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At least 181 records · Page 10

Experimental study of the edge radial electric field in different drift configurations and its role in the access to H-mode at ASDEX Upgrade

The formation of the equilibrium radial electric field (Er) has been studied experimentally at ASDEX Upgrade (AUG) in L-modes of “favorable” (ion ∇ B-drift toward primary X-point) and “unfavorable” (ion ∇ B-drift away from primary X-point) drift configurations, in view of its impact on H-mode access, which changes with drift configurations. Edge electron and ion kinetic profiles and impurity velocity and mean-field Er profiles across the separatrix are investigated, employing new and improved measurement techniques. The experimental results are compared to local neoclassical theory as well as to a simple 1D scrape-off layer (SOL) model. It is found that in L-modes of matched heating power and plasma density, the upstream SOL Er and the main ion pressure gradient in the plasma edge are the same for either drift configurations, whereas the Er well in the confined plasma is shallower in unfavorable compared to the favorable drift configuration. The contributions of toroidal and poloidal main ion flows to Er, which are inferred from local neoclassical theory and the experiment, cannot account for these observed differences. Furthermore, it is found that in the L-mode, the intrinsic toroidal edge rotation decreases with increasing collisionality and it is co-current in the banana-plateau regime for all different drift configurations at AUG. This gives rise to a possible interaction of parallel Pfirsch–Schlüter flows in the SOL with the confined plasma. Thus, the different H-mode power threshold for the two drift configurations cannot be explained in the same way at AUG as suggested by LaBombard et al. [Phys. Plasmas 12, 056111 (2005)] for Alcator C-Mod. Finally, comparisons of Er profiles in favorable and unfavorable drift configurations at the respective confinement transitions show that also the Er gradients are all different, which indirectly indicates a different type or strength of the characteristic edge turbulence in the two drift configurations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Performance prediction applying different reduced turbulence models to the SMART tokamak

The SMall Aspect Ratio Tokamak (SMART) is currently being commissioned at the University of Seville and will be able to compare the performance of positive and negative triangularity plasmas at low aspect ratio. Predictive simulations have been performed for different machine scenarios and heating schemes using the TRANSP code. The objectives of these simulations are to predict the parameters expected in positive triangularity plasmas, to guide diagnostic development, and to validate transport models. Several reduced turbulence models have been used to predict electron and ion temperatures for the operational phase 2. All models provide similar results from approximately mid-radius to the separatrix but important discrepancies are found in the core region. These positive triangularity results are compared with experiments from a similar size machine like GLOBUS-M2. The multi-mode model (MMM) shows the best agreement. Simulations with different boundary conditions have been performed and no strong differences have been observed between them. The impact of neutral beam injection (NBI) on the predicted profiles has also been addressed. Rotation reduces turbulence levels so higher temperatures are achieved when included in the simulations. Studying the different contributions to the thermal diffusivities, it is observed that electron temperature gradient (ETG) turbulence dominates at the plasma core while micro-tearing modes (MTM) dominate at the edge in the electron channel. In the ion channel, the neoclassical contribution is dominant at the core and at the very edge while the Weiland component, which includes ion temperature gradient mode (ITG), trapped electron mode (TEM), kinetic ballooning mode (KBM), peeling mode (PM) and collisionless and collision dominated magnetohydrodynamic (MHD) modes governs the mid-radius region. For phase 3, two plasmas with different electron densities have been studied. The case with lower density matches well a specific discharge of GLOBUS-M2. The higher density plasma shows high performance with β N ≈ 3.8.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Experimental study of different silicon sensor options for the upgrade of the CMS Outer Tracker

