Combined Resonance Research Articles

High-resolution compositional mapping of surfaces in non-contact atomic force microscopy by a new multi-frequency excitation

In this paper, a new multi-frequency excitation method based on combination resonance is introduced to enhance the non-contact atomic force microscopy performance. In combination resonance, excitation frequencies are selected so that summation/subtraction of excitation frequencies is close to the natural frequencies of the microcantilever. Due to the nonlinear nature of this method, the probe response to excitation is very sensitive to change in tip-sample forces. This could be used to generate high-resolution compositional mapping and topographical images of the surface. The present study reveals that both amplitude and phase shift of the combination resonance are sensitive to change in parameters such as Hamaker constant, damping coefficient, Young’s modulus and tip-sample initial distance. It is observed that because of high sensitivity to Hamaker constant a small change in the surface material leads to considerable variations in amplitude and phase shift. This sensitivity is employed to improve compositional mapping of the surface materials. It is also found out that the response amplitude in the combination resonance is very sensitive to change in the tip-sample initial distance. This sensitivity may be used to reduce the vertical noise and increase image resolution, especially in environments with low quality factors. Overall, using this technique the image contrast increases significantly and high resolution compositional mapping of surfaces is achieved.

Stability analysis of rotating shaft under electromagnetic and bearing oil-film forces

The stability of the fixed pints of a flexible rotor supported by journal bearings is investigated through the Bifurcation diagrams. In this paper the effect of nonlinear electromagnetic harmonic force is added to the simultaneous consideration of the effects of the nonlinearity in curvature and inertia, mass eccentricity and hydrodynamic forces of the journal bearings. Solution of the Reynolds equation renders the pressure distribution in the bearings. The bearing forces are found from integrating the pressure distribution on the surface of bearings. Derivation of the equations is performed using the Hamilton's principle and the nonlinearity terms are related to the eccentricity and the curvature of shaft. Primary and combination resonances are imposed to the rotor-bearing system and steady state responses show the effects of magnetic and bearing forces on the stability of amplitudes. In combination resonance, frequency of the electromagnetic load is tuned as the average of the forward and backward natural frequencies of the rotor. Existence of unstable Hopf points demonstrates that periodic, quasi-periodic and chaotic motions may be arisen in the nonlinear behavior of rotor.

Acute conceptual disorganization in untreated first-episode psychosis: a combined magnetic resonance spectroscopy and diffusion imaging study of the cingulum

Background:Disorganized thinking is a core feature of acute psychotic episodes that is linked to social and vocational functioning. Several lines of evidence implicate disrupted cognitive control, excitatory overdrive and oxidative stress relating to the anterior cingulate cortex as mechanisms of conceptual disorganization (CD). We examined 3 candidate mechanistic markers related to CD in first-episode psychosis: glutamate excess, cortical antioxidant (glutathione) status and the integrity of the cingulum bundle that connects regions implicated in cognitive control.Methods:We used fractional anisotropy maps from 7 T diffusion-weighted imaging to investigate the bilateral cingulum based on a probabilistic white matter atlas. We compared high CD, low CD and healthy control groups and performed probabilistic fibre tracking from the identified clusters (regions of interest within the cingulum) to the rest of the brain. We quantified glutamate and glutathione using magnetic resonance spectroscopy (MRS) in the dorsal anterior cingulate cortex.Results:We found a significant fractional anisotropy reduction in a cluster in the left cingulum in the high CD group compared to the low CD group (Cohen’s d = 1.39; p < 0.001) and controls (Cohen’s d = 0.86; p = 0.009). Glutamate levels did not vary among groups, but glutathione levels were higher in the high CD group than in the low CD group. We also found higher glutathione related to lower fractional anisotropy in the cingulum cluster in the high CD group.Limitations:The MRS measures of glutamine were highly uncertain, and MRS was acquired from a single voxel only.Conclusion:Acute CD relates to indicators of oxidative stress, as well as reduced white matter integrity of the cingulum, but not to MRI-based glutamatergic excess. We propose that both oxidative imbalance and structural dysconnectivity underlie acute disorganization.

