Normal Modes Research Articles

Nonlinear Normal Modes of Vibrating Mechanical Systems: 10 Years of Progress

Abstract This paper contains a review of the theory and applications of nonlinear normal modes, which have been developed during last decade. This review has more than 200 references. It is a continuation of two previous review papers by the same authors. The following theoretical issues of nonlinear normal modes are treated: basic concepts and definitions; application of the normal form theory for nonlinear modes construction; nonlinear modes in finite degrees-of-freedom systems; resonances and bifurcations; reduced-order modeling; nonlinear modes in stochastic dynamical systems; numerical methods; identification of mechanical systems using nonlinear modes. The following applied issues of this theory are treated in this review: experimental measurement of nonlinear modes; nonlinear modes in continuous systems; engineering applications (aerospace engineering, power engineering, piecewise-linear systems and structures with dry friction); nonlinear modes in nanostructures and physical systems; targeted energy transfer and absorption problem.

Recent Advances on PKM2 Inhibitors and Activators in Cancer Applications.

Metabolic reprogramming of cells, from the normal mode of glucose metabolism named glycolysis, is a pivotal characteristic of impending cancerous cells. Pyruvate kinase M2 (PKM2), an important enzyme that catalyzes the final rate-limiting stage during glycolysis, is highly expressed in numerous types of tumors and aids in development of favorable conditions for the survival of tumor cells. Increasing evidence has suggested that PKM2 is one of promising targets for innovative drug discovery, especially for the developments of antitumor therapeutics. Herein, we systematically summarize the recent advancement on PKM2 modulators including inhibitors and activators in cancer applications. We also discussed the classifications of pyruvate kinases in mammals and the biological functions of PKM2 in this review. We do hope that this review would provide a comprehensive understanding of the current research on PKM2 modulators, which may benefit the development of more potent PKM2-related drug candidates to treat PKM2-associated diseases including cancers in future.

Predicting the PSQA results of volumetric modulated arc therapy based on dosiomics features: a multi-center study

Backgroud and objectivesThe implementation of patient-specific quality assurance (PSQA) has become a crucial aspect of the radiation therapy process. Machine learning models have demonstrated their potential as virtual QA tools, accurately predicting the gamma passing rate (GPR) of volumetric modulated arc therapy (VMAT)plans, thereby ensuring safe and efficient treatment for patients. However, there is limited multi-center research dedicated to predicting the GPR. In this study, a dosiomics-based machine learning approach was employed to construct a prediction model for classifying GPR in multiple radiotherapy institutions. Additionally, the model’s performance was compared by evaluating the impact of two distinct feature selection methods.MethodsA retrospective data collection was conducted on 572 VMAT patients across three radiotherapy institutions. Utilizing a three-dimensional dose verification technique grounded in real-time measurements, γ analysis was conducted according to the criteria of 3%/2 mm and 2%/2 mm, employing a dose threshold of 10% along with absolute dose and global normalization mode. Dosiomics features were extracted from the dose files, and distinct subsets of features were selected as inputs for the model using the random forest (RF) and RF combined with SHapley Additive exPlanations (SHAP) methods. The data underwent training using the extreme gradient boosting (XGBoost) algorithm, and the model’s classification performance was assessed through F1-score and area under the curve (AUC) values.ResultsThe model exhibited optimal performance under the 3%/2 mm criteria, utilizing a subset of 20 features and attaining an AUC value of 0.88 and an F1-score of 0.89. Similarly, under the 2%/2 mm criteria, the model demonstrated superior performance with a subset of 10 features, resulting in an AUC value of 0.91 and an F1-score of 0.89. The feature selection methods of RF and RF + SHAP have achieved good model performance by selecting as few features as possible.ConclusionBased on the multi-center PSQA results, it is possible to utilize dosiomics features extracted from dose files to construct a machine learning predictive model. This model demonstrates excellent discriminative abilities, thus promoting the progress of gamma passing rate prognostic models in clinical application and implementation. Furthermore, it holds potential in providing patients with secure and efficient personalized QA management, while also reducing the workload of medical physicists.

Fast Attack Detection for Cyber-Physical Systems Using Dynamic Data Encryption.