During the high-luminosity phase of the LHC (HL-LHC), planned to start in 2027, the accelerator is expected to deliver an instantaneous peak luminosity of up to 7.5×10 34 cm –2 s –1 . A total integrated luminosity of 3000 or even 4000 fb –1 is foreseen to be delivered to the general purpose detectors ATLAS and CMS over a decade, thereby increasing the discovery potential of the LHC experiments significantly. The CMS detector will undergo a major upgrade for the HL-LHC,with entirely new tracking detectors consisting of an Outer Tracker and Inner Tracker. However, the new tracking system will be exposed to a significantly higher radiation than the current tracker, requiring new radiation-hard sensors. CMS initiated an extensive irradiation and measurement campaign starting in 2009 to systematically compare the properties of different silicon materials and design choices for the Outer Tracker sensors. Several test structures and sensors were designed and implemented on 18 different combinations of wafer materials, thicknesses, and production technologies. The devices were electrically characterized before and after irradiation with neutrons,and with protons of different energies, with fluences corresponding to those expected at different radii of the CMS Outer Tracker after 3000 fb –1 . The tests performed include studies with β sources, lasers, and beam scans. This paper compares the performance of different options for the HL-LHC silicon sensors with a focus on silicon bulk material and thickness.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

RRab variables with identical light-curve shapes at different pulsation periods

In this paper, we report on the detection of RRab stars with quasi-identical-shape light curves but period differences as large as 0.05–0.21 d using the Galactic bulge data of the OGLE-IV survey. We have examined stars with shorter periods than the Oosterhoff I ridge of the bulge. These stars generally have smaller amplitudes and larger Fourier phase-differences than the typical bulge RRab stars have at the same period. Many of these ‘anomalous’ stars have good-quality light curves without any sign of the Blazhko modulation. Examining their Fourier parameters revealed that several of these stars show very similar light curve to the typical bulge RR Lyrae. We found hundreds of quasi-identical-shape light-curve pairs with different periods between the ‘anomalous’- and the ‘normal’-position RRab stars based on the OGLE I-band data. The OGLE V-band, and the archive VVV and MACHO surveys K s -, b- and r -band data of these stars were also checked for light-curve-shape similarity. Finally, 149 pairs with identical-shape light curves in each available photometric band were identified. Calculating the physical properties of the variables using empirical formulae, on average, −0.5 dex, −0.13 mag, 0.67, and 165 K differences between the [Fe/H], M V , R/R ⊙ , and T eff values of the members of the pairs are derived, being the short-period stars less metal-poor, fainter, smaller, and hotter than the long-period variables. To explain the existence of variables with different physical properties and pulsation periods but with identical-shape light curves is a challenging task for modelling.

79 ASTRONOMY AND ASTROPHYSICS↗

Higher-order correlations between different moments of two flow amplitudes in Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV

The correlations between different moments of two flow amplitudes, extracted with the recently developed asymmetric cumulants, are measured in Pb-Pb collisions at $\sqrt {s_{NN}}$ = 5.02 TeV recorded by the ALICE detector at the CERN Large Hadron Collider. The magnitudes of the measured observables show a dependence on the different moments as well as on the collision centrality, indicating the presence of nonlinear response in all even moments up to the eighth. Furthermore, the higher-order asymmetric cumulants show different signatures than the symmetric and lower-order asymmetric cumulants. Comparisons with state-of-the-art event generators using two different parametrizations obtained from Bayesian optimization show differences between data and simulations in many of the studied observables, indicating a need for further tuning of the models behind those event generators. These results provide new and independent constraints on the initial conditions and transport properties of the system created in heavy-ion collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Numerical and Visual Representations of Uncertainty Lead to Different Patterns of Decision Making

Although visualizations are a useful tool for helping people to understand information, they can also have unintended effects on human cognition. This is especially true for uncertain information, which is difficult for people to understand. Prior work has found that different methods of visualizing uncertain information can produce different patterns of decision making from users. However, uncertainty can also be represented via text or numerical information, and few studies have systematically compared these types of representations to visualizations of uncertainty. We present two experiments that compared visual representations of risk (icon arrays) to numerical representations (natural frequencies) in a wildfire evacuation task. Like prior studies, we found that different types of visual cues led to different patterns of decision making. In addition, our comparison of visual and numerical representations of risk found that people were more likely to evacuate when they saw visualizations than when they saw numerical representations. These experiments reinforce the idea that design choices are not neutral: seemingly minor differences in how information is represented can have important impacts on human risk perception and decision making.

