Normal Modes Research Articles

Theoretical Study of Efficient Photon-Phonon Resonance Absorption in the Tungsten-Related Vibrational Mode of Scheelite.

Tungsten (W) is an extremely rare and vital metal extensively used in metallurgy, the chemical industry, optoelectronic devices, and machinery manufacturing. In this work, an environmentally friendly and efficient physical method based on photon-phonon resonance absorption (PPRA) is proposed for separating W from scheelite. We calculated the vibrational spectrum of calcium tungstate (CaWO4) and assigned the infrared (IR) absorption and Raman scattering peaks through a dynamic analysis of the normal modes. We focused on the strong IR absorption peaks related to W and identified three high-intensity IR-active modes at around 830 cm-1, corresponding to the stretching of the W-O bonds. Therefore, we propose the use of high-power terahertz (∼25 THz) laser radiation to facilitate W extraction from compounds, leveraging the high efficiency of PPRA. Experimental testing is required to determine the precise absorption frequency under industrial production conditions.

Kinetic effects of dust size distribution on Alfvén waves in magnetized space plasmas

ABSTRACT Dust populations in space plasmas are often described by a size distribution function, generally a power law distribution. In view of that, we include this feature in the kinetic description of a homogeneous magnetized dusty plasma with electrically charged immobile dust grains, in order to study its effects in the propagation and damping of Alfvén waves. The dispersion relation is numerically solved using parameters typically found in the dust-driven stellar winds of carbon-rich stars and in Earth’s auroral acceleration region, two space systems with unalike plasma parameters and in which Alfvén waves are known to play important roles in the plasma acceleration and heating processes. We show that the characteristics of the normal modes, namely the ion cyclotron and whistler modes, will change when one considers a power law distribution of dust sizes in the theory, as compared to a mono-sized dust population; and that these differences will depend on the exponent p of the power law, which alters the plasma charge imbalance between electrons and ions. We also notice that power-law distribution functions will modify the waves’ damping rate values. In particular, we show that in a stellar wind environment the ion cyclotron mode at very small wavenumber decreases with the reduction of p, while for higher wavenumber the damping of this mode increases with the reduction of p. For the Earth’s magnetosphere, the results obtained show that the wave damping increases with the decrease of p for all wavenumbers, for the parameters considered in the analysis.

Development of a universal method for vibrational analysis of the terminal alkyne C≡C stretch.

The terminal alkyne C≡C stretch has a large Raman scattering cross section in the "silent" region for biomolecules. This has led to many Raman tag and probe studies using this moiety to study biomolecular systems. A computational investigation of these systems is vital to aid in the interpretation of these results. In this work, we develop a method for computing terminal alkyne vibrational frequencies and isotropic transition polarizabilities that can easily and accurately be applied to any terminal alkyne molecule. We apply the discrete variable representation method to a localized version of the C≡C stretch normal mode. The errors of (1) vibrational localization to the terminal alkyne moiety, (2) anharmonic normal mode isolation, and (3) discretization of the Born-Oppenheimer potential energy surface are quantified and found to be generally small and cancel each other. This results in a method with low error compared to other anharmonic vibrational methods like second-order vibrational perturbation theory and to experiments. Several density functionals are tested using the method, and TPSS-D3, an inexpensive nonempirical density functional with dispersion corrections, is found to perform surprisingly well. Diffuse basis functions are found to be important for the accuracy of computed frequencies. Finally, the computation of vibrational properties like isotropic transition polarizabilities and the universality of the localized normal mode for terminal alkynes are demonstrated.

Using neural network super‐twisting sliding mode to improve power control of a dual‐rotor wind turbine system in normal and unbalanced grid fault modes

SummaryAccording to recent research work, increasing electric power generation is one of the significant advantages of the dual‐rotor wind turbine (DRWT) compared to the other types for the same wind speed. In this research work, a modified super‐twisting sliding mode control (STSMC) based on the neural network (NN) is suggested to regulate the stator powers of a DRWT‐based doubly‐fed induction generator (DFIG) in normal and unbalanced grid fault modes. The design of this strategy involves replacing the gains of conventional STSMC with the NN algorithm to enhance robustness, mitigate the impact of unbalanced grid voltage, and consequently improve the quality of the generated power of DRWT‐based DFIG. This forms the primary contribution of this work. The suggested strategy is compared with vector control (VC) and conventional STSMC in terms of reference tracking, power ripples, response dynamics, harmonic distortion of stator current, and the effect of an unbalanced grid fault. Finally, the utility and effectiveness of the designed controller are confirmed through computer simulations. Furthermore, when the grid is subjected to a 20% voltage drop, the results demonstrate that the suggested strategy reduced the total harmonic distortion (THD) value of the stator current by 12.92% compared to VC and by 9.29% compared to conventional STSMC.