To defend the cyber-physical system (CPSs) from cyber-attacks, this work proposes an unified intrusion detection mechanism which is capable to fast hunt various types of attacks. Focusing on securing the data transmission, a novel dynamic data encryption scheme is developed and historical system data is used to dynamically update a secret key involved in the encryption. The core idea of the dynamic data encryption scheme is to establish a dynamic relationship between original data, secret key, ciphertext and its decrypted value, and in particular, this dynamic relationship will be destroyed once an attack occurs, which can be used to detect attacks. Then, based on dynamic data encryption, a unified fast attack detection method is proposed to detect different attacks, including replay, false data injection (FDI), zero-dynamics, and setpoint attacks. Extensive comparison studies are conducted by using the power system and flight control system. It is verified that the proposed method can immediately trigger the alarm as soon as attacks are launched while the conventional χ2 detection could only capture the attacks after the estimation residual goes over the predetermined threshold. Furthermore, the proposed method does not degrade the system performance. Last but not the least, the proposed dynamic encryption scheme turns to normal operation mode as the attacks stop.

Influence of variable viscosity and local thermal non-equilibrium on nanofluid flow stability in an inclined porous channel

This study delves into the influence of local thermal non-equilibrium and changing viscosity on the stability of nanofluid flow in an inclined porous channel. The flow in the porous region governs Brinkman’s equation as well as a three-field model for temperature, with each field constitute the fluid, particle, and solid-matrix phases individually. Eigenvalue problem for a perturbed state is obtained using a normal mode analysis, and the problem is afterwards solved by the utilization of the Chebyshev spectral collocation method. Impact of various local thermal non-equilibrium parameters, critical Rayleigh number, and associated wavenumber are graphically displayed. Increasing values of the modified thermal capacity ratios, modified thermal diffusivity ratios, variable viscosity parameter, and channel inclination decrease the system’s stability for the interphase heat transfer parameter, which means these parameters destabilize the flow. Flow is most unstable when the channel is vertically oriented and the variable viscosity parameter ([Formula: see text]) = 0.5.

Positive Lynden-Bell derivative as a ticket to the bar trap?

ABSTRACT We have translated the results of N-body simulations of one barred model into the language of action variables and frequencies. Using this language, we analysed the behaviour of all orbits in the model on a large time-scale at the stage of a mature bar. We show that the orbits join the bar while preserving their adiabatic invariant, which takes into account the three-dimensional structure of the orbits. This allows us to apply the concept of the Lynden-Bell derivative for each of these orbits and trace how the sign of the derivative changes; i.e. how asynchronous changes in angular momentum Lz and orbital precession rate Ωpr (normal orbital mode) change to synchronous (abnormal mode). The transition to the abnormal mode occurs when Ωpr reaches the angular velocity of the pattern Ωp, after which the orbit becomes stuck in the bar trap. All this happens against the background of secular changes in actions (Lz decreases, JR and Jz increase). At the same time, corotating particles near two stable Lagrange points are also subject to secular changes in their actions. They increase Lz and drift to the periphery, shifting corotation outwards. We also show that a change in the orbital mode from normal to abnormal and the trapping of orbits in a bar are possible only when the bar speed decreases with time, regardless of what is causing the bar to slow down. Our findings clarify and expand the picture of bar formation and evolution in numerical models.

Molecular factors determining brightness in fluorescence-encoded infrared vibrational spectroscopy.

Fluorescence-encoded infrared (FEIR) spectroscopy is a recently developed technique for solution-phase vibrational spectroscopy with detection sensitivity at the single-molecule level. While its spectroscopic information content and important criteria for its practical experimental optimization have been identified, a general understanding of the electronic and nuclear properties required for highly sensitive detection, i.e., what makes a molecule a "good FEIR chromophore," is lacking. This work explores the molecular factors that determine FEIR vibrational activity and assesses computational approaches for its prediction. We employ density functional theory (DFT) and its time-dependent version (TD-DFT) to compute vibrational and electronic transition dipole moments, their relative orientation, and the Franck-Condon factors involved in FEIR activity. We apply these methods to compute the FEIR activities of normal modes of chromophores from the coumarin family and compare these predictions with experimental FEIR cross sections. We discuss the extent to which we can use computational models to predict the FEIR activity of individual vibrations in a candidate molecule. The results discussed in this work provide the groundwork for computational strategies for choosing FEIR vibrational probes or informing the structure of designer chromophores for single-molecule spectroscopic applications.

