the train and sperling index are more sensitive to bilateral vertical rotation deformation mode. Unloading rate of wheel is more sensitive to single vertical translation deformation mode. In the process of enhancing daily operation, single vertical rotation and multiple vertical translation should receive significant attention.

Temporal evolution of sound pulse in shallow water under conditions of horizontal refraction. Vertical modes and space-time horizontal rays

As is known, to describe horizontal refraction in a shallow water waveguide, the “vertical modes and horizontal rays” approach (Burridge & Weinberg, 1974) is used, within which the two-dimensional eikonal equation for the modal amplitude includes the refractive index determined by the eigenvalues depending on the horizontal coordinates (x,y) and frequency (f). In other words, we have an effective two-dimensional inhomogeneous dispersive medium, to describe the propagation of signals in which, the authors propose to use the so-called space-time rays (Rytov, 1940, Connor & Felsen, 1974, Hillion, 1993) applied for the horizontal plane (STHR). The set of STHRs in a given situation is constructed for each mode. Within the framework of this approach, it is possible to obtain the evolution of the pulses of each mode from the solution of the nonstationary eikonal equation in the horizontal plane or from the corresponding Hamilton-Jacobi equations, obtained using non-local integral wave equation. Examples of constructing STHR in some typical situations (in particular in a wedge) are considered, some specific effects during signal propagation are considered, in particular, the so-called the pulse front tilt, previously discovered in laser optics (Bor & Rasz, 1985). Work was supported by ISF, grant 946/20.

Why Is the Westward Rossby Wave Propagation from the California Coast “Too Fast”?

Abstract Past work has shown that interannual California coastal sea level variability is mostly of equatorial origin, and decades of satellite sea surface height (SSH) and in situ dynamic height observations indicate that this interannual signal propagates westward from the California coast as nondispersive Rossby waves (RWs). These observations agree with standard linear vertical mode theory except that even when mean flow and bottom topography are considered, the fastest baroclinic vertical mode RW in each case is always much slower (1.6–2.3 cm s−1) than the observed 4.2 cm s−1. This order-1 disagreement is only resolved if the standard bottom boundary condition that the vertical velocity w′ = 0 is replaced by perturbation pressure p′ = 0. Zero p′ is an appropriate bottom boundary condition because south of San Francisco the northeastern Pacific Ocean boundary acts approximately like an impermeable vertical wall to the interannual equatorial wave signal, and therefore equatorial quasigeostrophic p′ is horizontally constant along the boundary. Thus, if equatorial p′ = 0 at the bottom, then this condition also applies off California. The large-scale equatorial ocean boundary signal is due to wind-forced eastward group velocity equatorial Kelvin waves, which at interannual and lower frequencies propagate at such a shallow angle to the horizontal that none of the baroclinic equatorial Kelvin wave signal reaches the ocean floor before striking the eastern Pacific boundary. Off California this signal can thus be approximated by a first baroclinic mode with p′ = 0 at the bottom, and hence the long RW speed there agrees with that observed (both approximately 4.2 cm s−1). Significance Statement The California Current System is one of the most biologically rich and best-documented coastal regions in the world. In this region coastal sea level propagates westward from the coast at about 110 km month−1, slow enough to enable us to make large-scale ocean climate forecasts of the California Current ecosystem using coastal sea level. Although the westward speed seems slow, theoretically it is about double what we would expect. Offered here is an explanation of why this speed is “too fast” by linking the California wave signal to the equator, El Niño, and the shallow equatorial ocean response to the wind.

Powering of IOTs through single jersey wearable tribo-electric nano generator

A simple, lightweight, and easy to develop Single Jersey Wearable Tribo-Electric Nano Generators (SJ-WTENG) were constructed using Cotton and Acrylic fabrics (Triboelectric series materials). Fabrics were also coated with Maghemite (γ-Fe2O3) nanoparticles (13 nm) to increase the electrical conductance of the samples. Compression and Vertical contact-separation modes were adopted for studying the performance of the developed samples. Along with a Single WTENG sample, the outputs of two samples connected in series were also measured. To study the effect of developed Maghemite (γ-Fe2O3) nanoparticle coating, non-coated fabrics WTENGs were also constructed and tested. The maximum voltage reached with the Maghemite (γ-Fe2O3) nanoparticle-coated SJ-WTENG samples was a time-varying signal of 7.68 volts peak to peak volts with an approximate frequency of 50.5 Hertz. A shotky diode-based full bridge rectifier was used to get the DC voltage. The rectified DC signal was observed to be 5 volts which was enough to light up an LED with a threshold voltage of 1.7 volts DC as well as charge 3.7 volts, 3.6Ah Li-ion battery pack. Results confirmed that the application of Maghemite (γ-Fe2O3) nanoparticles was useful in augmenting the output of the proposed SJ-WTENG design. The proposed system can be used to power the battery powered IOT (Internet of Things) devices, widely used in medical and body sensor network applications.