Features of MRI of the prostate gland when planning targeted biopsy with combined ultrasound and magnetic resonance imaging control

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A randomized study of natalizumab dosing regimens for relapsing–remitting multiple sclerosis

Background: REFINE was an exploratory, dose- and frequency-blinded, prospective, randomized, dose-ranging study in relapsing–remitting multiple sclerosis (RRMS) patients. Objective: To examine the efficacy, safety, and tolerability of natalizumab administered via various regimens in RRMS patients. Methods: Clinically stable RRMS patients previously treated with 300 mg natalizumab intravenously for ⩾12 months were randomized to one of six natalizumab regimens over 60 weeks: 300 mg administered intravenously or subcutaneously every 4 weeks (Q4W), 300 mg intravenously or subcutaneously every 12 weeks (Q12W), or 150 mg intravenously or subcutaneously Q12W. The primary endpoint was the mean cumulative number of combined unique active magnetic resonance imaging (MRI) lesions at week 60. Results: In total, 290 patients were enrolled. All Q12W dosing arms were associated with increased clinical and MRI disease activity and closed early; ⩾39.5% of patients in each Q12W arm met rescue criteria. In the 300 mg intravenous and subcutaneous Q4 W arms, the mean cumulative number of combined unique active MRI lesions was 0.23 and 0.02, respectively; annualized relapse rates were 0.07 and 0.08, respectively; and trough natalizumab serum levels and α4-integrin saturation were comparable. Conclusion: Natalizumab 300 mg subcutaneous Q4W was comparable to 300 mg intravenous Q4W dosing with respect to efficacy, pharmacokinetics/pharmacodynamics, and safety.

Combination resonance analysis of imperfect functionally graded conical shell resting on nonlinear viscoelastic foundation in thermal environment under multi-excitation

In this work, nonlinear forced vibrations of truncated conical shells are presented using a semi-analytical method. The material properties are varied along the thickness direction as a power law distribution. The functionally graded truncated conical shells are exposed to external harmonic load and placed in the thermal environment and have an initial imperfection. Furthermore, the functionally graded truncated conical shells rests on generalized nonlinear viscoelastic foundations which consisted of a Winkler and Pasternak foundation parameters augmented by a Kelvin–Voigt viscoelastic model and a nonlinear cubic stiffness. The fundamental equations are extracted using first-order shear deformation theory in conjunction with nonlinear von Kármán relationships. The partial differential equations of truncated conical shells are reduced through Galerkin’s method, and the result is extracted using the multiple scales method. To analyze the resonance analyses, a two-term external excitation is considered. In this regard, various secondary resonances are investigated, and finally, the analyses about combination resonances are represented. To investigate the presented approach, a comparison study is performed with those addressed by other researchers. To analyze the nonlinear combination resonance behavior of truncated conical shells, the effect of geometrical characteristics, material properties, power law index, thermal effects, external load amplitude, and initial imperfection are examined. Finally, the steady-state responses of the nonlinear system are analyzed. As one of the most interesting results, the softening behavior of truncated conical shells with inverse quadratic distribution is the most, and for the quadratic distribution is the least.

Reward-Related Responses and Tonic Craving in Cocaine Addiction: An Imaging Study of the Monetary Incentive Delay Task.

BackgroundCocaine addiction is associated with altered sensitivity to natural reinforcers and intense drug craving. However, previous findings on reward-related responses were mixed, and few studies have examined whether reward responses relate to tonic cocaine craving.MethodsWe combined functional magnetic resonance imaging and a monetary incentive delay task to investigate these issues. Imaging data were processed with published routines, and the results were evaluated with a corrected threshold. We compared reward responses of 50 cocaine-dependent individuals (CDs) and 45 healthy controls (HCs) for the ventral striatum (VS) and the whole brain. We also examined the regional responses in association with tonic cocaine craving, as assessed by the Cocaine Craving Questionnaire (CCQ) in CDs. We performed mediation analyses to evaluate the relationship between regional responses, CCQ score, and recent cocaine use.ResultsThe VS showed higher activation to large as compared with small or no wins, but this reward-related activity did not differ between CDs and HCs. The precentral gyrus (PCG), anterior insula, and supplementary motor area showed higher activation during large vs no wins in positive correlation with the CCQ score in CDs. Mediation analyses suggested that days of cocaine use in the prior month contributed to higher CCQ scores and, in turn, PCG reward responses.ConclusionsThe results highlight a unique relationship between reward responses of the primary motor cortex, tonic cocaine craving, and recent cocaine use. The motor cortex may partake in the cognitive motor processes critical to drug-seeking behavior in addicted individuals.