97 MATHEMATICS AND COMPUTING↗

Different CT slice thickness and contrast‐enhancement phase in radiomics models on the differential performance of lung adenocarcinoma

Abstract Background To investigate the effects of computed tomography (CT) reconstruction slice thickness and contrast‐enhancement phase on the differential diagnosis performance of radiomic signature in lung adenocarcinoma. Methods A total of 187 patients who had been pathologically confirmed with lung adenocarcinoma and nonadenocarcinoma were divided into a training cohort ( n = 149) and validation cohort ( n = 38). All the patients underwent contrast‐enhanced CT and the images were reconstructed with different slice thickness. The radiomic features were extracted from different slice thickness and scan phase. The logistic regression (LR) algorithm was used to build a machine learning model for each group. The area under the curve (AUC) obtained from the receiver operating characteristic (ROC) curve and DeLong test was used to evaluate its discriminating performance. Results Finally, 34 image features and five semantic features were selected to establish a radiomics model. Based on the three contrast‐enhanced CT phases and four reconstruction slice thickness, 12 groups of radiomics models showed good discrimination ability with the AUCs range from 0.9287 to 0.9631, sensitivity range from 0.8349 to 0.9083, specificity range from 0.825 to 0.925 in the training group. Similar results were observed in the validation group. However, there was no statistical significance between the different CT scan phase groups and different slice thickness ( p > 0.05). Conclusions The radiomic analysis of contrast‐enhanced CT can be used for the differential diagnosis of lung adenocarcinoma. Moreover, different slice thickness and contrast‐enhanced scan phase did not affect the discriminating ability in the radiomics models.

Wang, Yang↗

Characterisation of motor cortex organisation in patients with different presentations of persistent low back pain

Abstract Persistence of low back pain is thought to be associated with different underlying pain mechanisms, including ongoing nociceptive input and central sensitisation. We hypothesised that primary motor cortex (M1) representations of back muscles (a measure of motor system adaptation) would differ between pain mechanisms, with more consistent observations in individuals presumed to have an ongoing contribution of nociceptive input consistently related to movement/posture. We tested 28 participants with low back pain sub‐grouped by the presumed underlying pain mechanisms: nociceptive pain, nociplastic pain and a mixed group with features consistent with both. Transcranial magnetic stimulation was used to study M1 organisation of back muscles. M1 maps of multifidus (deep and superficial) and longissimus erector spinae were recorded with fine‐wire electromyography and thoracic erector spinae with surface electromyography. The nociplastic pain group had greater variability in M1 map location (centre of gravity) than other groups ( p < .01), which may suggest less consistency, and perhaps relevance, of motor cortex adaptation for that group. The mixed group had greater overlap of M1 representations between deep/superficial muscles than nociceptive pain (deep multifidus/longissimus: p = .001, deep multifidus/thoracic erector spinae: p = .008) and nociplastic pain (deep multifidus/longissimus: p = .02, deep multifidus/thoracic erector spinae: p = .02) groups. This study provides preliminary evidence of differences in M1 organisation in subgroups of low back pain classified by likely underlying pain mechanisms. Despite the sample size, differences in cortical re‐organisation between subgroups were detected. Differences in M1 organisation in subgroups of low back pain supports tailoring of treatment based on pain mechanism and motor adaptation.

Elgueta‐Cancino, Edith↗

The Frequency of Sex: Population Genomics Reveals Differences in Recombination and Population Structure of the Aflatoxin-Producing Fungus Aspergillus flavus

The apparent rarity of sex in many fungal species has raised questions about how much sex is needed to purge deleterious mutations and how differences in frequency of sex impact fungal evolution. We sought to determine how differences in the extent of recombination between populations of Aspergillus flavus impact the evolution of genes associated with the synthesis of aflatoxin, a notoriously potent carcinogen. We sequenced the genomes of, and quantified aflatoxin production in, 94 isolates of A. flavus sampled from seven states in eastern and central latitudinal transects of the United States. The overall population is subdivided into three genetically differentiated populations (A, B, and C) that differ greatly in their extent of recombination, diversity, and aflatoxin-producing ability. Estimates of the number of recombination events and linkage disequilibrium decay suggest relatively frequent sex only in population A. Population B is sympatric with population A but produces significantly less aflatoxin and is the only population where the inability of nonaflatoxigenic isolates to produce aflatoxin was explained by multiple gene deletions. Population expansion evident in population B suggests a recent introduction or range expansion. Population C is largely nonaflatoxigenic and restricted mainly to northern sampling locations through restricted migration and/or selection. Despite differences in the number and type of mutations in the aflatoxin gene cluster, codon optimization and site frequency differences in synonymous and nonsynonymous mutations suggest that low levels of recombination in some A. flavus populations are sufficient to purge deleterious mutations.