Soft and Stiff Normal Modes in Floppy Colloidal Square Lattices.

Floppy microscale spring networks are widely studied in theory and simulations, but no well-controlled experimental system currently exists. Here, we show that square lattices consisting of colloid-supported lipid bilayers functionalized with DNA linkers act as microscale floppy spring networks. We extract their normal modes by inverting the particle displacement correlation matrix, showing the emergence of a spectrum of soft modes with low effective stiffness in addition to stiff modes that derive from linker interactions. Evaluation of the softest mode, a uniform shear mode, reveals that shear stiffness decreases with lattice size. Experiments match well with Brownian particle simulations, and we develop a theoretical description based on mapping interactions onto a linear response model to describe the modes. Our results reveal the importance of entropic steric effects and can be used for developing reconfigurable materials at the colloidal length scale.

Transmission challenges in metropolitan area optical networks

Abstract For implementing wide/metropolitan area network in optical fiber communication system the key technology that can be utilized is wavelength division multiplexing (WDM). We discuss the use of WDM in metropolitan networks along with its special feature of using optical add drop multiplexers and also design issues in implementing these systems. The issue of nonlinear crosstalk induced in metropolitan networks is considered in terms of power penalty. Also, the effect of dispersion induced in optical fibers is considered by using two types of transmission systems. One is considering the non-zero dispersion shifted fiber (NZDSF) in dispersion effected environment and second is, implementing dispersion compensation after normal single mode fiber (SMF + DCF). The effect of nonlinear cross talk which can limit transmission performance is discussed in both cases in context with different parameters like power penalty, frequency difference between signal & crosstalk and transmission distance etc.

Numerical continuation and stability of nonlinear systems with distributed delays: Application to fluid-induced impacts of tubes in cross-flow

Fluid–elastic instability is the main source of concern during the design of heat-exchanger tube bundles. The associated research has focused on the understanding of the physical mechanisms behind this phenomenon and the establishing of models capable of predicting its onset; also some concomitant work has been done to establish post-instability behaviour and to prevent from excessive wear in possible sliding contacts. Moreover, the existing studies make use of time-integration methods alone for this purpose, through which it is difficult to get a comprehensive insight of global dynamics. Continuation methods, which give access to unstable branches and precise bifurcation information, are a precious tool to unfold the attainable dynamic regimes. In this paper, the parametric behaviour of two representative systems under cross-flow excitation is explored through pseudo arc-length continuation with mean flow velocity as a main driving parameter, wherein the nonlinear modal equations of motion are solved by harmonic balance at each step. As the quasi-unsteady model used for fluid–elastic coupling introduces convolution integrals, this approach is quite natural and we show that, despite some difficulties regarding the treatment of stiff intermittent contacts, it allows for a thorough exploration of the system’s response. For the first case -a benchmark model-, increasingly complex dynamics arise as more modes are kept in the truncated modal basis, which is due to a series of modal interactions as the impacts distribute mechanical energy from the linearly-unstable first mode to the higher ones. This can be anticipated by studying the nonlinear normal modes of the system, as they expose the allowed internal resonances. In the second case, consisting of a realistic heat-exchanger tube configuration, a similar pattern is observed.

Normal Mode Copulas for Nonmonotonic Dependence

Abstract Copulas are helpful in studying joint distributions of two variables, in particular, when confounders are unobserved. However, most conventional copulas cannot model joint distributions where one variable does not increase or decrease in the other in a monotonic manner. For instance, suppose that two variables are linearly positively correlated for one type of unit and negatively for another type of unit. If the type is unobserved, we can observe only a mixture of both types. Seemingly, one variable tends to take either a high or low value (or a middle value) when the other variable is small (large), or vice versa. To address this issue, I consider an overlooked copula with trigonometric functions (Chesneau [2021, Applied Mathematics, 1(1), pp. 3–17]) that I name the “normal mode copula.” I apply the copula to a dataset about government formation and duration to demonstrate that the normal mode copula has better performance than other conventional copulas.