Diffusion property and functional connectivity of superior longitudinal fasciculus underpin human metacognition

Metacognition as the capacity of monitoring one's own cognition operates across domains. Here, we addressed whether metacognition in different cognitive domains rely on common or distinct neural substrates with combined diffusion tensor imaging (DTI) and functional magnetic resonance imaging (fMRI) techniques. After acquiring DTI and resting-state fMRI data, we asked participants to perform a temporal-order memory task and a perceptual discrimination task, followed by trial-specific confidence judgments. DTI analysis revealed that the structural integrity (indexed by fractional anisotropy) in the anterior portion of right superior longitudinal fasciculus (SLF) was associated with both perceptual and mnemonic metacognitive abilities. Using perturbed mnemonic metacognitive scores produced by inhibiting the precuneus using TMS, the mnemonic metacognition scores did not correlate with individuals' SLF structural integrity anymore, revealing the relevance of this tract in memory metacognition. To further verify the involvement of several cortical regions connected by SLF, we took the TMS-targeted precuneus region as a seed in a functional connectivity analysis and found the functional connectivity between precuneus and two SLF-connected regions (inferior parietal cortex and precentral gyrus) mediated mnemonic metacognition performance. These results illustrate the importance of SLF and a putative white-matter grey-matter circuitry that supports human metacognition.

DDRE-01. METABOLIC PLASTICITY AND HETEROGENEITY IN IDH1MUT CELL LINES PRODUCES RESISTANCE TO GLUTAMINASE INHIBITION BY CB839

BACKGROUNDMutant IDH1 (IDH1mut) gliomas have characteristic genetic and metabolic profiles and exhibit phenotype that is distinct from their wild-type counterparts. The glutamine/glutamate pathway has been hypothesized as a selective therapeutic target in IDH1mut gliomas. However, little information exists on the contribution of this pathway to the formation of D-2-hydroxyglutarate (D-2HG), a hallmark of IDHmut cells, and the metabolic consequences of inhibiting this pathway.METHODSWe employed an untargeted metabolic profiling approach in order to detect metabolic changes arising from glutaminase (GLS) inhibition treatment. Subsequently, 13C metabolic tracing analysis through a combined Nuclear Magnetic Resonance and Liquid Chromatography-Mass Spectrometry approach, we explored the fate of glutamine and glucose under treatment with CB839 a glutaminase-GLS-inhibitor and their respective contributions to D-2HG formation.RESULTS AND CONCLUSIONSThe effects of CB839 on cellular proliferation differed among the cell lines tested, leading to designations of GLS-inhibition super-sensitive, -sensitive or -resistant. Our data indicates a decrease in the production of downstream metabolites of glutamate, including those involved in the TCA cycle, when treating the sensitive cells with CB839 (glutaminase -GLS- inhibitor). Notably, CB839-sensitive IDH1mutcells respond to GLS inhibition by upregulating glycolysis and lactate production. In contrast, CB839-resistantIDH1mut cell lines do not rely only on glutamine for the sustenance of TCA cycle. In these cells, glucose contribution to TCA is enough to compensate the downregulation of glutamine-derived TCA metabolites. This investigation reveals that the glutamine/glutamate pathway contributes differentially to D-2HG in a cell-line dependent fashion on a panel of IDHmut cell lines. Further, these results demonstrate that there is a heterogeneous landscape of IDH1mut metabolic phenotypes. This underscores the importance of detailed metabolic profiling of IDH1mut patients prior to the decision to target glutamine/glutamate pathway clinically.

Terahertz Magneto-Optical Excitations of the sd-Hybrid States of Lithium Nitridocobaltate Li2(Li1–xCox)N