59 BASIC BIOLOGICAL SCIENCES↗

ESTIMATION OF THE WAKEFIELD RESONANT FREQUENCY USING DIFFERENT SIMULATION TOOLS

Reliable and fast wakefield calculations are important for beam dynamics and THz generation in accelerators. We compare approaches and limitations with different available simulation tools and compare results. As an example, we analyse a cylindrical corrugated waveguide with narrower and wider radii of 5 and 6 mm, and aperture width and periodicity of 1 and 2 mm using ABCI by KEK and ANSYS HFSS simulation software. First, ABCI was used to determine the resonant frequency of the cylindri-cal corrugated waveguide with different lengths. The corresponding results were taken as a reference to exam-ine the simulation method in the ANSYS HFSS environ-ment. The eigenmode solver of ANSYS HFSS was used to determine different resonant frequencies. This was fol-lowed by examining a cylindrical corrugated waveguide that was implemented having a length of 17 mm for dif-ferent conductor settings. The corresponding waveguide was fed by a plane wave having a resonant frequency that satisfies the intersection of the light line and dispersion curve of the corresponding mode. The analysis showed that the maximum loss factor was achieved at 39.20 and 40.07 GHz using ANSYS HFSS simulation data for differ-ent conductors, whereas ABCI resulted in 38.50 GHz. The talk will present the results gathered by different simula-tion setups implemented in ANSYS HFSS.

Unutmaz, Muhammed [SLAC National Accelerator Labor↗

Risk Ratio and Risk Difference Estimation in Case-cohort Studies

Background: In case-cohort studies with binary outcomes, ordinary logistic regression analyses have been widely used because of their computational simplicity. However, the resultant odds ratio estimates cannot be interpreted as relative risk measures unless the event rate is low. The risk ratio and risk difference are more favorable outcome measures that are directly interpreted as effect measures without the rare disease assumption. Methods: We provide pseudo-Poisson and pseudo-normal linear regression methods for estimating risk ratios and risk differences in analyses of case-cohort studies. These multivariate regression models are fitted by weighting the inverses of sampling probabilities. Also, the precisions of the risk ratio and risk difference estimators can be improved using auxiliary variable information, specifically by adapting the calibrated or estimated weights, which are readily measured on all samples from the whole cohort. Finally, we provide computational code in R (R Foundation for Statistical Computing, Vienna, Austria) that can easily perform these methods. Results: Through numerical analyses of artificially simulated data and the National Wilms Tumor Study data, accurate risk ratio and risk difference estimates were obtained using the pseudo-Poisson and pseudo-normal linear regression methods. Also, using the auxiliary variable information from the whole cohort, precisions of these estimators were markedly improved. Conclusion: The ordinary logistic regression analyses may provide uninterpretable effect measure estimates, and the risk ratio and risk difference estimation methods are effective alternative approaches for case-cohort studies. These methods are especially recommended under situations in which the event rate is not low.

60 APPLIED LIFE SCIENCES↗

Uncertainty in Atlantic Multidecadal Oscillation derived from different observed datasets and their possible causes

As a leading mode of sea surface temperature (SST) variability over the North Atlantic in both observations and model simulations, the Atlantic Multidecadal Oscillation (AMO) can have a substantial influence on regional and global climate. By using Low-Frequency Component Analysis, we explore the uncertainties of the resulting AMO indices and the corresponding spatial patterns derived from three observational SST datasets. We found that the known coherent spatial pattern of the AMO at the basin scale over the North Atlantic appears in two out of the three datasets. Further analysis indicates that both the warming trend and the different techniques used to construct these observed gridded SSTs contribute to the AMO’s spatial coherence over the North Atlantic, especially during periods of sparse data sampling. The SST in the Extended Reconstructed SST dataset version 5 (ERSSTv5), changes from being systematically below the other datasets during the dense sampling periods on either side of the Second World War (WWII), to systematically above the other datasets during WWII, thereby introducing an artificial 10–20-year variability that affects the AMO’s spatial coherence. This coherence in the AMO’s spatial pattern is also affected by bias adjustment in ERSSTv5 at relative cool (i.e., non-summer) seasons, and by the heterogeneous North Atlantic warming pattern. The different AMO patterns can induce the different effects of wind, surface heat fluxes, and then drive ocean circulation and its heat transport convergence, especially for some seasons. For AMO indices, both the different detrending methods and different observational data result in uncertainty for the period 1935–1950. Such SST uncertainty is important to detect the relative role of the atmosphere and ocean in shaping the AMO.