Physical insight into optical spectroscopy of chiral covalent organic pillars as molecular nanotubes

In this paper, we theoretically investigate chiral covalent organic pillars synthesized by connecting rim-desymmetrized macrocycle, stimulated by recent experimental synthesis [Nat. Synth. 2023, 2, 395–402]. Transition densities reveal physical mechanism of spectral intensity in one-photon absorption (OPA) and two-photon absorption (TPA), and solvent effect strongly influence the spectral profile and intensity in TPA, but little influence the spectrum in OPA. The intra-unit and inter-unit charge transfer are visualized in five phenylenediamine linkers. The chirality of covalent organic pillars is revealed by electronic circular dichroism (ECD) spectroscopy, and interpreted by the visualized transition electric and magnetic dipole moments. Molecular vibrational information is demonstrated by normal and resonance Raman spectra and vibrational modes. The visualization of static and dynamic (hyper) polarization can reveal the physical mechanisms of polarization dependent normal and resonance Raman scattering. Our results provide deeper understanding on the physical mechanism of chiral covalent organic pillars as molecular nanotubes.

Analytical study of micropolar thermoelastic rectangular plate under three theories

A three-dimensional micropolar thermoelastic problem is considered for an isotropic rectangular plate that is subjected to simply support and isothermal on its four adjacent edges. Normal mode analysis is applied to the governing equations to form a vector-matrix differential equation and the analytical solution of the vector-matrix differential equation is obtained by using eigenvalue approach methodology. Numerical results are presented graphically along with theoretical analysis for sinusoidal variation of the stresses applied on the top surface of the rectangular plate.

Brickwall in rotating BTZ: a dip-ramp-plateau story

In this article, building on our recent investigations and motivated by the fuzzball-paradigm, we explore normal modes of a probe massless scalar field in the rotating BTZ-geometry in an asymptotically AdS spacetime and correspondingly obtain the Spectral Form Factor (SFF) of the scalar field. In particular, we analyze the SFF obtained from the single-particle partition function. We observe that, a non-trivial Dip-Ramp-Plateau (DRP) structure, with a Ramp of slope one (within numerical precision) exists in the SFF which is obtained from the grand-canonical partition function. This behaviour is observed to remain stable close to extremality as well. However, at exact extremality, we observe a loss of the DRP-structure in the corresponding SFF. Technically, we have used two methods to obtain our results: (i) An explicit and direct numerical solution of the boundary conditions to obtain the normal modes, (ii) A WKB-approximation, which yields analytic, semi-analytic and efficient numerical solutions for the modes in various regimes. We further re-visit the non-rotating case and elucidate the effectiveness of the WKB-approximation in this case, which allows for an analytic expression of the normal modes in the regime where a level-repulsion exists. This regime corresponds to the lower end of the spectrum as a function of the scalar angular momentum, while the higher end of this spectrum tends to become flat. By analyzing the classical stress-tensor of the probe sector, we further demonstrate that the back-reaction of the scalar field grows fast as the angular momenta of the scalar modes increase in the large angular momenta regime, while the back-reaction remains controllably small in the regime where the spectrum has non-trivial level correlations. This further justifies cutting the spectrum off at a suitable value of the scalar angular momenta, beyond which the scalar back-reaction significantly modifies the background geometry.

The Harmonic and Gaussian Approximations in the Potential Energy Landscape Formalism for Quantum Liquids.

The potential energy landscape (PEL) formalism has been used in the past to describe the behavior of classical low-temperature liquids and glasses. Here, we extend the PEL formalism to describe the behavior of liquids and glasses that obey quantum mechanics. In particular, we focus on the (i) harmonic and (ii) Gaussian approximations of the PEL, which have been commonly used to describe classical systems, and show how these approximations can be applied to quantum liquids/glasses. Contrary to the case of classical liquids/glasses, the PEL of quantum liquids is temperature-dependent, and hence, the main expressions resulting from approximations (i) and (ii) depend on the nature (classical vs quantum) of the system. The resulting theoretical expressions from the PEL formalism are compared with results from path-integral Monte Carlo (PIMC) simulations of a monatomic model liquid. In the PIMC simulations, every atom of the quantum liquid is represented by a ring-polymer. Our PIMC simulations show that at the local minima of the PEL (inherent structures, or IS), sampled over a wide range of temperatures and volumes, the ring-polymers are collapsed. This considerably facilitates the description of quantum liquids using the PEL formalism. Specifically, the normal modes of the ring-polymer system/quantum liquid at an IS can be calculated analytically if the normal modes of the classical liquid counterpart are known (as obtained, e.g., from classical MC or molecular dynamics simulations of the corresponding atomic liquid).