We report the results of the experimental and theoretical study of the magnetic anisotropy of single crystals of the Co-doped lithium nitride Li2(Li1-xCox)N with x = 0.005, 0.01, and 0.02. It was shown recently that doping of the Li3N crystalline matrix with 3d transition metal (TM) ions yields superior magnetic properties comparable with the strongly anisotropic single-molecule magnetism of rare-earth complexes. Our combined electron spin resonance (ESR) and THz spectroscopic investigations of Li2(Li1-xCox)N in a very broad frequency range up to 1.7 THz and in magnetic fields up to 16 T enable an accurate determination of the energies of the spin levels of the ground state multiplet Ŝ = 1 of the paramagnetic Co(I) ion. In particular, we find a very large zero field splitting (ZFS) of almost 1 THz (∼4 meV or 33 cm-1) between the ground-state singlet and the first excited doublet state. On the computational side, ab initio many-body quantum chemistry calculations reveal a ZFS gap consistent with the experimental value. Such a large ZFS energy yields a very strong single-ion magnetic anisotropy of easy-plane type resembling that of rare-earth ions. Its microscopic origin is the unusual linear coordination of the Co(I) ions in Li2(Li1-xCox)N with two nitrogen ligands. Our calculations also evidence a strong 3d-4s hybridization of the electronic shells resulting in significant electron spin density at the 59Co nuclei, which may be responsible for the experimentally observed extraordinary large hyperfine structure of the ESR signals. Altogether, our experimental spectroscopic and computational results enable comprehensive insights into the remarkable properties of the Li2[Li1-x(TM)x]N magnets on the microscopic level.

Nyuzenamides A and B: Bicyclic Peptides with Antifungal and Cytotoxic Activity from a Marine-Derived Streptomyces sp.

Two bicyclic peptides, nyuzenamides A (1) and B (2), were discovered from Streptomyces isolated from suspended matter in deep sea water collected in the Sea of Japan. Their structures were determined through nuclear magnetic resonance and mass spectrometry analyses in combination with X-ray crystallography and the chiral-phase gas chromatography-mass spectrometry method to comprise ten amino acid residues containing four unusual amino acids along with aromatic acyl units. Both compounds displayed antifungal activity against pathogenic fungi and cytotoxicity against P388 murine leukemia cells.

Enhancement of the performance of nonlinear vibration energy harvesters by exploiting secondary resonances in multi-frequency excitations

This study is concerned with utilizing secondary resonances in order to harvest energy from low-frequency excitations. Nonlinearities give rise to secondary resonances, which can potentially activate large-amplitude responses when the excitation frequency is a fraction of the fundamental frequency of the system. Such resonances offer an untapped and unique opportunity for harvesting vibratory energy from excitation sources with low-frequency components. This issue has propelled the current study. Based on multi-frequency excitation, we develop a novel theoretical framework for a piezomagnetoelastic energy harvester to enhance its performance. The proposed scheme is implemented in both monostable and bistable piezomagnetoelastic under low-frequency excitations. It is shown throughout the paper that when the excitation frequencies are certain fractions of the system's fundamental frequency, the combination and simultaneous resonance activate large-amplitude responses. Another advantage of the scheme is that the energy could be harvested from low-frequency ambient vibrations, which is a considerable concern in this field of study. Different responses of the system, such as low-amplitude and high-amplitude limit-cycle oscillations and chaotic motions, are studied through perturbation theory and numerical techniques. Various numerical tools, including phase portrait, Poincare section, and Lyapunov exponent, are used to explore complex dynamical behavior of the system. The performance of the harvester is also compared in different regions. Numeral simulations clearly confirm that the proposed framework dramatically enhances the performance of the energy harvester.

Combined clinical test and magnetic resonance imaging have similar diagnostic values in the diagnosis of subscapularis tear

The aim of the present study was to compare the diagnostic values of clinical tests and magnetic resonance imaging (MRI) which used for the diagnosis of subscapularis (SSc) tears in the patients who underwent arthroscopic rotator cuff surgery. Two-hundred and nine consecutive patients who underwent arthroscopic rotator cuff surgery between 2015 and 2019 were analyzed. The lift-off test, belly-press test and bear-hug test were performed preoperatively. 1.5T MRI scans of all patients were evaluated for SSc integrity. The diagnostic values of both clinical tests and MRI were calculated. SSc tears were graded according to Fox and Romeo. Arthroscopic findings were used as the gold standard for diagnosis of SSc tears. There were 54 SSc tears accounting for an prevalence of 29%. The BHT showed the greatest sensitivity for both type II-II-IV (73.3%) and all types of (68.5%) SSc tears. The sensitivity and specificity of the combined test and MRI were 91.1-87.2% and 93.3-90.8% in Type II-III-IV SSc tears, respectively, and 81.5-88.6% and 88.9-94.7% in all SSc tears, respectively. There were no statistically significant difference between combined test and MRI in terms of sensitivity and specificity (n.s.). The present study is the first that compared both clinical tests and MRI with arthroscopic findings in terms of sensitivity and specificity in the same patient group. A combination of clinical tests increases their diagnostic values and shows similar sensitivity and specificity as MRI. I.