The non-muscle actinopathy-associated mutation E334Q in cytoskeletal γ-actin perturbs interaction of actin filaments with myosin and ADF/cofilin family proteins.

Various heterozygous cytoskeletal γ-actin mutations have been shown to cause Baraitser-Winter cerebrofrontofacial syndrome, non-syndromic hearing loss, or isolated eye coloboma. Here, we report the biochemical characterization of human cytoskeletal γ-actin carrying mutation E334Q, a mutation that leads to a hitherto unspecified non-muscle actinopathy. Following expression, purification, and removal of linker and thymosin β4 tag sequences, the p.E334Q monomers show normal integration into linear and branched actin filaments. The mutation does not affect thermal stability, actin filament nucleation, elongation, and turnover. Model building and normal mode analysis predict significant differences in the interaction of p.E334Q filaments with myosin motors and members of the ADF/cofilin family of actin-binding proteins. Assays probing the interactions of p.E334Q filaments with human class 2 and class 5 myosin motor constructs show significant reductions in sliding velocity and actin affinity. E334Q differentially affects cofilin-mediated actin dynamics by increasing the rate of cofilin-mediated de novo nucleation of actin filaments and decreasing the efficiency of cofilin-mediated filament severing. Thus, it is likely that p.E334Q-mediated changes in myosin motor activity, as well as filament turnover, contribute to the observed disease phenotype.

The non-muscle actinopathy-associated mutation E334Q in cytoskeletal γ-actin perturbs interaction of actin filaments with myosin and ADF/cofilin family proteins

Various heterozygous cytoskeletal γ-actin mutations have been shown to cause Baraitser–Winter cerebrofrontofacial syndrome, non-syndromic hearing loss, or isolated eye coloboma. Here, we report the biochemical characterization of human cytoskeletal γ-actin carrying mutation E334Q, a mutation that leads to a hitherto unspecified non-muscle actinopathy. Following expression, purification, and removal of linker and thymosin β4 tag sequences, the p.E334Q monomers show normal integration into linear and branched actin filaments. The mutation does not affect thermal stability, actin filament nucleation, elongation, and turnover. Model building and normal mode analysis predict significant differences in the interaction of p.E334Q filaments with myosin motors and members of the ADF/cofilin family of actin-binding proteins. Assays probing the interactions of p.E334Q filaments with human class 2 and class 5 myosin motor constructs show significant reductions in sliding velocity and actin affinity. E334Q differentially affects cofilin-mediated actin dynamics by increasing the rate of cofilin-mediated de novo nucleation of actin filaments and decreasing the efficiency of cofilin-mediated filament severing. Thus, it is likely that p.E334Q-mediated changes in myosin motor activity, as well as filament turnover, contribute to the observed disease phenotype.

Cyanocyclopentadiene-Annulated Polycyclic Aromatic Radical Anions: Predicted Negative Ion Photoelectron Spectra and Singlet-Triplet Energies of Cyanoindene and Cyanofluorene Radical Anions.

Isomer-specific negative ion photoelectron spectra (NIPES) of cyanoindene (C9H7CN) and cyanofluorene (C14H9N), acquired through the computation of Franck-Condon (FC) factors that utilize harmonic vibrational frequencies and normal mode vectors derived from density functional theory (DFT) at the B3LYP/aug-cc-pVQZ and 6-311++G(2d,2p) basis sets, are reported. The adiabatic electron affinity (EA) values of the ground singlet (S0) and the lowest lying triplet (T1) states are used to predict site-specific S0-T1 energies (ΔEST). The vibrational spectra of the S0 and T1 states are typified by ring distortion and ring C-C stretching vibrational progressions. Among all the S0 isomers in C9H7CN, the 2-cyanoindene (2-C9H7CN) is found to be the most stable at an EA of 0.716 eV, with the least stable isomer being the 1-C9H7CN at an EA of 0.208 eV. In C14H9N, the most stable S0 isomer, 2-cyanofluorene (2-C14H9N), has an EA of 0.781 eV. The least stable S0 isomer in C14H9N is the 9-C14H9N, with an EA of 0.364 eV. The FC calculations are designed to mimic simulations that would be performed to aid in the analysis of experimental spectra obtained in NIPE spectroscopic techniques. The vibrational spectra, adiabatic EAs, and ΔEST values reported in this study are intended to act as a guide for future gas-phase ion spectroscopic experiments and astronomical searches, especially with regard to the hitherto largely unexplored C14H9N isomers.