Predicting Surface Oscillations in Lake Superior from Normal Mode Dynamics

Abstract Satellite observation of sea surface height (SSH) may soon have sufficient accuracy and resolution to map geostrophic currents in Lake Superior. A dynamic atmosphere correction will be needed to remove SSH variance due to basinwide seiching. Here, the dynamics of rotating barotropic gravity modes are examined using numerical models and lake-level gauges. Gravity modes explain 94% of SSH variance in a general circulation model and evolve as forced, damped oscillators. These modes have significant SSH, but negligible kinetic energy (2 J m−2) and dissipation rates (0.01 mW m−2) relative to other motions in Lake Superior. Removing gravity modes from instantaneous SSH allows geostrophic currents to be accurately computed. Complex empirical orthogonal functions (CEOFs) from 50 years of data at eight lake-level gauges show patterns consistent with the first two gravity modes. The frequency spectra of these CEOFs are consistent with forced, damped oscillators with natural frequencies of 3.05 and 4.91 cycles per day (cpd) and decay time scales of 4.5 and 1.0 days. Modal amplitudes from the general circulation model and lake-level gauges are 80% coherent at 1 cpd, but only 50% coherent at 3 cpd, indicating that the atmospheric reanalysis used to force the general circulation model is not accurate at the high natural frequencies of the gravity modes. The results indicate that a dynamic atmosphere correction should combine modeled gravity modes below 1 cpd and observed mode-1 and mode-2 amplitudes (from lake-level gauges) at higher frequencies. An inverted barometer correction is also recommended to account for low-frequency atmospheric pressure gradients that do not project onto gravity modes.

Dynamic sloshing in a rectangular vessel with porous baffles

The damping efficiency of vertical porous baffles is investigated for a dynamically coupled fluid-vessel system. The system comprises of a two-dimensional vessel, with a rectangular cross-section, partially filled with fluid, undergoing rectilinear motions with porous baffles obstructing the fluid motion. The baffles pierce the surface of the fluid, thus the problem can be considered as separate fluid filled regions of the vessel, connected by infinitely thin porous baffles, at which transmission conditions based on Darcy’s law are applied. The fluid is assumed to be inviscid, incompressible and irrotational such that the flow in each region is governed by a velocity potential. The application of Darcy’s law at the baffles is significant as it makes the system non-conservative, and thus the resulting characteristic equation for the normal modes leads to damped modes coupled to the moving vessel. Numerical evaluations of the characteristic equation show that the lowest frequency mode typically has the smallest decay rate, and hence will persist longest in an experimental setup. The maximum decay rate of the lowest frequency mode occurs when the baffles split the vessel into identically sized regions.

Amyloid beta misfolding status in γ-secretase: Insights from molecular dynamics and excited normal modes analysis

Amyloid beta misfolding status in γ-secretase: Insights from molecular dynamics and excited normal modes analysis

On the eigenvalues and eigendisplacement of the critical mode in horizontally layered media

Wave propagation in horizontally layered media is a classical problem in seismic-wave theory. In semi-infinite space, a nondispersive Rayleigh wave mode exists, and the eigendisplacement decays exponentially with depth. In a layered model with increasing layer velocity, the phase velocity of the Rayleigh wave varies between the S-wave velocity of the bottom half-space and that of the classical Rayleigh wave propagated in a supposed half-space formed by the parameters of the top layer. If the phase velocity is the same as the P- or S-wave velocity of the layer, which is called the critical mode or critical phase velocity of surface waves, the general solution of the wave equation is not a homogeneous (expressed by trigonometric functions) or inhomogeneous (expressed by exponential functions) plane wave, but one whose amplitude changes linearly with depth (expressed by a linear function). Theories based on a general solution containing only trigonometric or exponential functions do not apply to the critical mode, owing to the singularity at the critical phase velocity. In this study, based on the classical framework of generalized reflection and transmission coefficients, the propagation of surface waves in horizontally layered media was studied by introducing a solution for the linear function at the critical phase velocity. Therefore, the eigenvalues and eigenfunctions of the critical mode can be calculated by solving a singular problem. The eigendisplacement characteristics associated with the critical phase velocity were investigated for different layered models. In contrast to the normal mode, the eigendisplacement associated with the critical phase velocity exhibits different characteristics. If the phase velocity is equal to the S-wave velocity in the bottom half-space, the eigendisplacement remains constant with increasing depth.