Fatty acid amide hydrolase binding is inversely correlated with amygdalar functional connectivity: a combined positron emission tomography and magnetic resonance imaging study in healthy individuals.

BackgroundUpregulation of the endocannabinoid enzyme fatty acid amide hydrolase (FAAH) has been linked to abnormal activity in frontoamygdalar circuits, a hallmark of posttraumatic stress disorder. We tested the hypothesis that FAAH levels in the amygdala were negatively correlated with functional connectivity between the amygdala and prefrontal cortex, subserving stress and affect control.MethodsThirty-one healthy participants completed positron emission tomography (PET) imaging with the FAAH probe [C-11]CURB, and resting-state functional MRI scans. Participants were genotyped for the FAAH polymorphism rs324420, and trait neuroticism was assessed. We calculated amygdala functional connectivity using pre-determined regions of interest (including the subgenual ventromedial prefrontal cortex [sgvmPFC] and the dorsal anterior cingulate cortex [dACC]) and a seed-to-voxel approach. We conducted correlation analyses on functional connectivity, with amygdala [C-11]CURB binding as a variable of interest.ResultsThe strength of amygdala functional connectivity with the sgvmPFC and dACC was negatively correlated with [C-11]CURB binding in the amygdala (sgvmPFC: r = −0.38, q = 0.04; dACC: r = −0.44; q = 0.03). Findings were partly replicated using the seed-to-voxel approach, which showed a cluster in the ventromedial prefrontal cortex, including voxels in the dACC but not the sgvmPFC (cluster-level, family-wise error rate corrected p < 0.05).LimitationsWe did not replicate earlier findings of a relationship between an FAAH polymorphism (rs324420) and amygdala functional connectivity.ConclusionOur data provide preliminary evidence that lower levels of FAAH in the amygdala relate to increased frontoamygdalar functional coupling. Our findings were consistent with the role of FAAH in regulating brain circuits that underlie fear and emotion processing in humans.

Nonlinear vibrations of planar curved pipes conveying fluid

The study investigates the dynamic behaviour of curved pipes in the shape of circular arcs conveying fluid. The effects of flow velocity and tube curvature on vibration modes and natural frequencies are analysed recalling the linear model of the system. A good agreement is observed between experimental results and theoretical predictions based on the model assuming pipe centreline to be extensible. To analyse the vibration due to pulsating flow, the additional non-linear component of the axial force was included and the model of the system was modified accordingly. Instability ranges were determined by the Floquet method a detailed analysis of the non-linear model was performed. The analysis of time histories, phase portraits, motion trajectory, vibration modes, spectral analysis was carried out and bifurcation diagrams were prepared. The effects of pulsation frequency and amplitude, as well as flow velocity, on the range and type of excited parametric vibration were established for pipes with varied curvature. The possibility of simple parametric resonance of single modes as well as combination resonance was confirmed. Calculation results are verified by experiments investigating various forms of parametric resonances.

Design and analysis of an ultra-thin polarization-insensitive wide-angle triple-band metamaterial absorber for X-band application

This paper presents an ultra-thin triple-band metamaterial absorber (TMMA) for the X-band which is insensitive to polarization and has high absorbance to wide incident angles. The TMMA is a three-layer structure based on the combined resonator which is made of a slotted rhomboid ring and a double cross pattern structure. The calculation indicates that the proposed absorber has three absorption peaks at 7.48 GHz, 9.70 GHz and 11.27 GHz with absorption rates 99.88%, 99.99% and 99.97% respectively. The TMMA’s structure is simple and ultra-thin, its thickness is only 0.0258 λ (the wavelength at the minimum absorption frequency can be expressed as λ). Also, it has the characteristics of being insensitive to the polarization of incident waves and it attains high absorbance to wide incident angle. The distribution of electric field, magnetic field and surface current in the TMMA is discussed, and the absorption mechanism of the proposed TMMA is expounded. Experiment results indicate that theoretical calculations and simulations are effective. The MMA can be used in broadcasting, communications, meteorology and earth observation satellites.