Influence of thermal load on a rotating thermoelastic medium with diffusion and double porosity

In the present work, we have studied the thermodynamical interactions in a two-dimensional thermoelastic medium with diffusion, rotation and double porosity in the context of Green–Lindsay theory. A thermal load is applied at the outer free surface of the medium. The normal mode technique is employed to derive the analytic expressions of the field quantities such as stresses, displacement components, temperature field and mass concentration. Numerical computations are performed with the help of MATLAB software for a specific material for illustrating the results. To the author’s best knowledge, no attempt has been made to investigate the therodynamical interactions in a rotating double porous thermoelastic medium with diffusion under the influence of a thermal load. Comparisons of the physical quantities are shown in figures to study the effects of time, double porosity, rotation, thermal load and diffusion. Some particular cases of interest have also been inferred from the present problem. The theoretical and numerical computations are found to be in close agreement.

A smooth horizon without a smooth horizon

Recent observations on type III algebras in AdS/CFT raise the possibility that smoothness of the black hole horizon is an emergent feature of the large-N limit. In this paper, we present a bulk model for the finite-N mechanism underlying this transition. We quantize a free scalar field on a BTZ black hole with a Planckian stretched horizon placed as a Dirichlet boundary for the field. This is a tractable model for the stretched horizon that does not ignore the angular directions, and it defines a black hole vacuum which has similarities to (but is distinct from) the Boulware state. Using analytic approximations for the normal modes, we first improve upon ’t Hooft’s brick wall calculation: we are able to match both the entropy and the temperature, exactly. Emboldened by this, we compute the boundary Wightman function of the scalar field in a typical pure state built on our stretched horizon vacuum, at an energy sliver at the mass of the black hole. A key result is that despite the manifest lack of smoothness, this single-sided pure state calculation yields precisely the Hartle-Hawking thermal correlator associated to the smooth horizon, in the small-GN limit. At finite GN, there are variance corrections that are suppressed as Oe−SBH/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({e}^{-{S}_{BH}/2}\\right) $$\\end{document}. They become important at late times and resolve Maldacena’s information paradox. Highly excited typical pure states on the stretched horizon vacuum are therefore models for black hole microstates, while the smooth horizon describes the thermal state. We note that heavy excited states on the stretched horizon are better defined than the vacuum itself. These results suggest that complementarity in the bulk EFT could arise from a UV complete bulk description in which the black hole interior is not manifest.

Time dependent vibrational electronic coupled cluster (VECC) theory for non-adiabatic nuclear dynamics.

A time-dependent vibrational electronic coupled-cluster (VECC) approach is proposed to simulate photo-electron/UV-VIS absorption spectra as well as time-dependent properties for non-adiabatic vibronic models, going beyond the Born-Oppenheimer approximation. A detailed derivation of the equations of motion and a motivation for the ansatz are presented. The VECC method employs second-quantized bosonic construction operators and a mixed linear and exponential ansatz to form a compact representation of the time-dependent wave-function. Importantly, the method does not require a basis set, has only a few user-defined inputs, and has a classical (polynomial) scaling with respect to the number of degrees of freedom (of the vibronic model), resulting in a favorable computational cost. In benchmark applications to small models and molecules, the VECC method provides accurate results compared to multi-configurational time-dependent Hartree calculations when predicting short-time dynamical properties (i.e., photo-electron/UV-VIS absorption spectra) for non-adiabatic vibronic models. To illustrate the capabilities, the VECC method is also successfully applied to a large vibronic model for hexahelicene with 14 electronic states and 63 normal modes, developed in the group by Aranda and Santoro [J. Chem. Theory Comput. 17, 1691, (2021)].