54 ENVIRONMENTAL SCIENCES↗

Effects of different cultivation media on root bacterial community characteristics of greenhouse tomatoes

Tomato, as a typical greenhouse crop, is commonly first planted as seedlings in a variety of substrates before being transplanted into soil. However, there is rare research on the characteristics of the bacterial community in tomato roots under this planting mode. In this study, tomatoes were planted in pots containing three different cultivation media, including soil and two types of substrates in a greenhouse, followed by a transplanting treatment. After collecting tomato root samples, high-throughput sequencing and bioinformatic analysis were used to compare the differences in bacterial diversity and functions between tomato roots before and after transplanting in different cultivation media. In total, 702776 sequences were obtained, and the OTUs were belonging to 109 genera, 58 families, 41 orders, 14 classes, and 12 phyla. Among the three cultivation media, the β -diversity was significant, and there was a slight difference in bacterial species diversity along with a large difference in their abundance at the genus level. Soil and both substrates had 79 bacterial genera in common, these genera accounted for 68.70%, 76.70%, and 71.17% of the total genera found in the soil, substrate 1, and substrate 2, respectively. After being transplanted from the two substrates to the soil, the bacterial community structure and abundance exhibited similarities with those found in the soil. Furthermore, based on microbial function prediction, the microbial communities in the two-substrate environment demonstrated a greater potential for promoting growth, while the microbial communities in the soil exhibited a greater tendency to exert their antibacterial potential. Our findings offer theoretical support for the creation of artificially reconstructed microbial communities in greenhouse cultivation.

Zhang, Xinjian↗

Vehicle Electrification Impacts on Energy Consumption for Different Connected-Autonomous Vehicle Scenario Runs

Transportation system simulation is a widely accepted approach to evaluate the impact of transport policy deployment. In developing a transportation system deployment model, the energy impact of the model is extremely valuable for sustainability and validation. It is expected that different penetration levels of Connected-Autonomous Vehicles (CAVs) will impact travel behavior due to changes in potential factors such as congestion, miles traveled, etc. Along with such impact analyses, it is also important to further quantify the regional energy impact of CAV deployment under different factors of interest. The objective of this paper is to study the energy consumption of electrified vehicles in the future for different penetration levels of CAVs deployment in the City of Chicago. The paper will further provide a statistical analysis of the results to evaluate the impact of the different penetration levels on the different electrified powertrains used in the study.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

The mechanisms and seasonal differences of the impact of aerosols on daytime surface urban heat island effect