Net gain in C+L band from LED pumped broadband emission in Er3+-doped oxyhalide tellurite glass

Expanding gain bandwidth into the L-band for erbium-doped fiber amplifiers (EDFAs) is a crucial strategy to overcome limitations in prevalent C-band focused commercial silica-based EDFAs, significantly boosting optical network transmission capacity. Herein, we synthesized Er3+-doped broadband near-infrared emission tellurite glasses utilizing the melt quenching process, systematically exploring the impact of ZnCl2 on the glass structure and optical properties. The 82TeO2–3Nb2O5–15ZnCl2–3Er2O3 (TNZ15) glass emerged as a standout candidate for broadband amplifiers around wavelength at 1.55 μm. With escalating ZnCl2 concentration, a discernible red shift in the emission peak wave lines was observed, accompanied by an expansion of the full width at half maximum (FWHM) from 98 nm to 106 nm. Noteworthy characteristics of all samples included exceptional thermal stability and elevated near-infrared (NIR) transmittance. Application of the Judd-Ofelt (J-O) theory facilitated the calculation of J-O parameter intensity, providing deeper insights into the optical behavior of the materials. Finally, the evaluation of TNZ15 planar optical waveguides, employing the vertical top pumping mode of two 980 nm LEDs, encompassed both the C-band (1530–1565 nm) and the L-band (1565–1625 nm). The results underscore the potential of TNZ15 glass as a promising gain material for broadband optical amplifiers and lasers, offering valuable insights into the development of next-generation optical amplification technologies.

High-quality Development Model of Industrial Integration of Sports Characteristic Towns in Northeast China

Background and Aims: The integrated development of industries is an important part of promoting the supply-side reform of sports-characteristic towns in China and cultivating a new economy and new driving force for sports development. This study aimed to develop a model to operate sports tourism events in Northeast China. and to confirm the developed model by stakeholders on satisfaction, appropriateness, and practicability. Methodology: The researcher performed the following research steps. The first step was to survey the current situation of 1200 customers in 6 cities in Northeast China. After that, a total of 20 experts were interviewed. Subsequently, the researcher entered the step of gathering ideas and placing elements on different levels, involving a total of 22 experts. When confirmed by the experts, all three dimensions of elements were brought into prioritization using the Analytical Hierarchy Process (AHP) hierarchical model. Results: (1) The demand characteristics of the consumption market in small towns with sports characteristics in Northeast China are mainly young and middle-aged men with higher educational background, more knowledge worker, and higher per capita monthly household income; Most consumers have a strong sense of sports and leisure, and recognize the role of sports and leisure, but do not have a deep understanding of sports and leisure items, consumers are keen on mountain sports, water sports, air sports, and so on, most consumers stay a short time, the amount of consumption is low, to the weekend short-distance personal or family-based travel. (2) The evaluation system of influencing factors of industry integration development of the small town with sports characteristics mainly includes five first-level indexes, such as government support, technological innovation, market demand, etc., industry development guide funds, government support provisions and other 18 secondary indicators. (3) There are three most representative models in the industry integration development of small towns with sports characteristics in our country. Vertical extension mode, horizontal extension mode, mixed cross mode. Conclusion: The high-quality development model of industrial integration of sports-characteristic towns in Northeast China could be summarized as First-Level Indicators with a total of 5 aspects and Second-Level Indicators with a total of 18 aspects. All experts opined that the resulting model was reliable. When put into practice, relevant agencies could apply it.

Scattering of mode-1 M2 internal tide in the South China Sea

When the internal tides encounter topography during propagation, the scattering effect will induce the baroclinic energy to transfer from the low mode to the higher mode, which may cause the internal tide to become unstable or even enhance dissipation. The characteristics of scattering of mode-1 M2 internal tide in the northern South China Sea (SCS) and its impact on baroclinic energy dissipation are explored in this study based on numerical simulations. The results show that the energy flux of the mode-1 M2 internal tide gradually weakens during propagation into the South China Sea. In the northern SCS, which has more complex topography, such as the continental slope, scattering will occur, resulting in a vertical mode increase and shear enhancement, and finally, the baroclinic energy is dissipated. Next, the effect of different topographies on mode-1 M2 internal tide scattering is analyzed by ideal experiments. The mode-1 M2 internal tide is scattered by topography, and the propagation as well as dissipation are also modified. The results show that the strong energy flux is mainly distributed on the surface of the continental slope and the area near the slope break. With the increase in criticality, the energy flux around the seamount and on the shelf gradually weakens, and the dissipation rate increases continuously. In addition, the slope topography is more likely to induce internal tide scattering than the seamount topography.