Interaction of Carbon Nanotubes, Capped Carbon Nanotubes, CNT2–5, C60, C70, HO-C60, [C60]2, and [C60]3 Fullerenes with Virulence Factors of Gram-Negative and Gram-Positive Bacteria: Potential Applications for 3D-Printed Scaffolds

The antimicrobial application of carbon nanomaterials, such as carbon nanotubes (CNTs), capped CNTs, CNT2–5, C60, C70, HO-C60, [C60]2, and [C60]3 fullerenes, is increasing, owing to their low cytotoxicity properties compared to other nanomaterials such as metallic nanoparticles. Enhanced mechanical properties and antibacterial activity can be caused by the incorporation of CNTs in 3-dimensional (3D) printed nanocomposites (NCs). The interruption of the bacterial membrane resulting from the cylindrical shape and high aspect ratio properties has been found to be the most prominent antibacterial mechanism of CNTs. However, the unraveling interaction of CNTs, capped CNTs, CNT2–5, C60, C70, HO-C60, [C60]2, and [C60]3 fullerenes with virulence factors of the main bacterial pathogenesis has not yet been understood. Therefore, in the present study, interactions of these carbon-based nanomaterials with the eight virulence factors, including protein kinase A and (ESX)-secreted protein B of Mycobacterium tuberculosis, pseudomonas elastase and exotoxin A of Pseudomonas aeruginosa, alpha-hemolysin and penicillin-binding protein 2a of Staphylococcus aureus, and shiga toxin 2a and heat-labile enterotoxin of Escherichia coli, were evaluated with the molecular docking method of AutoDock Vina. This study disclosed that the binding affinity was highest for CNT2–5 and [C60]3 toward alpha-hemolysin, with binding energies of −32.7 and −26.6 kcal/mol, respectively. The stability of the CNT2–5–alpha-hemolysin complex at different times was obtained according to the normal mode analysis of ElNémo and iMOD servers.

Сравнительный анализ принципов проектирования электрогидравлических рулевых машин скоростных судов

The composition and control principles of steering electro-hydraulic machines of a simple and follower type, intended for rudder shifting of small and high-speed vessels are considered. An analysis of the functioning of existing steering gears for the specified group of vessels was carried out. Deficiencies in the work associated with the element base and composition of the control and electric drive systems of the analyzed steering machines have been formed. The features of the operation of hydraulic systems with drive electric motors of pumps made on direct current, revealed as a result of experiments, are shown. Variants of technical solutions for improving the energy performance of the electric drive are proposed. A comparative analysis of the operation of steering machines with AC and DC drives has been carried out. An assessment of steering machines operation in normal and emergency modes is given. Structural diagrams of control systems of simple and follow-up action are proposed, taking into account the operating features identified during the analysis and the requirements of the Russian classification society. The possibility of implementing an SM electric drive built using a frequency converter – asynchronous motor system powered by an alternating current network and an emergency source has been shown. Options for the implementation of electric drives for pumps of hydraulic stations with a high-voltage battery are proposed. The possibility of creating domestic installations for steering and other ship mechanisms, according to the proposed structural diagrams of control systems for hydraulic stations for high-speed ships, is shown. Recommendations are given for the construction of steering gears for high-speed vessels with a total displacement of up to 100 tons using domestic electrical equipment.

Electromagnetic field on a photothermal semiconducting voids medium under Lord–Shulman and refined multi-phase lag models in thermoelasticity

This study investigates the contemporary thermoelasticity theories in a photothermal semiconducting medium with voids influenced by the electromagnetic field. Boundary conditions of the phenomenon were based on the equations that regulate it concerning the stresses, carrier density, change in volume fraction field and temperature on the surface space. The equations were solved in normal mode technique, and the results are displayed by graphs. A comparison has been made with the findings of the literature when neglecting the new external parameters. The findings show that the presence or absence of electromagnetic field and carrier density significantly impacts on the phenomenon. From the results obtained, it is clear that the effects of electromagnetic field, carrier density, volume fraction and thermal relaxation times are very pronounced and applicable in diverse fields including geophysics, astronomy, engineering, biology, etc.