The urban heat island intensity (UHII) is the temperature difference between urban areas and their rural surroundings. It is commonly attributed to changes in the underlying surface structure caused by urbanization. Air pollution caused by aerosol particles can affect the UHII through changing (1) the surface energy balance by the aerosol radiative effect (ARE) and (2) planetary-boundary-layer (PBL) stability and airflow intensity by modifying thermodynamic structure, which is referred to as the aerosol dynamic effect (ADE). By analyzing satellite data and ground-based observations collected from 2001 to 2010 at 35 cities in China and using the WRF-Chem model, we find that the impact of aerosols on UHII differs considerably: reducing the UHII in summer but increasing the UHII in winter. This seasonal contrast is proposed to be caused by the different strengths of the ARE and ADE between summer and winter. In summer, the ARE on UHII is dominant over the ADE, cooling down surface temperature more strongly in urban areas than in rural areas because of much higher aerosol loading, and offsets the urban heating, therefore weakening UHII. In winter, however, the ADE is more dominant, because aerosols stabilize the PBL more in the polluted condition, weakening the near-surface heat transport over urban areas in both vertical and horizontal directions. This means that the heat accumulated in urban areas is dispersed less effectively, and thus the UHII is enhanced. These findings shed new light on the impact of the interaction between urbanization-induced surface changes and air pollution on urban climate.urban areas and their rural surroundings. It is commonly attributed to changes in the underlying surface structure caused by urbanization. Air pollution caused by aerosol particles can affect the UHII through changing (1) the surface energy balance by the aerosol radiative effect (ARE) and (2) planetary-boundary-layer (PBL) stability and airflow intensity by modifying thermodynamic structure, which is referred to as the aerosol dynamic effect (ADE). By analyzing satellite data and ground-based observations collected from 2001 to 2010 at 35 cities in China and using the WRF-Chem model, we find that the impact of aerosols on UHII differs considerably: reducing the UHII in summer but increasing the UHII in winter. This seasonal contrast is proposed to be caused by the different strengths of the ARE and ADE between summer and winter. In summer, the ARE on UHII is dominant over the ADE, cooling down surface temperature more strongly in urban areas than in rural areas because of much higher aerosol loading, and offsets the urban heating, therefore weakening UHII. In winter, however, the ADE is more dominant, because aerosols stabilize the PBL more in the polluted condition, weakening the near-surface heat transport over urban areas in both vertical and horizontal directions. This means that the heat accumulated in urban areas is dispersed less effectively, and thus the UHII is enhanced. These findings shed new light on the impact of the interaction between urbanization-induced surface changes and air pollution on urban climate.

54 ENVIRONMENTAL SCIENCES↗

A cross-sectional study of the nasal and fecal microbiota of sows from different health status within six commercial swine farms

Cull sows are a unique population on swine farms, often representing poor producing or compromised animals, and even though recent studies have reported that the microbiome is associated with susceptibility to diseases, the microbiome of the cull sow population has not been explored. The main objective of this study was to investigate whether there were differences in fecal and upper respiratory tract microbiota composition for groups of sows of different health status (healthy, cull, and compromised/ clinical sows) and from different farms (1 to 6). Six swine farms were visited once. Thirty individual fecal samples and nasal swabs were obtained at each farm and pooled by five across health status and farm. Samples underwent 16S rRNA gene amplicon sequencing and nasal and fecal microbiota were analyzed using QIIME2 v.2021.4. Overall, the diversity of the nasal microbiota was lower than the fecal microbiota (p < 0.01). No significant differences were found in fecal or nasal alpha diversity by sow’s health status or by farm. Furthermore, there were significant differences in nasal microbial composition by farm and health status (PERMANOVA, p < 0.05), and in fecal microbiota by farm (PERMANOVA, p < 0.05), but not by health status. Lastly, at the L7 level, there was one differentially abundant taxa across farms for each nasal and fecal pooled samples. This study provided baseline information for nasal and fecal microbiota of sows under field conditions, and results suggest that farm of origin can affect microbial diversity and composition. Furthermore, sow’s health status may have an impact on the nasal microbiota composition.

59 BASIC BIOLOGICAL SCIENCES↗

Monthly and annual percentage levels of wind speed differences computed by using FPS-16 radar/Jimsphere wind profile data from Cape Kennedy, Florida

The percentage levels of wind speed differences are presented computed from sequential FPS-16 radar/Jimsphere wind profiles. The results are based on monthly profiles obtained from December 1964 to July 1970 at Cape Kennedy, Florida. The profile sequences contain a series of three to ten Jimspheres released at approximately 1.5-hour intervals. The results given are the persistence analysis of wind speed difference at 1.5-hour intervals to a maximum time interval of 12 hours. The monthly percentage of wind speed differences and the annual percentage of wind speed differences are tabulated. The percentage levels are based on the scalar wind speed changes calculated over an altitude interval of approximately 50 meters and printed out every 25 meters as a function of initial wind speed within each five-kilometer layer from near sea level to 20 km. In addition, analyses were made of the wind speed difference for the 0.2 to 1 km layer as an aid for studies associated with take-off and landing of the space shuttle.

Susko, M.↗

Mixed finite-difference scheme for free vibration analysis of noncircular cylinders

A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.

Noor, A. K.↗