Modeling and Validation of a Passenger Car Tire Using Finite Element Analysis

This paper focuses on the modeling and analysis of a four-groove passenger car tire, size 235/55R19, using finite element analysis. The Mooney–Rivlin material model is employed to define the hyperelastic behavior of the tire rubber compounds for all solid elements. The tire rim is modeled as a rigid body using aluminum alloy material, and the beads are modeled as beam elements using steel material. The tire model is validated in both static and dynamic domains through several simulations and is compared to published measured data. The tire is validated using footprint and vertical stiffness tests in the static domain. In the static footprint test, a steady-state vertical load is applied, and the tire–road contact area is computed. In the vertical stiffness test, a ramp vertical load is applied, and the tire’s vertical displacement is measured to calculate the tire’s vertical stiffness. In the dynamic domain, the tire is validated using drum-cleat and cornering tests. In the drum-cleat test, a drum with a 2.5 m diameter and a cleat with a 15 mm radius is used to excite the tire structure and obtain the frequency of the vertical and longitudinal first modes of vibration, that is, by applying the fast Fourier transformation (FFT) of the vertical and longitudinal reaction forces at the tire center. In addition to this test, the tire model is pre-steered on a flat surface with a two-degree slip angle and subjected to a steady state linear speed of 10 km/h to predict the cornering force and compute the cornering stiffness. In addition, the effect of tire longitudinal speed on the rolling resistance coefficient is then predicted at zero slip angle using the ISO 28580 rolling resistance test. The findings of this research work provide insights into passenger car tire–road interaction analysis and will be further used to perform tire rubber compound material model sensitivity analysis.

In plane quantification of in vivo muscle elastic anisotropy factor by steered ultrasound pushing beams

Objective. Skeletal muscles are organized into distinct layers and exhibit anisotropic characteristics across various scales. Assessing the arrangement of skeletal muscles may provide valuable biomarkers for diagnosing muscle-related pathologies and evaluating the efficacy of clinical interventions. Approach. In this study, we propose a novel ultrafast ultrasound sequence constituted of steered pushing beams was proposed for ultrasound elastography applications in transverse isotropic muscle. Based on the propagation of the shear wave vertical mode, it is possible to fit the experimental results to retrieve in the same imaging plane, the shear modulus parallel to fibers as well as the elastic anisotropy factor (ratio of Young’s moduli times the shear modulus perpendicular to fibers). Main results. The technique was demonstrated in vitro in phantoms and ex vivo in fusiform beef muscles. At last, the technique was applied in vivo on fusiform muscles (biceps brachii) and mono-pennate muscles (gastrocnemius medialis) during stretching and contraction. Significance. This novel sequence provides access to new structural and mechanical biomarkers of muscle tissue, including the elastic anisotropy factor, within the same imaging plane. Additionally, it enables the investigation of multiples parameters during muscle active and passive length changes.

Efficient Top-k Frequent Itemset Mining on Massive Data

Top-k frequent itemset mining (top-k FIM) plays an important role in many practical applications. It reports the k itemsets with the highest supports. Rather than the subtle minimum support threshold specified in FIM, top-k FIM only needs the more understandable parameter of the result number. The existing algorithms require at least two passes of scan on the table, and incur high execution cost on massive data. This paper develops a prefix-partitioning-based PTF algorithm to mine top-k frequent itemsets efficiently, where each prefix-based partition keeps the transactions sharing the same prefix item. PTF can skip most of the partitions directly which cannot generate any top-k frequent itemsets. Vertical mining is developed to process the partitions of vertical representation with the high-support-first principle, and only a small fraction of the items are involved in the processing of the partitions. Two improvements are proposed to reduce execution cost further. Hybrid vertical storage mode maintains the prefix-based partitions adaptively and the candidate pruning reduces the number of the explored candidates. The extensive experimental results show that, on massive data, PTF can achieve up to 1348.53 times speedup ratio and involve up to 355.31 times less I/O cost compared with the state-of-the-art algorithms.

Linear NIMROD simulations of n = 0 modes for straight tokamak configuration and comparison with analytic results

Comparison between the analytic theory of n = 0 vertical displacement modes in magnetically confined plasmas of fusion interest and numerical simulations using the extended-MHD code NIMROD is presented. Agreement between analytic and numerical results is highly satisfactory. Differences are interpreted to be caused mostly by the different wall shape and by the presence of a halo plasma surrounding the hot plasma adopted in NIMROD. A numerical study of vertical displacement oscillatory modes [Barberis et al., J. Plasma Phys. 88, 905880511 (2022)] is presented. Axisymmetric X-point currents supported by the halo plasma are discussed. The article provides a successful benchmark and a useful starting point for future numerical investigations of n = 0 modes using more realistic tokamak geometry and plasma equilibria.