A thermal nociceptive patch in the S2 cortex of nonhuman primates: a combined functional magnetic resonance imaging and electrophysiology study.

Human functional magnetic resonance imaging (fMRI) and behavioral studies have established the roles of cortical areas along the Sylvian fissure in sensing subjective pain. Yet, little is known about how sensory aspects of painful information are represented and processed by neurons in these regions and how their electrophysiological activities are related to fMRI signals. The current study aims to partially address this critical knowledge gap by performing fMRI-guided microelectrode mapping and recording studies in the homologous region of the parietal operculum in squirrel monkeys under light anesthesia. In each animal studied (n = 8), we detected mesoscale mini-networks for heat nociception in cortical regions around the lateral sulcus. Within the network, we discovered a ∼1.5 × 1.5-mm2-sized cortical patch that solely contained heat nociceptive neurons that aligned with the heat fMRI activation locus. These neurons responded slowly to thermal (heat and cold) nociceptive stimuli exclusively, continued firing for several seconds after the succession of stimulation, and exhibited multidigit receptive fields and high spontaneous firing rates. Similar to the fMRI responses, increasing temperatures in the nociceptive range led to a nonlinear increase in firing rates. The finding of a clustering of heat nociceptive neurons provides novel insights into the unique functional organization of thermal nociception in the S2 subregion of the primate brain. With fMRI, it supports the existence of a modality-preferred heat nociceptive patch that is spatially separated and intermingled with touch patches containing neurons with comparable receptive fields and the presence of functionally distinct mini-networks in primate opercular cortex.

Nonlinear resonant analysis of space tethered satellite system in elliptical orbits

The nonlinear resonant motions of a tethered satellite system (TSS) in elliptical orbits are studied in this paper. The mathematical model of the system was derived using Lagrange's equations and an analysis of the parametric domain of the resonance was performed. It was revealed that internal resonance or combination resonance could occur in the system, but they did not occur simultaneously. The steady-state solutions of the system under combination resonance and internal resonance were analytically analyzed using the multiple scales method. The results showed that the steady-state solutions of the combination resonance and internal resonance had different bifurcation characteristics. Finally, the Poincaré maps was employed to verify the analytical results.

Rapid Detection of Adulteration in Extra Virgin Olive Oil by Low-Field Nuclear Magnetic Resonance Combined with Pattern Recognition

Intentional addition of cheaper oils into olive oil (OL) for economic motivation has been becoming particularly attractive due to the favorable flavor and healthy characteristics of OL, but it is very challenging to identify such adulteration because of the compositional similarity between the oils. In this study, low-field nuclear magnetic resonance (LF-NMR) in combination with multivariate statistical analysis was used to identify the adulterated olive oil with different rations of soybean oil (SO) or corn oil (CO). Significant differences in multi-component relaxation time (T21 and T22) and peak area proportions (S21 and S22) were detected between pure and adulterated OL. As the adulteration ratio increased, S21 and S22 changed linearly, while T21 and T22 only changed slightly. The detection by gas chromatography suggested that T21 and T22 values might be influenced by triacylglycerol components, and the changes of S21 and S22 were attributed to the varied mono-/polyunsaturated fatty acids. In the relaxation time-based pattern recognition models, the authentic OL could be correctly identified from the adulterated ones with at least 20% of SO or CO by principal component analysis (PCA) or partial least squares discriminant analysis (PLS-DA). The multi-blended oil could be 100% classified by orthogonal partial least squares discriminant analysis (OPLS-DA) and 98.8% classified by principal component analysis followed by linear discriminant analysis (PCA-LDA) when the adulteration ratio was above 30%, demonstrating a promising technique of LF-NMR combined with pattern recognition in rapid screening of the edible oils.

Pervasive nonlinear vibrations due to rod-obstacle contact

Simple mechanical contact between a deformable body and a rigid obstacle can lead to rich nonlinear behavior even when the equations governing the body’s motion are otherwise linear. We study the nonlinear dynamics of contact both numerically and analytically in a model problem of an Euler–Bernoulli beam and a flat substrate. This problem is relevant to microelectromechanical systems (MEMS) and marine structures. We show the nonlinearity to be dominantly quadratic, thereby giving rise to superharmonic and combination resonances of order two. We then demonstrate that similar nonlinear dynamics can in fact arise in far more general circumstances with nonlinear rods in contact with curved surfaces.