Linear instability and weakly nonlinear effects in eastward dipoles

The linear instability and weakly nonlinear dynamics of eastward-propagating, steady-state Larichev–Reznik vortex dipoles are explored in terms of two-dimensional normal-mode analysis. To extract the fastest growing normal modes, we apply both breeding methodology based on solving the initial-value problem, as well as a direct-solution approach through the full-spectrum eigenproblem involving large matrices. We find that the amplification rate of dipole instability decreases with respect to increase in dipole intensity. In our study, both approaches yield consistent results and are systematically compared to provide guidance for further studies of vortex structures.We consider nonlinear self-interaction of the fastest growing mode, along with the induced eddy fluxes, their divergence and mechanical energy balance. Through this analysis, we find that the unstable mode leads to weakening of the dipole by extracting its energy and exchanging potential vorticity content in the down-gradient sense, thus, providing a nonlinear physical mechanism for the dipole destruction. In particular, we highlight the fundamental importance of the west-east asymmetry of the normal mode for destruction to be realized. In summary, we consider this work to be a foundational demonstration of useful methodology for future studies of dynamics and stability of isolated vortices without simplifying spatial symmetries, such as ubiquitous vortices in geophysical fluids.

Role of Hydrogen in I.C Engines

The development of combustion models, paired with the usage of biofuels, has been viewed as an effective way to minimize pollutant emissions such as CO, HC, NOx, and smoke. Indeed, homogenous Charge Compression Ignition is a novel strategy to significantly reducing NOx emissions and smoke due to lower cylinder temperature and a higher rate of homogenous air fuel mixture as compared to compression ignition engines. The experimental findings demonstrated the maximum brake thermal efficiency, despite a 4.1% decrease compared to diesel in normal mode. Hydrogen energy is a key technical pathway for achieving carbon peak and neutrality. One method of utilizing hydrogen energy is through a direct injection engine. It has the advantage of increasing thermal efficiency and reducing aberrant combustion phenomena.The impact of using hydrogen to increase fuel economy and considerably reduce exhaust emissions. The use of hydrogen in S.I. and C.I. engines has been researched. Keywords: 1) Hydrogen. 2) Internal Combustion Engine. 3) Combustion with High Pressure Injection 4) Zero emissions.

Vibration Analysis and Motion Control Method for an Under-Actuated Tower Crane

In this paper, we developed a solution for controlling a tower crane thought as a no-rigid system, and therefore able to have deformation and, during the motion, vibrations. Particularly, large tower cranes show high structural dynamics. Under external excitations, the payload tends to sway around its vertical position and this motion is coupled to the resulting dynamic vibration of the crane structure. These induced vibrations may cause instability and serious damage to the crane system. Furthermore, the energy stored in the flexible structure of a tower crane causes vibrations in the structure during the acceleration and deceleration of slewing movements. A crane operator perceives these vibrations as an unstable speed of the boom. Such behavior involves the control of the crane, particularly precise positioning and manual control of the crane movement at low pivoting speed. We define an Elastic model of the Slewing crane and analyze the bending and Torsional elasticity of the Tower, and the Jib Elasticity. With an approximated method, we calculate the natural wavelengths of the crane structure in the slewing direction. We consider the tower crane as a nonlinear under-actuated system. The motion equations are obtained considering both the normal vibration modes of the tower crane and the sway of the payload. An elastic model of the Slewing crane is achieved, modeling the crane jib as an Euler-Bernoulli beam. Even the payload dynamic is considered, developing an Anti-sway solution by the equation of the movement. We define an iterative calculation of the sway angles and obtain the corresponding velocity profiles, implementing two kinds of solution: an input-shaping control in open-loop, to be used with automatic positioning, and a “command smoothing” method in open-loop, used for reducing the sway of the payload with the operator control. These solutions lead to a reduction of the vibrations of the crane structure. As a consequence, the tower crane is not subject to the strong horizontal and vertical oscillations during the motion of the elastic structure.

Scaling-up VPT2: A feasible route to include anharmonic correction on large molecules

Vibrational analysis plays a crucial role in the investigation of molecular systems. Though methodologies like second-order vibrational perturbation theory (VPT2) have paved the way to more accurate simulations, the computational cost remains a difficult barrier to overcome when the molecular size increases. Building upon recent advances in the identification of resonances, we propose an approach making anharmonic simulations possible for large-size systems, typically unreachable by standard means. This relies on the fact that, often, only portions of the whole spectra are of actual interest. Therefore, the anharmonic corrections can be included selectively on subsets of normal modes directly related to the regions of interest. Starting from the VPT2 equations, we evaluate rigorously and systematically the impact of the truncated anharmonic treatment onto simulations. The limit and feasibility of the reduced-dimensionality approach are detailed, starting on a smaller model system. The methodology is then challenged on the IR absorption and vibrational circular dichroism spectra of an organometallic complex in three different spectral ranges.