Tidal Migration of Exoplanets around M Dwarfs: Frequency-dependent Tidal Dissipation

The orbital architectures of short-period exoplanet systems are shaped by tidal dissipation in their host stars. For low-mass M dwarfs whose dynamical tidal response comprises a dense spectrum of inertial modes at low frequencies, resolving the frequency dependence of tidal dissipation is crucial to capturing the effect of tides on planetary orbits throughout the evolutionary stages of the host star. We use nonperturbative spectral methods to calculate the normal mode oscillations of a fully convective M dwarf modeled using realistic stellar profiles from MESA. We compute the dissipative tidal response composed of contributions from each mode, as well as nonadiabatic coupling between the modes, which we find to be an essential component of the dissipative calculations. Using our results for dissipation, we then compute the evolution of circular, coplanar planetary orbits under the influence of tides in the host star. We find that orbital migration driven by resonance locking affects the orbits of Earth-mass planets at orbital periods P orb ≲ 1.5 days and of Jupiter-mass planets at P orb ≲ 2.5 days. Due to resonantly driven orbital decay and outward migration, we predict a dearth of small planets closer than P orb ∼ 1 day and similarly sparse numbers of more massive planets out to P orb ∼ 3 days.

Multi-channel general reservation of NPP own needs on the basis of combination with autonomous hydrogen energy complex

The authors have developed an autonomous hydrogen energy complex and analyzed its economic efficiency. The developed energy complex is multifunctional. The main result of the work is the production and supply of electricity to the power system during hours of increased load. In addition, the low-power steam turbines included in the energy complex can provide plant-wide backup of the NPP's own needs in the event of a station blackout: based on the experimental data of the Balakovo NPP, it was previously shown that one power unit with a low-power turbine using the energy of the residual heat from the reactor can for a long time to provide electricity to required power units. Thanks to the installation of low-power turbines as part of the hydrogen energy complex, their constant warm state and self-sufficiency will be ensured by generating electricity for the power grid or for own needs in the normal mode. The paper considers options for installing an autonomous hydrogen power complex with and without replacing expensive external heat exchangers of the system for passive removal of heat from the reactor core. The efficiency of an alternative option without installing a storage system with the sale of off-peak electricity to the power system, which, in the option with AHC, is used to generate hydrogen/oxygen by electrolysis, depending on the tariff for off-peak electricity, is also calculated. Due to the lack of existing analogues of the hydrogen energy complex, several options for the proposed investment were considered. The results of the study revealed that the replacement of expensive equipment of the passive heat removal system significantly increases the economic efficiency of the proposed redundancy system. For the accepted options for capital investments, the boundary values of the off-peak selling tariff for electricity are shown, at which the use of the storage system is more efficient in comparison with the sale of nightly electricity to the power system.

On the indices of the normal modes of Laplace's tidal equations for zonal wavenumber zero

AbstractThe normal modes of Laplace's tidal equations seem to be a consolidated subject in the literature. However, up until now, no mode for the zonal wavenumber zero, (i.e., independent of longitude) had been identified as a mixed Rossby–gravity mode with physical meaning. Moreover, the meridional structures of westward gravity modes were not considered to be similar to the meridional structures of the corresponding inertio‐gravity modes for non‐zero wavenumbers (k>0). Here, a mixed Rossby–gravity mode with zero zonal wavenumber () is identified for the first time, and a new classification of the normal modes for the zonal wavenumber zero is proposed. Under the new classification, all the meridional structures corresponding to zero wavenumber modes are similar to the meridional structures of their respective non‐zero wavenumber modes. Moreover, using the new classification, all modes of a given type show smooth frequency variations with the zonal wavenumber, which approach asymptotically the analytic dispersion curves from the ‐plane shallow‐water equations as the fluid height tends to zero.

Nonlocal and dual‐phase‐lag effects in a transversely isotropic exponentially graded thermoelastic medium with voids

AbstractThe aim of the present work is to examine the thermally induced disturbances in a transversely isotropic nonlocal exponentially graded (nonhomogeneous) thermoelastic half‐space with voids within the framework of dual‐phase‐lag (DPL) theory. It is supposed that the material's properties are graded in ‐direction. By employing normal mode technique, the exact expressions of the temperature field, the change in volume fraction field, displacement and stress components are obtained. The obtained results are computed numerically for a magnesium crystal‐like material and depicted graphically to display the effects of material's anisotropy, non‐homogeneity parameter, generalized theories, nonlocal parameter, void parameter and time on the variations of different physical fields. Certain limiting cases of interest have been deduced from the present investigation.